Finite Group Databasebeta

← #11906269

Subgroups — #11906269

Order 1152.

2028 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic
3C3×#5721C211yesmaximal, characteristic, complemented
4#10595420C212yesmaximal, complemented
5Q8×#627C212yesmaximal, complemented
6#10595368C212yesmaximal
7#10595367C212yesmaximal
8#10594596C214yesmaximal, complemented
9#10594505C212yesmaximal
10#10594389C214yesmaximal
11#10594357C212yesmaximal
12#10594324C212yesmaximal, complemented
13#10594321C212yesmaximal, complemented
14C4×D3×Dic6C211yesmaximal, characteristic
15#10593873C211yesmaximal, characteristic
16#10593856C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#87031—31nomaximal
19#86258—31nomaximal
20C2×D3×Dic6C2211yescharacteristic
21C32×C4⋊Q8C2211yescharacteristic
22Q8×C3⋊Dic3C2212yes—
23#64153C2212yes—
24#64099C2212yes—
25#64098C2214yes—
26#64096C2212yes—
27C4×#634C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C3×#946C2212yes—
30C3×Q8×Dic3C2212yes—
31C3×Q8×Dic3C2212yes—
32C3×#944C2212yes—
33C3×#897C2212yes—
34C3×#892C2212yes—
35C3×#890C2212yes—
36C3×#890C2212yes—
37C3×#889C2214yes—
38C3×#887C2212yes—
39C3×#887C2212yes—
40C3×C42×D3C2211yescharacteristic
41C3×#869C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44#63919C2212yes—
45#63919C2214yes—
46#63919C2212yes—
47#63918C2212yes—
48#63918C2214yes—
49#63918C2214yes—
50#63918C2212yes—
51#63918C2211yescharacteristic
52C4×#627C2212yes—
53C4×#627C2214yes—
54C4×#627C2212yes—
55#63899C2214yes—
56#63893C2214yes—
57D3×C4⋊Dic3C2211yescharacteristic
58#63878C2214yes—
59#63877C2214yes—
60D3×Dic3⋊C4C2212yes—
61C4×D3×Dic3C2212yes—
62#63867C2212yes—
63#63867C2214yes—
64#63866C2211yescharacteristic
65#63857C2211yescharacteristic
66#63856C2211yescharacteristic
67#63855C2212yes—
68#63851C2212yes—
69#63847C2214yes—
70#63847C2214yes—
71#63846C2214yes—
72#63845C2214yes—
73#63844C2211yescharacteristic
74#63844C2212yes—
75#63844C2212yes—
76#63843C2212yes—
77#63843C2212yes—
78Dic3×Dic6C2211yescharacteristic
79#63839C2214yes—
80#63839C2214yes—
81#63838C2214yes—
82#63837C2214yes—
83#63837C2212yes—
84#63837C2214yes—
85C3×#557—31no—
86C3×#533—31no—
87#5728—32no—
88#5728D311yescharacteristic
89#5722—31no—
90#5722—31no—
91#5721—31no—
92#5721—31no—
93#5721—32no—
94#5721—61no—
95#5721D311yescharacteristic, complemented
96#5689—34no—
97#5689—32no—
98#5685—32no—
99#5685—32no—
100#5685—32no—
101#5685—34no—
102#5623—34no—
103#5622—32no—
104#5622—32no—
105#5578—32no—
106#5578—31no—
107#5572—32no—
108C4×D3×Q8—31no—
109#5570—32no—
110#5567—32no—
111#5567—34no—
112Q8×Dic6—32no—
113Q8×Dic6—32no—
114Q8×Dic6—31no—
115Q8×Dic6—31no—
116#5519—32no—
117#5516—32no—
118#5470—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2311yescharacteristic
122C2×#634C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×Dic6C2311yescharacteristic
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×#627C2314yes—
