Finite Group Databasebeta

← #33292781

Subgroups — #33292781

Order 18688.

2782 conjugacy classes of subgroups.

The subgroup lattice has 1800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989166C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×D73C211yesmaximal, characteristic, complemented
3#22618212C211yesmaximal, characteristic, complemented
4#22618210C211yesmaximal, characteristic, complemented
5#22616433C211yesmaximal, characteristic, complemented
6#22616431C211yesmaximal, characteristic, complemented
7#22616430C211yesmaximal, characteristic, complemented
8#22616428C211yesmaximal, characteristic, complemented
9#22616426C211yesmaximal, characteristic, complemented
10#22616425C211yesmaximal, characteristic, complemented
11#22616424C211yesmaximal, characteristic, complemented
12#22616423C211yesmaximal, characteristic, complemented
13#22616239C211yesmaximal, characteristic, complemented
14#22616237C211yesmaximal, characteristic, complemented
15#22616234C211yesmaximal, characteristic, complemented
16#22616232C211yesmaximal, characteristic, complemented
17#22616227C211yesmaximal, characteristic, complemented
18#22616226C211yesmaximal, characteristic, complemented
19#22616225C211yesmaximal, characteristic, complemented
20#22615678C211yesmaximal, characteristic, complemented
21#22615672C211yesmaximal, characteristic, complemented
22#22614860C211yesmaximal, characteristic, complemented
23#22614856C211yesmaximal, characteristic, complemented
24#22613586C211yesmaximal, characteristic, complemented
25#22613584C211yesmaximal, characteristic, complemented
26#22613264C211yesmaximal, characteristic, complemented
27#22613261C211yesmaximal, characteristic, complemented
28#22613248C211yesmaximal, characteristic, complemented
29#22613245C211yesmaximal, characteristic, complemented
30#22612530C211yesmaximal, characteristic, complemented
31C73×#2676C211yesmaximal, characteristic, complemented
32C22×#11924028C2211yescharacteristic
33C22×#11924027C2211yescharacteristic
34C22×Q8×D73C2211yescharacteristic
35C23×C4×D73C2211yescharacteristic
36#17989166—28no—
37C2×#14556578C2211yescharacteristic, complemented
38C2×#14556577C2211yescharacteristic, complemented
39C2×#14556577C2211yescharacteristic, complemented
40C2×#14556576C2211yescharacteristic
41C2×#14556573C2211yescharacteristic
42C2×#14556573C2211yescharacteristic
43C2×#14556573C2211yescharacteristic
44C2×#14556571C2211yescharacteristic
45C2×#14556571C2211yescharacteristic, complemented
46C2×#14556570C2211yescharacteristic
47C2×#14556570C2211yescharacteristic, complemented
48C2×#14556569C2211yescharacteristic
49C2×#14556569C2211yescharacteristic
50C2×#14556568C2211yescharacteristic
51C2×#14556568C2211yescharacteristic
52C2×#14556568C2211yescharacteristic, complemented
53C2×#14556568C2211yescharacteristic, complemented
54C2×#14556567C2211yescharacteristic
55C22⋊Q8×D73—28no—
56C2×#14556564C2211yescharacteristic
57C2×#14556564C2211yescharacteristic
58C2×#14556564C2211yescharacteristic
59C2×#14556563C2211yescharacteristic
60C2×#14556563C2211yescharacteristic, complemented
61C2×#14556563C2211yescharacteristic, complemented
62C2×#14556562C2211yescharacteristic
63C2×#14556562C2211yescharacteristic
64C2×#14556562C2211yescharacteristic
65C2×#14556562C2211yescharacteristic, complemented
66C2×#14556561C2211yescharacteristic
67C2×#14556559C2211yescharacteristic
68C2×#14556559C2211yescharacteristic
69C2×#14556559C2211yescharacteristic
70C2×C4⋊C4×D73C2211yescharacteristic
71C2×C4⋊C4×D73C2211yescharacteristic
72C2×C4⋊C4×D73C2211yescharacteristic
73C2×C22⋊C4×D73C2211yescharacteristic
74C2×C22⋊C4×D73C2211yescharacteristic
75#17988524C2211yescharacteristic
76#17988523C2211yescharacteristic
77#17988523C2211yescharacteristic
78#17988522C2211yescharacteristic
79#17988521C2211yescharacteristic, complemented
80#17988520C2211yescharacteristic, complemented
81#17988519C2211yescharacteristic, complemented
82#17988517C2211yescharacteristic, complemented
83#17988510C2211yescharacteristic, complemented
84#17988510C2211yescharacteristic, complemented
85#17988510C2211yescharacteristic, complemented
86#17988510C2211yescharacteristic, complemented
87#17988510C2211yescharacteristic, complemented
88#17988509C2211yescharacteristic, complemented
89#17988509C2211yescharacteristic, complemented
90#17988508C2211yescharacteristic, complemented
91#17988508C2211yescharacteristic, complemented
92#17988507C2211yescharacteristic, complemented
93#17988507C2211yescharacteristic, complemented
94#17988503C2211yescharacteristic, complemented
95#17988503C2211yescharacteristic, complemented
96#17988502C2211yescharacteristic, complemented
97#17988502C2211yescharacteristic, complemented
98#17988501C2211yescharacteristic, complemented
99#17988501C2211yescharacteristic, complemented
100#17988500C2211yescharacteristic
101#17988500C2211yescharacteristic
102#17988500C2211yescharacteristic, complemented
103#17988499C2211yescharacteristic
104#17988499C2211yescharacteristic
105#17988499C2211yescharacteristic, complemented
106#17988499C2211yescharacteristic, complemented
107#17988499C2211yescharacteristic, complemented
108#17988499C2211yescharacteristic, complemented
