Finite Group Databasebeta

← #7662423

Subgroups — #7662423

Order 512.

5482 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52244C213yesmaximal, complemented
2#42983C213yesmaximal, complemented
3#42982C213yesmaximal, complemented
4#42858C216yesmaximal, complemented
5#42857C216yesmaximal, complemented
6#40218C216yesmaximal, complemented
7#39908C216yesmaximal, complemented
8#39222C216yesmaximal, complemented
9#37381C213yesmaximal, complemented
10#37371C216yesmaximal, complemented
11#36578C212yesmaximal, complemented
12#36434C212yesmaximal, complemented
13#36428C212yesmaximal, complemented
14#36059C212yesmaximal, complemented
15#35948C212yesmaximal, complemented
16#35711C211yesmaximal, characteristic, complemented
17#35700C211yesmaximal, characteristic, complemented
18#34291C212yesmaximal, complemented
19#34174C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×D4×Q8C2212yes—
23C2×D4×Q8C2211yescharacteristic, complemented
24C2×#548C2212yes—
25C2×#548C2212yes—
26C2×#519C2211yescharacteristic
27C2×#519C2211yescharacteristic
28C22×C4×Q8C2212yescomplemented
29#2854C2216yescomplemented
30#2850C2216yescomplemented
31#2848C2216yes—
32#2830C2216yescomplemented
33#2830C2216yescomplemented
34#2808C22112yescomplemented
35#2800C22112yescomplemented
36#2797C22112yescomplemented
37#2788C22112yescomplemented
38#2787C2216yescomplemented
39#2784C2216yescomplemented
40#2771C2213yes—
41#2770C22112yescomplemented
42#2764C2216yes—
43#2760C2211yescharacteristic
44#2750C2216yes—
45#2750C2216yescomplemented
46#2736C2216yes—
47#2736C2213yes—
48#2735C2216yes—
49#2735C22112yes—
50#2710C22112yescomplemented
51#2708C2216yescomplemented
52#2697C2216yes—
53#2684C22112yes—
54#2668C2213yes—
55#2652C22112yescomplemented
56#2651C22112yescomplemented
57#2648C22112yescomplemented
58#2644C2216yescomplemented
59#2640C2216yescomplemented
60#2628C2213yes—
61#2621C2213yes—
62#2593C2216yescomplemented
63#2592C2216yescomplemented
64#2589C22112yescomplemented
65#2581C2213yescomplemented
66#2578C22112yescomplemented
67#2568C2213yescomplemented
68#2555C2216yescomplemented
69#2547C2216yescomplemented
70#2546C2213yescomplemented
71#2545C2216yescomplemented
72#2536C2216yescomplemented
73#2536C2213yescomplemented
74#2513C2216yescomplemented
75#2513C2216yescomplemented
76#2513C2216yescomplemented
77#2504C2216yescomplemented
78#2495C2216yescomplemented
79#2495C2216yescomplemented
80#2495C2216yescomplemented
81#2492C2216yescomplemented
82#2492C2216yescomplemented
83#2491C2216yescomplemented
84#2491C2216yescomplemented
85#2487C2216yescomplemented
86#2451C2216yescomplemented
87#2448C2216yescomplemented
88#2448C2216yescomplemented
89#2439C2216yes—
90#2435C2216yes—
91#2432C2216yes—
92#2432C2216yes—
93#2429C2216yescomplemented
94#2429C2216yescomplemented
95#2426C2216yescomplemented
96#2421C2216yescomplemented
97#2421C2216yescomplemented
98#2417C2216yescomplemented
99#2416C2216yescomplemented
100#2415C2216yes—
101#2408C2216yes—
102#2407C2216yes—
