Finite Group Databasebeta

← #33258931

Subgroups — #33258931

Order 18688.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989174C211yesmaximal, characteristic, complemented
2C2×#17989172C211yesmaximal, characteristic, complemented
3#22618297C211yesmaximal, characteristic, complemented
4#22618285C211yesmaximal, characteristic, complemented
5#22618274C211yesmaximal, characteristic, complemented
6#22618259C211yesmaximal, characteristic, complemented
7#22616069C211yesmaximal, characteristic, complemented
8#22616067C211yesmaximal, characteristic, complemented
9#22616058C211yesmaximal, characteristic, complemented
10#22616056C211yesmaximal, characteristic, complemented
11#22615004C211yesmaximal, characteristic, complemented
12#22615003C211yesmaximal, characteristic, complemented
13#22614990C211yesmaximal, characteristic, complemented
14#22614988C211yesmaximal, characteristic, complemented
15#22614510C211yesmaximal, characteristic, complemented
16#22614287C211yesmaximal, characteristic, complemented
17#22614059C211yesmaximal, characteristic, complemented
18#22614051C211yesmaximal, characteristic, complemented
19#22613689C211yesmaximal, characteristic, complemented
20#22613632C211yesmaximal, characteristic, complemented
21#22613566C211yesmaximal, characteristic, complemented
22#22613512C211yesmaximal, characteristic, complemented
23#22613461C211yesmaximal, characteristic, complemented
24#22613368C211yesmaximal, characteristic, complemented
25#22613284C211yesmaximal, characteristic, complemented
26#22612592C211yesmaximal, characteristic, complemented
27#22612588C211yesmaximal, characteristic, complemented
28#22612441C211yesmaximal, characteristic, complemented
29C2×#17988487C211yesmaximal, characteristic, complemented
30C4×D4×Dic73C211yesmaximal, characteristic, complemented
31C73×#2424C211yesmaximal, characteristic, complemented
32C23×C22⋊D73C2211yescharacteristic
33#17989174—28no—
34#17989172—28no—
35C2×#14556590C2211yescharacteristic, complemented
36C2×#14556587C2211yescharacteristic
37C2×#14556587C2211yescharacteristic
38C2×#14556586C2211yescharacteristic, complemented
39C2×#14556586C2211yescharacteristic, complemented
40C2×#14556584C2211yescharacteristic, complemented
41C2×#14556584C2211yescharacteristic, complemented
42C2×#14556578C2211yescharacteristic, complemented
43C2×#14556577C2211yescharacteristic, complemented
44C2×#14556577C2211yescharacteristic, complemented
45C2×#14556577C2211yescharacteristic, complemented
46C2×#14556577C2211yescharacteristic, complemented
47C2×#14556577C2211yescharacteristic, complemented
48C2×#14556575C2211yescharacteristic, complemented
49C2×#14556575C2211yescharacteristic, complemented
50C2×#14556573C2211yescharacteristic, complemented
51C2×#14556572C2211yescharacteristic, complemented
52C2×#14556570C2211yescharacteristic
53C2×#14556568C2211yescharacteristic
54C2×#14556565C2211yescharacteristic, complemented
55C2×#14556563C2211yescharacteristic
56C2×#14556563C2211yescharacteristic
57C2×#14556563C2211yescharacteristic
58C2×#14556563C2211yescharacteristic
59C2×#14556563C2211yescharacteristic, complemented
60C2×#14556563C2211yescharacteristic, complemented
61C2×#14556563C2211yescharacteristic, complemented
62C2×#14556563C2211yescharacteristic, complemented
63C2×#14556562C2211yescharacteristic, complemented
64C2×#14556561C2211yescharacteristic
65C2×#14556560C2211yescharacteristic
66C2×#14556559C2211yescharacteristic
67C2×#14556559C2211yescharacteristic
68C2×D4×Dic73C2211yescharacteristic
69C2×D4×Dic73C2211yescharacteristic
70C2×D4×Dic73C2211yescharacteristic
71C2×#14556551C2211yescharacteristic
72C2×#14556551C2211yescharacteristic, complemented
73C22×#11924007C2211yescharacteristic
74C22×C22⋊Dic73C2211yescharacteristic
75C22×#11924005C2211yescharacteristic
76C22×#11924005C2211yescharacteristic
77C22×C4×Dic73C2211yescharacteristic
78C22×C4×Dic73C2211yescharacteristic, complemented
79#17988521C2211yescharacteristic, complemented
80#17988520C2211yescharacteristic, complemented
81#17988516C2211yescharacteristic, complemented
82#17988515C2211yescharacteristic, complemented
83#17988510C2211yescharacteristic, complemented
84#17988509C2211yescharacteristic, complemented
85#17988509C2211yescharacteristic, complemented
86#17988508C2211yescharacteristic, complemented
87#17988507C2211yescharacteristic, complemented
88#17988504C2211yescharacteristic, complemented
89#17988503C2211yescharacteristic
90#17988503C2211yescharacteristic
91#17988503C2211yescharacteristic, complemented
92#17988503C2211yescharacteristic, complemented
93#17988503C2211yescharacteristic, complemented
94#17988502C2211yescharacteristic, complemented
95#17988502C2211yescharacteristic, complemented
96#17988502C2211yescharacteristic, complemented
97#17988501C2211yescharacteristic, complemented
98#17988500C2211yescharacteristic, complemented
99#17988499C2211yescharacteristic, complemented
100#17988496C2211yescharacteristic
101#17988496C2211yescharacteristic
102#17988496C2211yescharacteristic, complemented
103#17988495C2211yescharacteristic
104#17988495C2211yescharacteristic
105#17988495C2211yescharacteristic
106#17988495C2211yescharacteristic
107#17988490C2211yescharacteristic, complemented
108#17988490C2211yescharacteristic, complemented
109#17988489C2211yescharacteristic, complemented
110#17988488C2211yescharacteristic, complemented
111#17988488C2211yescharacteristic, complemented
112#17988487C2211yescharacteristic
113#17988487C2211yescharacteristic
114#17988487C2211yescharacteristic
115#17988487C2211yescharacteristic
116#17988487C2211yescharacteristic
117#17988487C2211yescharacteristic
118#17988487C2211yescharacteristic
119#17988487C2211yescharacteristic
120#17988487C2211yescharacteristic
121#17988487C2211yescharacteristic
122#17988487C2211yescharacteristic
123#17988487C2211yescharacteristic
124#17988487C2211yescharacteristic, complemented
125#17988487C2211yescharacteristic, complemented
126#17988487C2211yescharacteristic, complemented
127#17988487C2211yescharacteristic, complemented
