Finite Group Databasebeta

← #11884267

Subgroups — #11884267

Order 1152.

1167 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596021C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5011C211yesmaximal, characteristic, complemented
6#10591184C211yesmaximal, characteristic, complemented
7#10591183C211yesmaximal, characteristic, complemented
8#10591177C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10591163C211yesmaximal, characteristic, complemented
11#10591121C211yesmaximal, characteristic, complemented
12#10590379C211yesmaximal, characteristic, complemented
13#10590374C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590346C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#79496—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23#64146—21no—
24#64139C2211yescharacteristic
25#64133C2211yescharacteristic
26#64103—21no—
27#64093—21no—
28C22⋊C4×C3⋊D3—21no—
29#64084C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C3×#938—21no—
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×D3×C4⋊C4—21no—
37C3×#883—21no—
38C3×#883—21no—
39C3×C4×D12C2211yescharacteristic, complemented
40C3×#869C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47#63829—24no—
48C2×#3716C2211yescharacteristic, complemented
49#63825—24no—
50C2×#3714C2211yescharacteristic
51C2×#3714C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×#830C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63564C2211yescharacteristic
62#63563C2211yescharacteristic, complemented
63C3×#547—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5551D311yescharacteristic, complemented
69#5550—31no—
70#5550—31no—
71#5550—61no—
72C3×#435—31no—
73#5239—31no—
74#5238—31no—
75#5137—31no—
76#5114—31no—
77#5086—31no—
78#5083—31no—
79#5052—31no—
80#5048—31no—
81#5047—31no—
82#5046—31no—
83#5016—31no—
84#5014—31no—
85#5011D311yescharacteristic, complemented
86#4844—31no—
87#4841—31no—
88#4734—31no—
89#4733—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4711—31no—
94C23×C3⋊D3—21no—
95C2×C32×D4D411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100#3828—22no—
101#3828—41no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3—21no—
109C2×#634C2311yescharacteristic
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C3×#235—22no—
113C3×#235—22no—
114C3×#235—41no—
115C3×#235—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3—21no—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C32×C4⋊C4D411yescharacteristic
123C32×C22⋊C4D411yescharacteristic
124C32×C22⋊C4D411yescharacteristic
125C32×C42C2311yescharacteristic
126#3757—21no—
127#3752—21no—
128#3752—21no—
129#3752—21no—
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3750—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×#208—22no—
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3719—22no—
148#3719—41no—
149#3717—22no—
150#3717—22no—
151#3717—22no—
152#3717—41no—
153#3716—22no—
154#3714—22no—
155#3714D414yescomplemented
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#235—31no—
160C2×#235—31no—
161C2×#235—61no—
162C2×#235C2×D311yescharacteristic
163C2×#235C2×D311yescharacteristic, complemented
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×C4⋊Q8—31no—
170C3×#123—61no—
171C3×#123—61no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×#121—61no—
175C3×C4×D4—21no—
176C3×C4×D4—31no—
177C3×C4×D4C2×D311yescharacteristic
178C3×C4×D4C2×D311yescharacteristic
179C2×C3×C4⋊C4—61no—
180#950—64no—
181#949—64no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188#938—21no—
189#937—62no—
190#937—61no—
191#937—61no—
192C2×#214—31no—
193C2×#213—31no—
194C2×#213—31no—
195#930—31no—
196#930—31no—
197#930—61no—
198#924—31no—
199#924—31no—
200#924—61no—
201#924C2×D311yescharacteristic
202#924C2×D311yescharacteristic, complemented
203C2×#208C2×D311yescharacteristic
204C22×C3⋊C8C2×D311yescharacteristic, complemented
205#908—64no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208#904—64no—
209C2×D24—31no—
210C2×D24—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—31no—