103#2407C2216yes—
104#2401C2216yescomplemented
105#2398C2216yescomplemented
106#2396C2213yes—
107#2392C2213yes—
108#2365C2216yescomplemented
109#2362C2216yes—
110#2360C2216yescomplemented
111#2352C2216yes—
112#2351C2212yescomplemented
113#2351C2211yescharacteristic, complemented
114#2351C2211yescharacteristic, complemented
115#2351C2212yescomplemented
116#2341C2216yes—
117#2341C2216yes—
118#2341C2212yes—
119#2341C2212yes—
120#2341C2212yes—
121#2341C2212yes—
122Q8×C22⋊C4C2212yes—
123Q8×C22⋊C4C2212yescomplemented
124Q8×C22⋊C4C2212yescomplemented
125#2337C22112yescomplemented
126#2327C2216yescomplemented
127#2323C2216yes—
128#2309C2213yes—
129#2309C2213yes—
130C4×C22⋊Q8C2216yescomplemented
131C4×#123C2216yescomplemented
132C4×#121C2216yescomplemented
133C4×#120C2216yes—
134#2290C2216yes—
135#2280C2213yes—
136#2280C2213yes—
137#2276C2212yescomplemented
138C22×#41—28no—
139C22×#41—44no—
140C22×#41—44no—
141C22×#41C2312yes—
142C22×#41C2316yes—
143C23×Q8C2312yes—
144C23×Q8C2311yescharacteristic
145C23×D4C2313yes—
146C24×C4C2313yes—
147Q82—44no—
148D4×Q8—216no—
149D4×Q8—44no—
150#548—48no—
151#548—48no—
152C2×C4⋊Q8C2316yes—
153C2×C4⋊Q8C2313yes—
154C2×C4⋊Q8C2313yes—
155C2×C4⋊Q8C2316yes—
156C2×#124C2316yes—
157C2×#124C23112yes—
158C2×#124C2316yes—
159C2×#123C2316yes—
160C2×C22⋊Q8C2316yes—
161C2×C22⋊Q8C2316yes—
162C2×C22⋊Q8C2316yes—
163C2×C22⋊Q8C2316yes—
164C2×C22⋊Q8C2316yes—
165C2×#121C2316yes—
166C2×#121C2316yes—
167C2×#121C2316yes—
168C2×#120C2316yes—
169#519—44no—
170#519—44no—
171C2×C4×Q8—48no—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2312yes—
174C2×C4×Q8C2311yescharacteristic
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×Q8C2313yes—
179C2×C4×Q8C2316yes—
180C2×C4×Q8C2313yes—
181C2×C4×Q8C2316yes—
182C2×C4×Q8C2313yes—
183C2×C4×Q8C2316yes—
184C2×C4×D4C2316yes—
185C2×C4×D4C2313yes—
186C2×C4×D4C2316yes—
187C2×C4×D4C2316yes—
188C2×#117C2313yes—
189C2×#117C2313yes—
190C2×#117C2313yes—
191C2×#117C2313yes—
192C22×C4⋊C4C2316yes—
193C22×C42C2316yes—
194#401C2312yes—
195#400C2313yes—
196#400C2316yes—
197#400C23112yes—
198#400C2316yes—
199#400C2316yes—
200#400C2316yes—
201#400C2316yes—
202#400C2316yes—
203#399C23112yes—
204#399C2313yes—
205#398C2313yes—
206#398C2316yes—
207#398C23112yes—
208#398C2316yes—
209#398C2316yes—
210#397C2316yes—
211#397C23112yes—
212#397C23112yes—
213#397C23112yes—
214#397C2316yes—
215#397C23112yes—
216#397C2313yes—
217#397C2316yes—
218#397C2316yes—
219#397C23112yes—
220#397C23112yes—
221#397C2316yes—
222#397C2316yes—
223#396C23112yes—
224#396C23112yes—
225#396C2316yes—
226#396C2316yes—
227#396C2316yes—
228#395C2313yes—
229#395C2316yes—
230#394C23112yes—
231#394C23112yes—
232#394C23112yes—
233#394C23112yes—
234#394C2316yes—
235#394C2313yes—
236#394C2316yes—
237#394C2316yes—
238#393C2316yes—
239#393C23112yes—
240#393C2316yes—
241#393C23112yes—
242#393C2311yescharacteristic
243#393C2312yes—
244#392C2311yescharacteristic
245#392C23112yes—
246#391C23112yes—
247#391C2316yes—
