Finite Group Databasebeta

← #11904207

Subgroups — #11904207

Order 1152.

2328 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2C3×#5732C211yesmaximal, characteristic, complemented
3C3×#5728C211yesmaximal, characteristic, complemented
4#10595382C212yesmaximal, complemented
5Q8×#624C212yesmaximal, complemented
6#10595362C212yesmaximal, complemented
7#10595344C212yesmaximal, complemented
8#10594576C212yesmaximal, complemented
9#10594530C212yesmaximal, complemented
10#10594478C214yesmaximal, complemented
11#10594417C214yesmaximal, complemented
12#10594385C212yesmaximal, complemented
13#10594362C212yesmaximal, complemented
14C4×#3799C211yesmaximal, characteristic, complemented
15C4×#3795C211yesmaximal, characteristic, complemented
16#10593869C211yesmaximal, characteristic, complemented
17#10593864C211yesmaximal, characteristic, complemented
18#86981—31nomaximal
19#86278—31nomaximal
20C2×Q8×C3⋊D3C2212yes—
21C2×#3799C2212yes—
22C2×#3799C2211yescharacteristic
23C2×#3795C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic
25#64155C2212yes—
26#64105C2214yes—
27#64102C2212yes—
28#64097C2212yes—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×#947C2212yes—
32C3×#946C2212yes—
33C3×Q8×Dic3C2212yes—
34C3×Q8×Dic3C2212yes—
35C3×#898C2214yes—
36C3×#897C2212yes—
37C3×#897C2212yes—
38C3×#892C2212yes—
39C3×#892C2212yes—
40C3×#890C2212yes—
41C3×#887C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C42×D3C2211yescharacteristic
44C3×#869C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63916C2212yes—
47#63913C2214yes—
48#63912C2214yes—
49#63904C2212yes—
50C4×#626C2212yes—
51C4×#625C2212yes—
52#63900C2212yes—
53#63900C2214yes—
54#63896C2214yes—
55#63894C2211yescharacteristic
56Dic3×D12C2211yescharacteristic
57C4×#624C2212yes—
58C4×#624C2214yes—
59#63881C2214yes—
60#63880C2214yes—
61#63879C2212yes—
62#63877C2214yes—
63#63877C2212yes—
64C4×D3×Dic3C2212yes—
65#63873C2212yes—
66#63869C2212yes—
67#63859C2214yes—
68#63858C2214yes—
69#63856C2212yes—
70#63854C2214yes—
71#63854C2214yes—
72#63854C2214yes—
73#63847C2214yes—
74#63847C2214yes—
75#63844C2214yes—
76#63844C2212yes—
77#63844C2211yescharacteristic
78#63844C2214yes—
79#63843C2212yes—
80Dic3×Dic6C2211yescharacteristic
81#63841C2211yescharacteristic
82#63841C2211yescharacteristic
83#63836C2214yes—
84#63836C2212yes—
85C3×#556—31no—
86C3×#533—31no—
87#5732D311yescharacteristic, complemented
88#5728D311yescharacteristic, complemented
89#5727—31no—
90#5727—31no—
91#5727—61no—
92#5726—31no—
93#5721—31no—
94#5708—34no—
95#5706—34no—
96#5693—34no—
97#5680—32no—
98#5677—32no—
99#5641—32no—
100#5639—32no—
101#5633—32no—
102#5631—32no—
103#5631—32no—
104#5622—32no—
105#5581—32no—
106#5580—32no—
107#5578—32no—
108C4×#239—32no—
109C4×#239—31no—
110C4×D3×Q8—32no—
111C4×D3×Q8—32no—
112#5567—31no—
113#5551—31no—
114C4×#237—31no—
115#5533—32no—
116#5528—34no—
117#5522—32no—
118C4×#235—31no—
119C4×#235—31no—
120C2×C32×Q8C2312yes—
121Q8×C3⋊D3—28no—
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2314yes—
