Finite Group Databasebeta

← #11906345

Subgroups — #11906345

Order 1152.

2231 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic, complemented
2C3×Q8×D12C211yesmaximal, characteristic, complemented
3C3×#5567C211yesmaximal, characteristic, complemented
4#10595403C212yesmaximal, complemented
5D3×#944C212yesmaximal, complemented
6#10594395C214yesmaximal, complemented
7#10594389C214yesmaximal, complemented
8#10594385C212yesmaximal, complemented
9#10594383C212yesmaximal, complemented
10#10593941C212yesmaximal, complemented
11#10593909C211yesmaximal, characteristic, complemented
12#10593904C211yesmaximal, characteristic, complemented
13#10593889C212yesmaximal
14C4×#3796C211yesmaximal, characteristic
15#10593861C211yesmaximal, characteristic, complemented
16#10593856C212yesmaximal, complemented
17#10593855C212yesmaximal, complemented
18#87018—31nomaximal
19#86747—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3797C2212yes—
22C2×#3796C2211yescharacteristic
23C2×D3×Dic6C2212yes—
24C32×C4×Q8C2211yescharacteristic
25#64155C2211yescharacteristic
26#64153C2211yescharacteristic
27#64106C2211yescharacteristic
28#64105C2212yes—
29#64098C2212yes—
30#64097C2211yescharacteristic
31#64081C2212yes—
32C42×C3⋊D3C2211yescharacteristic
33C4×#634C2212yes—
34C4×#634C2211yescharacteristic
35C3×#944C2212yes—
36C3×#897C2212yes—
37C3×#897C2214yes—
38C3×#889C2214yes—
39C3×#887C2212yes—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2212yes—
42C3×#870C2212yes—
43C3×#869C2212yes—
44C3×#869C2211yescharacteristic
45C3×#869C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48#63919C2212yes—
49#63919C2212yes—
50#63919C2212yes—
51#63918C2214yes—
52#63904C2214yes—
53C4×#626C2212yes—
54#63900C2212yes—
55#63900C2212yes—
56#63899C2214yes—
57#63898C2211yescharacteristic
58#63898C2212yes—
59#63896C2214yes—
60#63895C2214yes—
61#63893C2214yes—
62#63888C2214yes—
63#63881C2212yes—
64#63880C2214yes—
65#63878C2212yes—
66#63877C2214yes—
67D3×Dic3⋊C4C2214yes—
68D3×Dic3⋊C4C2214yes—
69C4×D3×Dic3C2212yes—
70#63873C2212yes—
71#63872C2212yes—
72#63866C2212yes—
73#63856C2212yes—
74#63851C2214yes—
75#63849C2211yescharacteristic
76#63847C2214yes—
77#63846C2214yes—
78#63844C2214yes—
79#63843C2211yescharacteristic
80#63843C2212yes—
81Dic3×Dic6C2212yes—
82#63839C2214yes—
83#63839C2214yes—
84#63839C2214yes—
85C3×#557—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88C2×#944—32no—
89#5729—32no—
90#5727—32no—
91#5727—31no—
92D3×C4⋊Q8—32no—
93D3×C4⋊Q8—31no—
94D3×C4⋊Q8—31no—
95#5722—32no—
96#5721—31no—
97#5690—34no—
98#5690—32no—
99#5689—34no—
100#5689—32no—
101#5636—34no—
102#5632—32no—
103#5623—34no—
104#5622—32no—
105#5578—31no—
106#5578—31no—
107#5578—32no—
108#5578—61no—
109Q8×D12—32no—
110Q8×D12D311yescharacteristic, complemented
111#5574—32no—
112C4×#239—31no—
113#5570—31no—
114#5567D311yescharacteristic, complemented
115Q8×Dic6—32no—
116#5546—32no—
117#5539—32no—
118D4×Dic6—31no—
119C4×#237—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×#634C2311yescharacteristic
