Finite Group Databasebeta

← #7697086

Subgroups — #7697086

Order 512.

5985 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59843C213yesmaximal, complemented
2#59820C216yesmaximal, complemented
3#52257C213yesmaximal, complemented
4#45251C213yesmaximal, complemented
5#45188C216yesmaximal, complemented
6#45088C213yesmaximal, complemented
7#45013C216yesmaximal, complemented
8#39562C216yesmaximal, complemented
9#38250C216yesmaximal, complemented
10#38110C216yesmaximal, complemented
11#36457C211yesmaximal, characteristic, complemented
12#36456C212yesmaximal, complemented
13#36091C211yesmaximal, characteristic
14#36076C211yesmaximal, characteristic, complemented
15#36005C212yesmaximal, complemented
16#35898C212yesmaximal, complemented
17#34295C212yesmaximal, complemented
18#34263C212yesmaximal, complemented
19#34258C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×#551C2216yescomplemented
23C2×#550C2212yes—
24C2×#550C2211yescharacteristic
25C2×#520C2212yes—
26C2×#520C2211yescharacteristic, complemented
27C2×C4×#41C2212yes—
28#2858C2213yescomplemented
29#2857C2216yescomplemented
30#2799C2211yescharacteristic, complemented
31#2798C2216yescomplemented
32#2797C2216yescomplemented
33#2796C2216yescomplemented
34#2789C2213yescomplemented
35#2786C2216yescomplemented
36#2782C2213yescomplemented
37#2778C2216yescomplemented
38#2760C2216yescomplemented
39#2751C22112yescomplemented
40#2736C2216yescomplemented
41#2730C2216yescomplemented
42#2730C22112yescomplemented
43#2728C2213yescomplemented
44#2705C22112yescomplemented
45#2697C2216yescomplemented
46#2696C22112yescomplemented
47#2684C22112yescomplemented
48#2644C2216yescomplemented
49#2624C2216yescomplemented
50#2624C2213yescomplemented
51#2615C2213yes—
52#2609C2216yescomplemented
53#2607C2216yescomplemented
54#2563C2213yescomplemented
55#2563C2216yescomplemented
56#2557C22112yescomplemented
57#2548C2213yescomplemented
58#2538C2216yescomplemented
59#2534C22112yescomplemented
60#2513C2216yescomplemented
61#2512C2216yescomplemented
62#2512C2216yescomplemented
63#2504C2213yescomplemented
64#2501C2216yescomplemented
65#2497C2216yescomplemented
66#2496C2216yescomplemented
67#2494C2216yescomplemented
68#2491C2216yescomplemented
69#2491C2216yescomplemented
70#2487C2216yescomplemented
71#2486C2213yescomplemented
72#2480C22112yescomplemented
73#2472C22112yescomplemented
74#2471C22112yescomplemented
75#2467C22112yescomplemented
76#2457C22112yescomplemented
77#2452C2216yescomplemented
78#2452C2216yescomplemented
79#2445C2216yescomplemented
80#2445C2216yescomplemented
81#2445C2216yescomplemented
82#2439C2216yescomplemented
83#2439C2216yescomplemented
84#2437C2216yescomplemented
85#2433C2216yes—
86#2433C2213yes—
87#2422C2216yescomplemented
88#2422C2216yescomplemented
89#2420C2216yescomplemented
90#2412C22112yescomplemented
91#2411C22112yescomplemented
92#2408C2213yes—
93#2408C2216yes—
94#2401C2216yescomplemented
95#2395C2213yescomplemented
96#2395C2216yescomplemented
97#2388C2213yes—
98#2366C2216yescomplemented
99#2363C2216yescomplemented
100#2361C2216yescomplemented
101#2357C2216yescomplemented
102#2354C2216yescomplemented
