Finite Group Databasebeta

← #11884266

Subgroups — #11884266

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596022C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×#63829C211yesmaximal, characteristic, complemented
5C3×#5011C211yesmaximal, characteristic, complemented
6#10591184C211yesmaximal, characteristic, complemented
7#10591182C211yesmaximal, characteristic, complemented
8#10591175C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10591172C211yesmaximal, characteristic, complemented
11#10591121C211yesmaximal, characteristic, complemented
12#10590372C211yesmaximal, characteristic, complemented
13#10590365C211yesmaximal, characteristic, complemented
14#10590356C211yesmaximal, characteristic, complemented
15#10590346C211yesmaximal, characteristic, complemented
16#83503—31nomaximal
17#79496—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23#64147—21no—
24#64133C2211yescharacteristic
25#64133C2211yescharacteristic, complemented
26C4⋊C4×C3⋊D3—21no—
27#64092—21no—
28#64092—21no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
30#64078C2211yescharacteristic, complemented
31C3×#937—21no—
32C3×#930C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#894—21no—
37C3×#884—21no—
38C3×D3×C22⋊C4—21no—
39C3×#875C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C2×#3719C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic, complemented
44#63830—24no—
45#63829—24no—
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
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#63567C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic
63C3×#546—31no—
64C2×#950—31no—
65C2×#932—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5551—31no—
69#5551—31no—
70#5551—61no—
71#5550D311yescharacteristic, complemented
72C3×#435—31no—
73#5239—31no—
74#5218—31no—
75#5137—31no—
76#5114—31no—
77#5060—31no—
78#5057—31no—
79#5052—31no—
80#5047—31no—
81#5041—31no—
82#5037—31no—
83#5019—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—22no—
102#3828—41no—
103#3828—41no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3—21no—
108C2×#634C2311yescharacteristic
109C2×#634C2311yescharacteristic
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C3×#235—22no—
113C3×#235—41no—
114C2×C3×D12—22no—
115C2×C3×D12—21no—
116C2×C3×D12—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×Dic6C2311yescharacteristic
122C32×C4⋊C4D411yescharacteristic
123C32×C22⋊C4D411yescharacteristic
124C32×C22⋊C4D411yescharacteristic
125C32×C42C2311yescharacteristic
126#3757—21no—
127#3757—21no—
128#3752—21no—
129C4⋊(C3⋊Dic3)—21no—
130C4⋊(C3⋊Dic3)—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3750—21no—
133#3750—21no—
134C3×#217—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
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#3716—22no—
151#3716—22no—
152#3716—22no—
153#3716—41no—
154#3714—22no—
155#3714D414yescomplemented
156#3267—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#235—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—61no—
164C2×#235—61no—
165C2×#235C2×D311yescharacteristic
166C22×D12C2×D311yescharacteristic
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×#124—31no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#120—61no—
175C3×C4×D4—21no—
176C3×C4×D4—31no—
177C3×C4×D4C2×D311yescharacteristic
178C3×C4×D4C2×D311yescharacteristic
179C2×C3×C22⋊C4—61no—
180#950—64no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#215—31no—
184#938—62no—
185#938—61no—
186#938—61no—
187#937—21no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192#932—64no—
193C2×#213—31no—
194C2×#213—31no—
195#930C2×D311yescharacteristic
