Finite Group Databasebeta

← #11889740

Subgroups — #11889740

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2#10594005C211yesmaximal, characteristic
3C3×#5089C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590618C211yesmaximal, characteristic, complemented
6#10590612C211yesmaximal, characteristic, complemented
7#10590597C211yesmaximal, characteristic, complemented
8#10590593C211yesmaximal, characteristic, complemented
9#10590528C211yesmaximal, characteristic, complemented
10#10590525C211yesmaximal, characteristic, complemented
11#10590510C211yesmaximal, characteristic, complemented
12#10590506C211yesmaximal, characteristic, complemented
13#10590378C211yesmaximal, characteristic, complemented
14#10590360C211yesmaximal, characteristic, complemented
15#10590328C211yesmaximal, characteristic, complemented
16#81700—31nomaximal
17#80982—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21#64155—21no—
22#64155—21no—
23#64106C2211yescharacteristic
24#64106C2211yescharacteristic, complemented
25#64102—21no—
26C4⋊C4×C3⋊D3C2211yescharacteristic
27C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
28#64099—21no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30C4×#634C2211yescharacteristic, complemented
31C3×#875C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33#63923—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916C2211yescharacteristic
36#63906—21no—
37#63891—21no—
38#63871C2211yescharacteristic
39C2×#3719C2211yescharacteristic, complemented
40C2×#3716C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3712C2211yescharacteristic, complemented
43C2×#3710C2211yescharacteristic
44C3×#810C2211yescharacteristic, complemented
45C3×#810C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic, complemented
61#5730—31no—
62#5730—31no—
63#5730—61no—
64#5676—31no—
65#5554—31no—
66C3×#489—31no—
67C3×#474—31no—
68#5089D311yescharacteristic, complemented
69#5087D311yescharacteristic, complemented
70#5054—31no—
71#5018—31no—
72#4887—31no—
73#4886—31no—
74#4884—31no—
75#4882—31no—
76#4845—31no—
77#4836—31no—
78#4813—31no—
79#4811—31no—
80#4808—31no—
81#4803—31no—
82#4783—31no—
83#4780—31no—
84#4776—31no—
85#4776—31no—
86#4774—31no—
87#4771—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8—21no—
94C2×C4⋊(C3⋊D3)D411yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108#3802—22no—
109#3802—41no—
110#3796—22no—
111#3796—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118#3752D411yescharacteristic
119#3752D411yescharacteristic
120C4⋊(C3⋊Dic3)—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)D411yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126#3750—21no—
127C4×C3⋊Dic3—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3719—41no—
140#3716—22no—
141#3716—41no—
142#3712—41no—
143#3710—41no—
144#3314—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C3×C4⋊Q8—21no—
150C3×C4⋊Q8C2×D311yescharacteristic, complemented
151C3×C4⋊Q8C2×D311yescharacteristic, complemented
152C3×#124—31no—
153C3×C4×D4—31no—
154#946—31no—
155#946—61no—
156#946—61no—
157#946—61no—
158#946—61no—
159#946—62no—
160#946—62no—
161C2×#216—31no—
162#938—31no—
163C2×#214—31no—
164C2×#214—31no—
165#930—61no—
166C2×(C2×D3)⋊C4—61no—
167C2×Dic12—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×ΓL(1,𝔽25)—31no—
171C2×ΓL(1,𝔽25)—31no—
172C2×D3×C8—31no—
173C2×D3×C8—31no—
174#897—31no—
175#897—31no—
176#897—31no—
177#897—31no—
178#897—31no—
179#897—61no—
180#897—61no—
181#895—31no—
182#893—61no—
183#893—61no—
184#893—62no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4—61no—
191#890—61no—
192#890—61no—
193#890—62no—
194#886—61no—
195#884—61no—
196#883—61no—
197#882—61no—
198#882—61no—
199D3×C22⋊C4—61no—
200#875C2×D311yescharacteristic
201C4×D12—31no—
202C4×D12—31no—
203C4×D12—61no—
204C4×D12C2×D311yescharacteristic
205C4×Dic6—31no—
206C4×Dic6—31no—
207C4×Dic6—61no—
208C3×#107—31no—
209C3×#107—31no—
210C3×C4⋊C8—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#97—31no—
218#835—31no—
219#832—31no—
220#832—31no—
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228#816—31no—
229#816—31no—
230#810—31no—
231#810C2×D311yescharacteristic, complemented
232#810C2×D311yescharacteristic, complemented
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic
237#807—31no—
238#807C2×D311yescharacteristic, complemented
239#807C2×D311yescharacteristic, complemented
