Finite Group Databasebeta

← #33258628

Subgroups — #33258628

Order 18688.

2834 conjugacy classes of subgroups.

The subgroup lattice has 1666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989183C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#22618226C211yesmaximal, characteristic, complemented
4#22618222C211yesmaximal, characteristic, complemented
5#22618215C211yesmaximal, characteristic, complemented
6#22618212C211yesmaximal, characteristic
7#22615743C211yesmaximal, characteristic, complemented
8#22615716C211yesmaximal, characteristic, complemented
9#22615712C211yesmaximal, characteristic, complemented
10#22615678C211yesmaximal, characteristic, complemented
11#22614197C211yesmaximal, characteristic, complemented
12#22614193C211yesmaximal, characteristic, complemented
13#22614190C211yesmaximal, characteristic, complemented
14#22614186C211yesmaximal, characteristic, complemented
15#22614078C211yesmaximal, characteristic, complemented
16#22614074C211yesmaximal, characteristic, complemented
17#22614069C211yesmaximal, characteristic, complemented
18#22614065C211yesmaximal, characteristic, complemented
19#22613737C211yesmaximal, characteristic, complemented
20#22613736C211yesmaximal, characteristic, complemented
21#22613733C211yesmaximal, characteristic, complemented
22#22613672C211yesmaximal, characteristic, complemented
23#22613669C211yesmaximal, characteristic, complemented
24#22613665C211yesmaximal, characteristic, complemented
25#22613660C211yesmaximal, characteristic, complemented
26#22612598C211yesmaximal, characteristic, complemented
27#22612595C211yesmaximal, characteristic, complemented
28#22612530C211yesmaximal, characteristic, complemented
29#22612432C211yesmaximal, characteristic, complemented
30C4×#14556559C211yesmaximal, characteristic, complemented
31C73×#2449C211yesmaximal, characteristic, complemented
32C23×C4×D73C2211yescharacteristic
33C23×C4×D73C2211yescharacteristic
34C23×C4×D73C2211yescharacteristic
35#17989183—28no—
36C2×#14556586C2211yescharacteristic, complemented
37C2×#14556584C2211yescharacteristic, complemented
38C2×#14556581C2211yescharacteristic, complemented
39C2×#14556581C2211yescharacteristic, complemented
40C2×#14556576C2211yescharacteristic
41C2×#14556576C2211yescharacteristic
42C2×#14556574C2211yescharacteristic, complemented
43C2×#14556573C2211yescharacteristic
44C2×#14556573C2211yescharacteristic
45C2×#14556573C2211yescharacteristic, complemented
46C2×#14556567C2211yescharacteristic
47C2×#14556567C2211yescharacteristic
48C2×#14556567C2211yescharacteristic, complemented
49C2×#14556564C2211yescharacteristic
50C2×#14556564C2211yescharacteristic
51C2×#14556563C2211yescharacteristic
52C2×#14556561C2211yescharacteristic
53C2×#14556559C2211yescharacteristic
54C2×#14556553C2211yescharacteristic
55C2×#14556553C2211yescharacteristic
56C2×C4×C22⋊D73C2211yescharacteristic
57C2×C4×C22⋊D73C2211yescharacteristic
58C2×#14556551C2211yescharacteristic
59C22×C4⋊Dic73C2211yescharacteristic
60C22×#11924007C2211yescharacteristic
61C22×#11924007C2211yescharacteristic
62C2×C4⋊C4×D73—28no—
63C2×C4⋊C4×D73C2211yescharacteristic
64C2×C4⋊C4×D73C2211yescharacteristic
65C2×C4⋊C4×D73C2211yescharacteristic
66C2×C4⋊C4×D73C2211yescharacteristic
67C2×C4⋊C4×D73C2211yescharacteristic
68C2×C4⋊C4×D73C2211yescharacteristic
69C2×C4⋊C4×D73C2211yescharacteristic
70C2×C4⋊C4×D73C2211yescharacteristic
71#17988528C2211yescharacteristic, complemented
72#17988528C2211yescharacteristic, complemented
73#17988527C2211yescharacteristic, complemented
74#17988527C2211yescharacteristic, complemented
75#17988526C2211yescharacteristic, complemented
76#17988525C2211yescharacteristic, complemented
77#17988523C2211yescharacteristic, complemented
78#17988522C2211yescharacteristic, complemented
79#17988522C2211yescharacteristic, complemented
80#17988521C2211yescharacteristic, complemented
81#17988521C2211yescharacteristic, complemented
82#17988521C2211yescharacteristic, complemented
83#17988520C2211yescharacteristic, complemented
84#17988520C2211yescharacteristic, complemented
85#17988520C2211yescharacteristic, complemented
86#17988518C2211yescharacteristic, complemented
87#17988518C2211yescharacteristic, complemented
88#17988517C2211yescharacteristic, complemented
89#17988515C2211yescharacteristic, complemented
90#17988515C2211yescharacteristic, complemented
91#17988514C2211yescharacteristic, complemented
92#17988513C2211yescharacteristic, complemented
93#17988510C2211yescharacteristic, complemented
94#17988509C2211yescharacteristic, complemented
95#17988509C2211yescharacteristic, complemented
96#17988506C2211yescharacteristic, complemented
97#17988503C2211yescharacteristic, complemented
98#17988502C2211yescharacteristic, complemented
99#17988484C2211yescharacteristic, complemented
100#17988483C2211yescharacteristic, complemented