109#17988499C2211yescharacteristic, complemented
110#17988498C2211yescharacteristic, complemented
111#17988496C2211yescharacteristic
112#17988496C2211yescharacteristic
113#17988495C2211yescharacteristic
114#17988495C2211yescharacteristic
115#17988495C2211yescharacteristic
116#17988495C2211yescharacteristic
117#17988494C2211yescharacteristic, complemented
118#17988493C2211yescharacteristic, complemented
119#17988491C2211yescharacteristic, complemented
120#17988491C2211yescharacteristic, complemented
121#17988490C2211yescharacteristic
122#17988490C2211yescharacteristic
123#17988489C2211yescharacteristic
124#17988487C2211yescharacteristic
125#17988487C2211yescharacteristic
126#17988487C2211yescharacteristic
127#17988487C2211yescharacteristic
128#17988474C2211yescharacteristic, complemented
129#17988473C2211yescharacteristic, complemented
130#17988472C2211yescharacteristic, complemented
131#17988471C2211yescharacteristic, complemented
132#17988470C2211yescharacteristic, complemented
133#17988469C2211yescharacteristic, complemented
134#17988468C2211yescharacteristic, complemented
135#17988467C2211yescharacteristic
136#17988467C2211yescharacteristic
137#17988467C2211yescharacteristic
138#17988467C2211yescharacteristic
139#17988466C2211yescharacteristic
140#17988466C2211yescharacteristic
141#17988465C2211yescharacteristic
142#17988465C2211yescharacteristic
143#17988465C2211yescharacteristic
144#17988465C2211yescharacteristic
145#17988464C2211yescharacteristic
146#17988464C2211yescharacteristic
147#17988463C2211yescharacteristic
148#17988463C2211yescharacteristic
149#17988463C2211yescharacteristic
150#17988463C2211yescharacteristic
151#17988463C2211yescharacteristic
152#17988463C2211yescharacteristic
153#17988463C2211yescharacteristic
154#17988463C2211yescharacteristic
155#17988463C2211yescharacteristic
156#17988463C2211yescharacteristic
157#17988462C2211yescharacteristic, complemented
158#17988462C2211yescharacteristic, complemented
159#17988461C2211yescharacteristic, complemented
160#17988460C2211yescharacteristic, complemented
161#17988459C2211yescharacteristic, complemented
162#17988459C2211yescharacteristic, complemented
163#17988458C2211yescharacteristic, complemented
164#17988449C2211yescharacteristic
165#17988449C2211yescharacteristic
166#17988447C2211yescharacteristic
167#17988446C2211yescharacteristic
168#17988446C2211yescharacteristic
169#17988445C2211yescharacteristic
170#17988444C2211yescharacteristic
171#17988444C2211yescharacteristic
172C4×#11924005C2211yescharacteristic
173#17988434C2211yescharacteristic
174C2×#124×C73C2211yescharacteristic, complemented
175C2×C22⋊Q8×C73C2211yescharacteristic
176C2×#121×C73C2211yescharacteristic
177C2×#121×C73C2211yescharacteristic, complemented
178#396×C73C2211yescharacteristic, complemented
179#394×C73C2211yescharacteristic, complemented
180#394×C73C2211yescharacteristic, complemented
181#393×C73C2211yescharacteristic, complemented
182#392×C73C2211yescharacteristic
183#392×C73C2211yescharacteristic
184#390×C73C2211yescharacteristic
185#387×C73C2211yescharacteristic, complemented
186#386×C73C2211yescharacteristic
187#386×C73C2211yescharacteristic
188#385×C73C2211yescharacteristic, complemented
189C24×D73C2311yescharacteristic
190C2×#11924028—24no—
191C2×#11924028—42no—
192C2×#11924028—42no—
193C2×#11924027—24no—
194C2×#11924027—42no—
195C2×#11924027—42no—
196C22×Dic146C2311yescharacteristic
197C22×Dic146C2311yescharacteristic
198C22×Dic146C2311yescharacteristic
199C22×Dic146C2311yescharacteristic
200C22×Dic146C2311yescharacteristic
201C2×Q8×D73—24no—
202C2×Q8×D73—42no—
203C2×Q8×D73—42no—
204C22×D292C2311yescharacteristic
205C22×D292C2311yescharacteristic
206C22×C22⋊D73C2311yescharacteristic
207C22×C22⋊D73C2311yescharacteristic
208C22×C22⋊D73C2311yescharacteristic
209C22×C22⋊D73C2311yescharacteristic
210C22×C22⋊D73C2311yescharacteristic
211C22×C22⋊D73C2311yescharacteristic
212C22×C22⋊D73C2311yescharacteristic
213C22×C22⋊D73C2311yescharacteristic
214C22×C22⋊D73C2311yescharacteristic
215C22×C22⋊D73C2311yescharacteristic
216C23×Dic73C2311yescharacteristic
217C23×Dic73C2311yescharacteristic
218C23×Dic73C2311yescharacteristic
219C22×C4×D73—24no—
220C22×C4×D73—42no—
221C22×C4×D73—42no—
222C22×C4×D73C2311yescharacteristic
223C22×C4×D73C2311yescharacteristic
224C22×C4×D73C2311yescharacteristic
225C22×C4×D73C2311yescharacteristic
226C22×C4×D73C2311yescharacteristic
227C22×C4×D73C2311yescharacteristic
228C22×C4×D73C2311yescharacteristic
229C22×C4×D73C2311yescharacteristic
230C22×C4×D73C2311yescharacteristic
231#14556578—42no—
232#14556577—42no—
233#14556577—42no—
234#14556576—42no—
235#14556573—42no—
236#14556573—42no—
237#14556573—42no—
238#14556571—24no—
239#14556571—24no—
240#14556570—24no—
241#14556570—24no—
242#14556569—24no—
243#14556569—24no—
244#14556568—24no—
245#14556568—24no—
246#14556568—24no—
247#14556568—24no—
248#14556567—24no—
249#14556564—24no—
250#14556564—24no—
251#14556564—42no—
252#14556563—24no—
253#14556563—24no—
254#14556563—42no—
255#14556562—24no—
256#14556562—24no—
257#14556562—24no—
258#14556562—42no—
259#14556561—42no—
260#14556559—42no—
261#14556559—42no—
262#14556559—42no—
263C2×C4⋊Dic73C2311yescharacteristic