103#2352C2216yescomplemented
104#2351C2212yescomplemented
105#2351C2212yescomplemented
106Q8×C4⋊C4C2212yescomplemented
107Q8×C4⋊C4C2212yescomplemented
108#2345C2216yescomplemented
109#2344C2216yescomplemented
110#2341C2211yescharacteristic
111#2341C2212yes—
112#2341C2212yes—
113#2341C2212yes—
114#2341C2212yes—
115#2341C2212yes—
116#2341C2212yescomplemented
117#2341C2211yescharacteristic, complemented
118D4×C22⋊C4C2216yes—
119D4×C22⋊C4C2216yes—
120D4×C22⋊C4C2216yes—
121D4×C22⋊C4C2216yes—
122#2328C2216yescomplemented
123#2324C2216yescomplemented
124#2319C2216yescomplemented
125#2314C2216yescomplemented
126#2311C2216yes—
127#2309C2216yes—
128C4×#124C2213yescomplemented
129C4×C22⋊Q8C2216yescomplemented
130C4×#121C2216yescomplemented
131#2298C2216yescomplemented
132#2297C2216yes—
133#2293C2216yescomplemented
134C2×#390C2216yes—
135#2290C2216yescomplemented
136#2276C2212yescomplemented
137C42×Q8C2211yescharacteristic, complemented
138C2×H(5,𝔽2)—216no—
139C2×H(5,𝔽2)—44no—
140C22×#41C2311yescharacteristic
141C22×#41C2311yescharacteristic
142C22×#41C2313yes—
143C22×#41C2312yes—
144C23×D4C2316yes—
145C23×D4C2313yes—
146Q82—44no—
147#551—424no—
148#550—216no—
149#550—44no—
150C2×C4⋊Q8C2316yes—
151C2×C4⋊Q8C2313yes—
152C2×#127C2316yes—
153C2×#127C2313yes—
154C2×#126C23112yes—
155C2×#124C2313yes—
156C2×#124C23112yes—
157C2×#123C23112yes—
158C2×#123C2316yes—
159C2×#123C23112yes—
160C2×C22⋊Q8C2316yes—
161C2×C22⋊Q8C23112yes—
162C2×#121C2316yes—
163C2×#121C2316yes—
164C2×#121C2313yes—
165C2×#121C2313yes—
166C2×#120C2316yes—
167C2×#120C23112yes—
168#520—216no—
169#520—44no—
170C4×#41—48no—
171C2×C4×Q8C2312yes—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2311yescharacteristic
177C2×C4×Q8C2313yes—
178C2×C4×D4C2316yes—
179C2×C4×D4C2316yes—
180C2×C4×D4C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2313yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C2316yes—
185C2×C4×D4C23112yes—
186C2×#117C2316yes—
187C2×#117C2316yes—
188C2×#117C2313yes—
189C2×#117C23112yes—
190C22×C4⋊C4C2316yes—
191C22×C4⋊C4C2313yes—
192C22×C22⋊C4C23112yes—
193C22×C22⋊C4C23112yes—
194C22×C42C2316yes—
195#401C2316yes—
196#400C2311yescharacteristic
197#400C2316yes—
198#400C2312yes—
199#400C2316yes—
200#400C2316yes—
201#399C23112yes—
202#399C2313yes—
203#399C2316yes—
204#398C2313yes—
205#398C2312yes—
206#397C2316yes—
207#397C2316yes—
208#397C2316yes—
209#397C23112yes—
210#397C23112yes—
211#397C2316yes—
212#397C2316yes—
213#397C2316yes—
214#397C2313yes—
215#397C2316yes—
216#397C2316yes—
217#396C23112yes—
218#396C23112yes—
219#396C2316yes—
220#396C23112yes—
221#395C2311yescharacteristic
222#394C2313yes—
223#394C23112yes—
224#394C23112yes—
225#394C23112yes—
226#394C2316yes—
227#394C2316yes—
228#394C2316yes—
229#394C2316yes—
230#394C23112yes—
231#393C2316yes—
232#393C23112yes—
233#393C23112yes—
234#393C2316yes—
235#393C2313yes—
236#392C2316yes—
237#392C23112yes—
238#392C2316yes—
239#392C2313yes—
240#391C2316yes—
241#391C23112yes—
242#391C2311yescharacteristic
243#391C2312yes—
244#391C2312yes—
245#390C2316yes—
246#390C2316yes—
247#390C2316yes—
248#390C2316yes—
249#390C23112yes—
250#390C2316yes—
251#390C2316yes—
