Finite Group Databasebeta

← #11872352

Subgroups — #11872352

Order 1152.

856 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593989C211yesmaximal, characteristic, complemented
2#10593887C211yesmaximal, characteristic, complemented
3#10592547C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4840C211yesmaximal, characteristic, complemented
6#10590968C211yesmaximal, characteristic, complemented
7#10590968C211yesmaximal, characteristic, complemented
8#10590773C211yesmaximal, characteristic, complemented
9#10590758C211yesmaximal, characteristic, complemented
10#10590746C211yesmaximal, characteristic, complemented
11#10590745C211yesmaximal, characteristic, complemented
12#10590679C211yesmaximal, characteristic, complemented
13#10590677C211yesmaximal, characteristic, complemented
14#10590349C211yesmaximal, characteristic, complemented
15#10590292C211yesmaximal, characteristic, complemented
16#81144—31nomaximal
17#79384—31nomaximal
18C2×#3795C2211yescharacteristic
19C2×#3744C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21#64083C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25C3×#870C2211yescharacteristic
26#63910—21no—
27#63910—21no—
28#63909C2211yescharacteristic
29#63909C2211yescharacteristic
30#63902—21no—
31#63897—21no—
32#63897—21no—
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63879—21no—
38#63878—21no—
39D3×Dic3⋊C4—21no—
40#63844C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C4⋊(C3⋊C8)C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5697—31no—
62#5546—31no—
63#5535—31no—
64#5523—31no—
65C3×#478—31no—
66C3×#433—31no—
67#5063—31no—
68#5015—31no—
69#4889—31no—
70#4882—31no—
71#4863—31no—
72#4852—31no—
73#4848—31no—
74#4848—31no—
75#4848—61no—
76#4847D311yescharacteristic, complemented
77#4843—31no—
78#4840D311yescharacteristic, complemented
79#4829—31no—
80#4785—31no—
81#4781—31no—
82#4781—31no—
83#4756—31no—
84#4736—31no—
85#4735—31no—
86#4734—31no—
87#4734—31no—
88#4711—31no—
89#4710—31no—
90C4×D24—31no—
91C4×#204—31no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×#626—21no—
101C2×#626—21no—
102C2×#625—21no—
103C2×#624—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—22no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3—21no—
116#3744—22no—
117#3744—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#237—31no—
143C2×#235—31no—
144C3×#125—31no—
145C3×C4×D4—31no—
146C3×#117—31no—
147D4×Dic3—31no—
148C2×#213—31no—
149C2×#213—31no—
150#930—31no—
151#930—31no—
152C4×#67—61no—
153C2×C4⋊Dic3—31no—
154C2×Dic3⋊C4—61no—
155C2×D24—31no—
156C2×D24—31no—
157C2×#204—31no—
158C2×#204—31no—
159C2×#204—31no—
160C2×#204—31no—
161C2×#204—61no—
162C2×#204—61no—
163#895—31no—
164#895—31no—
165#895—61no—
166#895—61no—
167#894—61no—
168#894—61no—
169#894—61no—
170#894—61no—
171#893—31no—
172#893—31no—
173#892—61no—
174D3×C4⋊C4—31no—
175D3×C4⋊C4—61no—
176#887—31no—
177#884—61no—
178#884—61no—
179#67⋊C4—61no—
180#67⋊C4—61no—
181#67⋊C4—61no—
182#877—61no—
183#874—31no—
184#874—31no—
185#874—61no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12C2×D311yescharacteristic
190#872C2×D311yescharacteristic
191#870C2×D311yescharacteristic
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—31no—
195C4×Dic6—61no—
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C2×D311yescharacteristic
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207C3×C4×C8—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215#821—61no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#818C2×D311yescharacteristic
222#817—31no—
223#817C2×D311yescharacteristic
224#816—31no—
225#816—31no—
226#815C2×D311yescharacteristic
227C8×Dic3C2×D311yescharacteristic
228#810—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—81no—
249C4⋊(C3⋊D3)—81no—
250#634—21no—
251#634#4112yes—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—81no—
263#626—81no—
264#626—81no—
265#625—24no—
266#624—81no—
267#624—81no—
268D3×Dic3—24no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—91no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—31no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—31no—
290C2×C3×D4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—61no—
293C2×#67—61no—
294C2×#67—61no—
295C2×#67—61no—
296C2×#67—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300#237—62no—
301#237—62no—
302#235—62no—
303#235—62no—
304C2×D12—31no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—61no—
309C2×D12—61no—
310C2×D12—61no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—121no—
317C2×D12—121no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353#217—61no—
354#213—62no—
355#213—62no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4D1211yescharacteristic
367(C2×D3)⋊C4D1211yescharacteristic
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—121no—
383Dic3⋊C4D1211yescharacteristic
384Dic3⋊C4D1211yescharacteristic
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—121no—
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393D24—62no—
394D24—62no—
395#204—62no—
396#204—62no—
397#204—62no—
398#204—62no—
399#204—122no—
400#204—122no—
401C22×C32C22×D411yescharacteristic
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—22no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—22no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C2×#41—91no—
427C2×SD16—91no—
428C2×SD16—91no—
429C2×D8—91no—
430C2×D8—91no—
431#127—91no—
432#125—31no—
433#123—181no—