264C2×C4⋊Dic73C2311yescharacteristic
265C2×C4⋊Dic73C2311yescharacteristic
266C2×C4⋊Dic73C2311yescharacteristic
267C2×C4⋊Dic73C2311yescharacteristic
268C2×C4⋊Dic73C2311yescharacteristic
269C2×C4⋊Dic73C2311yescharacteristic
270C2×C4⋊Dic73C2311yescharacteristic
271C2×C4⋊Dic73C2311yescharacteristic
272C2×#11924007C2311yescharacteristic
273C2×#11924007C2311yescharacteristic
274C2×#11924007C2311yescharacteristic
275C2×#11924007C2311yescharacteristic
276C2×#11924007C2311yescharacteristic
277C2×#11924007C2311yescharacteristic
278C2×#11924007C2311yescharacteristic
279C2×#11924007C2311yescharacteristic
280C2×#11924007C2311yescharacteristic
281C2×#11924007C2311yescharacteristic
282C2×#11924007C2311yescharacteristic
283C2×#11924007C2311yescharacteristic
284C2×#11924007C2311yescharacteristic
285C2×#11924007C2311yescharacteristic
286C4⋊C4×D73—24no—
287C4⋊C4×D73—24no—
288C4⋊C4×D73D418yescomplemented
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×C22⋊Dic73C2311yescharacteristic
298C2×C22⋊Dic73C2311yescharacteristic
299C2×C22⋊Dic73C2311yescharacteristic
300C2×C22⋊Dic73C2311yescharacteristic
301C2×C22⋊Dic73C2311yescharacteristic
302C2×C22⋊Dic73C2311yescharacteristic
303C2×C22⋊Dic73C2311yescharacteristic
304C2×C22⋊Dic73C2311yescharacteristic
305C2×C22⋊Dic73C2311yescharacteristic
306C2×C22⋊Dic73C2311yescharacteristic
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×#11924005C2311yescharacteristic
325C2×#11924005C2311yescharacteristic
326C2×#11924005C2311yescharacteristic
327C22⋊C4×D73—24no—
328C22⋊C4×D73—24no—
329C2×C4×Dic73C2311yescharacteristic
330C2×C4×Dic73C2311yescharacteristic
331C2×C4×Dic73C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
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
356#14556498C2311yescharacteristic
357#14556498C2311yescharacteristic
358C22×Q8×C73C2311yescharacteristic
359C22×D4×C73C2311yescharacteristic
360C22×D4×C73C2311yescharacteristic
361C22×D4×C73C2311yescharacteristic
362C22×D4×C73C2311yescharacteristic
363C22×D4×C73C2311yescharacteristic
364C22×D4×C73C2311yescharacteristic
365C23×C4×C73C2311yescharacteristic
366C23×C4×C73C2311yescharacteristic
367#124×C73—42no—
368C22⋊Q8×C73—24no—
369#121×C73—24no—
370#121×C73—42no—
371C2×C4⋊C4×C73C2311yescharacteristic
372C2×C4⋊C4×C73C2311yescharacteristic
373C2×C4⋊C4×C73C2311yescharacteristic
374C2×C4⋊C4×C73C2311yescharacteristic
375C2×C4⋊C4×C73C2311yescharacteristic
376C2×C22⋊C4×C73C2311yescharacteristic
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×C42×C73C2311yescharacteristic
391#95×C73C2311yescharacteristic
392#95×C73C2311yescharacteristic
393#95×C73C2311yescharacteristic
394#95×C73C2311yescharacteristic
395#95×C73C2311yescharacteristic
396#95×C73C2311yescharacteristic
397C23×D73—22no—
398C23×D73—22no—
399C23×D73—22no—
400C23×D73—22no—
401C23×D73—22no—
402C23×D73—41no—
403C23×D73—41no—
404C23×D73C2411yescharacteristic
405C23×D73C2411yescharacteristic
406C23×D73C2411yescharacteristic
407#11924028—416no—
408#11924027—416no—
409C2×Dic146—22no—
410C2×Dic146—22no—
411C2×Dic146—22no—
412C2×Dic146—22no—
413C2×Dic146—22no—
414C2×Dic146—22no—
415C2×Dic146—22no—
416C2×Dic146—22no—
417C2×Dic146—41no—
418C2×Dic146—41no—
419C2×Dic146—41no—
420C2×Dic146—41no—
421C2×Dic146—41no—
422C2×Dic146—41no—
423C2×Dic146—41no—
424Q8×D73—416no—
425C2×D292—22no—
426C2×D292—22no—
427C2×D292—22no—
428C2×D292—22no—
429C2×D292—41no—
430C2×D292—41no—
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—22no—
441C2×C22⋊D73—22no—
442C2×C22⋊D73—22no—
443C2×C22⋊D73—22no—
444C2×C22⋊D73—22no—
445C2×C22⋊D73—22no—
446C2×C22⋊D73—22no—
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—
459C2×C22⋊D73—41no—
460C2×C22⋊D73—41no—
461C22×Dic73—22no—
462C22×Dic73—22no—
463C22×Dic73—22no—
464C22×Dic73—22no—
465C22×Dic73—41no—
466C22×Dic73—41no—
467C22×Dic73—41no—
468C22×Dic73—41no—
469C22×Dic73—41no—
470C22×Dic73C2411yescharacteristic
471C22×Dic73C2411yescharacteristic
472C22×Dic73C2411yescharacteristic
473C22×Dic73C2411yescharacteristic
474C22×Dic73C2411yescharacteristic
475C22×Dic73C2411yescharacteristic
476C22×Dic73C2411yescharacteristic
477C22×Dic73C2411yescharacteristic
478C22×Dic73C2411yescharacteristic
479C22×Dic73C2411yescharacteristic
480C22×Dic73C2411yescharacteristic
481C22×Dic73C2411yescharacteristic
482C22×Dic73C2411yescharacteristic
483C2×C4×D73—22no—
484C2×C4×D73—22no—
485C2×C4×D73—22no—
486C2×C4×D73—22no—
487C2×C4×D73—22no—
488C2×C4×D73—22no—
489C2×C4×D73—22no—
490C2×C4×D73—22no—
491C2×C4×D73—22no—
492C2×C4×D73—22no—
493C2×C4×D73—22no—
494C2×C4×D73—22no—
495C2×C4×D73—22no—
496C2×C4×D73—22no—
497C2×C4×D73—416no—
498C2×C4×D73—41no—
499C2×C4×D73—41no—
500C2×C4×D73—41no—
501C2×C4×D73—41no—
502C2×C4×D73—41no—
503C2×C4×D73—41no—
504C2×C4×D73—41no—
505C2×C4×D73—41no—
506C2×C4×D73—41no—
507C2×C4×D73—41no—
508C2×C4×D73C2×D414yes—
509C2×C4×D73C2×D414yes—
510C2×C4×D73C2×D414yes—
511C4⋊Dic73—22no—
512C4⋊Dic73—22no—
513C4⋊Dic73—22no—
514C4⋊Dic73—22no—
515C4⋊Dic73—41no—
516C4⋊Dic73—41no—
517C4⋊Dic73—41no—
518C4⋊Dic73—41no—
519C4⋊Dic73C2×D414yes—
520#11924007—22no—
521#11924007—22no—
522#11924007—22no—
523#11924007—22no—
524#11924007—22no—
525#11924007—22no—
526#11924007—41no—
527#11924007—41no—
528#11924007—41no—