130C2×#627C2314yes—
131C2×#627C2312yes—
132C2×#627C2312yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2312yes—
135D3×Dic6Q818yescomplemented
136C32×C4⋊C4C2312yes—
137C32×C4⋊C4C2312yes—
138C32×C42C2311yescharacteristic
139C4⋊(C3⋊Dic3)C2311yescharacteristic
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2314yes—
142#3750C2312yes—
143#3750C2312yes—
144#3750C2314yes—
145#3750C2314yes—
146C4×C3⋊Dic3C2312yes—
147C4×C3⋊Dic3C2312yes—
148C4×C3⋊Dic3C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×C4⋊Dic3C2314yes—
151C3×C4⋊Dic3C2311yescharacteristic
152C3×C4⋊Dic3C2312yes—
153C3×C4⋊Dic3C2314yes—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×C4⋊Dic3C2312yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2312yes—
159C3×Dic3⋊C4C2312yes—
160C3×Dic3⋊C4C2314yes—
161C3×C4×Dic3C2311yescharacteristic
162C3×C4×Dic3C2314yes—
163C3×C4×Dic3C2312yes—
164C3×C4×Dic3C2314yes—
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2312yes—
167C3×C4×Dic3C2311yescharacteristic
168#3724C2312yes—
169#3724C2314yes—
170#3724C2314yes—
171#3724C2312yes—
172Dic3⋊Dic3C2312yes—
173Dic3⋊Dic3C2312yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182Dic32C2312yes—
183Dic32C2314yes—
184Dic32C2312yes—
185Dic32C2314yes—
186#3502—91noSylow
187C2×D3×Q8—31no—
188C22×Dic6—31no—
189C3×C4⋊Q8—21no—
190C3×C4⋊Q8—32no—
191C3×C4⋊Q8—31no—
192C3×C4⋊Q8C2×D311yescharacteristic
193C3×C4⋊Q8C2×D311yescharacteristic
194C3×#125—34no—
195C3×#125—32no—
196C3×#125—32no—
197C3×C22⋊Q8—32no—
198C3×C22⋊Q8—32no—
199C3×C4×Q8—32no—
200C3×C4×Q8—32no—
201C3×C4×Q8—32no—
202C3×C4×Q8—32no—
203C3×C4×Q8—31no—
204C3×C4×Q8—31no—
205C3×#117—32no—
206C2×C3×C42—31no—
207#946—31no—
208#946C2×D312yes—
209Q8×Dic3—32no—
210Q8×Dic3—32no—
211Q8×Dic3—32no—
212Q8×Dic3—32no—
213Q8×Dic3—31no—
214Q8×Dic3—62no—
215Q8×Dic3C2×D312yes—
216Q8×Dic3C2×D312yes—
217#944—32no—
218#944—32no—
219#944—34no—
220#944—34no—
221#944—31no—
222#944—62no—
223#944C2×D312yes—
224#926—32no—
225C2×C4⋊Dic3—31no—
226#924—31no—
227#924—31no—
228#924—32no—
229C2×Dic3⋊C4—32no—
230C2×C4×Dic3—32no—
231#897—31no—
232#897—34no—
233#897C2×D312yes—
234#896—32no—
235#896—34no—
236#892—34no—
237#892C2×D312yes—
238D3×C4⋊C4—32no—
239D3×C4⋊C4—31no—
240#890—32no—
241#890—32no—
242#890—34no—
243#890—34no—
244#890—62no—
245#890C2×D312yes—
246#890C2×D312yes—
247#889—34no—
248#889—34no—
249#889—34no—
250#889—34no—
251#889—34no—
252#889—34no—
253#889—34no—
254#889—34no—
255#889—32no—
256#889—34no—
257#889—64no—
258#889C2×D314yes—
259#888—34no—
260#888—34no—
261#888—32no—
262#888—34no—
263#888—32no—
264#888—34no—
265#888—32no—
266#888—32no—
267#888—34no—
268#888—32no—
269#888—34no—
270#888—32no—
271#888—31no—
272#887—32no—
273#887—32no—
274#887—32no—
275#887—32no—
276#887—34no—
277#887—34no—
278#887—32no—
279#887—31no—
280#887—34no—
281#887—32no—
282#887—34no—
283#887—32no—
284#887—62no—
285#887C2×D312yes—
286#887C2×D312yes—
