Finite Group Databasebeta

← #11884119

Subgroups — #11884119

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic, complemented
2C2×#63946C211yesmaximal, characteristic, complemented
3#10594886C211yesmaximal, characteristic
4C22×#3715C211yesmaximal, characteristic, complemented
5#10592750C211yesmaximal, characteristic, complemented
6C3×#5046C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591564C211yesmaximal, characteristic, complemented
10#10591186C211yesmaximal, characteristic, complemented
11#10591158C211yesmaximal, characteristic, complemented
12#10590614C211yesmaximal, characteristic, complemented
13#10590532C211yesmaximal, characteristic, complemented
14#10590503C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#80169—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24#64133C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×#896—21no—
32C3×#888—21no—
33C3×#887C2211yescharacteristic, complemented
34C3×#67⋊C4—21no—
35C3×#878—21no—
36#63976—21no—
37D3×#217—21no—
38#63946—24no—
39#63908C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63885—21no—
42#63884—21no—
43#63860C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3715—24no—
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64C2×#942—31no—
65C22×#215—31no—
66#5806—31no—
67C22×#214—31no—
68C2×#915—31no—
69#5632D311yescharacteristic, complemented
70#5550—31no—
71C3×#450—31no—
72#5228—31no—
73#5227—31no—
74#5170—31no—
75#5167—31no—
76#5162—31no—
77#5086—31no—
78#5083—31no—
79#5051—31no—
80#5051—31no—
81#5051—61no—
82#5049—31no—
83#5047—31no—
84#5046D311yescharacteristic, complemented
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4783—31no—
89#4780—31no—
90#4767—31no—
91#4757—31no—
92#4739—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—22no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6—41no—
113C2×C3×Dic6C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#625—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119#3795—22no—
120#3795—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3757—21no—
125#3756—22no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C2×C3⋊(C3⋊C8)—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217D411yescharacteristic
132C3×#215—22no—
133C3×#215—41no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×C4⋊Dic3—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4D411yescharacteristic
141C3×C4×Dic3—21no—
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—22no—
150#3719—41no—
151#3715—22no—
152#3715—22no—
153#3715—22no—
154#3715D414yescomplemented
155#3711—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C22×C3×D4—31no—
160C2×D3×Q8C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×#235—31no—
163C22×D12C2×D311yescharacteristic
164C22×Dic6C2×D311yescharacteristic
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—31no—
168C3×C4⋊Q8—61no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—61no—
172C3×C22⋊Q8—61no—
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×C22⋊Q8C2×D311yescharacteristic
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178#953—61no—
179C2×#217—61no—
180#944C2×D311yescharacteristic, complemented
181C2×#216—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—61no—
186#942—64no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—64no—
192C2×#215C2×D311yescharacteristic
193C2×#215C2×D311yescharacteristic
194#939—61no—
195#938—31no—
196#937—61no—
197#936—31no—
198#935—61no—
199D4×Dic3—31no—
200C2×#214—31no—
201C2×#214—31no—
202C2×#214—31no—
203C2×#214—31no—
204C2×#214—64no—
205#930—31no—
206C4×#67C2×D311yescharacteristic
207#924—31no—
208#924—31no—
209#924—61no—
210C2×#208—31no—
211C22×C3⋊C8—31no—
212C22×C3⋊C8—31no—
213C22×C3⋊C8—61no—
214#915—64no—
215C2×Dic12—31no—
216C2×Dic12—31no—
217C2×ΓL(1,𝔽25)—31no—
218#897C2×D311yescharacteristic, complemented
219#896—21no—
220#894—61no—
221#888—21no—
222#887C2×D311yescharacteristic, complemented
223#884—61no—
224#67⋊C4—21no—
225D3×C22⋊C4—61no—
226#878—21no—
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—31no—
236#835—61no—
237#830—31no—
238#830C2×D311yescharacteristic
239(C2×D3)⋊C8—31no—
240#816—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#807—31no—
250#807—31no—
251#807—61no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271#634—21no—
272#634—21no—
273C3×#67—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—42no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#625—42no—