529#11924007—41no—
530#11924007—41no—
531#11924007—41no—
532#11924007C2×D414yes—
533#11924007C2×D414yes—
534C22⋊Dic73—22no—
535C22⋊Dic73—22no—
536C22⋊Dic73—22no—
537C22⋊Dic73—22no—
538C22⋊Dic73—22no—
539C22⋊Dic73—22no—
540C22⋊Dic73—22no—
541C22⋊Dic73—22no—
542C22⋊Dic73—22no—
543C22⋊Dic73—41no—
544C22⋊Dic73—41no—
545C22⋊Dic73—41no—
546C22⋊Dic73—41no—
547C22⋊Dic73—41no—
548C22⋊Dic73—41no—
549C22⋊Dic73—41no—
550C22⋊Dic73—41no—
551C22⋊Dic73—41no—
552#11924005—22no—
553#11924005—22no—
554#11924005—22no—
555#11924005—22no—
556#11924005—22no—
557#11924005—22no—
558#11924005—22no—
559#11924005—22no—
560#11924005—22no—
561#11924005—22no—
562#11924005—22no—
563#11924005—22no—
564#11924005—41no—
565#11924005—41no—
566#11924005—41no—
567#11924005—41no—
568#11924005—41no—
569#11924005—41no—
570#11924005—41no—
571#11924005—41no—
572C4×Dic73—41no—
573C4×Dic73—41no—
574C4×Dic73—41no—
575C24×C73C2411yescharacteristic
576C24×C73C2411yescharacteristic
577C24×C73C2411yescharacteristic
578C24×C73C2411yescharacteristic
579C2×Q8×C73—22no—
580C2×Q8×C73—22no—
581C2×Q8×C73—41no—
582C2×D4×C73—22no—
583C2×D4×C73—22no—
584C2×D4×C73—22no—
585C2×D4×C73—22no—
586C2×D4×C73—22no—
587C2×D4×C73—22no—
588C2×D4×C73—41no—
589C2×D4×C73—41no—
590C2×D4×C73—41no—
591C2×D4×C73—41no—
592C2×D4×C73—41no—
593C2×D4×C73—41no—
594C2×D4×C73—41no—
595C2×D4×C73—41no—
596C2×D4×C73—41no—
597C2×D4×C73—41no—
598C2×D4×C73—41no—
599C2×D4×C73—41no—
600C22×C4×C73—22no—
601C22×C4×C73—22no—
602C22×C4×C73—22no—
603C22×C4×C73—41no—
604C22×C4×C73—41no—
605C22×C4×C73—41no—
606C22×C4×C73C2411yescharacteristic
607C22×C4×C73C2411yescharacteristic
608C22×C4×C73C2411yescharacteristic
609C22×C4×C73C2411yescharacteristic
610C22×C4×C73C2411yescharacteristic
611C22×C4×C73C2411yescharacteristic
612C22×C4×C73C2411yescharacteristic
613C22×C4×C73C2411yescharacteristic
614C22×C4×C73C2411yescharacteristic
615C22×C4×C73C2411yescharacteristic
616C22×C4×C73C2411yescharacteristic
617C4⋊C4×C73—22no—
618C4⋊C4×C73—22no—
619C4⋊C4×C73—41no—
620C4⋊C4×C73—41no—
621C4⋊C4×C73C2×D414yes—
622C22⋊C4×C73—22no—
623C22⋊C4×C73—22no—
624C22⋊C4×C73—22no—
625C22⋊C4×C73—22no—
626C22⋊C4×C73—22no—
627C22⋊C4×C73—22no—
628C22⋊C4×C73—22no—
629C22⋊C4×C73—41no—
630C22⋊C4×C73—41no—
631C22⋊C4×C73—41no—
632C22⋊C4×C73—41no—
633C22⋊C4×C73—41no—
634C22⋊C4×C73—41no—
635C22⋊C4×C73—41no—
636C42×C73—41no—
637C23×C73—21no—
638C23×C73—21no—
639C23×C73—21no—
640C23×C73—21no—
641C23×C73—21no—
642C23×C73—21no—
643C23×C73—21no—
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×C732−1+412yes—
665C23×C73C2511yescharacteristic
666C22×D73—21no—
667C22×D73—21no—
668C22×D73—21no—
669C22×D73—21no—
670C22×D73—28no—
671C22×D73—21no—
672C22×D73—21no—
673C22×D73—21no—
674C22×D73—21no—
675C22×D73—21no—
676C22×D73—21no—
677C22×D73—21no—
678C22×D73—21no—
679C22×D73—21no—
680C22×D73—21no—
681C22×D73—21no—
682C22×D73—21no—
683C22×D73—21no—
684C22×D73—44no—
685C22×D73—44no—
686C22×D73—44no—
687C22×D73—44no—
688C22×D73—44no—
689C22×D73—44no—
690C22×D73C22×D412yes—
691C22×D73H(5,𝔽2)12yes—
692C22×D73H(5,𝔽2)12yes—
693C22×D732−1+412yes—
694Q8×C73—44no—
695D4×C73—44no—
696D4×C73—82no—
697D4×C73—82no—
698D4×C73—82no—
699D4×C73—82no—
700D4×C73—82no—
701C2×C4×C73—21no—
702C2×C4×C73—21no—
703C2×C4×C73—21no—
704C2×C4×C73—21no—
705C2×C4×C73—21no—
706C2×C4×C73—21no—
707C2×C4×C73—21no—
708C2×C4×C73—21no—
709C2×C4×C73—21no—
710C2×C4×C73—21no—
711C2×C4×C73—21no—
712C2×C4×C73—21no—
713C2×C4×C73—21no—
714C2×C4×C73—21no—
715C2×C4×C73—21no—
716C2×C4×C73—21no—
717C2×C4×C73—21no—
718C2×C4×C73—21no—
719C2×C4×C73—21no—
720C2×C4×C73—21no—
721C2×C4×C73—21no—
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—44no—
731C2×C4×C73—44no—
732C2×C4×C73C22×D412yes—
733C2×C4×C73C22×D412yes—
734C2×C4×C73C22×D412yes—
735C2×C4×C73H(5,𝔽2)12yes—
736C22⋊D73—44no—
737C22⋊D73—44no—
738C22⋊D73—44no—
739C22⋊D73—44no—
740C22⋊D73—82no—
741C22⋊D73—82no—
742C22⋊D73—82no—
743C22⋊D73—82no—
744C22⋊D73—82no—
745C22⋊D73—82no—
746C2×Dic73—21no—
747C2×Dic73—21no—
748C2×Dic73—21no—
749C2×Dic73—21no—
750C2×Dic73—21no—
751C2×Dic73—21no—
752C2×Dic73—21no—
753C2×Dic73—21no—
754C2×Dic73—21no—
755C2×Dic73—21no—
756C2×Dic73—21no—
757C2×Dic73—21no—
758C2×Dic73—21no—
759C2×Dic73—21no—
760C2×Dic73—21no—
761C2×Dic73—21no—
762C2×Dic73—21no—
763C2×Dic73—21no—
764C2×Dic73—21no—
765C2×Dic73—21no—
766C2×Dic73—21no—
767C2×Dic73—21no—
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—21no—
779C2×Dic73—21no—
780C2×Dic73—21no—
781C2×Dic73—44no—
782C2×Dic73—44no—
783C2×Dic73—44no—
784C2×Dic73C22×D412yes—
785C2×Dic73C22×D412yes—
786C2×Dic73C22×D412yes—
787C2×Dic73H(5,𝔽2)12yes—
788D292—44no—
789D292—82no—
790C4×D73—28no—
791C4×D73—28no—
792C4×D73—44no—
793C4×D73—44no—
794C4×D73—44no—
795C4×D73—44no—
796C4×D73—44no—
797C4×D73—44no—
798C4×D73—44no—
799Dic146—44no—
800Dic146—44no—
801Dic146—44no—
802Dic146—44no—
803Dic146—44no—
804C22×C73—22no—
805C22×C73—22no—
806C22×C73—22no—
807C22×C73—41no—
808C22×C73—41no—
809C22×C73—41no—
810C22×C73—41no—
811C22×C73—41no—
812C22×C73—41no—
813C22×C73—41no—
814C22×C73—41no—
815C22×C73—41no—
816C22×C73—41no—
817C22×C73—41no—
818C22×C73—41no—
819C22×C73—41no—
820C22×C73—41no—
821C22×C73—41no—
822C22×C73—41no—
823C22×C73—41no—
824C22×C73—41no—
