Finite Group Databasebeta

← #11885829

Subgroups — #11885829

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596101C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic, complemented
3#10594889C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C3×#5051C211yesmaximal, characteristic, complemented
6C3×#5046C211yesmaximal, characteristic, complemented
7#10591610C211yesmaximal, characteristic, complemented
8#10591593C211yesmaximal, characteristic, complemented
9#10591570C211yesmaximal, characteristic, complemented
10#10591183C211yesmaximal, characteristic, complemented
11#10591148C211yesmaximal, characteristic, complemented
12#10590617C211yesmaximal, characteristic, complemented
13#10590540C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#80773—31nomaximal
17#80168—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C32×C22⋊Q8C2211yescharacteristic
23#64156C2211yescharacteristic, complemented
24C4×#638C2211yescharacteristic
25#64104—21no—
26#64104C2211yescharacteristic, complemented
27#64103—21no—
28#64102C2211yescharacteristic, complemented
29#64091—21no—
30C22⋊C4×C3⋊D3—21no—
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#215C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic, complemented
34C3×#924C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic
36#63977—21no—
37D3×#217—21no—
38#63950—24no—
39#63916C2211yescharacteristic, complemented
40#63898C2211yescharacteristic, complemented
41#63886—21no—
42#63884—21no—
43#63863C2211yescharacteristic, complemented
44C2×#3717C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3714—24no—
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3710C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#830C2211yescharacteristic
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58#63572C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63#5806—31no—
64C22×#213—31no—
65C2×#919—31no—
66C2×#916—31no—
67C22×D24—31no—
68#5630—31no—
69#5630—31no—
70#5630—31no—
71#5630—61no—
72C3×#467—31no—
73C3×#450—31no—
74#5191—31no—
75#5172—31no—
76#5168—31no—
77#5165—31no—
78C8×#67—31no—
79#5051D311yescharacteristic, complemented
80#5046—31no—
81#5046D311yescharacteristic, complemented
82#4883—31no—
83#4872—31no—
84#4819—31no—
85#4819—31no—
86#4810—31no—
87#4810—31no—
88#4787—31no—
89#4781—31no—
90#4775—31no—
91#4756—31no—
92#4731—31no—
93#67⋊C8—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638D411yescharacteristic
99#3832—22no—
100#3832—41no—
101C2×C4⋊(C3⋊D3)—22no—
102C2×C4⋊(C3⋊D3)—21no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)—41no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3—21no—
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×C3×D12—22no—
112C2×C3×D12—21no—
113C2×C3×D12—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×D3×Dic3—21no—
120C2×D3×Dic3—21no—
121#3796—22no—
122#3796—41no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C22⋊C4—21no—
126#3757D411yescharacteristic
127#3752—21no—
128#3752—21no—
129#3752—21no—
130#3752—21no—
131#3752D411yescharacteristic
132#3750D411yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134C3×#217—21no—
135C3×#216—22no—
136C3×#215—22no—
137C3×#215—41no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C2×C3×C3⋊C8—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3717—22no—
150#3717—41no—
151#3714—22no—
152#3714—22no—
153#3714—22no—
154#3714D414yescomplemented
155#3710—22no—
156#3280—91noSylow
157C22×C3×D4—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—61no—
162C2×#237—31no—
