Finite Group Databasebeta

← #11884422

Subgroups — #11884422

Order 1152.

1187 conjugacy classes of subgroups.

The subgroup lattice has 959 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596021C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5011C211yesmaximal, characteristic, complemented
6#10591182C211yesmaximal, characteristic, complemented
7#10591176C211yesmaximal, characteristic, complemented
8#10591173C211yesmaximal, characteristic, complemented
9#10591168C211yesmaximal, characteristic, complemented
10#10591164C211yesmaximal, characteristic, complemented
11#10591163C211yesmaximal, characteristic, complemented
12#10590371C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15#10590355C211yesmaximal, characteristic, complemented
16#83577—31nomaximal
17#79497—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×#940—21no—
32C3×#930C2211yescharacteristic
33C3×#930C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#893—21no—
37C3×#884—21no—
38C3×#884—21no—
39C3×#874C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44#63829—24no—
45C2×#3716C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47#63825—24no—
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×#3714C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×#830C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C3×#550—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5553D311yescharacteristic, complemented
69#5550—31no—
70#5550—31no—
71#5550—61no—
72C3×#435—31no—
73#5239—31no—
74#5238—31no—
75#5134—31no—
76#5115—31no—
77#5074—31no—
78#5072—31no—
79#5042—31no—
80#5038—31no—
81#5037—31no—
82#5036—31no—
83#5028—31no—
84#5026—31no—
85#5011D311yescharacteristic, complemented
86#4845—31no—
87#4843—31no—
88#4734—31no—
89#4734—31no—
90#4733—31no—
91#4732—31no—
92#4712—31no—
93#4710—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—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C3×#235—22no—
115C3×#235—22no—
116C3×#235—41no—
117C3×#235—41no—
118C2×C3×D12—21no—
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3—21no—
124C2×C3×Dic6C2311yescharacteristic
125C32×C4⋊C4D411yescharacteristic
126C32×C22⋊C4D411yescharacteristic
127C32×C22⋊C4D411yescharacteristic
128C32×C42C2311yescharacteristic
129#3757—21no—
130#3752—21no—
131#3752—21no—
132#3752—21no—
133#3752—21no—
134C4⋊(C3⋊Dic3)C2311yescharacteristic
135#3750—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—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#3717—22no—
149#3717D414yescomplemented
150#3716—22no—
151#3716—41no—
152#3714—22no—
153#3714—22no—
154#3714—22no—
155#3714—41no—
156#3268—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×#127—31no—
170C3×#127—61no—
171C3×#121—31no—
172C3×#121—31no—
173C3×#121—61no—
174C3×#121—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—21no—
177C3×C4×D4—61no—
178C3×C4×D4C2×D311yescharacteristic
179C3×C4×D4C2×D311yescharacteristic
180#950—64no—
181#949—64no—
182C2×#216—31no—
183C2×#215—31no—
184C2×#215—31no—
185#940—21no—
186#937—62no—
187#937—61no—
188#937—61no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195#930—31no—
196#930—31no—
197#930—61no—
198#930C2×D311yescharacteristic
199#930C2×D311yescharacteristic, complemented
200#924—31no—
201#924—31no—
202#924—61no—
203C2×#208C2×D311yescharacteristic
204C22×C3⋊C8C2×D311yescharacteristic, complemented
205#908—64no—
206C2×Dic12—31no—
207#904—64no—
208C2×D24—31no—
209C2×D24—31no—
210C2×D24—31no—
211C2×D24—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—31no—
216#894—62no—
217#894—61no—
218#894—61no—
219#893—21no—
220#884—21no—
221#884—21no—
222#884—62no—
223#884—61no—
224#884—61no—
225D3×C22⋊C4—62no—
226D3×C22⋊C4—61no—
227D3×C22⋊C4—61no—
228#875—31no—
229#875—31no—
230#875—61no—
231#874C2×D311yescharacteristic, complemented
232C4×D12—31no—
233C4×D12—31no—
234C4×D12—61no—
235C4×Dic6C2×D311yescharacteristic, complemented
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#821—31no—