825C22×C73—41no—
826C22×C73—41no—
827C22×C73—41no—
828C22×C73—41no—
829C22×C73—41no—
830C22×C73—41no—
831C22×C73—41no—
832C22×C73C23×D411yescharacteristic
833C22×C73C2×H(5,𝔽2)11yescharacteristic
834C22×C73C2×H(5,𝔽2)11yescharacteristic
835C22×C73C2×H(5,𝔽2)11yescharacteristic
836C22×C73C2×H(5,𝔽2)11yescharacteristic
837C22×C73C2×2−1+411yescharacteristic
838C22×C73C2×2−1+411yescharacteristic
839C2×D73—22no—
840C2×D73—22no—
841C2×D73—22no—
842C2×D73—22no—
843C2×D73—22no—
844C2×D73—22no—
845C2×D73—22no—
846C2×D73—22no—
847C2×D73—22no—
848C2×D73—416no—
849C2×D73—41no—
850C2×D73—41no—
851C2×D73—41no—
852C2×D73—41no—
853C2×D73—41no—
854C2×D73—41no—
855C2×D73—41no—
856C2×D73—41no—
857C2×D73—41no—
858C2×D73—41no—
859C2×D73—41no—
860C2×D73#53514yes—
861C4×C73—22no—
862C4×C73—22no—
863C4×C73—22no—
864C4×C73—22no—
865C4×C73—41no—
866C4×C73—41no—
867C4×C73—41no—
868C4×C73—41no—
869C4×C73—41no—
870C4×C73—41no—
871C4×C73—41no—
872Dic73—22no—
873Dic73—22no—
874Dic73—22no—
875Dic73—22no—
876Dic73—41no—
877Dic73—41no—
878Dic73—41no—
879Dic73—41no—
880Dic73—41no—
881Dic73—41no—
882Dic73—41no—
883Dic73—41no—
884Dic73—41no—
885#36707—731nomaximal, Sylow
886C2×C73—42no—
887C2×C73—81no—
888C2×C73—81no—
889C2×C73—81no—
890C2×C73C2×#53511yescharacteristic
891C2×C73#348411yescharacteristic
892C2×C73#348611yescharacteristic
893C2×C73#353611yescharacteristic
894C2×C73#353611yescharacteristic
895C2×C73#353611yescharacteristic
896C2×C73#353611yescharacteristic
897D73—24no—
898D73—42no—
899D73—81no—
900C2×#537—731no—
901C22×C22⋊Q8—731no—
902#2847—731no—
903#2847—731no—
904#2692—731no—
905#2692—731no—
906#2692—731no—
907#2692—731no—
908#2692—731no—
909#2692—731no—
910#2692—731no—
911#2692—731no—
912#2676—731no—
913#2676—731no—
914#2676—731no—
915#2676—731no—
916#2676—731no—
917#2676—731no—
918#2676—731no—
919#2676D7311yescharacteristic, complemented
920#2618—731no—
921#2618—731no—
922#2539—731no—
923#2539—731no—
924#2436—731no—
925#2436—731no—
926#2406—731no—
927#2406—731no—
928#2404—731no—
929#2404—731no—
930#2313—731no—
931C73#3670711yescharacteristic, complemented, Sylow
932C22×#41—731no—
933C22×#41—731no—
934C23×Q8—731no—
935C24×C4—731no—
936#537—1468no—
937C2×#124—731no—
938C2×#124—731no—
939C2×#124—731no—
940C2×#124C2×D7311yescharacteristic, complemented
941C2×#123—731no—
942C2×#123—731no—
943C2×#123—731no—
944C2×#123—731no—
945C2×C22⋊Q8—731no—
946C2×C22⋊Q8—731no—
947C2×C22⋊Q8—731no—
948C2×C22⋊Q8—731no—
949C2×C22⋊Q8—731no—
950C2×C22⋊Q8—731no—
951C2×C22⋊Q8—731no—
952C2×C22⋊Q8—731no—
953C2×C22⋊Q8—731no—
954C2×C22⋊Q8—731no—
955C2×C22⋊Q8—731no—
956C2×C22⋊Q8—1468no—
957C2×C22⋊Q8C2×D7311yescharacteristic
958C2×#121—731no—
959C2×#121—731no—
960C2×#121—731no—
961C2×#121—731no—
962C2×#121—731no—
963C2×#121—731no—
964C2×#121—731no—
965C2×#121—731no—
966C2×#121—731no—
967C2×#121—731no—
968C2×#121C2×D7311yescharacteristic
969C2×#121C2×D7311yescharacteristic, complemented
970C2×#120—731no—
971C2×#120—731no—
972C2×#120—731no—
973C2×#120—731no—
974C22×C4⋊C4—731no—
975C22×C4⋊C4—731no—
976C22×C4⋊C4—731no—
977C22×C22⋊C4—731no—
978C22×C22⋊C4—731no—
979#399—731no—
980#399—731no—
981#399—731no—
982#399—731no—
983#398—731no—
984#398—731no—
985#398—731no—
986#398—731no—
987#396—731no—
988#396—731no—
989#396—731no—
990#396—731no—
991#396—731no—
992#396—731no—
993#396—731no—
994#396C2×D7311yescharacteristic, complemented
995#395—731no—
996#395—731no—
997#395—731no—
998#395—731no—
999#394—731no—
1000#394—731no—
1001#394—731no—
1002#394—731no—
1003#394—731no—
1004#394—731no—
1005#394C2×D7311yescharacteristic, complemented
1006#394C2×D7311yescharacteristic, complemented
1007#393—731no—
1008#393—731no—
1009#393—731no—
1010#393—731no—
1011#393—731no—
1012#393—731no—
1013#393—731no—
1014#393—731no—
1015#393—731no—
1016#393—731no—
1017#393—731no—
1018#393C2×D7311yescharacteristic, complemented
1019#392—731no—
1020#392—731no—
1021#392—731no—
1022#392—731no—
1023#392—731no—
1024#392—731no—
1025#392C2×D7311yescharacteristic
1026#392C2×D7311yescharacteristic
1027#391—731no—
1028#391—731no—
1029#391—731no—
1030#391—731no—
1031#390—731no—
1032#390—731no—
1033#390—731no—
1034#390—731no—
1035#390—731no—
1036#390—731no—
1037#390—731no—
1038#390C2×D7311yescharacteristic
1039#387—731no—
1040#387—731no—
1041#387—731no—
1042#387—731no—
1043#387—731no—
1044#387—731no—
1045#387—731no—
1046#387C2×D7311yescharacteristic, complemented
1047#386—731no—
1048#386—731no—
1049#386—731no—
1050#386—731no—
1051#386—731no—
1052#386—731no—
1053#386—731no—
1054#386—731no—
1055#386—731no—
1056#386—731no—
1057#386—731no—
1058#386—731no—
1059#386—731no—
1060#386—731no—
1061#386—731no—
1062#386—731no—
1063#386—731no—
1064#386—731no—
1065#386—731no—
1066#386—731no—
1067#386—731no—
1068#386—731no—
1069#386C2×D7311yescharacteristic
1070#386C2×D7311yescharacteristic
1071#385—731no—
1072#385—731no—
1073#385—731no—
1074#385—731no—
1075#385—731no—
1076#385—731no—
1077#385—731no—
1078#385C2×D7311yescharacteristic, complemented
1079#381—731no—
1080#381—731no—
1081#380—731no—
1082#380—731no—
1083#380—731no—
1084#380—731no—
1085#380—731no—
1086#380—731no—
1087C4×C22⋊C4—731no—
1088C4×C22⋊C4—731no—
1089C25—731no—
1090C2×#41—2922no—
1091C2×#41—2922no—
1092C2×#41—2922no—
