Finite Group Databasebeta

← #11909922

Subgroups — #11909922

Order 1152.

2084 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2C3×#5732C211yesmaximal, characteristic, complemented
3C3×#5728C211yesmaximal, characteristic, complemented
4#10595389C212yesmaximal, complemented
5#10595377C212yesmaximal
6#10595367C212yesmaximal, complemented
7#10595351C212yesmaximal, complemented
8#10594526C212yesmaximal, complemented
9#10594488C214yesmaximal, complemented
10#10594456C212yesmaximal, complemented
11#10594409C214yesmaximal, complemented
12#10594357C212yesmaximal, complemented
13#10594345C212yesmaximal, complemented
14#10593974C211yesmaximal, characteristic
15#10593904C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593864C211yesmaximal, characteristic, complemented
18#86993—31nomaximal
19#86266—31nomaximal
20C2×D3×Dic6C2212yes—
21C2×D3×Dic6C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2212yes—
24#64153C2212yes—
25#64099C2212yes—
26#64098C2214yes—
27#64096C2212yes—
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C3×#947C2212yes—
31C3×#946C2212yes—
32C3×Q8×Dic3C2212yes—
33C3×Q8×Dic3C2212yes—
34C3×#898C2214yes—
35C3×#897C2212yes—
36C3×#897C2212yes—
37C3×#892C2212yes—
38C3×#892C2212yes—
39C3×#890C2212yes—
40C3×#887C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63919C2212yes—
46#63919C2214yes—
47C4×#627C2214yes—
48C4×#627C2212yes—
49#63908C2211yescharacteristic
50#63905C2212yes—
51#63902C2214yes—
52C4×#625C2212yes—
53#63899C2214yes—
54#63899C2214yes—
55#63899C2214yes—
56#63898C2212yes—
57#63891C2214yes—
58D3×C4⋊Dic3C2211yescharacteristic
59#63878C2214yes—
60#63877C2214yes—
61#63877C2214yes—
62D3×Dic3⋊C4C2212yes—
63C4×D3×Dic3C2212yes—
64#63873C2212yes—
65#63869C2211yescharacteristic
66#63869C2214yes—
67#63869C2212yes—
68#63869C2214yes—
69#63861C2214yes—
70#63860C2211yescharacteristic
71#63859C2214yes—
72#63859C2212yes—
73#63858C2214yes—
74#63857C2211yescharacteristic
75#63856C2212yes—
76#63855C2212yes—
77#63847C2214yes—
78#63847C2214yes—
79#63844C2212yes—
80#63844C2211yescharacteristic
81#63843C2212yes—
82Dic3×Dic6C2211yescharacteristic
83#63837C2214yes—
84#63837C2212yes—
85C3×#556—31no—
86C3×#533—31no—
87#5732D311yescharacteristic, complemented
88#5728D311yescharacteristic, complemented
89#5727—31no—
90#5721—31no—
91#5721—31no—
92#5721—31no—
93#5721—61no—
94#5708—34no—
95#5701—34no—
96#5696—34no—
97#5680—32no—
98#5671—32no—
99#5642—32no—
100#5632—32no—
101#5632—32no—
102#5625—32no—
103#5624—32no—
104#5622—32no—
105#5583—32no—
106#5578—32no—
107#5572—32no—
108C4×D3×Q8—31no—
109#5569—32no—
110#5569—32no—
111#5568—32no—
112#5567—31no—
113#5557—31no—
114D4×Dic6—31no—
115#5531—34no—
116#5529—32no—
117#5516—32no—
118#5479—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2311yescharacteristic
122C2×#634C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2311yescharacteristic
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2311yescharacteristic
130C2×#627C2314yes—
131C2×#627C2312yes—
132C2×#625C2312yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2314yes—
135C2×D3×Dic3C2312yes—
136D3×Dic6—28no—
137D3×Dic6—24no—
138C32×C4⋊C4C2312yes—
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2314yes—
144#3750C2312yes—
145#3750C2312yes—
146#3750C2314yes—
147#3750C2314yes—
148C4×C3⋊Dic3C2312yes—
149C4×C3⋊Dic3C2312yes—