216#894—62no—
217#894—61no—
218#894—61no—
219D3×C4⋊C4—21no—
220#884—62no—
221#884—61no—
222#884—61no—
223#883—21no—
224#883—21no—
225D3×C22⋊C4—62no—
226D3×C22⋊C4—61no—
227D3×C22⋊C4—61no—
228#875—31no—
229#875—31no—
230#875—61no—
231C4×D12—31no—
232C4×D12—31no—
233C4×D12—61no—
234C4×D12C2×D311yescharacteristic, complemented
235#869C2×D311yescharacteristic, complemented
236C3×C4⋊C8—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#835—31no—
241#835—31no—
242#832—31no—
243#830C2×D311yescharacteristic
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247#821—31no—
248#817—31no—
249#816—31no—
250#816—31no—
251#816—31no—
252#810—31no—
253#809—31no—
254#809—31no—
255#808—31no—
256C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
257#803C2×D311yescharacteristic, complemented
258C23×C32C2×D411yescharacteristic
259C23×C32C2×D411yescharacteristic
260C22×C3⋊D3—21no—
261C22×C3⋊D3—21no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—81no—
265C22×C3×D3—21no—
266C32×D4—41no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276#638—42no—
277#638—81no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)—42no—
284C4⋊(C3⋊D3)C2×D412yes—
285C4×C3⋊D3—42no—
286C4×C3⋊D3—81no—
287#634—21no—
288#634—21no—
289C3×#67—42no—
290C3×#67—42no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C3×D12—21no—
295C3×D12C2×D412yes—
296C3×C4×D3—42no—
297C3×C4×D3—42no—
298C3×C4×D3—42no—
299C3×Dic6—21no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302C3×Dic6—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C3×C3⋊C8C2×D412yes—
307C2×AGL(1,ℤ/8)—91no—
308C2×#135—91no—
309#547—31no—
310#546—91no—
311#497—91no—
312#470—91no—
313#465—91no—
314#463—91no—
315#461—91no—
316#452—91no—
317#452—91no—
318#450—91no—
319#449—91no—
320#442—91no—
321#435—31no—
322C23×D3—62no—
323C23×D3—61no—
324C23×D3—61no—
325C3×#41—62no—
326C3×#41—62no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—31no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4D1211yescharacteristic
336C2×C3×D4#6711yescharacteristic
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—62no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—62no—
352C2×#67—61no—
353C2×#67—61no—
354#235—22no—
355#235—22no—
356#235—41no—
357#235—41no—
358#235—62no—
359#235—62no—
360#235—122no—
361#235—121no—
362#235—121no—
363#235—122no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—122no—
376C2×D12—121no—
377C2×D12—121no—
378C2×D12—122no—
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—62no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—62no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×Dic6—31no—
390C2×Dic6—31no—
391C2×Dic6—61no—
392C2×Dic6C22×D311yescharacteristic
393C2×Dic6C22×D311yescharacteristic
394C3×M16—62no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4—61no—
406C3×C4⋊C4D1211yescharacteristic
407C3×C4⋊C4#6711yescharacteristic
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4D1211yescharacteristic
414C3×C22⋊C4D1211yescharacteristic
415C3×C22⋊C4#6711yescharacteristic
416C3×C22⋊C4#6711yescharacteristic
417C3×C42—21no—
418C3×C42C22×D311yescharacteristic
419C3×C42C22×D311yescharacteristic
420#217—21no—
421#217—21no—
422#217—62no—
423#217—61no—
424#217—61no—
425#216—62no—
426#216—121no—
427#215—62no—
428#215—62no—
429#215—62no—
430#215—121no—
431#214—62no—
432#213—34no—
433#213—62no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
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—
447C4⋊Dic3—21no—
448C4⋊Dic3—21no—
449C4⋊Dic3—31no—
450C4⋊Dic3—31no—
451C4⋊Dic3—61no—
452C4⋊Dic3C22×D311yescharacteristic
453Dic3⋊C4—21no—
454Dic3⋊C4—21no—
455Dic3⋊C4—62no—
456Dic3⋊C4—61no—
457Dic3⋊C4—61no—
458#208—22no—
459C2×C3⋊C8—22no—
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463C2×C3⋊C8C22×D311yescharacteristic
464Dic12—62no—
465Dic12—121no—
466D24—34no—
467D24—62no—
468#204—62no—
469#204—62no—
470#204—62no—
471#204—62no—
472#204—121no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—84no—
487C2×C3×D3—22no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—21no—