1093C2×#41—2922no—
1094C2×#41—1464no—
1095C2×#41—1464no—
1096C22×Q8—2922no—
1097C22×Q8—2922no—
1098C22×Q8—731no—
1099C22×Q8—731no—
1100C22×Q8—731no—
1101C22×Q8—731no—
1102C22×Q8—731no—
1103C22×Q8—1464no—
1104C22×Q8C22×D7311yescharacteristic
1105C22×D4—731no—
1106C22×D4—731no—
1107C22×D4—731no—
1108C22×D4—731no—
1109C22×D4—731no—
1110C22×D4—731no—
1111C22×D4—731no—
1112C22×D4—731no—
1113C22×D4—731no—
1114C22×D4—731no—
1115C22×D4—731no—
1116C22×D4—731no—
1117C22×D4C22×D7311yescharacteristic
1118C22×D4C22×D7311yescharacteristic
1119C22×D4C22×D7311yescharacteristic
1120C22×D4C22×D7311yescharacteristic
1121C22×D4C22×D7311yescharacteristic
1122C22×D4C22×D7311yescharacteristic
1123C23×C4—2922no—
1124C23×C4—2922no—
1125C23×C4—731no—
1126C23×C4—731no—
1127C23×C4—731no—
1128C23×C4—731no—
1129C23×C4—731no—
1130C23×C4—731no—
1131C23×C4—731no—
1132C23×C4—731no—
1133C23×C4—731no—
1134C23×C4—731no—
1135C23×C4—731no—
1136C23×C4—731no—
1137C23×C4—1464no—
1138C23×C4C22×D7311yescharacteristic
1139C23×C4C22×D7311yescharacteristic
1140#124—42no—
1141#124—2922no—
1142#124—2922no—
1143#124—2922no—
1144#123—2922no—
1145#123—2922no—
1146#123—2922no—
1147#123—2922no—
1148C22⋊Q8—24no—
1149C22⋊Q8—1464no—
1150C22⋊Q8—1464no—
1151C22⋊Q8—1464no—
1152C22⋊Q8—1464no—
1153C22⋊Q8—1464no—
1154C22⋊Q8—1464no—
1155C22⋊Q8—1464no—
1156C22⋊Q8—1464no—
1157C22⋊Q8—1464no—
1158C22⋊Q8—1464no—
1159C22⋊Q8—1464no—
1160#121—24no—
1161#121—42no—
1162#121—2922no—
1163#121—2922no—
1164#121—2922no—
1165#121—1464no—
1166#121—1464no—
1167#121—1464no—
1168#121—1464no—
1169#121—1464no—
1170#121—1464no—
1171#121—1464no—
1172#120—2922no—
1173#120—2922no—
1174#120—2922no—
1175#120—2922no—
1176C2×C4⋊C4—731no—
1177C2×C4⋊C4—731no—
1178C2×C4⋊C4—731no—
1179C2×C4⋊C4—731no—
1180C2×C4⋊C4—731no—
1181C2×C4⋊C4—731no—
1182C2×C4⋊C4—731no—
1183C2×C4⋊C4—731no—
1184C2×C4⋊C4—731no—
1185C2×C4⋊C4—731no—
1186C2×C4⋊C4—731no—
1187C2×C4⋊C4—731no—
1188C2×C4⋊C4—731no—
1189C2×C4⋊C4—738no—
1190C2×C4⋊C4—731no—
1191C2×C4⋊C4—731no—
1192C2×C4⋊C4—731no—
1193C2×C4⋊C4—731no—
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—1464no—
1201C2×C4⋊C4—1464no—
1202C2×C4⋊C4C22×D7311yescharacteristic
1203C2×C4⋊C4C22×D7311yescharacteristic
1204C2×C4⋊C4C22×D7311yescharacteristic
1205C2×C4⋊C4C22×D7311yescharacteristic
1206C2×C4⋊C4C22×D7311yescharacteristic
1207C2×C22⋊C4—731no—
1208C2×C22⋊C4—731no—
1209C2×C22⋊C4—731no—
1210C2×C22⋊C4—731no—
1211C2×C22⋊C4—731no—
1212C2×C22⋊C4—731no—
1213C2×C22⋊C4—731no—
1214C2×C22⋊C4—731no—
1215C2×C22⋊C4—731no—
1216C2×C22⋊C4—731no—
1217C2×C22⋊C4—731no—
1218C2×C22⋊C4—731no—
1219C2×C22⋊C4—731no—
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—1464no—
1246C2×C22⋊C4—1464no—
1247C2×C22⋊C4C22×D7311yescharacteristic
1248C2×C22⋊C4C22×D7311yescharacteristic
1249C2×C22⋊C4C22×D7311yescharacteristic
1250C2×C22⋊C4C22×D7311yescharacteristic
1251C2×C22⋊C4C22×D7311yescharacteristic
1252C2×C22⋊C4C22×D7311yescharacteristic
1253C2×C22⋊C4C22×D7311yescharacteristic
1254C2×C22⋊C4C22×D7311yescharacteristic
1255C2×C22⋊C4C22×D7311yescharacteristic
1256C2×C22⋊C4C22×D7311yescharacteristic
1257C2×C22⋊C4C22×D7311yescharacteristic
1258C2×C22⋊C4C22×D7311yescharacteristic
1259C2×C22⋊C4C22×D7311yescharacteristic
1260C2×C22⋊C4C22×D7311yescharacteristic
1261C2×C42—731no—
1262C2×C42—731no—
1263C2×C42—731no—
1264C2×C42C22×D7311yescharacteristic
1265#95—731no—
1266#95—731no—
1267#95—731no—
1268#95—731no—
1269#95—731no—
1270#95—731no—
1271#95—731no—
1272#95—731no—
1273#95—731no—
1274#95—731no—
1275#95—731no—
1276#95—731no—
1277#95—731no—
1278#95—731no—
1279#95—731no—
1280#95—731no—
1281#95—731no—
1282#95—731no—
1283#95—731no—
1284#95—731no—
1285#95—731no—
1286#95—731no—
1287#95—731no—
1288#95—731no—
1289#95—731no—
1290#95—731no—
1291#95C22×D7311yescharacteristic
1292#95C22×D7311yescharacteristic
1293#95C22×D7311yescharacteristic
1294#95C22×D7311yescharacteristic
1295#95C22×D7311yescharacteristic
1296#95C22×D7311yescharacteristic
1297C24—2921no—
1298C24—2921no—
1299C24—731no—
1300C24—731no—
1301C24—731no—
1302C24—1462no—
1303C24—1462no—
1304C24—1462no—
1305C24—1462no—
1306C24—1462no—
1307C24C23×D7311yescharacteristic
1308C24C23×D7311yescharacteristic
1309C24C23×D7311yescharacteristic
1310C24C23×D7311yescharacteristic
1311#41—29216no—
1312#41—29216no—
1313C2×Q8—22no—
1314C2×Q8—22no—
1315C2×Q8—41no—
1316C2×Q8—2921no—
1317C2×Q8—2921no—
1318C2×Q8—2921no—
1319C2×Q8—2921no—
1320C2×Q8—2921no—
1321C2×Q8—2921no—
1322C2×Q8—2921no—
1323C2×Q8—29216no—
1324C2×Q8—1462no—
1325C2×Q8—1462no—
1326C2×Q8—1462no—
1327C2×Q8—1462no—
1328C2×Q8—1462no—
1329C2×Q8—1462no—
1330C2×Q8—1462no—
1331C2×Q8—1462no—
1332C2×D4—22no—
1333C2×D4—22no—
1334C2×D4—22no—
1335C2×D4—22no—
1336C2×D4—22no—
1337C2×D4—22no—
1338C2×D4—41no—
1339C2×D4—41no—
1340C2×D4—41no—
1341C2×D4—41no—
1342C2×D4—41no—
1343C2×D4—41no—
1344C2×D4—41no—
1345C2×D4—41no—
1346C2×D4—41no—
1347C2×D4—41no—
1348C2×D4—41no—
1349C2×D4—41no—
1350C2×D4—2921no—
1351C2×D4—2921no—
1352C2×D4—2921no—
1353C2×D4—2921no—
1354C2×D4—2921no—
1355C2×D4—2921no—
1356C2×D4—2921no—
1357C2×D4—2921no—
1358C2×D4—2921no—
1359C2×D4—2921no—
1360C2×D4—2921no—
1361C2×D4—2921no—
1362C2×D4—2921no—
1363C2×D4—2921no—
1364C2×D4—2921no—
1365C2×D4—2921no—
1366C2×D4—1462no—