101#17988482C2211yescharacteristic, complemented
102#17988480C2211yescharacteristic, complemented
103#17988478C2211yescharacteristic, complemented
104#17988477C2211yescharacteristic, complemented
105#17988475C2211yescharacteristic, complemented
106#17988474C2211yescharacteristic, complemented
107#17988473C2211yescharacteristic, complemented
108#17988473C2211yescharacteristic, complemented
109#17988472C2211yescharacteristic, complemented
110#17988472C2211yescharacteristic, complemented
111#17988471C2211yescharacteristic, complemented
112#17988470C2211yescharacteristic, complemented
113#17988469C2211yescharacteristic, complemented
114#17988469C2211yescharacteristic, complemented
115#17988468C2211yescharacteristic, complemented
116#17988468C2211yescharacteristic, complemented
117#17988467C2211yescharacteristic
118#17988467C2211yescharacteristic
119#17988466C2211yescharacteristic
120#17988466C2211yescharacteristic
121#17988466C2211yescharacteristic
122#17988465C2211yescharacteristic
123#17988465C2211yescharacteristic
124#17988465C2211yescharacteristic
125#17988465C2211yescharacteristic
126#17988465C2211yescharacteristic
127#17988465C2211yescharacteristic
128#17988464C2211yescharacteristic
129#17988463C2211yescharacteristic
130#17988463C2211yescharacteristic
131#17988463C2211yescharacteristic
132#17988463C2211yescharacteristic
133#17988463C2211yescharacteristic
134#17988463C2211yescharacteristic
135#17988462C2211yescharacteristic
136#17988461C2211yescharacteristic
137#17988461C2211yescharacteristic
138#17988461C2211yescharacteristic, complemented
139#17988460C2211yescharacteristic
140#17988460C2211yescharacteristic, complemented
141#17988459C2211yescharacteristic
142#17988459C2211yescharacteristic
143#17988459C2211yescharacteristic
144#17988459C2211yescharacteristic
145#17988458C2211yescharacteristic
146#17988458C2211yescharacteristic
147#17988458C2211yescharacteristic
148#17988458C2211yescharacteristic
149#17988458C2211yescharacteristic
150#17988458C2211yescharacteristic
151#17988458C2211yescharacteristic
152#17988458C2211yescharacteristic
153#17988458C2211yescharacteristic
154#17988458C2211yescharacteristic
155#17988458C2211yescharacteristic, complemented
156#17988449C2211yescharacteristic
157#17988449C2211yescharacteristic
158#17988449C2211yescharacteristic
159#17988449C2211yescharacteristic
160#17988447C2211yescharacteristic
161#17988446C2211yescharacteristic
162#17988446C2211yescharacteristic
163#17988445C2211yescharacteristic
164#17988444C2211yescharacteristic
165#17988444C2211yescharacteristic
166#17988442C2211yescharacteristic
167#17988442C2211yescharacteristic
168C22⋊C4×Dic73C2211yescharacteristic
169C4×#11924005C2211yescharacteristic
170C4×#11924005C2211yescharacteristic
171C4×C22⋊Dic73C2211yescharacteristic
172#17988434C2211yescharacteristic
173#17988434C2211yescharacteristic
174C2×C22⋊Q8×C73C2211yescharacteristic
175C2×C22⋊Q8×C73C2211yescharacteristic, complemented
176C2×C4×D4×C73C2211yescharacteristic
177C22×C4⋊C4×C73C2211yescharacteristic
178#399×C73C2211yescharacteristic, complemented
179#398×C73C2211yescharacteristic, complemented
180#396×C73C2211yescharacteristic, complemented
181#395×C73C2211yescharacteristic, complemented
182#389×C73C2211yescharacteristic, complemented
183#387×C73C2211yescharacteristic, complemented
184#386×C73C2211yescharacteristic
185#386×C73C2211yescharacteristic
186#385×C73C2211yescharacteristic
187#385×C73C2211yescharacteristic
188#385×C73C2211yescharacteristic, complemented
189C24×D73C2311yescharacteristic
190C22×D292C2311yescharacteristic
191C22×D292C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C22×C4×D73—24no—
200C22×C4×D73—24no—
201C22×C4×D73—24no—
202C22×C4×D73—24no—
203C22×C4×D73—24no—
204C22×C4×D73—42no—
205C22×C4×D73—42no—
206C22×C4×D73—42no—
207C22×C4×D73—42no—
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212C22×C4×D73C2311yescharacteristic
213C22×C4×D73C2311yescharacteristic
214C22×C4×D73C2311yescharacteristic
215C22×C4×D73C2311yescharacteristic
216C22×C4×D73C2311yescharacteristic
217C22×C4×D73C2311yescharacteristic
218C22×C4×D73C2311yescharacteristic
219C22×C4×D73C2311yescharacteristic
220C22×C4×D73C2311yescharacteristic
221#14556586—24no—
222#14556584—24no—
223#14556581—24no—
224#14556581—24no—
225#14556576—24no—
226#14556576—24no—
227#14556574—24no—
228#14556573—24no—
229#14556573—24no—
230#14556573—24no—
231#14556567—24no—
232#14556567—24no—
233#14556567—42no—
234#14556564—24no—
235#14556564—42no—
236#14556563—42no—
237#14556561—24no—
238#14556559—24no—
239#14556553—24no—
240#14556553—42no—
241C4×C22⋊D73—24no—
242C4×C22⋊D73—42no—
243#14556551—42no—
244C2×C4⋊Dic73—24no—
245C2×C4⋊Dic73C2311yescharacteristic
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
251C2×C4⋊Dic73C2311yescharacteristic
252C2×C4⋊Dic73C2311yescharacteristic