295#625—81no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—31no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—31no—
314#448—91no—
315#440—91no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—61no—
323C2×C3×Q8—62no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—121no—
327C2×C3×Q8—121no—
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—121no—
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67#6711yescharacteristic
347C22×Dic3—21no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350D3×Q8—22no—
351D3×Q8—41no—
352#237—62no—
353#237—121no—
354#235—62no—
355#235—121no—
356C2×D12—22no—
357C2×D12—21no—
358C2×D12—41no—
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—22no—
366C2×Dic6—21no—
367C2×Dic6—21no—
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—41no—
371C2×Dic6—61no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—62no—
375C3×SD16—121no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—31no—
382C3×C4⋊C4—41no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—41no—
394C3×C22⋊C4—61no—
395C3×C42—31no—
396C3×C42—61no—
397#217—61no—
398#217—61no—
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—62no—
408#216—122no—
409#216—121no—
410#215—22no—
411#215—34no—
412#215—41no—
413#215—62no—
414#215—62no—
415#215—62no—
416#214—34no—
417#214—62no—
418#214—62no—
419#214—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4#6711yescharacteristic
426C4⋊Dic3—21no—
427C4⋊Dic3—31no—
428C4⋊Dic3—31no—
429C4⋊Dic3—61no—
430Dic3⋊C4—21no—
431Dic3⋊C4—21no—
432Dic3⋊C4—21no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—121no—
436Dic3⋊C4#6711yescharacteristic
437C4×Dic3—21no—
438C4×Dic3C22×D311yescharacteristic
439#208—62no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8—122no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451Dic12—62no—
452Dic12—121no—
453ΓL(1,𝔽25)—62no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32#13712yescomplemented
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—22no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×Q8—31no—
482C22×Q8—31no—
483C22×D4—31no—
484#137—184no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—91no—
497C4⋊Q8—31no—
498C4⋊Q8—61no—
499#124—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—61no—
503C22⋊Q8—61no—
504C22⋊Q8—91no—
505C22⋊Q8D3211yescharacteristic
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—31no—
510C4×D4—31no—
511C4×D4—61no—
512C4×D4—91no—
513C2×C22⋊C4—181no—
514#107—91no—
515C4⋊C8—91no—
516#103—91no—
517#103—91no—
518#103—91no—
519#103—91no—
520#102—31no—
521#102—31no—
522C22⋊C8—31no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—241no—
532C23×C3D3×D411yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—81no—
539C22×D3C2×#6711yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—32no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—122no—
551C3×Q8—122no—
552C3×D4—32no—
553C3×D4—62no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—122no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—122no—
580C2×C3×C4—122no—
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4C2×#6711yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—22no—
586#67—122no—
587#67—122no—
588#67—241no—
589#67—241no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—42no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—122no—
600C2×Dic3—241no—
601C2×Dic3C2×#6711yescharacteristic
602C2×Dic3C2×#6711yescharacteristic
603C2×Dic3C2×#6711yescharacteristic
604D12—21no—
605D12—21no—
606D12—21no—
607D12—42no—
608D12D3×D412yes—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—42no—
612C4×D3—122no—
613C4×D3—241no—
614Dic6—21no—
615Dic6—21no—
616Dic6—21no—
617Dic6—42no—
618Dic6—42no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—121no—
624Dic6—121no—
625Dic6D3×D412yes—
626C3×C8—61no—
627C3×C8—61no—
628C3⋊C8—21no—
629C3⋊C8—21no—
630C3⋊C8—32no—
631C3⋊C8—32no—
632C3⋊C8—62no—
633C3⋊C8—61no—
634C3⋊C8—61no—
635C3⋊C8—121no—
636C2×C32—22no—
637C2×C32D4211yescharacteristic
638C2×C32C2×#13711yescharacteristic
639C2×C32#57711yescharacteristic
640C3×D3—41no—
641C3×D3—42no—
642C3×D3—81no—
643C24—61no—
644#41—182no—
645#41—361no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—61no—
649C2×Q8—62no—
650C2×Q8—61no—
651C2×Q8—62no—
652C2×Q8—91no—
653C2×Q8—121no—
654C2×Q8—121no—
655C2×Q8C2×D3211yescharacteristic
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—121no—
662C2×D4—181no—