126C2×#634C2311yescharacteristic
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#626C2314yes—
135C2×#626C2312yes—
136C2×#625C2312yes—
137C2×#624C2312yes—
138C2×#624C2314yes—
139C2×#624C2312yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142#3799—28no—
143#3799—24no—
144#3795—24no—
145C32×C4⋊C4C2312yes—
146C32×C4⋊C4C2312yes—
147C32×C42C2311yescharacteristic
148#3752C2312yes—
149#3752C2314yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152#3750C2312yes—
153#3750C2314yes—
154C4×C3⋊Dic3C2312yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2314yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2314yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2312yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2314yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2314yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2312yes—
173#3724C2312yes—
174#3724C2314yes—
175#3724C2314yes—
176#3724C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179#3722C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Dic32C2312yes—
189#3482—91noSylow
190C2×#239—32no—
191C2×#239—31no—
192C2×D3×Q8—32no—
193C2×D3×Q8—32no—
194C2×D3×Q8—62no—
195C2×#237—31no—
196C2×#235—31no—
197C2×#235—31no—
198C2×#235—32no—
199C3×C4⋊Q8—21no—
200C3×C4⋊Q8—31no—
201C3×C4⋊Q8C2×D311yescharacteristic
202C3×C4⋊Q8C2×D311yescharacteristic
203C3×#126—34no—
204C3×#125—32no—
205C3×#124—32no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—32no—
208C3×C22⋊Q8—32no—
209C3×C4×Q8—32no—
210C3×C4×Q8—32no—
211C3×C4×Q8—32no—
212C3×C4×Q8—31no—
213C3×C4×D4—31no—
214C3×#117—32no—
215C3×#117—32no—
216C2×C3×C42—31no—
217#947C2×D312yes—
218#946—32no—
219#946—32no—
220#946—32no—
221#946—62no—
222#946C2×D312yes—
223Q8×Dic3—32no—
224Q8×Dic3—31no—
225Q8×Dic3C2×D312yes—
226Q8×Dic3C2×D312yes—
227#944—32no—
228#944—32no—
229#938—32no—
230D4×Dic3—31no—
231C4×#67—32no—
232C4×#67—32no—
233C4×#67—32no—
234C4×#67—32no—
235C4×#67—32no—
236#926—31no—
237#926—31no—
238#924—32no—
239C2×C4×Dic3—32no—
240#898—34no—
241#898C2×D314yes—
242#897C2×D312yes—
243#897C2×D312yes—
244#896—34no—
245#896—34no—
246#896—34no—
247#896—64no—
248#895—32no—
249#894—34no—
250#894—34no—
251#894—34no—
252#893—32no—
253#893—32no—
254#893—32no—
255#893—34no—
256#893—31no—
257#893—62no—
258#892—31no—
259#892—31no—
260#892—34no—
261#892—32no—
262#892C2×D312yes—
263#892C2×D312yes—
264D3×C4⋊C4—32no—
265D3×C4⋊C4—34no—
266D3×C4⋊C4—34no—
267D3×C4⋊C4—32no—
268#890—32no—
269#890C2×D312yes—
270#889—34no—
271#889—34no—
272#889—34no—
273#889—34no—
274#888—32no—
275#888—32no—
276#888—62no—
277#887—32no—
278#887—32no—
279#887—34no—
280#887—34no—
281#887—31no—
282#887C2×D312yes—
283#885—34no—
284#885—34no—
285#884—34no—
286#884—34no—
287#883—34no—
288#883—34no—
289#883—34no—
290#67⋊C4—32no—
291#67⋊C4—34no—
292#67⋊C4—34no—
293#879—34no—
294#879—34no—
295#878—34no—
296#877—34no—
297#877—32no—
298#876—34no—
299C4×D12—31no—
300C4×D12—32no—
301C4×D12—31no—
302C4×D12—31no—
303C4×D12—34no—
304C4×D12—31no—