253C2×#11924007—24no—
254C2×#11924007—24no—
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×#11924007C2311yescharacteristic
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×#11924007C2311yescharacteristic
277C4⋊C4×D73—24no—
278C4⋊C4×D73—24no—
279C4⋊C4×D73—24no—
280C4⋊C4×D73—24no—
281C4⋊C4×D73—24no—
282C4⋊C4×D73—24no—
283C4⋊C4×D73—24no—
284C4⋊C4×D73D418yescomplemented
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×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C2×#11924005C2311yescharacteristic
296C2×#11924005C2311yescharacteristic
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2311yescharacteristic
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×C4×Dic73C2311yescharacteristic
316C2×C4×Dic73C2311yescharacteristic
317C2×C4×Dic73C2311yescharacteristic
318C2×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
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
352C22×Q8×C73C2311yescharacteristic
353C22×D4×C73C2311yescharacteristic
354C23×C4×C73C2311yescharacteristic
355C23×C4×C73C2311yescharacteristic
356C23×C4×C73C2311yescharacteristic
357C23×C4×C73C2311yescharacteristic
358C22⋊Q8×C73—24no—
359C22⋊Q8×C73—42no—
360C4×D4×C73—42no—
361C2×C4⋊C4×C73—24no—
362C2×C4⋊C4×C73C2311yescharacteristic
363C2×C4⋊C4×C73C2311yescharacteristic
364C2×C4⋊C4×C73C2311yescharacteristic
365C2×C4⋊C4×C73C2311yescharacteristic
366C2×C4⋊C4×C73C2311yescharacteristic
367C2×C4⋊C4×C73C2311yescharacteristic
368C2×C4⋊C4×C73C2311yescharacteristic
369C2×C4⋊C4×C73C2311yescharacteristic
370C2×C4⋊C4×C73C2311yescharacteristic
371C2×C4⋊C4×C73C2311yescharacteristic
372C2×C4⋊C4×C73C2311yescharacteristic
373C2×C4⋊C4×C73C2311yescharacteristic
374C2×C22⋊C4×C73C2311yescharacteristic
375C2×C22⋊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×C42×C73C2311yescharacteristic
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385#95×C73C2311yescharacteristic
386#95×C73C2311yescharacteristic
387#95×C73C2311yescharacteristic
388#95×C73C2311yescharacteristic
389#95×C73C2311yescharacteristic
390#95×C73C2311yescharacteristic
391C23×D73—22no—
392C23×D73—22no—
393C23×D73—22no—
394C23×D73—22no—
395C23×D73—22no—
396C23×D73—22no—
397C23×D73#4114yes—
398C23×D73C2411yescharacteristic
399C23×D73C2411yescharacteristic
400C23×D73C2411yescharacteristic
401C2×D292—22no—
402C2×D292—22no—
403C2×D292—22no—
404C2×D292—22no—
405C2×D292—22no—
406C2×D292—22no—
407C2×C22⋊D73—22no—
408C2×C22⋊D73—22no—
409C2×C22⋊D73—22no—
410C2×C22⋊D73—22no—
411C2×C22⋊D73—22no—
412C2×C22⋊D73—22no—
413C2×C22⋊D73—22no—
414C2×C22⋊D73—22no—
415C2×C22⋊D73—22no—
416C2×C22⋊D73—22no—
417C2×C22⋊D73—41no—
418C2×C22⋊D73—41no—
419C22×Dic73—22no—
420C22×Dic73—22no—
421C22×Dic73—22no—
422C22×Dic73—22no—
423C22×Dic73—22no—
424C22×Dic73—22no—
425C22×Dic73—22no—
426C22×Dic73—41no—
427C22×Dic73—41no—
428C22×Dic73C2411yescharacteristic
429C22×Dic73C2411yescharacteristic
430C22×Dic73C2411yescharacteristic
431C22×Dic73C2411yescharacteristic
432C22×Dic73C2411yescharacteristic
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2411yescharacteristic
437C22×Dic73C2411yescharacteristic
438C22×Dic73C2411yescharacteristic
439C22×Dic73C2411yescharacteristic
440C22×Dic73C2411yescharacteristic
441C2×C4×D73—232no—
442C2×C4×D73—22no—
443C2×C4×D73—22no—
444C2×C4×D73—22no—
445C2×C4×D73—22no—
446C2×C4×D73—22no—
447C2×C4×D73—22no—
448C2×C4×D73—22no—
449C2×C4×D73—22no—
450C2×C4×D73—22no—
451C2×C4×D73—22no—
452C2×C4×D73—22no—
453C2×C4×D73—22no—
454C2×C4×D73—22no—
455C2×C4×D73—22no—
456C2×C4×D73—22no—
457C2×C4×D73—22no—
458C2×C4×D73—22no—
459C2×C4×D73—22no—
460C2×C4×D73—22no—
461C2×C4×D73—22no—
462C2×C4×D73—22no—
463C2×C4×D73—41no—
464C2×C4×D73—41no—
465C2×C4×D73—41no—
466C2×C4×D73—41no—
467C2×C4×D73—41no—
468C2×C4×D73—41no—
469C2×C4×D73—41no—
470C2×C4×D73—41no—
471C2×C4×D73—41no—
472C2×C4×D73—41no—
473C2×C4×D73—41no—
474C2×C4×D73—41no—
475C2×C4×D73—416no—
476C2×C4×D73—416no—
477C2×C4×D73—41no—
478C2×C4×D73—41no—
479C2×C4×D73C2×D414yes—
480C2×C4×D73C2×D414yes—
481C2×C4×D73C2×D414yes—
482C2×C4×D73#4114yes—
483C4⋊Dic73—22no—
484C4⋊Dic73—22no—
485C4⋊Dic73—22no—
486C4⋊Dic73—22no—
487C4⋊Dic73—22no—
488C4⋊Dic73—22no—
489C4⋊Dic73—41no—
490C4⋊Dic73C2×D414yes—
491#11924007—22no—
492#11924007—22no—
493#11924007—22no—
494#11924007—22no—
495#11924007—22no—
496#11924007—22no—
497#11924007—22no—
498#11924007—22no—
499#11924007—22no—
500#11924007—22no—
501#11924007—22no—
502#11924007—22no—
503#11924007—22no—
504#11924007—22no—
505#11924007—41no—
506#11924007—41no—
507#11924007—41no—
508#11924007—41no—
509#11924007—41no—
510#11924007—41no—
511#11924007C2×D414yes—
512#11924007C2×D414yes—
513C22⋊Dic73—22no—
514C22⋊Dic73—22no—
515C22⋊Dic73—22no—
516C22⋊Dic73—22no—
517C22⋊Dic73—22no—
518C22⋊Dic73—22no—
519C22⋊Dic73—41no—
520C22⋊Dic73—41no—
521#11924005—22no—
522#11924005—22no—
523#11924005—22no—
524#11924005—22no—