494C32×C4C22×D411yescharacteristic
495C32×C4H(5,𝔽2)11yescharacteristic
496C3⋊Dic3—41no—
497C3⋊Dic3—41no—
498C3×Dic3—41no—
499C3×Dic3—41no—
500C3×Dic3—41no—
501C2×#41—31no—
502C2×#41—31no—
503C2×#41—91no—
504C22×D4—91no—
505AGL(1,ℤ/8)—184no—
506#135—184no—
507C2×Q16—91no—
508C2×Q16—91no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—91no—
513C2×SD16—91no—
514C2×D8—91no—
515C2×D8—91no—
516C2×M16—31no—
517C22×C8—31no—
518C4⋊Q8—31no—
519#124—91no—
520#123—61no—
521#123—61no—
522#123—181no—
523C22⋊Q8—31no—
524C22⋊Q8—31no—
525C22⋊Q8—91no—
526#121—61no—
527#121—91no—
528#121—181no—
529#120—181no—
530C4×D4—31no—
531C4×D4—91no—
532C4×D4D3211yescharacteristic
533C2×C4⋊C4—61no—
534C2×C22⋊C4—181no—
535#106—91no—
536C4⋊C8—31no—
537#103—91no—
538#103—91no—
539#103—91no—
540#102—91no—
541#102—91no—
542#102—91no—
543C22⋊C8—31no—
544C22⋊C8—31no—
545#97—31no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—61no—
549C23×C3C2×D1211yescharacteristic
550C23×C3C2×D1211yescharacteristic
551C23×C3C2×#6711yescharacteristic
552C23×C3C2×#6711yescharacteristic
553C22×D3—21no—
554C22×D3—62no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—62no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—124no—
563C22×D3—124no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3—242no—
569C3×Q8—61no—
570C3×Q8—61no—
571C3×Q8—61no—
572C3×Q8—61no—
573C3×D4—32no—
574C3×D4—41no—
575C3×D4—41no—
576C3×D4—42no—
577C3×D4—61no—
578C3×D4—122no—
579C3×D4—122no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—122no—
601C2×C3×C4—122no—
602C2×C3×C4—122no—
603C2×C3×C4C2×D1211yescharacteristic
604C2×C3×C4C2×D1211yescharacteristic
605C2×C3×C4C2×D1211yescharacteristic
606C2×C3×C4C2×D1211yescharacteristic
607C2×C3×C4C2×#6711yescharacteristic
608C2×C3×C4C2×#6711yescharacteristic
609C2×C3×C4C2×#6711yescharacteristic
610C2×C3×C4C2×#6711yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612C2×C3×C4C23×D311yescharacteristic
613#67—42no—
614#67—42no—
615#67—122no—
616#67—122no—
617#67—124no—
618#67—241no—
619#67—241no—
620#67—242no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630D12—21no—
631D12—32no—
632D12—32no—
633D12—62no—
634D12—62no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—61no—
640D12—61no—
641D12—121no—
642D12—121no—
643D12—122no—
644D12—122no—
645D12—124no—
646D12D3×D412yes—
647C4×D3—42no—
648C4×D3—42no—
649C4×D3—42no—
650C4×D3—122no—
651C4×D3—122no—
652C4×D3—124no—
653C4×D3—241no—
654C4×D3—241no—
655C4×D3—242no—
656Dic6—21no—
657Dic6—21no—
658Dic6—21no—
659Dic6—21no—
660Dic6—61no—
661Dic6—61no—
662Dic6—61no—
663Dic6—61no—
664Dic6—121no—
665Dic6—121no—
666C3×C8—32no—
667C3×C8—61no—
668C3×C8—61no—
669C3×C8—61no—
670C3⋊C8—21no—
671C3⋊C8—21no—
672C3⋊C8—21no—
673C3⋊C8D3×D412yes—
674C2×C32—41no—
675C2×C32—41no—
676C2×C32D4211yescharacteristic
677C2×C32#57511yescharacteristic
678C2×C32#57711yescharacteristic
679C3⋊D3—42no—
680C3⋊D3—81no—
681C3×D3—42no—
682C24—181no—
683#41—62no—
684#41—62no—
685#41—121no—
686#41—121no—
687#41—182no—
688#41—361no—
689C2×Q8—31no—
690C2×Q8—31no—
691C2×Q8—91no—
692C2×D4—31no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—91no—
696C2×D4—91no—
697C2×D4—182no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—361no—
702C2×D4#62611yescharacteristic
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—181no—
707C22×C4—181no—
708C22×C4C2×D3211yescharacteristic
709C22×C4C2×D3211yescharacteristic
710Q16—182no—
711Q16—361no—
712SD16—182no—
713SD16—182no—
714SD16—182no—
715SD16—182no—
716SD16—361no—
717D8—94no—
718D8—182no—
719M16—62no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—31no—
723C2×C8—31no—
724C2×C8—62no—
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—61no—
728C4⋊C4—61no—
729C4⋊C4—61no—
730C4⋊C4—91no—
731C4⋊C4—181no—
732C4⋊C4#62611yescharacteristic
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C22⋊C4—181no—
740C22⋊C4—181no—
741C22⋊C4#62611yescharacteristic
742C22⋊C4#62611yescharacteristic
743C42C2×D3211yescharacteristic