434#123—181no—
435#121—91no—
436#121—91no—
437#121—181no—
438#121—181no—
439C4×Q8—91no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—31no—
448#117—181no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—181no—
451#107—31no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—31no—
456C4⋊C8D3211yescharacteristic
457#103—91no—
458#103—91no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—31no—
467#97—31no—
468C4×C8—31no—
469C23×C3—31no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—61no—
476C22×D3—121no—
477C22×D3—121no—
478C22×D3C2×D1211yescharacteristic
479C3×D4—32no—
480C3×D4—61no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—241no—
493C2×C3×C4C2×D1211yescharacteristic
494C2×C3×C4C2×D1211yescharacteristic
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498C2×C3×C4C23×D311yescharacteristic
499#67—64no—
500#67—64no—
501#67—241no—
502#67—241no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—64no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—121no—
512C2×Dic3—121no—
513C2×Dic3—241no—
514C2×Dic3—241no—
515C2×Dic3C2×D1211yescharacteristic
516C2×Dic3C2×D1211yescharacteristic
517C2×Dic3C2×D1211yescharacteristic
518D12—21no—
519D12—61no—
520D12—61no—
521D12—61no—
522D12—61no—
523D12—61no—
524D12—61no—
525D12—61no—
526D12—61no—
527D12—121no—
528D12—121no—
529D12—121no—
530D12—121no—
531D12—241no—
532D12—241no—
533D12—241no—
534D12—241no—
535D12—242no—
536D12—242no—
537D12—241no—
538D12—241no—
539D12#23912yes—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—64no—
543C4×D3—81no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550Dic6—32no—
551Dic6—32no—
552Dic6—62no—
553Dic6—61no—
554Dic6—61no—
555Dic6—121no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—41no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32#52511yescharacteristic
567C2×C32#57611yescharacteristic
568C2×C32#57711yescharacteristic
569C3⋊D3—81no—
570C3⋊D3—81no—
571C3×D3—41no—
572C3×D3—42no—
573#41—182no—
574#41—182no—
575C2×Q8—91no—
576C2×D4—31no—
577C2×D4—91no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4—181no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591SD16—182no—
592SD16—182no—
593D8—182no—
594D8—182no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8C2×D3211yescharacteristic
598C2×C8C2×D3211yescharacteristic
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—91no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—181no—
620C42—181no—
621C42C2×D3211yescharacteristic
622C22×C3—21no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—62no—
626C22×C3—61no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C22×D1211yescharacteristic
630C22×C3C2×D3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—22no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C2×D3—241no—
653C2×D3—241no—
654C2×D3—241no—
655C3×C4—22no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—61no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23911yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—122no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685C32#311911yescharacteristic, complemented, Sylow
686C23—31no—
687C23—61no—
688C23—181no—
689C23—181no—
690Q8—92no—
691Q8—181no—
692D4—32no—
693D4—61no—
694D4—184no—
695D4—181no—
696D4—181no—
697D4—181no—
698D4—181no—
699D4—721no—
700D4—721no—
701D4—721no—
702D4—721no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—184no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—241no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4D3×D1211yescharacteristic
720C2×C4D3×D1211yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—21no—
723C8—21no—
724C8—61no—
725C8—61no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—122no—
730C2×C3—121no—
731C2×C3#552411yescharacteristic
732C2×C3#562711yescharacteristic
733C2×C3#575111yescharacteristic
734C2×C3#575211yescharacteristic
735C2×C3#577011yescharacteristic
736C2×C3#577411yescharacteristic
737D3—41no—
738D3—42no—
739D3—241no—
740D3—241no—
741D3—241no—
742D3—241no—
743D3—481no—
744D3—481no—
745C22—61no—
746C22—62no—
747C22—61no—
748C22—61no—
749C22—121no—
750C22—121no—
751C22—361no—
752C22—361no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22—361no—
757C22C2×D3×D1211yescharacteristic
758C4—21no—
759C4—21no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—182no—
767C4—361no—
768C4#6431211yescharacteristic
769C4D3×#23911yescharacteristic
770C3—21no—
771C3#7938411yescharacteristic, complemented
772C3#8114411yescharacteristic, complemented
773C2—121no—
774C2—122no—
775C2—721no—
776C2—721no—
777C2#1059462711yescharacteristic
778C2#1059467911yescharacteristic
779C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593989C2semidirect
2. #10593887C2semidirect
3. #10592547C2semidirect
4. C3×#4847C2semidirect
5. C3×#4840C2semidirect
6. #10590968C2semidirect
7. #10590968C2semidirect
8. #10590773C2semidirect
9. #10590758C2semidirect
10. #10590746C2semidirect
11. #10590745C2semidirect
12. #10590679C2semidirect
13. #10590677C2semidirect
14. #10590349C2semidirect
15. #10590292C2semidirect
76. #4847D3semidirect
78. #4840D3semidirect
685. C32#3119semidirect
771. C3#79384semidirect
772. C3#81144semidirect

Maximal subgroups

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

subgroupindex
#105939892
#105938872
#105925472
C3×#48472
C3×#48402
#105909682
#105907732
#105907582
#105907462
#105907452
#105906792
#105906772
#105903492
#105902922
#811443
#793843