Finite Group Databasebeta

← #11884304

Subgroups — #11884304

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3#10594886C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592751C211yesmaximal, characteristic, complemented
6C3×#5046C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591173C211yesmaximal, characteristic, complemented
11#10591151C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590530C211yesmaximal, characteristic, complemented
14#10590501C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80157—31nomaximal
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×#894—21no—
32C3×#893C2211yescharacteristic, complemented
33C3×D3×C4⋊C4—21no—
34C3×#884—21no—
35C3×#883—21no—
36#63976—21no—
37D3×#217—21no—
38#63947—24no—
39#63908C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63885—21no—
42#63884—21no—
43#63860C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48#63823—24no—
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63635C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#547—31no—
64C2×#950—31no—
65C2×#949—31no—
66#5806—31no—
67C2×#932—31no—
68C2×#916—31no—
69#5631D311yescharacteristic, complemented
70#5550—31no—
71C3×#450—31no—
72#5239—31no—
73#5238—31no—
74#5172—31no—
75#5167—31no—
76#5162—31no—
77#5086—31no—
78#5083—31no—
79#5052—31no—
80#5052—31no—
81#5052—61no—
82#5048—31no—
83#5047—31no—
84#5046D311yescharacteristic, complemented
85#5016—31no—
86#5014—31no—
87#5011—31no—
88#4787—31no—
89#4785—31no—
90#4783—31no—
91#4778—31no—
92#4733—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×#239—22no—
101C3×#239—41no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—41no—
108C2×C3×D12C2311yescharacteristic
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×#625—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120#3795—22no—
121#3795—41no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125#3757—21no—
126#3756—22no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129#3748—22no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217D411yescharacteristic
133C3×#215—22no—
134C3×#215—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4D411yescharacteristic
142C3×C4×Dic3C2311yescharacteristic
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#3719—41no—
150#3716—22no—
151#3715—22no—
152#3715—22no—
153#3713—22no—
154#3713D414yescomplemented
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C2×#239C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×#235—31no—
163C2×#235C2×D311yescharacteristic
164C22×D12C2×D311yescharacteristic
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—31no—
168C3×#123—61no—
169C3×#123—61no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8C2×D311yescharacteristic
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×#121—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C2×C3×C4⋊C4—61no—
178#953—61no—
179C2×#217—61no—
180#950—64no—
181#949—64no—
182#944C2×D311yescharacteristic, complemented
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—61no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215C2×D311yescharacteristic
190C2×#215C2×D311yescharacteristic
191#939—61no—
192#938—31no—
193#937—61no—
194#936—31no—
195#935—61no—
196D4×Dic3—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200#932—64no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205#930—31no—
206C4×#67C2×D311yescharacteristic
207#924—31no—
208#924—31no—
209#924—61no—
210C2×#208—31no—
211C2×#208—31no—
212C2×#208—61no—
213C22×C3⋊C8—31no—
214#916—64no—
215C2×Dic12—31no—
216C2×#204—31no—
217C2×D3×C8—31no—
218#897C2×D311yescharacteristic, complemented
219#894—21no—
220#894—61no—
221#893C2×D311yescharacteristic, complemented
222D3×C4⋊C4—21no—
223#884—21no—
224#884—61no—
225#883—21no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#830—31no—
238#830C2×D311yescharacteristic
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#809C2×D311yescharacteristic
248#809C2×D311yescharacteristic
249#808—31no—
250#808—31no—
251#808—61no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
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×Q8—21no—
263C32×Q8—21no—
264C2×C32×C4—21no—
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—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—42no—
285C3×D12—42no—
286C3×D12C2×D412yes—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#625—42no—
296#625—81no—
297D3×Dic3—42no—
298D3×Dic3—81no—
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—31no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—31no—
315#449—91no—
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—21no—
325C2×C3×Q8—31no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—121no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—21no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67#6711yescharacteristic
350C22×Dic3—61no—
351C22×Dic3—61no—
352#239—22no—
353#239—41no—
354#237—62no—
355#237—121no—
356#235—22no—
357#235—41no—
358#235—62no—
359#235—121no—
360C2×D12—22no—
361C2×D12—21no—
362C2×D12—21no—
363C2×D12—41no—
364C2×D12C22×D311yescharacteristic
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
377C3×SD16—62no—
378C3×SD16—121no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—41no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C4⋊C4C22×D311yescharacteristic
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—41no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—31no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—121no—
406#217#6711yescharacteristic
407#216—62no—
408#216—62no—
409#216—122no—
410#216—121no—
411#215—22no—
412#215—41no—
413#215—62no—
414#215—62no—
415#214—62no—
416#214—62no—
417#214—62no—
418#213—34no—
419#213—34no—
420#213—62no—
421#213—62no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4#6711yescharacteristic
429C4⋊Dic3—21no—
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—61no—
433Dic3⋊C4—21no—
434Dic3⋊C4—21no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—121no—
438Dic3⋊C4#6711yescharacteristic
439C4×Dic3C22×D311yescharacteristic
440#208—62no—
441#208—62no—
442#208—122no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—62no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—121no—
453#204—62no—
454D3×C8—62no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
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×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—21no—
