Finite Group Databasebeta

← #33102146

Subgroups — #33102146

Order 18688.

1068 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989277C211yesmaximal, characteristic
2D4×#11924012C211yesmaximal, characteristic
3#22610924C211yesmaximal, characteristic, complemented
4#22610923C211yesmaximal, characteristic, complemented
5#22610399C211yesmaximal, characteristic, complemented
6#22610399C211yesmaximal, characteristic, complemented
7#22610397C211yesmaximal, characteristic, complemented
8#22610397C211yesmaximal, characteristic, complemented
9#22610012C211yesmaximal, characteristic, complemented
10#22610009C211yesmaximal, characteristic, complemented
11#22609924C211yesmaximal, characteristic, complemented
12C4×#14556509C211yesmaximal, characteristic, complemented
13#22609669C211yesmaximal, characteristic, complemented
14C2×#17988355C211yesmaximal, characteristic, complemented
15D4×M16×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C22×#11924012C2211yescharacteristic
18#17989277—21no—
19#17989277—21no—
20#17989277—21no—
21#17989277—21no—
22#17989277—21no—
23#17989277—21no—
24#17989277—21no—
25#17989277—21no—
26C2×#14556584C412yes—
27C2×#14556583C2211yescharacteristic
28C2×#14556581C412yes—
29C2×#14556572C412yes—
30C2×#14556570C2211yescharacteristic
31C2×#14556570C2211yescharacteristic
32C2×C4×Dic146C2211yescharacteristic
33C2×#14556550C2211yescharacteristic
34C2×#14556547C412yes—
35C22×C4⋊Dic73C2211yescharacteristic
36#17988665—21no—
37#17988659—21no—
38#17988659—21no—
39D4×#10596831—21no—
40#17988611C2211yescharacteristic
41C2×#14556509C2211yescharacteristic
42C2×#14556509C2211yescharacteristic
43C2×#14556509C2211yescharacteristic
44C2×#14556509C2211yescharacteristic
45#17988551C2211yescharacteristic
46#17988551C2211yescharacteristic
47C4×#11924012C2211yescharacteristic
48#17988355C2211yescharacteristic
49#17988355C2211yescharacteristic
50#17988355C2211yescharacteristic
51#17988355C2211yescharacteristic
52#17988355C2211yescharacteristic
53#17988355C2211yescharacteristic
54#17988355C2211yescharacteristic
55#17988355C2211yescharacteristic
56#17988355C2211yescharacteristic
57#17988355C2211yescharacteristic
58#17988355C2211yescharacteristic
59#17988355C2211yescharacteristic
60C22×M16×C73C2211yescharacteristic
61C22×M16×C73C2211yescharacteristic
62C2×C4×D4×C73C2211yescharacteristic
63#436×C73—21no—
64#435×C73—21no—
65#435×C73—21no—
66C8×D4×C73—21no—
67#423×C73C2211yescharacteristic
68#407×C73C2211yescharacteristic
69#407×C73C2211yescharacteristic
70C4×M16×C73C2211yescharacteristic
71C22×Dic146C2311yescharacteristic
72C23×Dic73C2×C412yes—
73C2×#11924012—22no—
74C2×#11924012—22no—
75C2×#11924012—21no—
76C2×#11924012—21no—
77C2×#11924012—41no—
78C2×#11924012—41no—