525#11924005—22no—
526#11924005—22no—
527#11924005—22no—
528#11924005—22no—
529#11924005—22no—
530#11924005—22no—
531#11924005—22no—
532#11924005—22no—
533#11924005—22no—
534#11924005—22no—
535#11924005—22no—
536#11924005—22no—
537#11924005—22no—
538#11924005—22no—
539#11924005—41no—
540#11924005—41no—
541#11924005—41no—
542#11924005—41no—
543C4×Dic73—22no—
544C4×Dic73—22no—
545C4×Dic73—41no—
546C4×Dic73—41no—
547C4×Dic73—41no—
548C24×C73C2411yescharacteristic
549C24×C73C2411yescharacteristic
550C2×Q8×C73—22no—
551C2×Q8×C73—41no—
552C2×Q8×C73—41no—
553C2×D4×C73—22no—
554C2×D4×C73—22no—
555C2×D4×C73—22no—
556C22×C4×C73—22no—
557C22×C4×C73—22no—
558C22×C4×C73—22no—
559C22×C4×C73—22no—
560C22×C4×C73—22no—
561C22×C4×C73—22no—
562C22×C4×C73—22no—
563C22×C4×C73—22no—
564C22×C4×C73—41no—
565C22×C4×C73—41no—
566C22×C4×C73—41no—
567C22×C4×C73—41no—
568C22×C4×C73C2411yescharacteristic
569C22×C4×C73C2411yescharacteristic
570C22×C4×C73C2411yescharacteristic
571C22×C4×C73C2411yescharacteristic
572C22×C4×C73C2411yescharacteristic
573C22×C4×C73C2411yescharacteristic
574C22×C4×C73C2411yescharacteristic
575C22×C4×C73C2411yescharacteristic
576C22×C4×C73C2411yescharacteristic
577C22×C4×C73C2411yescharacteristic
578C22×C4×C73C2411yescharacteristic
579C22×C4×C73C2411yescharacteristic
580C22×C4×C73C2411yescharacteristic
581C4⋊C4×C73—22no—
582C4⋊C4×C73—22no—
583C4⋊C4×C73—22no—
584C4⋊C4×C73—22no—
585C4⋊C4×C73—22no—
586C4⋊C4×C73—22no—
587C4⋊C4×C73—41no—
588C4⋊C4×C73—41no—
589C4⋊C4×C73—41no—
590C4⋊C4×C73—41no—
591C4⋊C4×C73—41no—
592C4⋊C4×C73C2×D414yes—
593C22⋊C4×C73—22no—
594C22⋊C4×C73—22no—
595C22⋊C4×C73—22no—
596C22⋊C4×C73—22no—
597C22⋊C4×C73—22no—
598C22⋊C4×C73—22no—
599C22⋊C4×C73—41no—
600C22⋊C4×C73—41no—
601C42×C73—41no—
602C23×C73—21no—
603C23×C73—21no—
604C23×C73—21no—
605C23×C73—21no—
606C23×C73—21no—
607C23×C73—21no—
608C23×C73—21no—
609C23×C73—21no—
610C23×C73—21no—
611C23×C73—21no—
612C23×C73—21no—
613C23×C73C2×#4112yes—
614C23×C73H(5,𝔽2)12yes—
615C23×C732−1+412yes—
616C23×C73C2511yescharacteristic
617C22×D73—28no—
618C22×D73—28no—
619C22×D73—28no—
620C22×D73—28no—
621C22×D73—28no—
622C22×D73—21no—
623C22×D73—21no—
624C22×D73—21no—
625C22×D73—21no—
626C22×D73—21no—
627C22×D73—21no—
628C22×D73—21no—
629C22×D73—21no—
630C22×D73—28no—
631C22×D73—28no—
632C22×D73—21no—
633C22×D73—21no—
634C22×D73—21no—
635C22×D73—21no—
636C22×D73—21no—
637C22×D73—21no—
638C22×D73—21no—
639C22×D73C22×D412yes—
640C22×D73C2×#4112yes—
641C22×D73C2×#4112yes—
642C22×D73C2×#4112yes—
643C22×D73H(5,𝔽2)12yes—
644C22×D732−1+412yes—
645Q8×C73—82no—
646D4×C73—44no—
647C2×C4×C73—28no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—44no—
684C2×C4×C73—44no—
685C2×C4×C73—82no—
686C2×C4×C73C22×D412yes—
687C2×C4×C73C22×D412yes—
688C2×C4×C73C22×D412yes—
689C2×C4×C73C2×#4112yes—
690C22⋊D73—44no—
691C22⋊D73—44no—
692C22⋊D73—44no—
693C22⋊D73—82no—
694C2×Dic73—28no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—21no—
704C2×Dic73—21no—
705C2×Dic73—21no—
706C2×Dic73—21no—
707C2×Dic73—21no—
708C2×Dic73—21no—
709C2×Dic73—21no—
710C2×Dic73—21no—
711C2×Dic73—21no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—21no—
717C2×Dic73—21no—
718C2×Dic73—21no—
719C2×Dic73—21no—
720C2×Dic73—21no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
724C2×Dic73—21no—
725C2×Dic73—21no—
726C2×Dic73—21no—
727C2×Dic73—21no—
728C2×Dic73—21no—
729C2×Dic73—21no—
730C2×Dic73—44no—
731C2×Dic73—44no—
732C2×Dic73C22×D412yes—
733C2×Dic73C22×D412yes—
734C2×Dic73C22×D412yes—
735C2×Dic73C2×#4112yes—
736D292—44no—
737D292—44no—
738C4×D73—28no—
739C4×D73—28no—
740C4×D73—28no—
741C4×D73—28no—
742C4×D73—44no—
743C4×D73—44no—
744C4×D73—44no—
745C4×D73—44no—
746C4×D73—44no—
747C4×D73—44no—
748C4×D73—44no—
749C4×D73—44no—
750C4×D73—82no—
751C22×C73—22no—
752C22×C73—22no—
753C22×C73—22no—
754C22×C73—22no—
755C22×C73—22no—
756C22×C73—22no—
757C22×C73—41no—
758C22×C73—41no—
759C22×C73—41no—
760C22×C73—41no—
761C22×C73—41no—
762C22×C73—41no—
763C22×C73—41no—
764C22×C73#53914yescomplemented
765C22×C73C23×D411yescharacteristic
766C22×C73C22×#4111yescharacteristic
767C22×C73C22×#4111yescharacteristic
768C22×C73C2×H(5,𝔽2)11yescharacteristic
769C22×C73C2×H(5,𝔽2)11yescharacteristic
770C22×C73C2×2−1+411yescharacteristic
771C22×C73C2×2−1+411yescharacteristic
772C2×D73—232no—
773C2×D73—22no—
774C2×D73—22no—
775C2×D73—22no—
776C2×D73—22no—
777C2×D73—22no—
778C2×D73—22no—
779C2×D73—22no—
780C2×D73—22no—
781C2×D73—22no—
782C2×D73—22no—
783C2×D73—22no—
784C2×D73—22no—
785C2×D73—41no—
786C2×D73—41no—
787C2×D73—41no—
788C2×D73—41no—
789C2×D73—41no—
790C2×D73—41no—
791C2×D73—41no—
792C2×D73#52514yes—
793C2×D73#53914yescomplemented
794C4×C73—22no—
795C4×C73—22no—
796C4×C73—22no—
797C4×C73—22no—
798C4×C73—41no—
799C4×C73—41no—
800C4×C73—41no—
801C4×C73—41no—
802C4×C73—41no—
803C4×C73—41no—
804C4×C73—41no—