150C4×C3⋊Dic3C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2314yes—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×C4⋊Dic3C2314yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2312yes—
163C3×C4×Dic3C2311yescharacteristic
164C3×C4×Dic3C2314yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2314yes—
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2312yes—
169#3724C2314yes—
170#3724C2312yes—
171#3724C2314yes—
172#3724C2314yes—
173#3724C2312yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179(C2×D3)⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187#3523—91noSylow
188C2×D3×Q8—31no—
189C2×D3×Q8—32no—
190C22×Dic6—31no—
191C22×Dic6—32no—
192C3×C4⋊Q8—21no—
193C3×C4⋊Q8—31no—
194C3×C4⋊Q8C2×D311yescharacteristic
195C3×C4⋊Q8C2×D311yescharacteristic
196C3×#126—34no—
197C3×#125—32no—
198C3×#124—32no—
199C3×C22⋊Q8—32no—
200C3×C22⋊Q8—32no—
201C3×C22⋊Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—32no—
204C3×C4×Q8—32no—
205C3×C4×Q8—31no—
206C3×C4×D4—31no—
207C3×#117—32no—
208C3×#117—32no—
209C2×C3×C42—31no—
210#947C2×D312yes—
211#946—32no—
212#946C2×D312yes—
213Q8×Dic3—32no—
214Q8×Dic3—32no—
215Q8×Dic3—32no—
216Q8×Dic3—31no—
217Q8×Dic3—62no—
218Q8×Dic3C2×D312yes—
219Q8×Dic3C2×D312yes—
220#944—32no—
221#944—32no—
222#944—32no—
223#944—32no—
224#944—62no—
225#938—31no—
226#936—31no—
227D4×Dic3—32no—
228#930—31no—
229#929—32no—
230C4×#67—32no—
231C4×#67—32no—
232#926—32no—
233C2×C4⋊Dic3—31no—
234#924—32no—
235#924—31no—
236C2×Dic3⋊C4—32no—
237C2×C4×Dic3—32no—
238#898—34no—
239#898—34no—
240#898C2×D314yes—
241#897—31no—
242#897C2×D312yes—
243#897C2×D312yes—
244#896—34no—
245#896—34no—
246#896—34no—
247#893—32no—
248#892—34no—
249#892C2×D312yes—
250#892C2×D312yes—
251D3×C4⋊C4—32no—
252D3×C4⋊C4—31no—
253#890—32no—
254#890—32no—
255#890—34no—
256#890—34no—
257#890—32no—
258#890—31no—
259#890—62no—
260#890C2×D312yes—
261#889—34no—
262#889—34no—
263#889—34no—
264#889—34no—
265#889—34no—
266#889—34no—
267#889—64no—
268#888—34no—
269#888—34no—
270#888—32no—
271#888—32no—
272#887—32no—
273#887—32no—
274#887—32no—
275#887—34no—
276#887—32no—
277#887—32no—
278#887—31no—
279#887—62no—
280#887C2×D312yes—
281#886—34no—
282#883—32no—
283#883—34no—
284#67⋊C4—34no—
285#67⋊C4—34no—
286#879—34no—
287#879—34no—
288#879—34no—
289#879—32no—
290#878—34no—
291#878—34no—
292#878—34no—
293#877—34no—
294#877—34no—
295#877—34no—
296#876—32no—
297#876—34no—
298#875—31no—
299C4×D12C2×D311yescharacteristic
300#872—32no—
301#872—34no—
302#872—34no—
303C42×D3—32no—
304C42×D3C2×D311yescharacteristic
305#870—32no—
306#870—34no—
307#870—31no—
308#870—34no—
309#869C2×D311yescharacteristic
310C4×Dic6—31no—
311C4×Dic6—31no—
312C4×Dic6—31no—
313C4×Dic6—31no—
314C4×Dic6—31no—
315C4×Dic6—32no—
316C4×Dic6—31no—
317C4×Dic6—32no—
318C4×Dic6—34no—
319C4×Dic6—32no—
320C4×Dic6—34no—
321C4×Dic6—32no—
322C4×Dic6—34no—
323C4×Dic6—61no—
324C4×Dic6—61no—
325C4×Dic6C2×D311yescharacteristic
326C22×C3×D3C2412yes—
327C22×C3×D3C2411yescharacteristic
328C32×Q8—24no—
329C2×C32×C4C2414yes—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337#634—22no—
338#634#4114yes—
339C2×C3×Dic3C2411yescharacteristic
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2414yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C3×D12—22no—
347C3×C4×D3—22no—
348C3×C4×D3—22no—
349C3×C4×D3—24no—
350C3×C4×D3—22no—
351C3×Dic6—24no—
352C3×Dic6—22no—
353#627—24no—
354#627—28no—
355#625—24no—
356D3×Dic3—24no—
357D3×Dic3—24no—
358D3×Dic3—28no—
359#557—92no—
360#557—91no—
361#557—91no—