128#17988484C2211yescharacteristic, complemented
129#17988484C2211yescharacteristic, complemented
130#17988484C2211yescharacteristic, complemented
131#17988482C2211yescharacteristic, complemented
132#17988480C2211yescharacteristic, complemented
133#17988480C2211yescharacteristic, complemented
134#17988480C2211yescharacteristic, complemented
135#17988480C2211yescharacteristic, complemented
136#17988480C2211yescharacteristic, complemented
137#17988479C2211yescharacteristic, complemented
138#17988479C2211yescharacteristic, complemented
139#17988478C2211yescharacteristic, complemented
140#17988477C2211yescharacteristic, complemented
141#17988477C2211yescharacteristic, complemented
142#17988476C2211yescharacteristic, complemented
143#17988476C2211yescharacteristic, complemented
144#17988476C2211yescharacteristic, complemented
145#17988475C2211yescharacteristic, complemented
146#17988475C2211yescharacteristic, complemented
147#17988467C2211yescharacteristic
148#17988467C2211yescharacteristic, complemented
149#17988467C2211yescharacteristic, complemented
150#17988466C2211yescharacteristic
151#17988466C2211yescharacteristic
152#17988466C2211yescharacteristic, complemented
153#17988465C2211yescharacteristic, complemented
154#17988465C2211yescharacteristic, complemented
155#17988462C2211yescharacteristic
156#17988456C2211yescharacteristic, complemented
157#17988445C2211yescharacteristic
158#17988445C2211yescharacteristic, complemented
159#17988443C2211yescharacteristic
160#17988442C2211yescharacteristic
161C4⋊C4×Dic73C2211yescharacteristic, complemented
162C4⋊C4×Dic73C2211yescharacteristic, complemented
163C4×C4⋊Dic73C2211yescharacteristic, complemented
164#17988438C2211yescharacteristic, complemented
165C22⋊C4×Dic73C2211yescharacteristic
166C22⋊C4×Dic73C2211yescharacteristic
167C22⋊C4×Dic73C2211yescharacteristic, complemented
168C22⋊C4×Dic73C2211yescharacteristic, complemented
169C22⋊C4×Dic73C2211yescharacteristic, complemented
170C4×C22⋊Dic73C2211yescharacteristic
171C4×C22⋊Dic73C2211yescharacteristic, complemented
172#17988434C2211yescharacteristic, complemented
173C42×Dic73C2211yescharacteristic, complemented
174C2×#121×C73C2211yescharacteristic
175C2×#121×C73C2211yescharacteristic, complemented
176C2×#120×C73C2211yescharacteristic
177C2×#120×C73C2211yescharacteristic
178C2×C4×D4×C73C2211yescharacteristic
179C22×C22⋊C4×C73C2211yescharacteristic
180#396×C73C2211yescharacteristic, complemented
181#394×C73C2211yescharacteristic, complemented
182#394×C73C2211yescharacteristic, complemented
183#392×C73C2211yescharacteristic, complemented
184#390×C73C2211yescharacteristic, complemented
185#388×C73C2211yescharacteristic, complemented
186#386×C73C2211yescharacteristic
187#386×C73C2211yescharacteristic, complemented
188#385×C73C2211yescharacteristic
189C24×D73C2311yescharacteristic
190C22×Dic146C2311yescharacteristic
191C22×Dic146C2311yescharacteristic
192C22×D292C2311yescharacteristic
193C22×D292C2311yescharacteristic
194C22×C22⋊D73—24no—
195C22×C22⋊D73—42no—
196C22×C22⋊D73—42no—
197C22×C22⋊D73C2311yescharacteristic
198C22×C22⋊D73C2311yescharacteristic
199C22×C22⋊D73C2311yescharacteristic
200C22×C22⋊D73C2311yescharacteristic
201C22×C22⋊D73C2311yescharacteristic
202C22×C22⋊D73C2311yescharacteristic
203C22×C22⋊D73C2311yescharacteristic
204C22×C22⋊D73C2311yescharacteristic
205C22×C22⋊D73C2311yescharacteristic
206C22×C22⋊D73C2311yescharacteristic
207C22×C22⋊D73C2311yescharacteristic
208C22×C22⋊D73C2311yescharacteristic
209C22×C22⋊D73C2311yescharacteristic
210C23×Dic73C2311yescharacteristic
211C23×Dic73C2311yescharacteristic
212C23×Dic73C2311yescharacteristic
213C23×Dic73C2311yescharacteristic
214C23×Dic73C2311yescharacteristic
215C23×Dic73C2311yescharacteristic
216C22×C4×D73C2311yescharacteristic
217#14556590—42no—
218#14556587—42no—
219#14556587—42no—
220#14556586—24no—
221#14556586—24no—
222#14556584—24no—
223#14556584—24no—
224#14556578—24no—
225#14556577—24no—
226#14556577—24no—
227#14556577—24no—
228#14556577—42no—
229#14556577—42no—
230#14556575—24no—
231#14556575—24no—
232#14556573—24no—
233#14556572—24no—
234#14556570—24no—
235#14556568—24no—
236#14556565—42no—
237#14556563—24no—
238#14556563—24no—
239#14556563—24no—
240#14556563—24no—
241#14556563—24no—
242#14556563—42no—
243#14556563—42no—
244#14556563—42no—
245#14556562—24no—
246#14556561—24no—
247#14556560—24no—
248#14556559—24no—
249#14556559—24no—
250D4×Dic73—24no—
251D4×Dic73—24no—
252D4×Dic73D418yescomplemented
253#14556551—24no—
254#14556551—42no—
255C2×C4⋊Dic73C2311yescharacteristic
256C2×C4⋊Dic73C2311yescharacteristic
257C2×C4⋊Dic73C2311yescharacteristic
258C2×C4⋊Dic73C2311yescharacteristic
259C2×C4⋊Dic73C2311yescharacteristic
260C2×C4⋊Dic73C2311yescharacteristic
261C2×C4⋊Dic73C2311yescharacteristic
262C2×#11924007—42no—
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C2×#11924007C2311yescharacteristic
267C2×#11924007C2311yescharacteristic
268C2×#11924007C2311yescharacteristic
269C2×#11924007C2311yescharacteristic
270C2×#11924007C2311yescharacteristic
271C2×#11924007C2311yescharacteristic
272C2×#11924007C2311yescharacteristic
273C2×#11924007C2311yescharacteristic
274C2×#11924007C2311yescharacteristic
275C2×#11924007C2311yescharacteristic
276C2×C22⋊Dic73—24no—
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×C22⋊Dic73C2311yescharacteristic
282C2×C22⋊Dic73C2311yescharacteristic
283C2×C22⋊Dic73C2311yescharacteristic
284C2×C22⋊Dic73C2311yescharacteristic
285C2×C22⋊Dic73C2311yescharacteristic
286C2×C22⋊Dic73C2311yescharacteristic
287C2×C22⋊Dic73C2311yescharacteristic
288C2×C22⋊Dic73C2311yescharacteristic
289C2×C22⋊Dic73C2311yescharacteristic
290C2×C22⋊Dic73C2311yescharacteristic
291C2×C22⋊Dic73C2311yescharacteristic
292C2×C22⋊Dic73C2311yescharacteristic
293C2×C22⋊Dic73C2311yescharacteristic
294C2×C22⋊Dic73C2311yescharacteristic
295C2×C22⋊Dic73C2311yescharacteristic
296C2×C22⋊Dic73C2311yescharacteristic
297C2×#11924005—24no—
298C2×#11924005—42no—
299C2×#11924005C2311yescharacteristic
