Finite Group Databasebeta

← #8097020

Subgroups — #8097020

Order 512.

5963 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53018C213yesmaximal, complemented
2#53014C216yesmaximal, complemented
3#53007C213yesmaximal, complemented
4#52981C216yesmaximal, complemented
5#52297C213yesmaximal, complemented
6#46328C213yesmaximal, complemented
7#46061C216yesmaximal, complemented
8#45701C216yesmaximal, complemented
9#45647C216yesmaximal, complemented
10#45483C216yesmaximal, complemented
11#36576C212yesmaximal, complemented
12#36483C212yesmaximal, complemented
13#36465C211yesmaximal, characteristic, complemented
14#36458C212yesmaximal, complemented
15#36434C212yesmaximal, complemented
16#36091C211yesmaximal, characteristic, complemented
17#36082C212yesmaximal, complemented
18#36076C211yesmaximal, characteristic, complemented
19#35831C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×#560C2216yescomplemented
22C2×#550C2211yescharacteristic
23C2×#550C2212yes—
24C2×D4×Q8C2211yescharacteristic, complemented
25C2×#548C2212yes—
26C2×#548C2212yes—
27C2×#548C2212yes—
28C2×#548C2212yescomplemented
29C2×#520C2211yescharacteristic, complemented
30C22×C4×Q8C2212yescomplemented
31#2860C2216yescomplemented
32#2858C2213yescomplemented
33#2856C2216yescomplemented
34#2854C2216yescomplemented
35#2850C2216yescomplemented
36#2842C2216yescomplemented
37#2841C2216yescomplemented
38#2837C22112yescomplemented
39#2829C22112yescomplemented
40#2829C22112yescomplemented
41#2823C2216yescomplemented
42#2813C22112yescomplemented
43#2803C2216yescomplemented
44#2795C2213yescomplemented
45#2792C2213yescomplemented
46#2784C2211yescharacteristic, complemented
47#2756C22112yescomplemented
48#2756C2216yescomplemented
49#2752C2216yescomplemented
50#2737C2216yescomplemented
51#2735C2216yescomplemented
52#2714C2216yescomplemented
53#2705C22112yescomplemented
54#2705C2216yescomplemented
55#2703C22112yescomplemented
56#2699C22112yescomplemented
57#2699C2213yescomplemented
58#2697C22112yescomplemented
59#2697C2216yescomplemented
60#2685C22112yescomplemented
61#2685C22112yescomplemented
62#2678C22112yescomplemented
63#2673C2216yescomplemented
64#2668C22112yescomplemented
65#2624C2213yescomplemented
66#2620C2216yescomplemented
67#2616C2216yes—
68#2615C2213yes—
69#2548C2216yescomplemented
70#2545C2216yescomplemented
71#2544C2216yescomplemented
72#2542C2213yescomplemented
73#2541C2213yescomplemented
74#2540C2216yescomplemented
75#2540C2216yescomplemented
76#2538C2216yescomplemented
77#2537C2216yescomplemented
78#2536C2216yescomplemented
79#2513C2216yescomplemented
80#2512C2216yescomplemented
81#2512C2216yescomplemented
82#2504C2213yescomplemented
83#2501C2216yescomplemented
84#2497C2216yescomplemented
85#2496C2216yescomplemented
86#2495C2216yescomplemented