305C4×D12—61no—
306C4×D12C2×D311yescharacteristic
307#872—32no—
308#872—34no—
309#872—32no—
310#872—34no—
311C42×D3—32no—
312C42×D3—32no—
313C42×D3—34no—
314C42×D3—32no—
315C42×D3—34no—
316C42×D3C2×D311yescharacteristic
317#870—32no—
318#869C2×D311yescharacteristic
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—34no—
324C4×Dic6—31no—
325C4×Dic6—34no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic
328C22×C3⋊D3C2412yes—
329C22×C3×D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C32×Q8—24no—
332C2×C32×C4C2414yes—
333C2×C32×C4C2411yescharacteristic
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2412yes—
339C4⋊(C3⋊D3)#4114yescomplemented
340C4×C3⋊D3—24no—
341C4×C3⋊D3—28no—
342#634—28no—
343#634#4114yescomplemented
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C2×C3×Dic3C2414yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2411yescharacteristic
351C3×D12—22no—
352C3×C4×D3—22no—
353C3×C4×D3—24no—
354C3×C4×D3—22no—
355C3×C4×D3—22no—
356C3×Dic6—24no—
357C3×Dic6—22no—
358#626—28no—
359#626—24no—
360#625—24no—
361#624—24no—
362#624—28no—
363#624—24no—
364D3×Dic3—24no—
365D3×Dic3—24no—
366#557—91no—
367#556—31no—
368#556—92no—
369#552—92no—
370#552—94no—
371D4×Q8—91no—
372#548—92no—
373#547—91no—
374#547—92no—
375#533—31no—
376#533—92no—
377#529—94no—
378#529—92no—
379C4×#41—91no—
380C4×#41—91no—
381C4×#41—92no—
382C2×C4×Q8—92no—
383C2×C3×Q8—22no—
384C2×C3×Q8—31no—
385C2×C3×Q8—32no—
386C2×C3×Q8C22×D312yes—
387C2×C3×Q8C22×D312yes—
388C2×C3×D4—31no—
389C22×C3×C4—32no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C2×#67—32no—
394C2×#67—32no—
395C2×#67—34no—
396C2×#67—32no—
397C22×Dic3—32no—
398C22×Dic3—32no—
399#239—64no—
400#239—68no—
401D3×Q8—68no—
402D3×Q8—68no—
403D3×Q8—128no—
404#237—64no—
405#235—68no—
406#235—64no—
407#235—64no—
408C2×D12—31no—
409C2×D12—31no—
410C2×D12—32no—
411C2×D12—34no—
412C2×D12—61no—
413C2×D12C22×D311yescharacteristic
414C2×C4×D3—32no—
415C2×C4×D3—32no—
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—34no—
419C2×C4×D3—34no—
420C2×C4×D3—32no—
421C2×C4×D3—32no—
422C2×C4×D3—34no—
423C2×C4×D3—32no—
424C2×C4×D3—32no—
425C2×C4×D3—34no—
426C2×C4×D3—62no—
427C2×C4×D3—64no—
428C2×C4×D3C22×D312yes—
429C2×C4×D3C22×D311yescharacteristic
430C2×C4×D3C22×D311yescharacteristic
431C2×C4×D3C22×D311yescharacteristic
432C2×Dic6—31no—
433C2×Dic6—31no—
434C2×Dic6—34no—
435C2×Dic6—34no—
436C2×Dic6—61no—
437C2×Dic6—64no—
438C2×Dic6C22×D311yescharacteristic
439C2×Dic6C22×D312yes—
440C3×C4⋊C4—22no—
441C3×C4⋊C4—22no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—34no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—34no—
447C3×C4⋊C4—32no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4C22×D312yes—
451C3×C4⋊C4C22×D312yes—
452C3×C4⋊C4C22×D312yes—
453C3×C4⋊C4C22×D312yes—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—32no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C42—21no—
459C3×C42—32no—
460C3×C42—31no—
461C3×C42—31no—
462C3×C42—34no—
463C3×C42—34no—
