Finite Group Databasebeta

← #11910903

Subgroups — #11910903

Order 1152.

2293 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596124C211yesmaximal, characteristic, complemented
2C3×#5660C212yesmaximal, complemented
3#10595255C212yesmaximal, complemented
4#10595241C211yesmaximal, characteristic, complemented
5#10595169C211yesmaximal, characteristic, complemented
6#10595030C211yesmaximal, characteristic, complemented
7#10595018C212yesmaximal, complemented
8#10594811C211yesmaximal, characteristic, complemented
9#10594593C212yesmaximal, complemented
10#10594562C212yesmaximal, complemented
11#10594516C212yesmaximal, complemented
12#10594469C212yesmaximal, complemented
13#10594244C211yesmaximal, characteristic, complemented
14#10594232C212yesmaximal, complemented
15#10594228C212yesmaximal, complemented
16#10594202C212yesmaximal, complemented
17#10594165C211yesmaximal, characteristic, complemented
18#10594066C212yesmaximal, complemented
19#10594032C212yesmaximal, complemented
20#86457—32nomaximal
21C2×D4×C3⋊D3C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×#624C2211yescharacteristic, complemented
24C2×#3799C2212yes—
25C2×#3798C2211yescharacteristic, complemented
26C32×#123C2211yescharacteristic
27#64146C2211yescharacteristic
28#64138C2211yescharacteristic
29#64104C2212yes—
30#64103C2212yes—
31#64093C2212yes—
32#64091C2212yes—
33#64091C2211yescharacteristic
34C22⋊C4×C3⋊D3C2211yescharacteristic
35C3×#938C2212yes—
36C3×#935C2212yes—
37C3×C4×#67C2212yescomplemented
38C3×#924C2212yescomplemented
39C3×#896C2212yescomplemented
40C3×D3×C4⋊C4C2212yescomplemented
41C3×#890C2212yescomplemented
42C3×#889C2212yescomplemented
43C3×#883C2212yescomplemented
44C3×#883C2212yescomplemented
45C3×#67⋊C4C2212yescomplemented
46C3×#879C2212yescomplemented
47C3×#879C2212yescomplemented
48C3×#878C2212yescomplemented
49#63981C2212yes—
50#63981C2212yescomplemented
51#63981C2212yescomplemented
52#63979C2211yescharacteristic
53#63979C2211yescharacteristic, complemented
54#63978C2212yescomplemented
55#63975C2211yescharacteristic
56#63975C2211yescharacteristic
57#63974C2212yes—
58#63974C2211yescharacteristic, complemented
59#63974C2212yescomplemented
60#63966C2212yescomplemented
61#63959C2212yescomplemented
62#63958C2212yescomplemented
63#63956C2212yescomplemented
64#63953C2211yescharacteristic
65#63953C2211yescharacteristic, complemented
66#63953C2212yescomplemented
67#63952C2212yescomplemented
68#63910C2212yes—
69#63910C2212yescomplemented
70#63910C2212yescomplemented
71#63909C2212yescomplemented
72#63909C2212yescomplemented
73#63909C2212yescomplemented
74#63906C2212yescomplemented
75#63905C2212yescomplemented
76#63904C2212yescomplemented
77#63904C2212yescomplemented
78#63904C2212yescomplemented
79C4×#626C2212yescomplemented
80#63897C2212yes—
81#63897C2211yescharacteristic, complemented
82#63897C2212yescomplemented
83#63897C2211yescharacteristic, complemented
84#63897C2212yescomplemented
85#63895C2212yescomplemented
86#63895C2212yescomplemented
87#63895C2212yescomplemented
88#63894C2212yes—
89#63894C2212yescomplemented
90#63888C2212yescomplemented
