Finite Group Databasebeta

← #11884259

Subgroups — #11884259

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3#10594887C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592740C211yesmaximal, characteristic, complemented
6C3×#5037C211yesmaximal, characteristic, complemented
7#10591491C211yesmaximal, characteristic, complemented
8#10591458C211yesmaximal, characteristic, complemented
9#10591431C211yesmaximal, characteristic, complemented
10#10591173C211yesmaximal, characteristic, complemented
11#10591158C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590559C211yesmaximal, characteristic, complemented
14#10590520C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#83503—31nomaximal
17#80122—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×#3795C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24#64133C2211yescharacteristic, complemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#938—21no—
27C3×#937—21no—
28C3×#936C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#883—21no—
35C3×D3×C22⋊C4—21no—
36#63970—21no—
37#63969—21no—
38#63932—24no—
39#63905—21no—
40Dic3×D12C2211yescharacteristic, complemented
41D3×Dic3⋊C4—21no—
42#63866C2211yescharacteristic, complemented
43#63856C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49#63822—24no—
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63659C2211yescharacteristic
53#63637C2211yescharacteristic, complemented
54#63635C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64#5824—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#932—31no—
68C2×#911—31no—
69#5612D311yescharacteristic, complemented
70#5551—31no—
71C3×#449—31no—
72#5239—31no—
73#5218—31no—
74#5169—31no—
75#5167—31no—
76#5153—31no—
77#5060—31no—
78#5057—31no—
79#5052—31no—
80#5047—31no—
81#5041—31no—
82#5041—31no—
83#5041—61no—
84#5037D311yescharacteristic, complemented
85#5019—31no—
86#5014—31no—
87#5011—31no—
88#4818—31no—
89#4816—31no—
90#4785—31no—
91#4783—31no—
92#4733—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C3×#235—22no—
106C3×#235—22no—
107C3×#235—41no—
108C3×#235—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#625—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120#3795—22no—
121#3795—41no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3757—21no—
125#3754—22no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C2×C3⋊(C3⋊C8)—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217—21no—
132C3×#217—21no—
133C3×#217D411yescharacteristic
134C3×#214—41no—
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3719—41no—
150#3718—22no—
151#3716—22no—
152#3715—22no—
153#3715—22no—
154#3713D414yescomplemented
155#3711—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C2×#237—31no—
161C2×D3×D4C2×D311yescharacteristic
162C2×#235—31no—
163C2×#235C2×D311yescharacteristic
164C2×#235C2×D311yescharacteristic, complemented
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×#124—31no—
168C3×#123—61no—
169C3×C22⋊Q8—31no—
170C3×#121—21no—
171C3×#121—61no—
172C3×#121C2×D311yescharacteristic
173C3×#121C2×D311yescharacteristic
174C3×#120—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C2×C3×C22⋊C4—61no—
178#950—64no—
179#950—64no—
180#946—31no—
181#944—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#215—31no—
186C2×#215—31no—
187#939—61no—
188#938—21no—
189#938—61no—
190#937—21no—
191#936C2×D311yescharacteristic
192#935—61no—
193D4×Dic3—31no—
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—61no—
200C2×#214C2×D311yescharacteristic
201#932—64no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213C2×D311yescharacteristic
205#929—61no—
206C4×#67C2×D311yescharacteristic
207#924—31no—
208#924—31no—
209#924—31no—
210#924—61no—
211C2×Dic3⋊C4—61no—
212C2×#208—31no—
213C22×C3⋊C8—31no—
214C22×C3⋊C8—31no—
215C22×C3⋊C8—61no—
216#911—64no—
217C2×Dic12—31no—
218C2×#204—31no—
219C2×ΓL(1,𝔽25)—31no—
220#897C2×D311yescharacteristic
221#893C2×D311yescharacteristic
222D3×C4⋊C4—61no—
223#883—21no—
224#883—61no—
225#883—61no—
226D3×C22⋊C4—21no—
227C4×D12—31no—
228#869—31no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—61no—
237#830—31no—
238#830C2×D311yescharacteristic, complemented
239#821—31no—
240(C2×D3)⋊C8—31no—
241#816—31no—
242#815—31no—
243Dic3⋊C8—31no—
244#810—31no—
245#810—31no—
246#810—61no—
247#810C2×D311yescharacteristic, complemented