125C2×#634C2312yes—
126C3×D3×Q8—44no—
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2314yes—
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2314yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×#627C2314yes—
135C2×#627C2314yes—
136C2×#626C2312yes—
137C2×#624C2314yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2312yes—
141#3797—44no—
142#3796Q818yescomplemented
143D3×Dic6—44no—
144C32×C4⋊C4C2311yescharacteristic
145C32×C4⋊C4C2312yes—
146C32×C42C2311yescharacteristic
147C32×C42C2312yes—
148#3752C2312yes—
149#3752C2312yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2312yes—
152#3750C2312yes—
153#3750C2312yes—
154#3750C2312yes—
155#3750C2312yes—
156#3750C2312yes—
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2312yes—
159C4×C3⋊Dic3C2311yescharacteristic
160C4×C3⋊Dic3C2311yescharacteristic
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2314yes—
165C3×C4⋊Dic3C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2312yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2314yes—
173C3×Dic3⋊C4C2314yes—
174C3×C4×Dic3C2314yes—
175C3×C4×Dic3C2312yes—
176#3724C2314yes—
177#3724C2314yes—
178#3724C2314yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183#3722C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2314yes—
189#3503—91noSylow
190C22×C3×Q8—32no—
191C2×#239—31no—
192C2×D3×Q8—32no—
193C2×D3×Q8—32no—
194C2×D3×Q8—32no—
195C2×D3×Q8C2×D312yes—
196C2×#237—31no—
197C22×Dic6—32no—
198C3×C4⋊Q8—32no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—32no—
201C3×C4⋊Q8—31no—
202C3×#125—34no—
203C3×#125—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—34no—
206C3×C4×Q8—21no—
207C3×C4×Q8—32no—
208C3×C4×Q8—32no—
209C3×C4×Q8—31no—
210C3×C4×Q8C2×D311yescharacteristic
211C3×C4×Q8C2×D311yescharacteristic
212C3×C4×D4—31no—
213C3×C4×D4—32no—
214#946—31no—
215#946—31no—
216#946—32no—
217#946—34no—
218#946—61no—
219Q8×Dic3—31no—
220Q8×Dic3—32no—
221Q8×Dic3—32no—
222#944—31no—
223#944—31no—
224#944—32no—
225#944—32no—
226#944—34no—
227#944—34no—
228#944—34no—
229#944—32no—
230#944—61no—
231#944C2×D312yes—
232D4×Dic3—31no—
233D4×Dic3—32no—
234C4×#67—34no—
235C4×#67—32no—
236#924—32no—
237#924—34no—
238C2×Dic3⋊C4—34no—
239C2×Dic3⋊C4—34no—
240C2×C4×Dic3—32no—
241#897—31no—
242#897—31no—
243#897—34no—
244#897—34no—
245#897—61no—
246#897C2×D314yes—
247#897C2×D312yes—
248#896—34no—
249#896—34no—
250#896—32no—
251#896—32no—
252#896—34no—
253#896—34no—
254#896—34no—
255#896—62no—
256#893—31no—
257#893—32no—
258#893—34no—
259#893—32no—
260#892—32no—
261#892—31no—
262#892—31no—
263D3×C4⋊C4—34no—
264D3×C4⋊C4—34no—
265D3×C4⋊C4—32no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—32no—
268D3×C4⋊C4—32no—
269#890—34no—
270#890—32no—
271#890—32no—
272#889—32no—
273#889—32no—
274#889—34no—
275#889—34no—
276#889—34no—
277#889—62no—
278#889C2×D314yes—
279#888—34no—
280#888—34no—
281#888—34no—
282#888—31no—
283#888—31no—
284#888—32no—
285#888—32no—
286#888—32no—
287#888—32no—
288#888—32no—
289#888—32no—
290#888—34no—
291#888—61no—