805C4×C73—41no—
806C4×C73—41no—
807Dic73—22no—
808Dic73—22no—
809Dic73—22no—
810Dic73—22no—
811Dic73—41no—
812Dic73—41no—
813Dic73—41no—
814Dic73—41no—
815Dic73—41no—
816Dic73—41no—
817Dic73—41no—
818Dic73—41no—
819Dic73—41no—
820#34989—731nomaximal, Sylow
821C2×C73—24no—
822C2×C73—81no—
823C2×C73C2×#52511yescharacteristic
824C2×C73C2×#53911yescharacteristic
825C2×C73C2×#53911yescharacteristic
826C2×C73#348411yescharacteristic
827C2×C73#348611yescharacteristic
828C2×C73#349211yescharacteristic
829C2×C73#349211yescharacteristic
830D73—24no—
831D73—24no—
832D73—81no—
833C2×#539—731no—
834C23×C4⋊C4—731no—
835#2849—731no—
836#2849—731no—
837#2848—731no—
838#2847—731no—
839#2627—731no—
840#2623—731no—
841#2623—731no—
842#2618—731no—
843#2481—731no—
844#2481—731no—
845#2481—731no—
846#2481—731no—
847#2473—731no—
848#2473—731no—
849#2473—731no—
850#2473—731no—
851#2449—731no—
852#2449—731no—
853#2449—731no—
854#2449D7311yescharacteristic, complemented
855#2443—731no—
856#2443—731no—
857#2443—731no—
858#2443—731no—
859#2322—731no—
860#2322—731no—
861#2313—731no—
862C4×#120—731no—
863C4×#120—731no—
864C73#3498911yescharacteristic, complemented, Sylow
865C24×C4—731no—
866C24×C4—731no—
867C24×C4—731no—
868#539—1468no—
869C2×#126—731no—
870C2×#126—731no—
871C2×#125—731no—
872C2×#125—731no—
873C2×#123—731no—
874C2×#123—731no—
875C2×#123—731no—
876C2×#123—731no—
877C2×#123—731no—
878C2×#123—731no—
879C2×C22⋊Q8—731no—
880C2×C22⋊Q8—731no—
881C2×C22⋊Q8—731no—
882C2×C22⋊Q8C2×D7311yescharacteristic
883C2×C22⋊Q8C2×D7311yescharacteristic, complemented
884C2×#121—731no—
885C2×#121—731no—
886C2×#121—731no—
887C2×#120—731no—
888C2×#120—731no—
889C2×C4×D4—731no—
890C2×C4×D4—731no—
891C2×C4×D4—731no—
892C2×C4×D4—731no—
893C2×C4×D4—731no—
894C2×C4×D4C2×D7311yescharacteristic
895C22×C4⋊C4—731no—
896C22×C4⋊C4—731no—
897C22×C4⋊C4—731no—
898C22×C4⋊C4—731no—
899C22×C4⋊C4—731no—
900C22×C4⋊C4—731no—
901C22×C4⋊C4—731no—
902C22×C4⋊C4—731no—
903C22×C4⋊C4—731no—
904C22×C4⋊C4—731no—
905C22×C4⋊C4—731no—
906C22×C4⋊C4—1468no—
907C22×C4⋊C4C2×D7311yescharacteristic
908#400—731no—
909#400—731no—
910#400—731no—
911#400—731no—
912#400—731no—
913#400—731no—
914#399—731no—
915#399—731no—
916#399—731no—
917#399C2×D7311yescharacteristic, complemented
918#398—731no—
919#398—731no—
920#398—731no—
921#398—731no—
922#398—731no—
923#398—731no—
924#398—731no—
925#398—731no—
926#398—731no—
927#398C2×D7311yescharacteristic, complemented
928#397—731no—
929#397—731no—
930#397—731no—
931#397—731no—
932#396—731no—
933#396—731no—
934#396—731no—
935#396C2×D7311yescharacteristic, complemented
936#395—731no—
937#395C2×D7311yescharacteristic, complemented
938#394—731no—
939#394—731no—
940#389—731no—
941#389—731no—
942#389—731no—
943#389C2×D7311yescharacteristic, complemented
944#388—731no—
945#388—731no—
946#388—731no—
947#388—731no—
948#387—731no—
949#387—731no—
950#387—731no—
951#387—731no—
952#387—731no—
953#387—731no—
954#387—731no—
955#387—731no—
956#387—731no—
957#387—731no—
958#387—731no—
959#387C2×D7311yescharacteristic, complemented
960#386—731no—
961#386—731no—
962#386—731no—
963#386—731no—
964#386—731no—
965#386—731no—
966#386—731no—
967#386—731no—
968#386—731no—
969#386—731no—
970#386—731no—
971#386—731no—
972#386—731no—
973#386—731no—
974#386—731no—
975#386—731no—
976#386—731no—
977#386—731no—
978#386C2×D7311yescharacteristic
979#386C2×D7311yescharacteristic
980#385—731no—
981#385—731no—
982#385—731no—
983#385—731no—
984#385—731no—
985#385—731no—
986#385—731no—
987#385—731no—
988#385—731no—
989#385—731no—
990#385—731no—
991#385—731no—
992#385—731no—
993#385—731no—
994#385—731no—
995#385—731no—
996#385—731no—
997#385—731no—
998#385—731no—
999#385—731no—
1000#385—731no—
1001#385C2×D7311yescharacteristic
1002#385C2×D7311yescharacteristic
1003#385C2×D7311yescharacteristic, complemented
1004#381—731no—
1005#381—731no—
1006#381—731no—
1007#381—731no—
1008#380—731no—
1009#380—731no—
1010#380—731no—
1011#380—731no—
1012#380—731no—
1013#380—731no—
1014#379—731no—
1015#379—731no—
1016C4×C22⋊C4—731no—
1017C4×C22⋊C4—731no—
1018C4×C22⋊C4—731no—
1019C4×C22⋊C4—731no—
1020C4×C22⋊C4—731no—
1021C4×C22⋊C4—731no—
1022C25—731no—
1023C22×Q8C22×D7311yescharacteristic
1024C22×D4—731no—
1025C22×D4—731no—
1026C22×D4—731no—
1027C22×D4—731no—
1028C22×D4—731no—
1029C22×D4—731no—
1030C22×D4C22×D7311yescharacteristic
1031C23×C4—2922no—
1032C23×C4—2922no—
1033C23×C4—2922no—
1034C23×C4—2922no—
1035C23×C4—731no—
1036C23×C4—731no—
1037C23×C4—731no—
1038C23×C4—731no—
1039C23×C4—731no—
1040C23×C4—731no—
1041C23×C4—731no—
1042C23×C4—731no—
1043C23×C4—731no—
1044C23×C4—731no—
1045C23×C4—731no—
1046C23×C4—731no—
1047C23×C4—731no—
1048C23×C4—731no—
1049C23×C4—731no—
1050C23×C4—731no—
1051C23×C4—1464no—
1052C23×C4—1464no—
1053C23×C4—1464no—
1054C23×C4—1464no—
1055C23×C4—1464no—
1056C23×C4C22×D7311yescharacteristic