87#2486C2213yescomplemented
88#2486C2216yescomplemented
89#2448C2216yescomplemented
90#2448C2216yescomplemented
91#2445C2216yescomplemented
92#2435C2216yes—
93#2435C2216yes—
94#2435C2216yes—
95#2433C2213yes—
96#2433C2216yes—
97#2429C2216yescomplemented
98#2428C2216yescomplemented
99#2427C2216yescomplemented
100#2426C2216yescomplemented
101#2426C2216yescomplemented
102#2426C2216yescomplemented
103#2423C2216yescomplemented
104#2423C2216yescomplemented
105#2420C2216yescomplemented
106#2417C2216yescomplemented
107#2417C2216yescomplemented
108#2416C2216yescomplemented
109#2416C2216yescomplemented
110#2416C2216yescomplemented
111#2416C2216yescomplemented
112#2408C2213yes—
113#2408C2216yes—
114#2408C2216yes—
115#2408C2216yes—
116#2408C2216yes—
117#2395C2213yescomplemented
118#2392C2216yescomplemented
119#2388C2213yes—
120#2388C2216yes—
121#2375C22112yescomplemented
122#2351C2212yescomplemented
123Q8×C4⋊C4C2212yescomplemented
124Q8×C4⋊C4C2212yescomplemented
125#2341C2212yes—
126#2341C2212yes—
127#2341C2212yes—
128#2341C2211yescharacteristic
129#2341C2212yes—
130#2341C2211yescharacteristic, complemented
131Q8×C22⋊C4C2212yescomplemented
132C4×#127C2213yescomplemented
133C4×#126C2216yescomplemented
134C4×#123C2216yescomplemented
135C4×#121C2216yescomplemented
136C4×#121C2216yescomplemented
137C42×Q8C2211yescharacteristic, complemented
138C2×H(5,𝔽2)—44no—
139C2×H(5,𝔽2)—48no—
140C22×#41C2312yes—
141C22×#41C2311yescharacteristic
142C22×#41C2311yescharacteristic
143C22×#41C2313yes—
144C23×Q8C2312yes—
145C23×D4C2313yes—
146C23×D4C2316yes—
147#560—424no—
148#550—48no—
149#550—44no—
150D4×Q8—44no—
151#548—48no—
152#548—48no—
153#548—48no—
154#548—48no—
155C2×C4⋊Q8C2313yes—
156C2×#127C2313yes—
157C2×#127C2316yes—
158C2×#127C2313yes—
159C2×#126C2316yes—
160C2×#126C23112yes—
161C2×#124C2316yes—
162C2×#124C2316yes—
163C2×#124C2316yes—
164C2×#124C2316yes—
165C2×#123C23112yes—
166C2×#123C2316yes—
167C2×#123C2316yes—
168C2×C22⋊Q8C2316yes—
169C2×C22⋊Q8C2316yes—
170C2×C22⋊Q8C2316yes—
171C2×C22⋊Q8C2316yes—
172C2×C22⋊Q8C2316yes—
173C2×#121C2316yes—
174C2×#121C2316yes—
175C2×#121C2316yes—
176C2×#121C2316yes—
177C2×#121C2316yes—
178C2×#121C23112yes—
179C2×#121C2316yes—
180C2×#121C2316yes—
181C2×#121C2313yes—
182C2×#121C2316yes—
183C2×#121C2313yes—
184C2×#121C23112yes—
185C2×#120C23112yes—
186C2×#120C23112yes—
187C2×#120C2316yes—
188#520—44no—
189C2×C4×Q8—48no—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2316yes—
196C2×C4×Q8C2316yes—
197C2×C4×D4C2313yes—
198C2×C4×D4C2316yes—
199C2×C4×D4C2316yes—
200C2×C4×D4C2313yes—
201C2×C4×D4C2316yes—
202C2×C4×D4C2316yes—
203C2×C4×D4C2316yes—
204C2×C4×D4C2316yes—
205C2×#117C2313yes—
206C22×C4⋊C4C2316yes—
207C22×C4⋊C4C2313yes—
208C22×C42C2316yes—
209#400C23112yes—
210#400C2311yescharacteristic
211#399C2316yes—
