Finite Group Databasebeta

← #11889278

Subgroups — #11889278

Order 1152.

910 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596203C211yesmaximal, characteristic, complemented
2#10594005C211yesmaximal, characteristic
3C3×#5089C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590618C211yesmaximal, characteristic, complemented
6#10590611C211yesmaximal, characteristic, complemented
7#10590597C211yesmaximal, characteristic, complemented
8#10590594C211yesmaximal, characteristic, complemented
9#10590527C211yesmaximal, characteristic, complemented
10#10590524C211yesmaximal, characteristic, complemented
11#10590513C211yesmaximal, characteristic, complemented
12#10590507C211yesmaximal, characteristic, complemented
13#10590378C211yesmaximal, characteristic, complemented
14#10590360C211yesmaximal, characteristic, complemented
15#10590328C211yesmaximal, characteristic, complemented
16#81698—31nomaximal
17#81078—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic, complemented
21#64156—21no—
22Q8×C3⋊Dic3—21no—
23#64107—21no—
24#64107—21no—
25#64106C2211yescharacteristic
26#64106C2211yescharacteristic, complemented
27#64101C2211yescharacteristic
28#64101C2211yescharacteristic, complemented
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
43C2×#3710C2211yescharacteristic, complemented
44C3×#810C2211yescharacteristic, complemented
45C3×#810C2211yescharacteristic, complemented
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, 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#5732—31no—
62#5732—31no—
63#5732—61no—
64#5676—31no—
65#5554—31no—
66C3×#489—31no—
67C3×#476—31no—
68#5089D311yescharacteristic, complemented
69#5084D311yescharacteristic, complemented
70#5054—31no—
71#5018—31no—
72#4868—31no—
73#4867—31no—
74#4866—31no—
75#4864—31no—
76#4845—31no—
77#4836—31no—
78#4816—31no—
79#4814—31no—
80#4808—31no—
81#4804—31no—
82#4784—31no—
83#4783—31no—
84#4778—31no—
85#4776—31no—
86#4776—31no—
87#4772—31no—
88#4770—31no—
89#4770—31no—
90#4710—31no—
91#4706—31no—
92C22×D32—21no—
93C2×C32×Q8—21no—
94C2×C4⋊(C3⋊D3)D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C4×C3⋊D3C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—41no—
108#3796—22no—
109#3796—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115#3752—21no—
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—
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3—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#3311—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#947—61no—
155#947—61no—
156#947—62no—
157#946—31no—
158Q8×Dic3—61no—
159Q8×Dic3—61no—
160Q8×Dic3—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#898—61no—
175#898—61no—
176#898—61no—
177#898—61no—
178#898—62no—
179#898—62no—
180#897—31no—
181#897—31no—
182#897—31no—
183#897—31no—
184#897—31no—
185#897—61no—
186#897—61no—
187#895—31no—
188#892—31no—
189#892—31no—
190#892—31no—
191#892—31no—
192#892—61no—
193#892—61no—
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×#106—31no—
209C3×#106—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#808C2×D311yescharacteristic, complemented
238#808C2×D311yescharacteristic, complemented
239#807—31no—
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—42no—
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)—41no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264#634—21no—
265#634—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12#4112yes—
272C3×C4×D3—81no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#626—42no—
276#626—81no—
277#625—42no—
278D3×Dic3—42no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#556—91no—
284#546—91no—
285#489—31no—
286#485—91no—
287#482—91no—
288#476—31no—
289#470—91no—
290#465—91no—
291#464—91no—
292#452—91no—
293#450—91no—
294#440—91no—
295#435—91no—
296#418—91no—
297#416—91no—
298C23×D3—61no—
299C23×D3—61no—
300C2×C3×Q8—22no—