287#878—34no—
288#878—34no—
289#877—34no—
290#877—34no—
291#872—32no—
292#872—34no—
293C42×D3—32no—
294C42×D3C2×D311yescharacteristic
295#870—32no—
296#870—34no—
297#869—31no—
298#869—32no—
299#869—34no—
300#869—31no—
301#869—32no—
302#869—34no—
303#869C2×D311yescharacteristic
304C4×Dic6—31no—
305C4×Dic6—31no—
306C4×Dic6—31no—
307C4×Dic6—31no—
308C4×Dic6—31no—
309C4×Dic6—31no—
310C4×Dic6—32no—
311C4×Dic6—32no—
312C4×Dic6—34no—
313C4×Dic6—32no—
314C4×Dic6—34no—
315C4×Dic6—32no—
316C4×Dic6—34no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—32no—
320C4×Dic6—34no—
321C4×Dic6—61no—
322C4×Dic6—61no—
323C4×Dic6C2×D311yescharacteristic
324C4×Dic6C2×D311yescharacteristic
325C22×C3×D3C2411yescharacteristic
326C32×Q8—24no—
327C2×C32×C4C2414yes—
328C2×C32×C4C2411yescharacteristic
329C2×C32×C4C2411yescharacteristic
330C2×C32×C4C2411yescharacteristic
331C2×C3⋊Dic3C2412yes—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335#634—22no—
336#634C2×Q814yes—
337C2×C3×Dic3C2411yescharacteristic
338C2×C3×Dic3C2412yes—
339C2×C3×Dic3C2414yes—
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2411yescharacteristic
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2411yescharacteristic
345C3×C4×D3—22no—
346C3×C4×D3—41no—
347C3×C4×D3C2×Q814yes—
348C3×Dic6—22no—
349C3×Dic6—42no—
350C3×Dic6C2×Q814yes—
351#627—44no—
352#627—44no—
353#627—42no—
354#627C2×Q818yes—
355D3×Dic3—42no—
356D3×Dic3C2×Q818yes—
357Q82—92no—
358Q82—91no—
359Q82—91no—
360#557—31no—
361#557—94no—
362#557—92no—
363#557—92no—
364#557—92no—
365#557—91no—
366#544—92no—
367#544—94no—
368#533—31no—
369#533—91no—
370#533—92no—
371#533—92no—
372#519—92no—
373C2×C4×Q8—91no—
374C2×C3×Q8—22no—
375C2×C3×Q8—31no—
376C2×C3×Q8—31no—
377C2×C3×Q8—32no—
378C2×C3×Q8C22×D312yes—
379C2×C3×Q8C22×D312yes—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×Dic3—32no—
384C22×Dic3—32no—
385D3×Q8—38no—
386C2×C4×D3—32no—
387C2×C4×D3—32no—
388C2×C4×D3C22×D311yescharacteristic
389C2×C4×D3C22×D311yescharacteristic
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6—31no—
392C2×Dic6—31no—
393C2×Dic6—32no—
394C2×Dic6—32no—
395C2×Dic6—38no—
396C2×Dic6—31no—
397C2×Dic6—31no—
398C2×Dic6—32no—
399C2×Dic6—34no—
400C2×Dic6—32no—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—34no—
404C2×Dic6—61no—
405C2×Dic6—61no—
406C2×Dic6C22×D311yescharacteristic
407C2×Dic6C22×D312yes—
408C2×Dic6C22×D311yescharacteristic
409C3×C4⋊C4—22no—
410C3×C4⋊C4—22no—
411C3×C4⋊C4—32no—
412C3×C4⋊C4—32no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—32no—
415C3×C4⋊C4—31no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—31no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4C22×D312yes—
423C3×C4⋊C4C22×D312yes—
424C3×C4⋊C4C22×D312yes—
425C3×C4⋊C4C22×D312yes—
426C3×C22⋊C4—34no—
427C3×C42—21no—
428C3×C42—31no—
429C3×C42—31no—
430C3×C42—34no—
431C3×C42—32no—
432C3×C42—34no—
433C3×C42—32no—