79C2×#11924012C2311yescharacteristic
80C2×#11924012C2311yescharacteristic
81C2×#11924012C2311yescharacteristic
82C2×#11924012C2311yescharacteristic
83C22×#10596831—21no—
84C22×#10596831—21no—
85#14556584—22no—
86#14556584—22no—
87#14556584—22no—
88#14556584—22no—
89#14556583—21no—
90#14556583—21no—
91#14556583—21no—
92#14556583—21no—
93#14556581—22no—
94#14556581—22no—
95#14556581—22no—
96#14556581—22no—
97#14556572—22no—
98#14556572—22no—
99#14556572—22no—
100#14556572—22no—
101#14556570—21no—
102#14556570—21no—
103#14556570—21no—
104#14556570—21no—
105#14556570—21no—
106#14556570—21no—
107#14556570—21no—
108#14556570—21no—
109C4×Dic146—21no—
110C4×Dic146—21no—
111C4×Dic146—21no—
112C4×Dic146—21no—
113#14556550—21no—
114#14556550—21no—
115#14556550—21no—
116#14556550—21no—
117#14556547—22no—
118#14556547—22no—
119#14556547—22no—
120#14556547—22no—
121C2×C4⋊Dic73—21no—
122C2×C4⋊Dic73—21no—
123C2×C4⋊Dic73—21no—
124C2×C4⋊Dic73—21no—
125C2×C4⋊Dic73C2×C412yes—
126C2×C4⋊Dic73C2311yescharacteristic
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007C2×C412yes—
130C2×#11924007C2×C412yes—
131C2×#11924007C2×C412yes—
132C2×#11924007C2×C412yes—
133C2×#11924007C2×C412yes—
134C2×C22⋊Dic73C2×C412yes—
135C2×C22⋊Dic73C2×C412yes—
136C2×C22⋊Dic73C2×C412yes—
137C2×C4×Dic73C2×C412yes—
138C2×C4×Dic73C2×C412yes—
139C4⋊#10596831—21no—
140C4⋊#10596831—21no—
141#14556509—22no—
142#14556509—22no—
143#14556509—41no—
144#14556509—41no—
145C22⋊#10596831—21no—
146C22⋊#10596831—21no—
147C22⋊#10596831—21no—
148C22⋊#10596831—21no—
149#14556502—21no—
150C4×#10596831—21no—
151C22×D4×C73C2×C411yescharacteristic
152C23×C4×C73C2311yescharacteristic
153C23×C4×C73C2311yescharacteristic
154C2×M16×C73—21no—
155C2×M16×C73—21no—
156C2×M16×C73—22no—
157C2×M16×C73—22no—
158C2×M16×C73—41no—
159C2×M16×C73—41no—
160C2×M16×C73C2311yescharacteristic
161C2×M16×C73C2311yescharacteristic
162C2×M16×C73C2311yescharacteristic
163C2×M16×C73C2311yescharacteristic
164C22×C8×C73—21no—
165C22×C8×C73—21no—
166C4×D4×C73D411yescharacteristic
167C4×D4×C73D411yescharacteristic
168C4×D4×C73D411yescharacteristic
169C4×D4×C73D411yescharacteristic
170C4×D4×C73D411yescharacteristic
171C4×D4×C73D411yescharacteristic
172C4×D4×C73D411yescharacteristic
173C4×D4×C73D411yescharacteristic
174C2×C4⋊C4×C73C2×C411yescharacteristic
175C2×C22⋊C4×C73C2×C411yescharacteristic
176C2×C22⋊C4×C73C2×C411yescharacteristic
177C2×C42×C73C2311yescharacteristic
178C4⋊C8×C73—21no—
179C4⋊C8×C73—21no—
180C22⋊C8×C73—21no—
181C22⋊C8×C73—21no—
182C22⋊C8×C73—21no—
183C22⋊C8×C73—21no—
184#97×C73—21no—
185C4×C8×C73—21no—
186C2×Dic146—21no—
187C2×Dic146—21no—
188C2×Dic146—21no—
189C2×Dic146—21no—
190C2×Dic146—21no—
191C2×Dic146—21no—
192C22×Dic73—22no—
193C22×Dic73—22no—
194C22×Dic73—44no—