240C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
241#803C2×D311yescharacteristic, complemented
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C32×Q8—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—22no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C4×C3⋊D3—81no—
265C4×C3⋊D3—81no—
266#634—21no—
267#634—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12#4112yes—
274C3×C4×D3—81no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#626—42no—
278#626—81no—
279#625—42no—
280D3×Dic3—42no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#554—91no—
286#546—91no—
287#489—31no—
288#484—91no—
289#480—91no—
290#474—31no—
291#468—91no—
292#467—91no—
293#464—91no—
294#452—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#417—91no—
299C2×#102—91no—
300C23×D3—61no—
301C23×D3—61no—
302C2×C3×Q8—22no—
303C2×C3×Q8—21no—
304C2×C3×Q8—21no—
305C2×C3×Q8—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314#239—62no—
315#239—121no—
316#237—62no—
317#237—121no—
318D3×D4—62no—
319D3×D4—62no—
320D3×D4—121no—
321D3×D4—121no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12C22×D311yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—31no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—62no—
342C2×C4×D3—62no—
343C2×Dic6—31no—
344C2×Dic6—31no—
345C2×Dic6—61no—
346C2×Dic6C22×D311yescharacteristic
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—21no—
365C3×C42C22×D311yescharacteristic
366C3×C42C22×D311yescharacteristic
367#217—61no—
368#216—121no—
369#214—62no—
370#214—121no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—62no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—62no—
401C4⋊Dic3—62no—
402C4⋊Dic3C22×D311yescharacteristic
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—62no—
409Dic3⋊C4—62no—
410Dic3⋊C4—62no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413C4×Dic3—62no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420Dic12—121no—
421#204—62no—
422#204—121no—
423ΓL(1,𝔽25)—121no—
424ΓL(1,𝔽25)—121no—
425D3×C8—121no—
426D3×C8—121no—
427C22×C32C22×D411yescharacteristic
428C2×C3⋊D3—21no—
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3#13712yes—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440D32—84no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—41no—
444C32×C4—41no—
445C32×C4C2×#4111yescharacteristic
446C32×C4H(5,𝔽2)11yescharacteristic
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—91no—
454C22×D4—91no—
455C2×Q16—91no—
456C2×SD16—91no—
457C2×SD16—91no—
458C2×M16—91no—
459C22×C8—91no—
460C4⋊Q8D3211yescharacteristic, complemented
461#125—181no—
462#124—31no—
463#123—181no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467C22⋊Q8—181no—
468C22⋊Q8—181no—
469#121—91no—
470#121—181no—
471#120—181no—
472C4×Q8—91no—
473C4×D4—31no—
474C4×D4—91no—
475C4×D4—181no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C22⋊C4—181no—
479#107—31no—
480#107—31no—
481#107—91no—
482C4⋊C8—31no—
483#103—31no—
484#103—31no—
485#103—91no—
486#103—91no—
487#102—31no—
488#102—31no—
489#102—31no—
490#102—31no—
491#102—91no—
492#102—91no—
493C22⋊C8—91no—
494C22⋊C8—91no—
495#97—31no—
496C23×C3—61no—
497C23×C3—61no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—241no—
511C22×D3—241no—
512C3×Q8—61no—
513C3×Q8—61no—
514C3×Q8—81no—
515C3×Q8—81no—
516C3×Q8—82no—
517C3×D4—32no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—122no—
540#67—122no—
541#67—122no—
542#67—241no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—122no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—62no—
562D12—62no—
563D12—64no—
564D12—122no—
565D12—241no—
566D12#23912yes—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—81no—
576C4×D3—121no—
577C4×D3—121no—
578C4×D3—121no—
579C4×D3—121no—
580C4×D3—122no—
581C4×D3—241no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585C4×D3—242no—
586C4×D3—242no—
587Dic6—21no—
588Dic6—21no—
589Dic6—61no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—121no—
594Dic6—121no—
595C3×C8—61no—
596C3×C8—61no—
597C3×C8—61no—
598C3×C8—61no—
599C3⋊C8—21no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C2×C32#54611yescharacteristic
604C2×C32C2×#13711yescharacteristic
605C2×C32#57611yescharacteristic
606C3⋊D3—22no—
607C3⋊D3—41no—
608C3×D3—42no—
609C3×D3—81no—
610C24—181no—
611#41—182no—
612#41—361no—
613C2×Q8—21no—
614C2×Q8—31no—
615C2×Q8—91no—