300C2×#11924005C2311yescharacteristic
301C2×#11924005C2311yescharacteristic
302C2×#11924005C2311yescharacteristic
303C2×#11924005C2311yescharacteristic
304C2×#11924005C2311yescharacteristic
305C2×#11924005C2311yescharacteristic
306C2×#11924005C2311yescharacteristic
307C2×#11924005C2311yescharacteristic
308C2×#11924005C2311yescharacteristic
309C2×#11924005C2311yescharacteristic
310C2×#11924005C2311yescharacteristic
311C2×#11924005C2311yescharacteristic
312C2×#11924005C2311yescharacteristic
313C2×#11924005C2311yescharacteristic
314C2×#11924005C2311yescharacteristic
315C2×#11924005C2311yescharacteristic
316C2×#11924005C2311yescharacteristic
317C2×#11924005C2311yescharacteristic
318C2×#11924005C2311yescharacteristic
319C2×#11924005C2311yescharacteristic
320C2×#11924005C2311yescharacteristic
321C2×#11924005C2311yescharacteristic
322C2×#11924005C2311yescharacteristic
323C2×#11924005C2311yescharacteristic
324C2×C4×Dic73—42no—
325C2×C4×Dic73—42no—
326C2×C4×Dic73C2311yescharacteristic
327C2×C4×Dic73C2311yescharacteristic
328C2×C4×Dic73C2311yescharacteristic
329C2×C4×Dic73C2311yescharacteristic
330C2×C4×Dic73C2311yescharacteristic
331C2×C4×Dic73C2311yescharacteristic
332C2×C4×Dic73C2311yescharacteristic
333C2×C4×Dic73C2311yescharacteristic
334C2×C4×Dic73C2311yescharacteristic
335C2×C4×Dic73C2311yescharacteristic
336C2×C4×Dic73C2311yescharacteristic
337C2×C4×Dic73C2311yescharacteristic
338C2×C4×Dic73C2311yescharacteristic
339C2×C4×Dic73C2311yescharacteristic
340#14556498C2311yescharacteristic
341#14556498C2311yescharacteristic
342#14556498C2311yescharacteristic
343#14556498C2311yescharacteristic
344#14556498C2311yescharacteristic
345#14556498C2311yescharacteristic
346#14556498C2311yescharacteristic
347#14556498C2311yescharacteristic
348#14556498C2311yescharacteristic
349#14556498C2311yescharacteristic
350#14556498C2311yescharacteristic
351#14556498C2311yescharacteristic
352#14556498C2311yescharacteristic
353#14556498C2311yescharacteristic
354#14556498C2311yescharacteristic
355#14556498C2311yescharacteristic
356C25×C73C2311yescharacteristic
357C22×D4×C73C2311yescharacteristic
358C22×D4×C73C2311yescharacteristic
359C22×D4×C73C2311yescharacteristic
360C22×D4×C73C2311yescharacteristic
361C22×D4×C73C2311yescharacteristic
362C22×D4×C73C2311yescharacteristic
363C22×D4×C73C2311yescharacteristic
364C23×C4×C73C2311yescharacteristic
365C23×C4×C73C2311yescharacteristic
366C23×C4×C73C2311yescharacteristic
367#121×C73—24no—
368#121×C73—42no—
369#120×C73—24no—
370#120×C73—24no—
371C4×D4×C73—24no—
372C2×C4⋊C4×C73C2311yescharacteristic
373C2×C4⋊C4×C73C2311yescharacteristic
374C2×C4⋊C4×C73C2311yescharacteristic
375C2×C4⋊C4×C73C2311yescharacteristic
376C2×C22⋊C4×C73—42no—
377C2×C22⋊C4×C73C2311yescharacteristic
378C2×C22⋊C4×C73C2311yescharacteristic
379C2×C22⋊C4×C73C2311yescharacteristic
380C2×C22⋊C4×C73C2311yescharacteristic
381C2×C22⋊C4×C73C2311yescharacteristic
382C2×C22⋊C4×C73C2311yescharacteristic
383C2×C22⋊C4×C73C2311yescharacteristic
384C2×C22⋊C4×C73C2311yescharacteristic
385C2×C22⋊C4×C73C2311yescharacteristic
386C2×C22⋊C4×C73C2311yescharacteristic
387C2×C22⋊C4×C73C2311yescharacteristic
388C2×C22⋊C4×C73C2311yescharacteristic
389C2×C22⋊C4×C73C2311yescharacteristic
390C2×C22⋊C4×C73C2311yescharacteristic
391C2×C22⋊C4×C73C2311yescharacteristic
392C2×C42×C73C2311yescharacteristic
393#95×C73C2311yescharacteristic
394#95×C73C2311yescharacteristic
395#95×C73C2311yescharacteristic
396#95×C73C2311yescharacteristic
397C23×D73—22no—
398C23×D73—22no—
399C23×D73—22no—
400C23×D73—41no—
401C23×D73—41no—
402C23×D73—41no—
403C23×D73—41no—
404C23×D73C2411yescharacteristic
405C23×D73C2411yescharacteristic
406C23×D73C2411yescharacteristic
407C2×Dic146—22no—
408C2×Dic146—22no—
409C2×Dic146—41no—
410C2×Dic146—41no—
411C2×Dic146—41no—
412C2×Dic146—41no—
413C2×D292—22no—
414C2×D292—22no—
415C2×D292—41no—
416C2×D292—41no—
417C2×D292—41no—
418C2×D292—41no—
419C2×C22⋊D73—22no—
420C2×C22⋊D73—22no—
421C2×C22⋊D73—22no—
422C2×C22⋊D73—22no—
423C2×C22⋊D73—22no—
424C2×C22⋊D73—22no—
425C2×C22⋊D73—22no—
426C2×C22⋊D73—22no—
427C2×C22⋊D73—22no—
428C2×C22⋊D73—22no—
429C2×C22⋊D73—22no—
430C2×C22⋊D73—22no—
431C2×C22⋊D73—22no—
432C2×C22⋊D73—22no—
433C2×C22⋊D73—22no—
434C2×C22⋊D73—22no—
435C2×C22⋊D73—22no—
436C2×C22⋊D73—22no—
437C2×C22⋊D73—22no—
438C2×C22⋊D73—22no—
439C2×C22⋊D73—22no—
440C2×C22⋊D73—41no—
441C2×C22⋊D73—41no—
442C2×C22⋊D73—41no—
443C2×C22⋊D73—41no—
444C2×C22⋊D73—416no—
445C2×C22⋊D73—41no—
446C2×C22⋊D73—41no—
447C2×C22⋊D73—41no—
448C2×C22⋊D73—41no—
449C2×C22⋊D73—41no—
450C2×C22⋊D73—41no—
451C2×C22⋊D73—41no—
452C2×C22⋊D73—41no—
453C2×C22⋊D73—41no—
454C2×C22⋊D73—41no—
455C2×C22⋊D73—41no—
456C2×C22⋊D73—41no—
457C2×C22⋊D73—41no—
458C2×C22⋊D73—41no—
459C22×Dic73—22no—
460C22×Dic73—22no—
461C22×Dic73—22no—
462C22×Dic73—22no—
463C22×Dic73—22no—
464C22×Dic73—22no—
465C22×Dic73—22no—
466C22×Dic73—41no—
467C22×Dic73—41no—
468C22×Dic73—41no—
469C22×Dic73—41no—
470C22×Dic73—41no—
471C22×Dic73—41no—
472C22×Dic73—41no—
473C22×Dic73—41no—
474C22×Dic73C2×D414yes—
475C22×Dic73C2×D414yescomplemented
476C22×Dic73#4114yes—
477C22×Dic73C2411yescharacteristic
478C22×Dic73C2411yescharacteristic
479C22×Dic73C2411yescharacteristic
480C22×Dic73C2411yescharacteristic
481C22×Dic73C2411yescharacteristic
482C22×Dic73C2411yescharacteristic
483C22×Dic73C2411yescharacteristic
484C22×Dic73C2411yescharacteristic
485C22×Dic73C2411yescharacteristic
486C22×Dic73C2411yescharacteristic
487C22×Dic73C2411yescharacteristic
488C22×Dic73C2411yescharacteristic
489C22×Dic73C2411yescharacteristic
490C2×C4×D73—22no—
491C2×C4×D73—41no—
492C2×C4×D73—41no—
493C4⋊Dic73—22no—
494C4⋊Dic73—22no—
495C4⋊Dic73—22no—
496C4⋊Dic73—22no—
497C4⋊Dic73—41no—
498C4⋊Dic73—41no—
499C4⋊Dic73C2×D414yescomplemented
500#11924007—22no—
501#11924007—22no—
502#11924007—22no—
503#11924007—22no—
504#11924007—22no—
505#11924007—22no—
506#11924007—22no—
507#11924007—22no—
508#11924007—22no—
509#11924007—22no—
510#11924007—22no—
511#11924007—41no—
512#11924007—41no—
513C22⋊Dic73—22no—
514C22⋊Dic73—22no—
