Finite Group Databasebeta

← #7689014

Subgroups — #7689014

Order 512.

6279 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59945C213yesmaximal, complemented
2#59476C216yesmaximal, complemented
3#59273C216yesmaximal, complemented
4#45088C213yesmaximal, complemented
5#44959C216yesmaximal, complemented
6#44914C213yesmaximal, complemented
7#38206C216yesmaximal, complemented
8#37969C216yesmaximal, complemented
9#36458C212yesmaximal, complemented
10#36457C211yesmaximal, characteristic, complemented
11#36433C212yesmaximal, complemented
12#36264C216yesmaximal, complemented
13#36091C211yesmaximal, characteristic
14#36005C211yesmaximal, characteristic, complemented
15#35748C212yesmaximal, complemented
16#34871C213yesmaximal, complemented
17#34313C212yesmaximal, complemented
18#34258C212yesmaximal, complemented
19#34129C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×#551C22112yescomplemented
23C2×#550C2212yes—
24C2×#550C2211yescharacteristic
25C2×#520C2212yes—
26C2×#520C2211yescharacteristic, complemented
27C2×C4×#41C2212yes—
28#2860C2216yescomplemented
29#2858C2213yescomplemented
30#2854C2216yescomplemented
31#2782C2216yescomplemented
32#2763C2216yescomplemented
33#2753C22112yescomplemented
34#2736C2216yescomplemented
35#2723C22112yescomplemented
36#2706C22112yescomplemented
37#2696C22112yescomplemented
38#2685C22112yescomplemented
39#2684C2216yescomplemented
40#2628C2216yescomplemented
41#2624C2213yescomplemented
42#2615C2213yes—
43#2612C2213yescomplemented
44#2610C2216yescomplemented
45#2610C22112yescomplemented
46#2609C2213yescomplemented
47#2603C22112yescomplemented
48#2598C22112yescomplemented
49#2586C2211yescharacteristic, complemented
50#2580C2216yescomplemented
51#2572C2213yescomplemented
52#2563C2213yescomplemented
53#2554C2216yescomplemented
54#2548C2213yescomplemented
55#2542C2216yescomplemented
56#2532C2216yescomplemented
57#2526C2216yescomplemented
58#2513C2216yescomplemented
59#2512C2216yescomplemented
60#2512C2216yescomplemented
61#2501C2213yescomplemented
62#2500C2216yescomplemented
63#2497C2216yescomplemented
64#2496C2216yescomplemented
65#2495C2216yescomplemented
66#2491C2216yescomplemented
67#2491C2216yescomplemented
68#2487C2213yescomplemented
69#2485C2216yescomplemented
70#2482C22112yescomplemented
71#2479C2216yescomplemented
72#2472C22112yescomplemented
73#2471C2216yescomplemented
74#2463C2216yescomplemented
75#2461C22112yescomplemented
76#2452C2216yescomplemented
77#2452C2216yescomplemented
78#2445C2216yescomplemented
79#2445C2216yescomplemented
80#2445C2216yescomplemented
81#2440C2216yescomplemented
82#2440C2216yescomplemented
83#2437C2216yescomplemented
84#2433C2213yes—
85#2433C2216yes—
86#2422C2216yescomplemented
87#2422C2216yescomplemented
88#2420C2216yescomplemented
89#2418C22112yescomplemented
90#2411C22112yescomplemented
91#2408C2213yes—
92#2408C2216yes—
93#2396C2216yescomplemented
94#2395C2213yescomplemented
95#2388C2213yes—
96#2366C2216yescomplemented
97#2361C2216yescomplemented
98#2361C2216yescomplemented
99#2358C2216yescomplemented
100#2354C2216yescomplemented
