Finite Group Databasebeta

← #11888601

Subgroups — #11888601

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594843C211yesmaximal, characteristic, complemented
2#10594834C211yesmaximal, characteristic, complemented
3#10592433C211yesmaximal, characteristic, complemented
4C3×#4728C211yesmaximal, characteristic, complemented
5C3×#4721C211yesmaximal, characteristic, complemented
6#10591178C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic, complemented
8#10590967C211yesmaximal, characteristic, complemented
9#10590898C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590769C211yesmaximal, characteristic, complemented
12#10590768C211yesmaximal, characteristic, complemented
13#10590760C211yesmaximal, characteristic, complemented
14#10590709C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#81432—31nomaximal
17#79500—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64139C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63978—21no—
29#63975—21no—
30#63958—21no—
31#63952—21no—
32#63909C2211yescharacteristic
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35#63883—21no—
36#63869C2211yescharacteristic
37#63866C2211yescharacteristic
38#63857C2211yescharacteristic
39#63854—21no—
40#63853—21no—
41#63848—21no—
42#63841C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54#63575C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5631—31no—
62#5565—31no—
63#5551—31no—
64#5514—31no—
65C3×#483—31no—
66C3×#435—31no—
67#5134—31no—
68#5133—31no—
69#5114—31no—
70#5113—31no—
71#5049—31no—
72#4966—31no—
73#4871—31no—
74#4869—31no—
75#4868—31no—
76#4864—31no—
77#4847—31no—
78#4841—31no—
79#4818—31no—
80#4810—31no—
81#4804—31no—
82#4797—31no—
83#4734—31no—
84#4734—31no—
85#4734—31no—
86#4734—61no—
87#4728D311yescharacteristic, complemented
88#4723—31no—
89#4721D311yescharacteristic, complemented
90#4711—31no—
91#4703—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×#638—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×#634C2311yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—22no—
111#3799—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3745—22no—
117#3744—41no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C3×#208—41no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3717—41no—
144#3307—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—61no—
150C2×C3×M16—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#944—31no—
156C2×#215—31no—
157#939—61no—
158#938—61no—
159#930—31no—
160#930—31no—
161#930—31no—
162#930—61no—
163#930—61no—
164C4×#67—61no—
165C4×#67C2×D311yescharacteristic
166#926—31no—
167C2×C4⋊Dic3C2×D311yescharacteristic
168#924—31no—
169#924C2×D311yescharacteristic
170C2×#208C2×D311yescharacteristic
171C2×D24—31no—
172C2×D24—31no—
173C2×D24—61no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—61no—
178C2×D3×C8C2×D311yescharacteristic
179#898—61no—
180#898—61no—
181#897—31no—
182#895—31no—
183#894—61no—
184#894—61no—
185#893—31no—
186#893—31no—
187#892—31no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4—61no—
190#890—31no—
191#884—61no—
192#883—61no—
193#883—61no—
194#883—61no—
195#883—61no—
196#67⋊C4—61no—
197C4×D12—31no—
198C4×D12—31no—
199#870—31no—
200#869—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8C2×D311yescharacteristic
209C3×C22⋊C8C2×D311yescharacteristic
210C3×#97—31no—
211#835—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#818—31no—
220#817C2×D311yescharacteristic
221#817C2×D311yescharacteristic
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228#816C2×D311yescharacteristic
229#816C2×D311yescharacteristic
230#815C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232#810—31no—
233#810—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247#638—42no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—42no—
255#634—21no—
256#634—21no—
257C3×#67—41no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—42no—
271#626—81no—
272#624—42no—
273#624—42no—
274#624—81no—
275C32×C8—21no—
276C32×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—31no—
292#417—91no—
293#416—91no—
294C2×C3×Q8—31no—
295C2×C3×D4—31no—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C2×#67—121no—
309C2×#67D1211yescharacteristic
310C22×Dic3—21no—
311#239—62no—
312#239—121no—
313#235—62no—
314#235—62no—
315#235—62no—
316#235—122no—
317#235—121no—
318#235—121no—
319#235—121no—
320#235—122no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C2×Dic6C22×D311yescharacteristic
343C3×M16—121no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363#217—21no—
364#217—61no—
365#217—61no—
366#217D1211yescharacteristic
367#215—121no—
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—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—121no—
379(C2×D3)⋊C4D1211yescharacteristic
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4D1211yescharacteristic
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402#208—41no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405D24—62no—
406D24—62no—
407D24—122no—
408#204—121no—
409#204—121no—
410#204—122no—