515C22⋊Dic73—22no—
516C22⋊Dic73—22no—
517C22⋊Dic73—22no—
518C22⋊Dic73—22no—
519C22⋊Dic73—22no—
520C22⋊Dic73—22no—
521C22⋊Dic73—22no—
522C22⋊Dic73—22no—
523C22⋊Dic73—22no—
524C22⋊Dic73—22no—
525C22⋊Dic73—41no—
526C22⋊Dic73—41no—
527C22⋊Dic73—41no—
528C22⋊Dic73—41no—
529C22⋊Dic73—41no—
530C22⋊Dic73—41no—
531C22⋊Dic73C2×D414yes—
532C22⋊Dic73C2×D414yescomplemented
533#11924005—22no—
534#11924005—22no—
535#11924005—22no—
536#11924005—22no—
537#11924005—22no—
538#11924005—22no—
539#11924005—22no—
540#11924005—22no—
541#11924005—22no—
542#11924005—22no—
543#11924005—22no—
544#11924005—22no—
545#11924005—22no—
546#11924005—22no—
547#11924005—22no—
548#11924005—22no—
549#11924005—41no—
550#11924005—41no—
551#11924005—41no—
552#11924005—41no—
553#11924005—41no—
554#11924005—41no—
555#11924005—41no—
556#11924005—41no—
557#11924005—41no—
558C4×Dic73—22no—
559C4×Dic73—22no—
560C4×Dic73—22no—
561C4×Dic73—22no—
562C4×Dic73—22no—
563C4×Dic73—22no—
564C4×Dic73—22no—
565C4×Dic73—22no—
566C4×Dic73—41no—
567C4×Dic73—41no—
568C4×Dic73—41no—
569C4×Dic73—41no—
570C4×Dic73—41no—
571C4×Dic73C2×D414yescomplemented
572C24×C73—22no—
573C24×C73—22no—
574C24×C73—22no—
575C24×C73—41no—
576C24×C73—41no—
577C24×C73—41no—
578C24×C73—41no—
579C24×C73C2411yescharacteristic
580C24×C73C2411yescharacteristic
581C24×C73C2411yescharacteristic
582C24×C73C2411yescharacteristic
583C24×C73C2411yescharacteristic
584C2×D4×C73—22no—
585C2×D4×C73—22no—
586C2×D4×C73—22no—
587C2×D4×C73—22no—
588C2×D4×C73—22no—
589C2×D4×C73—22no—
590C2×D4×C73—22no—
591C2×D4×C73—22no—
592C2×D4×C73—22no—
593C2×D4×C73—22no—
594C2×D4×C73—41no—
595C2×D4×C73—41no—
596C2×D4×C73—41no—
597C2×D4×C73—41no—
598C2×D4×C73—41no—
599C2×D4×C73—41no—
600C2×D4×C73—41no—
601C2×D4×C73—41no—
602C2×D4×C73—41no—
603C2×D4×C73—41no—
604C2×D4×C73C2×D414yes—
605C22×C4×C73—22no—
606C22×C4×C73—22no—
607C22×C4×C73—22no—
608C22×C4×C73—22no—
609C22×C4×C73—22no—
610C22×C4×C73—41no—
611C22×C4×C73—41no—
612C22×C4×C73—41no—
613C22×C4×C73—41no—
614C22×C4×C73C2411yescharacteristic
615C22×C4×C73C2411yescharacteristic
616C22×C4×C73C2411yescharacteristic
617C22×C4×C73C2411yescharacteristic
618C22×C4×C73C2411yescharacteristic
619C22×C4×C73C2411yescharacteristic
620C22×C4×C73C2411yescharacteristic
621C22×C4×C73C2411yescharacteristic
622C22×C4×C73C2411yescharacteristic
623C22×C4×C73C2411yescharacteristic
624C4⋊C4×C73—22no—
625C4⋊C4×C73—22no—
626C4⋊C4×C73—41no—
627C4⋊C4×C73—41no—
628C22⋊C4×C73—22no—
629C22⋊C4×C73—22no—
630C22⋊C4×C73—22no—
631C22⋊C4×C73—22no—
632C22⋊C4×C73—22no—
633C22⋊C4×C73—22no—
634C22⋊C4×C73—22no—
635C22⋊C4×C73—22no—
636C22⋊C4×C73—22no—
637C22⋊C4×C73—22no—
638C22⋊C4×C73—22no—
639C22⋊C4×C73—41no—
640C22⋊C4×C73—41no—
641C22⋊C4×C73—41no—
642C22⋊C4×C73#4114yes—
643C42×C73—22no—
644C23×C73—21no—
645C23×C73—21no—
646C23×C73—21no—
647C23×C73—21no—
648C23×C73—21no—
649C23×C73—21no—
650C23×C73—21no—
651C23×C73—21no—
652C23×C73—21no—
653C23×C73—21no—
654C23×C73—21no—
655C23×C73—21no—
656C23×C73—21no—
657C23×C73—21no—
658C23×C73—21no—
659C23×C73—21no—
660C23×C73—21no—
661C23×C73—21no—
662C23×C73—21no—
663C23×C73—21no—
664C23×C73—21no—
665C23×C73—21no—
666C23×C73—21no—
667C23×C73—21no—
668C23×C73—21no—
669C23×C73—21no—
670C23×C73—21no—
671C23×C73—21no—
672C23×C73—21no—
673C23×C73—21no—
674C23×C73—21no—
675C23×C73—44no—
676C23×C73—44no—
677C23×C73—44no—
678C23×C73—82no—
679C23×C73—82no—
680C23×C73—82no—
681C23×C73—82no—
682C23×C73C22×D412yes—
683C23×C73C22×D412yes—
684C23×C73C2×#4112yes—
685C23×C73C2×#4112yes—
686C23×C73C2511yescharacteristic
687C22×D73—21no—
688C22×D73—21no—
689C22×D73—21no—
690C22×D73—21no—
691C22×D73—21no—
692C22×D73—21no—
693C22×D73—21no—
694C22×D73—21no—
695C22×D73—21no—
696C22×D73—21no—
697C22×D73—21no—
698C22×D73—21no—
699C22×D73—21no—
700C22×D73—21no—
701C22×D73—21no—
702C22×D73—21no—
703C22×D73—21no—
704C22×D73—21no—
705C22×D73—21no—
706C22×D73—21no—
707C22×D73—21no—
708C22×D73—44no—
709C22×D73—44no—
710C22×D73—44no—
711C22×D73—82no—
712C22×D73—82no—
713C22×D73—82no—
714C22×D73—82no—
715D4×C73—28no—
716D4×C73—44no—
717D4×C73—82no—
718D4×C73—82no—
719D4×C73—82no—
720D4×C73—82no—
721D4×C73—82no—
722C2×C4×C73—21no—
723C2×C4×C73—21no—
724C2×C4×C73—21no—
725C2×C4×C73—21no—
726C2×C4×C73—21no—
727C2×C4×C73—21no—
728C2×C4×C73—21no—
729C2×C4×C73—21no—
730C2×C4×C73—21no—
731C2×C4×C73—21no—
732C2×C4×C73—21no—
733C2×C4×C73—21no—
734C2×C4×C73—21no—
735C2×C4×C73—21no—
736C2×C4×C73—21no—
737C2×C4×C73—21no—
738C2×C4×C73—21no—
739C2×C4×C73—21no—
740C2×C4×C73—21no—
741C2×C4×C73—21no—
742C2×C4×C73—21no—
743C2×C4×C73—21no—
744C2×C4×C73—21no—
745C2×C4×C73—21no—
746C2×C4×C73—21no—
747C2×C4×C73—21no—
748C2×C4×C73—44no—
749C2×C4×C73—44no—
750C2×C4×C73—82no—
751C2×C4×C73C22×D412yes—
752C2×C4×C73C2×#4112yes—
753C2×C4×C73C2×#4112yes—
754C2×C4×C73H(5,𝔽2)12yes—
755C22⋊D73—44no—
756C22⋊D73—44no—
757C22⋊D73—44no—
758C22⋊D73—44no—
759C22⋊D73—44no—
760C22⋊D73—44no—
761C22⋊D73—82no—
762C22⋊D73—82no—
763C22⋊D73—82no—
764C22⋊D73—82no—
765C22⋊D73—82no—
766C22⋊D73—82no—
767C22⋊D73—82no—
768C2×Dic73—21no—
769C2×Dic73—21no—
770C2×Dic73—21no—
771C2×Dic73—21no—
772C2×Dic73—21no—
773C2×Dic73—21no—
774C2×Dic73—21no—
775C2×Dic73—21no—
776C2×Dic73—21no—
777C2×Dic73—21no—
778C2×Dic73—28no—
779C2×Dic73—21no—
780C2×Dic73—21no—
781C2×Dic73—21no—
782C2×Dic73—21no—
783C2×Dic73—21no—
784C2×Dic73—21no—
785C2×Dic73—21no—
786C2×Dic73—21no—
787C2×Dic73—21no—
788C2×Dic73—21no—
789C2×Dic73—21no—
790C2×Dic73—21no—
791C2×Dic73—21no—
792C2×Dic73—21no—
793C2×Dic73—21no—
794C2×Dic73—21no—
795C2×Dic73—21no—
796C2×Dic73—21no—
797C2×Dic73—21no—
798C2×Dic73—21no—
799C2×Dic73—21no—
800C2×Dic73—44no—
801C2×Dic73—44no—
802C2×Dic73—44no—
803C2×Dic73—82no—
804C2×Dic73—82no—
805C2×Dic73C22×D412yes—
806C2×Dic73C22×D412yes—
807C2×Dic73C22×D412yes—
808C2×Dic73C22×D412yes—
809C2×Dic73C2×#4112yes—
810C2×Dic73C2×#4112yes—
811C2×Dic73H(5,𝔽2)12yes—
812C2×Dic73H(5,𝔽2)12yes—
813D292—82no—
814D292—82no—
815C4×D73—82no—
816Dic146—82no—
817Dic146—82no—
818C22×C73—22no—
819C22×C73—22no—
820C22×C73—22no—
821C22×C73—22no—