434C3×C42—31no—
435C3×C42C22×D311yescharacteristic
436C3×C42C22×D311yescharacteristic
437#217—32no—
438#217—32no—
439(C2×D3)⋊C4—32no—
440(C2×D3)⋊C4—32no—
441(C2×D3)⋊C4C22×D314yes—
442C4⋊Dic3—31no—
443C4⋊Dic3—31no—
444C4⋊Dic3—31no—
445C4⋊Dic3—31no—
446C4⋊Dic3—34no—
447C4⋊Dic3—34no—
448C4⋊Dic3—32no—
449C4⋊Dic3—32no—
450C4⋊Dic3—32no—
451C4⋊Dic3—32no—
452C4⋊Dic3—34no—
453C4⋊Dic3—32no—
454C4⋊Dic3—32no—
455C4⋊Dic3—34no—
456C4⋊Dic3—61no—
457C4⋊Dic3—61no—
458C4⋊Dic3—64no—
459C4⋊Dic3C22×D311yescharacteristic
460C4⋊Dic3C22×D312yes—
461C4⋊Dic3C22×D312yes—
462C4⋊Dic3C22×D311yescharacteristic
463C4⋊Dic3C22×D314yes—
464C4⋊Dic3C22×D314yes—
465Dic3⋊C4—32no—
466Dic3⋊C4—32no—
467Dic3⋊C4—34no—
468Dic3⋊C4—32no—
469Dic3⋊C4—32no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—32no—
474Dic3⋊C4—34no—
475Dic3⋊C4—32no—
476Dic3⋊C4—32no—
477Dic3⋊C4—32no—
478Dic3⋊C4—32no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—32no—
482Dic3⋊C4—32no—
483Dic3⋊C4—32no—
484Dic3⋊C4—34no—
485Dic3⋊C4—32no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—32no—
489Dic3⋊C4—62no—
490Dic3⋊C4—62no—
491Dic3⋊C4—64no—
492Dic3⋊C4—64no—
493Dic3⋊C4C22×D312yes—
494Dic3⋊C4C22×D314yes—
495Dic3⋊C4C22×D314yes—
496Dic3⋊C4C22×D312yes—
497Dic3⋊C4C22×D314yes—
498C4×Dic3—32no—
499C4×Dic3—32no—
500C4×Dic3—32no—
501C4×Dic3—32no—
502C4×Dic3—34no—
503C4×Dic3—34no—
504C4×Dic3—32no—
505C4×Dic3—34no—
506C4×Dic3—32no—
507C4×Dic3—32no—
508C4×Dic3—34no—
509C4×Dic3—34no—
510C4×Dic3—34no—
511C4×Dic3—32no—
512C4×Dic3—62no—
513C4×Dic3—62no—
514C4×Dic3—64no—
515C4×Dic3C22×D311yescharacteristic
516C4×Dic3C22×D311yescharacteristic
517C4×Dic3C22×D312yes—
518C4×Dic3C22×D312yes—
519C4×Dic3C22×D314yes—
520C4×Dic3C22×D314yes—
521C4×Dic3C22×D311yescharacteristic
522C22×C32C2511yescharacteristic
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3C22×Q812yes—
526C32×C4—24no—
527C32×C4—21no—
528C32×C4C22×Q812yes—
529C32×C42−1+412yes—
530C3⋊Dic3—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3—22no—
533C3⋊Dic3C22×Q814yes—
534C3×Dic3—22no—
535C3×Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—22no—
538C3×Dic3—24no—
539C3×Dic3—21no—
540C3×Dic3C22×Q814yes—
541C3×Dic3C22×Q812yes—
542C22×Q8—91no—
543C4⋊Q8—32no—
544C4⋊Q8—31no—
545C4⋊Q8—91no—
546C4⋊Q8—92no—
547C4⋊Q8—94no—
548C4⋊Q8—92no—
549C4⋊Q8—94no—
550C4⋊Q8—91no—
551C4⋊Q8—92no—
552C4⋊Q8—92no—
553C4⋊Q8—94no—
554C4⋊Q8—94no—
555C4⋊Q8—94no—
556C4⋊Q8—92no—
557C4⋊Q8D3211yescharacteristic
558#125—32no—
559#125—34no—
560#125—32no—
561#125—92no—
562#125—94no—
563#125—94no—
564#125—94no—
565#125—94no—
566#125—94no—
567#125—94no—
568#125—92no—
569C22⋊Q8—32no—
570C22⋊Q8—32no—
571C22⋊Q8—94no—
572C22⋊Q8—94no—
573C22⋊Q8—91no—
574C22⋊Q8—92no—
575C22⋊Q8—91no—
576C4×Q8—32no—
577C4×Q8—32no—
578C4×Q8—32no—
579C4×Q8—32no—
580C4×Q8—31no—
581C4×Q8—31no—
582C4×Q8—92no—
583C4×Q8—94no—
584C4×Q8—92no—
585C4×Q8—92no—
586C4×Q8—91no—
587C4×Q8—94no—
588C4×Q8—92no—