212#399C23112yes—
213#399C2316yes—
214#399C23112yes—
215#399C2313yes—
216#398C2313yes—
217#398C23112yes—
218#398C23112yes—
219#398C2316yes—
220#397C2316yes—
221#397C2316yes—
222#397C23112yes—
223#397C23112yes—
224#397C2316yes—
225#397C23112yes—
226#397C2313yes—
227#396C23112yes—
228#396C23112yes—
229#396C23112yes—
230#396C23112yes—
231#396C23112yes—
232#396C23112yes—
233#396C2316yes—
234#396C2312yes—
235#395C2316yes—
236#395C2311yescharacteristic
237#394C2313yes—
238#394C23112yes—
239#394C23112yes—
240#394C2316yes—
241#394C2316yes—
242#394C23112yes—
243#394C23112yes—
244#394C23112yes—
245#394C23112yes—
246#394C23112yes—
247#394C2316yes—
248#394C23112yes—
249#394C2316yes—
250#394C2316yes—
251#394C2316yes—
252#394C2316yes—
253#394C2316yes—
254#394C23112yes—
255#393C2313yes—
256#393C2312yes—
257#392C2316yes—
258#392C23112yes—
259#392C2316yes—
260#392C2316yes—
261#392C2316yes—
262#392C2316yes—
263#392C2313yes—
264#392C2316yes—
265#392C23112yes—
266#391C2316yes—
267#391C2316yes—
268#390C2311yescharacteristic
269#390C2313yes—
270#390C2316yes—
271#390C2316yes—
272#390C23112yes—
273#390C23112yes—
274#390C2316yes—
275#390C2316yes—
276#390C2316yes—
277#390C2316yes—
278#390C2316yes—
279#390C2316yes—
280#390C2316yes—
281#390C2316yes—
282#390C2316yes—
283#390C2316yes—
284#390C23112yes—
285#390C2316yes—
286#390C2316yes—
287#390C2316yes—
288#389C2316yes—
289#389C2316yes—
290#389C2316yes—
291#389C2316yes—
292#389C2316yes—
293#389C2316yes—
294#389C2316yes—
295#389C2316yes—
296#388C2316yes—
297#388C2316yes—
298#388C2316yes—
299#388C23112yes—
300#388C23112yes—
301#388C23112yes—
302#388C23112yes—
303#388C23112yes—
304#388C23112yes—
305#388C2316yes—
306#388C2316yes—
307#388C2316yes—
308#388C2316yes—
309#388C2316yes—
310#388C2316yes—
311#387C2312yes—
312#387C2316yes—
313#387C2316yes—
314#387C2316yes—
315#387C2316yes—
316#386C2316yes—
317#386C23112yes—
318#386C2316yes—
319#386C23112yes—
320#386C23112yes—
321#386C23112yes—
322#386C2316yes—
323#386C2316yes—
324#386C2312yes—
325#385C2312yes—
326#384C2313yes—
327#384C2316yes—
328#384C2316yes—
329#383C2316yes—
330#382C2316yes—
331#381C2316yes—
332#381C2316yes—
333#380C23112yes—
334#380C2316yes—
335#380C2316yes—
336#380C2313yes—
337#380C2316yes—
338#380C2316yes—
339#380C2316yes—
340#380C2313yes—
341#380C2316yes—
342#380C2312yes—
343#379C2316yes—
344#379C23112yes—
345#379C23112yes—
346#379C23112yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2316yes—
349C4×C4⋊C4C2316yes—
350C4×C4⋊C4C2316yes—
351C4×C4⋊C4C2313yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C2313yes—
358C4×C22⋊C4C2313yes—
359C43C2313yes—
360C25C2416yes—
361H(5,𝔽2)—464no—
362C2×#41—24no—
363C2×#41—28no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—28no—
368C2×#41—24no—
369C2×#41—412no—
370C2×#41—46no—
371C22×Q8—28no—