195C22×Dic73C22×C412yes—
196C22×Dic73C22×C412yes—
197C22×Dic73C22×C412yes—
198C22×Dic73C22×C412yes—
199#11924012—21no—
200#11924012—21no—
201#11924012—21no—
202#11924012—21no—
203#11924012—21no—
204#11924012—21no—
205#11924012—21no—
206#11924012—42no—
207#11924012—42no—
208#11924012#4112yes—
209C2×#10596831—21no—
210C2×#10596831—21no—
211C2×#10596831—21no—
212C2×#10596831—21no—
213C2×#10596831—42no—
214C2×#10596831—42no—
215C4⋊Dic73—22no—
216C4⋊Dic73—22no—
217C4⋊Dic73—21no—
218C4⋊Dic73—21no—
219C4⋊Dic73—21no—
220C4⋊Dic73—21no—
221C4⋊Dic73—21no—
222C4⋊Dic73—21no—
223#11924007—22no—
224#11924007—22no—
225#11924007—22no—
226#11924007—22no—
227#11924007—22no—
228#11924007—22no—
229#11924007—22no—
230#11924007—22no—
231#11924007—22no—
232#11924007—22no—
233C22⋊Dic73—22no—
234C22⋊Dic73—22no—
235C22⋊Dic73—22no—
236C22⋊Dic73—22no—
237C22⋊Dic73—22no—
238C22⋊Dic73—22no—
239C4×Dic73—22no—
240C4×Dic73—22no—
241C4×Dic73—22no—
242C4×Dic73—22no—
243C24×C73C22×C411yescharacteristic
244C24×C73C22×C411yescharacteristic
245C2×D4×C73—42no—
246C2×D4×C73C22⋊C411yescharacteristic
247C2×D4×C73C22⋊C411yescharacteristic
248C2×D4×C73C22⋊C411yescharacteristic
249C2×D4×C73C22⋊C411yescharacteristic
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73C22×C411yescharacteristic
259C22×C4×C73C22×C411yescharacteristic
260C22×C4×C73C22×C411yescharacteristic
261C22×C4×C73C22×C411yescharacteristic
262C22×C4×C73C2×D411yescharacteristic
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2×D411yescharacteristic
266C22×C4×C73C2×D411yescharacteristic
267C22×C4×C73C2×D411yescharacteristic
268C22×C4×C73C2×D411yescharacteristic
269C22×C4×C73C2×D411yescharacteristic
270C22×C4×C73C2411yescharacteristic
271M16×C73—21no—
272M16×C73—21no—
273M16×C73—21no—
274M16×C73—21no—
275M16×C73—21no—
276M16×C73—21no—
277M16×C73—21no—
278M16×C73—42no—
279M16×C73—42no—
280M16×C73#4112yes—
281C2×C8×C73—21no—
282C2×C8×C73—21no—
283C2×C8×C73—21no—
284C2×C8×C73—21no—
285C2×C8×C73—42no—
286C2×C8×C73—42no—
287C4⋊C4×C73C22⋊C411yescharacteristic
288C4⋊C4×C73C22⋊C411yescharacteristic
289C4⋊C4×C73C22⋊C411yescharacteristic
290C4⋊C4×C73C22⋊C411yescharacteristic
291C22⋊C4×C73C22⋊C411yescharacteristic
292C22⋊C4×C73C22⋊C411yescharacteristic
293C22⋊C4×C73C22⋊C411yescharacteristic
294C22⋊C4×C73C22⋊C411yescharacteristic
295C22⋊C4×C73C22⋊C411yescharacteristic
296C22⋊C4×C73C22⋊C411yescharacteristic
297C22⋊C4×C73C22⋊C411yescharacteristic
298C22⋊C4×C73C22⋊C411yescharacteristic
299C42×C73C2×D411yescharacteristic
300C42×C73C2×D411yescharacteristic
301C42×C73C2×D411yescharacteristic
302C42×C73C2×D411yescharacteristic
303C23×C73—21no—
304C23×C73—21no—
305C23×C73—22no—
306C23×C73—21no—
307C23×C73—21no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73C2×C22⋊C411yescharacteristic