1057C23×C4C22×D7311yescharacteristic
1058C23×C4C22×D7311yescharacteristic
1059C23×C4C22×D7311yescharacteristic
1060#126—1464no—
1061#126—1464no—
1062#125—1464no—
1063#125—1464no—
1064#123—1464no—
1065#123—1464no—
1066#123—1464no—
1067#123—1464no—
1068#123—1464no—
1069#123—1464no—
1070C22⋊Q8—24no—
1071C22⋊Q8—42no—
1072C22⋊Q8—2922no—
1073C22⋊Q8—1464no—
1074C22⋊Q8—1464no—
1075#121—2922no—
1076#121—2922no—
1077#121—1464no—
1078#120—1464no—
1079#120—1464no—
1080C4×D4—42no—
1081C4×D4—2922no—
1082C4×D4—2922no—
1083C4×D4—2922no—
1084C4×D4—1464no—
1085C4×D4—1464no—
1086C2×C4⋊C4—24no—
1087C2×C4⋊C4—731no—
1088C2×C4⋊C4—731no—
1089C2×C4⋊C4—731no—
1090C2×C4⋊C4—731no—
1091C2×C4⋊C4—731no—
1092C2×C4⋊C4—731no—
1093C2×C4⋊C4—731no—
1094C2×C4⋊C4—731no—
1095C2×C4⋊C4—731no—
1096C2×C4⋊C4—731no—
1097C2×C4⋊C4—738no—
1098C2×C4⋊C4—731no—
1099C2×C4⋊C4—731no—
1100C2×C4⋊C4—731no—
1101C2×C4⋊C4—731no—
1102C2×C4⋊C4—731no—
1103C2×C4⋊C4—731no—
1104C2×C4⋊C4—731no—
1105C2×C4⋊C4—731no—
1106C2×C4⋊C4—731no—
1107C2×C4⋊C4—731no—
1108C2×C4⋊C4—731no—
1109C2×C4⋊C4—731no—
1110C2×C4⋊C4—731no—
1111C2×C4⋊C4—731no—
1112C2×C4⋊C4—731no—
1113C2×C4⋊C4—731no—
1114C2×C4⋊C4—731no—
1115C2×C4⋊C4—731no—
1116C2×C4⋊C4—731no—
1117C2×C4⋊C4—731no—
1118C2×C4⋊C4—1464no—
1119C2×C4⋊C4—1464no—
1120C2×C4⋊C4—1464no—
1121C2×C4⋊C4—1464no—
1122C2×C4⋊C4—1464no—
1123C2×C4⋊C4—1464no—
1124C2×C4⋊C4—1464no—
1125C2×C4⋊C4—1464no—
1126C2×C4⋊C4—1464no—
1127C2×C4⋊C4—1464no—
1128C2×C4⋊C4C22×D7311yescharacteristic
1129C2×C4⋊C4C22×D7311yescharacteristic
1130C2×C4⋊C4C22×D7311yescharacteristic
1131C2×C4⋊C4C22×D7311yescharacteristic
1132C2×C4⋊C4C22×D7311yescharacteristic
1133C2×C4⋊C4C22×D7311yescharacteristic
1134C2×C4⋊C4C22×D7311yescharacteristic
1135C2×C4⋊C4C22×D7311yescharacteristic
1136C2×C4⋊C4C22×D7311yescharacteristic
1137C2×C4⋊C4C22×D7311yescharacteristic
1138C2×C4⋊C4C22×D7311yescharacteristic
1139C2×C4⋊C4C22×D7311yescharacteristic
1140C2×C22⋊C4—731no—
1141C2×C22⋊C4—731no—
1142C2×C22⋊C4—731no—
1143C2×C22⋊C4—731no—
1144C2×C22⋊C4—731no—
1145C2×C22⋊C4—731no—
1146C2×C22⋊C4—731no—
1147C2×C22⋊C4—731no—
1148C2×C22⋊C4—731no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—731no—
1156C2×C22⋊C4—731no—
1157C2×C22⋊C4—731no—
1158C2×C22⋊C4—731no—
1159C2×C22⋊C4—731no—
1160C2×C22⋊C4—731no—
1161C2×C22⋊C4—731no—
1162C2×C22⋊C4—731no—
1163C2×C22⋊C4—731no—
1164C2×C22⋊C4—731no—
1165C2×C22⋊C4—731no—
1166C2×C22⋊C4—731no—
1167C2×C22⋊C4—731no—
1168C2×C22⋊C4—731no—
1169C2×C22⋊C4—731no—
1170C2×C22⋊C4C22×D7311yescharacteristic
1171C2×C22⋊C4C22×D7311yescharacteristic
1172C2×C22⋊C4C22×D7311yescharacteristic
1173C2×C22⋊C4C22×D7311yescharacteristic
1174C2×C22⋊C4C22×D7311yescharacteristic
1175C2×C22⋊C4C22×D7311yescharacteristic
1176C2×C22⋊C4C22×D7311yescharacteristic
1177C2×C22⋊C4C22×D7311yescharacteristic
1178C2×C42—731no—
1179C2×C42—731no—
1180C2×C42—731no—
1181C2×C42—731no—
1182C2×C42—731no—
1183C2×C42C22×D7311yescharacteristic
1184#95—731no—
1185#95—731no—
1186#95—731no—
1187#95—731no—
1188#95—731no—
1189#95—731no—
1190#95—731no—
1191#95—731no—
1192#95—731no—
1193#95—731no—
1194#95—731no—
1195#95—731no—
1196#95—731no—
1197#95—731no—
1198#95—731no—
1199#95—731no—
1200#95—731no—
1201#95—731no—
1202#95—731no—
1203#95—731no—
1204#95—731no—
1205#95—731no—
1206#95—731no—
1207#95—731no—
1208#95—731no—
1209#95—731no—
1210#95—731no—
1211#95—731no—
1212#95—731no—
1213#95—731no—
1214#95—731no—
1215#95—731no—
1216#95C22×D7311yescharacteristic
1217#95C22×D7311yescharacteristic
1218#95C22×D7311yescharacteristic
1219#95C22×D7311yescharacteristic
1220#95C22×D7311yescharacteristic
1221#95C22×D7311yescharacteristic
1222#95C22×D7311yescharacteristic
1223#95C22×D7311yescharacteristic
1224C24—731no—
1225C24—731no—
1226C24—734no—
1227C24—731no—
1228C24—1462no—
1229C24—1462no—
1230C24—1462no—
1231C24—1462no—
1232C24—1462no—
1233C24—1462no—
1234C24C23×D7311yescharacteristic
1235C24C23×D7311yescharacteristic
1236C2×Q8—22no—
1237C2×Q8—41no—
1238C2×Q8—41no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—22no—
1242C2×D4—2921no—
1243C2×D4—2921no—
1244C2×D4—1462no—
1245C2×D4—1462no—
1246C2×D4—1462no—
1247C2×D4—1462no—
1248C2×D4—1462no—
1249C2×D4—1462no—
1250C2×D4—1462no—
1251C2×D4—1462no—
1252C2×D4—1462no—
1253C2×D4—1462no—
1254C2×D4—1462no—
1255C2×D4—1462no—
1256C2×D4—1462no—
1257C2×D4—1462no—
1258C2×D4—1462no—
1259C2×D4—1462no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—41no—
1272C22×C4—2921no—
1273C22×C4—2921no—
1274C22×C4—2921no—
1275C22×C4—2921no—
1276C22×C4—2921no—
1277C22×C4—2921no—
1278C22×C4—2921no—
1279C22×C4—2921no—
1280C22×C4—2921no—
1281C22×C4—2921no—
1282C22×C4—2921no—
1283C22×C4—2921no—
1284C22×C4—2921no—
1285C22×C4—2921no—
1286C22×C4—29216no—
1287C22×C4—29216no—
1288C22×C4—2921no—
1289C22×C4—2921no—
1290C22×C4—734no—
1291C22×C4—734no—
1292C22×C4—731no—
1293C22×C4—731no—
1294C22×C4—731no—
1295C22×C4—731no—