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—61no—
166C22×D12C2×D311yescharacteristic
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C22×C3×C8—31no—
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×C22⋊Q8C2×D311yescharacteristic
175#953—61no—
176C2×#217—61no—
177#947—31no—
178#947—31no—
179#947—31no—
180#947—61no—
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215C2×D311yescharacteristic, complemented
185C2×#215C2×D311yescharacteristic, complemented
186#939—61no—
187#938—31no—
188#936—31no—
189#935—61no—
190D4×Dic3—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—64no—
196C4×#67—31no—
197C4×#67—31no—
198C4×#67—61no—
199#924C2×D311yescharacteristic
200C22×C3⋊C8C2×D311yescharacteristic
201#919—64no—
202#916—64no—
203C2×D24—31no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—31no—
207C2×D24—64no—
208C2×#204—31no—
209C2×#204—31no—
210C2×D3×C8—31no—
211C2×D3×C8—31no—
212#895—31no—
213#895—31no—
214#895—31no—
215#895—61no—
216#895—61no—
217#895—61no—
218#895—61no—
219#895—62no—
220#894—61no—
221#894—61no—
222#894—61no—
223#894—62no—
224#893—31no—
225#893—31no—
226#893—31no—
227#893—61no—
228#882—61no—
229#882—61no—
230#882—62no—
231#882—61no—
232D3×C22⋊C4—61no—
233D3×C22⋊C4—61no—
234D3×C22⋊C4—61no—
235D3×C22⋊C4—62no—
236C3×#107—31no—
237C3×#103—31no—
238C3×#103—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×C22⋊C8—31no—
242#835C2×D311yescharacteristic, complemented
243#830C2×D311yescharacteristic
244#821—31no—
245#821—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248Dic3⋊C8—31no—
249Dic3⋊C8—31no—
250C8×Dic3—31no—
251C8×Dic3—31no—
252#810C2×D311yescharacteristic, complemented
253#809—31no—
254#809—31no—
255#809C2×D311yescharacteristic, complemented
256#809C2×D311yescharacteristic, complemented
257#807C2×D311yescharacteristic, complemented
258C23×C32C2×D411yescharacteristic
259C22×C3⋊D3—21no—
260C22×C3⋊D3—21no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—81no—
264C22×C3⋊D3C2×D411yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—42no—
268C22×C3×D3—42no—
269C22×C3×D3—81no—
270C32×Q8—21no—
271C32×Q8—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278#638—22no—
279C2×C3⋊Dic3C2×D411yescharacteristic
280C2×C3⋊Dic3C2×D411yescharacteristic
281C2×C3⋊Dic3C2×D411yescharacteristic
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—42no—
286C4⋊(C3⋊D3)—42no—
287C4⋊(C3⋊D3)—81no—
288C4⋊(C3⋊D3)C2×D412yes—
289C4×C3⋊D3—21no—
290C4×C3⋊D3—21no—
291C4×C3⋊D3—42no—
292C4×C3⋊D3—81no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—42no—
299C3×D12C2×D412yes—
300C3×Dic6—21no—
301C3×Dic6—21no—
302#626—42no—
303#626—81no—
304D3×Dic3—42no—
305D3×Dic3—81no—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×#135—91no—
311C22×D8—91no—
312#546—91no—
313#546—91no—
314#495—91no—
315#467—31no—
316#466—91no—
317#463—91no—
318#463—91no—
319#450—31no—
320#450—91no—
321#449—91no—
322#449—91no—
323C4×D8—91no—
324C8×D4—91no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—62no—
328C23×D3—61no—
329C23×D3—61no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—121no—
339C22×C3×C4—21no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—31no—
343C2×#67—31no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349#239—62no—
350#239—62no—
351#239—62no—
352#239—122no—
353#239—121no—
354#239—121no—
355#239—121no—
356#239—122no—
357#237—62no—
358#237—121no—
359C2×D12—22no—
360C2×D12—21no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—41no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—62no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—122no—