1367C2×D4—1462no—
1368C2×D4—1462no—
1369C2×D4—1462no—
1370C2×D4—1462no—
1371C2×D4—1462no—
1372C2×D4—1462no—
1373C2×D4—1462no—
1374C2×D4—1462no—
1375C2×D4—1462no—
1376C2×D4—1462no—
1377C2×D4—1462no—
1378C2×D4—1462no—
1379C2×D4—1462no—
1380C2×D4—1462no—
1381C2×D4—1462no—
1382C2×D4—1462no—
1383C2×D4—1462no—
1384C2×D4—1462no—
1385C2×D4—1462no—
1386C22×C4—22no—
1387C22×C4—22no—
1388C22×C4—22no—
1389C22×C4—41no—
1390C22×C4—41no—
1391C22×C4—41no—
1392C22×C4—2921no—
1393C22×C4—2921no—
1394C22×C4—2921no—
1395C22×C4—2921no—
1396C22×C4—2921no—
1397C22×C4—2921no—
1398C22×C4—2921no—
1399C22×C4—2921no—
1400C22×C4—2921no—
1401C22×C4—2921no—
1402C22×C4—29216no—
1403C22×C4—2921no—
1404C22×C4—2921no—
1405C22×C4—2921no—
1406C22×C4—2921no—
1407C22×C4—2921no—
1408C22×C4—734no—
1409C22×C4—734no—
1410C22×C4—731no—
1411C22×C4—731no—
1412C22×C4—731no—
1413C22×C4—731no—
1414C22×C4—734no—
1415C22×C4—731no—
1416C22×C4—731no—
1417C22×C4—731no—
1418C22×C4—731no—
1419C22×C4—731no—
1420C22×C4—731no—
1421C22×C4—731no—
1422C22×C4—731no—
1423C22×C4—731no—
1424C22×C4—1462no—
1425C22×C4—1462no—
1426C22×C4—1462no—
1427C22×C4—1462no—
1428C22×C4—1462no—
1429C22×C4—1462no—
1430C22×C4—1462no—
1431C22×C4—1462no—
1432C22×C4—1462no—
1433C22×C4—1462no—
1434C22×C4—1462no—
1435C22×C4—1462no—
1436C22×C4—1462no—
1437C22×C4—1462no—
1438C22×C4—1462no—
1439C22×C4—1462no—
1440C22×C4—1462no—
1441C22×C4—1462no—
1442C22×C4C23×D7311yescharacteristic
1443C22×C4C23×D7311yescharacteristic
1444C22×C4C23×D7311yescharacteristic
1445C22×C4C23×D7311yescharacteristic
1446C22×C4C23×D7311yescharacteristic
1447C22×C4C23×D7311yescharacteristic
1448C22×C4C23×D7311yescharacteristic
1449C22×C4C23×D7311yescharacteristic
1450C22×C4C23×D7311yescharacteristic
1451C22×C4C23×D7311yescharacteristic
1452C22×C4C23×D7311yescharacteristic
1453C4⋊C4—22no—
1454C4⋊C4—22no—
1455C4⋊C4—41no—
1456C4⋊C4—41no—
1457C4⋊C4—2921no—
1458C4⋊C4—2921no—
1459C4⋊C4—2921no—
1460C4⋊C4—2921no—
1461C4⋊C4—2921no—
1462C4⋊C4—2921no—
1463C4⋊C4—2921no—
1464C4⋊C4—2921no—
1465C4⋊C4—2921no—
1466C4⋊C4—2921no—
1467C4⋊C4—734no—
1468C4⋊C4—734no—
1469C4⋊C4—734no—
1470C4⋊C4—1462no—
1471C4⋊C4—1462no—
1472C4⋊C4—1462no—
1473C4⋊C4—1462no—
1474C4⋊C4—1462no—
1475C4⋊C4—1462no—
1476C4⋊C4—1462no—
1477C4⋊C4—1462no—
1478C4⋊C4—1462no—
1479C4⋊C4—1462no—
1480C4⋊C4D4×D7314yes—
1481C22⋊C4—22no—
1482C22⋊C4—22no—
1483C22⋊C4—22no—
1484C22⋊C4—22no—
1485C22⋊C4—22no—
1486C22⋊C4—22no—
1487C22⋊C4—22no—
1488C22⋊C4—41no—
1489C22⋊C4—41no—
1490C22⋊C4—41no—
1491C22⋊C4—41no—
1492C22⋊C4—41no—
1493C22⋊C4—41no—
1494C22⋊C4—41no—
1495C22⋊C4—2921no—
1496C22⋊C4—2921no—
1497C22⋊C4—2921no—
1498C22⋊C4—2921no—
1499C22⋊C4—2921no—
1500C22⋊C4—2921no—
1501C22⋊C4—2921no—
1502C22⋊C4—2921no—
1503C22⋊C4—2921no—
1504C22⋊C4—2921no—
1505C22⋊C4—2921no—
1506C22⋊C4—2921no—
1507C22⋊C4—2921no—
1508C22⋊C4—2921no—
1509C22⋊C4—2921no—
1510C22⋊C4—2921no—
1511C22⋊C4—2921no—
1512C22⋊C4—1462no—
1513C22⋊C4—1462no—
1514C22⋊C4—1462no—
1515C22⋊C4—1462no—
1516C22⋊C4—1462no—
1517C22⋊C4—1462no—
1518C22⋊C4—1462no—
1519C22⋊C4—1462no—
1520C22⋊C4—1462no—
1521C22⋊C4—1462no—
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—
1533C42—41no—
1534C42—2921no—
1535C42—2921no—
1536C42—2921no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—21no—
1558C23—21no—
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—21no—
1563C23—21no—
1564C23—2924no—
1565C23—2924no—
1566C23—2924no—
1567C23—2924no—
1568C23—2924no—
1569C23—2924no—
1570C23—732no—
1571C23—732no—
1572C23—732no—
1573C23—732no—
1574C23—1468no—
1575C23—1461no—
1576C23—1461no—
1577C23—1461no—
1578C23—1461no—
1579C23—1461no—
1580C23—1461no—
1581C23—1461no—
1582C23—1461no—
1583C23—1461no—
1584C23—1461no—
1585C23—1461no—
1586C23—1461no—
1587C23—1461no—
1588C23—1461no—
1589C23—1461no—
1590C23—1461no—
1591C23—1461no—
1592C23#1455663812yes—
1593C23C24×D7311yescharacteristic
1594Q8—44no—
1595Q8—2924no—
1596Q8—2924no—
1597Q8—2924no—
1598Q8—2924no—
1599Q8—2924no—
1600D4—44no—
1601D4—82no—
1602D4—82no—
1603D4—82no—
1604D4—82no—
1605D4—82no—
1606D4—2924no—
1607D4—2924no—
1608D4—2924no—
1609D4—2924no—
1610D4—2924no—
1611D4—5842no—
1612D4—5842no—
1613D4—5842no—
1614D4—5842no—
1615D4—5842no—
1616D4—5842no—
1617D4—5842no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—44no—
1648C2×C4—44no—
1649C2×C4—2924no—
1650C2×C4—2924no—
1651C2×C4—2924no—
1652C2×C4—2924no—
1653C2×C4—2924no—
1654C2×C4—2924no—
1655C2×C4—2924no—
1656C2×C4—2924no—
1657C2×C4—2924no—
1658C2×C4—2924no—
1659C2×C4—732no—
1660C2×C4—732no—
1661C2×C4—732no—
1662C2×C4—732no—
1663C2×C4—1468no—
1664C2×C4—1468no—
1665C2×C4—1461no—
1666C2×C4—1461no—
1667C2×C4—1461no—
1668C2×C4—1461no—
1669C2×C4—1461no—
1670C2×C4—1461no—
1671C2×C4—1461no—
1672C2×C4—1461no—
1673C2×C4—1461no—
1674C2×C4—1461no—
1675C2×C4—1461no—
1676C2×C4—1461no—
1677C2×C4—1461no—
1678C2×C4—1461no—
1679C2×C4—1461no—
1680C2×C4—1461no—
1681C2×C4—1461no—
1682C2×C4—1461no—
1683C2×C4—1461no—
1684C2×C4—1461no—
1685C2×C4—1461no—
1686C2×C4—1461no—
1687C2×C4—1461no—
1688C2×C4—1461no—
1689C2×C4—1461no—
1690C2×C4—1461no—
1691C2×C4—1461no—
1692C2×C4—1461no—
1693C2×C4—1461no—
1694C2×C4—1461no—
1695C2×C4—1461no—
1696C2×C4—1461no—
1697C2×C4—1461no—
1698C2×C4—1461no—
1699C2×C4—1461no—
1700C2×C4C2×D4×D7312yes—