91#63883C2212yescomplemented
92#63865C2212yescomplemented
93#63864C2212yescomplemented
94#63854C2212yescomplemented
95#63853C2212yescomplemented
96#63852C2212yescomplemented
97#63850C2212yescomplemented
98#63849C2212yescomplemented
99#63849C2211yescharacteristic, complemented
100#63848C2212yescomplemented
101#63848C2212yescomplemented
102#63848C2212yescomplemented
103#63846C2212yescomplemented
104#63839C2212yescomplemented
105#63837C2212yescomplemented
106#63836C2212yescomplemented
107#63836C2212yescomplemented
108C3×#539—32no—
109#5710—32no—
110#5705—32no—
111#5705—32no—
112#5704—32no—
113#5700—32no—
114#5695—32no—
115#5694—32no—
116#5693—32no—
117#5666—32no—
118#5663—32no—
119#5660D312yescomplemented
120#5659—32no—
121#5657—32no—
122#5657—32no—
123#5653—32no—
124#5653—61no—
125D3×#123—32no—
126#5647—32no—
127#5646—32no—
128#5640—32no—
129#5631—32no—
130#5630—32no—
131#5627—32no—
132#5613—32no—
133#5607—32no—
134#5562—32no—
135#5559—32no—
136#5550—32no—
137#5547—32no—
138#5514—32no—
139#5507—32no—
140C23×C3⋊D3C2311yescharacteristic
141C23×C3⋊D3C2311yescharacteristic
142C23×C3⋊D3C2311yescharacteristic
143C2×C32×D4C2311yescharacteristic
144C22×C32×C4C2311yescharacteristic
145C2×#638C2312yes—
146C2×#638C2311yescharacteristic
147C2×#638C2311yescharacteristic
148D4×C3⋊D3—42no—
149C2×C4⋊(C3⋊D3)—42no—
150C2×C4⋊(C3⋊D3)C2312yes—
151C2×C4⋊(C3⋊D3)C2312yes—
152C2×C4⋊(C3⋊D3)C2312yes—
153C2×C4⋊(C3⋊D3)C2311yescharacteristic
154C2×C4×C3⋊D3C2311yescharacteristic
155C2×C4×C3⋊D3C2312yes—
156C2×C3×#67C2312yes—
157C2×C3×#67C2312yes—
158C22×C3×Dic3C2312yes—
159C2×C3×C4×D3C2312yes—
160C2×C3×C4×D3C2312yes—
161C2×C3×C4×D3C2312yes—
162C2×C3×Dic6C2312yes—
163C2×#627C2311yescharacteristic
164C2×#627C2312yes—
165C2×#626C2312yes—
166C2×#626C2312yes—
167C2×#626C2312yes—
168C2×#626C2312yes—
169C2×#626C2312yes—
170C2×#625C2311yescharacteristic
171C2×#624—42no—
172C2×#624C2312yes—
173C2×#624C2312yes—
174C2×#624C2311yescharacteristic
175C2×#624C2311yescharacteristic
176C2×#624C2312yes—
177C2×#624C2312yes—
178#3799—44no—
179#3798—42no—
180C32×C4⋊C4C2312yes—
181C32×C22⋊C4C2312yes—
182C32×C22⋊C4C2311yescharacteristic
183#3757C2311yescharacteristic
184#3752C2312yes—
185#3752C2312yes—
186#3752C2312yes—
187#3752C2312yes—
188#3750C2312yes—
189C3×#217C2312yes—
190C3×#217C2312yes—
191C3×#217C2312yes—
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×(C2×D3)⋊C4C2312yes—
195C3×(C2×D3)⋊C4C2312yes—
196C3×C4⋊Dic3C2312yes—
197C3×C4⋊Dic3C2312yes—
198C3×C4⋊Dic3C2312yes—
199C3×C4⋊Dic3C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×Dic3⋊C4C2312yes—
207C3×Dic3⋊C4C2312yes—
208C3×C4×Dic3C2312yes—
209C3×C4×Dic3C2312yes—
210#3724C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215#3722C2312yes—
216#3722C2312yes—
217#3722C2312yes—
218#3722C2311yescharacteristic
219#3722C2312yes—
220#3722C2312yes—
221#3722C2312yes—
222#3722C2312yes—
223#3722C2312yes—
224#3722C2311yescharacteristic
225#3722C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228Dic32C2311yescharacteristic
229Dic32C2312yes—
230Dic32C2311yescharacteristic
231Dic32C2312yes—
232#3533—91noSylow
233C2×#239—32no—
234C2×D3×D4—32no—