362#556—31no—
363#556—92no—
364#552—92no—
365#552—94no—
366D4×Q8—91no—
367D4×Q8—92no—
368#541—92no—
369#541—94no—
370#533—31no—
371#533—92no—
372#529—91no—
373#529—92no—
374#519—92no—
375C2×C4×Q8—91no—
376C2×C3×Q8—22no—
377C2×C3×Q8—31no—
378C2×C3×Q8—32no—
379C2×C3×Q8C22×D312yes—
380C2×C3×Q8C22×D312yes—
381C2×C3×D4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—32no—
385C22×C3×C4—31no—
386C2×#67—32no—
387C2×#67—32no—
388C22×Dic3—34no—
389C22×Dic3—32no—
390C22×Dic3—32no—
391D3×Q8—64no—
392D3×Q8—68no—
393C2×D12C22×D311yescharacteristic
394C2×C4×D3—32no—
395C2×C4×D3—32no—
396C2×C4×D3—34no—
397C2×C4×D3C22×D311yescharacteristic
398C2×C4×D3C22×D311yescharacteristic
399C2×C4×D3C22×D311yescharacteristic
400C2×C4×D3C22×D312yes—
401C2×Dic6—31no—
402C2×Dic6—31no—
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—34no—
406C2×Dic6—32no—
407C2×Dic6—32no—
408C2×Dic6—34no—
409C2×Dic6—61no—
410C2×Dic6—61no—
411C2×Dic6—68no—
412C2×Dic6—64no—
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D312yes—
415C3×C4⋊C4—22no—
416C3×C4⋊C4—22no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—32no—
419C3×C4⋊C4—32no—
420C3×C4⋊C4—34no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4—34no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4C22×D312yes—
426C3×C4⋊C4C22×D312yes—
427C3×C4⋊C4C22×D312yes—
428C3×C4⋊C4C22×D312yes—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—32no—
432C3×C22⋊C4—34no—
433C3×C42—21no—
434C3×C42—32no—
435C3×C42—34no—
436C3×C42—31no—
437C3×C42—31no—
438C3×C42—31no—
439C3×C42—34no—
440C3×C42C22×D311yescharacteristic
441C3×C42C22×D311yescharacteristic
442#217—32no—
443#217—32no—
444#217—32no—
445#217—32no—
446#217—34no—
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—32no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—32no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4C22×D314yes—
453(C2×D3)⋊C4C22×D314yes—
454(C2×D3)⋊C4C22×D312yes—
455(C2×D3)⋊C4C22×D314yes—
456C4⋊Dic3—31no—
457C4⋊Dic3—31no—
458C4⋊Dic3—31no—
459C4⋊Dic3—31no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—32no—
463C4⋊Dic3—32no—
464C4⋊Dic3—32no—
465C4⋊Dic3—32no—
466C4⋊Dic3—34no—
467C4⋊Dic3—61no—
468C4⋊Dic3—61no—
469C4⋊Dic3—64no—
470C4⋊Dic3C22×D311yescharacteristic
471C4⋊Dic3C22×D312yes—
472C4⋊Dic3C22×D312yes—
473C4⋊Dic3C22×D311yescharacteristic
474C4⋊Dic3C22×D314yes—
475C4⋊Dic3C22×D314yes—
476Dic3⋊C4—32no—
477Dic3⋊C4—32no—
478Dic3⋊C4—34no—
479Dic3⋊C4—32no—
480Dic3⋊C4—32no—
481Dic3⋊C4—34no—
482Dic3⋊C4—34no—
483Dic3⋊C4—34no—
484Dic3⋊C4—32no—
485Dic3⋊C4—32no—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—34no—
489Dic3⋊C4—32no—
490Dic3⋊C4—34no—
491Dic3⋊C4—32no—
492Dic3⋊C4—34no—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—32no—
498Dic3⋊C4—34no—
499Dic3⋊C4—62no—
500Dic3⋊C4—62no—
501Dic3⋊C4—64no—
502Dic3⋊C4—64no—
503Dic3⋊C4C22×D312yes—
504Dic3⋊C4C22×D314yes—
505C4×Dic3—32no—
506C4×Dic3—32no—
507C4×Dic3—32no—
508C4×Dic3—34no—
509C4×Dic3—34no—
510C4×Dic3—32no—
511C4×Dic3—32no—
512C4×Dic3—34no—
513C4×Dic3—32no—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—34no—
517C4×Dic3—62no—
518C4×Dic3—62no—
519C4×Dic3—64no—
520C4×Dic3C22×D311yescharacteristic
521C4×Dic3C22×D312yes—
522C4×Dic3C22×D314yes—
523C4×Dic3C22×D314yes—
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D311yescharacteristic
526C22×C32C2511yescharacteristic
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D32−1+412yes—
533C32×C4—21no—
534C32×C4—24no—