822C22×C73—22no—
823C22×C73—22no—
824C22×C73—22no—
825C22×C73—22no—
826C22×C73—22no—
827C22×C73—41no—
828C22×C73—41no—
829C22×C73—41no—
830C22×C73—41no—
831C22×C73—41no—
832C22×C73—41no—
833C22×C73—41no—
834C22×C73—41no—
835C22×C73—41no—
836C22×C73—41no—
837C22×C73—41no—
838C22×C73—41no—
839C22×C73—41no—
840C22×C73—41no—
841C22×C73—41no—
842C22×C73—41no—
843C22×C73—41no—
844C22×C73—41no—
845C22×C73—41no—
846C22×C73—41no—
847C22×C73—41no—
848C22×C73—41no—
849C22×C73—41no—
850C22×C73—41no—
851C22×C73—41no—
852C22×C73—88no—
853C22×C73#53214yes—
854C22×C73C23×D411yescharacteristic
855C22×C73C22×#4111yescharacteristic
856C22×C73C22×#4111yescharacteristic
857C22×C73C2×H(5,𝔽2)11yescharacteristic
858C22×C73C2×H(5,𝔽2)11yescharacteristic
859C22×C73C2×H(5,𝔽2)11yescharacteristic
860C22×C73#58511yescharacteristic
861C2×D73—41no—
862C2×D73—41no—
863C2×D73—41no—
864C2×D73—41no—
865C2×D73—41no—
866C2×D73—41no—
867C2×D73—41no—
868C2×D73—41no—
869C2×D73—41no—
870C2×D73—41no—
871C2×D73—41no—
872C2×D73—41no—
873C2×D73—41no—
874C2×D73—41no—
875C2×D73—41no—
876C2×D73—41no—
877C2×D73—41no—
878C2×D73—41no—
879C2×D73—41no—
880C2×D73—41no—
881C2×D73—41no—
882C2×D73—88no—
883C4×C73—22no—
884C4×C73—22no—
885C4×C73—22no—
886C4×C73—22no—
887C4×C73—41no—
888C4×C73—41no—
889C4×C73—41no—
890C4×C73—41no—
891C4×C73—41no—
892C4×C73—41no—
893Dic73—22no—
894Dic73—22no—
895Dic73—22no—
896Dic73—22no—
897Dic73—22no—
898Dic73—41no—
899Dic73—41no—
900Dic73—41no—
901Dic73—41no—
902Dic73—41no—
903Dic73—41no—
904Dic73—41no—
905Dic73#53814yescomplemented
906#35007—731nomaximal, Sylow
907C2×C73—24no—
908C2×C73—42no—
909C2×C73—81no—
910C2×C73—81no—
911C2×C73—81no—
912C2×C73C2×#53211yescharacteristic
913C2×C73C2×#53811yescharacteristic
914C2×C73#346011yescharacteristic
915C2×C73#349611yescharacteristic
916C2×C73#349811yescharacteristic
917C2×C73#351411yescharacteristic
918C2×C73#351911yescharacteristic
919D73—81no—
920D73—81no—
921D73—81no—
922C2×#538—731no—
923C2×#538—731no—
924#2860—731no—
925#2858—731no—
926#2856—731no—
927#2854—731no—
928#2662—731no—
929#2662—731no—
930#2661—731no—
931#2661—731no—
932#2555—731no—
933#2555—731no—
934#2554—731no—
935#2554—731no—
936#2512—731no—
937#2491—731no—
938#2472—731no—
939#2472—731no—
940#2445—731no—
941#2440—731no—
942#2433—731no—
943#2428—731no—
944#2424—731no—
945#2424D7311yescharacteristic, complemented
946#2416—731no—
947#2408—731no—
948#2321—731no—
949#2321—731no—
950C4×#121—731no—
951C2×#390—731no—
952C42×D4—731no—
953C73#3500711yescharacteristic, complemented, Sylow
954C23×D4—731no—
955#538—1468no—
956#538—1468no—
957C2×C4⋊Q8—731no—
958C2×#127—731no—
959C2×#127—731no—
960C2×#126—731no—
961C2×#126—731no—
962C2×#126—731no—
963C2×#126—731no—
964C2×#124—731no—
965C2×#124—731no—
966C2×#124—731no—
967C2×#124—731no—
968C2×#124—731no—
969C2×#124—731no—
970C2×#123—731no—
971C2×#123—731no—
972C2×#123—731no—
973C2×#123—731no—
974C2×C22⋊Q8—731no—
975C2×C22⋊Q8—731no—
976C2×#121—731no—
977C2×#121—731no—
978C2×#121—731no—
979C2×#121—731no—
980C2×#121—731no—
981C2×#121—731no—
982C2×#121—731no—
983C2×#121—731no—
984C2×#121—731no—
985C2×#121—731no—
986C2×#121C2×D7311yescharacteristic
987C2×#121C2×D7311yescharacteristic, complemented
988C2×#120—731no—
989C2×#120—731no—
990C2×#120—731no—
991C2×#120—731no—
992C2×#120C2×D7311yescharacteristic
993C2×#120C2×D7311yescharacteristic
994C2×C4×D4—731no—
995C2×C4×D4—731no—
996C2×C4×D4—731no—
997C2×C4×D4—731no—
998C2×C4×D4—731no—
999C2×C4×D4C2×D7311yescharacteristic
1000C22×C4⋊C4—731no—
1001C22×C22⋊C4—731no—
1002C22×C22⋊C4—731no—
1003C22×C22⋊C4—731no—
1004C22×C22⋊C4C2×D7311yescharacteristic
1005C22×C42—731no—
1006C22×C42—731no—
1007#398—731no—
1008#398—731no—
1009#397—731no—
1010#397—731no—
1011#396—731no—
1012#396—731no—
1013#396—731no—
1014#396C2×D7311yescharacteristic, complemented
1015#395—731no—
1016#395—731no—
1017#394—731no—
1018#394—731no—
1019#394—731no—
1020#394—731no—
1021#394—731no—
1022#394—731no—
1023#394—731no—
1024#394—731no—
1025#394—731no—
1026#394—731no—
1027#394C2×D7311yescharacteristic, complemented
1028#394C2×D7311yescharacteristic, complemented
1029#393—731no—
1030#393—731no—
1031#392—731no—
1032#392—731no—
1033#392—731no—
1034#392—731no—
1035#392—731no—
1036#392—731no—
1037#392—731no—
1038#392C2×D7311yescharacteristic, complemented
1039#390—731no—
1040#390—731no—
1041#390—731no—
1042#390—731no—
1043#390—731no—
1044#390—731no—
1045#390—731no—
1046#390—731no—
1047#390—731no—
1048#390—731no—
1049#390—731no—
1050#390—731no—
1051#390—731no—
1052#390—731no—
1053#390—731no—
1054#390—731no—
1055#390—731no—
1056#390—731no—
1057#390—731no—
1058#390—731no—
1059#390—731no—
1060#390C2×D7311yescharacteristic, complemented
1061#389—731no—
1062#389—731no—
1063#389—731no—
1064#389—731no—
1065#388—731no—
1066#388—731no—
1067#388—731no—
1068#388—731no—
1069#388—731no—
1070#388—731no—
1071#388—731no—
1072#388—731no—
1073#388—731no—
1074#388—731no—
1075#388—731no—
1076#388—731no—
1077#388—731no—
1078#388—731no—
1079#388—731no—
1080#388C2×D7311yescharacteristic, complemented
1081#386—731no—
1082#386—731no—
1083#386—731no—
1084#386—731no—
1085#386—731no—
1086#386—731no—
1087#386—731no—
1088#386—731no—
1089#386C2×D7311yescharacteristic
1090#386C2×D7311yescharacteristic, complemented
1091#385—731no—
1092#385C2×D7311yescharacteristic
1093#384—731no—
1094#380—731no—
1095#380—731no—
1096#379—731no—
1097#379—731no—
1098C4×C4⋊C4—731no—
1099C4×C4⋊C4—731no—
1100C4×C4⋊C4—731no—
1101C4×C4⋊C4—731no—
1102C4×C22⋊C4—731no—
1103C4×C22⋊C4—731no—
1104C4×C22⋊C4—731no—
1105C4×C22⋊C4—731no—
1106C4×C22⋊C4—731no—
1107C4×C22⋊C4—731no—
1108C4×C22⋊C4—731no—
1109C4×C22⋊C4—731no—
1110C43—731no—
1111C25—731no—
1112C25C22×D7311yescharacteristic
1113C22×Q8—731no—
1114C22×Q8—731no—
1115C22×D4—2922no—
1116C22×D4—2922no—
1117C22×D4—731no—
1118C22×D4—731no—
1119C22×D4—731no—
1120C22×D4—731no—
1121C22×D4—731no—
1122C22×D4—731no—
1123C22×D4—731no—
1124C22×D4—731no—
1125C22×D4—731no—
1126C22×D4—731no—
1127C22×D4—731no—
1128C22×D4—731no—
1129C22×D4—731no—
1130C22×D4—731no—
