Finite Group Databasebeta

← #11884151

Subgroups — #11884151

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic, complemented
2C2×#63948C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594007C211yesmaximal, characteristic
5#10592782C211yesmaximal, characteristic, complemented
6C3×#5086C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591635C211yesmaximal, characteristic, complemented
10#10591594C211yesmaximal, characteristic, complemented
11#10591587C211yesmaximal, characteristic, complemented
12#10591583C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#81881—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#896—21no—
33C3×#896—21no—
34C3×#893—21no—
35C3×#888—21no—
36C3×#875C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×Dic6C2211yescharacteristic, complemented
39#63948—24no—
40D3×#215—24no—
41#63922—21no—
42#63921—21no—
43#63912—21no—
44#63908C2211yescharacteristic
45#63856C2211yescharacteristic
46#63854—21no—
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64C2×#942—31no—
65C22×#215—31no—
66C2×#918—31no—
67C2×D3×SD16—31no—
68#5727D311yescharacteristic, complemented
69#5676—31no—
70#5550—31no—
71C3×#497—31no—
72#5228—31no—
73#5227—31no—
74#5188—31no—
75#5187—31no—
76#5186—31no—
77#5174—31no—
78#5170—31no—
79#5169—31no—
80#5086D311yescharacteristic, complemented
81#5083—31no—
82#5083—31no—
83#5083—61no—
84#5054—31no—
85#5051—31no—
86#5049—31no—
87#5047—31no—
88#5046—31no—
89#5028—31no—
90#5026—31no—
91#5011—31no—
92#4710—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C3×D3×Q8—41no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#624—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3799—22no—
120#3799—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C42C2311yescharacteristic
124#3755—22no—
125#3755—22no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#216—22no—
131C3×#216—41no—
132C3×#215—22no—
133C3×#215—41no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3D411yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×C4×Dic3—21no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3724—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3718—22no—
152#3717D414yescomplemented
153#3715—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×D3×Q8C2×D311yescharacteristic
161C2×D3×Q8C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C4⋊Q8—21no—
170C3×C4⋊Q8—61no—
171C3×C4⋊Q8C2×D311yescharacteristic, complemented
172C3×C4⋊Q8C2×D311yescharacteristic, complemented
173C3×#124—31no—
174C3×C22⋊Q8—31no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—61no—
177C3×C22⋊Q8—61no—
178C3×C4×Q8—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181#946—31no—
182#946C2×D311yescharacteristic
183#946C2×D311yescharacteristic, complemented
184C2×#216—31no—
185C2×#216—31no—
186C2×#216C2×D311yescharacteristic, complemented
187C2×#216C2×D311yescharacteristic, complemented
188#942—64no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—61no—
196C2×#215—61no—
197C2×#215—64no—
198C2×#215C2×D311yescharacteristic
199C2×#215C2×D311yescharacteristic
200#938—31no—
201#937—61no—
202C2×#214—31no—
203#930—31no—
204#924—31no—
205C2×#208—31no—
206C22×C3⋊C8—31no—
207#918—64no—
208D3×SD16—64no—
209C2×#204—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#896—21no—
213#896—21no—
214#894—61no—
215#893—21no—
216#888—21no—
217#884—61no—
218#884—61no—
219#883—61no—
220#882—61no—
221D3×C22⋊C4—61no—
222D3×C22⋊C4—61no—
223#875C2×D311yescharacteristic
224C4×D12—31no—
225C4×D12—31no—
226C4×D12—61no—
227C4×D12C2×D311yescharacteristic
228C4×Dic6C2×D311yescharacteristic, complemented
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—31no—
236#835—61no—
237#835—61no—
238#832—31no—
239#830—31no—
240#830—31no—
241#821—31no—
242(C2×D3)⋊C8—31no—
243(C2×D3)⋊C8—31no—
244#818—31no—
245#816—31no—
246#810—31no—
247#809—31no—
248#809—31no—
249#807—31no—
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253#803C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)C2×D412yes—
273C4×C3⋊D3—81no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—22no—
280C3×D12—21no—
281C3×D12—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292C3×Dic6—42no—
293C3×Dic6C2×D412yes—
294#626—42no—
295#626—42no—
296#625—81no—
297#624—42no—
298C3⋊(C3⋊C8)—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—31no—
305#546—91no—
306#497—31no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×Q8—61no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8—121no—