196#924—31no—
197#924—31no—
198#924—31no—
199#924—31no—
200#924—61no—
201#924—61no—
202#924C2×D311yescharacteristic
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—21no—
217D3×C4⋊C4—62no—
218D3×C4⋊C4—61no—
219D3×C4⋊C4—61no—
220#884—21no—
221#883—62no—
222#883—62no—
223#883—61no—
224#883—61no—
225#883—61no—
226#883—61no—
227D3×C22⋊C4—21no—
228#875C2×D311yescharacteristic
229C4×D12—31no—
230C4×D12—31no—
231C4×D12—61no—
232C4×D12C2×D311yescharacteristic
233#869—31no—
234#869—31no—
235#869—61no—
236C3×C4⋊C8—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#835—31no—
241#832—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#810—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—21no—
263C22×C3×D3—42no—
264C22×C3×D3—42no—
265C22×C3×D3—81no—
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—42no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)C2×D412yes—
283C4×C3⋊D3—42no—
284C4×C3⋊D3—42no—
285C4×C3⋊D3—42no—
286#634—21no—
287#634—21no—
288#634—21no—
289#634—21no—
290C3×#67—42no—
291C3×#67—81no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—42no—
298C3×D12C2×D412yes—
299C3×C4×D3—42no—
300C3×C4×D3—81no—
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—91no—
310#546—31no—
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—
322C24×C3—61no—
323C23×D3—21no—
324C3×#41—62no—
325C3×#41—121no—
326C2×C3×Q8—31no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—62no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—121no—
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×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353#235—22no—
354#235—41no—
355#235—62no—
356#235—62no—
357#235—62no—
358#235—62no—
359#235—122no—
360#235—122no—
361#235—121no—
362#235—121no—
363#235—121no—
364#235—121no—
365#235—122no—
366#235—122no—
367C2×D12—22no—
368C2×D12—21no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—41no—
372C2×D12—61no—
373C2×D12C22×D311yescharacteristic
374C2×D12C22×D311yescharacteristic
375C2×C4×D3—21no—
376C2×C4×D3—21no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×Dic6—31no—
387C2×Dic6—31no—
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C2×Dic6—61no—
392C2×Dic6C22×D311yescharacteristic
393C3×M16—62no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—62no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4D1211yescharacteristic
403C3×C4⋊C4#6711yescharacteristic
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4D1211yescharacteristic
412C3×C22⋊C4D1211yescharacteristic
413C3×C22⋊C4#6711yescharacteristic
414C3×C22⋊C4#6711yescharacteristic
415C3×C42—21no—
416C3×C42C22×D311yescharacteristic
417C3×C42C22×D311yescharacteristic
418#217—21no—
419#217—62no—
420#217—62no—
421#217—61no—
422#217—61no—
423#217—61no—
424#217—61no—
425#216—62no—
426#216—121no—
427#215—62no—
428#214—62no—
429#214—62no—
430#214—62no—
431#214—121no—
432#213—34no—
433#213—62no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441C4⋊Dic3—31no—
442C4⋊Dic3—31no—
443C4⋊Dic3—61no—
444C4⋊Dic3—62no—
445C4⋊Dic3—62no—
446C4⋊Dic3—61no—
447C4⋊Dic3—61no—
448C4⋊Dic3—61no—
449C4⋊Dic3—61no—
450C4⋊Dic3C22×D311yescharacteristic
451Dic3⋊C4—21no—
452Dic3⋊C4—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—61no—
455Dic3⋊C4—61no—
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—22no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—84no—
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—91no—
503C2×#41—91no—
504C22×D4—31no—
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—91no—
519#124—31no—
520#123—61no—
521#123—181no—
522#123—181no—
523C22⋊Q8—31no—
524C22⋊Q8—91no—
525C22⋊Q8—91no—
526#121—31no—
527#121—61no—