292#887—32no—
293#887—31no—
294#887—34no—
295#887C2×D312yes—
296#67⋊C4—32no—
297#67⋊C4—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#877—32no—
302#877—34no—
303C4×D12—32no—
304C4×D12—34no—
305C4×D12C2×D312yes—
306C4×D12C2×D311yescharacteristic
307#872—32no—
308#872—32no—
309#872—34no—
310#872—62no—
311C42×D3—32no—
312C42×D3—31no—
313C42×D3—31no—
314C42×D3—61no—
315#870C2×D312yes—
316#869—32no—
317#869—34no—
318#869C2×D312yes—
319#869C2×D311yescharacteristic
320#869C2×D311yescharacteristic
321C4×Dic6—32no—
322C4×Dic6—32no—
323C4×Dic6—31no—
324C4×Dic6—32no—
325C4×Dic6—31no—
326C4×Dic6—34no—
327C4×Dic6—61no—
328C4×Dic6—62no—
329C4×Dic6C2×D311yescharacteristic
330C4×Dic6C2×D312yes—
331C22×C3⋊D3C2411yescharacteristic
332C22×C3×D3C2412yes—
333C32×Q8—22no—
334C2×C32×C4C2412yes—
335C2×C32×C4C2412yes—
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C3⋊Dic3C2412yes—
340C2×C3⋊Dic3C2411yescharacteristic
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2411yescharacteristic
343C2×C3⋊Dic3C2411yescharacteristic
344C4×C3⋊D3—22no—
345C4×C3⋊D3—22no—
346C4×C3⋊D3C2×Q814yescomplemented
347#634—22no—
348#634—24no—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2414yes—
353C2×C3×Dic3C2412yes—
354C3×D12C2×Q814yescomplemented
355C3×C4×D3—24no—
356C3×C4×D3—44no—
357C3×Dic6—24no—
358C3×Dic6—24no—
359C3×Dic6—44no—
360C3×Dic6C2×Q814yescomplemented
361#627—44no—
362#627—44no—
363#626C2×Q818yescomplemented
364#624—44no—
365D3×Dic3—24no—
366D3×Dic3—44no—
367D3×Dic3C2×Q818yescomplemented
368Q82—92no—
369#557—31no—
370#557—91no—
371#554—92no—
372#554—94no—
373D4×Q8—31no—
374D4×Q8—91no—
375D4×Q8—92no—
376D4×Q8—92no—
377#544—94no—
378#544—92no—
379#533—92no—
380#533—91no—
381C2×C4⋊Q8—91no—
382C2×C4⋊Q8—92no—
383#520—92no—
384C4×#41—91no—
385C2×C3×Q8—21no—
386C2×C3×Q8—31no—
387C2×C3×Q8—32no—
388C2×C3×Q8—32no—
389C2×C3×Q8—34no—
390C2×C3×Q8—124no—
391C2×C3×Q8C22×D311yescharacteristic
392C2×C3×Q8C22×D311yescharacteristic
393C2×C3×D4—31no—
394C22×C3×C4—32no—
395C22×C3×C4—34no—
396C2×#67—32no—
397C22×Dic3—32no—
398C22×Dic3—32no—
399C22×Dic3—34no—
400#239—38no—
401D3×Q8—44no—
402D3×Q8—124no—
403D3×Q8—124no—
404D3×Q8—124no—
405#237—38no—
406C2×D12—32no—
407C2×D12C22×D311yescharacteristic
408C2×C4×D3—32no—
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—32no—
412C2×C4×D3—31no—
413C2×C4×D3—31no—
414C2×C4×D3—31no—
415C2×C4×D3—31no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—61no—
420C2×C4×D3—61no—
421C2×C4×D3—61no—
422C2×C4×D3C22×D312yes—
423C2×C4×D3C22×D314yes—
424C2×Dic6—32no—
425C2×Dic6—31no—
426C2×Dic6—32no—
427C2×Dic6—31no—
428C2×Dic6—34no—
429C2×Dic6—34no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—62no—
433C2×Dic6—61no—
434C2×Dic6—124no—
435C2×Dic6C22×D312yes—
436C2×Dic6C22×D312yes—
437C2×Dic6C22×D314yes—
438C2×Dic6C22×D311yescharacteristic
439C3×C4⋊C4—21no—
440C3×C4⋊C4—22no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—34no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4—32no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4C22×D311yescharacteristic