312C23×C73C2×C22⋊C411yescharacteristic
313C23×C73C2×C22⋊C411yescharacteristic
314C23×C73C2×C22⋊C411yescharacteristic
315C23×C73C23×C411yescharacteristic
316D4×C73—22no—
317D4×C73—22no—
318D4×C73—41no—
319D4×C73—41no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73C2×C22⋊C411yescharacteristic
343C2×C4×C73C2×C22⋊C411yescharacteristic
344C2×C4×C73C2×C22⋊C411yescharacteristic
345C2×C4×C73C2×C22⋊C411yescharacteristic
346C2×C4×C73C2×C22⋊C411yescharacteristic
347C2×C4×C73C2×C22⋊C411yescharacteristic
348C2×C4×C73C2×C22⋊C411yescharacteristic
349C2×C4×C73C2×C22⋊C411yescharacteristic
350C2×C4×C73C22×D411yescharacteristic
351C2×C4×C73C22×D411yescharacteristic
352C2×C4×C73C2×#4111yescharacteristic
353C2×C4×C73C2×#4111yescharacteristic
354C2×C4×C73H(5,𝔽2)11yescharacteristic
355C2×C4×C732−1+411yescharacteristic
356C2×Dic73—22no—
357C2×Dic73—22no—
358C2×Dic73—22no—
359C2×Dic73—22no—
360C2×Dic73—22no—
361C2×Dic73—22no—
362C2×Dic73—44no—
363C2×Dic73—44no—
364C2×Dic73—42no—
365C2×Dic73—42no—
366C2×Dic73—42no—
367Dic146—41no—
368Dic146—41no—
369Dic146—41no—
370Dic146—41no—
371C8×C73—22no—
372C8×C73—41no—
373C8×C73—41no—
374C8×C73—41no—
375#10596831—22no—
376#10596831—41no—
377#10596831—41no—
378#10596831—41no—
379C22×C73—21no—
380C22×C73—21no—
381C22×C73—21no—
382C22×C73—21no—
383C22×C73—21no—
384C22×C73—21no—
385C22×C73—21no—
386C22×C73—21no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—42no—
393C22×C73—42no—
394C22×C73—81no—
395C22×C73—81no—
396C22×C73#41312yes—
397C22×C73C22×C22⋊C411yescharacteristic
398C22×C73C4×#4111yescharacteristic
399C22×C73#52011yescharacteristic
400C4×C73—21no—
401C4×C73—21no—
402C4×C73—21no—
403C4×C73—21no—
404C4×C73—21no—
405C4×C73—21no—
406C4×C73—21no—
407C4×C73—21no—
408C4×C73#54611yescharacteristic
409C4×C73#54611yescharacteristic
410C4×C73#54711yescharacteristic
411C4×C73#54711yescharacteristic
412Dic73—42no—
413Dic73—42no—
414Dic73—42no—
415Dic73—42no—
416#22480—731nomaximal, Sylow
417C2×C73—21no—
418C2×C73—21no—
419C2×C73—22no—
420C2×C73—41no—
421C2×C73—41no—
422C2×C73—41no—
423C2×C73#233911yescharacteristic
424C2×C73C2×#41311yescharacteristic
425C2×C73#288911yescharacteristic
426C2×#552—731no—
427D4×M16—731no—
428D4×M16D7311yescharacteristic
429#1998—731no—
430#1998—731no—
431#1901—731no—
432#1901—731no—
433#1901—731no—
434#1901—731no—
435#1822—731no—
436#1821—731no—
437#1801—731no—
438C4×#101—731no—
439#1742—731no—
440C2×#343—731no—
441C73#2248011yescharacteristic, complemented, Sylow
442C22×M16—731no—
443C22×M16—731no—
444C22×M16C2×D7311yescharacteristic
445C22×M16C2×D7311yescharacteristic
446#552—1461no—
447#552—1461no—
448#552—1461no—
449#552—1461no—
450#552—1461no—
451#552—1461no—
452#552—1461no—