382C2×D12—121no—
383C2×D12—121no—
384C2×D12—122no—
385C2×D12C22×D311yescharacteristic
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—62no—
394C2×C4×D3—61no—
395C2×C4×D3—61no—
396C2×C4×D3—61no—
397C2×C4×D3—62no—
398C2×Dic6C22×D311yescharacteristic
399C3×Q16—62no—
400C3×SD16—62no—
401C3×SD16—121no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8—62no—
407C3×C4⋊C4—22no—
408C3×C4⋊C4—21no—
409C3×C4⋊C4—21no—
410C3×C4⋊C4—21no—
411C3×C4⋊C4—31no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4C22×D311yescharacteristic
414C3×C4⋊C4C22×D311yescharacteristic
415C3×C22⋊C4—22no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—61no—
419#217—21no—
420#217—31no—
421#217—31no—
422#217—61no—
423#217—61no—
424#217—61no—
425#217—61no—
426#217—61no—
427#216—22no—
428#215—22no—
429#215—41no—
430#215—62no—
431#215—121no—
432#213—34no—
433#213—62no—
434#213—62no—
435#213—62no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—62no—
452(C2×D3)⋊C4—62no—
453(C2×D3)⋊C4—62no—
454(C2×D3)⋊C4—62no—
455C4⋊Dic3C22×D311yescharacteristic
456Dic3⋊C4—21no—
457Dic3⋊C4—31no—
458Dic3⋊C4—31no—
459Dic3⋊C4—61no—
460C4×Dic3—31no—
461C4×Dic3—31no—
462C4×Dic3—61no—
463C2×C3⋊C8—22no—
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466C2×C3⋊C8C22×D311yescharacteristic
467C2×C3⋊C8C22×D311yescharacteristic
468D24—34no—
469D24—62no—
470D24—62no—
471D24—62no—
472#204—62no—
473#204—121no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32#13512yescomplemented
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—41no—
489C2×C3⋊D3—84no—
490C2×C3×D3—22no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—84no—
497C32×C4—21no—
498C32×C4—41no—
499C32×C4—41no—
500C32×C4C22×D411yescharacteristic
501C32×C4H(5,𝔽2)11yescharacteristic
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—21no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C2×#41—91no—
508C2×#41—91no—
509C22×D4—31no—
510C22×D4—91no—
511#135—184no—
512C2×Q16—31no—
513C2×SD16—31no—
514C2×SD16—31no—
515C2×SD16—91no—
516C2×SD16—91no—
517C2×D8—91no—
518C2×D8—91no—
519C2×D8—91no—
520C2×D8—91no—
521C2×D8—184no—
522C22×C8—31no—
523C22×C8—91no—
524#124—91no—
525#124—91no—
526#123—181no—
527#123—181no—
528C22⋊Q8—31no—
529C22⋊Q8D3211yescharacteristic
530#121—91no—
531#121—91no—
532#121—181no—
533#121—181no—
534#120—181no—
535#120—181no—
536C4×D4—91no—
537C4×D4—91no—
538C4×D4—91no—
539C2×C22⋊C4—181no—
540C2×C22⋊C4—181no—
541#107—31no—
542C4⋊C8—91no—
543#103—31no—
544#103—31no—
545#102—31no—
546#102—31no—
547#102—91no—
548#102—91no—
549C22⋊C8—31no—
550C22⋊C8—91no—
551C4×C8—91no—
552C23×C3—21no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—122no—
556C23×C3—122no—
557C23×C3—241no—
558C23×C3D3×D411yescharacteristic
559C23×C3D3×D411yescharacteristic
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—31no—
563C22×D3—31no—
564C22×D3—42no—
565C22×D3—42no—
566C22×D3—61no—
567C22×D3—62no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—62no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—81no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—124no—
577C22×D3—124no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3—241no—
581C22×D3—241no—
582C22×D3—242no—
583C3×Q8—21no—
584C3×Q8—21no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—41no—
588C3×Q8—41no—
589C3×Q8—61no—
590C3×Q8—61no—
591C3×D4—32no—
592C3×D4—61no—
593C3×D4—61no—
594C3×D4—61no—
595C3×D4—122no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4D3×D411yescharacteristic