453C3×C4⋊C4C22×D311yescharacteristic
454C3×C4⋊C4C22×D312yes—
455C3×C4⋊C4C22×D312yes—
456C3×C22⋊C4—32no—
457C3×C22⋊C4—34no—
458C3×C42—21no—
459C3×C42—22no—
460C3×C42—32no—
461C3×C42—34no—
462C3×C42C22×D311yescharacteristic
463C3×C42C22×D312yes—
464C3×C42C22×D311yescharacteristic
465C3×C42C22×D312yes—
466#217—34no—
467#217—32no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—32no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—62no—
478(C2×D3)⋊C4C22×D314yes—
479(C2×D3)⋊C4C22×D312yes—
480C4⋊Dic3—31no—
481C4⋊Dic3—32no—
482C4⋊Dic3—32no—
483C4⋊Dic3—31no—
484C4⋊Dic3—32no—
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487C4⋊Dic3—34no—
488C4⋊Dic3—61no—
489C4⋊Dic3—62no—
490C4⋊Dic3C22×D314yes—
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D311yescharacteristic
493C4⋊Dic3C22×D311yescharacteristic
494C4⋊Dic3C22×D312yes—
495C4⋊Dic3C22×D312yes—
496C4⋊Dic3C22×D312yes—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—32no—
502Dic3⋊C4—32no—
503Dic3⋊C4—32no—
504Dic3⋊C4—32no—
505Dic3⋊C4—32no—
506Dic3⋊C4—32no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—32no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—62no—
518Dic3⋊C4—62no—
519Dic3⋊C4—62no—
520Dic3⋊C4—62no—
521Dic3⋊C4—62no—
522Dic3⋊C4C22×D312yes—
523Dic3⋊C4C22×D314yes—
524Dic3⋊C4C22×D314yes—
525Dic3⋊C4C22×D314yes—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—32no—
535C4×Dic3—34no—
536C4×Dic3—32no—
537C4×Dic3—34no—
538C4×Dic3—32no—
539C4×Dic3—32no—
540C4×Dic3—61no—
541C4×Dic3—62no—
542C4×Dic3—61no—
543C4×Dic3—61no—
544C4×Dic3C22×D314yes—
545C4×Dic3C22×D312yes—
546C22×C32C2511yescharacteristic
547C2×C3⋊D3—21no—
548C2×C3⋊D3—21no—
549C2×C3⋊D3C22×Q812yes—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
552C2×C3×D3C22×Q814yes—
553C32×C4—22no—
554C32×C4—22no—
555C32×C4—21no—
556C32×C4C22×Q812yes—
557C32×C4H(5,𝔽2)12yes—
558C3⋊Dic3—22no—
559C3⋊Dic3—21no—
560C3⋊Dic3—22no—
561C3⋊Dic3C22×Q812yes—
562C3⋊Dic32−1+412yes—
563C3×Dic3—24no—
564C3×Dic3—24no—
565C3×Dic3—22no—
566C3×Dic3—22no—
567C3×Dic3C22×Q814yes—
568C2×#41—91no—
569C22×Q8—32no—
570C22×Q8—92no—
571C22×Q8—92no—
572C4⋊Q8—32no—
573C4⋊Q8—31no—
574C4⋊Q8—31no—
575C4⋊Q8—32no—
576C4⋊Q8—94no—
577C4⋊Q8—92no—
578C4⋊Q8—92no—
579C4⋊Q8—92no—
580C4⋊Q8—92no—
581C4⋊Q8—94no—
582C4⋊Q8—94no—
583C4⋊Q8—94no—
584C4⋊Q8—92no—
585C4⋊Q8—91no—
586C4⋊Q8—91no—
587#125—34no—
588#125—32no—
589#125—94no—
590#125—94no—
591#125—92no—
592#125—92no—
593C22⋊Q8—32no—
594C22⋊Q8—34no—
595C22⋊Q8—94no—
596C22⋊Q8—94no—
597C22⋊Q8—94no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—92no—
602C22⋊Q8—91no—
603C22⋊Q8—91no—
604C22⋊Q8—92no—
605C4×Q8—32no—
606C4×Q8—31no—
607C4×Q8—32no—
608C4×Q8—94no—
609C4×Q8—92no—
610C4×Q8—91no—
611C4×Q8—92no—
612C4×Q8—91no—
613C4×Q8—92no—
614C4×Q8D3211yescharacteristic
615C4×D4—31no—
616C4×D4—32no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—92no—
620C4×D4—94no—
621C4×D4—91no—
622C4×D4—92no—
623#117—94no—
624#117—92no—
625#117—91no—
626#117—92no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—92no—
