Finite Group Databasebeta

← #11888618

Subgroups — #11888618

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595252C211yesmaximal, characteristic, complemented
2#10595245C211yesmaximal, characteristic, complemented
3#10592851C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic, complemented
5C3×#5158C211yesmaximal, characteristic, complemented
6#10591502C211yesmaximal, characteristic, complemented
7#10591499C211yesmaximal, characteristic, complemented
8#10591497C211yesmaximal, characteristic, complemented
9#10591479C211yesmaximal, characteristic, complemented
10#10591420C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12#10590904C211yesmaximal, characteristic, complemented
13#10590725C211yesmaximal, characteristic, complemented
14#10590711C211yesmaximal, characteristic, complemented
15#10590675C211yesmaximal, characteristic, complemented
16#80108—31nomaximal
17#80107—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27#63980—21no—
28#67⋊Dic3—21no—
29#63970—21no—
30C2×#3724—21no—
31#63962—21no—
32#63961—21no—
33#63961—21no—
34#63956—21no—
35C4×#625C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63873C2211yescharacteristic
38#63872C2211yescharacteristic
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63644C2211yescharacteristic
47#63642C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#5824—31no—
62#5824—31no—
63#5618—31no—
64#5614—31no—
65C3×#449—31no—
66C3×#449—31no—
67#5233—31no—
68#5232—31no—
69#5174—31no—
70#5171—31no—
71#5162—31no—
72#5162—31no—
73#5158D311yescharacteristic, complemented
74#5158D311yescharacteristic, complemented
75#5152—31no—
76#5152—31no—
77#5152—61no—
78#5042—31no—
79#5041—31no—
80#4815—31no—
81#4805—31no—
82#4797—31no—
83#4797—31no—
84#4772—31no—
85#4771—31no—
86#4766—31no—
87#4763—31no—
88#4730—31no—
89#4728—31no—
90#4723—31no—
91#4721—31no—
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—22no—
104C3×#237—41no—
105C3×#237—41no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#625D411yescharacteristic
111C2×D3×Dic3—21no—
112C32×D8—22no—
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#214—41no—
123C3×#214—41no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129#3724—21no—
130#3724—21no—
131#3724—21no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#237C2×D311yescharacteristic
148C2×#237C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—21no—
152C2×C3×D8C2×D311yescharacteristic
153C2×C3×D8C2×D311yescharacteristic
154C3×#121—31no—
155C3×#121—31no—
156#946—31no—
157#946—31no—
158#944—31no—
159#944—31no—
160#939—61no—
161#939—61no—
162#939—61no—
163#938—61no—
164#938C2×D311yescharacteristic
165#938C2×D311yescharacteristic
166#935—61no—
167#935—61no—
168#935—61no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—31no—
172D4×Dic3—31no—
173D4×Dic3—61no—
174D4×Dic3—61no—
175D4×Dic3—61no—
176C2×#214C2×D311yescharacteristic
177C2×#214C2×D311yescharacteristic
178#929—61no—
179#929—61no—
180C4×#67—31no—
181C4×#67—31no—
182#926—31no—
183C2×C4⋊Dic3—31no—
184#924—31no—
185#924—31no—
186C2×Dic3⋊C4—61no—
187C2×Dic3⋊C4—61no—
188C2×#208—31no—
189C22×C3⋊C8—31no—
190C2×ΓL(1,𝔽25)—31no—
191C2×D3×C8—31no—
192#892—31no—
193D3×C4⋊C4—31no—
194#890—31no—
195#890—31no—
196#886—61no—
197#67⋊C4—61no—
198#879—61no—
199#879—61no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832—61no—
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#817—31no—
222#817—31no—
223#817—31no—
224#817—61no—
225#816—31no—
226#816—31no—
227#816C2×D311yescharacteristic
228#816C2×D311yescharacteristic
229#815—31no—
230#815—31no—
231#815—61no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234#810—31no—
235#810—31no—
236#808—31no—
237#807—31no—
238C23×C32—21no—
239C23×C32—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4#4112yes—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—42no—
250C2×C3⋊Dic3—81no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C3×#67—42no—
254C3×#67—42no—
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#625—41no—
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—91no—
284#478—91no—
285#468—91no—
286#465—91no—
287#461—91no—
288#449—31no—
289#449—31no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C3×#41—62no—
295C3×#41—62no—
296C3×#41—121no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—31no—
319C2×#67—31no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—121no—
328C22×Dic3—121no—
329#237—22no—
330#237—22no—
331#237—41no—
332#237—41no—
333C2×C4×D3—61no—
334C2×C4×D3C22×D311yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C3×SD16—121no—
339C3×SD16—121no—
340C3×D8—24no—
341C3×D8—22no—