589C4×Q8—94no—
590C4×Q8—92no—
591C4×Q8—91no—
592C4×Q8—94no—
593C4×Q8—92no—
594C4×Q8—92no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—91no—
598C4×Q8—91no—
599#117—32no—
600#117—94no—
601#117—92no—
602#117—94no—
603C2×C4⋊C4—92no—
604C2×C4⋊C4—91no—
605C2×C42—31no—
606C2×C42—92no—
607C23×C3—31no—
608C22×D3C23×D311yescharacteristic
609C3×Q8—24no—
610C3×Q8—24no—
611C3×Q8—34no—
612C3×Q8—44no—
613C3×Q8—62no—
614C3×Q8—122no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—24no—
618C2×C3×C4—21no—
619C2×C3×C4—32no—
620C2×C3×C4—31no—
621C2×C3×C4—34no—
622C2×C3×C4—31no—
623C2×C3×C4—34no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—31no—
627C2×C3×C4—32no—
628C2×C3×C4—62no—
629C2×C3×C4—121no—
630C2×C3×C4C23×D314yes—
631C2×C3×C4C23×D314yes—
632C2×C3×C4C23×D311yescharacteristic
633C2×C3×C4C23×D311yescharacteristic
634C2×C3×C4C23×D311yescharacteristic
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637C2×C3×C4C23×D311yescharacteristic
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—38no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—62no—
648C2×Dic3—62no—
649C2×Dic3—62no—
650C2×Dic3—62no—
651C2×Dic3—122no—
652C2×Dic3C23×D311yescharacteristic
653C2×Dic3C23×D312yes—
654C2×Dic3C23×D314yes—
655C2×Dic3C23×D312yes—
656C2×Dic3C23×D312yes—
657C2×Dic3C23×D311yescharacteristic
658C2×Dic3C23×D312yes—
659C2×Dic3C23×D311yescharacteristic
660C4×D3—22no—
661C4×D3—38no—
662C4×D3—41no—
663C4×D3—122no—
664C4×D3D3×Q814yes—
665Dic6—22no—
666Dic6—34no—
667Dic6—34no—
668Dic6—38no—
669Dic6—38no—
670Dic6—42no—
671Dic6—64no—
672Dic6—62no—
673Dic6—62no—
674Dic6—122no—
675Dic6—124no—
676Dic6—124no—
677Dic6—122no—
678Dic6—122no—
679Dic6—124no—
680Dic6—124no—
681Dic6D3×Q814yes—
682C2×C32C23×Q811yescharacteristic
683C2×C32C2×2−1+411yescharacteristic
684C2×C32#58511yescharacteristic
685C3×D3—22no—
686C2×Q8—31no—
687C2×Q8—31no—
688C2×Q8—32no—
689C2×Q8—92no—
690C2×Q8—92no—
691C2×Q8—94no—
692C2×Q8—94no—
693C2×Q8—98no—
694C2×Q8—91no—
695C2×Q8—91no—
696C2×Q8C2×D3212yes—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—92no—
701C22×C4—92no—
702C4⋊C4—32no—
703C4⋊C4—31no—
704C4⋊C4—32no—
705C4⋊C4—34no—
706C4⋊C4—31no—
707C4⋊C4—34no—
708C4⋊C4—32no—
709C4⋊C4—34no—
710C4⋊C4—32no—
711C4⋊C4—34no—
712C4⋊C4—34no—
713C4⋊C4—92no—
714C4⋊C4—92no—
715C4⋊C4—92no—
716C4⋊C4—92no—
717C4⋊C4—94no—
718C4⋊C4—92no—
719C4⋊C4—94no—
720C4⋊C4—92no—
721C4⋊C4—92no—
722C4⋊C4—92no—
723C4⋊C4—94no—
724C4⋊C4—94no—
725C4⋊C4—92no—
726C4⋊C4—91no—
727C4⋊C4—94no—
728C4⋊C4—91no—
729C4⋊C4—94no—
730C4⋊C4—92no—
731C4⋊C4—94no—
732C4⋊C4C2×D3212yes—
733C4⋊C4C2×D3212yes—
734C22⋊C4—34no—
735C22⋊C4—92no—
736C22⋊C4—92no—
737C42—31no—
738C42—31no—
739C42—31no—
740C42—32no—
741C42—34no—
742C42—34no—
743C42—32no—
744C42—92no—
745C42—92no—
746C42—94no—
747C42—94no—
748C42—92no—
749C42—94no—
750C42—92no—
751C42C2×D3211yescharacteristic
752C22×C3—21no—