629C2×C4⋊C4—94no—
630C2×C4⋊C4—94no—
631C2×C42—92no—
632C2×C42—91no—
633C23×C3—32no—
634C22×D3—31no—
635C22×D3—31no—
636C22×D3—61no—
637C22×D3C23×D312yes—
638C3×Q8—22no—
639C3×Q8—22no—
640C3×Q8—34no—
641C3×Q8—42no—
642C3×Q8—64no—
643C3×Q8—64no—
644C3×Q8—124no—
645C3×D4—34no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—34no—
654C2×C3×C4—32no—
655C2×C3×C4—34no—
656C2×C3×C4—64no—
657C2×C3×C4—124no—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—38no—
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—38no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—64no—
686C2×Dic3—124no—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D314yes—
690C2×Dic3C23×D314yes—
691C2×Dic3C23×D312yes—
692D12—38no—
693D12D3×Q814yescomplemented
694C4×D3—24no—
695C4×D3—38no—
696C4×D3—34no—
697C4×D3—34no—
698C4×D3—44no—
699C4×D3—64no—
700C4×D3—62no—
701C4×D3—62no—
702C4×D3—64no—
703C4×D3—62no—
704C4×D3—62no—
705C4×D3—122no—
706C4×D3—122no—
707C4×D3—124no—
708C4×D3—124no—
709C4×D3—124no—
710Dic6—24no—
711Dic6—24no—
712Dic6—44no—
713Dic6—64no—
714Dic6—64no—
715Dic6—62no—
716Dic6—62no—
717Dic6—124no—
718Dic6—122no—
719Dic6—124no—
720Dic6—124no—
721Dic6—124no—
722Dic6—124no—
723Dic6D3×Q814yescomplemented
724C2×C32C23×Q811yescharacteristic
725C2×C32C2×H(5,𝔽2)11yescharacteristic
726C2×C32C2×2−1+411yescharacteristic
727C3⋊D3—22no—
728C3×D3—24no—
729#41—98no—
730C2×Q8—31no—
731C2×Q8—32no—
732C2×Q8—32no—
733C2×Q8—34no—
734C2×Q8—94no—
735C2×Q8—94no—
736C2×Q8—92no—
737C2×Q8—91no—
738C2×Q8—124no—
739C2×Q8—364no—
740C2×Q8—364no—
741C2×Q8C2×D3211yescharacteristic
742C2×D4—31no—
743C2×D4—92no—
744C22×C4—32no—
745C22×C4—34no—
746C22×C4—94no—
747C22×C4—92no—
748C22×C4—92no—
749C22×C4—94no—
750C22×C4—91no—
751C22×C4—91no—
752C22×C4—91no—
753C4⋊C4—32no—
754C4⋊C4—34no—
755C4⋊C4—32no—
756C4⋊C4—32no—
757C4⋊C4—34no—
758C4⋊C4—32no—
759C4⋊C4—31no—
760C4⋊C4—32no—
761C4⋊C4—31no—
762C4⋊C4—34no—
763C4⋊C4—34no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4—94no—
767C4⋊C4—94no—
768C4⋊C4—92no—
769C4⋊C4—94no—
770C4⋊C4—94no—
771C4⋊C4—92no—
772C4⋊C4—92no—
773C4⋊C4—92no—
774C4⋊C4—91no—
775C4⋊C4—92no—
776C4⋊C4—92no—
777C4⋊C4—92no—
778C4⋊C4C2×D3211yescharacteristic
779C4⋊C4C2×D3212yes—
780C22⋊C4—32no—
781C22⋊C4—34no—
782C22⋊C4—92no—
783C22⋊C4—92no—
784C22⋊C4—94no—
785C22⋊C4—92no—
786C22⋊C4—92no—
787C42—32no—
788C42—34no—
789C42—92no—
790C42—92no—
791C42—94no—
792C42—91no—
793C42—91no—
794C42—91no—
795C42—92no—
796C42C2×D3211yescharacteristic
797C42C2×D3212yes—
798C22×C3—21no—
799C22×C3—34no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3C24×D311yescharacteristic
803C22×C3C24×D311yescharacteristic
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—32no—
807C2×D3—32no—
808C2×D3—62no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—121no—
814C2×D3—121no—
815C2×D3C2×D3×Q814yes—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—34no—
825C3×C4—42no—
826C3×C4—41no—
827C3×C4—42no—
828C3×C4—64no—
829C3×C4—62no—
830C3×C4—64no—
831C3×C4—62no—