535C32×C4C2×#4112yes—
536C32×C42−1+412yes—
537C3⋊Dic3—22no—
538C3⋊Dic3—22no—
539C3⋊Dic3—22no—
540C3⋊Dic3C2×#4114yes—
541C3×Dic3—24no—
542C3×Dic3—22no—
543C3×Dic3—21no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—21no—
547C3×Dic3—21no—
548C22×Q8—91no—
549C22×Q8—92no—
550C4⋊Q8—31no—
551C4⋊Q8—92no—
552C4⋊Q8—94no—
553C4⋊Q8—92no—
554C4⋊Q8—92no—
555C4⋊Q8D3211yescharacteristic
556#126—34no—
557#126—92no—
558#126—94no—
559#126—94no—
560#126—94no—
561#125—32no—
562#125—91no—
563#125—92no—
564#125—94no—
565#125—94no—
566#125—94no—
567#125—94no—
568#125—94no—
569#125—92no—
570#124—32no—
571#124—91no—
572#123—94no—
573#123—92no—
574C22⋊Q8—32no—
575C22⋊Q8—32no—
576C22⋊Q8—32no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—91no—
581C22⋊Q8—92no—
582#121—91no—
583C4×Q8—32no—
584C4×Q8—32no—
585C4×Q8—32no—
586C4×Q8—31no—
587C4×Q8—92no—
588C4×Q8—94no—
589C4×Q8—91no—
590C4×Q8—92no—
591C4×Q8—94no—
592C4×Q8—92no—
593C4×Q8—91no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—91no—
598C4×Q8—91no—
599C4×D4—31no—
600C4×D4—94no—
601C4×D4—92no—
602C4×D4—92no—
603#117—32no—
604#117—32no—
605#117—94no—
606#117—94no—
607#117—92no—
608#117—94no—
609C2×C4⋊C4—92no—
610C2×C4⋊C4—91no—
611C2×C42—31no—
612C2×C42—92no—
613C23×C3—31no—
614C23×C3—32no—
615C22×D3C23×D312yes—
616C22×D3C23×D311yescharacteristic
617C3×Q8—24no—
618C3×Q8—24no—
619C3×Q8—44no—
620C3×Q8—62no—
621C3×Q8—64no—
622C3×D4—62no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—24no—
626C2×C3×C4—21no—
627C2×C3×C4—31no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—34no—
631C2×C3×C4—31no—
632C2×C3×C4—32no—
633C2×C3×C4—31no—
634C2×C3×C4—62no—
635C2×C3×C4—64no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4C23×D314yes—
639C2×C3×C4C23×D314yes—
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D311yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646#67—64no—
647#67—64no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—64no—
661C2×Dic3—68no—
662C2×Dic3—64no—
663C2×Dic3C23×D311yescharacteristic
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D314yes—
667C2×Dic3C23×D311yescharacteristic
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D311yescharacteristic
670D12—22no—
671C4×D3—22no—
672C4×D3—22no—
673C4×D3—24no—
674C4×D3—22no—
675C4×D3—68no—
676C4×D3—64no—
677C4×D3—64no—
678Dic6—24no—
679Dic6—22no—
680Dic6—34no—
681Dic6—34no—
682Dic6—64no—
683Dic6—64no—
684Dic6—68no—
685Dic6—68no—
686Dic6—64no—
687Dic6—62no—
688Dic6—62no—
689Dic6—122no—
690C2×C32C22×#4111yescharacteristic
691C2×C32C2×2−1+411yescharacteristic
692C2×C32C2×2−1+411yescharacteristic
693C3×D3—22no—
694C3×D3—42no—
695C2×Q8—31no—
696C2×Q8—32no—
697C2×Q8—94no—
698C2×Q8—92no—
699C2×Q8—91no—
700C2×Q8—91no—
701C2×Q8—184no—
702C2×Q8—188no—
703C2×Q8C2×D3212yes—
704C2×D4—31no—
705C2×D4—92no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—32no—
710C22×C4—92no—
711C22×C4—92no—
712C22×C4—94no—
713C4⋊C4—31no—
714C4⋊C4—32no—
715C4⋊C4—32no—
716C4⋊C4—34no—
717C4⋊C4—31no—
718C4⋊C4—32no—
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—92no—
722C4⋊C4—92no—
723C4⋊C4—92no—
724C4⋊C4—92no—
725C4⋊C4—92no—
726C4⋊C4—94no—
727C4⋊C4—94no—
728C4⋊C4—92no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—92no—
732C4⋊C4—91no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—91no—
736C4⋊C4—92no—
737C4⋊C4—94no—
738C4⋊C4C2×D3212yes—
739C4⋊C4C2×D3212yes—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—32no—