753C22×C3—32no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3C24×D311yescharacteristic
757C22×C3C24×D311yescharacteristic
758C2×D3—21no—
759C2×D3—21no—
760C2×D3C2×D3×Q812yes—
761C3×C4—24no—
762C3×C4—24no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—32no—
768C3×C4—34no—
769C3×C4—44no—
770C3×C4—41no—
771C3×C4—61no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4—61no—
776C3×C4—64no—
777C3×C4C2×D3×Q812yes—
778C3×C4C2×D3×Q812yes—
779C3×C4#101012yes—
780C3×C4#101012yes—
781Dic3—22no—
782Dic3—21no—
783Dic3—24no—
784Dic3—21no—
785Dic3—22no—
786Dic3—22no—
787Dic3—34no—
788Dic3—34no—
789Dic3—64no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—62no—
794Dic3—62no—
795Dic3—62no—
796Dic3—122no—
797Dic3—122no—
798Dic3—122no—
799Dic3C2×D3×Q812yes—
800Dic3C2×D3×Q814yes—
801C32#350211yescharacteristic, complemented, Sylow
802C23—31no—
803Q8—24no—
804Q8—34no—
805Q8—62no—
806Q8—98no—
807Q8—94no—
808Q8—122no—
809Q8—182no—
810Q8—362no—
811Q8—364no—
812Q8—364no—
813C2×C4—31no—
814C2×C4—32no—
815C2×C4—34no—
816C2×C4—32no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—34no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—62no—
823C2×C4—98no—
824C2×C4—92no—
825C2×C4—92no—
826C2×C4—92no—
827C2×C4—92no—
828C2×C4—121no—
829C2×C4—362no—
830C2×C4C22×D3214yes—
831C2×C4C22×D3211yescharacteristic
832C2×C4C22×D3211yescharacteristic
833C2×C4C22×D3211yescharacteristic
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—62no—
838C2×C3C22×D3×Q811yescharacteristic
839C2×C3C22×D3×Q811yescharacteristic
840C2×C3C2×#101011yescharacteristic
841C2×C3C2×#101011yescharacteristic
842C2×C3#596411yescharacteristic
843C2×C3#596811yescharacteristic
844D3—22no—
845C22—32no—
846C22—61no—
847C22—61no—
848C22C23×D3211yescharacteristic
849C4—24no—
850C4—21no—
851C4—32no—
852C4—34no—
853C4—61no—
854C4—62no—
855C4—61no—
856C4—62no—
857C4—64no—
858C4—62no—
859C4—94no—
860C4—182no—
861C4—182no—
862C4—182no—
863C4#6430912yes—
864C4D32×Q812yes—
865C3—21no—
866C3#8625811yescharacteristic, complemented
867C3#8703111yescharacteristic, complemented
868C2—62no—
869C2C2×#6430911yescharacteristic
870C2C2×D32×Q811yescharacteristic
871C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC22×C3×D3C24
hypercenterC4⋊Q8D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596192C2semidirect
3. C3×#5721C2semidirect
4. #10595420C2semidirect
5. Q8×#627C2semidirect
8. #10594596C2semidirect
12. #10594324C2semidirect
13. #10594321C2semidirect
16. #10593856C2semidirect
17. #10593856C2semidirect
95. #5721D3semidirect
135. D3×Dic6Q8semidirect
801. C32#3502semidirect
866. C3#86258semidirect
867. C3#87031semidirect

Maximal subgroups

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

subgroupindex
#105961922
C3×#57282
C3×#57212
#105954202
Q8×#6272
#105953682
#105953672
#105945962
#105945052
#105943892
#105943572
#105943242
#105943212
C4×D3×Dic62
#105938732
#105938562
#870313
#862583