464C3×C42—31no—
465C3×C42C22×D311yescharacteristic
466C3×C42C22×D311yescharacteristic
467#217—34no—
468#217—32no—
469#217—32no—
470#217—32no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—32no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—32no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—32no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—62no—
482(C2×D3)⋊C4—64no—
483(C2×D3)⋊C4C22×D312yes—
484(C2×D3)⋊C4C22×D314yes—
485(C2×D3)⋊C4C22×D314yes—
486(C2×D3)⋊C4C22×D314yes—
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—31no—
491C4⋊Dic3—32no—
492C4⋊Dic3—34no—
493C4⋊Dic3—61no—
494C4⋊Dic3—61no—
495C4⋊Dic3C22×D312yes—
496C4⋊Dic3C22×D311yescharacteristic
497C4⋊Dic3C22×D314yes—
498C4⋊Dic3C22×D314yes—
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D312yes—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—32no—
506Dic3⋊C4—32no—
507Dic3⋊C4—32no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—62no—
516Dic3⋊C4—64no—
517Dic3⋊C4C22×D312yes—
518Dic3⋊C4C22×D314yes—
519C4×Dic3—32no—
520C4×Dic3—32no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—34no—
530C4×Dic3—32no—
531C4×Dic3—62no—
532C4×Dic3C22×D312yes—
533C4×Dic3C22×D311yescharacteristic
534C4×Dic3C22×D314yes—
535C4×Dic3C22×D314yes—
536C4×Dic3C22×D311yescharacteristic
537C4×Dic3C22×D311yescharacteristic
538C22×C32C2511yescharacteristic
539C2×C3⋊D3—22no—
540C2×C3⋊D3—22no—
541C2×C3⋊D3C2×#4114yes—
542C2×C3×D3—22no—
543C2×C3×D3—21no—
544C2×C3×D3—21no—
545C2×C3×D3—22no—
546C2×C3×D3—22no—
547C2×C3×D3—21no—
548C32×C4—24no—
549C32×C4—21no—
550C32×C4C2×#4112yes—
551C32×C4C2×#4112yes—
552C3⋊Dic3—22no—
553C3⋊Dic3—22no—
554C3⋊Dic3C2×#4114yes—
555C3×Dic3—21no—
556C3×Dic3—21no—
557C3×Dic3—22no—
558C3×Dic3—24no—
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic32−1+412yes—
562C2×#41—91no—
563C2×#41—91no—
564C2×#41—92no—
565C22×Q8—92no—
566C4⋊Q8—31no—
567C4⋊Q8—92no—
568C4⋊Q8—92no—
569C4⋊Q8D3211yescharacteristic
570#126—34no—
571#126—94no—
572#126—94no—
573#125—32no—
574#125—92no—
575#125—94no—
576#125—94no—
577#124—32no—
578#124—94no—
579#123—94no—
580#123—94no—
581#123—94no—
582C22⋊Q8—32no—
583C22⋊Q8—32no—
584C22⋊Q8—32no—
585C22⋊Q8—94no—
586C22⋊Q8—92no—
587C22⋊Q8—92no—
588C22⋊Q8—94no—
589#121—94no—
590#121—92no—
591C4×Q8—32no—
592C4×Q8—32no—
593C4×Q8—32no—
594C4×Q8—31no—
595C4×Q8—91no—
596C4×Q8—94no—
597C4×Q8—92no—
598C4×Q8—94no—
599C4×Q8—91no—
600C4×Q8—92no—
601C4×Q8—91no—
602C4×D4—31no—
603C4×D4—94no—
604C4×D4—91no—
605C4×D4—92no—
606C4×D4—91no—
607C4×D4—94no—
608C4×D4—92no—
609C4×D4—92no—
610C4×D4—92no—
611C4×D4—92no—
612C4×D4—91no—
613#117—32no—
614#117—32no—
615#117—92no—
616#117—94no—
617#117—92no—
618#117—94no—
619#117—91no—
620#117—91no—
621C2×C4⋊C4—92no—
622C2×C4⋊C4—94no—
623C2×C42—31no—
624C2×C42—92no—
625C2×C42—94no—
626C2×C42—92no—
627C23×C3—31no—
628C23×C3—32no—
629C22×D3—32no—
630C22×D3—32no—
631C22×D3—62no—
632C22×D3C23×D311yescharacteristic
633C22×D3C23×D312yes—
634C3×Q8—24no—
635C3×Q8—24no—
636C3×Q8—44no—
637C3×Q8—62no—