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—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—91no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—31no—
501#124—91no—
502#123—61no—
503#123—61no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507C22⋊Q8D3211yescharacteristic
508#121—61no—
509#121—91no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—91no—
515C2×C4⋊C4—61no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—91no—
527#97—91no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—241no—
536C23×C3D3×D411yescharacteristic
537C23×C3C2×#6711yescharacteristic
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—81no—
544C22×D3C2×#6711yescharacteristic
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—32no—
554C3×D4—32no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C3×D4—122no—
561C3×D4—121no—
562C3×D4—122no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
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—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—122no—
584C2×C3×C4—122no—
585C2×C3×C4—122no—
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4C2×#6711yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—41no—
591#67—42no—
592#67—122no—
593#67—122no—
594#67—241no—
595#67—241no—
596C2×Dic3—21no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—122no—
604C2×Dic3—241no—
605C2×Dic3C2×#6711yescharacteristic
606C2×Dic3C2×#6711yescharacteristic
607C2×Dic3C2×#6711yescharacteristic
608D12—21no—
609D12—21no—
610D12—21no—
611D12—21no—
612D12—42no—
613D12—42no—
614D12D3×D412yes—
615D12D3×D412yes—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—42no—
619C4×D3—42no—
620C4×D3—42no—
621C4×D3—122no—
622C4×D3—241no—
623Dic6—21no—
624Dic6—21no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631C3×C8—61no—
632C3×C8—61no—
633C3⋊C8—21no—
634C3⋊C8—21no—
635C3⋊C8—32no—
636C3⋊C8—32no—
637C3⋊C8—62no—
638C3⋊C8—61no—
639C3⋊C8—61no—
640C3⋊C8—121no—
641C2×C32—41no—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3×D3—41no—
646C3×D3—42no—
647C3×D3—42no—
648C3×D3—81no—
649C24—61no—
650#41—62no—
651#41—62no—
652#41—121no—
653#41—121no—
654#41—182no—
655#41—361no—
656C2×Q8—31no—
657C2×Q8—91no—
658C2×Q8C2×D3211yescharacteristic
659C2×D4—31no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—62no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—121no—
668C2×D4—181no—
669C2×D4—181no—
670C22×C4—31no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4C2×D3211yescharacteristic
677Q16—182no—
678Q16—361no—
679SD16—62no—
680SD16—121no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684D8—94no—
685D8—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—91no—
690C2×C8—91no—
691C2×C8—182no—
692C4⋊C4—21no—
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4C2×D3211yescharacteristic
700C22⋊C4—21no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—62no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—244no—
734C22×C3C2×D3×D411yescharacteristic
735C22×C3C22×#6711yescharacteristic
736C2×D3—21no—
737C2×D3—22no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—22no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—84no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—81no—
762C3×C4—81no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4#100411yescharacteristic
767C3×C4#100411yescharacteristic
768Dic3—21no—
769Dic3—21no—
770Dic3—21no—
771Dic3—41no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—241no—
777Dic3—241no—
778C32#326711yescharacteristic, complemented, Sylow
779C23—31no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—122no—
784C23—122no—
785C23—241no—
786C23D3×#6711yescharacteristic
787Q8—21no—
788Q8—21no—
789Q8—61no—
790Q8—61no—
791Q8—181no—
792Q8—181no—
793D4—32no—
794D4—32no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—61no—
799D4—122no—
800D4—122no—
801D4—121no—
802D4—122no—
803D4—362no—
804D4—721no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—362no—
821C2×C4—721no—
822C2×C4D3×#6711yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C8—61no—
825C8—61no—
826C8—92no—
827C8—181no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—41no—
832C2×C3—41no—
833C2×C3—81no—
834C2×C3—121no—
835C2×C3—122no—
836C2×C3—122no—
837C2×C3—241no—
838C2×C3#559011yescharacteristic
839C2×C3#576211yescharacteristic
840C2×C3#577311yescharacteristic
841C2×C3D4×#6711yescharacteristic
842C2×C3#582211yescharacteristic
843C2×C3#583711yescharacteristic
844D3—42no—
845D3—41no—
846D3—42no—
847D3—81no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—61no—
852C22—61no—
853C22—62no—
854C22—62no—
855C22—61no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—244no—
864C22C2×D3×#6711yescharacteristic
865C4—21no—
866C4—41no—
867C4—41no—
868C4—61no—
869C4—61no—
870C4—61no—
871C4—121no—
872C4—361no—
873C4—361no—
874C4D32×D411yescharacteristic
875C4#6431311yescharacteristic
876C3—21no—
877C3#8015711yescharacteristic, complemented
878C3#8352211yescharacteristic, complemented
879C2—41no—
880C2—121no—
881C2—122no—
882C2—122no—
883C2—241no—
884C2#1059528711yescharacteristic
885C2#1059531811yescharacteristic
886C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3267
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. C3×#5631C2semidirect
2. C2×#63947C2semidirect
3. #10594886C2semidirect
4. C2×#63823C2semidirect
5. #10592751C2semidirect
6. C3×#5046C2semidirect
7. #10591605C2semidirect
8. #10591586C2semidirect
9. #10591564C2semidirect
10. #10591173C2semidirect
11. #10591151C2semidirect
12. #10590614C2semidirect
13. #10590530C2semidirect
14. #10590501C2semidirect
15. #10590455C2semidirect
18. C2×C3×#239C22semidirect
23. C2×#3756C22semidirect
26. C3×#944C22semidirect
30. C3×#897C22semidirect
32. C3×#893C22semidirect
44. C2×#3719C22semidirect
45. C2×#3716C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63637C22semidirect
54. #63635C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
69. #5631D3semidirect
84. #5046D3semidirect
154. #3713D4semidirect
160. C2×#239C2×D3semidirect
182. #944C2×D3semidirect
218. #897C2×D3semidirect
221. #893C2×D3semidirect
778. C32#3267semidirect
877. C3#80157semidirect
878. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C3×#56312
C2×#639472
#105948862
C2×#638232
#105927512
C3×#50462
#105916052
#105915862
#105915642
#105911732
#105911512
#105906142
#105905302
#105905012
#105904552
#835223
#801573