372C22×Q8—28no—
373C22×Q8—28no—
374C22×Q8C2416yes—
375C22×Q8C2411yescharacteristic
376C22×Q8C2411yescharacteristic
377C22×D4—46no—
378C22×D4—412no—
379C22×D4—412no—
380C22×D4—412no—
381C22×D4—412no—
382C22×D4C2413yes—
383C22×D4C2416yes—
384C22×D4C2413yes—
385C22×D4C2416yes—
386C22×D4C2416yes—
387C22×D4C2416yes—
388C22×D4C2416yes—
389C22×D4C2413yes—
390C22×D4C2416yes—
391C22×D4C24112yes—
392C22×D4C2416yes—
393C22×D4C2413yes—
394C22×D4C2416yes—
395C22×D4C2411yescharacteristic
396C23×C4C2413yes—
397C23×C4C2416yes—
398C23×C4C2413yes—
399C23×C4C2416yes—
400C23×C4C2416yes—
401C23×C4C2412yes—
402C23×C4C2416yes—
403C4⋊Q8—46no—
404#127—212no—
405#127—412no—
406#127—46no—
407#126—424no—
408#126—412no—
409#124—412no—
410#124—412no—
411#124—412no—
412#124—412no—
413#123—412no—
414#123—424no—
415#123—412no—
416C22⋊Q8—412no—
417C22⋊Q8—412no—
418C22⋊Q8—412no—
419C22⋊Q8—412no—
420C22⋊Q8—412no—
421#121—224no—
422#121—424no—
423#121—412no—
424#121—412no—
425#121—412no—
426#121—412no—
427#121—412no—
428#121—412no—
429#121—412no—
430#121—46no—
431#121—46no—
432#121—424no—
433#120—424no—
434#120—412no—
435#120—424no—
436C4×Q8—28no—
437C4×Q8—28no—
438C4×Q8—28no—
439C4×Q8—28no—
440C4×Q8—24no—
441C4×Q8—412no—
442C4×Q8—412no—
443C4×D4—412no—
444C4×D4—412no—
445C4×D4—412no—
446C4×D4—412no—
447C4×D4—412no—
448C4×D4—46no—
449C4×D4—412no—
450C4×D4—46no—
451#117—46no—
452C2×C4⋊C4—412no—
453C2×C4⋊C4—46no—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2416yes—
457C2×C4⋊C4C2413yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2416yes—
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2413yes—
463C2×C4⋊C4C24112yes—
464C2×C4⋊C4C2411yescharacteristic
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2411yescharacteristic
467C2×C4⋊C4C2416yes—
468C2×C4⋊C4C2416yes—
469C2×C4⋊C4C2416yes—
470C2×C4⋊C4C2416yes—
471C2×C4⋊C4C2413yes—
472C2×C4⋊C4C24112yes—
473C2×C4⋊C4C24112yes—
474C2×C4⋊C4C2416yes—
475C2×C4⋊C4C2416yes—
476C2×C4⋊C4C2416yes—
477C2×C4⋊C4C2412yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2412yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2412yes—
485C2×C22⋊C4C2412yes—
486C2×C22⋊C4C2412yes—
487C2×C22⋊C4C2412yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2413yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2413yes—
492C2×C22⋊C4C2416yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C2416yes—
496C2×C22⋊C4C2416yes—
497C2×C22⋊C4C24112yes—
498C2×C22⋊C4C24112yes—
499C2×C22⋊C4C24112yes—
500C2×C22⋊C4C2416yes—
501C2×C22⋊C4C24112yes—
502C2×C22⋊C4C2416yes—
503C2×C22⋊C4C24112yes—
504C2×C22⋊C4C24112yes—
505C2×C22⋊C4C24112yes—
506C2×C22⋊C4C24112yes—
507C2×C22⋊C4C2416yes—
508C2×C22⋊C4C2416yes—
509C2×C22⋊C4C2416yes—
510C2×C22⋊C4C2416yes—
511C2×C22⋊C4C2416yes—
512C2×C22⋊C4C2416yes—
513C2×C22⋊C4C2416yes—
514C2×C42—412no—
