Finite Group Databasebeta

← #11884306

Subgroups — #11884306

Order 1152.

1060 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5726C211yesmaximal, characteristic, complemented
2C2×#63949C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10594007C211yesmaximal, characteristic, complemented
5#10592782C211yesmaximal, characteristic, complemented
6C3×#5086C211yesmaximal, characteristic, complemented
7#10591657C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591638C211yesmaximal, characteristic, complemented
10#10591634C211yesmaximal, characteristic, complemented
11#10591597C211yesmaximal, characteristic, complemented
12#10591586C211yesmaximal, characteristic, complemented
13#10590348C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#81882—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, 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×#895—21no—
33C3×#894—21no—
34C3×#894—21no—
35C3×D3×C4⋊C4—21no—
36C3×#875C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic, complemented
39#63949—24no—
40#63939—24no—
41#63922—21no—
42#63921—21no—
43#63912—21no—
44#63908C2211yescharacteristic
45#63856C2211yescharacteristic
46#63854—21no—
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#547—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#919—31no—
67C2×#914—31no—
68#5726D311yescharacteristic, complemented
69#5676—31no—
70#5550—31no—
71C3×#497—31no—
72#5239—31no—
73#5238—31no—
74#5189—31no—
75#5187—31no—
76#5187—31no—
77#5172—31no—
78#5171—31no—
79#5169—31no—
80#5086D311yescharacteristic, complemented
81#5083—31no—
82#5083—31no—
83#5083—61no—
84#5057—31no—
85#5052—31no—
86#5048—31no—
87#5047—31no—
88#5046—31no—
89#5016—31no—
90#5014—31no—
91#5011—31no—
92#4711—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C3×#239—22no—
100C3×#239—22no—
101C3×#239—41no—
102C3×#239—41no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12D411yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#624—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3799—22no—
121#3799—41no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—21no—
124C32×C42C2311yescharacteristic
125#3755—22no—
126#3755—22no—
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×#215—22no—
134C3×#215—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3D411yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3724—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3715—22no—
152#3714D414yescomplemented
153#3713—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#239C2×D311yescharacteristic
161C2×#239C2×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⋊Q8C2×D311yescharacteristic, complemented
171C3×C4⋊Q8C2×D311yescharacteristic, complemented
172C3×#124—31no—
173C3×#123—61no—
174C3×#123—61no—
175C3×C22⋊Q8—31no—
176C3×C22⋊Q8—31no—
177C3×#121—61no—
178C3×C4×D4—31no—
179C3×C4×D4—31no—
180C2×C3×C4⋊C4—61no—
181#950—64no—
182#949—64no—
183#946—31no—
184#946C2×D311yescharacteristic
185#946C2×D311yescharacteristic, complemented
186C2×#216C2×D311yescharacteristic, complemented
187C2×#216C2×D311yescharacteristic, complemented
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—61no—
194C2×#215—61no—
195C2×#215C2×D311yescharacteristic
196C2×#215C2×D311yescharacteristic
197#938—31no—
198#937—61no—
199C2×#214—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203#930—31no—
204#924—31no—
205C2×#208—31no—
206C22×C3⋊C8—31no—
207#919—64no—
208#914—64no—
209C2×D24—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#895—21no—
213#894—21no—
214#894—21no—
215#894—61no—
216D3×C4⋊C4—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×D12C2×D311yescharacteristic, complemented
229C3×#97—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#835—61no—
237#832—31no—
238#832—31no—
239#830—31no—
240#830—31no—
241#821—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245#817—31no—
246#810—31no—
247#809—31no—
248#809—31no—
249#808—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×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)C2×D412yes—
274C4×C3⋊D3—81no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—41no—
283C3×D12—42no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
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#626—42no—
296#626—42no—