1296C22×C4—734no—
1297C22×C4—734no—
1298C22×C4—731no—
1299C22×C4—731no—
1300C22×C4—731no—
1301C22×C4—731no—
1302C22×C4—731no—
1303C22×C4—731no—
1304C22×C4—731no—
1305C22×C4—731no—
1306C22×C4—731no—
1307C22×C4—1462no—
1308C22×C4—1462no—
1309C22×C4—1462no—
1310C22×C4—1462no—
1311C22×C4—1462no—
1312C22×C4—1462no—
1313C22×C4—1462no—
1314C22×C4—1462no—
1315C22×C4—1462no—
1316C22×C4—1462no—
1317C22×C4—1462no—
1318C22×C4—1462no—
1319C22×C4—1462no—
1320C22×C4—1462no—
1321C22×C4—1462no—
1322C22×C4—1462no—
1323C22×C4—1462no—
1324C22×C4—14632no—
1325C22×C4—1462no—
1326C22×C4—1462no—
1327C22×C4—1462no—
1328C22×C4—1462no—
1329C22×C4—1462no—
1330C22×C4—1462no—
1331C22×C4—1462no—
1332C22×C4—1462no—
1333C22×C4—1462no—
1334C22×C4—1462no—
1335C22×C4—1462no—
1336C22×C4C23×D7311yescharacteristic
1337C22×C4C23×D7311yescharacteristic
1338C22×C4C23×D7311yescharacteristic
1339C22×C4C23×D7311yescharacteristic
1340C22×C4C23×D7311yescharacteristic
1341C22×C4C23×D7311yescharacteristic
1342C22×C4C23×D7311yescharacteristic
1343C22×C4C23×D7311yescharacteristic
1344C22×C4C23×D7311yescharacteristic
1345C22×C4C23×D7311yescharacteristic
1346C22×C4C23×D7311yescharacteristic
1347C22×C4C23×D7311yescharacteristic
1348C22×C4C23×D7311yescharacteristic
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—41no—
1356C4⋊C4—41no—
1357C4⋊C4—41no—
1358C4⋊C4—41no—
1359C4⋊C4—41no—
1360C4⋊C4—2921no—
1361C4⋊C4—2921no—
1362C4⋊C4—2921no—
1363C4⋊C4—2921no—
1364C4⋊C4—2921no—
1365C4⋊C4—2921no—
1366C4⋊C4—2921no—
1367C4⋊C4—734no—
1368C4⋊C4—734no—
1369C4⋊C4—734no—
1370C4⋊C4—1462no—
1371C4⋊C4—1462no—
1372C4⋊C4—1462no—
1373C4⋊C4—1462no—
1374C4⋊C4—1462no—
1375C4⋊C4—1462no—
1376C4⋊C4—1462no—
1377C4⋊C4—1462no—
1378C4⋊C4—1462no—
1379C4⋊C4—1462no—
1380C4⋊C4—1462no—
1381C4⋊C4—1462no—
1382C4⋊C4—1462no—
1383C4⋊C4—1462no—
1384C4⋊C4—1462no—
1385C4⋊C4—1462no—
1386C4⋊C4—1462no—
1387C4⋊C4—1462no—
1388C4⋊C4—1462no—
1389C4⋊C4—1462no—
1390C4⋊C4D4×D7314yes—
1391C22⋊C4—22no—
1392C22⋊C4—22no—
1393C22⋊C4—22no—
1394C22⋊C4—22no—
1395C22⋊C4—22no—
1396C22⋊C4—22no—
1397C22⋊C4—41no—
1398C22⋊C4—41no—
1399C22⋊C4—2921no—
1400C22⋊C4—2921no—
1401C22⋊C4—2921no—
1402C22⋊C4—2921no—
1403C22⋊C4—2921no—
1404C22⋊C4—2921no—
1405C22⋊C4—1462no—
1406C22⋊C4—1462no—
1407C22⋊C4—1462no—
1408C22⋊C4—1462no—
1409C22⋊C4—1462no—
1410C22⋊C4—1462no—
1411C22⋊C4—1462no—
1412C22⋊C4—1462no—
1413C22⋊C4—1462no—
1414C22⋊C4—1462no—
1415C22⋊C4—1462no—
1416C22⋊C4—1462no—
1417C22⋊C4—1462no—
1418C22⋊C4—1462no—
1419C22⋊C4—1462no—
1420C22⋊C4—1462no—
1421C22⋊C4—1462no—
1422C22⋊C4—1462no—
1423C22⋊C4—1462no—
1424C22⋊C4—1462no—
1425C22⋊C4—1462no—
1426C22⋊C4—1462no—
1427C22⋊C4—1462no—
1428C22⋊C4—1462no—
1429C42—41no—
1430C42—2921no—
1431C42—2921no—
1432C42—2921no—
1433C42—1462no—
1434C42—1462no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—732no—
1447C23—732no—
1448C23—732no—
1449C23—732no—
1450C23—732no—
1451C23—732no—
1452C23—1468no—
1453C23—1468no—
1454C23—1468no—
1455C23—1468no—
1456C23—1468no—
1457C23—1468no—
1458C23—1461no—
1459C23—1461no—
1460C23—1461no—
1461C23—1461no—
1462C23—1461no—
1463C23—1461no—
1464C23—1461no—
1465C23—1461no—
1466C23—1461no—
1467C23—1461no—
1468C23—1461no—
1469C23—1461no—
1470C23—1461no—
1471C23—1461no—
1472C23—1461no—
1473C23—1468no—
1474C23#41×D7312yes—
1475C23#1455663612yes—
1476C23#1455663912yes—
1477C23C24×D7311yescharacteristic
1478Q8—82no—
1479D4—44no—
1480D4—2924no—
1481D4—2924no—
1482D4—2924no—
1483D4—2924no—
1484D4—2924no—
1485D4—5842no—
1486C2×C4—28no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—44no—
1523C2×C4—44no—
1524C2×C4—82no—
1525C2×C4—2924no—
1526C2×C4—2924no—
1527C2×C4—2924no—
1528C2×C4—2924no—
1529C2×C4—2924no—
1530C2×C4—2924no—
1531C2×C4—2924no—
1532C2×C4—2924no—
1533C2×C4—2924no—
1534C2×C4—2924no—
1535C2×C4—5842no—
1536C2×C4—732no—
1537C2×C4—732no—
1538C2×C4—732no—
1539C2×C4—732no—
1540C2×C4—1468no—
1541C2×C4—1468no—
1542C2×C4—1468no—
1543C2×C4—1468no—
1544C2×C4—1461no—
1545C2×C4—1461no—
1546C2×C4—1461no—
1547C2×C4—1461no—
1548C2×C4—1461no—
1549C2×C4—1461no—
1550C2×C4—1461no—
1551C2×C4—1461no—
1552C2×C4—1461no—
1553C2×C4—1461no—
1554C2×C4—1461no—
1555C2×C4—1461no—
1556C2×C4—1461no—
1557C2×C4—1461no—
1558C2×C4—1461no—
1559C2×C4—1461no—
1560C2×C4—1461no—
1561C2×C4—1461no—
1562C2×C4—1461no—
1563C2×C4—1461no—
1564C2×C4—1461no—
1565C2×C4—1461no—
1566C2×C4—1461no—
1567C2×C4—1461no—
1568C2×C4—1461no—
1569C2×C4—1461no—
1570C2×C4—1461no—
1571C2×C4—1468no—
1572C2×C4—1461no—
1573C2×C4—1461no—
1574C2×C4—1461no—
1575C2×C4—1461no—
1576C2×C4—1461no—
1577C2×C4—1461no—
1578C2×C4—1461no—
1579C2×C4—1461no—
1580C2×C4C2×D4×D7312yes—
1581C2×C4C2×D4×D7312yes—
1582C2×C4C2×D4×D7312yes—
1583C2×C4#41×D7312yes—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—2921no—
1598C22—2921no—
1599C22—2921no—
1600C22—2921no—
1601C22—2921no—
1602C22—2921no—
1603C22—2921no—
1604C22—734no—
1605C22—734no—