411#204—121no—
412D3×C8—41no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C2×#41—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×D8—91no—
443C2×M16—31no—
444C22×C8—31no—
445C4⋊Q8—91no—
446#126—181no—
447#125—91no—
448#123—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453#121—91no—
454#121—91no—
455#121—181no—
456#121—181no—
457C4×D4—31no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461#117—91no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—181no—
464#107—91no—
465#106—31no—
466#106—31no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8D3211yescharacteristic
480#97—31no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3C2×D1211yescharacteristic
484C23×C3D3×D411yescharacteristic
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3—121no—
491C22×D3C2×D1211yescharacteristic
492C3×Q8—61no—
493C3×Q8—61no—
494C3×D4—121no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
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—241no—
513C2×C3×C4C2×D1211yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—41no—
518#67—122no—
519#67—122no—
520#67—122no—
521#67—122no—
522#67—122no—
523#67—124no—
524#67—242no—
525#67—241no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—81no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3C2×D1211yescharacteristic
538C2×Dic3C2×D1211yescharacteristic
539C2×Dic3C2×D1211yescharacteristic
540D12—32no—
541D12—32no—
542D12—62no—
543D12—61no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—61no—
548D12—61no—
549D12—121no—
550D12—121no—
551D12—121no—
552D12—122no—
553D12—241no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—124no—
563C4×D3—241no—
564C4×D3—241no—
565Dic6—21no—
566Dic6—21no—
567Dic6—62no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—121no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—41no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C2×C32—41no—
584C2×C32#54611yescharacteristic
585C2×C32#57511yescharacteristic
586C2×C32#57711yescharacteristic
587C3⋊D3—42no—
588C3⋊D3—81no—
589C3×D3—41no—
590#41—182no—
591#41—182no—
592#41—361no—
593#41—361no—
594C2×Q8—31no—
595C2×Q8—91no—
596C2×D4—31no—
597C2×D4—91no—
598C2×D4—91no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—181no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610SD16—361no—
611SD16—361no—
612D8—182no—
613M16—121no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—121no—
617C2×C8C2×D3211yescharacteristic
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—181no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3C22×D1211yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—241no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4#100411yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4#100911yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707C32#330711yescharacteristic, complemented, Sylow
708C23—31no—
709C23—181no—
710C23—181no—
711C23D3×D1211yescharacteristic
712Q8—61no—
713Q8—61no—
714Q8—181no—
715Q8—181no—
716D4—92no—
717D4—121no—
718D4—181no—
719D4—181no—
720D4—181no—
721D4—362no—
722D4—362no—
723D4—362no—
724D4—721no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—241no—
739C2×C4—362no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4—721no—
743C2×C4D3×D1211yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—21no—
746C8—21no—
747C8—61no—
748C8—61no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—81no—
755C2×C3—121no—
756C2×C3#555411yescharacteristic
757C2×C3#565411yescharacteristic
758C2×C3#574811yescharacteristic
759C2×C3#575111yescharacteristic
760C2×C3#576211yescharacteristic
761C2×C3#577711yescharacteristic
762D3—41no—
763D3—122no—
764D3—122no—
765D3—242no—
766D3—241no—
767D3—241no—
768D3—481no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—182no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22C2×D3×D1211yescharacteristic
782C4—21no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—361no—
791C4—361no—
792C4#6431211yescharacteristic
793C4#6431411yescharacteristic
794C3—21no—
795C3#7950011yescharacteristic, complemented
796C3#8143211yescharacteristic, complemented
797C2—41no—
798C2—121no—
799C2—362no—
800C2—721no—
801C2#1059429311yescharacteristic
802C2#1059467711yescharacteristic
803C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594843C2semidirect
2. #10594834C2semidirect
3. #10592433C2semidirect
4. C3×#4728C2semidirect
5. C3×#4721C2semidirect
6. #10591178C2semidirect
7. #10591106C2semidirect
8. #10590967C2semidirect
9. #10590898C2semidirect
10. #10590830C2semidirect
11. #10590769C2semidirect
12. #10590768C2semidirect
13. #10590760C2semidirect
14. #10590709C2semidirect
15. #10590690C2semidirect
87. #4728D3semidirect
89. #4721D3semidirect
707. C32#3307semidirect
795. C3#79500semidirect
796. C3#81432semidirect

Maximal subgroups

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

subgroupindex
#105948432
#105948342
#105924332
C3×#47282
C3×#47212
#105911782
#105911062
#105909672
#105908982
#105908302
#105907692
#105907682
#105907602
#105907092
#105906902
#814323
#795003