515C2×C42C2416yes—
516C2×C42C2416yes—
517C2×C42C2413yes—
518C2×C42C2416yes—
519C2×C42C2416yes—
520C2×C42C2413yes—
521C2×C42C2416yes—
522C2×C42C2416yes—
523C2×C42C2416yes—
524C2×C42C2411yescharacteristic
525#95C2411yescharacteristic
526#95C2412yes—
527#95C2411yescharacteristic
528#95C2412yes—
529#95C2412yes—
530#95C2412yes—
531#95C2416yes—
532#95C2416yes—
533#95C2416yes—
534#95C2413yes—
535#95C2413yes—
536#95C2416yes—
537#95C2416yes—
538#95C2416yes—
539#95C2412yes—
540#95C2416yes—
541#95C2416yes—
542#95C2416yes—
543#95C2416yes—
544#95C2416yes—
545#95C2416yes—
546#95C24112yes—
547#95C24112yes—
548C24—412no—
549C24—46no—
550C24—46no—
551C24—412no—
552C24—46no—
553C24C2516yes—
554C24C2513yes—
555C24C2513yes—
556C24C2512yes—
557#41—448no—
558#41—416no—
559#41—432no—
560#41—416no—
561C2×Q8—212no—
562C2×Q8—212no—
563C2×Q8—212no—
564C2×Q8—42no—
565C2×Q8—41no—
566C2×Q8—432no—
567C2×Q8H(5,𝔽2)18yes—
568C2×Q8H(5,𝔽2)14yes—
569C2×D4—212no—
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—212no—
573C2×D4—26no—
574C2×D4—212no—
575C2×D4—212no—
576C2×D4—212no—
577C2×D4—212no—
578C2×D4—212no—
579C2×D4—26no—
580C2×D4—26no—
581C2×D4—212no—
582C2×D4—41no—
583C2×D4—46no—
584C2×D4—43no—
585C2×D4—46no—
586C2×D4—46no—
587C2×D4—46no—
588C2×D4—41no—
589C2×D4—46no—
590C2×D4—46no—
591C2×D4—46no—
592C2×D4—46no—
593C2×D4—46no—
594C2×D4—43no—
595C2×D4—46no—
596C2×D4—46no—
597C2×D4—46no—
598C2×D4—43no—
599C2×D4—46no—
600C2×D4—46no—
601C2×D4—412no—
602C2×D4—412no—
603C2×D4—412no—
604C2×D4—412no—
605C2×D4—46no—
606C2×D4—448no—
607C2×D4—496no—
608C2×D4H(5,𝔽2)14yescomplemented
609C22×C4—212no—
610C22×C4—212no—
611C22×C4—26no—
612C22×C4—212no—
613C22×C4—212no—
614C22×C4—212no—
615C22×C4—212no—
616C22×C4—26no—
617C22×C4—212no—
618C22×C4—212no—
619C22×C4—212no—
620C22×C4—24no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—46no—
624C22×C4—46no—
625C22×C4—46no—
626C22×C4—46no—
627C22×C4—46no—
628C22×C4C2512yes—
629C22×C4C2511yescharacteristic
630C22×C4C2512yes—
631C22×C4C2513yes—
632C22×C4C2516yes—
633C22×C4C2512yes—
634C22×C4C2516yes—
635C22×C4C2512yes—
636C22×C4C2516yes—
637C22×C4C2516yes—
638C22×C4C2516yes—
639C22×C4C2511yescharacteristic
640C22×C4C2511yescharacteristic
641C22×C4C2512yes—
642C22×C4C2513yes—
643C4⋊C4—212no—
644C4⋊C4—212no—
645C4⋊C4—212no—
646C4⋊C4—26no—
647C4⋊C4—212no—
648C4⋊C4—212no—
649C4⋊C4—212no—
650C4⋊C4—24no—
651C4⋊C4—43no—
652C4⋊C4—412no—
653C4⋊C4—42no—
654C4⋊C4—41no—
655C4⋊C4—42no—
656C4⋊C4—41no—
657C4⋊C4—46no—
658C4⋊C4—46no—
659C4⋊C4—46no—
660C4⋊C4—46no—
661C4⋊C4—43no—
662C4⋊C4—412no—
663C4⋊C4—412no—
664C4⋊C4—46no—
665C4⋊C4—46no—
666C4⋊C4—46no—
667C22⋊C4—212no—
668C22⋊C4—212no—
669C22⋊C4—212no—
670C22⋊C4—212no—
671C22⋊C4—24no—
672C22⋊C4—46no—
673C22⋊C4—46no—
674C22⋊C4—46no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—46no—