249#818—31no—
250#816—31no—
251#816—31no—
252#810—31no—
253#809—31no—
254#809—31no—
255#807—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—
266C22×C3×D3—21no—
267C32×D4—41no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—42no—
278#638—81no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)—21no—
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—42no—
285C4⋊(C3⋊D3)C2×D412yes—
286C4×C3⋊D3—42no—
287C4×C3⋊D3—81no—
288#634—21no—
289#634—21no—
290C3×#67—42no—
291C3×#67—42no—
292C3×#67—81no—
293C3×#67—81no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×D12—42no—
301C3×D12—81no—
302C3×C4×D3—42no—
303C3×C4×D3—42no—
304C3×Dic6—21no—
305C3×Dic6C2×D412yes—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×AGL(1,ℤ/8)—91no—
311C2×#135—91no—
312#550—31no—
313#546—91no—
314#496—91no—
315#468—91no—
316#466—91no—
317#464—91no—
318#459—91no—
319#452—91no—
320#449—91no—
321#449—91no—
322#447—91no—
323#440—91no—
324#435—31no—
325C23×D3—62no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—62no—
330C3×#41—121no—
331C3×#41—121no—
332C2×C3×Q8—31no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4D1211yescharacteristic
343C2×C3×D4#6711yescharacteristic
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—62no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—62no—
360C2×#67—61no—
361C2×#67—61no—
362#235—22no—
363#235—22no—
364#235—41no—
365#235—41no—
366#235—62no—
367#235—62no—
368#235—122no—
369#235—121no—
370#235—121no—
371#235—122no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—62no—
381C2×D12—62no—
382C2×D12—62no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12—122no—
386C2×D12—121no—
387C2×D12—121no—
388C2×D12—122no—
389C2×D12C22×D311yescharacteristic
390C2×D12C22×D311yescharacteristic
391C2×C4×D3—21no—
392C2×C4×D3—21no—
393C2×C4×D3—62no—
394C2×C4×D3—61no—
395C2×C4×D3—61no—
396C2×C4×D3—62no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×Dic6—31no—
400C2×Dic6—31no—
401C2×Dic6—61no—
402C2×Dic6C22×D311yescharacteristic
403C3×M16—62no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8—31no—
408C2×C3×C8—62no—
409C3×C4⋊C4—21no—
410C3×C4⋊C4—31no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4D1211yescharacteristic
413C3×C4⋊C4#6711yescharacteristic
414C3×C22⋊C4—21no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—61no—
417C3×C22⋊C4—61no—
418C3×C22⋊C4D1211yescharacteristic
419C3×C22⋊C4D1211yescharacteristic
420C3×C22⋊C4#6711yescharacteristic
421C3×C22⋊C4#6711yescharacteristic
422C3×C42—21no—
423C3×C42—61no—
424C3×C42C22×D311yescharacteristic
425C3×C42C22×D311yescharacteristic
426#217—62no—
427#217—61no—
428#217—61no—
429#216—62no—
430#215—34no—
431#215—62no—
432#214—62no—
433#214—121no—
434#213—62no—
435#213—62no—
436#213—62no—
437#213—121no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
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—61no—
452C4⋊Dic3—31no—
453C4⋊Dic3—31no—
454C4⋊Dic3—61no—
455C4⋊Dic3C22×D311yescharacteristic
456Dic3⋊C4—21no—
457Dic3⋊C4—62no—
458Dic3⋊C4—61no—
459Dic3⋊C4—61no—
460C4×Dic3—21no—
461#208—22no—
462C2×C3⋊C8—22no—
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466C2×C3⋊C8C22×D311yescharacteristic
467Dic12—62no—
468D24—62no—
469D24—62no—
470D24—62no—
471D24—121no—
472#204—34no—
473#204—62no—
474#204—62no—
475#204—121no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32C22×D411yescharacteristic
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—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C32×C4—21no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—21no—
500C32×C4C22×D411yescharacteristic
501C32×C4H(5,𝔽2)11yescharacteristic
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—41no—
506C2×#41—31no—
507C2×#41—31no—
508C2×#41—91no—
509C22×D4—91no—
510AGL(1,ℤ/8)—184no—
511#135—184no—
512C2×Q16—91no—
513C2×SD16—91no—
514C2×SD16—91no—
515C2×SD16—91no—
516C2×SD16—91no—
517C2×D8—91no—
518C2×D8—91no—
519C2×D8—91no—
520C2×D8—91no—
521C2×M16—31no—