235C2×D3×D4—61no—
236C2×#235—32no—
237C2×#235—32no—
238C22×D12—32no—
239C22×D12—61no—
240C22×C4×D3—32no—
241C3×#126—32no—
242C3×#126—32no—
243C3×#125—32no—
244C3×#125—32no—
245C3×#123—21no—
246C3×#123—32no—
247C3×#123—32no—
248C3×#123—32no—
249C3×#123C2×D312yes—
250C3×C22⋊Q8—32no—
251C3×C22⋊Q8—32no—
252C3×C22⋊Q8—32no—
253C3×#121—32no—
254C3×C4×D4—32no—
255C3×C4×D4—32no—
256C2×C3×C4⋊C4—32no—
257#947—32no—
258#946—32no—
259#944—32no—
260#940—32no—
261#940—32no—
262#939—32no—
263#938—32no—
264#938C2×D312yes—
265#937—32no—
266#937—32no—
267#937—32no—
268#937—32no—
269#937—61no—
270#936—32no—
271#935C2×D312yes—
272#930—32no—
273#930—32no—
274#930—32no—
275#930—32no—
276#930—32no—
277#929—32no—
278#929—32no—
279#929—32no—
280#929—32no—
281#929—61no—
282C4×#67—32no—
283C4×#67—32no—
284C4×#67—32no—
285C4×#67—32no—
286C4×#67—32no—
287C4×#67C2×D312yescomplemented
288#924C2×D312yescomplemented
289#898—32no—
290#898—32no—
291#898—32no—
292#898—32no—
293#898—32no—
294#898—32no—
295#897—32no—
296#897—32no—
297#897—32no—
298#896—32no—
299#896—32no—
300#896—32no—
301#896—32no—
302#896—32no—
303#896—32no—
304#896C2×D312yescomplemented
305#895—32no—
306#895—32no—
307#895—32no—
308#895—32no—
309#895—32no—
310#895—32no—
311#895—32no—
312#895—32no—
313#895—62no—
314#894—32no—
315#894—32no—
316#894—32no—
317#894—32no—
318#894—32no—
319#894—32no—
320#894—32no—
321#894—32no—
322#894—32no—
323#894—32no—
324#894—32no—
325#894—32no—
326#894—32no—
327#894—62no—
328#893—32no—
329#893—32no—
330#893—32no—
331#893—32no—
332#893—32no—
333#892—32no—
334#892—32no—
335#892—32no—
336#892—32no—
337#892—32no—
338D3×C4⋊C4—32no—
339D3×C4⋊C4—32no—
340D3×C4⋊C4C2×D312yescomplemented
341#890—32no—
342#890C2×D312yescomplemented
343#889—32no—
344#889C2×D312yescomplemented
345#888—32no—
346#887—32no—
347#886—32no—
348#885—32no—
349#885—32no—
350#885—32no—
351#885—32no—
352#885—32no—
353#885—32no—
354#884—32no—
355#884—32no—
356#884—32no—
357#884—32no—
358#884—32no—
359#884—32no—
360#884—32no—
361#884—62no—
362#883—32no—
363#883—32no—
364#883—32no—
365#883—32no—
366#883—32no—
367#883C2×D312yescomplemented
368#883C2×D312yescomplemented
369#882—32no—
370#882—32no—
371#882—32no—
372#882—32no—
373#882—32no—
374#882—32no—
375#882—62no—
376#882—61no—
377#67⋊C4—32no—
378#67⋊C4C2×D312yescomplemented
379D3×C22⋊C4—32no—
380D3×C22⋊C4—32no—
381D3×C22⋊C4—32no—
382D3×C22⋊C4—32no—
383D3×C22⋊C4—32no—
384D3×C22⋊C4—32no—
385D3×C22⋊C4—61no—
386#879—32no—
387#879—32no—
388#879C2×D312yescomplemented
389#879C2×D312yescomplemented
390#878C2×D312yescomplemented
391#875—32no—
392#875—32no—
393C4×D12—32no—
394C4×D12—32no—
395C4×D12—32no—
396#872—32no—
397#872—32no—
398C4×Dic6—32no—
399C23×C32C2411yescharacteristic
400C23×C32C2411yescharacteristic
401C22×C3⋊D3—22no—
402C22×C3⋊D3—22no—
403C22×C3⋊D3—41no—
404C22×C3⋊D3—42no—
405C22×C3⋊D3—42no—
406C22×C3⋊D3—42no—
407C22×C3⋊D3C2411yescharacteristic
408C22×C3⋊D3C2411yescharacteristic
409C22×C3⋊D3C2412yes—
410C22×C3⋊D3C2411yescharacteristic
411C22×C3×D3C2412yes—
412C32×D4—41no—
413C2×C32×C4—41no—
414C2×C32×C4C2412yes—
415C2×C32×C4C2412yes—
416C2×C32×C4C2411yescharacteristic