252#390C2316yes—
253#390C2316yes—
254#390C23112yes—
255#390C2316yes—
256#390C2316yes—
257#390C2316yes—
258#390C2316yes—
259#390C2316yes—
260#390C2316yes—
261#390C2316yes—
262#390C2316yes—
263#390C2313yes—
264#390C2316yes—
265#389C2316yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2316yes—
270#389C2316yes—
271#389C2316yes—
272#389C2316yes—
273#389C2316yes—
274#388C23112yes—
275#388C23112yes—
276#388C2316yes—
277#388C23112yes—
278#388C2316yes—
279#388C2316yes—
280#388C2316yes—
281#388C23112yes—
282#388C2316yes—
283#388C2316yes—
284#388C2316yes—
285#388C23112yes—
286#388C2316yes—
287#387C2316yes—
288#387C23112yes—
289#387C2316yes—
290#387C2316yes—
291#387C23112yes—
292#387C2316yes—
293#387C2316yes—
294#387C2316yes—
295#387C2312yes—
296#387C2312yes—
297#386C23112yes—
298#386C23112yes—
299#386C23112yes—
300#386C2316yes—
301#386C23112yes—
302#386C23112yes—
303#386C2316yes—
304#386C2316yes—
305#386C2316yes—
306#386C2316yes—
307#386C2316yes—
308#386C23112yes—
309#386C23112yes—
310#385C2316yes—
311#385C23112yes—
312#385C2316yes—
313#385C2316yes—
314#385C2316yes—
315#384C2316yes—
316#384C2316yes—
317#382C2313yes—
318#382C2316yes—
319#382C2316yes—
320#381C23112yes—
321#381C2316yes—
322#380C2316yes—
323#380C2316yes—
324#380C2316yes—
325#380C23112yes—
326#380C2316yes—
327#380C2316yes—
328#380C2316yes—
329#380C2316yes—
330#380C23112yes—
331#380C2313yes—
332#380C2313yes—
333#379C23112yes—
334#379C23112yes—
335#379C2316yes—
336C4×C4⋊C4C2313yes—
337C4×C4⋊C4C2316yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C22⋊C4C2316yes—
346C4×C22⋊C4C2316yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2313yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2313yes—
353C4×C22⋊C4C23112yes—
354C4×C22⋊C4C23112yes—
355#376C2316yes—
356C43C2313yes—
357C25C2416yes—
358H(5,𝔽2)—464no—
359C2×#41—28no—
360C2×#41—28no—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—24no—
364C2×#41—24no—
365C2×#41—224no—
366C2×#41—46no—
367C2×#41#41116yes—
368C22×Q8C2411yescharacteristic
369C22×Q8C2416yes—
370C22×Q8C2411yescharacteristic
371C22×Q8C2411yescharacteristic
372C22×D4—224no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—412no—
376C22×D4—46no—
377C22×D4C2413yes—
378C22×D4C2413yes—
379C22×D4C2413yes—
380C22×D4C2416yes—
381C22×D4C2416yes—
382C22×D4C24112yes—
383C22×D4C2413yes—
384C22×D4C2416yes—
385C22×D4C2416yes—
386C23×C4C2413yes—
387C23×C4C2413yes—
388C23×C4C2416yes—
389C23×C4C24112yes—
390C23×C4C2416yes—
391C23×C4C2416yes—
392C23×C4C2416yes—
393C4⋊Q8—412no—
394C4⋊Q8—46no—
395#127—224no—
396#127—46no—
397#126—424no—
398#124—212no—
399#124—812no—
400#123—424no—
401#123—412no—
402#123—812no—
403C22⋊Q8—224no—
404C22⋊Q8—812no—
405#121—224no—
406#121—224no—
407#121—46no—
408#121—46no—
409#120—412no—
410#120—812no—
411C4×Q8—28no—
412C4×Q8—28no—
413C4×Q8—28no—
414C4×Q8—28no—
415C4×Q8—28no—
416C4×Q8—24no—
417C4×Q8—46no—
418C4×D4—224no—
419C4×D4—224no—
420C4×D4—224no—
421C4×D4—412no—
422C4×D4—412no—
423C4×D4—412no—
424C4×D4—46no—
425C4×D4—424no—
426#117—224no—
427#117—46no—
428#117—424no—
429#117—412no—
430C2×C4⋊C4—224no—
431C2×C4⋊C4—46no—
432C2×C4⋊C4C2416yes—
433C2×C4⋊C4C2416yes—