744C22×C3—22no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—62no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3C22×D1211yescharacteristic
767C22×C3C22×#6711yescharacteristic
768C2×D3—22no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—64no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—122no—
775C2×D3—122no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—248no—
790C2×D3—244no—
791C2×D3—244no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—121no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4C2×D3×D411yescharacteristic
810C3×C4C2×D3×D411yescharacteristic
811C3×C4#100411yescharacteristic
812C3×C4#100911yescharacteristic
813Dic3—41no—
814Dic3—41no—
815Dic3—41no—
816Dic3—122no—
817Dic3—122no—
818Dic3—121no—
819Dic3—121no—
820Dic3—121no—
821Dic3—121no—
822C32#326711yescharacteristic, complemented, Sylow
823C23—61no—
824C23—181no—
825C23—181no—
826C23—362no—
827C23—362no—
828C23—721no—
829C23C2×#62611yescharacteristic
830C23C2×#62611yescharacteristic
831Q8—61no—
832Q8—61no—
833Q8—61no—
834Q8—61no—
835Q8—181no—
836Q8—181no—
837D4—32no—
838D4—41no—
839D4—61no—
840D4—92no—
841D4—122no—
842D4—122no—
843D4—181no—
844D4—181no—
845D4—181no—
846D4—362no—
847D4—362no—
848D4—721no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—122no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—362no—
862C2×C4—721no—
863C2×C4C2×#62611yescharacteristic
864C2×C4C2×#62611yescharacteristic
865C2×C4C2×#62611yescharacteristic
866C2×C4C2×#62611yescharacteristic
867C2×C4C22×D3211yescharacteristic
868C8—32no—
869C8—61no—
870C8—61no—
871C8—61no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—42no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—41no—
879C2×C3—41no—
880C2×C3—81no—
881C2×C3—122no—
882C2×C3D4×D1211yescharacteristic
883C2×C3#574811yescharacteristic
884C2×C3#575111yescharacteristic
885C2×C3D4×#6711yescharacteristic
886C2×C3#582211yescharacteristic
887C2×C3#583711yescharacteristic
888D3—42no—
889D3—124no—
890D3—122no—
891D3—122no—
892D3—242no—
893D3—241no—
894D3—241no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—62no—
902C22—121no—
903C22—121no—
904C22—182no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—724no—
911C22C22×#62611yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—121no—
917C4—121no—
918C4—121no—
919C4—361no—
920C4—361no—
921C4D32×D411yescharacteristic
922C4#6431411yescharacteristic
923C3—21no—
924C3#7949611yescharacteristic, complemented
925C3#8352211yescharacteristic, complemented
926C2—41no—
927C2—41no—
928C2—122no—
929C2—362no—
930C2—721no—
931C2#1059479511yescharacteristic
932C2D4×#62611yescharacteristic
933C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596021C2semidirect
2. C3×#5551C2semidirect
3. C2×#63829C2semidirect
4. C2×#63825C2semidirect
5. C3×#5011C2semidirect
6. #10591184C2semidirect
7. #10591183C2semidirect
8. #10591177C2semidirect
9. #10591173C2semidirect
10. #10591163C2semidirect
11. #10591121C2semidirect
12. #10590379C2semidirect
13. #10590374C2semidirect
14. #10590366C2semidirect
15. #10590346C2semidirect
21. C2×C3×#235C22semidirect
33. C3×#924C22semidirect
35. C22×C3×C3⋊C8C22semidirect
39. C3×C4×D12C22semidirect
40. C3×#869C22semidirect
41. C2×#3719C22semidirect
42. C2×#3719C22semidirect
48. C2×#3716C22semidirect
53. C3×#830C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. C3×#803C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
59. #63566C22semidirect
62. #63563C22semidirect
68. #5551D3semidirect
85. #5011D3semidirect
155. #3714D4semidirect
163. C2×#235C2×D3semidirect
202. #924C2×D3semidirect
204. C22×C3⋊C8C2×D3semidirect
234. C4×D12C2×D3semidirect
235. #869C2×D3semidirect
244. #830C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
822. C32#3267semidirect
924. C3#79496semidirect
925. C3#83522semidirect

Maximal subgroups

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

subgroupindex
#105960212
C3×#55512
C2×#638292
C2×#638252
C3×#50112
#105911842
#105911832
#105911772
#105911732
#105911632
#105911212
#105903792
#105903742
#105903662
#105903462
#835223
#794963