528#121—181no—
529#120—61no—
530C4×D4—31no—
531C4×D4—91no—
532C4×D4D3211yescharacteristic
533C2×C4⋊C4—181no—
534C2×C22⋊C4—61no—
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×C3—61no—
550C23×C3—122no—
551C23×C3—122no—
552C23×C3—241no—
553C23×C3C2×D1211yescharacteristic
554C23×C3C2×D1211yescharacteristic
555C23×C3C2×#6711yescharacteristic
556C23×C3C2×#6711yescharacteristic
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—42no—
560C22×D3—42no—
561C22×D3—62no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—81no—
565C3×Q8—61no—
566C3×Q8—61no—
567C3×D4—32no—
568C3×D4—41no—
569C3×D4—41no—
570C3×D4—42no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—122no—
575C3×D4—122no—
576C3×D4—241no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
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—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—122no—
597C2×C3×C4—241no—
598C2×C3×C4C2×D1211yescharacteristic
599C2×C3×C4C2×D1211yescharacteristic
600C2×C3×C4C2×D1211yescharacteristic
601C2×C3×C4C2×D1211yescharacteristic
602C2×C3×C4C2×#6711yescharacteristic
603C2×C3×C4C2×#6711yescharacteristic
604C2×C3×C4C2×#6711yescharacteristic
605C2×C3×C4C2×#6711yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608#67—42no—
609#67—81no—
610#67—122no—
611#67—122no—
612#67—122no—
613#67—122no—
614#67—124no—
615#67—124no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—32no—
631D12—32no—
632D12—42no—
633D12—62no—
634D12—62no—
635D12—61no—
636D12—61no—
637D12D3×D412yes—
638C4×D3—42no—
639C4×D3—81no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—124no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—124no—
648C4×D3—124no—
649Dic6—21no—
650Dic6—21no—
651Dic6—61no—
652Dic6—61no—
653Dic6—61no—
654Dic6—61no—
655Dic6—61no—
656Dic6—61no—
657Dic6—61no—
658Dic6—61no—
659Dic6—121no—
660Dic6—121no—
661Dic6—121no—
662Dic6—121no—
663C3×C8—32no—
664C3×C8—61no—
665C3×C8—61no—
666C3×C8—61no—
667C3⋊C8—21no—
668C3⋊C8—21no—
669C3⋊C8—21no—
670C3⋊C8D3×D412yes—
671C2×C32—41no—
672C2×C32—41no—
673C2×C32D4211yescharacteristic
674C2×C32#57511yescharacteristic
675C2×C32#57711yescharacteristic
676C3⋊D3—42no—
677C3×D3—42no—
678C3×D3—81no—
679C24—61no—
680#41—62no—
681#41—121no—
682#41—182no—
683#41—182no—
684#41—361no—
685#41—361no—
686C2×Q8—31no—
687C2×Q8—91no—
688C2×Q8—91no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—62no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—91no—
696C2×D4—121no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4#62611yescharacteristic
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—181no—
703C22×C4—181no—
704C22×C4—181no—
705C22×C4C2×D3211yescharacteristic
706C22×C4C2×D3211yescharacteristic
707Q16—182no—
708Q16—361no—
709SD16—182no—
710SD16—182no—
711SD16—182no—
712SD16—182no—
713SD16—361no—
714D8—94no—
715D8—182no—
716M16—62no—
717C2×C8—31no—
718C2×C8—31no—
719C2×C8—31no—
720C2×C8—31no—
721C2×C8—62no—
722C4⋊C4—31no—
723C4⋊C4—61no—
724C4⋊C4—91no—
725C4⋊C4—181no—
726C4⋊C4—181no—
727C4⋊C4—181no—
728C4⋊C4—181no—
729C4⋊C4#62611yescharacteristic
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4#62611yescharacteristic
739C22⋊C4#62611yescharacteristic
740C42C2×D3211yescharacteristic
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
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—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—62no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—244no—
767C22×C3C22×D1211yescharacteristic
768C22×C3C22×#6711yescharacteristic
769C2×D3—22no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—64no—
776C2×D3—62no—
777C2×D3—62no—
