Finite Group Databasebeta

← #11888684

Subgroups — #11888684

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595357C211yesmaximal, characteristic, complemented
2#10594559C211yesmaximal, characteristic, complemented
3#10592517C211yesmaximal, characteristic, complemented
4C3×#4805C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6#10591616C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591588C211yesmaximal, characteristic, complemented
9#10590968C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590782C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590428C211yesmaximal, characteristic, complemented
16#81432—31nomaximal
17#78853—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64153C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23#64102C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28#63909C2211yescharacteristic
29#63909C2211yescharacteristic
30#63906—21no—
31#63905—21no—
32C4×#626—21no—
33C4×#625C2211yescharacteristic
34#63898C2211yescharacteristic
35#63885—21no—
36#63884—21no—
37D3×Dic3⋊C4—21no—
38#63872C2211yescharacteristic
39#63868—21no—
40#63857C2211yescharacteristic
41#63853—21no—
42C2×#3714C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63641C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63576C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic
61#5824—31no—
62#5631—31no—
63#5530—31no—
64#5514—31no—
65C3×#483—31no—
66C3×#416—31no—
67#5238—31no—
68#5114—31no—
69#5111—31no—
70#5049—31no—
71#4996—31no—
72#4966—31no—
73#4871—31no—
74#4869—31no—
75#4868—31no—
76#4864—31no—
77#4818—31no—
78#4818—31no—
79#4818—61no—
80#4812—31no—
81#4810—31no—
82#4805D311yescharacteristic, complemented
83#4804D311yescharacteristic, complemented
84#4797—31no—
85#4797—31no—
86#4785—31no—
87#4781—31no—
88#4771—31no—
89#4763—31no—
90#4734—31no—
91#4728—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#625D411yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3755—41no—
115#3752—21no—
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3744—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3714—22no—
143#3711—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×#237—31no—
148C2×#235—31no—
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153#946C2×D311yescharacteristic
154#944—31no—
155#944—31no—
156#944—61no—
157C2×#215—31no—
158C2×#215—31no—
159C2×#215—61no—
160#939—61no—
161#935—61no—
162D4×Dic3—31no—
163C2×#213—31no—
164#930—31no—
165#930—31no—
166#930—61no—
167#929—61no—
168C4×#67—31no—
169C4×#67—31no—
170C4×#67—61no—
171#924—31no—
172C2×Dic3⋊C4—61no—
173C2×#208—31no—
174C2×D24—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—61no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8C2×D311yescharacteristic
180#898—61no—
181#897—31no—
182#895—31no—
183#895—31no—
184#894—61no—
185#894—61no—
186#893—31no—
187#893—31no—
188#893—31no—
189#893—61no—
190#892C2×D311yescharacteristic
191D3×C4⋊C4—61no—
192D3×C4⋊C4C2×D311yescharacteristic
193#890—31no—
194#890—31no—
195#884—61no—
196#884—61no—
197#883—61no—
198#883—61no—
199#876—61no—
200C4×D12—61no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C2×D311yescharacteristic
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211#835C2×D311yescharacteristic
212#835C2×D311yescharacteristic
213#832—31no—
214#830—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#817C2×D311yescharacteristic
220#816—31no—
221#816—31no—
222#815—31no—
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—61no—
232#809—31no—
233#809—31no—
234#809C2×D311yescharacteristic
235#808C2×D311yescharacteristic
236#807—31no—
237#807—31no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4×C3⋊D3—81no—
253#634—21no—
254#634—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—42no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×C4×D3—81no—
269#626—42no—
270#626—81no—
271#625—41no—
272#625—42no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—31no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—91no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—31no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#239—22no—
314#239—41no—
315#237—62no—
316#237—121no—
317#235—62no—
318#235—121no—
319C2×D12—21no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—121no—
333C2×C4×D3C22×D311yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—61no—
355#217—31no—
356#217—31no—
357#217—61no—
358#217—61no—
359#215—121no—
360#215—121no—
361#215—122no—
362#213—62no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
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—121no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—121no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399#208—121no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—62no—