248#809C2×D311yescharacteristic, complemented
249#808—31no—
250#808—31no—
251#808—61no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—81no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272#634—21no—
273#634—21no—
274C3×#67—41no—
275C3×#67—42no—
276C3×#67—42no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12C2×D412yes—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×C4×D3—81no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#625—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—91no—
306#546—31no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—31no—
316#442—91no—
317#435—91no—
318C24×C3—61no—
319C23×D3—21no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—41no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—121no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—21no—
341C22×C3×C4—31no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67#6711yescharacteristic
353C22×Dic3—61no—
354C22×Dic3—61no—
355#237—62no—
356#237—121no—
357D3×D4—22no—
358D3×D4—41no—
359#235—22no—
360#235—22no—
361#235—41no—
362#235—41no—
363#235—62no—
364#235—121no—
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—21no—
368C2×C4×D3—21no—
369C2×C4×D3—21no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—121no—
379C3×D8—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4C22×D311yescharacteristic
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—31no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C42—31no—
397#217—21no—
398#217—21no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—121no—
404#217#6711yescharacteristic
405#216—62no—
406#216—62no—
407#216—121no—
408#215—62no—
409#215—62no—
410#214—41no—
411#214—62no—
412#214—62no—
413#214—62no—
414#214—62no—
415#214—62no—
416#214—122no—
417#213—22no—
418#213—34no—
419#213—34no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4#6711yescharacteristic
425C4⋊Dic3—21no—
426C4⋊Dic3—31no—
427C4⋊Dic3—31no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430C4⋊Dic3—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—121no—
438Dic3⋊C4#6711yescharacteristic
439C4×Dic3C22×D311yescharacteristic
440#208—62no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8—62no—
449C2×C3⋊C8—122no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—121no—
453#204—62no—
454ΓL(1,𝔽25)—62no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C32×C4—21no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—91no—
486C22×D4—31no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—91no—
501#124—31no—
502#123—61no—
503#123—181no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—61no—
509#121—181no—
510#121D3211yescharacteristic
511#120—61no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—61no—
517#106—91no—
518C4⋊C8—91no—
519#103—31no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—241no—
538C23×C3D3×D411yescharacteristic
539C23×C3C2×#6711yescharacteristic
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—81no—
545C22×D3C2×#6711yescharacteristic
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—32no—
555C3×D4—32no—
556C3×D4—41no—
557C3×D4—41no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—81no—
561C3×D4—81no—
562C3×D4—82no—
563C3×D4—121no—
564C3×D4—122no—
565C3×D4—122no—
566C3×D4—122no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—122no—
586C2×C3×C4—122no—
587C2×C3×C4—241no—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4C2×#6711yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—41no—
593#67—42no—
594#67—42no—
595#67—42no—
596#67—122no—
597#67—122no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3C2×#6711yescharacteristic
609C2×Dic3C2×#6711yescharacteristic
610C2×Dic3C2×#6711yescharacteristic
611D12—21no—
612D12—21no—
613D12D3×D412yes—
614D12D3×D412yes—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—42no—
618C4×D3—42no—
619C4×D3—81no—
620C4×D3—122no—
621C4×D3—122no—
622Dic6—21no—
623Dic6—21no—
624Dic6—21no—
625Dic6—21no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—61no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C3⋊C8—32no—
637C3⋊C8—32no—
638C3⋊C8—62no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C2×C32—41no—
643C2×C32—81no—
644C2×C32D4211yescharacteristic
645C2×C32#57511yescharacteristic
646C2×C32#57711yescharacteristic
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—42no—