434C2×C4⋊C4C2416yes—
435C2×C4⋊C4C2416yes—
436C2×C4⋊C4C2412yes—
437C2×C4⋊C4C2416yes—
438C2×C4⋊C4C2416yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2413yes—
442C2×C4⋊C4C2416yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C2413yes—
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C24112yes—
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C2413yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C24112yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2412yes—
456C2×C22⋊C4—424no—
457C2×C22⋊C4—812no—
458C2×C22⋊C4C2416yes—
459C2×C22⋊C4C2416yes—
460C2×C22⋊C4C2416yes—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C2416yes—
464C2×C22⋊C4C2416yes—
465C2×C22⋊C4C2416yes—
466C2×C22⋊C4C2416yes—
467C2×C22⋊C4C2416yes—
468C2×C22⋊C4C24112yes—
469C2×C22⋊C4C24112yes—
470C2×C22⋊C4C24112yes—
471C2×C22⋊C4C24112yes—
472C2×C22⋊C4C24112yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2413yes—
475C2×C22⋊C4C2413yes—
476C2×C22⋊C4C2416yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C24112yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C24112yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C2416yes—
488C2×C42—412no—
489C2×C42C2413yes—
490C2×C42C2416yes—
491C2×C42C2416yes—
492C2×C42C2416yes—
493C2×C42C2413yes—
494C2×C42C2416yes—
495C2×C42C2416yes—
496C2×C42C2416yes—
497C2×C42C24112yes—
498C2×C42C2416yes—
499C2×C42C2411yescharacteristic
500C2×C42C2412yes—
501#95C2412yes—
502#95C2416yes—
503#95C2416yes—
504#95C2416yes—
505#95C2416yes—
506#95C2412yes—
507#95C2412yes—
508#95C2412yes—
509#95C2412yes—
510#95C2412yes—
511#95C2412yes—
512#95C2411yescharacteristic
513#95C2411yescharacteristic
514#95C2416yes—
515#95C2416yes—
516#95C2416yes—
517#95C2416yes—
518#95C2413yes—
519#95C2416yes—
520#95C2416yes—
521#95C2413yes—
522#95C24112yes—
523#95C24112yes—
524#95C2416yes—
525#95C2412yes—
526#95C2412yes—
527#95C2416yes—
528#95C2416yes—
529#95C2416yes—
530#95C2416yes—
531#95C2416yes—
532C24—224no—
533C24—46no—
534C24—46no—
535C24—412no—
536C24—46no—
537C24C2513yes—
538C24C2513yes—
539C24C2516yes—
540#41—264no—
541#41—448no—
542#41—416no—
543#41—416no—
544C2×Q8—24no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8—412no—
549C2×Q8—46no—
550C2×Q8C2×#4118yes—
551C2×Q8H(5,𝔽2)14yes—
552C2×Q8H(5,𝔽2)14yescomplemented
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—212no—
556C2×D4—224no—
557C2×D4—212no—
558C2×D4—212no—
559C2×D4—212no—
560C2×D4—212no—
561C2×D4—212no—
562C2×D4—26no—
563C2×D4—26no—
564C2×D4—26no—
565C2×D4—496no—
566C2×D4—46no—
567C2×D4—43no—
568C2×D4—412no—
569C2×D4—43no—
570C2×D4—46no—
571C2×D4—412no—
572C2×D4—43no—
573C2×D4—46no—
574C2×D4—412no—
575C2×D4—46no—
576C2×D4—448no—
577C2×D4C2×#41124yes—
578C22×C4—212no—
579C22×C4—212no—
580C22×C4—224no—
581C22×C4—212no—
582C22×C4—212no—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—212no—
586C22×C4—46no—
587C22×C4—46no—
588C22×C4—412no—
589C22×C4—46no—
590C22×C4—412no—
591C22×C4—46no—
592C22×C4—46no—
593C22×C4—46no—
594C22×C4—46no—
595C22×C4—46no—
596C22×C4C2×#41124yes—
597C22×C4C2511yescharacteristic
598C22×C4C2512yes—
599C22×C4C2511yescharacteristic
600C22×C4C2512yes—
601C22×C4C2516yes—