101#2354C2216yescomplemented
102#2351C2212yescomplemented
103Q8×C4⋊C4C2212yescomplemented
104Q8×C4⋊C4C2212yescomplemented
105Q8×C4⋊C4C2212yescomplemented
106D4×C4⋊C4C2216yescomplemented
107#2346C2216yescomplemented
108#2346C2216yescomplemented
109#2341C2212yes—
110#2341C2212yes—
111#2341C2212yes—
112#2341C2212yes—
113#2341C2211yescharacteristic
114#2341C2212yes—
115#2341C2212yescomplemented
116#2341C2211yescharacteristic, complemented
117D4×C22⋊C4C2216yes—
118D4×C22⋊C4C2216yes—
119D4×C22⋊C4C2216yes—
120D4×C22⋊C4C2216yes—
121#2324C2216yescomplemented
122#2324C2216yescomplemented
123#2311C2216yes—
124#2309C2216yes—
125C4×#127C2216yescomplemented
126C4×#126C2216yescomplemented
127C4×#124C2213yescomplemented
128C4×#123C2216yescomplemented
129#2297C2216yes—
130#2293C2216yescomplemented
131#2293C2216yescomplemented
132#2293C2216yescomplemented
133C2×#390C2216yes—
134#2285C2216yescomplemented
135C42×Q8C2212yescomplemented
136C42×Q8C2211yescharacteristic, complemented
137C4×#117C2216yescomplemented
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—448no—
148#550—216no—
149#550—44no—
150C2×C4⋊Q8C2313yes—
151C2×C4⋊Q8C2316yes—
152C2×#127C2316yes—
153C2×#127C2313yes—
154C2×#126C2316yes—
155C2×#126C23112yes—
156C2×#124C23112yes—
157C2×#124C2313yes—
158C2×#123C2316yes—
159C2×#123C23112yes—
160C2×#123C23112yes—
161C2×C22⋊Q8C23112yes—
162C2×C22⋊Q8C23112yes—
163C2×#121C2316yes—
164C2×#121C2316yes—
165C2×#121C2313yes—
166C2×#121C2313yes—
167C2×#120C2316yes—
168C2×#120C23112yes—
169#520—48no—
170#520—44no—
171C4×#41—216no—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×Q8C2313yes—
179C2×C4×D4C2316yes—
180C2×C4×D4C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2316yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C23112yes—
185C2×C4×D4C23112yes—
186C2×C4×D4C2313yes—
187C2×C4×D4C2316yes—
188C2×#117C2316yes—
189C2×#117C2316yes—
190C2×#117C2316yes—
191C2×#117C2313yes—
192C2×#117C23112yes—
193C2×#117C2316yes—
194C22×C4⋊C4C2316yes—
195C22×C4⋊C4C2313yes—
196C22×C22⋊C4C23112yes—
197C22×C22⋊C4C23112yes—
198C22×C42C2316yes—
199#400C2313yes—
200#400C23112yes—
201#400C2316yes—
202#399C23112yes—
203#399C2316yes—
204#399C2313yes—
205#399C2316yes—
206#398C2311yescharacteristic
207#398C2316yes—
208#398C2316yes—
209#397C23112yes—
210#397C2313yes—
211#397C2316yes—
212#397C23112yes—
213#397C23112yes—
214#396C2316yes—
215#396C2316yes—
216#396C23112yes—
217#395C2312yes—
218#395C2311yescharacteristic
219#395C23112yes—
220#394C2313yes—
221#394C23112yes—
222#394C23112yes—
223#394C23112yes—
224#394C2316yes—
225#394C2316yes—
226#394C23112yes—
227#394C23112yes—
228#393C2316yes—
229#393C2316yes—
230#393C2316yes—
231#393C23112yes—
232#393C2313yes—
233#392C2316yes—
234#392C2316yes—
235#392C23112yes—
236#392C2313yes—
237#391C2316yes—
238#391C2311yescharacteristic
239#391C2312yes—
240#390C2316yes—
241#390C23112yes—
242#390C2316yes—
243#390C2316yes—
244#390C2316yes—
245#390C2316yes—
246#390C23112yes—
247#390C2316yes—
248#390C2316yes—
249#390C2316yes—
250#390C2316yes—
251#390C2316yes—
252#390C2316yes—
253#390C2316yes—