522C22×C8—31no—
523#127—31no—
524#127—61no—
525#124—91no—
526#123—181no—
527C22⋊Q8—91no—
528#121—31no—
529#121—31no—
530#121—61no—
531#121—61no—
532#121—91no—
533#121—181no—
534#120—181no—
535C4×Q8—31no—
536C4×D4—61no—
537C4×D4—91no—
538C4×D4D3211yescharacteristic
539C2×C22⋊C4—181no—
540#107—91no—
541C4⋊C8—31no—
542#103—91no—
543#103—91no—
544#102—91no—
545#102—91no—
546#102—91no—
547#102—91no—
548C22⋊C8—31no—
549C22⋊C8—31no—
550#97—31no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3C2×D1211yescharacteristic
556C23×C3C2×D1211yescharacteristic
557C23×C3C2×#6711yescharacteristic
558C23×C3C2×#6711yescharacteristic
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—62no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—62no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—124no—
570C22×D3—124no—
571C22×D3—122no—
572C22×D3—122no—
573C22×D3—241no—
574C22×D3—241no—
575C22×D3—242no—
576C3×Q8—32no—
577C3×Q8—61no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—42no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—241no—
589C3×D4—241no—
590C3×D4—241no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—122no—
611C2×C3×C4—122no—
612C2×C3×C4C2×D1211yescharacteristic
613C2×C3×C4C2×D1211yescharacteristic
614C2×C3×C4C2×D1211yescharacteristic
615C2×C3×C4C2×D1211yescharacteristic
616C2×C3×C4C2×#6711yescharacteristic
617C2×C3×C4C2×#6711yescharacteristic
618C2×C3×C4C2×#6711yescharacteristic
619C2×C3×C4C2×#6711yescharacteristic
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622#67—42no—
623#67—42no—
624#67—81no—
625#67—81no—
626#67—122no—
627#67—122no—
628#67—124no—
629#67—241no—
630#67—241no—
631#67—242no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640D12—21no—
641D12—21no—
642D12—21no—
643D12—21no—
644D12—32no—
645D12—32no—
646D12—42no—
647D12—62no—
648D12—62no—
649D12—61no—
650D12—61no—
651D12—61no—
652D12—61no—
653D12—61no—
654D12—61no—
655D12—81no—
656D12—121no—
657D12—121no—
658D12—122no—
659D12—122no—
660D12—124no—
661C4×D3—42no—
662C4×D3—42no—
663C4×D3—122no—
664C4×D3—122no—
665C4×D3—124no—
666C4×D3—241no—
667C4×D3—241no—
668C4×D3—242no—
669Dic6—21no—
670Dic6—61no—
671Dic6—61no—
672Dic6—61no—
673Dic6—61no—
674Dic6—121no—
675Dic6—121no—
676Dic6D3×D412yes—
677C3×C8—32no—
678C3×C8—61no—
679C3×C8—61no—
680C3×C8—61no—
681C3⋊C8—21no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8D3×D412yes—
685C2×C32—41no—
686C2×C32—41no—
687C2×C32D4211yescharacteristic
688C2×C32#57511yescharacteristic
689C2×C32#57611yescharacteristic
690C3⋊D3—42no—
691C3⋊D3—81no—
692C3×D3—81no—
693C3×D3—81no—
694C24—181no—
695#41—62no—
696#41—62no—
697#41—121no—
698#41—121no—
699#41—182no—
700#41—361no—
701C2×Q8—31no—
702C2×Q8—91no—
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—61no—
706C2×D4—61no—
707C2×D4—61no—
708C2×D4—61no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—91no—
712C2×D4—91no—
713C2×D4—182no—
714C2×D4—181no—
715C2×D4—181no—
716C2×D4—181no—
717C2×D4—361no—
718C2×D4#62611yescharacteristic
719C22×C4—61no—
720C22×C4—61no—
721C22×C4—181no—
722C22×C4—181no—
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725Q16—182no—
726SD16—94no—
727SD16—182no—
728SD16—182no—
729SD16—361no—
730D8—182no—
731D8—182no—
732D8—182no—
733D8—361no—
734M16—62no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—31no—
738C2×C8—31no—
739C2×C8—62no—
740C4⋊C4—31no—
741C4⋊C4—61no—
742C4⋊C4—91no—
743C4⋊C4—181no—
744C4⋊C4#62611yescharacteristic
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—181no—
748C22⋊C4—181no—
749C22⋊C4—181no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4#62611yescharacteristic
753C22⋊C4#62611yescharacteristic
754C42—61no—
755C42C2×D3211yescharacteristic
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3C22×D1211yescharacteristic
782C22×C3C22×#6711yescharacteristic
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—64no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—122no—