680C22⋊C4—46no—
681C22⋊C4—43no—
682C22⋊C4—43no—
683C22⋊C4—46no—
684C22⋊C4—46no—
685C22⋊C4—46no—
686C22⋊C4—46no—
687C22⋊C4—46no—
688C22⋊C4—412no—
689C22⋊C4—412no—
690C22⋊C4—412no—
691C22⋊C4—46no—
692C22⋊C4—412no—
693C22⋊C4—46no—
694C22⋊C4—46no—
695C22⋊C4—46no—
696C22⋊C4—412no—
697C22⋊C4—412no—
698C22⋊C4—412no—
699C22⋊C4—412no—
700C22⋊C4—46no—
701C22⋊C4—46no—
702C22⋊C4—46no—
703C42—212no—
704C42—212no—
705C42—212no—
706C42—212no—
707C42—26no—
708C42—26no—
709C42—46no—
710C42—46no—
711C42—41no—
712C42—46no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—26no—
720C23—23no—
721C23—26no—
722C23—23no—
723C23—26no—
724C23—26no—
725C23—26no—
726C23—23no—
727C23—26no—
728C23—23no—
729C23—26no—
730C23—26no—
731C23—26no—
732C23—26no—
733C23—23no—
734C23—26no—
735C23—23no—
736C23—424no—
737C23—1612no—
738C23—166no—
739C23—166no—
740C23—1612no—
741C23C2×H(5,𝔽2)14yes—
742C23C2611yescharacteristic
743Q8—44no—
744Q8—424no—
745Q8#560116yescomplemented
746D4—44no—
747D4—424no—
748D4—412no—
749D4—412no—
750D4—424no—
751D4—412no—
752D4—86no—
753D4—812no—
754D4—812no—
755D4—812no—
756D4—812no—
757D4—812no—
758D4—1612no—
759D4—166no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—26no—
768C2×C4—26no—
769C2×C4—26no—
770C2×C4—23no—
771C2×C4—26no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—26no—
775C2×C4—26no—
776C2×C4—26no—
777C2×C4—26no—
778C2×C4—22no—
779C2×C4—26no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—26no—
788C2×C4—26no—
789C2×C4—22no—
790C2×C4—26no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—26no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—26no—
797C2×C4—48no—
798C2×C4—424no—
799C2×C4—412no—
800C2×C4—424no—
801C2×C4—412no—
802C2×C4—812no—
803C2×C4—166no—
804C2×C4C2×H(5,𝔽2)12yes—
805C2×C4C2×H(5,𝔽2)112yes—
806C2×C4C2×H(5,𝔽2)16yes—
807C2×C4#58514yes—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—46no—
816C22—46no—
817C22—46no—
818C22—46no—
819C22—43no—
820C22—43no—
821C22—46no—
822C22—43no—
823C22—43no—
824C22—46no—
825C22—46no—
826C22—46no—
827C22—46no—
828C22—46no—
829C22—43no—
830C22—46no—
831C22—43no—
832C22—1624no—
833C22C22×H(5,𝔽2)11yescharacteristic
834C22C22×H(5,𝔽2)12yes—
835C22C22×H(5,𝔽2)11yescharacteristic
836C22C2×#58512yes—
837C222−1+611yescharacteristic
838C4—22no—
839C4—24no—
840C4—46no—
841C4—46no—
842C4—46no—
843C4—42no—
844C4—43no—
845C4—46no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—41no—
851C4—46no—
852C4C2×#560112yes—
853C2—44no—
854C2—83no—
855C2—83no—
856C2—86no—
857C2C22×#56011yescharacteristic
858C2#6289511yescharacteristic
859C2#6291912yes—
860C2#6301412yes—
861C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53018C2semidirect
2. #53014C2semidirect
3. #53007C2semidirect
4. #52981C2semidirect
5. #52297C2semidirect
6. #46328C2semidirect