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C22×C3×C4—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312#239—62no—
313#239—121no—
314#237—62no—
315#237—121no—
316D3×D4—62no—
317D3×D4—62no—
318D3×D4—121no—
319D3×D4—121no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#217—61no—
360#216—121no—
361#214—62no—
362#214—121no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
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—62no—
384(C2×D3)⋊C4—62no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—62no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—62no—
399C4⋊Dic3—62no—
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—61no—
402Dic3⋊C4—62no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—62no—
410C4×Dic3—62no—
411C4×Dic3—62no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418Dic12—121no—
419#204—62no—
420#204—121no—
421ΓL(1,𝔽25)—121no—
422ΓL(1,𝔽25)—121no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—21no—
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438D32—84no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4C2×#4111yescharacteristic
444C32×C4H(5,𝔽2)11yescharacteristic
445C3⋊Dic3—21no—
446C3⋊Dic3—21no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—91no—
452C22×D4—91no—
453C2×Q16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—91no—
457C22×C8—91no—
458C4⋊Q8D3211yescharacteristic, complemented
459#126—181no—
460#126—181no—
461#124—31no—
462#124—181no—
463#123—181no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—91no—
467#121—91no—
468#121—181no—
469#120—181no—
470C4×Q8—91no—
471C4×Q8—181no—
472C4×D4—31no—
473C4×D4—91no—
474#117—91no—
475#117—91no—
476C2×C22⋊C4—181no—
477#107—91no—
478#106—31no—
479#106—31no—
480C4⋊C8—31no—
481#103—31no—
482#103—31no—
483#103—91no—
484#103—91no—
485#102—31no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—91no—
490#102—91no—
491C22⋊C8—91no—
492C22⋊C8—91no—
493#97—31no—
494C23×C3—61no—
495C23×C3—61no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—31no—
499C22×D3—31no—
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—241no—
509C22×D3—241no—
510C3×Q8—44no—
511C3×Q8—42no—
512C3×Q8—42no—
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—32no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—241no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—122no—
538#67—122no—
539#67—122no—
540#67—241no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—122no—
556D12—21no—
557D12—21no—
558D12—21no—
559D12—121no—
560D12—121no—
561D12—122no—
562D12—122no—
563D12—241no—
564D12#23912yes—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—61no—
568C4×D3—61no—
569C4×D3—61no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—81no—
574C4×D3—121no—
575C4×D3—121no—
576C4×D3—121no—
577C4×D3—121no—
578C4×D3—122no—
579Dic6—21no—
580Dic6—21no—
581Dic6—61no—
582Dic6—61no—
583Dic6—61no—
584Dic6—61no—
585Dic6—121no—
586Dic6—121no—
587C3×C8—61no—
588C3×C8—61no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C2×C32#54611yescharacteristic
596C2×C32#57511yescharacteristic
597C2×C32#57711yescharacteristic
598C3⋊D3—41no—
599C3⋊D3—41no—
600C3×D3—42no—
601C3×D3—81no—
602C24—181no—
603#41—182no—
604#41—361no—
605C2×Q8—21no—
606C2×Q8—31no—
607C2×Q8—91no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—91no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4—182no—
615C2×D4—361no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—181no—
620Q16—361no—
621SD16—182no—
622SD16—361no—
623M16—361no—
624C2×C8—31no—
625C2×C8—31no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—361no—
629C4⋊C4—21no—
630C4⋊C4—31no—
631C4⋊C4—91no—
632C4⋊C4—91no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4C2×D3211yescharacteristic
638C4⋊C4C2×D3211yescharacteristic
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—91no—
643C22⋊C4—91no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C42—181no—