417#638—41no—
418#638—41no—
419#638—42no—
420C2×C3⋊Dic3C2412yes—
421C2×C3⋊Dic3C2411yescharacteristic
422C4⋊(C3⋊D3)—24no—
423C4⋊(C3⋊D3)—42no—
424C4⋊(C3⋊D3)—41no—
425C4⋊(C3⋊D3)—42no—
426C4×C3⋊D3—22no—
427C4×C3⋊D3—42no—
428C3×#67—42no—
429C3×#67—42no—
430C2×C3×Dic3—42no—
431C2×C3×Dic3C2412yes—
432C2×C3×Dic3C2412yes—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C2×C3×Dic3C2412yes—
436C2×C3×Dic3C2412yes—
437C2×C3×Dic3C2412yes—
438C3×C4×D3—42no—
439C3×C4×D3—42no—
440C3×C4×D3—42no—
441C3×Dic6—42no—
442#627—41no—
443#627—42no—
444#626—24no—
445#626—42no—
446#626—42no—
447#626—42no—
448#626—42no—
449#625—41no—
450#624—24no—
451#624—42no—
452#624—41no—
453#624—41no—
454#624—42no—
455#624—42no—
456#563—91no—
457#562—92no—
458#560—91no—
459#559—91no—
460#553—92no—
461#552—92no—
462#551—92no—
463#551—91no—
464#547—92no—
465#546—92no—
466#542—92no—
467#540—92no—
468#539—32no—
469#538—92no—
470#538—92no—
471#535—91no—
472#534—91no—
473#525—92no—
474C2×#123—91no—
475C23×D3—32no—
476C23×D3—32no—
477C23×D3—32no—
478C23×D3—61no—
479C23×D3—61no—
480C23×D3—61no—
481C2×C3×Q8—32no—
482C2×C3×D4—21no—
483C2×C3×D4—32no—
484C2×C3×D4—32no—
485C2×C3×D4C22×D312yes—
486C22×C3×C4—21no—
487C22×C3×C4—32no—
488C22×C3×C4—32no—
489C22×C3×C4—32no—
490C22×C3×C4—32no—
491C22×C3×C4C22×D312yes—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—32no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—32no—
498C2×#67—32no—
499C2×#67—32no—
500C2×#67—32no—
501C2×#67—32no—
502C2×#67—61no—
503C2×#67—61no—
504C2×#67—62no—
505C2×#67C22×D312yes—
506C2×#67C22×D312yes—
507C22×Dic3C22×D312yes—
508#239—124no—
509D3×D4—124no—
510D3×D4—124no—
511#235—124no—
512#235—124no—
513C2×D12—32no—
514C2×D12—32no—
515C2×D12—32no—
516C2×D12—32no—
517C2×D12—32no—
518C2×D12—32no—
519C2×D12—32no—
520C2×D12—32no—
521C2×D12—32no—
522C2×D12—32no—
523C2×D12—32no—
524C2×D12—32no—
525C2×D12—62no—
526C2×D12—62no—
527C2×D12—61no—
528C2×D12—62no—
529C2×D12—124no—
530C2×D12—124no—
531C2×C4×D3—32no—
532C2×C4×D3—32no—
533C2×C4×D3—32no—
534C2×C4×D3—32no—
535C2×C4×D3—32no—
536C2×C4×D3—32no—
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—61no—
545C2×C4×D3—62no—
546C2×C4×D3—124no—
547C2×C4×D3C22×D312yes—
548C2×C4×D3C22×D312yes—
549C2×C4×D3C22×D312yes—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6—32no—
553C2×Dic6C22×D312yes—
554C3×C4⋊C4—22no—
555C3×C4⋊C4—32no—
556C3×C4⋊C4—32no—
557C3×C4⋊C4—32no—
558C3×C4⋊C4—32no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—32no—
561C3×C4⋊C4—32no—
562C3×C4⋊C4—32no—
563C3×C4⋊C4—32no—
564C3×C4⋊C4—32no—
565C3×C4⋊C4—32no—
566C3×C4⋊C4—32no—
567C3×C4⋊C4C22×D312yes—
568C3×C4⋊C4C22×D312yes—
569C3×C22⋊C4—21no—
570C3×C22⋊C4—22no—
571C3×C22⋊C4—32no—
572C3×C22⋊C4—32no—
573C3×C22⋊C4—32no—
574C3×C22⋊C4—32no—
575C3×C22⋊C4—32no—
576C3×C22⋊C4—32no—
577C3×C22⋊C4—32no—
578C3×C22⋊C4C22×D312yes—
579C3×C22⋊C4C22×D312yes—
580C3×C22⋊C4C22×D312yes—
581C3×C42—32no—
582C3×C42—32no—
583#217—32no—
584#217—32no—
585#217—32no—
586#217—61no—
587#217C22×D312yes—
588#217C22×D312yes—
589#217C22×D312yes—
590#217C22×D312yes—