778C2×D3—84no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C3×C4—22no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—121no—
800C3×C4—121no—
801C3×C4C2×D3×D411yescharacteristic
802C3×C4C2×D3×D411yescharacteristic
803C3×C4#100411yescharacteristic
804C3×C4#100911yescharacteristic
805Dic3—41no—
806Dic3—41no—
807Dic3—122no—
808Dic3—122no—
809Dic3—122no—
810Dic3—121no—
811Dic3—121no—
812Dic3—121no—
813Dic3—121no—
814Dic3—121no—
815Dic3—121no—
816C32#326711yescharacteristic, complemented, Sylow
817C23—61no—
818C23—61no—
819C23—122no—
820C23—122no—
821C23—181no—
822C23—241no—
823C23C2×#62611yescharacteristic
824C23C2×#62611yescharacteristic
825Q8—61no—
826Q8—61no—
827Q8—181no—
828Q8—181no—
829Q8—181no—
830Q8—181no—
831D4—32no—
832D4—41no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—92no—
837D4—122no—
838D4—122no—
839D4—181no—
840D4—241no—
841D4—362no—
842D4—362no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—122no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—181no—
853C2×C4—241no—
854C2×C4—362no—
855C2×C4—362no—
856C2×C4—362no—
857C2×C4C2×#62611yescharacteristic
858C2×C4C2×#62611yescharacteristic
859C2×C4C2×#62611yescharacteristic
860C2×C4C2×#62611yescharacteristic
861C2×C4C22×D3211yescharacteristic
862C8—32no—
863C8—61no—
864C8—61no—
865C8—61no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—41no—
870C2×C3—41no—
871C2×C3—41no—
872C2×C3—41no—
873C2×C3—81no—
874C2×C3—81no—
875C2×C3—122no—
876C2×C3—241no—
877C2×C3D4×D1211yescharacteristic
878C2×C3#574811yescharacteristic
879C2×C3#575111yescharacteristic
880C2×C3D4×#6711yescharacteristic
881C2×C3#582211yescharacteristic
882C2×C3#583611yescharacteristic
883D3—42no—
884D3—81no—
885D3—124no—
886D3—122no—
887D3—122no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—62no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—182no—
901C22—244no—
902C22—361no—
903C22—361no—
904C22C22×#62611yescharacteristic
905C4—21no—
906C4—21no—
907C4—21no—
908C4—21no—
909C4—121no—
910C4—121no—
911C4—361no—
912C4—361no—
913C4—361no—
914C4D32×D411yescharacteristic
915C4#6431411yescharacteristic
916C3—21no—
917C3#7949611yescharacteristic, complemented
918C3#8350311yescharacteristic, complemented
919C2—41no—
920C2—41no—
921C2—122no—
922C2—241no—
923C2—362no—
924C2#1059479511yescharacteristic
925C2D4×#62611yescharacteristic
926C2#1059544711yescharacteristic
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. #10596022C2semidirect
2. C3×#5550C2semidirect
3. C2×#63830C2semidirect
4. C2×#63829C2semidirect
5. C3×#5011C2semidirect
6. #10591184C2semidirect
7. #10591182C2semidirect
8. #10591175C2semidirect
9. #10591173C2semidirect
10. #10591172C2semidirect
11. #10591121C2semidirect
12. #10590372C2semidirect
13. #10590365C2semidirect
14. #10590356C2semidirect
15. #10590346C2semidirect
19. C2×#3828C22semidirect
25. #64133C22semidirect
29. C4×C4⋊(C3⋊D3)C22semidirect
30. #64078C22semidirect
35. C22×C3×C3⋊C8C22semidirect
41. C2×#3719C22semidirect
42. C2×#3719C22semidirect
43. C2×#3717C22semidirect
53. C3×#830C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. C3×#803C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
71. #5550D3semidirect
85. #5011D3semidirect
155. #3714D4semidirect
204. C22×C3⋊C8C2×D3semidirect
244. #830C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
816. C32#3267semidirect
917. C3#79496semidirect
918. C3#83503semidirect

Maximal subgroups

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

subgroupindex
#105960222
C3×#55502
C2×#638302
C2×#638292
C3×#50112
#105911842
#105911822
#105911752
#105911732
#105911722
#105911212
#105903722
#105903652
#105903562
#105903462
#835033
#794963