663C2×D4—181no—
664C22×C4—31no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—181no—
668C22×C4—181no—
669C22×C4C2×D3211yescharacteristic
670Q16—182no—
671Q16—182no—
672Q16—361no—
673SD16—62no—
674SD16—94no—
675SD16—121no—
676SD16—182no—
677SD16—182no—
678SD16—182no—
679M16—182no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—91no—
683C2×C8—91no—
684C2×C8—182no—
685C4⋊C4—21no—
686C4⋊C4—31no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—91no—
692C4⋊C4—181no—
693C4⋊C4C2×D3211yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—31no—
696C22⋊C4—31no—
697C22⋊C4—61no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—31no—
704C42—61no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—22no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—62no—
716C22×C3—61no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3#91512yescomplemented
724C22×C3#94212yescomplemented
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C22×#6711yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—22no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—84no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—61no—
749C3×C4—62no—
750C3×C4—81no—
751C3×C4—81no—
752C3×C4—121no—
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D411yescharacteristic
755C3×C4#100411yescharacteristic
756C3×C4#100411yescharacteristic
757Dic3—22no—
758Dic3—21no—
759Dic3—21no—
760Dic3—21no—
761Dic3—41no—
762Dic3—121no—
763Dic3—121no—
764Dic3—121no—
765Dic3—121no—
766Dic3—241no—
767Dic3—241no—
768C32#326611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—61no—
771C23—61no—
772C23—122no—
773C23—122no—
774C23—241no—
775C23D3×#6711yescharacteristic
776Q8—21no—
777Q8—21no—
778Q8—32no—
779Q8—61no—
780Q8—61no—
781Q8—61no—
782Q8—122no—
783Q8—122no—
784Q8—181no—
785Q8—181no—
786D4—32no—
787D4—62no—
788D4—61no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—362no—
793D4—721no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—362no—
810C2×C4—721no—
811C2×C4D3×#6711yescharacteristic
812C2×C4C22×D3211yescharacteristic
813C8—61no—
814C8—61no—
815C8—92no—
816C8—181no—
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—42no—
823C2×C3—121no—
824C2×C3—122no—
825C2×C3—241no—
826C2×C3#559011yescharacteristic
827C2×C3C2×#91511yescharacteristic
828C2×C3#577511yescharacteristic
829C2×C3D4×#6711yescharacteristic
830C2×C3C2×#94211yescharacteristic
831C2×C3#583711yescharacteristic
832D3—42no—
833D3—41no—
834D3—81no—
835C22—21no—
836C22—21no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—62no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—244no—
847C22#6394612yescomplemented
848C22C2×D3×#6711yescharacteristic
849C4—21no—
850C4—41no—
851C4—41no—
852C4—61no—
853C4—61no—
854C4—61no—
855C4—62no—
856C4—121no—
857C4—361no—
858C4—361no—
859C4D32×D411yescharacteristic
860C4#6431311yescharacteristic
861C3—21no—
862C3#8016911yescharacteristic, complemented
863C3#8355911yescharacteristic, complemented
864C2—22no—
865C2—121no—
866C2—122no—
867C2—241no—
868C2#1059528711yescharacteristic
869C2C2×#6394611yescharacteristic
870C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22⋊Q8D32
hypocenterC32#3266
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×#5632C2semidirect
2. C2×#63946C2semidirect
4. C22×#3715C2semidirect
5. #10592750C2semidirect
6. C3×#5046C2semidirect
7. #10591605C2semidirect
8. #10591583C2semidirect
9. #10591564C2semidirect
10. #10591186C2semidirect
11. #10591158C2semidirect
12. #10590614C2semidirect
13. #10590532C2semidirect
14. #10590503C2semidirect
15. #10590454C2semidirect
18. C2×C3×D3×Q8C22semidirect
23. C2×#3756C22semidirect
26. C3×#944C22semidirect
30. C3×#897C22semidirect
33. C3×#887C22semidirect
44. C2×#3719C22semidirect
45. C2×#3719C22semidirect
51. C2×#3711C22semidirect
52. #63662C22semidirect
53. #63637C22semidirect
54. #63634C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
69. #5632D3semidirect
84. #5046D3semidirect
154. #3715D4semidirect
160. C2×D3×Q8C2×D3semidirect
180. #944C2×D3semidirect
218. #897C2×D3semidirect
222. #887C2×D3semidirect
456. C22×C32#137semidirect
723. C22×C3#915semidirect
724. C22×C3#942semidirect
768. C32#3266semidirect
847. C22#63946semidirect
862. C3#80169semidirect
863. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
C2×#639462
#105948862
C22×#37152
#105927502
C3×#50462
#105916052
#105915832
#105915642
#105911862
#105911582
#105906142
#105905322
#105905032
#105904542
#835593
#801693