7. #46061C2semidirect
8. #45701C2semidirect
9. #45647C2semidirect
10. #45483C2semidirect
11. #36576C2semidirect
12. #36483C2semidirect
13. #36465C2semidirect
14. #36458C2semidirect
15. #36434C2semidirect
16. #36091C2semidirect
17. #36082C2semidirect
18. #36076C2semidirect
19. #35831C2semidirect
21. C2×#560C22semidirect
24. C2×D4×Q8C22semidirect
28. C2×#548C22semidirect
29. C2×#520C22semidirect
30. C22×C4×Q8C22semidirect
31. #2860C22semidirect
32. #2858C22semidirect
33. #2856C22semidirect
34. #2854C22semidirect
35. #2850C22semidirect
36. #2842C22semidirect
37. #2841C22semidirect
38. #2837C22semidirect
39. #2829C22semidirect
40. #2829C22semidirect
41. #2823C22semidirect
42. #2813C22semidirect
43. #2803C22semidirect
44. #2795C22semidirect
45. #2792C22semidirect
46. #2784C22semidirect
47. #2756C22semidirect
48. #2756C22semidirect
49. #2752C22semidirect
50. #2737C22semidirect
51. #2735C22semidirect
52. #2714C22semidirect
53. #2705C22semidirect
54. #2705C22semidirect
55. #2703C22semidirect
56. #2699C22semidirect
57. #2699C22semidirect
58. #2697C22semidirect
59. #2697C22semidirect
60. #2685C22semidirect
61. #2685C22semidirect
62. #2678C22semidirect
63. #2673C22semidirect
64. #2668C22semidirect
65. #2624C22semidirect
66. #2620C22semidirect
69. #2548C22semidirect
70. #2545C22semidirect
71. #2544C22semidirect
72. #2542C22semidirect
73. #2541C22semidirect
74. #2540C22semidirect
75. #2540C22semidirect
76. #2538C22semidirect
77. #2537C22semidirect
78. #2536C22semidirect
79. #2513C22semidirect
80. #2512C22semidirect
81. #2512C22semidirect
82. #2504C22semidirect
83. #2501C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2495C22semidirect
87. #2486C22semidirect
88. #2486C22semidirect
89. #2448C22semidirect
90. #2448C22semidirect
91. #2445C22semidirect
97. #2429C22semidirect
98. #2428C22semidirect
99. #2427C22semidirect
100. #2426C22semidirect
101. #2426C22semidirect
102. #2426C22semidirect
103. #2423C22semidirect
104. #2423C22semidirect
105. #2420C22semidirect
106. #2417C22semidirect
107. #2417C22semidirect
108. #2416C22semidirect
109. #2416C22semidirect
110. #2416C22semidirect
111. #2416C22semidirect
117. #2395C22semidirect
118. #2392C22semidirect
121. #2375C22semidirect
122. #2351C22semidirect
123. Q8×C4⋊C4C22semidirect
124. Q8×C4⋊C4C22semidirect
130. #2341C22semidirect
131. Q8×C22⋊C4C22semidirect
132. C4×#127C22semidirect
133. C4×#126C22semidirect
134. C4×#123C22semidirect
135. C4×#121C22semidirect
136. C4×#121C22semidirect
137. C42×Q8C22semidirect
608. C2×D4H(5,𝔽2)semidirect
745. Q8#560semidirect

Maximal subgroups

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

subgroupindex
#530182
#530142
#530072
#529812
#522972
#463282
#460612
#457012
#456472
#454832
#365762
#364832
#364652
#364582
#364342
#360912
#360822
#360762
#358312