Finite Group Databasebeta

← #11872327

Subgroups — #11872327

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593986C211yesmaximal, characteristic, complemented
2#10593890C211yesmaximal, characteristic, complemented
3#10592410C211yesmaximal, characteristic, complemented
4C3×#4710C211yesmaximal, characteristic, complemented
5C3×#4709C211yesmaximal, characteristic, complemented
6#10590967C211yesmaximal, characteristic, complemented
7#10590823C211yesmaximal, characteristic, complemented
8#10590815C211yesmaximal, characteristic, complemented
9#10590799C211yesmaximal, characteristic, complemented
10#10590774C211yesmaximal, characteristic, complemented
11#10590765C211yesmaximal, characteristic, complemented
12#10590679C211yesmaximal, characteristic, complemented
13#10590676C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15C4×#3714C211yesmaximal, characteristic, complemented
16#79812—31nomaximal
17#79384—31nomaximal
18C2×#3799C2211yescharacteristic
19C2×#3745C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#204C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63912—21no—
27#63911C2211yescharacteristic
28#63909C2211yescharacteristic
29#63908C2211yescharacteristic
30#63906—21no—
31#63894C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33#63883—21no—
34#63881—21no—
35#63880—21no—
36#63869C2211yescharacteristic
37#63853—21no—
38#63850—21no—
39Dic3×Dic6C2211yescharacteristic
40#63836—21no—
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#97C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63644C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C4×C3⋊C8C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5574—31no—
62#5562—31no—
63#5535—31no—
64#5523—31no—
65C3×#440—31no—
66C3×#433—31no—
67#5172—31no—
68#5163—31no—
69C4×#215—31no—
70C4×#213—31no—
71#4891—31no—
72#4882—31no—
73#4848—31no—
74#4847—31no—
75#4843—31no—
76#4829—31no—
77#4810—31no—
78#4799—31no—
79#4786—31no—
80#4777—31no—
81#4736—31no—
82#4735—31no—
83#4734—31no—
84#4734—31no—
85#4711—31no—
86#4711—31no—
87#4711—61no—
88#4710D311yescharacteristic, complemented
89#4709D311yescharacteristic, complemented
90C4×D24—31no—
91C4×#204—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#626—21no—
101C2×#626—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108#3799—22no—
109#3799—22no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3745—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4D411yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×#204—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3119—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×SD16—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147C3×#117—31no—
148Q8×Dic3—31no—
149C2×#215—31no—
150#940—31no—
151#938—31no—
152C2×#213—31no—
153#930—31no—
154#930—31no—
155#930—61no—
156#929—61no—
157C2×C4⋊Dic3—31no—
158C2×D24—31no—
159C2×D24—31no—
160C2×D24—31no—
161C2×D24—61no—
162C2×#204—31no—
163C2×#204C2×D311yescharacteristic
164#895—31no—
165#894—61no—
166#894—61no—
167#893—31no—
168#893—61no—
169#892—61no—
170D3×C4⋊C4—31no—
171D3×C4⋊C4—61no—
172D3×C4⋊C4—61no—
173#890—31no—
174#884—61no—
175#884—61no—
176#884—61no—
177#883—61no—
178#67⋊C4—61no—
179#67⋊C4—61no—
180#874—31no—
181C4×D12—31no—
182C4×D12—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—61no—
187C4×D12—61no—
188C4×D12—61no—
189C4×D12C2×D311yescharacteristic
190#872—61no—
191#872C2×D311yescharacteristic
192#870—31no—
193C4×Dic6—31no—
194C4×Dic6C2×D311yescharacteristic
195C3×#107—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202C3×#97—21no—
203C3×#97C2×D311yescharacteristic
204C3×#97C2×D311yescharacteristic
205C3×C4×C8—31no—
206#835—31no—
207#832—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821—61no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#818C2×D311yescharacteristic
222#817—31no—
223#817—31no—
224#817—31no—
225#817—61no—
226#816—31no—
227#816C2×D311yescharacteristic
228Dic3⋊C8C2×D311yescharacteristic
229Dic3⋊C8C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234C4×C3⋊C8C2×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)#4112yes—
248C4×C3⋊D3—81no—
249C4×C3⋊D3—81no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—81no—
261C3×Dic6—21no—
262C3×Dic6#4112yes—
263#626—24no—
264#626—81no—
265#626—81no—
266#626—81no—
267#625—81no—
268#624—24no—
269#624—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—91no—
281#460—91no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—31no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294C2×#67—61no—
295C2×#67—61no—
296C2×#67—61no—
297C2×#67—61no—
298C2×#67—61no—
299C2×#67—61no—
300C22×Dic3—61no—
301#239—62no—
302#239—62no—
303#235—62no—
304#235—62no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—61no—
310C2×D12—61no—
311C2×D12—61no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
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—121no—
327C2×C4×D3—121no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C3×SD16—62no—
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—61no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42C22×D311yescharacteristic
351C3×C42C22×D311yescharacteristic
352#217—61no—
353#215—62no—
354#213—62no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—61no—
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—121no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4D1211yescharacteristic
368(C2×D3)⋊C4D1211yescharacteristic
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4D1211yescharacteristic
387Dic3⋊C4D1211yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394D24—62no—
395D24—62no—
396D24—64no—