406#204—121no—
407#204—121no—
408#204—122no—
409ΓL(1,𝔽25)—121no—
410D3×C8—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—91no—
438C2×SD16—91no—
439C2×SD16—91no—
440C2×D8—91no—
441C2×M16—91no—
442C22×C8—31no—
443C4⋊Q8—91no—
444#126—181no—
445#125—91no—
446#123—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—91no—
452#121—91no—
453#121—181no—
454#121—181no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—181no—
459#117—31no—
460C2×C4⋊C4—31no—
461C2×C4⋊C4—181no—
462#107—91no—
463#106—31no—
464#106—31no—
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103D3211yescharacteristic
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—91no—
478#97—91no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3D3×D411yescharacteristic
487C22×D3D3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×D4—32no—
495C3×D4—61no—
496C3×D4—122no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4—241no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—122no—
518#67—121no—
519#67—121no—
520#67—122no—
521#67—122no—
522#67—241no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3—122no—
536C2×Dic3—122no—
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539D12—21no—
540D12—42no—
541D12—62no—
542D12—61no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—121no—
547D12—122no—
548D12—241no—
549D12#23512yes—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—42no—
555C4×D3—81no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32#54611yescharacteristic
578C2×C32#57511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—81no—
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—42no—
584#41—62no—
585#41—121no—
586#41—182no—
587#41—361no—
588C2×Q8—91no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—181no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604SD16—361no—
605SD16—361no—
606D8—182no—
607M16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—121no—
612C2×C8C2×D3211yescharacteristic
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4C2×D3211yescharacteristic
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—61no—
635C42—91no—
636C22×C3—21no—
637C22×C3—62no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—22no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—241no—
665C2×D3—241no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23511yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4#100911yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—62no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#330711yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—61no—
701C23—181no—
702Q8—21no—
703Q8—21no—
704Q8—181no—
705Q8—181no—
706D4—32no—
707D4—61no—
708D4—122no—
709D4—181no—
710D4—181no—
711D4—362no—
712D4—361no—
713D4—362no—
714D4—721no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—241no—
731C2×C4—362no—
732C2×C4—362no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—121no—
743C2×C3—121no—
744C2×C3—122no—
745C2×C3#549011yescharacteristic
746C2×C3#565411yescharacteristic
747C2×C3#576211yescharacteristic
748C2×C3#576811yescharacteristic
749C2×C3#577011yescharacteristic
750C2×C3#577711yescharacteristic
751D3—41no—
752D3—42no—
753D3—41no—
754D3—242no—
755D3—241no—
756D3—241no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—62no—
764C22—121no—
765C22—121no—
766C22—361no—
767C22—361no—
768C22—361no—
769C22D32×D411yescharacteristic
770C4—41no—
771C4—41no—
772C4—61no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—181no—
779C4—361no—
780C4D3×#23511yescharacteristic
781C4#6431411yescharacteristic
782C3—21no—
783C3#7885311yescharacteristic, complemented
784C3#8143211yescharacteristic, complemented
785C2—121no—
786C2—121no—
787C2—122no—
788C2—721no—
789C2#1059427211yescharacteristic
790C2#1059475311yescharacteristic
791C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595357C2semidirect
2. #10594559C2semidirect
3. #10592517C2semidirect
4. C3×#4805C2semidirect
5. C3×#4804C2semidirect
6. #10591616C2semidirect
7. #10591589C2semidirect
8. #10591588C2semidirect
9. #10590968C2semidirect
10. #10590830C2semidirect
11. #10590782C2semidirect
12. #10590723C2semidirect
13. #10590607C2semidirect
14. #10590462C2semidirect
15. #10590428C2semidirect
82. #4805D3semidirect
83. #4804D3semidirect
697. C32#3307semidirect
783. C3#78853semidirect
784. C3#81432semidirect

Maximal subgroups

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

subgroupindex
#105953572
#105945592
#105925172
C3×#48052
C3×#48042
#105916162
#105915892
#105915882
#105909682
#105908302
#105907822
#105907232
#105906072
#105904622
#105904282
#814323
#788533