254#390C2316yes—
255#390C2316yes—
256#390C2316yes—
257#390C2316yes—
258#390C2316yes—
259#390C2313yes—
260#390C2316yes—
261#390C2316yes—
262#389C2316yes—
263#389C2316yes—
264#389C2316yes—
265#389C2312yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2316yes—
270#389C2316yes—
271#389C2316yes—
272#388C2316yes—
273#388C2316yes—
274#388C2316yes—
275#388C2316yes—
276#388C2316yes—
277#388C2316yes—
278#388C2316yes—
279#388C23112yes—
280#388C2316yes—
281#388C23112yes—
282#388C23112yes—
283#388C23112yes—
284#388C23112yes—
285#388C23112yes—
286#388C23112yes—
287#388C2316yes—
288#388C2316yes—
289#388C2316yes—
290#387C2312yes—
291#387C2316yes—
292#387C2316yes—
293#387C2312yes—
294#387C2316yes—
295#386C23112yes—
296#386C23112yes—
297#386C2316yes—
298#386C23112yes—
299#386C23112yes—
300#386C2316yes—
301#386C2316yes—
302#386C2316yes—
303#386C23112yes—
304#386C2316yes—
305#386C2316yes—
306#385C23112yes—
307#385C23112yes—
308#385C23112yes—
309#385C23112yes—
310#385C2316yes—
311#385C2316yes—
312#384C2316yes—
313#384C2316yes—
314#384C2316yes—
315#383C2316yes—
316#382C2313yes—
317#382C2316yes—
318#382C23112yes—
319#381C2316yes—
320#380C2316yes—
321#380C2316yes—
322#380C2316yes—
323#380C2316yes—
324#380C2316yes—
325#380C2316yes—
326#380C2313yes—
327#380C2313yes—
328#380C23112yes—
329#379C23112yes—
330#379C23112yes—
331#379C2316yes—
332C4×C4⋊C4C2316yes—
333C4×C4⋊C4C2316yes—
334C4×C4⋊C4C2316yes—
335C4×C4⋊C4C2313yes—
336C4×C4⋊C4C2316yes—
337C4×C4⋊C4C2312yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2316yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C22⋊C4C2313yes—
344C4×C22⋊C4C2316yes—
345C4×C22⋊C4C2316yes—
346C4×C22⋊C4C2316yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2313yes—
352C4×C22⋊C4C2316yes—
353#376C2316yes—
354#376C2316yes—
355C43C2316yes—
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×Q8C2411yescharacteristic
370C22×Q8C2416yes—
371C22×Q8C2411yescharacteristic
372C22×D4—224no—
373C22×D4—224no—
374C22×D4—224no—
375C22×D4—412no—
376C22×D4—46no—
377C22×D4C2413yes—
378C22×D4C2413yes—
379C22×D4C2416yes—
380C22×D4C2413yes—
381C22×D4C2416yes—
382C22×D4C2416yes—
383C22×D4C24112yes—
384C22×D4C2413yes—
385C22×D4C2416yes—
386C23×C4C2413yes—
387C23×C4C2413yes—
388C23×C4C2416yes—
389C23×C4C2416yes—
390C23×C4C2416yes—
391C23×C4C24112yes—
392C23×C4C2416yes—
393C4⋊Q8—412no—
394C4⋊Q8—46no—
395#127—224no—
396#127—46no—
397#126—224no—
398#126—424no—
399#124—424no—
400#124—46no—
401#123—224no—
402#123—424no—
403#123—424no—
404C22⋊Q8—424no—
405C22⋊Q8—424no—
406#121—224no—
407#121—224no—
408#121—46no—
409#121—46no—
410#120—412no—
411#120—424no—
412C4×Q8—28no—
413C4×Q8—28no—
414C4×Q8—28no—
415C4×Q8—28no—
416C4×Q8—28no—
417C4×Q8—24no—
418C4×Q8—46no—
419C4×D4—224no—
420C4×D4—224no—
421C4×D4—224no—
422C4×D4—424no—
423C4×D4—412no—
424C4×D4—412no—
425C4×D4—412no—
426C4×D4—424no—
427C4×D4—46no—
428#117—224no—
429#117—224no—
430#117—46no—
431#117—412no—
432#117—424no—
433#117—412no—
434C2×C4⋊C4—46no—
435C2×C4⋊C4—412no—
436C2×C4⋊C4C2416yes—
437C2×C4⋊C4C2416yes—
