Finite Group Databasebeta

← #8097790

Subgroups — #8097790

Order 512.

5540 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53129C216yesmaximal, complemented
2#53103C213yesmaximal, complemented
3#53045C216yesmaximal, complemented
4#53043C216yesmaximal, complemented
5#53018C216yesmaximal, complemented
6#53007C213yesmaximal, complemented
7#52981C216yesmaximal, complemented
8#45697C213yesmaximal, complemented
9#45642C216yesmaximal, complemented
10#36677C213yesmaximal, complemented
11#36483C211yesmaximal, characteristic, complemented
12#36434C212yesmaximal, complemented
13#36082C212yesmaximal, complemented
14#36082C211yesmaximal, characteristic, complemented
15#35927C211yesmaximal, characteristic, complemented
16#35898C212yesmaximal, complemented
17#35801C212yesmaximal, complemented
18#35771C212yesmaximal, complemented
19#35771C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×D4×Q8C2212yescomplemented
22C2×D4×Q8C2211yescharacteristic, complemented
23C2×#548C2212yes—
24C2×#548C2212yes—
25C2×#548C2211yescharacteristic
26C2×#548C2212yes—
27C2×#548C2212yes—
28C2×#519C2212yescomplemented
29C22×C4×Q8C2211yescharacteristic, complemented
30#2854C2213yescomplemented
31#2850C2216yescomplemented
32#2842C22112yescomplemented
33#2841C2213yescomplemented
34#2838C2216yescomplemented
35#2837C22112yescomplemented
36#2837C2216yescomplemented
37#2837C22112yescomplemented
38#2829C2216yescomplemented
39#2829C22112yescomplemented
40#2829C22112yescomplemented
41#2828C2216yescomplemented
42#2826C2213yescomplemented
43#2825C2216yescomplemented
44#2824C2211yescharacteristic, complemented
45#2823C2216yescomplemented
46#2815C2213yescomplemented
47#2813C2216yescomplemented
48#2812C2216yescomplemented
49#2803C22112yescomplemented
50#2801C22112yescomplemented
51#2795C22112yescomplemented
52#2792C2216yescomplemented
53#2752C2216yescomplemented
54#2735C22112yescomplemented
55#2735C2216yescomplemented
56#2735C22112yescomplemented
57#2705C22112yescomplemented
58#2697C2216yescomplemented
59#2685C22112yescomplemented
60#2685C22112yescomplemented
61#2678C22112yescomplemented
62#2658C2213yescomplemented
63#2644C2216yescomplemented
64#2624C2216yescomplemented
65#2620C2216yescomplemented
66#2620C2216yescomplemented
67#2616C2216yes—
68#2616C2213yes—
69#2545C2216yescomplemented
70#2545C2216yescomplemented
71#2545C2216yescomplemented
72#2542C2213yescomplemented
73#2542C2216yescomplemented
74#2540C2216yescomplemented
75#2540C2213yescomplemented
76#2538C2216yescomplemented
77#2538C2216yescomplemented
78#2536C2216yescomplemented
79#2513C2216yescomplemented
80#2512C2216yescomplemented
81#2512C2216yescomplemented
82#2501C2213yescomplemented
83#2500C2216yescomplemented
84#2497C2216yescomplemented
85#2496C2216yescomplemented
86#2494C2216yescomplemented
87#2486C2213yescomplemented
88#2485C2216yescomplemented
89#2448C2216yescomplemented
90#2448C2216yescomplemented
91#2448C2216yescomplemented
92#2435C2213yes—
93#2435C2216yes—
94#2435C2216yes—
95#2435C2216yes—
96#2435C2216yes—
97#2429C2216yescomplemented
98#2429C2216yescomplemented
99#2429C2216yescomplemented
100#2426C2216yescomplemented
101#2426C2216yescomplemented
102#2426C2216yescomplemented