248#391C2316yes—
249#391C2316yes—
250#391C2316yes—
251#391C23112yes—
252#391C2316yes—
253#391C2316yes—
254#390C2316yes—
255#390C2316yes—
256#390C2316yes—
257#390C2316yes—
258#390C2316yes—
259#390C2316yes—
260#390C23112yes—
261#390C2316yes—
262#390C2316yes—
263#390C2316yes—
264#390C2316yes—
265#390C2316yes—
266#389C2316yes—
267#389C23112yes—
268#389C2316yes—
269#389C23112yes—
270#389C2316yes—
271#389C2316yes—
272#389C2316yes—
273#389C2316yes—
274#389C2316yes—
275#388C23112yes—
276#388C23112yes—
277#388C2316yes—
278#388C23112yes—
279#388C23112yes—
280#388C23112yes—
281#388C23112yes—
282#388C2316yes—
283#388C23112yes—
284#388C23112yes—
285#388C2316yes—
286#388C23112yes—
287#388C23112yes—
288#388C2316yes—
289#388C2316yes—
290#388C23112yes—
291#388C2316yes—
292#387C23112yes—
293#387C23112yes—
294#387C23112yes—
295#387C23112yes—
296#387C2316yes—
297#387C2316yes—
298#387C2316yes—
299#387C2316yes—
300#386C2316yes—
301#386C23112yes—
302#386C2316yes—
303#386C23112yes—
304#386C2316yes—
305#386C2316yes—
306#386C2316yes—
307#386C2312yes—
308#386C2312yes—
309#386C2312yes—
310#385C23112yes—
311#385C2316yes—
312#385C2316yes—
313#385C23112yes—
314#385C2316yes—
315#385C2316yes—
316#385C2316yes—
317#385C2316yes—
318#383C23112yes—
319#382C2316yes—
320#382C2313yes—
321#382C2316yes—
322#382C2313yes—
323#381C2313yes—
324#381C2312yes—
325#381C2311yescharacteristic
326#380C2316yes—
327#380C2316yes—
328#380C2316yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335#380C2316yes—
336#379C2313yes—
337#379C2316yes—
338#379C2313yes—
339#379C23112yes—
340#379C2316yes—
341C4×C4⋊C4C2313yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C23112yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2313yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2316yes—
349C4×C22⋊C4C23112yes—
350C4×C22⋊C4C23112yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C2316yes—
358#376C2316yes—
359C25C2413yes—
360C2×#41—224no—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—28no—
364C2×#41—412no—
365C2×#41—412no—
366C2×#41—464no—
367C22×Q8—24no—
368C22×Q8—24no—
369C22×Q8—28no—
370C22×Q8—28no—
371C22×Q8—28no—
372C22×Q8#4118yes—
373C22×Q8C2416yes—
374C22×Q8C2413yes—
375C22×Q8C2411yescharacteristic
376C22×Q8C2416yes—
377C22×Q8C2411yescharacteristic
378C22×D4—212no—
379C22×D4—46no—
380C22×D4—46no—
381C22×D4C2416yes—
382C22×D4C2412yes—
383C22×D4C2411yescharacteristic
384C22×D4C2416yes—
385C22×D4C2416yes—
386C22×D4C2416yes—
387C23×C4—212no—
388C23×C4—46no—
389C23×C4—46no—
390C23×C4C2416yes—
391C23×C4C2416yes—
392C23×C4C2413yes—
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2416yes—
396C23×C4C2416yes—
397C4⋊Q8—224no—
398C4⋊Q8—46no—
399C4⋊Q8—412no—
400C4⋊Q8—46no—
401#124—412no—
402#124—412no—
403#124—424no—
404#123—412no—
405C22⋊Q8—224no—
406C22⋊Q8—224no—
407C22⋊Q8—412no—
408C22⋊Q8—412no—
409C22⋊Q8—412no—
410#121—412no—
411#121—412no—
412#121—412no—
413#120—412no—
414C4×Q8—28no—
415C4×Q8—28no—
416C4×Q8—28no—
417C4×Q8—24no—
418C4×Q8—24no—