591#217C22×D312yes—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—32no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—32no—
614(C2×D3)⋊C4—32no—
615(C2×D3)⋊C4—32no—
616(C2×D3)⋊C4—32no—
617(C2×D3)⋊C4—32no—
618(C2×D3)⋊C4—32no—
619(C2×D3)⋊C4—32no—
620(C2×D3)⋊C4—32no—
621(C2×D3)⋊C4—32no—
622(C2×D3)⋊C4—62no—
623(C2×D3)⋊C4—62no—
624(C2×D3)⋊C4—62no—
625(C2×D3)⋊C4—62no—
626(C2×D3)⋊C4C22×D312yes—
627(C2×D3)⋊C4C22×D312yes—
628C4⋊Dic3—32no—
629C4⋊Dic3—32no—
630C4⋊Dic3—32no—
631C4⋊Dic3—32no—
632C4⋊Dic3C22×D312yes—
633C4⋊Dic3C22×D312yes—
634C4⋊Dic3C22×D312yes—
635C4⋊Dic3C22×D312yes—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—32no—
644Dic3⋊C4—62no—
645Dic3⋊C4C22×D312yes—
646Dic3⋊C4C22×D312yes—
647Dic3⋊C4C22×D312yes—
648Dic3⋊C4C22×D312yes—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653C4×Dic3—32no—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3C22×D312yes—
660C4×Dic3C22×D312yes—
661C22×C32—21no—
662C22×C32—21no—
663C22×C32—22no—
664C22×C32—22no—
665C22×C32C2511yescharacteristic
666C2×C3⋊D3—21no—
667C2×C3⋊D3—22no—
668C2×C3⋊D3—21no—
669C2×C3⋊D3—22no—
670C2×C3⋊D3—22no—
671C2×C3⋊D3—22no—
672C2×C3⋊D3—22no—
673C2×C3⋊D3—22no—
674C2×C3⋊D3—44no—
675C2×C3⋊D3—82no—
676C2×C3⋊D3—82no—
677C2×C3⋊D3H(5,𝔽2)12yes—
678C2×C3×D3—22no—
679C2×C3×D3—22no—
680C2×C3×D3—22no—
681C32×C4—22no—
682C32×C4—21no—
683C32×C4—22no—
684C3⋊Dic3—21no—
685C3⋊Dic3—22no—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—22no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3—22no—
693C2×#41—91no—
694C2×#41—92no—
695C22×D4—91no—
696C22×D4—91no—
697C23×C4—91no—
698C4⋊Q8—92no—
699#127—91no—
700#127—91no—
701#126—32no—
702#126—32no—
703#126—92no—
704#126—92no—
705#126—92no—
706#126—92no—
707#125—32no—
708#125—32no—
709#125—92no—
710#124—92no—
711#124—92no—
712#124—91no—
713#124—91no—
714#124—92no—
715#124—92no—
716#123—32no—
717#123—32no—
718#123—32no—
719#123—91no—
720#123—91no—
721#123—92no—
722#123—92no—
723#123—92no—
724#123—92no—
725#123—91no—
726#123—91no—
727#123—92no—
728#123—92no—
729#123—92no—
730#123—92no—
731#123—91no—
732#123—92no—
733#123D3211yescharacteristic
734C22⋊Q8—32no—
735C22⋊Q8—32no—
736C22⋊Q8—32no—
737C22⋊Q8—92no—
738C22⋊Q8—92no—
739C22⋊Q8—92no—
740C22⋊Q8—92no—
741C22⋊Q8—92no—
742#121—32no—
743#121—92no—
744#121—92no—
745#121—92no—
746#121—92no—
747#121—92no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121—92no—
752#121—92no—
753#121—92no—
754#120—92no—
755#120—92no—
756#120—92no—
757#120—91no—
758#120—92no—
759#120—91no—
760C4×Q8—92no—
761C4×D4—32no—
762C4×D4—32no—
763C4×D4—92no—
764C4×D4—92no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—92no—
770#117—92no—
771#117—92no—
772#117—91no—
773#117—92no—
774C2×C4⋊C4—32no—
775C2×C4⋊C4—92no—
776C2×C22⋊C4—91no—
777C2×C22⋊C4—92no—
778C2×C22⋊C4—92no—
779C2×C22⋊C4—91no—
780C23×C3—21no—
781C23×C3—21no—
782C23×C3—32no—
783C23×C3C23×D312yes—
784C23×C3C23×D312yes—
785C22×D3—32no—
786C22×D3—32no—
787C22×D3—32no—
788C22×D3—32no—
789C22×D3—32no—
790C22×D3—61no—
791C22×D3—61no—
792C22×D3—62no—
793C22×D3—61no—
794C22×D3—64no—
795C22×D3—64no—
796C22×D3—64no—
797C22×D3—122no—
798C22×D3—122no—
799C22×D3—122no—
800C22×D3—122no—
801C22×D3—122no—