453#552—1461no—
454C2×#126—732no—
455C2×#125—732no—
456C2×#125—731no—
457C2×#123—732no—
458C2×C22⋊Q8—731no—
459C2×C22⋊Q8—731no—
460C2×C4×Q8—731no—
461C2×C4×D4C2×D7311yescharacteristic
462C2×#117—731no—
463C2×#117—732no—
464C22×C4⋊C4—731no—
465#436—21no—
466#436—1461no—
467#435—21no—
468#435—21no—
469#435—1461no—
470#435—1461no—
471C8×D4—21no—
472C8×D4—1461no—
473#423—731no—
474#423C2×D7311yescharacteristic
475C2×#101—731no—
476C2×#101—731no—
477C2×#101—731no—
478C2×#101—731no—
479#407—731no—
480#407—731no—
481#407C2×D7311yescharacteristic
482#407C2×D7311yescharacteristic
483C4×M16—731no—
484C4×M16C2×D7311yescharacteristic
485#343—731no—
486#343—731no—
487#343—731no—
488#343—731no—
489#343—731no—
490#343—731no—
491#343—731no—
492#343—731no—
493#343—731no—
494#343—731no—
495#343—731no—
496#343—731no—
497C22×Q8—731no—
498C22×D4C4×D7311yescharacteristic
499C23×C4—732no—
500C23×C4C22×D7311yescharacteristic
501C23×C4C22×D7311yescharacteristic
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—2921no—
509C2×M16—2921no—
510C2×M16—731no—
511C2×M16—731no—
512C2×M16—731no—
513C2×M16—731no—
514C2×M16—1462no—
515C2×M16—1462no—
516C2×M16—1461no—
517C2×M16—1461no—
518C2×M16C22×D7311yescharacteristic
519C2×M16C22×D7311yescharacteristic
520C2×M16C22×D7311yescharacteristic
521C2×M16C22×D7311yescharacteristic
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—1461no—
525C22×C8—1461no—
526#126—1462no—
527#126—1462no—
528#126—1462no—
529#126—1462no—
530#125—1462no—
531#125—1462no—
532#125—1462no—
533#125—1462no—
534#125—1461no—
535#125—1461no—
536#125—1461no—
537#125—1461no—
538#123—1462no—
539#123—1462no—
540#123—1462no—
541#123—1462no—
542C22⋊Q8—1461no—
543C22⋊Q8—1461no—
544C22⋊Q8—1461no—
545C22⋊Q8—1461no—
546C22⋊Q8—1461no—
547C22⋊Q8—1461no—
548C22⋊Q8—1461no—
549C22⋊Q8—1461no—
550C4×Q8—1461no—
551C4×Q8—1461no—
552C4×Q8—1461no—
553C4×Q8—1461no—
554C4×D4D29211yescharacteristic
555C4×D4D29211yescharacteristic
556C4×D4D29211yescharacteristic
557C4×D4D29211yescharacteristic
558C4×D4C22⋊D7311yescharacteristic
559C4×D4C22⋊D7311yescharacteristic
560C4×D4C22⋊D7311yescharacteristic
561C4×D4C22⋊D7311yescharacteristic
562#117—1461no—
563#117—1461no—
564#117—1461no—
565#117—1461no—
566#117—1462no—
567#117—1462no—
568#117—1462no—
569#117—1462no—
570C2×C4⋊C4—732no—
571C2×C4⋊C4—732no—
572C2×C4⋊C4—732no—
573C2×C4⋊C4—732no—
574C2×C4⋊C4—732no—
575C2×C4⋊C4—732no—
576C2×C4⋊C4—731no—
577C2×C4⋊C4—731no—
578C2×C4⋊C4—731no—
579C2×C4⋊C4—1461no—
580C2×C4⋊C4—1461no—
581C2×C4⋊C4—1461no—
582C2×C4⋊C4—1461no—
583C2×C4⋊C4C4×D7311yescharacteristic
584C2×C22⋊C4—732no—
585C2×C22⋊C4—732no—
586C2×C22⋊C4—732no—
587C2×C22⋊C4C4×D7311yescharacteristic
588C2×C22⋊C4C4×D7311yescharacteristic
589C2×C42—732no—
590C2×C42—732no—