419C4×Q8—28no—
420C4×Q8—46no—
421C4×Q8—412no—
422C4×Q8—412no—
423C4×Q8—412no—
424C4×Q8—46no—
425C4×Q8—46no—
426C4×D4—224no—
427C4×D4—412no—
428C4×D4—412no—
429C4×D4—46no—
430#117—46no—
431#117—46no—
432#117—46no—
433#117—46no—
434C2×C4⋊C4—412no—
435C2×C4⋊C4C2416yes—
436C2×C4⋊C4C2416yes—
437C2×C4⋊C4C2413yes—
438C2×C4⋊C4C2413yes—
439C2×C4⋊C4C2416yes—
440C2×C4⋊C4C2416yes—
441C2×C4⋊C4C2416yes—
442C2×C4⋊C4C24112yes—
443C2×C4⋊C4C24112yes—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2413yes—
446C2×C4⋊C4C2413yes—
447C2×C4⋊C4C2416yes—
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C2413yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C2413yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C2416yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2416yes—
457C2×C4⋊C4C2416yes—
458C2×C4⋊C4C2416yes—
459C2×C22⋊C4C2416yes—
460C2×C22⋊C4C2416yes—
461C2×C22⋊C4C2416yes—
462C2×C22⋊C4C2416yes—
463C2×C22⋊C4C2411yescharacteristic
464C2×C22⋊C4C2413yes—
465C2×C22⋊C4C2411yescharacteristic
466C2×C22⋊C4C2413yes—
467C2×C22⋊C4C2412yes—
468C2×C22⋊C4C2412yes—
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⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C24112yes—
481C2×C22⋊C4C24112yes—
482C2×C22⋊C4C2412yes—
483C2×C22⋊C4C2412yes—
484C2×C22⋊C4C2412yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C24112yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C24112yes—
490C2×C42—412no—
491C2×C42C2413yes—
492C2×C42C2413yes—
493C2×C42C2416yes—
494C2×C42C2416yes—
495C2×C42C2416yes—
496C2×C42C2416yes—
497C2×C42C2416yes—
498C2×C42C2416yes—
499C2×C42C2416yes—
500C2×C42C2416yes—
501C2×C42C24112yes—
502#95C2412yes—
503#95C2416yes—
504#95C2416yes—
505#95C2416yes—
506#95C2416yes—
507#95C2412yes—
508#95C2416yes—
509#95C2412yes—
510#95C2412yes—
511#95C2412yes—
512#95C2416yes—
513#95C2416yes—
514#95C2416yes—
515#95C24112yes—
516#95C2416yes—
517#95C24112yes—
518#95C2416yes—
519#95C2416yes—
520#95C2416yes—
521#95C2416yes—
522#95C2411yescharacteristic
523#95C2412yes—
524#95C2412yes—
525#95C2411yescharacteristic
526#95C24112yes—
527#95C2416yes—
528#95C2413yes—
529#95C2416yes—
530#95C2413yes—
531#95C24112yes—
532#95C2416yes—
533#95C24112yes—
534#95C2416yes—
535C24—26no—
536C24—43no—
537C24—43no—
538C24—46no—
539C24—46no—
540C24C2516yes—
541C24C2511yescharacteristic
542C24C2512yes—
543#41—496no—
544#41—432no—
545C2×Q8—232no—
546C2×Q8—212no—
547C2×Q8—26no—
548C2×Q8—26no—
549C2×Q8—212no—
550C2×Q8—212no—
551C2×Q8—41no—
552C2×Q8—42no—
553C2×Q8—412no—
554C2×Q8—46no—
555C2×Q8—432no—
556C2×Q8C2×#41112yes—
557C2×Q8C2×#4114yes—
558C2×Q8H(5,𝔽2)14yes—
559C2×Q8H(5,𝔽2)14yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—212no—
566C2×D4—212no—
567C2×D4—212no—
568C2×D4—212no—
569C2×D4—41no—
570C2×D4—46no—
571C2×D4—46no—
572C2×D4—42no—
573C2×D4—448no—
574C2×D4—46no—
575C2×D4—46no—
576C2×D4—46no—
577C2×D4—46no—
578C22×C4—26no—
579C22×C4—26no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—212no—
583C22×C4—212no—
584C22×C4—212no—
