Finite Group Databasebeta

← #7655194

Subgroups — #7655194

Order 512.

6400 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42977C213yesmaximal, complemented
2#42975C213yesmaximal, complemented
3#42923C216yesmaximal, complemented
4#40173C216yesmaximal, complemented
5#40164C216yesmaximal, complemented
6#39405C216yesmaximal, complemented
7#39401C216yesmaximal, complemented
8#37513C213yesmaximal, complemented
9#36458C212yesmaximal, complemented
10#36457C212yesmaximal, complemented
11#36455C212yesmaximal, complemented
12#36433C212yesmaximal, complemented
13#36091C212yesmaximal, complemented
14#36029C211yesmaximal, characteristic, complemented
15#35748C211yesmaximal, characteristic, complemented
16#35007C216yesmaximal, complemented
17#34962C213yesmaximal, complemented
18#34258C211yesmaximal, characteristic, complemented
19C4×#550C212yesmaximal, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×#550C2212yes—
23C2×#550C2212yes—
24C2×#550C2212yes—
25C2×#550C2211yescharacteristic, complemented
26C2×#538C22112yescomplemented
27C2×#520C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2212yescomplemented
30#2860C2216yescomplemented
31#2858C2216yescomplemented
32#2856C2216yescomplemented
33#2854C2216yescomplemented
34#2832C2216yescomplemented
35#2828C2216yescomplemented
36#2753C22112yescomplemented
37#2736C2216yescomplemented
38#2714C22112yescomplemented
39#2696C22112yescomplemented
40#2685C22112yescomplemented
41#2678C22112yescomplemented
42#2676C22112yescomplemented
43#2670C2216yescomplemented
44#2670C2216yescomplemented
45#2668C2216yescomplemented
46#2662C22112yescomplemented
47#2661C22112yescomplemented
48#2635C22112yescomplemented
49#2631C22112yescomplemented
50#2628C2213yescomplemented
51#2619C2213yescomplemented
52#2615C2216yes—
53#2593C2213yescomplemented
54#2586C2211yescharacteristic, complemented
55#2580C2213yescomplemented
56#2574C2216yescomplemented
57#2572C2213yescomplemented
58#2563C2216yescomplemented
59#2555C2216yescomplemented
60#2555C2213yescomplemented
61#2554C2216yescomplemented
62#2548C2216yescomplemented
63#2542C2213yescomplemented
64#2541C2216yescomplemented
65#2541C2213yescomplemented
66#2537C2216yescomplemented
67#2535C2213yescomplemented
68#2518C2216yescomplemented
69#2513C2216yescomplemented
70#2512C2216yescomplemented
71#2512C2216yescomplemented
72#2500C2216yescomplemented
73#2497C2216yescomplemented
74#2496C2216yescomplemented
75#2495C2216yescomplemented
76#2491C2216yescomplemented
77#2491C2216yescomplemented
78#2491C2216yescomplemented
79#2491C2216yescomplemented
80#2485C2216yescomplemented
81#2472C22112yescomplemented
82#2467C2216yescomplemented
83#2459C2216yescomplemented
84#2456C2216yescomplemented
85#2452C2216yescomplemented
86#2445C2216yescomplemented
87#2445C2216yescomplemented
88#2440C2216yescomplemented
89#2433C2216yes—
90#2433C2216yes—
91#2433C2216yes—
92#2428C2216yescomplemented
93#2428C2216yescomplemented
94#2428C2216yescomplemented
95#2424C22112yescomplemented
96#2422C2216yescomplemented
97#2420C2216yescomplemented
98#2416C2216yescomplemented