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C2413yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2413yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C24112yes—
453C2×C4⋊C4C24112yes—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C24112yes—
457C2×C4⋊C4C2413yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2412yes—
461C2×C22⋊C4—424no—
462C2×C22⋊C4—424no—
463C2×C22⋊C4C2416yes—
464C2×C22⋊C4C2416yes—
465C2×C22⋊C4C2416yes—
466C2×C22⋊C4C2416yes—
467C2×C22⋊C4C24112yes—
468C2×C22⋊C4C2416yes—
469C2×C22⋊C4C2416yes—
470C2×C22⋊C4C2416yes—
471C2×C22⋊C4C2416yes—
472C2×C22⋊C4C2416yes—
473C2×C22⋊C4C2416yes—
474C2×C22⋊C4C2416yes—
475C2×C22⋊C4C24112yes—
476C2×C22⋊C4C24112yes—
477C2×C22⋊C4C24112yes—
478C2×C22⋊C4C24112yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C24112yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2413yes—
485C2×C22⋊C4C2413yes—
486C2×C22⋊C4C24112yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2416yes—
492C2×C22⋊C4C2416yes—
493C2×C42—224no—
494C2×C42C2416yes—
495C2×C42C2416yes—
496C2×C42C2416yes—
497C2×C42C2413yes—
498C2×C42C2416yes—
499C2×C42C2416yes—
500C2×C42C2416yes—
501C2×C42C2413yes—
502C2×C42C2416yes—
503C2×C42C2416yes—
504C2×C42C2416yes—
505C2×C42C2412yes—
506C2×C42C2416yes—
507C2×C42C2411yescharacteristic
508C2×C42C2412yes—
509#95C2412yes—
510#95C2412yes—
511#95C2416yes—
512#95C2416yes—
513#95C2416yes—
514#95C2416yes—
515#95C2416yes—
516#95C2416yes—
517#95C2412yes—
518#95C2412yes—
519#95C2411yescharacteristic
520#95C2412yes—
521#95C2412yes—
522#95C2411yescharacteristic
523#95C2413yes—
524#95C2416yes—
525#95C2416yes—
526#95C2413yes—
527#95C2416yes—
528#95C2416yes—
529#95C2416yes—
530#95C24112yes—
531#95C2412yes—
532#95C2416yes—
533#95C2416yes—
534#95C2416yes—
535#95C24112yes—
536C24—224no—
537C24—46no—
538C24—412no—
539C24—46no—
540C24—46no—
541C24C2513yes—
542C24C2513yes—
543C24C2516yes—
544#41—264no—
545#41—448no—
546#41—416no—
547#41—416no—
548C2×Q8—24no—
549C2×Q8—22no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—412no—
554C2×Q8—46no—
555C2×Q8C2×#4118yes—
556C2×Q8H(5,𝔽2)14yes—
557C2×D4—212no—
558C2×D4—212no—
559C2×D4—212no—
560C2×D4—224no—
561C2×D4—212no—
562C2×D4—212no—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—212no—
566C2×D4—212no—
567C2×D4—26no—
568C2×D4—26no—
569C2×D4—26no—
570C2×D4—496no—
571C2×D4—46no—
572C2×D4—43no—
573C2×D4—46no—
574C2×D4—412no—
575C2×D4—43no—
576C2×D4—412no—
577C2×D4—43no—
578C2×D4—412no—
579C2×D4—46no—
580C2×D4—448no—
581C2×D4C2×#41124yes—
582C22×C4—212no—
583C22×C4—212no—
584C22×C4—212no—
585C22×C4—212no—
586C22×C4—212no—
587C22×C4—212no—
588C22×C4—212no—
589C22×C4—212no—
590C22×C4—26no—
591C22×C4—26no—
592C22×C4—46no—
593C22×C4—46no—
594C22×C4—412no—
595C22×C4—412no—
596C22×C4—46no—
597C22×C4—412no—
598C22×C4—412no—
599C22×C4C2×#41124yes—
600C22×C4C2511yescharacteristic
601C22×C4C2511yescharacteristic
602C22×C4C2512yes—
603C22×C4C2516yes—
604C22×C4C2516yes—
605C22×C4C2512yes—
606C22×C4C2516yes—
607C22×C4C2516yes—
608C22×C4C2513yes—
609C22×C4C2516yes—
610C22×C4C2512yes—
611C22×C4C2512yes—
612C22×C4C2512yes—
613C22×C4C2512yes—