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—91no—
619C2×D4—181no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—182no—
623C2×D4—361no—
624C22×C4—61no—
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4—181no—
630Q16—361no—
631SD16—182no—
632SD16—361no—
633M16—361no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—361no—
639C4⋊C4—21no—
640C4⋊C4—31no—
641C4⋊C4—91no—
642C4⋊C4—91no—
643C4⋊C4—181no—
644C4⋊C4—181no—
645C4⋊C4—181no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4C2×D3211yescharacteristic
650C4⋊C4C2×D3211yescharacteristic
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C42—181no—
661C42C2×D3211yescharacteristic
662C22×C3—21no—
663C22×C3—62no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C2×D3—22no—
672C2×D3—32no—
673C2×D3—32no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—62no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—62no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—244no—
696C2×D3—244no—
697C3×C4—22no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—41no—
705C3×C4—42no—
706C3×C4—42no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4C2×#23911yescharacteristic
714C3×C4D3×#4111yescharacteristic
715C3×C4#100911yescharacteristic
716C3×C4#100911yescharacteristic
717Dic3—41no—
718Dic3—41no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—122no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731C32#331411yescharacteristic, complemented, Sylow
732C23—61no—
733C23—61no—
734C23—91no—
735C23—91no—
736C23—362no—
737C23—362no—
738C23—721no—
739Q8—61no—
740Q8—61no—
741Q8—81no—
742Q8—181no—
743Q8—181no—
744D4—32no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—182no—
749D4—362no—
750D4—362no—
751D4—721no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—241no—
765C2×C4—362no—
766C2×C4—721no—
767C2×C4—721no—
768C2×C4#381111yescharacteristic
769C2×C4#381111yescharacteristic
770C2×C4C22×D3211yescharacteristic
771C8—61no—
772C8—61no—
773C8—61no—
774C8—61no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—122no—
779C2×C3—241no—
780C2×C3#563011yescharacteristic
781C2×C3#567611yescharacteristic
782C2×C3#575711yescharacteristic
783C2×C3#577411yescharacteristic
784C2×C3D3×#13711yescharacteristic
785C2×C3D3×#13711yescharacteristic
786D3—42no—
787D3—62no—
788D3—62no—
789D3—81no—
790D3—122no—
791D3—122no—
792D3—121no—
793D3—121no—
794C22—62no—
795C22—92no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—181no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—181no—
806C22—724no—
807C22C2×#381111yescharacteristic
808C4—21no—
809C4—21no—
810C4—41no—
811C4—41no—
812C4—121no—
813C4—121no—
814C4—181no—
815C4—181no—
816C4—361no—
817C4—361no—
818C4D3×#23911yescharacteristic
819C4#6432011yescharacteristic
820C3—21no—
821C3#8098211yescharacteristic, complemented
822C3#8170011yescharacteristic, complemented
823C2—122no—
824C2—182no—
825C2—241no—
826C2—361no—
827C2#1059510211yescharacteristic
828C2#1059532211yescharacteristic
829C2#1059543111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594005C2
hypercenterC4⋊Q8D32
hypocenterC32#3314
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. #10596201C2semidirect
3. C3×#5089C2semidirect
4. C3×#5087C2semidirect
5. #10590618C2semidirect
6. #10590612C2semidirect
7. #10590597C2semidirect
8. #10590593C2semidirect
9. #10590528C2semidirect
10. #10590525C2semidirect
11. #10590510C2semidirect
12. #10590506C2semidirect
13. #10590378C2semidirect
14. #10590360C2semidirect
15. #10590328C2semidirect
20. C32×C4⋊Q8C22semidirect
24. #64106C22semidirect
27. C4⋊C4×C3⋊D3C22semidirect
30. C4×#634C22semidirect
39. C2×#3719C22semidirect
42. C2×#3712C22semidirect
44. C3×#810C22semidirect
45. C3×#810C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
60. #63557C22semidirect
68. #5089D3semidirect
69. #5087D3semidirect
150. C3×C4⋊Q8C2×D3semidirect
151. C3×C4⋊Q8C2×D3semidirect
231. #810C2×D3semidirect
232. #810C2×D3semidirect
238. #807C2×D3semidirect
239. #807C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. #803C2×D3semidirect
460. C4⋊Q8D32semidirect
731. C32#3314semidirect
821. C3#80982semidirect
822. C3#81700semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105940052
C3×#50892
C3×#50872
#105906182
#105906122
#105905972
#105905932
#105905282
#105905252
#105905102
#105905062
#105903782
#105903602
#105903282
#817003
#809823