328C2×C3×Q8—121no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343#239—62no—
344#239—121no—
345D3×Q8—22no—
346D3×Q8—22no—
347D3×Q8—41no—
348D3×Q8—41no—
349D3×D4—62no—
350D3×D4—121no—
351#235—62no—
352#235—121no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—62no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—121no—
360C2×D12#6711yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—121no—
369C2×C4×D3C22×D311yescharacteristic
370C2×C4×D3C22×D311yescharacteristic
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6C22×D311yescharacteristic
374C2×Dic6C22×D311yescharacteristic
375C3×Q16—62no—
376C3×Q16—121no—
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—21no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—41no—
388C3×C4⋊C4—41no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C42—21no—
399C3×C42—61no—
400C3×C42C22×D311yescharacteristic
401C3×C42C22×D311yescharacteristic
402#217—61no—
403#217—61no—
404#216—22no—
405#216—41no—
406#216—62no—
407#216—62no—
408#215—22no—
409#215—34no—
410#215—41no—
411#215—62no—
412#215—62no—
413#215—62no—
414#215—62no—
415#215—62no—
416#215—122no—
417#215—122no—
418#214—62no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4#6711yescharacteristic
429(C2×D3)⋊C4#6711yescharacteristic
430C4⋊Dic3—31no—
431C4⋊Dic3—31no—
432C4⋊Dic3—61no—
433C4⋊Dic3#6711yescharacteristic
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—21no—
436Dic3⋊C4—21no—
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440C4×Dic3—21no—
441#208—62no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—62no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451#204—34no—
452ΓL(1,𝔽25)—62no—
453D3×C8—62no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—22no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#13712yescomplemented
467D32—84no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—22no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×Q8—31no—
482C22×Q8—31no—
483C22×D4—91no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—31no—
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—61no—
498C4⋊Q8D3211yescharacteristic, complemented
499#124—31no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—61no—
504C22⋊Q8—61no—
505C22⋊Q8—91no—
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—91no—
521#102—91no—
522C22⋊C8—91no—
523C22⋊C8—91no—
524#97—31no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—121no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—241no—
537C22×D3—241no—
538C22×D3C2×#6711yescharacteristic
539C22×D3C2×#6711yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—32no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—122no—
557C3×Q8—122no—
558C3×D4—62no—
559C3×D4—61no—
560C3×D4—61no—
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—41no—
571C2×C3×C4—41no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
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×C4D3×D411yescharacteristic
583C2×C3×C4C2×#6711yescharacteristic
584C2×C3×C4C2×#6711yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—122no—
588#67—122no—
589#67—241no—
590#67—241no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—121no—
597C2×Dic3C2×#6711yescharacteristic
598C2×Dic3C2×#6711yescharacteristic
599D12—22no—
600D12—21no—
601D12—21no—
602D12—32no—
603D12—32no—
604D12—62no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—122no—
609D12—122no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—42no—
615C4×D3—42no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—241no—
619C4×D3—241no—
620C4×D3—242no—
621Dic6—21no—
622Dic6—21no—
623Dic6—21no—
624Dic6—42no—
625Dic6—42no—
626Dic6D3×D412yes—
627C3×C8—32no—
628C3×C8—61no—
629C3⋊C8—21no—
630C3⋊C8—61no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—61no—
634C3⋊C8—121no—
635C3⋊C8—121no—
636C3⋊C8D3×D412yes—
637C2×C32D4211yescharacteristic
638C2×C32C2×#13711yescharacteristic
639C2×C32#57711yescharacteristic
640C3⋊D3—42no—
641C3×D3—22no—
642C3×D3—41no—
643C3×D3—81no—
644C24—181no—
645#41—182no—
646#41—361no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—61no—
650C2×Q8—61no—
651C2×Q8—62no—
652C2×Q8—62no—
653C2×Q8—121no—
654C2×Q8—121no—
655C2×Q8C2×D3211yescharacteristic
656C2×Q8C2×D3211yescharacteristic
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—91no—
660C2×D4—181no—
661C2×D4—182no—
662C2×D4—181no—
663C2×D4—181no—
664C2×D4—361no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4—181no—
670C22×C4—181no—
671Q16—62no—