103#2423C2216yescomplemented
104#2423C2216yescomplemented
105#2421C2216yescomplemented
106#2417C2216yescomplemented
107#2416C2216yescomplemented
108#2415C2216yescomplemented
109#2415C2216yescomplemented
110#2414C2216yescomplemented
111#2414C2216yescomplemented
112#2408C2216yes—
113#2408C2216yes—
114#2408C2216yes—
115#2408C2213yes—
116#2408C2216yes—
117#2401C2216yescomplemented
118#2397C2213yescomplemented
119#2395C2216yescomplemented
120#2392C2216yescomplemented
121#2392C2216yescomplemented
122#2388C2213yes—
123#2388C2216yes—
124#2375C2216yescomplemented
125#2351C2212yescomplemented
126Q8×C4⋊C4C2212yescomplemented
127Q8×C4⋊C4C2212yescomplemented
128#2341C2212yes—
129#2341C2212yes—
130#2341C2212yes—
131#2341C2212yes—
132#2341C2211yescharacteristic
133Q8×C22⋊C4C2212yescomplemented
134Q8×C22⋊C4C2211yescharacteristic, complemented
135C4×#123C2213yescomplemented
136C4×#121C2216yescomplemented
137#2276C2211yescharacteristic, complemented
138C2×H(5,𝔽2)—44no—
139C2×H(5,𝔽2)—48no—
140C22×#41C2312yes—
141C22×#41C2311yescharacteristic
142C22×#41C2313yes—
143C23×Q8C2311yescharacteristic
144C23×Q8C2312yes—
145C23×D4C2313yes—
146C23×D4C2316yes—
147D4×Q8—48no—
148D4×Q8—44no—
149#548—48no—
150#548—48no—
151#548—48no—
152#548—44no—
153#548—48no—
154C2×C4⋊Q8C2313yes—
155C2×C4⋊Q8C2316yes—
156C2×#126C23112yes—
157C2×#124C2316yes—
158C2×#124C2316yes—
159C2×#124C2316yes—
160C2×#124C2313yes—
161C2×#124C2316yes—
162C2×#123C2313yes—
163C2×#123C2316yes—
164C2×C22⋊Q8C2316yes—
165C2×C22⋊Q8C2316yes—
166C2×C22⋊Q8C2316yes—
167C2×C22⋊Q8C2316yes—
168C2×C22⋊Q8C2316yes—
169C2×C22⋊Q8C2313yes—
170C2×C22⋊Q8C2316yes—
171C2×C22⋊Q8C2316yes—
172C2×#121C2316yes—
173C2×#121C2313yes—
174C2×#121C2316yes—
175C2×#121C2316yes—
176C2×#121C2316yes—
177C2×#121C2316yes—
178C2×#120C2316yes—
179C2×#120C23112yes—
180#519—48no—
181C2×C4×Q8—44no—
182C2×C4×Q8C2312yes—
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2312yes—
185C2×C4×Q8C2311yescharacteristic
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2316yes—
188C2×C4×Q8C2316yes—
189C2×C4×Q8C2316yes—
190C2×C4×D4C2316yes—
191C2×C4×D4C2316yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C2313yes—
195C2×C4×D4C2313yes—
196C2×C4×D4C2316yes—
197C2×#117C2316yes—
198C2×#117C2316yes—
199C22×C4⋊C4C2313yes—
200C22×C42C2313yes—
201#401C2316yes—
202#400C2312yes—
203#400C2316yes—
204#400C2316yes—
205#400C2316yes—
206#399C2313yes—
207#399C2316yes—
208#399C23112yes—
209#399C2313yes—
210#399C2316yes—
211#399C2316yes—
212#399C23112yes—
213#399C23112yes—
214#398C2316yes—
215#398C2316yes—
216#398C23112yes—
217#398C2316yes—
218#398C2316yes—
219#397C2312yes—
220#397C2316yes—
221#397C2316yes—
222#397C2316yes—
223#397C2316yes—
224#397C2316yes—
225#397C2316yes—
226#397C23112yes—
227#397C23112yes—
228#397C2316yes—
229#397C2316yes—
230#397C23112yes—
231#396C23112yes—
232#396C23112yes—
233#396C23112yes—
234#396C2316yes—
235#396C2316yes—
236#396C2316yes—
237#396C2316yes—
238#396C23112yes—
239#396C2316yes—
240#396C23112yes—
241#396C23112yes—
242#396C23112yes—
243#395C2313yes—
244#395C2316yes—
245#394C2313yes—
246#394C23112yes—
247#394C2312yes—
248#394C2312yes—
249#394C2316yes—
250#394C2316yes—
251#394C2316yes—
252#394C2316yes—