602C22×C4C2512yes—
603C22×C4C2513yes—
604C22×C4C2516yes—
605C22×C4C2512yes—
606C22×C4C2516yes—
607C22×C4C2516yes—
608C22×C4C2516yes—
609C22×C4C2512yes—
610C22×C4C2511yescharacteristic
611C22×C4C2512yes—
612C22×C4C2513yes—
613C4⋊C4—212no—
614C4⋊C4—212no—
615C4⋊C4—212no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—212no—
619C4⋊C4—212no—
620C4⋊C4—212no—
621C4⋊C4—212no—
622C4⋊C4—212no—
623C4⋊C4—26no—
624C4⋊C4—212no—
625C4⋊C4—43no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—41no—
629C4⋊C4—412no—
630C4⋊C4—41no—
631C4⋊C4—46no—
632C4⋊C4—43no—
633C4⋊C4—46no—
634C4⋊C4—46no—
635C4⋊C4—412no—
636C4⋊C4—46no—
637C22⋊C4—212no—
638C22⋊C4—212no—
639C22⋊C4—212no—
640C22⋊C4—212no—
641C22⋊C4—212no—
642C22⋊C4—212no—
643C22⋊C4—212no—
644C22⋊C4—212no—
645C22⋊C4—412no—
646C22⋊C4—412no—
647C22⋊C4—46no—
648C22⋊C4—46no—
649C22⋊C4—412no—
650C22⋊C4—412no—
651C22⋊C4—46no—
652C22⋊C4—46no—
653C22⋊C4—46no—
654C22⋊C4—412no—
655C22⋊C4—43no—
656C22⋊C4—43no—
657C22⋊C4—46no—
658C22⋊C4—46no—
659C22⋊C4—46no—
660C22⋊C4—412no—
661C22⋊C4—46no—
662C22⋊C4—46no—
663C22⋊C4—46no—
664C22⋊C4—412no—
665C22⋊C4—46no—
666C22⋊C4—46no—
667C42—212no—
668C42—212no—
669C42—212no—
670C42—212no—
671C42—212no—
672C42—26no—
673C42—26no—
674C42—42no—
675C42—46no—
676C42—41no—
677C42—412no—
678C42—46no—
679C23—26no—
680C23—26no—
681C23—26no—
682C23—26no—
683C23—26no—
684C23—26no—
685C23—26no—
686C23—26no—
687C23—23no—
688C23—23no—
689C23—23no—
690C23—23no—
691C23—26no—
692C23—26no—
693C23—23no—
694C23—23no—
695C23—424no—
696C23—824no—
697C23—824no—
698C23—166no—
699C23—166no—
700C23C22×#41112yes—
701C23C2611yescharacteristic
702Q8—44no—
703Q8—44no—
704Q8—166no—
705Q8#551116yescomplemented
706D4—248no—
707D4—424no—
708D4—412no—
709D4—412no—
710D4—412no—
711D4—86no—
712D4—824no—
713D4—812no—
714D4—166no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—248no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—26no—
726C2×C4—26no—
727C2×C4—26no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—26no—
732C2×C4—26no—
733C2×C4—26no—
734C2×C4—23no—
735C2×C4—26no—
736C2×C4—26no—
737C2×C4—26no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—26no—
742C2×C4—26no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—26no—
749C2×C4—26no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—26no—
754C2×C4—22no—
755C2×C4—412no—
756C2×C4—412no—
757C2×C4—812no—
758C2×C4—824no—
759C2×C4—812no—
760C2×C4—166no—
761C2×C4C22×#4114yes—
762C2×C4C22×#41112yes—
763C2×C4C2×H(5,𝔽2)12yes—
764C2×C4C2×H(5,𝔽2)14yes—
765C2×C4C2×H(5,𝔽2)16yes—
766C22—212no—
767C22—212no—
768C22—212no—
769C22—46no—
770C22—46no—
771C22—46no—
772C22—46no—
773C22—46no—
774C22—46no—
775C22—43no—
776C22—43no—
777C22—46no—
778C22—46no—
779C22—43no—
780C22—43no—
781C22—43no—
782C22—43no—
783C22—1624no—
784C22C23×#4112yes—
785C22C22×H(5,𝔽2)11yescharacteristic
786C22C22×H(5,𝔽2)11yescharacteristic
787C22H(7,𝔽2)12yes—
788C222−1+611yescharacteristic
789C4—24no—
790C4—22no—
791C4—24no—
792C4—46no—
793C4—46no—
794C4—46no—
795C4—42no—
796C4—46no—
797C4—43no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—46no—
802C4—41no—
803C4—41no—
804C4C2×#551112yes—
805C2—412no—