672Q16—121no—
673Q16—182no—
674SD16—62no—
675SD16—94no—
676SD16—121no—
677SD16—182no—
678SD16—182no—
679SD16—182no—
680M16—182no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8—91no—
684C2×C8—91no—
685C2×C8—182no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—31no—
689C4⋊C4—31no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—91no—
694C4⋊C4—181no—
695C22⋊C4—31no—
696C22⋊C4—31no—
697C22⋊C4—61no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C22⋊C4—181no—
704C42—61no—
705C42C2×D3211yescharacteristic
706C22×C3—21no—
707C22×C3—32no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3C2×D3×D411yescharacteristic
717C22×C3C22×#6711yescharacteristic
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—62no—
727C2×D3—62no—
728C2×D3—122no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—241no—
734C2×D3—241no—
735C2×D3—244no—
736C2×D3—244no—
737C2×D3#94212yescomplemented
738C3×C4—22no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—62no—
753C3×C4—81no—
754C3×C4—81no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4C2×D3×D411yescharacteristic
758C3×C4C2×D3×D411yescharacteristic
759C3×C4#100411yescharacteristic
760C3×C4#100411yescharacteristic
761Dic3—22no—
762Dic3—21no—
763Dic3—21no—
764Dic3—41no—
765Dic3—41no—
766Dic3—121no—
767Dic3—121no—
768Dic3—241no—
769C32#326611yescharacteristic, complemented, Sylow
770C23—31no—
771C23—31no—
772C23—61no—
773C23—181no—
774C23—362no—
775C23—362no—
776C23—721no—
777Q8—21no—
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—32no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—122no—
786Q8—122no—
787D4—62no—
788D4—61no—
789D4—61no—
790D4—92no—
791D4—181no—
792D4—362no—
793D4—362no—
794D4—721no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—31no—
798C2×C4—31no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—122no—
807C2×C4—122no—
808C2×C4—181no—
809C2×C4—362no—
810C2×C4—721no—
811C2×C4D3×#6711yescharacteristic
812C2×C4D3×#6711yescharacteristic
813C2×C4C22×D3211yescharacteristic
814C8—32no—
815C8—61no—
816C8—181no—
817C8—181no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—62no—
822C2×C3—121no—
823C2×C3—241no—
824C2×C3#571711yescharacteristic
825C2×C3D3×#13711yescharacteristic
826C2×C3#577811yescharacteristic
827C2×C3D4×#6711yescharacteristic
828C2×C3C2×#94211yescharacteristic
829C2×C3#583711yescharacteristic
830D3—22no—
831D3—41no—
832D3—81no—
833D3—122no—
834D3—122no—
835D3—242no—
836C22—32no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—182no—
846C22—361no—
847C22—361no—
848C22—724no—
849C22C2×D3×#6711yescharacteristic
850C4—21no—
851C4—21no—
852C4—41no—
853C4—41no—
854C4—61no—
855C4—61no—
856C4—62no—
857C4—121no—
858C4—121no—
859C4—361no—
860C4D32×D411yescharacteristic
861C4#6431311yescharacteristic
862C3—21no—
863C3#8188111yescharacteristic, complemented
864C3#8355911yescharacteristic, complemented
865C2—62no—
866C2—121no—
867C2—241no—
868C2—362no—
869C2#1059529311yescharacteristic
870C2D3×#94211yescharacteristic
871C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594007C2
hypercenterC4⋊Q8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5727C2semidirect
2. C2×#63948C2semidirect
3. C2×D3×#215C2semidirect
5. #10592782C2semidirect
6. C3×#5086C2semidirect
7. #10591657C2semidirect
8. #10591651C2semidirect
9. #10591635C2semidirect
10. #10591594C2semidirect
11. #10591587C2semidirect
12. #10591583C2semidirect
13. #10590362C2semidirect
14. #10590326C2semidirect
15. #10590267C2semidirect
19. C2×C3×D3×Q8C22semidirect
22. C32×C4⋊Q8C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
38. C3×C4×Dic6C22semidirect
47. C2×#3718C22semidirect
50. C2×#3711C22semidirect
52. #63662C22semidirect
53. #63662C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#803C22semidirect
56. #63575C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5727D3semidirect
80. #5086D3semidirect
152. #3717D4semidirect
161. C2×D3×Q8C2×D3semidirect
171. C3×C4⋊Q8C2×D3semidirect
172. C3×C4⋊Q8C2×D3semidirect
183. #946C2×D3semidirect
186. C2×#216C2×D3semidirect
187. C2×#216C2×D3semidirect
228. C4×Dic6C2×D3semidirect
253. #803C2×D3semidirect
466. C2×C3×D3#137semidirect
498. C4⋊Q8D32semidirect
737. C2×D3#942semidirect
769. C32#3266semidirect
863. C3#81881semidirect
864. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
C2×#639482
C2×D3×#2152
#105940072
#105927822
C3×#50862
#105916572
#105916512
#105916352
#105915942
#105915872
#105915832
#105903622
#105903262
#105902672
#835593
#818813