802C22×D3—122no—
803C22×D3—122no—
804C22×D3—122no—
805C22×D3—122no—
806C22×D3—242no—
807C22×D3—242no—
808C22×D3—242no—
809C22×D3C23×D312yes—
810C3×Q8—122no—
811C3×D4—42no—
812C3×D4—42no—
813C3×D4—122no—
814C3×D4—122no—
815C2×C3×C4—22no—
816C2×C3×C4—22no—
817C2×C3×C4—21no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—32no—
821C2×C3×C4—32no—
822C2×C3×C4—32no—
823C2×C3×C4—32no—
824C2×C3×C4—32no—
825C2×C3×C4—42no—
826C2×C3×C4—42no—
827C2×C3×C4—122no—
828C2×C3×C4—122no—
829C2×C3×C4—122no—
830C2×C3×C4—122no—
831C2×C3×C4C23×D312yes—
832C2×C3×C4C23×D312yes—
833C2×C3×C4C23×D312yes—
834C2×C3×C4C23×D312yes—
835C2×C3×C4C23×D312yes—
836#67—42no—
837#67—42no—
838#67—64no—
839#67—122no—
840#67—122no—
841#67—122no—
842#67—122no—
843#67—122no—
844#67—122no—
845#67—122no—
846#67—122no—
847#67—122no—
848#67—122no—
849#67—122no—
850#67—242no—
851C2×Dic3—32no—
852C2×Dic3—32no—
853C2×Dic3—32no—
854C2×Dic3—42no—
855C2×Dic3—61no—
856C2×Dic3—62no—
857C2×Dic3C23×D312yes—
858C2×Dic3C23×D312yes—
859C2×Dic3C23×D312yes—
860C2×Dic3C23×D312yes—
861C2×Dic3C23×D312yes—
862C2×Dic3C23×D312yes—
863C2×Dic3C23×D312yes—
864D12—64no—
865D12—64no—
866D12—64no—
867D12—124no—
868D12—122no—
869D12—122no—
870D12—122no—
871D12—122no—
872D12—122no—
873D12—124no—
874D12—122no—
875D12—122no—
876D12—122no—
877D12—122no—
878D12—122no—
879D12—242no—
880C4×D3—42no—
881C4×D3—42no—
882C4×D3—42no—
883C4×D3—64no—
884C4×D3—64no—
885C4×D3—64no—
886C4×D3—122no—
887C4×D3—122no—
888C4×D3—122no—
889C4×D3—122no—
890C4×D3—122no—
891C4×D3—122no—
892C4×D3—122no—
893C4×D3—122no—
894C4×D3—122no—
895C4×D3—122no—
896C4×D3—122no—
897C4×D3—242no—
898Dic6—42no—
899Dic6—122no—
900Dic6—122no—
901Dic6—122no—
902C2×C32—41no—
903C2×C32—41no—
904C2×C32C2×H(5,𝔽2)11yescharacteristic
905C2×C32#58512yes—
906C3⋊D3—22no—
907C3⋊D3—41no—
908C3⋊D3—41no—
909C3⋊D3—42no—
910C3×D3—42no—
911C24—91no—
912C24—91no—
913C24—91no—
914#41—362no—
915#41—364no—
916C2×Q8—32no—
917C2×Q8—92no—
918C2×Q8—91no—
919C2×D4—32no—
920C2×D4—32no—
921C2×D4—92no—
922C2×D4—92no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—91no—
927C2×D4—92no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—92no—
931C2×D4—92no—
932C2×D4—91no—
933C2×D4—92no—
934C2×D4—362no—
935C2×D4—362no—
936C2×D4C2×D3211yescharacteristic
937C22×C4—32no—
938C22×C4—32no—
939C22×C4—32no—
940C22×C4—32no—
941C22×C4—92no—
942C22×C4—92no—
943C22×C4—92no—
944C22×C4—92no—
945C22×C4—91no—
946C22×C4—91no—
947C22×C4—91no—
948C22×C4—92no—
949C22×C4—362no—
950C22×C4C2×D3211yescharacteristic
951C4⋊C4—32no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—32no—
956C4⋊C4—32no—
957C4⋊C4—32no—
958C4⋊C4—32no—
959C4⋊C4—32no—
960C4⋊C4—32no—
961C4⋊C4—32no—
962C4⋊C4—32no—
963C4⋊C4—92no—
964C4⋊C4—92no—
965C4⋊C4—92no—
966C4⋊C4—92no—
967C4⋊C4—92no—
968C4⋊C4—92no—
969C4⋊C4C2×D3212yes—
970C22⋊C4—32no—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—32no—
975C22⋊C4—32no—
976C22⋊C4—32no—
977C22⋊C4—92no—
978C22⋊C4—92no—
979C22⋊C4—91no—
980C22⋊C4—92no—
981C22⋊C4—92no—
982C22⋊C4—91no—
983C22⋊C4—92no—
984C22⋊C4—92no—
985C22⋊C4—92no—
986C22⋊C4—92no—
987C22⋊C4—92no—
988C22⋊C4—92no—
989C22⋊C4—92no—