1131C22×D4—731no—
1132C22×D4—1464no—
1133C22×D4C22×D7311yescharacteristic
1134C22×D4C22×D7311yescharacteristic
1135C22×D4C22×D7311yescharacteristic
1136C22×D4C22×D7311yescharacteristic
1137C22×D4C22×D7311yescharacteristic
1138C22×D4C22×D7311yescharacteristic
1139C22×D4C22×D7311yescharacteristic
1140C23×C4—731no—
1141C23×C4—731no—
1142C23×C4—731no—
1143C23×C4—731no—
1144C23×C4—731no—
1145C23×C4—731no—
1146C23×C4—731no—
1147C23×C4C22×D7311yescharacteristic
1148C23×C4C22×D7311yescharacteristic
1149C23×C4C22×D7311yescharacteristic
1150C4⋊Q8—2922no—
1151#127—2922no—
1152#127—2922no—
1153#126—1464no—
1154#126—1464no—
1155#126—1464no—
1156#126—1464no—
1157#124—2922no—
1158#124—2922no—
1159#124—1464no—
1160#124—1464no—
1161#124—1464no—
1162#124—1464no—
1163#123—1464no—
1164#123—1464no—
1165#123—1464no—
1166#123—1464no—
1167C22⋊Q8—1464no—
1168C22⋊Q8—1464no—
1169#121—24no—
1170#121—42no—
1171#121—2922no—
1172#121—2922no—
1173#121—2922no—
1174#121—2922no—
1175#121—1464no—
1176#121—1464no—
1177#121—1464no—
1178#121—1464no—
1179#121—1464no—
1180#121—1464no—
1181#120—24no—
1182#120—24no—
1183#120—1464no—
1184#120—1464no—
1185#120—1464no—
1186#120—1464no—
1187C4×D4—24no—
1188C4×D4—2922no—
1189C4×D4—738no—
1190C4×D4—1464no—
1191C4×D4—1464no—
1192C4×D4—1464no—
1193C2×C4⋊C4—2922no—
1194C2×C4⋊C4—731no—
1195C2×C4⋊C4—731no—
1196C2×C4⋊C4—731no—
1197C2×C4⋊C4—731no—
1198C2×C4⋊C4—731no—
1199C2×C4⋊C4—731no—
1200C2×C4⋊C4—731no—
1201C2×C4⋊C4—731no—
1202C2×C4⋊C4—731no—
1203C2×C4⋊C4—731no—
1204C2×C4⋊C4—731no—
1205C2×C4⋊C4—731no—
1206C2×C4⋊C4—731no—
1207C2×C4⋊C4—731no—
1208C2×C4⋊C4—731no—
1209C2×C4⋊C4—731no—
1210C2×C4⋊C4—731no—
1211C2×C4⋊C4—731no—
1212C2×C4⋊C4—731no—
1213C2×C4⋊C4—731no—
1214C2×C4⋊C4C22×D7311yescharacteristic
1215C2×C4⋊C4C22×D7311yescharacteristic
1216C2×C4⋊C4C22×D7311yescharacteristic
1217C2×C4⋊C4C22×D7311yescharacteristic
1218C2×C22⋊C4—42no—
1219C2×C22⋊C4—2922no—
1220C2×C22⋊C4—731no—
1221C2×C22⋊C4—731no—
1222C2×C22⋊C4—731no—
1223C2×C22⋊C4—731no—
1224C2×C22⋊C4—731no—
1225C2×C22⋊C4—731no—
1226C2×C22⋊C4—731no—
1227C2×C22⋊C4—731no—
1228C2×C22⋊C4—731no—
1229C2×C22⋊C4—731no—
1230C2×C22⋊C4—731no—
1231C2×C22⋊C4—731no—
1232C2×C22⋊C4—731no—
1233C2×C22⋊C4—731no—
1234C2×C22⋊C4—731no—
1235C2×C22⋊C4—731no—
1236C2×C22⋊C4—731no—
1237C2×C22⋊C4—731no—
1238C2×C22⋊C4—731no—
1239C2×C22⋊C4—731no—
1240C2×C22⋊C4—731no—
1241C2×C22⋊C4—731no—
1242C2×C22⋊C4—731no—
1243C2×C22⋊C4—731no—
1244C2×C22⋊C4—731no—
1245C2×C22⋊C4—731no—
1246C2×C22⋊C4—731no—
1247C2×C22⋊C4—731no—
1248C2×C22⋊C4—731no—
1249C2×C22⋊C4—731no—
1250C2×C22⋊C4—731no—
1251C2×C22⋊C4—731no—
1252C2×C22⋊C4—731no—
1253C2×C22⋊C4—731no—
1254C2×C22⋊C4—731no—
1255C2×C22⋊C4—731no—
1256C2×C22⋊C4—731no—
1257C2×C22⋊C4—731no—
1258C2×C22⋊C4—731no—
1259C2×C22⋊C4—731no—
1260C2×C22⋊C4—731no—
1261C2×C22⋊C4—731no—
1262C2×C22⋊C4—731no—
1263C2×C22⋊C4—731no—
1264C2×C22⋊C4—731no—
1265C2×C22⋊C4—1464no—
1266C2×C22⋊C4—1464no—
1267C2×C22⋊C4C22×D7311yescharacteristic
1268C2×C22⋊C4C22×D7311yescharacteristic
1269C2×C22⋊C4C22×D7311yescharacteristic
1270C2×C22⋊C4C22×D7311yescharacteristic
1271C2×C22⋊C4C22×D7311yescharacteristic
1272C2×C22⋊C4C22×D7311yescharacteristic
1273C2×C22⋊C4C22×D7311yescharacteristic
1274C2×C22⋊C4C22×D7311yescharacteristic
1275C2×C22⋊C4C22×D7311yescharacteristic
1276C2×C22⋊C4C22×D7311yescharacteristic
1277C2×C22⋊C4C22×D7311yescharacteristic
1278C2×C22⋊C4C22×D7311yescharacteristic
1279C2×C22⋊C4C22×D7311yescharacteristic
1280C2×C22⋊C4C22×D7311yescharacteristic
1281C2×C22⋊C4C22×D7311yescharacteristic
1282C2×C42—2922no—
1283C2×C42—2922no—
1284C2×C42—731no—
1285C2×C42—731no—
1286C2×C42—731no—
1287C2×C42—731no—
1288C2×C42—731no—
1289C2×C42—731no—
1290C2×C42—731no—
1291C2×C42—731no—
1292C2×C42—731no—
1293C2×C42—731no—
1294C2×C42—731no—
1295C2×C42—731no—
1296C2×C42—731no—
1297C2×C42—731no—
1298C2×C42C22×D7311yescharacteristic
1299#95—731no—
1300#95—731no—
1301#95—731no—
1302#95—731no—
1303#95—731no—
1304#95—731no—
1305#95—731no—
1306#95—731no—
1307#95—731no—
1308#95—731no—
1309#95—731no—
1310#95—731no—
1311#95—731no—
1312#95—731no—
1313#95—731no—
1314#95—731no—
1315#95C22×D7311yescharacteristic
1316#95C22×D7311yescharacteristic
1317#95C22×D7311yescharacteristic
1318#95C22×D7311yescharacteristic
1319C24—22no—
1320C24—22no—
1321C24—22no—
1322C24—41no—
1323C24—41no—
1324C24—41no—
1325C24—41no—
1326C24—2921no—
1327C24—2921no—
1328C24—2921no—
1329C24—2921no—
1330C24—731no—
1331C24—731no—
1332C24—731no—
1333C24—1462no—
1334C24—1462no—
1335C24—1462no—
1336C24C23×D7311yescharacteristic
1337C24C23×D7311yescharacteristic
1338C24C23×D7311yescharacteristic
1339C24C23×D7311yescharacteristic
1340C24C23×D7311yescharacteristic
1341C2×Q8—2921no—
1342C2×Q8—2921no—
1343C2×Q8—2921no—
1344C2×Q8—2921no—
1345C2×Q8—1462no—
1346C2×Q8—1462no—
1347C2×D4—22no—
1348C2×D4—22no—
1349C2×D4—22no—
1350C2×D4—22no—
1351C2×D4—22no—
1352C2×D4—22no—
1353C2×D4—22no—
1354C2×D4—22no—
1355C2×D4—22no—
1356C2×D4—22no—
1357C2×D4—41no—
1358C2×D4—41no—
1359C2×D4—41no—
1360C2×D4—41no—
1361C2×D4—41no—
1362C2×D4—41no—
1363C2×D4—41no—
1364C2×D4—41no—
1365C2×D4—41no—
1366C2×D4—41no—
1367C2×D4—2921no—
1368C2×D4—2921no—
1369C2×D4—2921no—
1370C2×D4—2921no—
1371C2×D4—2921no—
1372C2×D4—2921no—
1373C2×D4—2921no—
1374C2×D4—2921no—
1375C2×D4—29216no—
1376C2×D4—2921no—
1377C2×D4—2921no—
1378C2×D4—2921no—
1379C2×D4—2921no—
1380C2×D4—2921no—
1381C2×D4—2921no—
1382C2×D4—2921no—
1383C2×D4—2921no—
1384C2×D4—2921no—
1385C2×D4—2921no—
1386C2×D4—2921no—
1387C2×D4—2921no—
1388C2×D4—2921no—
1389C2×D4—2921no—
1390C2×D4—1462no—
1391C2×D4—1462no—
1392C2×D4—1462no—
1393C2×D4—1462no—
1394C2×D4—1462no—
1395C2×D4—1462no—
1396C2×D4—1462no—
1397C2×D4—1462no—
1398C2×D4—1462no—
1399C2×D4—1462no—
1400C2×D4—1462no—
1401C2×D4—1462no—
1402C2×D4—1462no—
1403C2×D4—1462no—
1404C2×D4—1462no—
1405C2×D4—1462no—
1406C2×D4—1462no—
1407C2×D4—1462no—
1408C2×D4—1462no—
1409C2×D4—1462no—
1410C2×D4—1462no—
1411C2×D4—1462no—
1412C2×D4—1462no—
1413C2×D4D4×D7314yes—
1414C22×C4—22no—
1415C22×C4—22no—
1416C22×C4—22no—
1417C22×C4—22no—
1418C22×C4—22no—