253#394C2316yes—
254#394C2316yes—
255#394C2316yes—
256#394C2316yes—
257#394C2316yes—
258#394C23112yes—
259#394C23112yes—
260#394C23112yes—
261#394C23112yes—
262#394C2316yes—
263#394C23112yes—
264#394C23112yes—
265#394C2316yes—
266#394C23112yes—
267#393C2312yes—
268#393C2311yescharacteristic
269#392C2311yescharacteristic
270#392C2316yes—
271#392C2316yes—
272#392C2316yes—
273#392C2316yes—
274#392C2313yes—
275#392C2313yes—
276#392C2316yes—
277#392C2316yes—
278#392C2316yes—
279#391C2316yes—
280#391C2316yes—
281#391C2316yes—
282#390C2316yes—
283#390C23112yes—
284#390C23112yes—
285#390C2316yes—
286#390C2316yes—
287#390C2316yes—
288#390C2316yes—
289#390C2316yes—
290#390C2316yes—
291#390C2316yes—
292#390C2316yes—
293#390C2316yes—
294#390C23112yes—
295#390C2316yes—
296#389C2316yes—
297#389C23112yes—
298#389C23112yes—
299#389C2316yes—
300#389C2316yes—
301#389C2316yes—
302#389C2316yes—
303#389C2316yes—
304#389C2316yes—
305#388C2316yes—
306#388C2316yes—
307#388C2316yes—
308#388C23112yes—
309#388C23112yes—
310#388C23112yes—
311#388C23112yes—
312#388C23112yes—
313#388C23112yes—
314#388C23112yes—
315#388C23112yes—
316#388C23112yes—
317#388C23112yes—
318#388C23112yes—
319#388C23112yes—
320#387C2316yes—
321#387C23112yes—
322#387C23112yes—
323#386C2312yes—
324#386C2313yes—
325#386C2316yes—
326#386C23112yes—
327#385C2311yescharacteristic
328#384C2316yes—
329#384C2316yes—
330#384C2316yes—
331#382C2316yes—
332#381C2313yes—
333#380C2316yes—
334#380C2313yes—
335#380C2316yes—
336#380C2316yes—
337#380C2316yes—
338#380C2316yes—
339#380C2313yes—
340#380C2316yes—
341#379C23112yes—
342#379C23112yes—
343#379C23112yes—
344#379C23112yes—
345#379C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2316yes—
349C4×C4⋊C4C2316yes—
350C4×C4⋊C4C2313yes—
351C4×C22⋊C4C2313yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2313yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C2316yes—
358#376C2313yes—
359C25C2416yes—
360H(5,𝔽2)—464no—
361C2×#41—28no—
362C2×#41—24no—
363C2×#41—28no—
364C2×#41—28no—
365C2×#41—28no—
366C2×#41—46no—
367C2×#41—412no—
368C22×Q8—24no—
369C22×Q8—28no—
370C22×Q8—28no—
371C22×Q8—28no—
372C22×Q8—28no—
373C22×Q8C2413yes—
374C22×Q8C2416yes—
375C22×Q8C2411yescharacteristic
376C22×Q8C2411yescharacteristic
377C22×D4—46no—
378C22×D4—412no—
379C22×D4—412no—
380C22×D4—412no—
381C22×D4—412no—
382C22×D4C2416yes—
383C22×D4C2413yes—
384C22×D4C2412yes—
385C22×D4C2416yes—
386C22×D4C2413yes—
387C22×D4C2411yescharacteristic
388C22×D4C2416yes—
389C22×D4C2416yes—
390C22×D4C2416yes—
391C22×D4C2416yes—
392C22×D4C2413yes—
393C23×C4C2413yes—
394C23×C4C2416yes—
395C23×C4C2416yes—
396C23×C4C2413yes—
397C23×C4C2413yes—
398C23×C4C2411yescharacteristic
399C4⋊Q8—46no—
400C4⋊Q8—412no—
401#126—812no—
402#124—412no—
403#124—412no—
404#124—412no—
405#124—46no—
406#124—412no—
407#123—46no—
408#123—86no—
409C22⋊Q8—412no—
410C22⋊Q8—412no—
411C22⋊Q8—412no—
412C22⋊Q8—412no—
413C22⋊Q8—46no—
414C22⋊Q8—412no—
415C22⋊Q8—412no—
416C22⋊Q8—412no—
417#121—412no—
418#121—412no—
419#121—412no—
420#121—46no—
421#121—412no—
422#121—412no—
423#120—412no—
424#120—812no—
425C4×Q8—28no—
426C4×Q8—28no—
427C4×Q8—28no—
428C4×Q8—24no—
429C4×Q8—28no—
430C4×Q8—412no—