650C24—61no—
651#41—62no—
652#41—62no—
653#41—121no—
654#41—121no—
655#41—182no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—91no—
660C2×D4—21no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—61no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—121no—
669C2×D4—181no—
670C2×D4C2×D3211yescharacteristic
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4C2×D3211yescharacteristic
678Q16—182no—
679Q16—361no—
680SD16—121no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685D8—62no—
686D8—94no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—91no—
692C2×C8—182no—
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—91no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—21no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—62no—
731C22×C3—61no—
732C22×C3—62no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—244no—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C22×#6711yescharacteristic
743C2×D3—21no—
744C2×D3—22no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—22no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—84no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—81no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4C2×D3×D411yescharacteristic
767C3×C4C2×D3×D411yescharacteristic
768C3×C4#100411yescharacteristic
769C3×C4#100411yescharacteristic
770Dic3—21no—
771Dic3—21no—
772Dic3—21no—
773Dic3—41no—
774Dic3—41no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—241no—
780Dic3—241no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—21no—
783C23—31no—
784C23—61no—
785C23—61no—
786C23—122no—
787C23—122no—
788C23—241no—
789C23D3×#6711yescharacteristic
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—181no—
795Q8—181no—
796D4—21no—
797D4—21no—
798D4—32no—
799D4—32no—
800D4—61no—
801D4—61no—
802D4—81no—
803D4—121no—
804D4—122no—
805D4—122no—
806D4—122no—
807D4—362no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—241no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4D3×#6711yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C8—61no—
828C8—61no—
829C8—92no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—81no—
838C2×C3—81no—
839C2×C3—122no—
840C2×C3—121no—
841C2×C3—122no—
842C2×C3—161no—
843C2×C3#559011yescharacteristic
844C2×C3#576811yescharacteristic
845C2×C3#577511yescharacteristic
846C2×C3D4×#6711yescharacteristic
847C2×C3#582211yescharacteristic
848C2×C3#583611yescharacteristic
849D3—41no—
850D3—42no—
851D3—42no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—62no—
862C22—62no—
863C22—121no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—244no—
868C22C2×D3×#6711yescharacteristic
869C4—21no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—121no—
875C4—121no—
876C4—361no—
877C4—361no—
878C4D32×D411yescharacteristic
879C4#6431311yescharacteristic
880C3—21no—
881C3#8012211yescharacteristic, complemented
882C3#8350311yescharacteristic, complemented
883C2—41no—
884C2—81no—
885C2—121no—
886C2—122no—
887C2—122no—
888C2#1059510611yescharacteristic
889C2#1059528711yescharacteristic
890C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5612C2semidirect
2. C2×#63932C2semidirect
3. #10594887C2semidirect
4. C2×#63822C2semidirect
5. #10592740C2semidirect
6. C3×#5037C2semidirect
7. #10591491C2semidirect
8. #10591458C2semidirect
9. #10591431C2semidirect
10. #10591173C2semidirect
11. #10591158C2semidirect
12. #10590614C2semidirect
13. #10590559C2semidirect
14. #10590520C2semidirect
15. #10590455C2semidirect
20. C2×C3×#235C22semidirect
24. #64133C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
40. Dic3×D12C22semidirect
42. #63866C22semidirect
44. C2×#3719C22semidirect
45. C2×#3718C22semidirect
48. C2×#3715C22semidirect
53. #63637C22semidirect
54. #63635C22semidirect
55. C3×#830C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
62. #63554C22semidirect
69. #5612D3semidirect
84. #5037D3semidirect
154. #3713D4semidirect
164. C2×#235C2×D3semidirect
238. #830C2×D3semidirect
247. #810C2×D3semidirect
248. #809C2×D3semidirect
781. C32#3267semidirect
881. C3#80122semidirect
882. C3#83503semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
C2×#639322
#105948872
C2×#638222
#105927402
C3×#50372
#105914912
#105914582
#105914312
#105911732
#105911582
#105906142
#105905592
#105905202
#105904552
#835033
#801223