614C22×C4C2511yescharacteristic
615C22×C4C2513yes—
616C4⋊C4—212no—
617C4⋊C4—212no—
618C4⋊C4—24no—
619C4⋊C4—212no—
620C4⋊C4—212no—
621C4⋊C4—212no—
622C4⋊C4—212no—
623C4⋊C4—212no—
624C4⋊C4—26no—
625C4⋊C4—212no—
626C4⋊C4—212no—
627C4⋊C4—24no—
628C4⋊C4—46no—
629C4⋊C4—43no—
630C4⋊C4—42no—
631C4⋊C4—46no—
632C4⋊C4—42no—
633C4⋊C4—41no—
634C4⋊C4—412no—
635C4⋊C4—412no—
636C4⋊C4—41no—
637C4⋊C4—412no—
638C4⋊C4—43no—
639C4⋊C4—46no—
640C4⋊C4H(5,𝔽2)18yescomplemented
641C22⋊C4—224no—
642C22⋊C4—212no—
643C22⋊C4—212no—
644C22⋊C4—212no—
645C22⋊C4—212no—
646C22⋊C4—212no—
647C22⋊C4—212no—
648C22⋊C4—212no—
649C22⋊C4—212no—
650C22⋊C4—212no—
651C22⋊C4—212no—
652C22⋊C4—212no—
653C22⋊C4—412no—
654C22⋊C4—412no—
655C22⋊C4—412no—
656C22⋊C4—412no—
657C22⋊C4—46no—
658C22⋊C4—46no—
659C22⋊C4—46no—
660C22⋊C4—46no—
661C22⋊C4—46no—
662C22⋊C4—46no—
663C22⋊C4—46no—
664C22⋊C4—412no—
665C22⋊C4—43no—
666C22⋊C4—43no—
667C22⋊C4—412no—
668C22⋊C4—46no—
669C22⋊C4—46no—
670C22⋊C4—46no—
671C42—24no—
672C42—212no—
673C42—212no—
674C42—212no—
675C42—212no—
676C42—212no—
677C42—212no—
678C42—212no—
679C42—212no—
680C42—212no—
681C42—26no—
682C42—26no—
683C42—41no—
684C42—42no—
685C42—46no—
686C23—26no—
687C23—26no—
688C23—26no—
689C23—26no—
690C23—26no—
691C23—26no—
692C23—26no—
693C23—26no—
694C23—26no—
695C23—26no—
696C23—23no—
697C23—23no—
698C23—23no—
699C23—23no—
700C23—23no—
701C23—23no—
702C23—424no—
703C23—824no—
704C23—824no—
705C23—166no—
706C23—166no—
707C23C22×#41112yes—
708C23C2611yescharacteristic
709Q8—44no—
710Q8—44no—
711Q8—166no—
712Q8#551116yescomplemented
713D4—248no—
714D4—424no—
715D4—424no—
716D4—412no—
717D4—412no—
718D4—412no—
719D4—86no—
720D4—824no—
721D4—166no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—248no—
733C2×C4—26no—
734C2×C4—26no—
735C2×C4—26no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—26no—
741C2×C4—26no—
742C2×C4—26no—
743C2×C4—26no—
744C2×C4—26no—
745C2×C4—26no—
746C2×C4—23no—
747C2×C4—26no—
748C2×C4—26no—
749C2×C4—26no—
750C2×C4—26no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—26no—
754C2×C4—22no—
755C2×C4—26no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—26no—
759C2×C4—22no—
760C2×C4—424no—
761C2×C4—424no—
762C2×C4—412no—
763C2×C4—412no—
764C2×C4—166no—
765C2×C4—1612no—
766C2×C4C22×#4114yes—
767C2×C4C22×#41112yes—
768C2×C4C2×H(5,𝔽2)14yes—
769C2×C4C2×H(5,𝔽2)14yes—
770C2×C4C2×H(5,𝔽2)14yes—
771C2×C4C2×H(5,𝔽2)16yes—
772C2×C4#58512yes—
773C22—212no—
774C22—212no—
775C22—212no—
776C22—46no—
777C22—46no—
778C22—46no—
779C22—46no—
780C22—46no—
781C22—46no—
782C22—43no—
783C22—43no—
784C22—46no—
785C22—46no—
786C22—43no—
787C22—43no—
788C22—43no—
789C22—43no—
790C22—1624no—
791C22C23×#4112yes—
792C22C22×H(5,𝔽2)12yes—
793C22C22×H(5,𝔽2)11yescharacteristic
794C22C2×#58511yescharacteristic
795C222−1+611yescharacteristic
796C4—24no—
797C4—24no—
798C4—24no—
799C4—22no—
800C4—24no—
801C4—46no—
802C4—46no—
803C4—46no—
804C4—43no—
805C4—46no—
806C4—46no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4C2×#551112yes—
812C2—412no—
813C2—83no—
814C2—83no—
815C2C22×#55111yescharacteristic
