Finite Group Databasebeta

← #11888690

Subgroups — #11888690

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595357C211yesmaximal, characteristic, complemented
2#10594560C211yesmaximal, characteristic, complemented
3#10592496C211yesmaximal, characteristic, complemented
4C3×#4810C211yesmaximal, characteristic, complemented
5C3×#4805C211yesmaximal, characteristic, complemented
6#10591587C211yesmaximal, characteristic, complemented
7#10591569C211yesmaximal, characteristic, complemented
8#10591556C211yesmaximal, characteristic, complemented
9#10590962C211yesmaximal, characteristic, complemented
10#10590781C211yesmaximal, characteristic, complemented
11#10590725C211yesmaximal, characteristic, complemented
12#10590709C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590578C211yesmaximal, characteristic, complemented
15#10590474C211yesmaximal, characteristic, complemented
16#81432—31nomaximal
17#80107—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64153C2211yescharacteristic
21#64099C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27#63908—21no—
28#63908C2211yescharacteristic
29#63905—21no—
30C4×#625C2211yescharacteristic
31#63898C2211yescharacteristic
32#63898C2211yescharacteristic
33#63885—21no—
34#63884—21no—
35#63884—21no—
36#63879—21no—
37D3×Dic3⋊C4—21no—
38#63861—21no—
39#63857C2211yescharacteristic
40#63841C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63643C2211yescharacteristic
47#63642C2211yescharacteristic
48#63637C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63575C2211yescharacteristic
56#63572C2211yescharacteristic
57#63567C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5824—31no—
62#5631—31no—
63#5614—31no—
64#5514—31no—
65C3×#483—31no—
66C3×#449—31no—
67#5233—31no—
68#5174—31no—
69#5162—31no—
70#5158—31no—
71#5152—31no—
72#5049—31no—
73#5041—31no—
74#4966—31no—
75#4871—31no—
76#4869—31no—
77#4868—31no—
78#4864—31no—
79#4818—31no—
80#4810D311yescharacteristic, complemented
81#4805D311yescharacteristic, complemented
82#4804—31no—
83#4797—31no—
84#4797—31no—
85#4797—61no—
86#4771—31no—
87#4766—31no—
88#4734—31no—
89#4730—31no—
90#4728—31no—
91#4723—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C3×#239—22no—
95C3×#239—41no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#625—21no—
105C2×#625—21no—
106C2×#625D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#215—41no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—22no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3716—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×#237—31no—
148C2×#235—31no—
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C3×C22⋊Q8—31no—
152C3×#121—31no—
153C2×C3×C4⋊C4—31no—
154#946C2×D311yescharacteristic
155#944—31no—
156#944—31no—
157#944—61no—
158C2×#215C2×D311yescharacteristic
159#939—61no—
160#938—31no—
161#938—61no—
162#935—61no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166C2×#214—31no—
167#930—31no—
168#930—61no—
169#929—61no—
170C4×#67—31no—
171C4×#67—31no—
172C4×#67—61no—
173#926—31no—
174#924—31no—
175C2×Dic3⋊C4—61no—
176C2×#208—31no—
177C22×C3⋊C8—31no—
178C2×D24C2×D311yescharacteristic
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×D3×C8—31no—
182#898—61no—
183#897—31no—
184#895C2×D311yescharacteristic
185#894—61no—
186#894—61no—
187#893—31no—
188#893—31no—
189#892—31no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4C2×D311yescharacteristic
192#890—31no—
193#890—31no—
194#890—61no—
195#884—61no—
196#883—61no—
197#67⋊C4—61no—
198#879—61no—
199C3×#106—31no—
200C3×#106—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic
204C3×#103C2×D311yescharacteristic
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#835C2×D311yescharacteristic
212#832—31no—
213#832—31no—
214#832—31no—
215#821—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#817C2×D311yescharacteristic
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#815—31no—
225#815—31no—
226#815—61no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#809—31no—
234#809—31no—
235#809C2×D311yescharacteristic
236#808C2×D311yescharacteristic
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⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251#634—21no—
252#634—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—42no—
261C3×D12—81no—
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#625—41no—
270#625—42no—
271#625—42no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
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—31no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
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—31no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—31no—
308C2×#67—31no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316#239—22no—
317#239—41no—
318#237—62no—
319#237—121no—
320#235—62no—
321#235—121no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12C22×D311yescharacteristic
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×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C3×SD16—121no—
337C3×D8—62no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#215—41no—
360#214—121no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391Dic3⋊C4—121no—