591C2×C42C22×D7311yescharacteristic
592C4⋊C8—21no—
593C4⋊C8—21no—
594C4⋊C8—1461no—
595C4⋊C8—1461no—
596#101—2921no—
597#101—2921no—
598#101—1462no—
599#101—1462no—
600C22⋊C8—21no—
601C22⋊C8—21no—
602C22⋊C8—21no—
603C22⋊C8—21no—
604C22⋊C8—1461no—
605C22⋊C8—1461no—
606C22⋊C8—1461no—
607C22⋊C8—1461no—
608#97—21no—
609#97—1461no—
610C4×C8—21no—
611C4×C8—1461no—
612C24C2×C4×D7311yescharacteristic
613C24C2×C4×D7311yescharacteristic
614C2×Q8—1461no—
615C2×Q8—1461no—
616C2×Q8—1461no—
617C2×Q8—1461no—
618C2×Q8—1461no—
619C2×Q8—1461no—
620C2×D4—42no—
621C2×D4#1192400511yescharacteristic
622C2×D4#1192400511yescharacteristic
623C2×D4#1192400511yescharacteristic
624C2×D4#1192400511yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—2924no—
634C22×C4—732no—
635C22×C4—732no—
636C22×C4—732no—
637C22×C4—732no—
638C22×C4—1462no—
639C22×C4—1462no—
640C22×C4C2×C4×D7311yescharacteristic
641C22×C4C2×C4×D7311yescharacteristic
642C22×C4C2×C4×D7311yescharacteristic
643C22×C4C2×C4×D7311yescharacteristic
644C22×C4C2×C22⋊D7311yescharacteristic
645C22×C4C2×C22⋊D7311yescharacteristic
646C22×C4C2×C22⋊D7311yescharacteristic
647C22×C4C2×C22⋊D7311yescharacteristic
648C22×C4C2×D29211yescharacteristic
649C22×C4C2×D29211yescharacteristic
650C22×C4C2×D29211yescharacteristic
651C22×C4C2×D29211yescharacteristic
652C22×C4C23×D7311yescharacteristic
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—42no—
661M16—42no—
662M16—2922no—
663M16—2922no—
664M16—732no—
665M16—1461no—
666M16—1461no—
667M16—1461no—
668M16—1461no—
669M16—1461no—
670M16—1461no—
671M16—1461no—
672M16#1192402712yes—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—2922no—
680C2×C8—2922no—
681C2×C8—1461no—
682C2×C8—1461no—
683C2×C8—1461no—
684C2×C8—1461no—
685C4⋊C4—1462no—
686C4⋊C4—1462no—
687C4⋊C4—1462no—
688C4⋊C4—1462no—
689C4⋊C4—1462no—
690C4⋊C4—1462no—
691C4⋊C4—1462no—
692C4⋊C4—1462no—
693C4⋊C4—1462no—
694C4⋊C4—1462no—
695C4⋊C4—1462no—
696C4⋊C4—1462no—
697C4⋊C4—1461no—
698C4⋊C4—1461no—
699C4⋊C4—1461no—
700C4⋊C4—1461no—
701C4⋊C4—1461no—
702C4⋊C4—1461no—
703C4⋊C4#1192400511yescharacteristic
704C4⋊C4#1192400511yescharacteristic
705C4⋊C4#1192400511yescharacteristic
706C4⋊C4#1192400511yescharacteristic
707C22⋊C4—1462no—
708C22⋊C4—1462no—
709C22⋊C4—1462no—
710C22⋊C4—1462no—
711C22⋊C4—1462no—
712C22⋊C4—1462no—
713C22⋊C4#1192400511yescharacteristic
714C22⋊C4#1192400511yescharacteristic
715C22⋊C4#1192400511yescharacteristic
716C22⋊C4#1192400511yescharacteristic
717C22⋊C4#1192400511yescharacteristic
718C22⋊C4#1192400511yescharacteristic
719C22⋊C4#1192400511yescharacteristic
720C22⋊C4#1192400511yescharacteristic
721C42—1462no—
722C42—1462no—
723C42—1462no—
724C42—1462no—
725C42C2×C22⋊D7311yescharacteristic
726C42C2×C22⋊D7311yescharacteristic