297#625—81no—
298#624—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—31no—
306#546—91no—
307#497—31no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—21no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345#239—22no—
346#239—22no—
347#239—41no—
348#239—41no—
349#239—62no—
350#239—121no—
351D3×D4—62no—
352D3×D4—121no—
353#235—62no—
354#235—121no—
355C2×D12—21no—
356C2×D12—21no—
357C2×D12—31no—
358C2×D12—31no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12—61no—
362C2×D12—61no—
363C2×D12—121no—
364C2×D12#6711yescharacteristic
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×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3C22×D311yescharacteristic
376C2×C4×D3C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×Q16—121no—
380C3×SD16—62no—
381C3×SD16—121no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—41no—
391C3×C4⋊C4—41no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C42—21no—
402C3×C42C22×D311yescharacteristic
403C3×C42C22×D311yescharacteristic
404#217—61no—
405#217—61no—
406#216—22no—
407#216—41no—
408#215—22no—
409#215—41no—
410#215—62no—
411#215—62no—
412#215—62no—
413#215—62no—
414#215—62no—
415#215—122no—
416#215—122no—
417#214—62no—
418#213—34no—
419#213—62no—
420#213—62no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—121no—
431(C2×D3)⋊C4#6711yescharacteristic
432(C2×D3)⋊C4#6711yescharacteristic
433C4⋊Dic3—31no—
434C4⋊Dic3—31no—
435C4⋊Dic3—61no—
436C4⋊Dic3#6711yescharacteristic
437C4⋊Dic3C22×D311yescharacteristic
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442#208—62no—
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
452D24—34no—
453ΓL(1,𝔽25)—62no—
454D3×C8—62no—
455C22×C32C22×D411yescharacteristic
456C2×C3⋊D3—22no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—41no—
475C32×C4—41no—
476C32×C4C22×D411yescharacteristic
477C32×C4H(5,𝔽2)11yescharacteristic
478C3⋊Dic3—41no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—31no—
490C2×Q16—31no—
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⋊Q8D3211yescharacteristic, complemented
501#124—31no—
502#123—61no—
503#123—61no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507C22⋊Q8—91no—
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—91no—
523#102—91no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—31no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—61no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C22×D3C2×#6711yescharacteristic
544C22×D3C2×#6711yescharacteristic
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—41no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×D4—32no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—121no—
564C3×D4—122no—
565C3×D4—122no—
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—41no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
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×C4D3×D411yescharacteristic
588C2×C3×C4C2×#6711yescharacteristic
589C2×C3×C4C2×#6711yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592#67—122no—
593#67—122no—
594#67—241no—
595#67—241no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—121no—
601C2×Dic3C2×#6711yescharacteristic
602C2×Dic3C2×#6711yescharacteristic
603D12—21no—
604D12—21no—
605D12—21no—
606D12—32no—
607D12—32no—
608D12—41no—
609D12—42no—
610D12—42no—
611D12—62no—
612D12—61no—
613D12—61no—
614D12—121no—
615D12—122no—
616D12—122no—
617D12D3×D412yes—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—42no—
623C4×D3—42no—
624C4×D3—42no—
625C4×D3—122no—
626C4×D3—122no—
627C4×D3—241no—
628C4×D3—241no—
629C4×D3—242no—
630Dic6—21no—
631Dic6—21no—
632C3×C8—32no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C3⋊C8—121no—
641C3⋊C8D3×D412yes—
642C2×C32D4211yescharacteristic
643C2×C32#57511yescharacteristic
644C2×C32#57711yescharacteristic
645C3⋊D3—42no—
646C3×D3—41no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—81no—
650C24—181no—
651#41—62no—
652#41—62no—
653#41—121no—
654#41—121no—
655#41—182no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8C2×D3211yescharacteristic
659C2×Q8C2×D3211yescharacteristic
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—91no—
666C2×D4—181no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4—181no—
678Q16—62no—
679Q16—121no—