743C22⋊C4—34no—
744C22⋊C4—92no—
745C22⋊C4—92no—
746C22⋊C4—92no—
747C22⋊C4—94no—
748C22⋊C4—92no—
749C42—31no—
750C42—31no—
751C42—31no—
752C42—32no—
753C42—34no—
754C42—34no—
755C42—92no—
756C42—92no—
757C42—94no—
758C42—92no—
759C42—94no—
760C42—92no—
761C42C2×D3211yescharacteristic
762C22×C3—21no—
763C22×C3—32no—
764C22×C3—61no—
765C22×C3—61no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3C24×D311yescharacteristic
770C22×C3C24×D311yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3#100712yes—
777C3×C4—21no—
778C3×C4—24no—
779C3×C4—24no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—44no—
784C3×C4—41no—
785C3×C4—62no—
786C3×C4—61no—
787C3×C4—62no—
788C3×C4—64no—
789C3×C4—62no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4D3×#4112yes—
793C3×C4D3×#4112yes—
794C3×C4#101012yes—
795C3×C4#101012yes—
796Dic3—21no—
797Dic3—22no—
798Dic3—24no—
799Dic3—22no—
800Dic3—21no—
801Dic3—21no—
802Dic3—22no—
803Dic3—34no—
804Dic3—34no—
805Dic3—64no—
806Dic3—62no—
807Dic3—62no—
808Dic3—62no—
809Dic3—62no—
810Dic3—62no—
811Dic3—62no—
812Dic3—122no—
813Dic3—122no—
814Dic3—122no—
815C32#352311yescharacteristic, complemented, Sylow
816C23—31no—
817C23—32no—
818Q8—24no—
819Q8—62no—
820Q8—64no—
821Q8—94no—
822Q8—188no—
823Q8—184no—
824Q8—182no—
825D4—62no—
826D4—184no—
827C2×C4—31no—
828C2×C4—32no—
829C2×C4—31no—
830C2×C4—32no—
831C2×C4—31no—
832C2×C4—32no—
833C2×C4—34no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—64no—
838C2×C4—92no—
839C2×C4—92no—
840C2×C4—92no—
841C2×C4—92no—
842C2×C4—184no—
843C2×C4—188no—
844C2×C4—184no—
845C2×C4C22×D3214yes—
846C2×C4C22×D3211yescharacteristic
847C2×C4C22×D3211yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—62no—
853C2×C3—122no—
854C2×C3C2×#100711yescharacteristic
855C2×C3C2×D3×#4111yescharacteristic
856C2×C3C2×D3×#4111yescharacteristic
857C2×C3C2×#101011yescharacteristic
858C2×C3C2×#101011yescharacteristic
859C2×C3D3×2−1+411yescharacteristic
860D3—22no—
861D3—42no—
862C22—32no—
863C22—61no—
864C22—61no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22C23×D3211yescharacteristic
869C4—24no—
870C4—21no—
871C4—61no—
872C4—62no—
873C4—61no—
874C4—62no—
875C4—64no—
876C4—61no—
877C4—62no—
878C4—94no—
879C4—182no—
880C4—182no—
881C4—182no—
882C4#6430912yes—
883C4#6431912yes—
884C3—21no—
885C3#8626611yescharacteristic, complemented
886C3#8699311yescharacteristic, complemented
887C2—62no—
888C2—122no—
889C2C2×#6430911yescharacteristic
890C2C2×#6431911yescharacteristic
891C2D3×#100711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radical#63908C22
hypercenterC4⋊Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596192C2semidirect
2. C3×#5732C2semidirect
3. C3×#5728C2semidirect
4. #10595389C2semidirect
6. #10595367C2semidirect
7. #10595351C2semidirect
8. #10594526C2semidirect
9. #10594488C2semidirect
10. #10594456C2semidirect
11. #10594409C2semidirect
12. #10594357C2semidirect
13. #10594345C2semidirect
15. #10593904C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593864C2semidirect
87. #5732D3semidirect
88. #5728D3semidirect
815. C32#3523semidirect
885. C3#86266semidirect
886. C3#86993semidirect

Maximal subgroups

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

subgroupindex
#105961922
C3×#57322
C3×#57282
#105953892
#105953772
#105953672
#105953512
#105945262
#105944882
#105944562
#105944092
#105943572
#105943452
#105939742
#105939042
C4×D3×Dic62
#105938642
#869933
#862663