1606C22—14632no—
1607C22—1462no—
1608C22—1462no—
1609C22—1462no—
1610C22—1462no—
1611C22—1462no—
1612C22—1462no—
1613C22—1462no—
1614C22—1462no—
1615C22—1462no—
1616C22—1462no—
1617C22—1462no—
1618C22—1462no—
1619C22#1798918314yescomplemented
1620C22C22×D4×D7311yescharacteristic
1621C22C2×#41×D7311yescharacteristic
1622C22C2×#41×D7311yescharacteristic
1623C22H(5,𝔽2)×D7311yescharacteristic
1624C22C2×#1455663611yescharacteristic
1625C222−1+4×D7311yescharacteristic
1626C22C2×#1455663911yescharacteristic
1627C4—22no—
1628C4—22no—
1629C4—22no—
1630C4—22no—
1631C4—41no—
1632C4—41no—
1633C4—41no—
1634C4—41no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—2921no—
1641C4—2921no—
1642C4—2921no—
1643C4—2921no—
1644C4—2921no—
1645C4—2921no—
1646C4—2921no—
1647C4—2921no—
1648C4—2921no—
1649C4—1462no—
1650C4—1462no—
1651C4—1462no—
1652C4—1462no—
1653C2—24no—
1654C2—81no—
1655C2—5841no—
1656C2—1464no—
1657C2—1464no—
1658C2#525×D7311yescharacteristic
1659C2#539×D7311yescharacteristic
1660C2C2×#1798918311yescharacteristic
1661C2#2262355911yescharacteristic
1662C2#2262358111yescharacteristic
1663C2#2262363311yescharacteristic
1664C2#2262363911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2449C2
prime radical#22618212C2
hypercenter#2449D73
hypocenterC73#34989
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2449

Complements

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

NH ≅ G/Ntype
1. C2×#17989183C2semidirect
2. C22×C4⋊C4×D73C2semidirect
3. #22618226C2semidirect
4. #22618222C2semidirect
5. #22618215C2semidirect
7. #22615743C2semidirect
8. #22615716C2semidirect
9. #22615712C2semidirect
10. #22615678C2semidirect
11. #22614197C2semidirect
12. #22614193C2semidirect
13. #22614190C2semidirect
14. #22614186C2semidirect
15. #22614078C2semidirect
16. #22614074C2semidirect
17. #22614069C2semidirect
18. #22614065C2semidirect
19. #22613737C2semidirect
20. #22613736C2semidirect
21. #22613733C2semidirect
22. #22613672C2semidirect
23. #22613669C2semidirect
24. #22613665C2semidirect
25. #22613660C2semidirect
26. #22612598C2semidirect
27. #22612595C2semidirect
28. #22612530C2semidirect
29. #22612432C2semidirect
30. C4×#14556559C2semidirect
31. C73×#2449C2semidirect
36. C2×#14556586C22semidirect
37. C2×#14556584C22semidirect
38. C2×#14556581C22semidirect
39. C2×#14556581C22semidirect
42. C2×#14556574C22semidirect
45. C2×#14556573C22semidirect
48. C2×#14556567C22semidirect
71. #17988528C22semidirect
72. #17988528C22semidirect
73. #17988527C22semidirect
74. #17988527C22semidirect
75. #17988526C22semidirect
76. #17988525C22semidirect
77. #17988523C22semidirect
78. #17988522C22semidirect
79. #17988522C22semidirect
80. #17988521C22semidirect
81. #17988521C22semidirect
82. #17988521C22semidirect
83. #17988520C22semidirect
84. #17988520C22semidirect
85. #17988520C22semidirect
86. #17988518C22semidirect
87. #17988518C22semidirect
88. #17988517C22semidirect
89. #17988515C22semidirect
90. #17988515C22semidirect
91. #17988514C22semidirect
92. #17988513C22semidirect
93. #17988510C22semidirect
94. #17988509C22semidirect
95. #17988509C22semidirect
96. #17988506C22semidirect
97. #17988503C22semidirect
98. #17988502C22semidirect
99. #17988484C22semidirect
100. #17988483C22semidirect
101. #17988482C22semidirect
102. #17988480C22semidirect
103. #17988478C22semidirect
104. #17988477C22semidirect
105. #17988475C22semidirect
106. #17988474C22semidirect
107. #17988473C22semidirect
108. #17988473C22semidirect
109. #17988472C22semidirect
110. #17988472C22semidirect
111. #17988471C22semidirect
112. #17988470C22semidirect
113. #17988469C22semidirect
114. #17988469C22semidirect
115. #17988468C22semidirect
116. #17988468C22semidirect
138. #17988461C22semidirect
140. #17988460C22semidirect
155. #17988458C22semidirect
175. C2×C22⋊Q8×C73C22semidirect
178. #399×C73C22semidirect
179. #398×C73C22semidirect
180. #396×C73C22semidirect
181. #395×C73C22semidirect
182. #389×C73C22semidirect
183. #387×C73C22semidirect
188. #385×C73C22semidirect
284. C4⋊C4×D73D4semidirect
764. C22×C73#539semidirect
793. C2×D73#539semidirect
854. #2449D73semidirect
864. C73#34989semidirect
883. C2×C22⋊Q8C2×D73semidirect
917. #399C2×D73semidirect
927. #398C2×D73semidirect
935. #396C2×D73semidirect
937. #395C2×D73semidirect
943. #389C2×D73semidirect
959. #387C2×D73semidirect
1003. #385C2×D73semidirect
1619. C22#17989183semidirect

Maximal subgroups

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

subgroupindex
C2×#179891832
C22×C4⋊C4×D732
#226182262
#226182222
#226182152
#226182122
#226157432
#226157162
#226157122
#226156782
#226141972
#226141932
#226141902
#226141862
#226140782
#226140742
#226140692
#226140652
#226137372
#226137362
#226137332
#226136722
#226136692
#226136652
#226136602
#226125982
#226125952
#226125302
#226124322
C4×#145565592
C73×#24492
#3498973