680SD16—62no—
681SD16—121no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685D8—94no—
686D8—182no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—91no—
692C2×C8—182no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—31no—
696C4⋊C4—31no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—91no—
700C4⋊C4—181no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42C2×D3211yescharacteristic
712C22×C3—21no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—62no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C22×#6711yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—22no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—62no—
740C2×D3—62no—
741C2×D3—122no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—244no—
749C2×D3—244no—
750C3×C4—22no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—61no—
763C3×C4—61no—
764C3×C4—81no—
765C3×C4—81no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4C2×D3×D411yescharacteristic
769C3×C4C2×D3×D411yescharacteristic
770C3×C4#100411yescharacteristic
771C3×C4#100411yescharacteristic
772Dic3—21no—
773Dic3—21no—
774Dic3—41no—
775Dic3—41no—
776Dic3—121no—
777Dic3—121no—
778Dic3—241no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—31no—
781C23—31no—
782C23—61no—
783C23—61no—
784C23—181no—
785C23—362no—
786C23—362no—
787C23—721no—
788Q8—21no—
789Q8—21no—
790Q8—21no—
791Q8—21no—
792Q8—61no—
793Q8—61no—
794D4—32no—
795D4—61no—
796D4—61no—
797D4—61no—
798D4—92no—
799D4—121no—
800D4—122no—
801D4—122no—
802D4—181no—
803D4—362no—
804D4—362no—
805D4—721no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—181no—
820C2×C4—362no—
821C2×C4—721no—
822C2×C4D3×#6711yescharacteristic
823C2×C4D3×#6711yescharacteristic
824C2×C4C22×D3211yescharacteristic
825C8—32no—
826C8—61no—
827C8—181no—
828C8—181no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—121no—
833C2×C3—121no—
834C2×C3—122no—
835C2×C3—241no—
836C2×C3#571711yescharacteristic
837C2×C3#577711yescharacteristic
838C2×C3#577811yescharacteristic
839C2×C3D4×#6711yescharacteristic
840C2×C3#582211yescharacteristic
841C2×C3#583711yescharacteristic
842D3—41no—
843D3—41no—
844D3—42no—
845D3—81no—
846D3—122no—
847D3—122no—
848D3—242no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—121no—
857C22—121no—
858C22—121no—
859C22—121no—
860C22—121no—
861C22—182no—
862C22—361no—
863C22—361no—
864C22—724no—
865C22C2×D3×#6711yescharacteristic
866C4—21no—
867C4—21no—
868C4—41no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—361no—
875C4D32×D411yescharacteristic
876C4#6431311yescharacteristic
877C3—21no—
878C3#8188211yescharacteristic, complemented
879C3#8352211yescharacteristic, complemented
880C2—121no—
881C2—121no—
882C2—122no—
883C2—241no—
884C2—362no—
885C2#1059529311yescharacteristic
886C2#1059531711yescharacteristic
887C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3267
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×#5726C2semidirect
2. C2×#63949C2semidirect
3. C2×#63939C2semidirect
4. #10594007C2semidirect
5. #10592782C2semidirect
6. C3×#5086C2semidirect
7. #10591657C2semidirect
8. #10591651C2semidirect
9. #10591638C2semidirect
10. #10591634C2semidirect
11. #10591597C2semidirect
12. #10591586C2semidirect
13. #10590348C2semidirect
14. #10590346C2semidirect
15. #10590326C2semidirect
19. C2×C3×#239C22semidirect
22. C32×C4⋊Q8C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
38. C3×C4×D12C22semidirect
47. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63662C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#803C22semidirect
56. #63573C22semidirect
57. #63565C22semidirect
59. #63563C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5726D3semidirect
80. #5086D3semidirect
152. #3714D4semidirect
161. C2×#239C2×D3semidirect
170. C3×C4⋊Q8C2×D3semidirect
171. C3×C4⋊Q8C2×D3semidirect
185. #946C2×D3semidirect
186. C2×#216C2×D3semidirect
187. C2×#216C2×D3semidirect
228. C4×D12C2×D3semidirect
253. #803C2×D3semidirect
500. C4⋊Q8D32semidirect
779. C32#3267semidirect
878. C3#81882semidirect
879. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C2×#639492
C2×#639392
#105940072
#105927822
C3×#50862
#105916572
#105916512
#105916382
#105916342
#105915972
#105915862
#105903482
#105903462
#105903262
#835223
#818823