431C4×Q8—412no—
432C4×Q8—412no—
433C4×D4—412no—
434C4×D4—412no—
435C4×D4—412no—
436C4×D4—46no—
437C4×D4—412no—
438C4×D4—46no—
439C4×D4—412no—
440#117—412no—
441#117—412no—
442C2×C4⋊C4—46no—
443C2×C4⋊C4C2416yes—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2416yes—
447C2×C4⋊C4C2413yes—
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2416yes—
452C2×C4⋊C4C2413yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2413yes—
457C2×C4⋊C4C2416yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C24112yes—
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C24112yes—
462C2×C4⋊C4C2416yes—
463C2×C4⋊C4C2416yes—
464C2×C4⋊C4C2416yes—
465C2×C4⋊C4C2412yes—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C24112yes—
468C2×C22⋊C4C2411yescharacteristic
469C2×C22⋊C4C2416yes—
470C2×C22⋊C4C2412yes—
471C2×C22⋊C4C2412yes—
472C2×C22⋊C4C2411yescharacteristic
473C2×C22⋊C4C2412yes—
474C2×C22⋊C4C2412yes—
475C2×C22⋊C4C2412yes—
476C2×C22⋊C4C2416yes—
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2413yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C24112yes—
485C2×C22⋊C4C24112yes—
486C2×C22⋊C4C24112yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C24112yes—
489C2×C22⋊C4C24112yes—
490C2×C22⋊C4C24112yes—
491C2×C22⋊C4C24112yes—
492C2×C22⋊C4C24112yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2416yes—
495C2×C22⋊C4C2416yes—
496C2×C22⋊C4C2413yes—
497C2×C22⋊C4C2416yes—
498C2×C22⋊C4C2416yes—
499C2×C22⋊C4C2412yes—
500C2×C22⋊C4C2416yes—
501C2×C22⋊C4C2416yes—
502C2×C22⋊C4C2416yes—
503C2×C22⋊C4C2416yes—
504C2×C22⋊C4C2416yes—
505C2×C22⋊C4C2416yes—
506C2×C42—46no—
507C2×C42C2416yes—
508C2×C42C2416yes—
509C2×C42C2413yes—
510C2×C42C2416yes—
511C2×C42C2416yes—
512C2×C42C24112yes—
513C2×C42C2416yes—
514C2×C42C2416yes—
515#95C2411yescharacteristic
516#95C2416yes—
517#95C2413yes—
518#95C2412yes—
519#95C2412yes—
520#95C2412yes—
521#95C2412yes—
522#95C2411yescharacteristic
523#95C2416yes—
524#95C2416yes—
525#95C2413yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C2416yes—
530#95C2416yes—
531#95C2412yes—
532#95C2416yes—
533#95C2416yes—
534#95C2416yes—
535#95C2416yes—
536#95C2416yes—
537#95C24112yes—
538#95C2416yes—
539#95C24112yes—
540C24—46no—
541C24—412no—
542C24—46no—
543C24—46no—
544C24—412no—
545C24C2513yes—
546C24C2516yes—
547C24C2512yes—
548C24C2511yescharacteristic
549#41—448no—
550#41—432no—
551#41—416no—
552C2×Q8—26no—
553C2×Q8—212no—
554C2×Q8—212no—
555C2×Q8—212no—
556C2×Q8—212no—
557C2×Q8—41no—
558C2×Q8—42no—
559C2×Q8—416no—
560C2×Q8—432no—
561C2×Q8H(5,𝔽2)14yes—
562C2×Q8H(5,𝔽2)18yes—
563C2×D4—24no—
564C2×D4—212no—
565C2×D4—26no—
566C2×D4—212no—
567C2×D4—26no—
568C2×D4—212no—
569C2×D4—212no—
570C2×D4—212no—
571C2×D4—42no—
572C2×D4—41no—
573C2×D4—46no—
574C2×D4—43no—
575C2×D4—46no—
576C2×D4—46no—
577C2×D4—46no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—46no—
581C2×D4—46no—
582C2×D4—46no—
583C2×D4—43no—
584C2×D4—46no—
585C2×D4—46no—
586C2×D4—46no—
587C2×D4—46no—
588C2×D4—46no—
589C2×D4—43no—
590C2×D4—46no—
591C2×D4—46no—
592C2×D4—46no—
593C2×D4—448no—
594C2×D4—496no—
595C22×C4—26no—
596C22×C4—26no—
597C22×C4—212no—
598C22×C4—212no—
599C22×C4—212no—
600C22×C4—212no—
601C22×C4—212no—
602C22×C4—26no—