816C2#6280012yes—
817C2#6291911yescharacteristic
818C2#6298512yes—
819C2#6304011yescharacteristic
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. #59945C2semidirect
2. #59476C2semidirect
3. #59273C2semidirect
4. #45088C2semidirect
5. #44959C2semidirect
6. #44914C2semidirect
7. #38206C2semidirect
8. #37969C2semidirect
9. #36458C2semidirect
10. #36457C2semidirect
11. #36433C2semidirect
12. #36264C2semidirect
14. #36005C2semidirect
15. #35748C2semidirect
16. #34871C2semidirect
17. #34313C2semidirect
18. #34258C2semidirect
19. #34129C2semidirect
21. C2×Q82C22semidirect
22. C2×#551C22semidirect
26. C2×#520C22semidirect
28. #2860C22semidirect
29. #2858C22semidirect
30. #2854C22semidirect
31. #2782C22semidirect
32. #2763C22semidirect
33. #2753C22semidirect
34. #2736C22semidirect
35. #2723C22semidirect
36. #2706C22semidirect
37. #2696C22semidirect
38. #2685C22semidirect
39. #2684C22semidirect
40. #2628C22semidirect
41. #2624C22semidirect
43. #2612C22semidirect
44. #2610C22semidirect
45. #2610C22semidirect
46. #2609C22semidirect
47. #2603C22semidirect
48. #2598C22semidirect
49. #2586C22semidirect
50. #2580C22semidirect
51. #2572C22semidirect
52. #2563C22semidirect
53. #2554C22semidirect
54. #2548C22semidirect
55. #2542C22semidirect
56. #2532C22semidirect
57. #2526C22semidirect
58. #2513C22semidirect
59. #2512C22semidirect
60. #2512C22semidirect
61. #2501C22semidirect
62. #2500C22semidirect
63. #2497C22semidirect
64. #2496C22semidirect
65. #2495C22semidirect
66. #2491C22semidirect
67. #2491C22semidirect
68. #2487C22semidirect
69. #2485C22semidirect
70. #2482C22semidirect
71. #2479C22semidirect
72. #2472C22semidirect
73. #2471C22semidirect
74. #2463C22semidirect
75. #2461C22semidirect
76. #2452C22semidirect
77. #2452C22semidirect
78. #2445C22semidirect
79. #2445C22semidirect
80. #2445C22semidirect
81. #2440C22semidirect
82. #2440C22semidirect
83. #2437C22semidirect
86. #2422C22semidirect
87. #2422C22semidirect
88. #2420C22semidirect
89. #2418C22semidirect
90. #2411C22semidirect
93. #2396C22semidirect
94. #2395C22semidirect
96. #2366C22semidirect
97. #2361C22semidirect
98. #2361C22semidirect
99. #2358C22semidirect
100. #2354C22semidirect
101. #2354C22semidirect
102. #2351C22semidirect
103. Q8×C4⋊C4C22semidirect
104. Q8×C4⋊C4C22semidirect
105. Q8×C4⋊C4C22semidirect
106. D4×C4⋊C4C22semidirect
107. #2346C22semidirect
108. #2346C22semidirect
115. #2341C22semidirect
116. #2341C22semidirect
121. #2324C22semidirect
122. #2324C22semidirect
125. C4×#127C22semidirect
126. C4×#126C22semidirect
127. C4×#124C22semidirect
128. C4×#123C22semidirect
130. #2293C22semidirect
131. #2293C22semidirect
132. #2293C22semidirect
134. #2285C22semidirect
135. C42×Q8C22semidirect
136. C42×Q8C22semidirect
137. C4×#117C22semidirect
640. C4⋊C4H(5,𝔽2)semidirect
712. Q8#551semidirect

Maximal subgroups

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

subgroupindex
#599452
#594762
#592732
#450882
#449592
#449142
#382062
#379692
#364582
#364572
#364332
#362642
#360912
#360052
#357482
#348712
#343132
#342582
#341292