1701C2×C4C2×D4×D7312yes—
1702C2×C4C2×D4×D7312yes—
1703C2×C4#1455663612yes—
1704C22—22no—
1705C22—22no—
1706C22—22no—
1707C22—41no—
1708C22—41no—
1709C22—41no—
1710C22—41no—
1711C22—41no—
1712C22—41no—
1713C22—41no—
1714C22—41no—
1715C22—41no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—41no—
1722C22—41no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—29216no—
1733C22—2921no—
1734C22—2921no—
1735C22—2921no—
1736C22—2921no—
1737C22—2921no—
1738C22—2921no—
1739C22—2921no—
1740C22—2921no—
1741C22—2921no—
1742C22—2921no—
1743C22—2921no—
1744C22—734no—
1745C22—1462no—
1746C22—1462no—
1747C22—1462no—
1748C22—1462no—
1749C22—1462no—
1750C22—1462no—
1751C22—1462no—
1752C22—1462no—
1753C22—1462no—
1754C22C22×D4×D7311yescharacteristic
1755C22H(5,𝔽2)×D7311yescharacteristic
1756C22H(5,𝔽2)×D7311yescharacteristic
1757C22H(5,𝔽2)×D7311yescharacteristic
1758C22C2×#1455663611yescharacteristic
1759C222−1+4×D7311yescharacteristic
1760C22C2×#1455663811yescharacteristic
1761C4—22no—
1762C4—22no—
1763C4—22no—
1764C4—22no—
1765C4—41no—
1766C4—41no—
1767C4—41no—
1768C4—41no—
1769C4—41no—
1770C4—41no—
1771C4—41no—
1772C4—2921no—
1773C4—2921no—
1774C4—2921no—
1775C4—2921no—
1776C4—2921no—
1777C4—2921no—
1778C4—2921no—
1779C4—2921no—
1780C4—2921no—
1781C4—1462no—
1782C4—1462no—
1783C4—1462no—
1784C4—1462no—
1785C2—42no—
1786C2—81no—
1787C2—81no—
1788C2—81no—
1789C2—2922no—
1790C2—5841no—
1791C2—1464no—
1792C2#535×D7311yescharacteristic
1793C2#2262355911yescharacteristic
1794C2#2262357711yescharacteristic
1795C2#2262414911yescharacteristic
1796C2#2262415011yescharacteristic
1797C2#2262415111yescharacteristic
1798C2#2262415211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2676C2
hypercenter#2676D73
hypocenterC73#36707
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2676

Complements

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

NH ≅ G/Ntype
1. C2×#17989166C2semidirect
2. C2×C22⋊Q8×D73C2semidirect
3. #22618212C2semidirect
4. #22618210C2semidirect
5. #22616433C2semidirect
6. #22616431C2semidirect
7. #22616430C2semidirect
8. #22616428C2semidirect
9. #22616426C2semidirect
10. #22616425C2semidirect
11. #22616424C2semidirect
12. #22616423C2semidirect
13. #22616239C2semidirect
14. #22616237C2semidirect
15. #22616234C2semidirect
16. #22616232C2semidirect
17. #22616227C2semidirect
18. #22616226C2semidirect
19. #22616225C2semidirect
20. #22615678C2semidirect
21. #22615672C2semidirect
22. #22614860C2semidirect
23. #22614856C2semidirect
24. #22613586C2semidirect
25. #22613584C2semidirect
26. #22613264C2semidirect
27. #22613261C2semidirect
28. #22613248C2semidirect
29. #22613245C2semidirect
30. #22612530C2semidirect
31. C73×#2676C2semidirect
37. C2×#14556578C22semidirect
38. C2×#14556577C22semidirect
39. C2×#14556577C22semidirect
45. C2×#14556571C22semidirect
47. C2×#14556570C22semidirect
52. C2×#14556568C22semidirect
53. C2×#14556568C22semidirect
60. C2×#14556563C22semidirect
61. C2×#14556563C22semidirect
65. C2×#14556562C22semidirect
79. #17988521C22semidirect
80. #17988520C22semidirect
81. #17988519C22semidirect
82. #17988517C22semidirect
83. #17988510C22semidirect
84. #17988510C22semidirect
85. #17988510C22semidirect
86. #17988510C22semidirect
87. #17988510C22semidirect
88. #17988509C22semidirect
89. #17988509C22semidirect
90. #17988508C22semidirect
91. #17988508C22semidirect
92. #17988507C22semidirect
93. #17988507C22semidirect
94. #17988503C22semidirect
95. #17988503C22semidirect
96. #17988502C22semidirect
97. #17988502C22semidirect
98. #17988501C22semidirect
99. #17988501C22semidirect
102. #17988500C22semidirect
105. #17988499C22semidirect
106. #17988499C22semidirect
107. #17988499C22semidirect
108. #17988499C22semidirect
109. #17988499C22semidirect
110. #17988498C22semidirect
117. #17988494C22semidirect
118. #17988493C22semidirect
119. #17988491C22semidirect
120. #17988491C22semidirect
128. #17988474C22semidirect
129. #17988473C22semidirect
130. #17988472C22semidirect
131. #17988471C22semidirect
132. #17988470C22semidirect
133. #17988469C22semidirect
134. #17988468C22semidirect
157. #17988462C22semidirect
158. #17988462C22semidirect
159. #17988461C22semidirect
160. #17988460C22semidirect
161. #17988459C22semidirect
162. #17988459C22semidirect
163. #17988458C22semidirect
174. C2×#124×C73C22semidirect
177. C2×#121×C73C22semidirect
178. #396×C73C22semidirect
179. #394×C73C22semidirect
180. #394×C73C22semidirect
181. #393×C73C22semidirect
185. #387×C73C22semidirect
188. #385×C73C22semidirect
288. C4⋊C4×D73D4semidirect
919. #2676D73semidirect
931. C73#36707semidirect
940. C2×#124C2×D73semidirect
969. C2×#121C2×D73semidirect
994. #396C2×D73semidirect
1005. #394C2×D73semidirect
1006. #394C2×D73semidirect
1018. #393C2×D73semidirect
1046. #387C2×D73semidirect
1078. #385C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891662
C2×C22⋊Q8×D732
#226182122
#226182102
#226164332
#226164312
#226164302
#226164282
#226164262
#226164252
#226164242
#226164232
#226162392
#226162372
#226162342
#226162322
#226162272
#226162262
#226162252
#226156782
#226156722
#226148602
#226148562
#226135862
#226135842
#226132642
#226132612
#226132482
#226132452
#226125302
C73×#26762
#3670773