603C22×C4—212no—
604C22×C4—212no—
605C22×C4—212no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—43no—
609C22×C4—43no—
610C22×C4C2512yes—
611C22×C4C2511yescharacteristic
612C22×C4C2511yescharacteristic
613C22×C4C2512yes—
614C22×C4C2512yes—
615C22×C4C2516yes—
616C22×C4C2512yes—
617C22×C4C2516yes—
618C22×C4C2516yes—
619C22×C4C2516yes—
620C22×C4C2512yes—
621C22×C4C2513yes—
622C22×C4C2516yes—
623C22×C4C2513yes—
624C22×C4C2513yes—
625C4⋊C4—212no—
626C4⋊C4—212no—
627C4⋊C4—212no—
628C4⋊C4—212no—
629C4⋊C4—26no—
630C4⋊C4—46no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—412no—
634C4⋊C4—46no—
635C4⋊C4—46no—
636C4⋊C4—46no—
637C4⋊C4—46no—
638C4⋊C4—46no—
639C4⋊C4—43no—
640C4⋊C4—46no—
641C4⋊C4—43no—
642C4⋊C4—46no—
643C4⋊C4—46no—
644C4⋊C4—412no—
645C4⋊C4—46no—
646C4⋊C4—46no—
647C4⋊C4—412no—
648C4⋊C4—46no—
649C4⋊C4—46no—
650C22⋊C4—22no—
651C22⋊C4—42no—
652C22⋊C4—46no—
653C22⋊C4—46no—
654C22⋊C4—46no—
655C22⋊C4—46no—
656C22⋊C4—46no—
657C22⋊C4—46no—
658C22⋊C4—42no—
659C22⋊C4—46no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—41no—
664C22⋊C4—42no—
665C22⋊C4—46no—
666C22⋊C4—46no—
667C22⋊C4—46no—
668C22⋊C4—46no—
669C22⋊C4—46no—
670C22⋊C4—46no—
671C22⋊C4—43no—
672C22⋊C4—46no—
673C22⋊C4—46no—
674C22⋊C4—412no—
675C22⋊C4—412no—
676C22⋊C4—412no—
677C22⋊C4—412no—
678C22⋊C4—46no—
679C22⋊C4—46no—
680C22⋊C4—412no—
681C22⋊C4—412no—
682C22⋊C4—412no—
683C22⋊C4—412no—
684C22⋊C4—46no—
685C22⋊C4—46no—
686C22⋊C4—43no—
687C22⋊C4—46no—
688C42—212no—
689C42—212no—
690C42—212no—
691C42—26no—
692C42—212no—
693C42—46no—
694C42—412no—
695C42—46no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—26no—
704C23—23no—
705C23—26no—
706C23—26no—
707C23—26no—
708C23—23no—
709C23—22no—
710C23—26no—
711C23—26no—
712C23—23no—
713C23—22no—
714C23—26no—
715C23—26no—
716C23—22no—
717C23—26no—
718C23—22no—
719C23—424no—
720C23—166no—
721C23—1612no—
722C23—166no—
723C23—1612no—
724C23#58512yes—
725C23C2611yescharacteristic
726Q8—44no—
727Q8—412no—
728Q8—424no—
729Q8#560116yes—
730D4—48no—
731D4—44no—
732D4—424no—
733D4—412no—
734D4—412no—
735D4—424no—
736D4—86no—
737D4—812no—
738D4—812no—
739D4—812no—
740D4—812no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—26no—
749C2×C4—26no—
750C2×C4—23no—
751C2×C4—23no—
752C2×C4—26no—
753C2×C4—26no—
754C2×C4—26no—
755C2×C4—26no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—26no—
763C2×C4—23no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—23no—
768C2×C4—26no—
769C2×C4—26no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—26no—
780C2×C4—44no—
781C2×C4—412no—
782C2×C4—424no—
783C2×C4—412no—
784C2×C4—424no—
785C2×C4—86no—
786C2×C4C2×H(5,𝔽2)16yes—
787C2×C4C2×H(5,𝔽2)112yes—
788C22—22no—
789C22—24no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—42no—
794C22—46no—
795C22—43no—
796C22—42no—
797C22—42no—
798C22—46no—
799C22—46no—
800C22—46no—
801C22—42no—
802C22—43no—
803C22—46no—
804C22—42no—
805C22—46no—
806C22—42no—
807C22—46no—
808C22—46no—
809C22—42no—
810C22—43no—
811C22—46no—
812C22—1624no—
813C22C22×H(5,𝔽2)11yescharacteristic
814C22C22×H(5,𝔽2)12yes—
815C22C2×#58511yescharacteristic
816C22H(7,𝔽2)11yescharacteristic
817C222−1+612yes—
818C4—42no—
819C4—41no—
820C4—42no—