990C22⋊C4—91no—
991C22⋊C4—92no—
992C22⋊C4—92no—
993C22⋊C4—92no—
994C22⋊C4—92no—
995C22⋊C4C2×D3211yescharacteristic
996C22⋊C4C2×D3212yes—
997C42—32no—
998C42—32no—
999C42—91no—
1000C42—92no—
1001C42—92no—
1002C42—91no—
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—22no—
1006C22×C3—22no—
1007C22×C3—22no—
1008C22×C3—22no—
1009C22×C3—22no—
1010C22×C3—21no—
1011C22×C3—42no—
1012C22×C3—41no—
1013C22×C3—42no—
1014C22×C3—62no—
1015C22×C3—62no—
1016C22×C3—62no—
1017C22×C3C24×D312yes—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—22no—
1021C2×D3—34no—
1022C2×D3—62no—
1023C2×D3—62no—
1024C2×D3—62no—
1025C2×D3—62no—
1026C2×D3—62no—
1027C2×D3—62no—
1028C2×D3—62no—
1029C2×D3—62no—
1030C2×D3—62no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—62no—
1037C2×D3—62no—
1038C2×D3—122no—
1039C2×D3—122no—
1040C2×D3—122no—
1041C2×D3—121no—
1042C2×D3—122no—
1043C2×D3—122no—
1044C2×D3—122no—
1045C2×D3—128no—
1046C2×D3—244no—
1047C2×D3—244no—
1048C2×D3—244no—
1049C2×D3—244no—
1050C2×D3—244no—
1051C3×C4—22no—
1052C3×C4—22no—
1053C3×C4—22no—
1054C3×C4—22no—
1055C3×C4—22no—
1056C3×C4—41no—
1057C3×C4—42no—
1058C3×C4—42no—
1059C3×C4—62no—
1060C3×C4—62no—
1061C3×C4—62no—
1062C3×C4—62no—
1063C3×C4—62no—
1064C3×C4—62no—
1065C3×C4—62no—
1066Dic3—22no—
1067Dic3—22no—
1068Dic3—22no—
1069Dic3—22no—
1070Dic3—22no—
1071Dic3—22no—
1072Dic3—22no—
1073Dic3—62no—
1074Dic3—62no—
1075Dic3—62no—
1076Dic3—121no—
1077Dic3—122no—
1078C32#353311yescharacteristic, complemented, Sylow
1079C23—32no—
1080C23—91no—
1081C23—91no—
1082C23—92no—
1083C23—91no—
1084C23—182no—
1085C23—182no—
1086C23—362no—
1087C23—361no—
1088C23—362no—
1089C23—362no—
1090C23C22×D3211yescharacteristic
1091C23C22×D3211yescharacteristic
1092Q8—122no—
1093Q8—361no—
1094Q8—362no—
1095D4—41no—
1096D4—122no—
1097D4—122no—
1098D4—184no—
1099D4—184no—
1100D4—362no—
1101D4—361no—
1102D4—362no—
1103D4—362no—
1104D4—362no—
1105D4—362no—
1106D4—362no—
1107D4—361no—
1108D4—361no—
1109D4—362no—
1110D4—361no—
1111C2×C4—32no—
1112C2×C4—32no—
1113C2×C4—32no—
1114C2×C4—32no—
1115C2×C4—32no—
1116C2×C4—32no—
1117C2×C4—32no—
1118C2×C4—41no—
1119C2×C4—92no—
1120C2×C4—91no—
1121C2×C4—122no—
1122C2×C4—122no—
1123C2×C4—122no—
1124C2×C4—122no—
1125C2×C4—182no—
1126C2×C4—184no—
1127C2×C4—362no—
1128C2×C4—361no—
1129C2×C4—361no—
1130C2×C4—362no—
1131C2×C4—362no—
1132C2×C4—362no—
1133C2×C4C22×D3212yes—
1134C2×C4C22×D3212yes—
1135C2×C4C22×D3211yescharacteristic
1136C2×C3—21no—
1137C2×C3—22no—
1138C2×C3—42no—
1139C2×C3—42no—
1140C2×C3—42no—
1141C2×C3—81no—
1142C2×C3—122no—
1143C2×C3#596412yes—
1144C2×C3D3×H(5,𝔽2)12yes—
1145C2×C3#596812yes—
1146D3—42no—
1147D3—64no—
1148D3—122no—
1149D3—122no—
1150D3—122no—
1151D3—122no—
1152D3—122no—
1153D3—122no—
1154D3—241no—
1155D3—242no—
1156C22—21no—
1157C22—21no—
1158C22—22no—
1159C22—22no—
1160C22—62no—
1161C22—62no—
1162C22—62no—
1163C22—92no—
1164C22—182no—
1165C22—181no—
1166C22—182no—
1167C22—181no—
1168C22—182no—
1169C22—182no—
1170C22—182no—
1171C22—182no—
1172C22—364no—
1173C22—722no—
1174C22—722no—
1175C22C23×D3211yescharacteristic
1176C4—22no—
1177C4—21no—
1178C4—22no—