392Dic3⋊C4—121no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398#208—121no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—22no—
406#204—121no—
407ΓL(1,𝔽25)—121no—
408D3×C8—121no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—22no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C2×#41—91no—
436C2×SD16—31no—
437C2×SD16—91no—
438C2×D8—31no—
439C2×M16—91no—
440C22×C8—91no—
441C4⋊Q8—91no—
442#126—181no—
443#125—91no—
444#123—181no—
445#123—181no—
446#123—181no—
447C22⋊Q8—31no—
448C22⋊Q8—91no—
449#121—31no—
450#121—91no—
451#121—181no—
452#121—181no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—181no—
457#117—91no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—181no—
460#107—91no—
461#106—31no—
462#106—31no—
463C4⋊C8—91no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103D3211yescharacteristic
470#102—31no—
471#102—91no—
472#102—91no—
473#102—91no—
474C22⋊C8—31no—
475C22⋊C8—31no—
476#97—91no—
477C23×C3—31no—
478C23×C3—31no—
479C23×C3—61no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3D3×D411yescharacteristic
484C22×D3D3×D411yescharacteristic
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×D4—32no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—122no—
496C3×D4—241no—
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—122no—
513C2×C3×C4—241no—
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—121no—
517#67—121no—
518#67—122no—
519#67—122no—
520#67—122no—
521#67—122no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—241no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541D12—21no—
542D12—21no—
543D12—21no—
544D12—42no—
545D12—81no—
546D12#23712yes—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—81no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—241no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
561Dic6—121no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C2×C32#54611yescharacteristic
573C2×C32#57511yescharacteristic
574C2×C32#57711yescharacteristic
575C3×D3—41no—
576C3×D3—41no—
577C3×D3—42no—
578C3×D3—81no—
579#41—62no—
580#41—121no—
581#41—182no—
582#41—361no—
583C2×Q8—91no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—181no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599SD16—121no—
600SD16—361no—
601D8—62no—
602M16—361no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—91no—
606C2×C8—361no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—91no—
630C42—181no—
631C22×C3—21no—
632C22×C3—62no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—81no—
667C3×C4—81no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23711yescharacteristic
671C3×C4#100411yescharacteristic
672C3×C4D3×#4111yescharacteristic
673C3×C4#100911yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—61no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—241no—
689Dic3—241no—
690C32#330711yescharacteristic, complemented, Sylow
691C23—31no—
692C23—31no—
693C23—61no—
694C23—61no—
695Q8—21no—
696Q8—21no—
697Q8—181no—
698Q8—181no—
699D4—32no—
700D4—61no—
701D4—61no—
702D4—61no—
703D4—122no—
704D4—241no—
705D4—361no—
706D4—362no—
707D4—362no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—122no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—241no—
724C2×C4—362no—
725C2×C4—362no—
726C2×C4—721no—
727C2×C4C22×D3211yescharacteristic
728C8—21no—
729C8—61no—
730C8—61no—
731C8—181no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—121no—
736C2×C3—122no—
737C2×C3—121no—
738C2×C3—241no—
739C2×C3#559111yescharacteristic
740C2×C3#565411yescharacteristic
741C2×C3#576211yescharacteristic
742C2×C3#576811yescharacteristic
743C2×C3#577511yescharacteristic
744C2×C3#577711yescharacteristic
745D3—41no—
746D3—41no—
747D3—42no—
748D3—81no—
749C22—61no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—61no—
754C22—61no—
755C22—62no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—121no—
761C22D32×D411yescharacteristic
762C4—41no—
763C4—41no—
764C4—61no—
765C4—61no—
766C4—121no—
767C4—121no—
768C4—181no—
769C4—181no—
770C4—361no—
771C4—361no—
772C4#6430711yescharacteristic
773C4D3×#23711yescharacteristic
774C3—21no—
775C3#8010711yescharacteristic, complemented
776C3#8143211yescharacteristic, complemented
777C2—121no—
778C2—121no—
779C2—122no—
780C2—241no—
781C2#1059427411yescharacteristic
782C2#1059474911yescharacteristic
783C2#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. #10594560C2semidirect
3. #10592496C2semidirect
4. C3×#4810C2semidirect
5. C3×#4805C2semidirect
6. #10591587C2semidirect
7. #10591569C2semidirect
8. #10591556C2semidirect
9. #10590962C2semidirect
10. #10590781C2semidirect
11. #10590725C2semidirect
12. #10590709C2semidirect
13. #10590607C2semidirect
14. #10590578C2semidirect
15. #10590474C2semidirect
80. #4810D3semidirect
81. #4805D3semidirect
690. C32#3307semidirect
775. C3#80107semidirect
776. C3#81432semidirect

Maximal subgroups

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

subgroupindex
#105953572
#105945602
#105924962
C3×#48102
C3×#48052
#105915872
#105915692
#105915562
#105909622
#105907812
#105907252
#105907092
#105906072
#105905782
#105904742
#814323
#801073