1419C22×C4—41no—
1420C22×C4—41no—
1421C22×C4—41no—
1422C22×C4—41no—
1423C22×C4—2921no—
1424C22×C4—2921no—
1425C22×C4—2921no—
1426C22×C4—2921no—
1427C22×C4—2921no—
1428C22×C4—2921no—
1429C22×C4—2921no—
1430C22×C4—2921no—
1431C22×C4—2921no—
1432C22×C4—2921no—
1433C22×C4—734no—
1434C22×C4—734no—
1435C22×C4—731no—
1436C22×C4—734no—
1437C22×C4—731no—
1438C22×C4—731no—
1439C22×C4—731no—
1440C22×C4—731no—
1441C22×C4—731no—
1442C22×C4—731no—
1443C22×C4—731no—
1444C22×C4—731no—
1445C22×C4—731no—
1446C22×C4—731no—
1447C22×C4—731no—
1448C22×C4—731no—
1449C22×C4—1462no—
1450C22×C4—1462no—
1451C22×C4—1462no—
1452C22×C4—1462no—
1453C22×C4—1462no—
1454C22×C4—1462no—
1455C22×C4—1462no—
1456C22×C4—1462no—
1457C22×C4C23×D7311yescharacteristic
1458C22×C4C23×D7311yescharacteristic
1459C22×C4C23×D7311yescharacteristic
1460C22×C4C23×D7311yescharacteristic
1461C22×C4C23×D7311yescharacteristic
1462C22×C4C23×D7311yescharacteristic
1463C22×C4C23×D7311yescharacteristic
1464C22×C4C23×D7311yescharacteristic
1465C22×C4C23×D7311yescharacteristic
1466C22×C4C23×D7311yescharacteristic
1467C4⋊C4—22no—
1468C4⋊C4—22no—
1469C4⋊C4—41no—
1470C4⋊C4—41no—
1471C4⋊C4—2921no—
1472C4⋊C4—2921no—
1473C4⋊C4—2921no—
1474C4⋊C4—2921no—
1475C4⋊C4—734no—
1476C4⋊C4—1462no—
1477C4⋊C4—1462no—
1478C4⋊C4—1462no—
1479C4⋊C4—1462no—
1480C4⋊C4—1462no—
1481C4⋊C4—1462no—
1482C4⋊C4—1462no—
1483C4⋊C4—1462no—
1484C4⋊C4—1462no—
1485C4⋊C4—1462no—
1486C4⋊C4—1462no—
1487C4⋊C4—1462no—
1488C4⋊C4—1462no—
1489C4⋊C4—1462no—
1490C4⋊C4—1462no—
1491C22⋊C4—22no—
1492C22⋊C4—22no—
1493C22⋊C4—22no—
1494C22⋊C4—22no—
1495C22⋊C4—22no—
1496C22⋊C4—22no—
1497C22⋊C4—22no—
1498C22⋊C4—22no—
1499C22⋊C4—22no—
1500C22⋊C4—22no—
1501C22⋊C4—22no—
1502C22⋊C4—41no—
1503C22⋊C4—41no—
1504C22⋊C4—41no—
1505C22⋊C4—2921no—
1506C22⋊C4—2921no—
1507C22⋊C4—2921no—
1508C22⋊C4—2921no—
1509C22⋊C4—2921no—
1510C22⋊C4—2921no—
1511C22⋊C4—2921no—
1512C22⋊C4—2921no—
1513C22⋊C4—2921no—
1514C22⋊C4—2921no—
1515C22⋊C4—2921no—
1516C22⋊C4—2921no—
1517C22⋊C4—2921no—
1518C22⋊C4—2921no—
1519C22⋊C4—2921no—
1520C22⋊C4—734no—
1521C22⋊C4—734no—
1522C22⋊C4—1462no—
1523C22⋊C4—1462no—
1524C22⋊C4—1462no—
1525C22⋊C4—1462no—
1526C22⋊C4—1462no—
1527C22⋊C4—1462no—
1528C22⋊C4—1462no—
1529C22⋊C4—1462no—
1530C22⋊C4—1462no—
1531C22⋊C4—1462no—
1532C22⋊C4—1462no—
1533C22⋊C4—1462no—
1534C22⋊C4—1462no—
1535C22⋊C4—1462no—
1536C22⋊C4—1462no—
1537C22⋊C4—1462no—
1538C22⋊C4—1462no—
1539C22⋊C4—1462no—
1540C22⋊C4—1462no—
1541C22⋊C4—1462no—
1542C22⋊C4—1462no—
1543C22⋊C4—1462no—
1544C22⋊C4—1462no—
1545C22⋊C4—1462no—
1546C22⋊C4—1462no—
1547C22⋊C4—1462no—
1548C22⋊C4—1462no—
1549C22⋊C4—1462no—
1550C22⋊C4#1192402714yes—
1551C42—22no—
1552C42—2921no—
1553C42—2921no—
1554C42—2921no—
1555C42—2921no—
1556C42—2921no—
1557C42—734no—
1558C42—1462no—
1559C42—1462no—
1560C42—1462no—
1561C42—1462no—
1562C42—1462no—
1563C42—1462no—
1564C42—1462no—
1565C42—1462no—
1566C23—21no—
1567C23—21no—
1568C23—21no—
1569C23—21no—
1570C23—21no—
1571C23—21no—
1572C23—21no—
1573C23—21no—
1574C23—21no—
1575C23—21no—
1576C23—21no—
1577C23—21no—
1578C23—21no—
1579C23—21no—
1580C23—21no—
1581C23—21no—
1582C23—21no—
1583C23—21no—
1584C23—21no—
1585C23—21no—
1586C23—21no—
1587C23—21no—
1588C23—21no—
1589C23—21no—
1590C23—21no—
1591C23—21no—
1592C23—21no—
1593C23—21no—
1594C23—21no—
1595C23—21no—
1596C23—21no—
1597C23—44no—
1598C23—44no—
1599C23—44no—
1600C23—82no—
1601C23—82no—
1602C23—82no—
1603C23—82no—
1604C23—2924no—
1605C23—2924no—
1606C23—2924no—
1607C23—5842no—
1608C23—5842no—
1609C23—5842no—
1610C23—5842no—
1611C23—1461no—
1612C23—1461no—
1613C23—1461no—
1614C23—1461no—
1615C23—1461no—
1616C23—1461no—
1617C23—1461no—
1618C23—1461no—
1619C23—1461no—
1620C23—1461no—
1621C23—1461no—
1622C23—1461no—
1623C23—1461no—
1624C23—1461no—
1625C23—1461no—
1626C23—1461no—
1627C23—1461no—
1628C23—1461no—
1629C23—1461no—
1630C23—1461no—
1631C23—1461no—
1632C23C2×D4×D7312yes—
1633C23C2×D4×D7312yes—
1634C23#41×D7312yes—
1635C23C2×#1192402712yes—
1636C23C24×D7311yescharacteristic
1637Q8—5842no—
1638Q8—5842no—
1639D4—28no—
1640D4—44no—
1641D4—82no—
1642D4—82no—
1643D4—82no—
1644D4—82no—
1645D4—82no—
1646D4—2924no—
1647D4—2924no—
1648D4—2924no—
1649D4—2924no—
1650D4—2924no—
1651D4—2924no—
1652D4—5842no—
1653D4—5842no—
1654D4—5842no—
1655D4—5842no—
1656D4—5842no—
1657D4—5842no—
1658D4—5842no—
1659D4—5842no—
1660D4—5842no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—21no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—21no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—21no—
1679C2×C4—21no—
1680C2×C4—21no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—21no—
1684C2×C4—21no—
1685C2×C4—21no—
1686C2×C4—21no—
1687C2×C4—44no—
1688C2×C4—44no—
1689C2×C4—82no—
1690C2×C4—2924no—
1691C2×C4—2924no—
1692C2×C4—2924no—
1693C2×C4—5842no—
1694C2×C4—5842no—
1695C2×C4—5842no—
1696C2×C4—732no—
1697C2×C4—732no—
1698C2×C4—732no—
1699C2×C4—732no—
1700C2×C4—732no—
1701C2×C4—732no—
1702C2×C4—732no—
1703C2×C4—732no—
1704C2×C4—1461no—
1705C2×C4—1461no—
1706C2×C4—1461no—
1707C2×C4—1461no—
1708C2×C4—1461no—
1709C2×C4—1461no—
1710C2×C4—1461no—
1711C2×C4—1461no—
1712C2×C4—1461no—
1713C2×C4—1461no—
1714C2×C4—1461no—
1715C2×C4—1461no—
1716C2×C4—1461no—
1717C2×C4—1461no—
1718C2×C4—1461no—
1719C2×C4—1461no—
1720C2×C4—1461no—
1721C2×C4—1461no—
1722C2×C4—1461no—
1723C2×C4—1461no—
1724C2×C4—1461no—
1725C2×C4—1468no—
1726C2×C4—1461no—
1727C2×C4—1461no—
1728C2×C4—1461no—
1729C2×C4—1461no—
1730C2×C4—1461no—
1731C2×C4—1461no—
1732C2×C4—1461no—
1733C2×C4—1461no—
1734C2×C4—1461no—
1735C2×C4—1461no—
1736C2×C4C2×D4×D7312yes—
1737C2×C4C2×#1192402712yes—
1738C2×C4C2×#1192402712yes—
1739C2×C4#1455663612yes—
1740C22—22no—
1741C22—22no—
1742C22—22no—
1743C22—22no—
1744C22—22no—
1745C22—22no—
1746C22—22no—
1747C22—22no—
1748C22—22no—
1749C22—41no—
1750C22—41no—
1751C22—41no—
1752C22—41no—
1753C22—41no—
1754C22—41no—
1755C22—41no—
1756C22—41no—
1757C22—41no—
1758C22—41no—
1759C22—41no—
1760C22—41no—
1761C22—41no—
1762C22—41no—
1763C22—41no—
1764C22—41no—
1765C22—41no—
1766C22—41no—
1767C22—41no—