1179C4—62no—
1180C4—62no—
1181C4—62no—
1182C4—62no—
1183C4—62no—
1184C4—62no—
1185C4—62no—
1186C4—181no—
1187C4—182no—
1188C3—21no—
1189C3#8645712yescomplemented
1190C2—41no—
1191C2—41no—
1192C2—122no—
1193C2—182no—
1194C2—361no—
1195C2—361no—
1196C2—362no—
1197C2#1059667511yescharacteristic
1198C2#1059669712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #10596124C2semidirect
2. C3×#5660C2semidirect
3. #10595255C2semidirect
4. #10595241C2semidirect
5. #10595169C2semidirect
6. #10595030C2semidirect
7. #10595018C2semidirect
8. #10594811C2semidirect
9. #10594593C2semidirect
10. #10594562C2semidirect
11. #10594516C2semidirect
12. #10594469C2semidirect
13. #10594244C2semidirect
14. #10594232C2semidirect
15. #10594228C2semidirect
16. #10594202C2semidirect
17. #10594165C2semidirect
18. #10594066C2semidirect
19. #10594032C2semidirect
23. C22×#624C22semidirect
25. C2×#3798C22semidirect
37. C3×C4×#67C22semidirect
38. C3×#924C22semidirect
39. C3×#896C22semidirect
40. C3×D3×C4⋊C4C22semidirect
41. C3×#890C22semidirect
42. C3×#889C22semidirect
43. C3×#883C22semidirect
44. C3×#883C22semidirect
45. C3×#67⋊C4C22semidirect
46. C3×#879C22semidirect
47. C3×#879C22semidirect
48. C3×#878C22semidirect
50. #63981C22semidirect
51. #63981C22semidirect
53. #63979C22semidirect
54. #63978C22semidirect
58. #63974C22semidirect
59. #63974C22semidirect
60. #63966C22semidirect
61. #63959C22semidirect
62. #63958C22semidirect
63. #63956C22semidirect
65. #63953C22semidirect
66. #63953C22semidirect
67. #63952C22semidirect
69. #63910C22semidirect
70. #63910C22semidirect
71. #63909C22semidirect
72. #63909C22semidirect
73. #63909C22semidirect
74. #63906C22semidirect
75. #63905C22semidirect
76. #63904C22semidirect
77. #63904C22semidirect
78. #63904C22semidirect
79. C4×#626C22semidirect
81. #63897C22semidirect
82. #63897C22semidirect
83. #63897C22semidirect
84. #63897C22semidirect
85. #63895C22semidirect
86. #63895C22semidirect
87. #63895C22semidirect
89. #63894C22semidirect
90. #63888C22semidirect
91. #63883C22semidirect
92. #63865C22semidirect
93. #63864C22semidirect
94. #63854C22semidirect
95. #63853C22semidirect
96. #63852C22semidirect
97. #63850C22semidirect
98. #63849C22semidirect
99. #63849C22semidirect
100. #63848C22semidirect
101. #63848C22semidirect
102. #63848C22semidirect
103. #63846C22semidirect
104. #63839C22semidirect
105. #63837C22semidirect
106. #63836C22semidirect
107. #63836C22semidirect
119. #5660D3semidirect
287. C4×#67C2×D3semidirect
288. #924C2×D3semidirect
304. #896C2×D3semidirect
340. D3×C4⋊C4C2×D3semidirect
342. #890C2×D3semidirect
344. #889C2×D3semidirect
367. #883C2×D3semidirect
368. #883C2×D3semidirect
378. #67⋊C4C2×D3semidirect
388. #879C2×D3semidirect
389. #879C2×D3semidirect
390. #878C2×D3semidirect
1078. C32#3533semidirect
1189. C3#86457semidirect

Maximal subgroups

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

subgroupindex
#105961242
C3×#56602
#105952552
#105952412
#105951692
#105950302
#105950182
#105948112
#105945932
#105945622
#105945162
#105944692
#105942442
#105942322
#105942282
#105942022
#105941652
#105940662
#105940322
#864573