806C2—83no—
807C2—83no—
808C2C22×#55111yescharacteristic
809C2#6285712yes—
810C2#6289511yescharacteristic
811C2#6298612yes—
812C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36091C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59843C2semidirect
2. #59820C2semidirect
3. #52257C2semidirect
4. #45251C2semidirect
5. #45188C2semidirect
6. #45088C2semidirect
7. #45013C2semidirect
8. #39562C2semidirect
9. #38250C2semidirect
10. #38110C2semidirect
11. #36457C2semidirect
12. #36456C2semidirect
14. #36076C2semidirect
15. #36005C2semidirect
16. #35898C2semidirect
17. #34295C2semidirect
18. #34263C2semidirect
19. #34258C2semidirect
21. C2×Q82C22semidirect
22. C2×#551C22semidirect
26. C2×#520C22semidirect
28. #2858C22semidirect
29. #2857C22semidirect
30. #2799C22semidirect
31. #2798C22semidirect
32. #2797C22semidirect
33. #2796C22semidirect
34. #2789C22semidirect
35. #2786C22semidirect
36. #2782C22semidirect
37. #2778C22semidirect
38. #2760C22semidirect
39. #2751C22semidirect
40. #2736C22semidirect
41. #2730C22semidirect
42. #2730C22semidirect
43. #2728C22semidirect
44. #2705C22semidirect
45. #2697C22semidirect
46. #2696C22semidirect
47. #2684C22semidirect
48. #2644C22semidirect
49. #2624C22semidirect
50. #2624C22semidirect
52. #2609C22semidirect
53. #2607C22semidirect
54. #2563C22semidirect
55. #2563C22semidirect
56. #2557C22semidirect
57. #2548C22semidirect
58. #2538C22semidirect
59. #2534C22semidirect
60. #2513C22semidirect
61. #2512C22semidirect
62. #2512C22semidirect
63. #2504C22semidirect
64. #2501C22semidirect
65. #2497C22semidirect
66. #2496C22semidirect
67. #2494C22semidirect
68. #2491C22semidirect
69. #2491C22semidirect
70. #2487C22semidirect
71. #2486C22semidirect
72. #2480C22semidirect
73. #2472C22semidirect
74. #2471C22semidirect
75. #2467C22semidirect
76. #2457C22semidirect
77. #2452C22semidirect
78. #2452C22semidirect
79. #2445C22semidirect
80. #2445C22semidirect
81. #2445C22semidirect
82. #2439C22semidirect
83. #2439C22semidirect
84. #2437C22semidirect
87. #2422C22semidirect
88. #2422C22semidirect
89. #2420C22semidirect
90. #2412C22semidirect
91. #2411C22semidirect
94. #2401C22semidirect
95. #2395C22semidirect
96. #2395C22semidirect
98. #2366C22semidirect
99. #2363C22semidirect
100. #2361C22semidirect
101. #2357C22semidirect
102. #2354C22semidirect
103. #2352C22semidirect
104. #2351C22semidirect
105. #2351C22semidirect
106. Q8×C4⋊C4C22semidirect
107. Q8×C4⋊C4C22semidirect
108. #2345C22semidirect
109. #2344C22semidirect
116. #2341C22semidirect
117. #2341C22semidirect
122. #2328C22semidirect
123. #2324C22semidirect
124. #2319C22semidirect
125. #2314C22semidirect
128. C4×#124C22semidirect
129. C4×C22⋊Q8C22semidirect
130. C4×#121C22semidirect
131. #2298C22semidirect
133. #2293C22semidirect
135. #2290C22semidirect
136. #2276C22semidirect
137. C42×Q8C22semidirect
552. C2×Q8H(5,𝔽2)semidirect
705. Q8#551semidirect

Maximal subgroups

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

subgroupindex
#598432
#598202
#522572
#452512
#451882
#450882
#450132
#395622
#382502
#381102
#364572
#364562
#360912
#360762
#360052
#358982
#342952
#342632
#342582