342C3×D8—22no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352#217—21no—
353#217—21no—
354#217—31no—
355#217—31no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364#217—121no—
365#214—41no—
366#214—41no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401#208—121no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408ΓL(1,𝔽25)—121no—
409D3×C8—121no—
410C22×C32—22no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C2×#41—31no—
437C2×SD16—31no—
438C2×SD16—31no—
439C2×D8D3211yescharacteristic
440C2×M16—91no—
441C22×C8—91no—
442C4⋊Q8—91no—
443#126—181no—
444#125—91no—
445#123—181no—
446#123—181no—
447#123—181no—
448C22⋊Q8—91no—
449C22⋊Q8—91no—
450#121—31no—
451#121—31no—
452#121—181no—
453#121—181no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—181no—
458#117—91no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—91no—
465#103—31no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8—31no—
477#97—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—41no—
486C22×D3D3×D411yescharacteristic
487C22×D3D3×D411yescharacteristic
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—22no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—122no—
503C3×D4—122no—
504C3×D4—122no—
505C3×D4—241no—
506C3×D4#23712yes—
507C3×D4#23712yes—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4—122no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—42no—
525#67—42no—
526#67—81no—
527#67—121no—
528#67—121no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—42no—
538C2×Dic3—42no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—122no—
548C2×Dic3—122no—
549C2×Dic3—242no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3—242no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—241no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32—42no—
576C2×C32—81no—
577C2×C32#54611yescharacteristic
578C2×C32#57511yescharacteristic
579C2×C32#57711yescharacteristic
580C3×D3—41no—
581C3×D3—41no—
582#41—62no—
583#41—62no—
584#41—121no—
585#41—121no—
586C2×Q8—31no—
587C2×Q8—31no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4C2×D3211yescharacteristic
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602SD16—121no—
603SD16—121no—
604D8—22no—
605M16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—91no—
626C22⋊C4—91no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—91no—
633C42—181no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4C2×#23711yescharacteristic
676C3×C4C2×#23711yescharacteristic
677C3×C4#100411yescharacteristic
678C3×C4#100411yescharacteristic
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#330711yescharacteristic, complemented, Sylow
698C23—21no—
699C23—21no—
700C23—31no—
701C23—31no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—122no—
710D4—122no—
711D4—122no—
712D4—241no—
713D4—361no—
714D4#380512yes—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—362no—
732C2×C4—721no—
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—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3—82no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—121no—
749C2×C3—121no—
750C2×C3#559111yescharacteristic
751C2×C3#559111yescharacteristic
752C2×C3#576811yescharacteristic
753C2×C3#577011yescharacteristic
754C2×C3#577311yescharacteristic
755C2×C3#577511yescharacteristic
756D3—41no—
757D3—41no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—61no—
770C22D32×D411yescharacteristic
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—181no—
779C4—361no—
780C4—361no—
781C4#6431311yescharacteristic
782C4C2×#380511yescharacteristic
783C3—21no—
784C3#8010711yescharacteristic, complemented
785C3#8010811yescharacteristic, complemented
786C2—42no—
787C2—81no—
788C2—121no—
789C2—121no—
790C2#1059472911yescharacteristic
791C2#1059473611yescharacteristic
792C2#1059522511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595252C2semidirect
2. #10595245C2semidirect
3. #10592851C2semidirect
4. C3×#5158C2semidirect
5. C3×#5158C2semidirect
6. #10591502C2semidirect
7. #10591499C2semidirect
8. #10591497C2semidirect
9. #10591479C2semidirect
10. #10591420C2semidirect
11. #10591414C2semidirect
12. #10590904C2semidirect
13. #10590725C2semidirect
14. #10590711C2semidirect
15. #10590675C2semidirect
73. #5158D3semidirect
74. #5158D3semidirect
697. C32#3307semidirect
784. C3#80107semidirect
785. C3#80108semidirect

Maximal subgroups

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

subgroupindex
#105952522
#105952452
#105928512
C3×#51582
#105915022
#105914992
#105914972
#105914792
#105914202
#105914142
#105909042
#105907252
#105907112
#105906752
#801083
#801073