638C3×Q8—64no—
639C3×D4—62no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—24no—
644C2×C3×C4—31no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—31no—
648C2×C3×C4—31no—
649C2×C3×C4—32no—
650C2×C3×C4—34no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—64no—
654C2×C3×C4—62no—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D314yes—
657C2×C3×C4C23×D314yes—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663#67—64no—
664#67—68no—
665#67—64no—
666#67—64no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—64no—
677C2×Dic3—64no—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D311yescharacteristic
681C2×Dic3C23×D311yescharacteristic
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D314yes—
684C2×Dic3C23×D311yescharacteristic
685D12—22no—
686D12—34no—
687D12—34no—
688D12—64no—
689D12—68no—
690D12—64no—
691C4×D3—22no—
692C4×D3—22no—
693C4×D3—24no—
694C4×D3—22no—
695C4×D3—64no—
696C4×D3—64no—
697C4×D3—68no—
698C4×D3—68no—
699C4×D3—64no—
700C4×D3—68no—
701C4×D3—68no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—64no—
706C4×D3—64no—
707C4×D3—128no—
708C4×D3—124no—
709Dic6—24no—
710Dic6—22no—
711Dic6—34no—
712Dic6—34no—
713Dic6—64no—
714Dic6—68no—
715Dic6—68no—
716Dic6—128no—
717C2×C32C22×#4111yescharacteristic
718C2×C32C22×#4111yescharacteristic
719C2×C32C2×2−1+411yescharacteristic
720C3⋊D3—24no—
721C3×D3—41no—
722C3×D3—42no—
723#41—184no—
724#41—184no—
725#41—188no—
726C2×Q8—31no—
727C2×Q8—32no—
728C2×Q8—91no—
729C2×Q8—94no—
730C2×Q8—188no—
731C2×Q8C2×D3212yes—
732C2×D4—31no—
733C2×D4—92no—
734C2×D4—94no—
735C2×D4—92no—
736C2×D4—91no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—32no—
741C22×C4—92no—
742C22×C4—94no—
743C22×C4—92no—
744C22×C4—92no—
745C22×C4—92no—
746C22×C4—94no—
747C22×C4—92no—
748C4⋊C4—31no—
749C4⋊C4—32no—
750C4⋊C4—34no—
751C4⋊C4—34no—
752C4⋊C4—31no—
753C4⋊C4—32no—
754C4⋊C4—34no—
755C4⋊C4—32no—
756C4⋊C4—92no—
757C4⋊C4—94no—
758C4⋊C4—94no—
759C4⋊C4—92no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4—92no—
763C4⋊C4—91no—
764C4⋊C4—91no—
765C4⋊C4—94no—
766C4⋊C4C2×D3212yes—
767C4⋊C4C2×D3212yes—
768C22⋊C4—34no—
769C22⋊C4—34no—
770C22⋊C4—32no—
771C22⋊C4—34no—
772C22⋊C4—92no—
773C22⋊C4—92no—
774C22⋊C4—92no—
775C22⋊C4—92no—
776C22⋊C4—94no—
777C22⋊C4—94no—
778C22⋊C4—92no—
779C42—31no—
780C42—31no—
781C42—31no—
782C42—34no—
783C42—34no—
784C42—32no—
785C42—92no—
786C42—92no—
787C42—92no—
788C42—92no—
789C42—94no—
790C42—92no—
791C42C2×D3211yescharacteristic
792C22×C3—21no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—61no—
796C22×C3—62no—
797C22×C3—61no—
798C22×C3—61no—
799C22×C3C24×D311yescharacteristic
800C22×C3C24×D311yescharacteristic
801C2×D3—21no—
802C2×D3—21no—
803C2×D3—22no—
804C2×D3—21no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—34no—
808C2×D3—34no—
809C2×D3—64no—
810C2×D3—62no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—122no—
815C2×D3—122no—
816C3×C4—21no—
817C3×C4—24no—
818C3×C4—24no—
819C3×C4—21no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—32no—