585C22×C4—212no—
586C22×C4—212no—
587C22×C4—212no—
588C22×C4—212no—
589C22×C4—42no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—46no—
593C22×C4—46no—
594C22×C4—42no—
595C22×C4—46no—
596C22×C4—46no—
597C22×C4—46no—
598C22×C4—448no—
599C22×C4C2×#41112yes—
600C22×C4C2512yes—
601C22×C4C2512yes—
602C22×C4C2516yes—
603C22×C4C2512yes—
604C22×C4C2511yescharacteristic
605C22×C4C2516yes—
606C22×C4C2516yes—
607C22×C4C2512yes—
608C22×C4C2512yes—
609C22×C4C2516yes—
610C22×C4C2513yes—
611C22×C4C2513yes—
612C22×C4C2511yescharacteristic
613C22×C4C2516yes—
614C22×C4C2513yes—
615C22×C4C2513yes—
616C4⋊C4—212no—
617C4⋊C4—212no—
618C4⋊C4—224no—
619C4⋊C4—212no—
620C4⋊C4—212no—
621C4⋊C4—26no—
622C4⋊C4—26no—
623C4⋊C4—212no—
624C4⋊C4—412no—
625C4⋊C4—46no—
626C4⋊C4—46no—
627C4⋊C4—46no—
628C4⋊C4—46no—
629C4⋊C4—43no—
630C4⋊C4—43no—
631C4⋊C4—46no—
632C4⋊C4—46no—
633C4⋊C4—43no—
634C4⋊C4—46no—
635C4⋊C4—43no—
636C4⋊C4—46no—
637C4⋊C4—46no—
638C4⋊C4—46no—
639C4⋊C4—46no—
640C22⋊C4—212no—
641C22⋊C4—212no—
642C22⋊C4—212no—
643C22⋊C4—212no—
644C22⋊C4—42no—
645C22⋊C4—46no—
646C22⋊C4—46no—
647C22⋊C4—46no—
648C22⋊C4—42no—
649C22⋊C4—412no—
650C22⋊C4—412no—
651C22⋊C4—42no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—43no—
655C22⋊C4—43no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—46no—
659C22⋊C4—46no—
660C22⋊C4—46no—
661C22⋊C4—46no—
662C22⋊C4—46no—
663C22⋊C4—46no—
664C22⋊C4—46no—
665C22⋊C4—412no—
666C22⋊C4—412no—
667C22⋊C4—46no—
668C22⋊C4—46no—
669C22⋊C4—412no—
670C22⋊C4—412no—
671C42—212no—
672C42—212no—
673C42—212no—
674C42—26no—
675C42—26no—
676C42—212no—
677C42—46no—
678C42—46no—
679C42—46no—
680C42—46no—
681C42—412no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—26no—
693C23—26no—
694C23—26no—
695C23—26no—
696C23—26no—
697C23—26no—
698C23—26no—
699C23—412no—
700C23—812no—
701C23—86no—
702C23—86no—
703C23—812no—
704C23C22×#4112yes—
705C23#58514yes—
706C23C2611yescharacteristic
707Q8—224no—
708Q8—44no—
709Q8—424no—
710Q8—166no—
711Q8#538116yes—
712D4—424no—
713D4—48no—
714D4—44no—
715D4—424no—
716D4—812no—
717D4—812no—
718C2×C4—23no—
719C2×C4—23no—
720C2×C4—224no—
721C2×C4—22no—
722C2×C4—26no—
723C2×C4—26no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—26no—
731C2×C4—23no—
732C2×C4—23no—
733C2×C4—26no—
734C2×C4—26no—
735C2×C4—26no—
736C2×C4—26no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—26no—
740C2×C4—26no—
741C2×C4—26no—
742C2×C4—26no—
743C2×C4—26no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—26no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—26no—
753C2×C4—26no—
754C2×C4—26no—
755C2×C4—26no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—424no—
760C2×C4—48no—
761C2×C4—44no—
762C2×C4—424no—
763C2×C4—424no—
764C2×C4—812no—
765C2×C4C22×#4116yes—
766C2×C4C22×#4116yes—
767C2×C4C2×H(5,𝔽2)16yes—
768C2×C4C2×H(5,𝔽2)16yes—
769C22—24no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—22no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—46no—
782C22—46no—
783C22—46no—