832C3×C4#100412yes—
833C3×C4C2×D3×Q812yes—
834C3×C4C2×D3×Q812yes—
835C3×C4#100912yes—
836Dic3—24no—
837Dic3—22no—
838Dic3—24no—
839Dic3—22no—
840Dic3—32no—
841Dic3—32no—
842Dic3—32no—
843Dic3—32no—
844Dic3—62no—
845Dic3—62no—
846Dic3—62no—
847Dic3—61no—
848Dic3—62no—
849Dic3—61no—
850Dic3—62no—
851Dic3—62no—
852Dic3—122no—
853Dic3—122no—
854Dic3—121no—
855Dic3C2×D3×Q814yes—
856C32#350311yescharacteristic, complemented, Sylow
857C23—32no—
858C23—91no—
859Q8—22no—
860Q8—34no—
861Q8—64no—
862Q8—64no—
863Q8—124no—
864Q8—184no—
865Q8—182no—
866Q8—364no—
867Q8—364no—
868D4—34no—
869D4—98no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—34no—
873C2×C4—32no—
874C2×C4—34no—
875C2×C4—64no—
876C2×C4—98no—
877C2×C4—91no—
878C2×C4—91no—
879C2×C4—94no—
880C2×C4—92no—
881C2×C4—91no—
882C2×C4—92no—
883C2×C4—124no—
884C2×C4—182no—
885C2×C4—184no—
886C2×C4—182no—
887C2×C4—364no—
888C2×C4—364no—
889C2×C4C22×D3212yes—
890C2×C4C22×D3211yescharacteristic
891C2×C4C22×D3212yes—
892C2×C4C22×D3211yescharacteristic
893C2×C4C22×D3211yescharacteristic
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—64no—
898C2×C3C2×#100411yescharacteristic
899C2×C3C22×D3×Q811yescharacteristic
900C2×C3C22×D3×Q811yescharacteristic
901C2×C3C2×#100911yescharacteristic
902C2×C3D3×2−1+411yescharacteristic
903C2×C3D3×2−1+411yescharacteristic
904D3—24no—
905D3—62no—
906D3—62no—
907D3—122no—
908C22—34no—
909C22—62no—
910C22—62no—
911C22—92no—
912C22—181no—
913C22—181no—
914C22C23×D3211yescharacteristic
915C4—22no—
916C4—21no—
917C4—22no—
918C4—34no—
919C4—62no—
920C4—64no—
921C4—64no—
922C4—62no—
923C4—92no—
924C4—92no—
925C4—181no—
926C4—182no—
927C4—182no—
928C4#6430712yes—
929C4D32×Q812yes—
930C3—21no—
931C3#8674711yescharacteristic, complemented
932C3#8701811yescharacteristic, complemented
933C2—64no—
934C2—182no—
935C2C2×#6430711yescharacteristic
936C2C2×D32×Q811yescharacteristic
937C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3796C22
hypercenterC4×Q8D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596049C2semidirect
2. C3×Q8×D12C2semidirect
3. C3×#5567C2semidirect
4. #10595403C2semidirect
5. D3×#944C2semidirect
6. #10594395C2semidirect
7. #10594389C2semidirect
8. #10594385C2semidirect
9. #10594383C2semidirect
10. #10593941C2semidirect
11. #10593909C2semidirect
12. #10593904C2semidirect
15. #10593861C2semidirect
16. #10593856C2semidirect
17. #10593855C2semidirect
110. Q8×D12D3semidirect
114. #5567D3semidirect
142. #3796Q8semidirect
346. C4×C3⋊D3C2×Q8semidirect
354. C3×D12C2×Q8semidirect
360. C3×Dic6C2×Q8semidirect
363. #626C2×Q8semidirect
367. D3×Dic3C2×Q8semidirect
693. D12D3×Q8semidirect
723. Dic6D3×Q8semidirect
856. C32#3503semidirect
931. C3#86747semidirect
932. C3#87018semidirect

Maximal subgroups

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

subgroupindex
#105960492
C3×Q8×D122
C3×#55672
#105954032
D3×#9442
#105943952
#105943892
#105943852
#105943832
#105939412
#105939092
#105939042
#105938892
C4×#37962
#105938612
#105938562
#105938552
#870183
#867473