1768C22—41no—
1769C22—41no—
1770C22—41no—
1771C22—41no—
1772C22—41no—
1773C22—41no—
1774C22—88no—
1775C22—2921no—
1776C22—2921no—
1777C22—2921no—
1778C22—2921no—
1779C22—2921no—
1780C22—2921no—
1781C22—2921no—
1782C22—2921no—
1783C22—2921no—
1784C22—2921no—
1785C22—2921no—
1786C22—2921no—
1787C22—2921no—
1788C22—2921no—
1789C22—2921no—
1790C22—2921no—
1791C22—2921no—
1792C22—2921no—
1793C22—2921no—
1794C22—2921no—
1795C22—2921no—
1796C22—5848no—
1797C22#1798913214yes—
1798C22C22×D4×D7311yescharacteristic
1799C22C2×#41×D7311yescharacteristic
1800C22C22×#1192402711yescharacteristic
1801C22H(5,𝔽2)×D7311yescharacteristic
1802C22H(5,𝔽2)×D7311yescharacteristic
1803C22C2×#1455663611yescharacteristic
1804C22#1798942311yescharacteristic
1805C4—22no—
1806C4—22no—
1807C4—22no—
1808C4—22no—
1809C4—41no—
1810C4—41no—
1811C4—41no—
1812C4—41no—
1813C4—41no—
1814C4—41no—
1815C4—2921no—
1816C4—2921no—
1817C4—2921no—
1818C4—2921no—
1819C4—2921no—
1820C4—2921no—
1821C4—2921no—
1822C4—734no—
1823C4—1462no—
1824C4—1462no—
1825C4—1462no—
1826C4—1462no—
1827C4—1462no—
1828C2—24no—
1829C2—42no—
1830C2—81no—
1831C2—81no—
1832C2—81no—
1833C2—5841no—
1834C2—5841no—
1835C2—5841no—
1836C2C2×#1798913211yescharacteristic
1837C2#538×D7311yescharacteristic
1838C2#2262334911yescharacteristic
1839C2#2262369111yescharacteristic
1840C2#2262370311yescharacteristic
1841C2#2262387911yescharacteristic
1842C2#2262395011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2424C2
hypercenter#2424D73
hypocenterC73#35007
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2424

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989174C2semidirect
2. C2×#17989172C2semidirect
3. #22618297C2semidirect
4. #22618285C2semidirect
5. #22618274C2semidirect
6. #22618259C2semidirect
7. #22616069C2semidirect
8. #22616067C2semidirect
9. #22616058C2semidirect
10. #22616056C2semidirect
11. #22615004C2semidirect
12. #22615003C2semidirect
13. #22614990C2semidirect
14. #22614988C2semidirect
15. #22614510C2semidirect
16. #22614287C2semidirect
17. #22614059C2semidirect
18. #22614051C2semidirect
19. #22613689C2semidirect
20. #22613632C2semidirect
21. #22613566C2semidirect
22. #22613512C2semidirect
23. #22613461C2semidirect
24. #22613368C2semidirect
25. #22613284C2semidirect
26. #22612592C2semidirect
27. #22612588C2semidirect
28. #22612441C2semidirect
29. C2×#17988487C2semidirect
30. C4×D4×Dic73C2semidirect
31. C73×#2424C2semidirect
35. C2×#14556590C22semidirect
38. C2×#14556586C22semidirect
39. C2×#14556586C22semidirect
40. C2×#14556584C22semidirect
41. C2×#14556584C22semidirect
42. C2×#14556578C22semidirect
43. C2×#14556577C22semidirect
44. C2×#14556577C22semidirect
45. C2×#14556577C22semidirect
46. C2×#14556577C22semidirect
47. C2×#14556577C22semidirect
48. C2×#14556575C22semidirect
49. C2×#14556575C22semidirect
50. C2×#14556573C22semidirect
51. C2×#14556572C22semidirect
54. C2×#14556565C22semidirect
59. C2×#14556563C22semidirect
60. C2×#14556563C22semidirect
61. C2×#14556563C22semidirect
62. C2×#14556563C22semidirect
63. C2×#14556562C22semidirect
72. C2×#14556551C22semidirect
78. C22×C4×Dic73C22semidirect
79. #17988521C22semidirect
80. #17988520C22semidirect
81. #17988516C22semidirect
82. #17988515C22semidirect
83. #17988510C22semidirect
84. #17988509C22semidirect
85. #17988509C22semidirect
86. #17988508C22semidirect
87. #17988507C22semidirect
88. #17988504C22semidirect
91. #17988503C22semidirect
92. #17988503C22semidirect
93. #17988503C22semidirect
94. #17988502C22semidirect
95. #17988502C22semidirect
96. #17988502C22semidirect
97. #17988501C22semidirect
98. #17988500C22semidirect
99. #17988499C22semidirect
102. #17988496C22semidirect
107. #17988490C22semidirect
108. #17988490C22semidirect
109. #17988489C22semidirect
110. #17988488C22semidirect
111. #17988488C22semidirect
124. #17988487C22semidirect
125. #17988487C22semidirect
126. #17988487C22semidirect
127. #17988487C22semidirect
128. #17988484C22semidirect
129. #17988484C22semidirect
130. #17988484C22semidirect
131. #17988482C22semidirect
132. #17988480C22semidirect
133. #17988480C22semidirect
134. #17988480C22semidirect
135. #17988480C22semidirect
136. #17988480C22semidirect
137. #17988479C22semidirect
138. #17988479C22semidirect
139. #17988478C22semidirect
140. #17988477C22semidirect
141. #17988477C22semidirect
142. #17988476C22semidirect
143. #17988476C22semidirect
144. #17988476C22semidirect
145. #17988475C22semidirect
146. #17988475C22semidirect
148. #17988467C22semidirect
149. #17988467C22semidirect
152. #17988466C22semidirect
153. #17988465C22semidirect
154. #17988465C22semidirect
156. #17988456C22semidirect
158. #17988445C22semidirect
161. C4⋊C4×Dic73C22semidirect
162. C4⋊C4×Dic73C22semidirect
163. C4×C4⋊Dic73C22semidirect
164. #17988438C22semidirect
167. C22⋊C4×Dic73C22semidirect
168. C22⋊C4×Dic73C22semidirect
169. C22⋊C4×Dic73C22semidirect
171. C4×C22⋊Dic73C22semidirect
172. #17988434C22semidirect
173. C42×Dic73C22semidirect
175. C2×#121×C73C22semidirect
180. #396×C73C22semidirect
181. #394×C73C22semidirect
182. #394×C73C22semidirect
183. #392×C73C22semidirect
184. #390×C73C22semidirect
185. #388×C73C22semidirect
187. #386×C73C22semidirect
252. D4×Dic73D4semidirect
475. C22×Dic73C2×D4semidirect
499. C4⋊Dic73C2×D4semidirect
532. C22⋊Dic73C2×D4semidirect
571. C4×Dic73C2×D4semidirect
905. Dic73#538semidirect
945. #2424D73semidirect
953. C73#35007semidirect
987. C2×#121C2×D73semidirect
1014. #396C2×D73semidirect
1027. #394C2×D73semidirect
1028. #394C2×D73semidirect
1038. #392C2×D73semidirect
1060. #390C2×D73semidirect
1080. #388C2×D73semidirect
1090. #386C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891742
C2×#179891722
#226182972
#226182852
#226182742
#226182592
#226160692
#226160672
#226160582
#226160562
#226150042
#226150032
#226149902
#226149882
#226145102
#226142872
#226140592
#226140512
#226136892
#226136322
#226135662
#226135122
#226134612
#226133682
#226132842
#226125922
#226125882
#226124412
C2×#179884872
C4×D4×Dic732
C73×#24242
#3500773