613C2×C3×C4D3×D411yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D311yescharacteristic
616#67—62no—
617#67—62no—
618#67—122no—
619#67—122no—
620#67—241no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—122no—
633C2×Dic3—241no—
634D12—21no—
635D12—21no—
636D12—21no—
637D12—32no—
638D12—32no—
639D12—42no—
640D12—62no—
641D12—62no—
642D12—61no—
643D12—61no—
644D12—61no—
645D12—61no—
646D12—61no—
647D12—61no—
648D12—121no—
649D12—121no—
650D12—122no—
651D12—122no—
652D12—122no—
653D12—122no—
654D12—124no—
655D12—124no—
656D12—122no—
657D12—241no—
658D12—241no—
659D12—242no—
660D12—241no—
661D12D3×D412yes—
662C4×D3—61no—
663C4×D3—61no—
664C4×D3—61no—
665C4×D3—61no—
666C4×D3—121no—
667C4×D3—121no—
668C4×D3—122no—
669C4×D3—122no—
670C4×D3—122no—
671C4×D3—124no—
672C4×D3—241no—
673C4×D3—241no—
674C4×D3—241no—
675C4×D3—242no—
676Dic6—21no—
677Dic6—21no—
678C3×C8—32no—
679C3×C8—61no—
680C3×C8—61no—
681C3×C8—61no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8—21no—
685C3⋊C8D3×D412yes—
686C2×C32—22no—
687C2×C32D4211yescharacteristic
688C2×C32C2×#13511yescharacteristic
689C2×C32#57611yescharacteristic
690C3⋊D3—42no—
691C3⋊D3—41no—
692C3⋊D3—81no—
693C3×D3—42no—
694C3×D3—81no—
695C24—61no—
696C24—181no—
697#41—182no—
698#41—182no—
699#41—361no—
700#41—361no—
701C2×Q8—31no—
702C2×Q8C2×D3211yescharacteristic
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—62no—
706C2×D4—61no—
707C2×D4—91no—
708C2×D4—91no—
709C2×D4—91no—
710C2×D4—121no—
711C2×D4—182no—
712C2×D4—181no—
713C2×D4—181no—
714C2×D4—181no—
715C2×D4—181no—
716C2×D4—181no—
717C2×D4—361no—
718C22×C4—91no—
719C22×C4—181no—
720C22×C4—181no—
721C22×C4—181no—
722C22×C4—181no—
723C22×C4C2×D3211yescharacteristic
724Q16—62no—
725SD16—62no—
726SD16—121no—
727SD16—182no—
728SD16—361no—
729D8—94no—
730D8—182no—
731D8—182no—
732D8—182no—
733C2×C8—31no—
734C2×C8—31no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—62no—
738C2×C8—182no—
739C4⋊C4—21no—
740C4⋊C4—31no—
741C4⋊C4—61no—
742C4⋊C4—91no—
743C4⋊C4C2×D3211yescharacteristic
744C22⋊C4—21no—
745C22⋊C4—61no—
746C22⋊C4—91no—
747C22⋊C4—91no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C22⋊C4—181no—
755C22⋊C4—181no—
756C42—91no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—22no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—62no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—244no—
772C22×C3#91612yescomplemented
773C22×C3#91912yescomplemented
774C22×C3C2×D3×D411yescharacteristic
775C22×C3C2×D3×D411yescharacteristic
776C2×D3—22no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—64no—
783C2×D3—61no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—62no—
789C2×D3—61no—
790C2×D3—62no—
791C2×D3—84no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—122no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—244no—
811C2×D3—244no—
812C2×D3—248no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—41no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4—41no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—121no—
825C3×C4—121no—
826C3×C4C2×D3×D411yescharacteristic
827C3×C4C2×D3×D411yescharacteristic
828C3×C4#100411yescharacteristic
829C3×C4#100911yescharacteristic
830Dic3—41no—
831Dic3—41no—
832Dic3—61no—
833Dic3—61no—
834Dic3—61no—
835Dic3—61no—
836Dic3—61no—
837Dic3—61no—
838Dic3—121no—
839Dic3—121no—
840Dic3—121no—
841C32#328011yescharacteristic, complemented, Sylow
842C23—61no—
843C23—61no—
844C23—91no—
845C23—122no—
846C23—122no—
847C23—181no—
848C23—181no—
849C23—241no—
850C23—362no—