784C22—46no—
785C22—46no—
786C22—46no—
787C22—46no—
788C22—824no—
789C22C23×#4111yescharacteristic
790C22C22×H(5,𝔽2)11yescharacteristic
791C22C22×H(5,𝔽2)11yescharacteristic
792C22C2×#58512yes—
793C222−1+612yes—
794C4—26no—
795C4—46no—
796C4—42no—
797C4—41no—
798C4—46no—
799C4—43no—
800C4—43no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—42no—
805C4—46no—
806C4—46no—
807C4—42no—
808C4—46no—
809C4C2×#538112yes—
810C2—44no—
811C2—42no—
812C2—86no—
813C2C22×#53811yescharacteristic
814C2#6289712yes—
815C2#6300512yes—
816C2#6302011yescharacteristic
817C2#6304411yescharacteristic
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. #52244C2semidirect
2. #42983C2semidirect
3. #42982C2semidirect
4. #42858C2semidirect
5. #42857C2semidirect
6. #40218C2semidirect
7. #39908C2semidirect
8. #39222C2semidirect
9. #37381C2semidirect
10. #37371C2semidirect
11. #36578C2semidirect
12. #36434C2semidirect
13. #36428C2semidirect
14. #36059C2semidirect
15. #35948C2semidirect
16. #35711C2semidirect
17. #35700C2semidirect
18. #34291C2semidirect
19. #34174C2semidirect
21. C2×Q82C22semidirect
23. C2×D4×Q8C22semidirect
28. C22×C4×Q8C22semidirect
29. #2854C22semidirect
30. #2850C22semidirect
32. #2830C22semidirect
33. #2830C22semidirect
34. #2808C22semidirect
35. #2800C22semidirect
36. #2797C22semidirect
37. #2788C22semidirect
38. #2787C22semidirect
39. #2784C22semidirect
41. #2770C22semidirect
45. #2750C22semidirect
50. #2710C22semidirect
51. #2708C22semidirect
55. #2652C22semidirect
56. #2651C22semidirect
57. #2648C22semidirect
58. #2644C22semidirect
59. #2640C22semidirect
62. #2593C22semidirect
63. #2592C22semidirect
64. #2589C22semidirect
65. #2581C22semidirect
66. #2578C22semidirect
67. #2568C22semidirect
68. #2555C22semidirect
69. #2547C22semidirect
70. #2546C22semidirect
71. #2545C22semidirect
72. #2536C22semidirect
73. #2536C22semidirect
74. #2513C22semidirect
75. #2513C22semidirect
76. #2513C22semidirect
77. #2504C22semidirect
78. #2495C22semidirect
79. #2495C22semidirect
80. #2495C22semidirect
81. #2492C22semidirect
82. #2492C22semidirect
83. #2491C22semidirect
84. #2491C22semidirect
85. #2487C22semidirect
86. #2451C22semidirect
87. #2448C22semidirect
88. #2448C22semidirect
93. #2429C22semidirect
94. #2429C22semidirect
95. #2426C22semidirect
96. #2421C22semidirect
97. #2421C22semidirect
98. #2417C22semidirect
99. #2416C22semidirect
104. #2401C22semidirect
105. #2398C22semidirect
108. #2365C22semidirect
110. #2360C22semidirect
112. #2351C22semidirect
113. #2351C22semidirect
114. #2351C22semidirect
115. #2351C22semidirect
123. Q8×C22⋊C4C22semidirect
124. Q8×C22⋊C4C22semidirect
125. #2337C22semidirect
126. #2327C22semidirect
130. C4×C22⋊Q8C22semidirect
131. C4×#123C22semidirect
132. C4×#121C22semidirect
137. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#522442
#429832
#429822
#428582
#428572
#402182
#399082
#392222
#373812
#373712
#365782
#364342
#364282
#360592
#359482
#357112
#357002
#342912
#341742