397D24—62no—
398#204—22no—
399#204—62no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—22no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×#41—91no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×D8—91no—
429C2×D8—91no—
430#127—91no—
431#125—91no—
432#123—181no—
433#123—181no—
434#121—91no—
435#121—91no—
436#121—181no—
437#121—181no—
438C4×Q8—31no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—31no—
447#117—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—181no—
450#107—31no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—31no—
455C4⋊C8—31no—
456#103—31no—
457#103—91no—
458#102—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—31no—
466#97D3211yescharacteristic
467C4×C8—31no—
468C23×C3—31no—
469C23×C3—61no—
470C22×D3—21no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—61no—
474C22×D3—61no—
475C22×D3—121no—
476C22×D3—121no—
477C22×D3C2×D1211yescharacteristic
478C3×Q8—32no—
479C3×Q8—61no—
480C3×D4—61no—
481C3×D4—61no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—241no—
494C2×C3×C4C2×D1211yescharacteristic
495C2×C3×C4C2×D1211yescharacteristic
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4C23×D311yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500#67—64no—
501#67—241no—
502#67—241no—
503#67—241no—
504#67—241no—
505#67—241no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—121no—
514C2×Dic3—121no—
515C2×Dic3—241no—
516C2×Dic3C2×D1211yescharacteristic
517C2×Dic3C2×D1211yescharacteristic
518C2×Dic3C2×D1211yescharacteristic
519D12—21no—
520D12—21no—
521D12—32no—
522D12—32no—
523D12—62no—
524D12—62no—
525D12—64no—
526D12—61no—
527D12—61no—
528D12—61no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—121no—
533D12—121no—
534D12—241no—
535D12—241no—
536D12—241no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—64no—
540C4×D3—64no—
541C4×D3—81no—
542C4×D3—241no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—242no—
550C4×D3—242no—
551Dic6—21no—
552Dic6#23512yes—
553C3×C8—22no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—42no—
567C3⋊D3—81no—
568C3×D3—41no—
569C3×D3—81no—
570#41—182no—
571#41—182no—
572C2×Q8—31no—
573C2×D4—31no—
574C2×D4—91no—
575C2×D4—91no—
576C2×D4—181no—
577C2×D4—181no—
578C2×D4—181no—
579C2×D4—181no—
580C2×D4—181no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588SD16—62no—
589SD16—182no—
590D8—182no—
591D8—182no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8C2×D3211yescharacteristic
595C2×C8C2×D3211yescharacteristic
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—61no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—61no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3C22×D1211yescharacteristic
627C22×C3C2×D3×D411yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—62no—
635C2×D3—62no—
636C2×D3—122no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—122no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—241no—
649C2×D3—241no—
650C2×D3—241no—
651C2×D3—241no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—62no—
663C3×C4—61no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C2×#23511yescharacteristic
667C3×C4D3×#4111yescharacteristic
668C3×C4D3×#4111yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—21no—
673Dic3—22no—
674Dic3—41no—
675Dic3—41no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682C32#311911yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—181no—
686C23—181no—
687Q8—32no—
688Q8—61no—
689D4—61no—
690D4—61no—
691D4—92no—
692D4—184no—
693D4—181no—
694D4—181no—
695D4—181no—
696D4—721no—
697D4—721no—
698D4—721no—
699D4—721no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—184no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×D1211yescharacteristic
717C2×C4D3×D1211yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—21no—
720C8—21no—
721C8—61no—
722C8—61no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—121no—
727C2×C3—241no—
728C2×C3#552411yescharacteristic
729C2×C3#554711yescharacteristic
730C2×C3#575111yescharacteristic
731C2×C3#575211yescharacteristic
732C2×C3#577411yescharacteristic
733C2×C3#577811yescharacteristic
734D3—41no—
735D3—81no—
736D3—122no—
737D3—122no—
738D3—242no—
739D3—242no—
740D3—241no—
741D3—241no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—182no—
749C22—361no—
750C22—361no—
751C22—361no—
752C22—361no—
753C22—361no—
754C22C2×D3×D1211yescharacteristic
755C4—21no—
756C4—21no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—62no—
761C4—121no—
762C4—121no—
763C4—361no—
764C4—361no—
765C4D3×#23511yescharacteristic
766C4#6430611yescharacteristic
767C3—21no—
768C3#7938411yescharacteristic, complemented
769C3#7981211yescharacteristic, complemented
770C2—121no—
771C2—241no—
772C2—362no—
773C2—721no—
774C2#1059399711yescharacteristic
775C2#1059471411yescharacteristic
776C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. #10593986C2semidirect
2. #10593890C2semidirect
3. #10592410C2semidirect
4. C3×#4710C2semidirect
5. C3×#4709C2semidirect
6. #10590967C2semidirect
7. #10590823C2semidirect
8. #10590815C2semidirect
9. #10590799C2semidirect
10. #10590774C2semidirect
11. #10590765C2semidirect
12. #10590679C2semidirect
13. #10590676C2semidirect
14. C4×#3717C2semidirect
15. C4×#3714C2semidirect
88. #4710D3semidirect
89. #4709D3semidirect
682. C32#3119semidirect
768. C3#79384semidirect
769. C3#79812semidirect

Maximal subgroups

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

subgroupindex
#105939862
#105938902
#105924102
C3×#47102
C3×#47092
#105909672
#105908232
#105908152
#105907992
#105907742
#105907652
#105906792
#105906762
C4×#37172
C4×#37142
#798123
#793843