851C23—362no—
852C23—721no—
853C23#381111yescharacteristic
854Q8—21no—
855Q8—21no—
856Q8—61no—
857Q8—61no—
858D4—32no—
859D4—61no—
860D4—61no—
861D4—61no—
862D4—92no—
863D4—122no—
864D4—182no—
865D4—181no—
866D4—181no—
867D4—181no—
868D4—362no—
869D4—362no—
870D4—362no—
871D4—721no—
872D4—721no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—91no—
880C2×C4—91no—
881C2×C4—91no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—362no—
885C2×C4—362no—
886C2×C4—721no—
887C2×C4—721no—
888C2×C4#381111yescharacteristic
889C2×C4C22×D3211yescharacteristic
890C8—32no—
891C8—61no—
892C8—61no—
893C8—61no—
894C2×C3—22no—
895C2×C3—22no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—42no—
900C2×C3—122no—
901C2×C3—241no—
902C2×C3#559011yescharacteristic
903C2×C3#560911yescharacteristic
904C2×C3C2×#91611yescharacteristic
905C2×C3C2×#91911yescharacteristic
906C2×C3#576911yescharacteristic
907C2×C3#577411yescharacteristic
908D3—42no—
909D3—81no—
910D3—124no—
911D3—121no—
912D3—122no—
913D3—121no—
914D3—122no—
915D3—241no—
916D3—242no—
917D3—241no—
918D3—241no—
919C22—21no—
920C22—21no—
921C22—62no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—181no—
928C22—181no—
929C22—181no—
930C22—182no—
931C22—244no—
932C22—361no—
933C22—361no—
934C22—361no—
935C22—361no—
936C22—361no—
937C22—724no—
938C22#6395012yescomplemented
939C22C2×#381111yescharacteristic
940C4—21no—
941C4—41no—
942C4—41no—
943C4—121no—
944C4—121no—
945C4—181no—
946C4—181no—
947C4—181no—
948C4D32×D411yescharacteristic
949C4#6431411yescharacteristic
950C3—21no—
951C3#8016811yescharacteristic, complemented
952C3#8077311yescharacteristic, complemented
953C2—22no—
954C2—122no—
955C2—241no—
956C2—361no—
957C2—362no—
958C2—721no—
959C2#1059529211yescharacteristic
960C2C2×#6395011yescharacteristic
961C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596101C2semidirect
2. C2×#63950C2semidirect
3. #10594889C2semidirect
4. C22×#3714C2semidirect
5. C3×#5051C2semidirect
6. C3×#5046C2semidirect
7. #10591610C2semidirect
8. #10591593C2semidirect
9. #10591570C2semidirect
10. #10591183C2semidirect
11. #10591148C2semidirect
12. #10590617C2semidirect
13. #10590540C2semidirect
14. #10590509C2semidirect
15. #10590459C2semidirect
18. C2×#3832C22semidirect
21. C2×#3796C22semidirect
23. #64156C22semidirect
26. #64104C22semidirect
28. #64102C22semidirect
31. C2×C3×#216C22semidirect
32. C2×C3×#215C22semidirect
33. C2×C3×#215C22semidirect
39. #63916C22semidirect
40. #63898C22semidirect
43. #63863C22semidirect
44. C2×#3717C22semidirect
45. C2×#3717C22semidirect
51. C2×#3710C22semidirect
52. C3×#835C22semidirect
54. C3×#810C22semidirect
55. C3×#809C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. #63572C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. #63553C22semidirect
79. #5051D3semidirect
81. #5046D3semidirect
154. #3714D4semidirect
181. C2×#216C2×D3semidirect
184. C2×#215C2×D3semidirect
185. C2×#215C2×D3semidirect
242. #835C2×D3semidirect
252. #810C2×D3semidirect
255. #809C2×D3semidirect
256. #809C2×D3semidirect
257. #807C2×D3semidirect
478. C22×C32#135semidirect
772. C22×C3#916semidirect
773. C22×C3#919semidirect
841. C32#3280semidirect
938. C22#63950semidirect
951. C3#80168semidirect
952. C3#80773semidirect

Maximal subgroups

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

subgroupindex
#105961012
C2×#639502
#105948892
C22×#37142
C3×#50512
C3×#50462
#105916102
#105915932
#105915702
#105911832
#105911482
#105906172
#105905402
#105905092
#105904592
#807733
#801683