821C4—46no—
822C4—46no—
823C4—46no—
824C4—43no—
825C4—42no—
826C4—42no—
827C4—46no—
828C4—42no—
829C4—41no—
830C4—43no—
831C4—46no—
832C4C2×#560112yes—
833C2—42no—
834C2—82no—
835C2—83no—
836C2—86no—
837C2C22×#56011yescharacteristic
838C2#6289911yescharacteristic
839C2#6291912yes—
840C2#6304811yescharacteristic
841C2#6305212yes—
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. #53129C2semidirect
2. #53103C2semidirect
3. #53045C2semidirect
4. #53043C2semidirect
5. #53018C2semidirect
6. #53007C2semidirect
7. #52981C2semidirect
8. #45697C2semidirect
9. #45642C2semidirect
10. #36677C2semidirect
11. #36483C2semidirect
12. #36434C2semidirect
13. #36082C2semidirect
14. #36082C2semidirect
15. #35927C2semidirect
16. #35898C2semidirect
17. #35801C2semidirect
18. #35771C2semidirect
19. #35771C2semidirect
21. C2×D4×Q8C22semidirect
22. C2×D4×Q8C22semidirect
28. C2×#519C22semidirect
29. C22×C4×Q8C22semidirect
30. #2854C22semidirect
31. #2850C22semidirect
32. #2842C22semidirect
33. #2841C22semidirect
34. #2838C22semidirect
35. #2837C22semidirect
36. #2837C22semidirect
37. #2837C22semidirect
38. #2829C22semidirect
39. #2829C22semidirect
40. #2829C22semidirect
41. #2828C22semidirect
42. #2826C22semidirect
43. #2825C22semidirect
44. #2824C22semidirect
45. #2823C22semidirect
46. #2815C22semidirect
47. #2813C22semidirect
48. #2812C22semidirect
49. #2803C22semidirect
50. #2801C22semidirect
51. #2795C22semidirect
52. #2792C22semidirect
53. #2752C22semidirect
54. #2735C22semidirect
55. #2735C22semidirect
56. #2735C22semidirect
57. #2705C22semidirect
58. #2697C22semidirect
59. #2685C22semidirect
60. #2685C22semidirect
61. #2678C22semidirect
62. #2658C22semidirect
63. #2644C22semidirect
64. #2624C22semidirect
65. #2620C22semidirect
66. #2620C22semidirect
69. #2545C22semidirect
70. #2545C22semidirect
71. #2545C22semidirect
72. #2542C22semidirect
73. #2542C22semidirect
74. #2540C22semidirect
75. #2540C22semidirect
76. #2538C22semidirect
77. #2538C22semidirect
78. #2536C22semidirect
79. #2513C22semidirect
80. #2512C22semidirect
81. #2512C22semidirect
82. #2501C22semidirect
83. #2500C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2494C22semidirect
87. #2486C22semidirect
88. #2485C22semidirect
89. #2448C22semidirect
90. #2448C22semidirect
91. #2448C22semidirect
97. #2429C22semidirect
98. #2429C22semidirect
99. #2429C22semidirect
100. #2426C22semidirect
101. #2426C22semidirect
102. #2426C22semidirect
103. #2423C22semidirect
104. #2423C22semidirect
105. #2421C22semidirect
106. #2417C22semidirect
107. #2416C22semidirect
108. #2415C22semidirect
109. #2415C22semidirect
110. #2414C22semidirect
111. #2414C22semidirect
117. #2401C22semidirect
118. #2397C22semidirect
119. #2395C22semidirect
120. #2392C22semidirect
121. #2392C22semidirect
124. #2375C22semidirect
125. #2351C22semidirect
126. Q8×C4⋊C4C22semidirect
127. Q8×C4⋊C4C22semidirect
133. Q8×C22⋊C4C22semidirect
134. Q8×C22⋊C4C22semidirect
135. C4×#123C22semidirect
136. C4×#121C22semidirect
137. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#531292
#531032
#530452
#530432
#530182
#530072
#529812
#456972
#456422
#366772
#364832
#364342
#360822
#359272
#358982
#358012
#357712