651C42—181no—
652C42—181no—
653C42C2×D3211yescharacteristic
654C22×C3—21no—
655C22×C3—62no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—22no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—244no—
688C2×D3—244no—
689C3×C4—22no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—41no—
697C3×C4—42no—
698C3×C4—42no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4C2×#23911yescharacteristic
706C3×C4D3×#4111yescharacteristic
707C3×C4#100911yescharacteristic
708C3×C4#100911yescharacteristic
709Dic3—41no—
710Dic3—41no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—121no—
716Dic3—121no—
717Dic3—122no—
718Dic3—122no—
719Dic3—121no—
720Dic3—121no—
721Dic3—121no—
722Dic3—121no—
723C32#331111yescharacteristic, complemented, Sylow
724C23—61no—
725C23—61no—
726C23—91no—
727C23—91no—
728C23—362no—
729C23—362no—
730C23—721no—
731Q8—42no—
732Q8—61no—
733Q8—61no—
734Q8—181no—
735Q8—181no—
736D4—32no—
737D4—61no—
738D4—61no—
739D4—61no—
740D4—361no—
741D4—362no—
742D4—362no—
743D4—721no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—91no—
749C2×C4—91no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—241no—
757C2×C4—362no—
758C2×C4#381111yescharacteristic
759C2×C4#381111yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—61no—
762C8—61no—
763C8—61no—
764C8—61no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—122no—
769C2×C3—241no—
770C2×C3#563011yescharacteristic
771C2×C3#567611yescharacteristic
772C2×C3#576211yescharacteristic
773C2×C3#577311yescharacteristic
774C2×C3#577311yescharacteristic
775C2×C3#577811yescharacteristic
776D3—42no—
777D3—81no—
778D3—121no—
779D3—121no—
780D3—121no—
781D3—121no—
782D3—241no—
783D3—241no—
784C22—62no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—181no—
791C22—181no—
792C22—181no—
793C22—181no—
794C22—181no—
795C22—181no—
796C22—724no—
797C22C2×#381111yescharacteristic
798C4—21no—
799C4—21no—
800C4—41no—
801C4—41no—
802C4—121no—
803C4—121no—
804C4—181no—
805C4—181no—
806C4—361no—
807C4—361no—
808C4D3×#23911yescharacteristic
809C4#6432011yescharacteristic
810C3—21no—
811C3#8107811yescharacteristic, complemented
812C3#8169811yescharacteristic, complemented
813C2—122no—
814C2—241no—
815C2—361no—
816C2—361no—
817C2#1059510111yescharacteristic
818C2#1059532411yescharacteristic
819C2#1059543111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594005C2
hypercenterC4⋊Q8D32
hypocenterC32#3311
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. #10596203C2semidirect
3. C3×#5089C2semidirect
4. C3×#5084C2semidirect
5. #10590618C2semidirect
6. #10590611C2semidirect
7. #10590597C2semidirect
8. #10590594C2semidirect
9. #10590527C2semidirect
10. #10590524C2semidirect
11. #10590513C2semidirect
12. #10590507C2semidirect
13. #10590378C2semidirect
14. #10590360C2semidirect
15. #10590328C2semidirect
20. C32×C4⋊Q8C22semidirect
26. #64106C22semidirect
28. #64101C22semidirect
30. C4×#634C22semidirect
39. C2×#3719C22semidirect
43. C2×#3710C22semidirect
44. C3×#810C22semidirect
45. C3×#810C22semidirect
50. C3×#808C22semidirect
51. C3×#808C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. C3×#803C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
60. #63557C22semidirect
68. #5089D3semidirect
69. #5084D3semidirect
150. C3×C4⋊Q8C2×D3semidirect
151. C3×C4⋊Q8C2×D3semidirect
231. #810C2×D3semidirect
232. #810C2×D3semidirect
237. #808C2×D3semidirect
238. #808C2×D3semidirect
240. C4⋊(C3⋊C8)C2×D3semidirect
241. #803C2×D3semidirect
458. C4⋊Q8D32semidirect
723. C32#3311semidirect
811. C3#81078semidirect
812. C3#81698semidirect

Maximal subgroups

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

subgroupindex
#105962032
#105940052
C3×#50892
C3×#50842
#105906182
#105906112
#105905972
#105905942
#105905272
#105905242
#105905132
#105905072
#105903782
#105903602
#105903282
#816983
#810783