793C2×D3—122no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—122no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—248no—
808C2×D3—244no—
809C2×D3—244no—
810C3×C4—21no—
811C3×C4—21no—
812C3×C4—21no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—41no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—62no—
825C3×C4—121no—
826C3×C4C2×D3×D411yescharacteristic
827C3×C4C2×D3×D411yescharacteristic
828C3×C4#100411yescharacteristic
829C3×C4#100911yescharacteristic
830Dic3—22no—
831Dic3—41no—
832Dic3—122no—
833Dic3—122no—
834Dic3—121no—
835Dic3—121no—
836Dic3—121no—
837Dic3—121no—
838C32#326811yescharacteristic, complemented, Sylow
839C23—61no—
840C23—61no—
841C23—181no—
842C23—181no—
843C23—362no—
844C23—362no—
845C23—721no—
846C23C2×#62611yescharacteristic
847C23C2×#62611yescharacteristic
848Q8—32no—
849Q8—61no—
850Q8—181no—
851Q8—181no—
852D4—41no—
853D4—61no—
854D4—61no—
855D4—61no—
856D4—61no—
857D4—92no—
858D4—122no—
859D4—122no—
860D4—122no—
861D4—181no—
862D4—181no—
863D4—181no—
864D4—241no—
865D4—241no—
866D4—241no—
867D4—362no—
868D4—362no—
869D4—721no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—122no—
877C2×C4—122no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—362no—
881C2×C4—721no—
882C2×C4C2×#62611yescharacteristic
883C2×C4C2×#62611yescharacteristic
884C2×C4C2×#62611yescharacteristic
885C2×C4C2×#62611yescharacteristic
886C2×C4C22×D3211yescharacteristic
887C8—32no—
888C8—61no—
889C8—61no—
890C8—61no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—42no—
895C2×C3—41no—
896C2×C3—41no—
897C2×C3—41no—
898C2×C3—41no—
899C2×C3—81no—
900C2×C3—241no—
901C2×C3—241no—
902C2×C3D4×D1211yescharacteristic
903C2×C3#574811yescharacteristic
904C2×C3#575211yescharacteristic
905C2×C3D4×#6711yescharacteristic
906C2×C3#582211yescharacteristic
907C2×C3#583511yescharacteristic
908D3—81no—
909D3—81no—
910D3—124no—
911D3—122no—
912D3—122no—
913D3—242no—
914D3—241no—
915D3—241no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—182no—
929C22—361no—
930C22—361no—
931C22—361no—
932C22—361no—
933C22—361no—
934C22—724no—
935C22C22×#62611yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—62no—
941C4—121no—
942C4—361no—
943C4—361no—
944C4D32×D411yescharacteristic
945C4#6431411yescharacteristic
946C3—21no—
947C3#7949711yescharacteristic, complemented
948C3#8357711yescharacteristic, complemented
949C2—41no—
950C2—41no—
951C2—241no—
952C2—241no—
953C2—362no—
954C2—721no—
955C2#1059479511yescharacteristic
956C2D4×#62611yescharacteristic
957C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3268
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×#5553C2semidirect
3. C2×#63829C2semidirect
4. C2×#63825C2semidirect
5. C3×#5011C2semidirect
6. #10591182C2semidirect
7. #10591176C2semidirect
8. #10591173C2semidirect
9. #10591168C2semidirect
10. #10591164C2semidirect
11. #10591163C2semidirect
12. #10590371C2semidirect
13. #10590368C2semidirect
14. #10590362C2semidirect
15. #10590355C2semidirect
21. C2×C3×#235C22semidirect
33. C3×#930C22semidirect
35. C22×C3×C3⋊C8C22semidirect
39. C3×#874C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3719C22semidirect
45. C2×#3716C22semidirect
46. C2×#3716C22semidirect
53. C3×#830C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. C3×#803C22semidirect
56. #63575C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
68. #5553D3semidirect
85. #5011D3semidirect
149. #3717D4semidirect
163. C2×#235C2×D3semidirect
199. #930C2×D3semidirect
204. C22×C3⋊C8C2×D3semidirect
231. #874C2×D3semidirect
235. C4×Dic6C2×D3semidirect
244. #830C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
838. C32#3268semidirect
947. C3#79497semidirect
948. C3#83577semidirect

Maximal subgroups

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

subgroupindex
#105960212
C3×#55532
C2×#638292
C2×#638252
C3×#50112
#105911822
#105911762
#105911732
#105911682
#105911642
#105911632
#105903712
#105903682
#105903622
#105903552
#835773
#794973