823C3×C4—44no—
824C3×C4—41no—
825C3×C4—62no—
826C3×C4—61no—
827C3×C4—62no—
828C3×C4—61no—
829C3×C4—62no—
830C3×C4—64no—
831C3×C4D3×#4112yes—
832C3×C4D3×#4112yes—
833C3×C4D3×#4112yes—
834C3×C4D3×#4112yes—
835Dic3—24no—
836Dic3—22no—
837Dic3—21no—
838Dic3—22no—
839Dic3—21no—
840Dic3—22no—
841Dic3—34no—
842Dic3—34no—
843Dic3—64no—
844Dic3—62no—
845Dic3—62no—
846Dic3—62no—
847Dic3—62no—
848Dic3—122no—
849Dic3—122no—
850Dic3#100712yes—
851C32#348211yescharacteristic, complemented, Sylow
852C23—32no—
853C23—31no—
854C23—92no—
855Q8—24no—
856Q8—62no—
857Q8—64no—
858Q8—94no—
859Q8—188no—
860D4—62no—
861D4—94no—
862D4—184no—
863D4—188no—
864D4—184no—
865C2×C4—31no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—31no—
869C2×C4—31no—
870C2×C4—32no—
871C2×C4—34no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—64no—
876C2×C4—92no—
877C2×C4—92no—
878C2×C4—92no—
879C2×C4—188no—
880C2×C4—184no—
881C2×C4—184no—
882C2×C4—188no—
883C2×C4—184no—
884C2×C4—184no—
885C2×C4—184no—
886C2×C4C22×D3214yes—
887C2×C4C22×D3211yescharacteristic
888C2×C4C22×D3211yescharacteristic
889C2×C4C22×D3211yescharacteristic
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—122no—
894C2×C3—121no—
895C2×C3C2×#100711yescharacteristic
896C2×C3C2×D3×#4111yescharacteristic
897C2×C3C2×D3×#4111yescharacteristic
898C2×C3C2×D3×#4111yescharacteristic
899C2×C3C2×D3×#4111yescharacteristic
900C2×C3D3×2−1+411yescharacteristic
901D3—41no—
902D3—42no—
903D3—64no—
904D3—64no—
905D3—124no—
906C22—61no—
907C22—62no—
908C22—62no—
909C22—61no—
910C22—61no—
911C22—62no—
912C22—94no—
913C22—182no—
914C22—182no—
915C22C23×D3211yescharacteristic
916C4—24no—
917C4—21no—
918C4—32no—
919C4—61no—
920C4—62no—
921C4—61no—
922C4—62no—
923C4—64no—
924C4—62no—
925C4—94no—
926C4—182no—
927C4—182no—
928C4#6431212yes—
929C4#6431912yes—
930C3—21no—
931C3#8627811yescharacteristic, complemented
932C3#8698111yescharacteristic, complemented
933C2—121no—
934C2—122no—
935C2—184no—
936C2C2×#6431211yescharacteristic
937C2C2×#6431911yescharacteristic
938C2D3×#100711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596198C2semidirect
2. C3×#5732C2semidirect
3. C3×#5728C2semidirect
4. #10595382C2semidirect
5. Q8×#624C2semidirect
6. #10595362C2semidirect
7. #10595344C2semidirect
8. #10594576C2semidirect
9. #10594530C2semidirect
10. #10594478C2semidirect
11. #10594417C2semidirect
12. #10594385C2semidirect
13. #10594362C2semidirect
14. C4×#3799C2semidirect
15. C4×#3795C2semidirect
16. #10593869C2semidirect
17. #10593864C2semidirect
87. #5732D3semidirect
88. #5728D3semidirect
339. C4⋊(C3⋊D3)#41semidirect
343. #634#41semidirect
851. C32#3482semidirect
931. C3#86278semidirect
932. C3#86981semidirect

Maximal subgroups

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

subgroupindex
#105961982
C3×#57322
C3×#57282
#105953822
Q8×#6242
#105953622
#105953442
#105945762
#105945302
#105944782
#105944172
#105943852
#105943622
C4×#37992
C4×#37952
#105938692
#105938642
#869813
#862783