727C42C2×D29211yescharacteristic
728C42C2×D29211yescharacteristic
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×#1192400511yescharacteristic
738C23C2×#1192400511yescharacteristic
739C23C2×#1192400511yescharacteristic
740C23C2×#1192400511yescharacteristic
741C23C22×C4×D7311yescharacteristic
742Q8—2921no—
743Q8—2921no—
744Q8—2921no—
745Q8—2921no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—2924no—
773C2×C4—2924no—
774C2×C4—2922no—
775C2×C4—2922no—
776C2×C4—2922no—
777C2×C4—1462no—
778C2×C4—1462no—
779C2×C4—1462no—
780C2×C4—1462no—
781C2×C4—1462no—
782C2×C4—1462no—
783C2×C4C2×#1192400511yescharacteristic
784C2×C4C2×#1192400511yescharacteristic
785C2×C4C2×#1192400511yescharacteristic
786C2×C4C2×#1192400511yescharacteristic
787C2×C4C2×#1192400511yescharacteristic
788C2×C4C2×#1192400511yescharacteristic
789C2×C4C2×#1192400511yescharacteristic
790C2×C4C2×#1192400511yescharacteristic
791C2×C4C22×C22⋊D7311yescharacteristic
792C2×C4C22×D29211yescharacteristic
793C2×C4#41×D7311yescharacteristic
794C2×C4C2×#1192402711yescharacteristic
795C2×C4#1455663611yescharacteristic
796C2×C4#1455663811yescharacteristic
797C8—22no—
798C8—41no—
799C8—41no—
800C8—41no—
801C8—2921no—
802C8—2921no—
803C8—2921no—
804C8—1462no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—42no—
819C22—42no—
820C22—81no—
821C22—81no—
822C22#1798856912yes—
823C22C22×#1192400511yescharacteristic
824C22C4×#1192402711yescharacteristic
825C22#1798906611yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—2922no—
835C4—2922no—
836C4—2922no—
837C4—2922no—
838C4#1798923111yescharacteristic
839C4#1798923211yescharacteristic
840C4#1798923611yescharacteristic
841C4#1798924111yescharacteristic
842C2—21no—
843C2—21no—
844C2—22no—
845C2—41no—
846C2—41no—
847C2—41no—
848C2#2261275611yescharacteristic
849C2C2×#1798856911yescharacteristic
850C2#2261841311yescharacteristic
subgroupG/H
centerC22C22×#11924005
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingD4×M16×C73C2
socleC22×C73C22×C22⋊C4
prime radicalC22×D4×C73C2×C4
cosocleC22×C4×C73C24
hypercenterD4×M16D73
hypocenterC73#22480
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
3. #22610924C2semidirect
4. #22610923C2semidirect
5. #22610399C2semidirect
6. #22610399C2semidirect
7. #22610397C2semidirect
8. #22610397C2semidirect
9. #22610012C2semidirect
10. #22610009C2semidirect
11. #22609924C2semidirect
12. C4×#14556509C2semidirect
13. #22609669C2semidirect
14. C2×#17988355C2semidirect
441. C73#22480semidirect

Maximal subgroups

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

subgroupindex
C2×#179892772
D4×#119240122
#226109242
#226109232
#226103992
#226103972
#226100122
#226100092
#226099242
C4×#145565092
#226096692
C2×#179883552
D4×M16×C732
#2248073