99#2414C2216yescomplemented
100#2414C2216yescomplemented
101#2408C2216yes—
102#2408C2216yes—
103#2408C2216yes—
104#2396C2213yescomplemented
105#2392C2213yescomplemented
106#2388C2216yes—
107#2366C2216yescomplemented
108#2363C2216yescomplemented
109#2363C2216yescomplemented
110#2354C2216yescomplemented
111#2351C2211yescharacteristic, complemented
112#2351C2211yescharacteristic, complemented
113Q8×C4⋊C4C2212yescomplemented
114Q8×C4⋊C4C2212yescomplemented
115#2341C2212yes—
116#2341C2212yes—
117#2341C2212yes—
118#2341C2212yes—
119#2341C2212yes—
120#2341C2212yescomplemented
121#2341C2212yescomplemented
122D4×C22⋊C4C2216yes—
123D4×C22⋊C4C2216yes—
124#2321C22112yescomplemented
125#2311C2213yes—
126#2309C2213yes—
127C4×#127C2216yescomplemented
128C4×#126C2216yescomplemented
129C4×#124C2216yescomplemented
130C4×#123C2216yescomplemented
131C4×#121C2216yescomplemented
132C4×#121C2216yescomplemented
133C4×#121C2216yescomplemented
134#2297C2213yes—
135C2×#390C2213yes—
136C42×Q8C2212yescomplemented
137C42×D4C2216yescomplemented
138C2×H(5,𝔽2)—28no—
139C2×H(5,𝔽2)—44no—
140C2×H(5,𝔽2)—44no—
141C22×#41C2312yes—
142C22×#41C2312yes—
143C22×#41C2311yescharacteristic
144C22×#41C2313yes—
145C23×D4C2313yes—
146C23×D4C2316yes—
147Q82—44no—
148#550—216no—
149#550—48no—
150#550—48no—
151#550—44no—
152#538—448no—
153C2×C4⋊Q8C2316yes—
154C2×C4⋊Q8C2313yes—
155C2×#127C2316yes—
156C2×#127C2316yes—
157C2×#127C2316yes—
158C2×#127C2313yes—
159C2×#126C2316yes—
160C2×#126C23112yes—
161C2×#124C23112yes—
162C2×#124C23112yes—
163C2×#124C2316yes—
164C2×#123C2316yes—
165C2×#123C23112yes—
166C2×C22⋊Q8C23112yes—
167C2×#121C2316yes—
168C2×#121C2316yes—
169C2×#121C2316yes—
170C2×#121C23112yes—
171C2×#121C23112yes—
172C2×#121C2316yes—
173C2×#121C2316yes—
174C2×#121C2316yes—
175C2×#121C2316yes—
176C2×#121C23112yes—
177C2×#121C2316yes—
178C2×#120C23112yes—
179C2×#120C23112yes—
180C2×#120C23112yes—
181#520—44no—
182C4×#41—44no—
183C4×#41—48no—
184C2×C4×Q8C2311yescharacteristic
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2312yes—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2311yescharacteristic
190C2×C4×Q8C2313yes—
191C2×C4×D4C2316yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2316yes—
194C2×C4×D4C23112yes—
195C2×C4×D4C2316yes—
196C2×C4×D4C2316yes—
197C2×C4×D4C2316yes—
198C2×C4×D4C2313yes—
199C2×C4×D4C2313yes—
200C2×C4×D4C2316yes—
201C2×C4×D4C2316yes—
202C2×C4×D4C2313yes—
203C2×#117C2313yes—
204C2×#117C2313yes—
205C2×#117C2316yes—
206C22×C4⋊C4C2313yes—
207C22×C22⋊C4C23112yes—
208C22×C42C2316yes—
209C22×C42C2313yes—
210#400C2313yes—
211#400C23112yes—
212#399C2316yes—
213#399C2313yes—
214#398C2316yes—
215#398C2311yescharacteristic
216#397C23112yes—
217#397C23112yes—
218#397C2313yes—
219#397C23112yes—
220#396C2316yes—
221#396C2316yes—
222#396C23112yes—
223#395C2312yes—
224#395C2316yes—
225#395C2311yescharacteristic
226#394C2313yes—
227#394C23112yes—
228#394C23112yes—
229#394C2316yes—
230#394C23112yes—
231#394C2316yes—
232#394C2316yes—
233#394C2316yes—
234#394C2316yes—
235#394C23112yes—
236#394C23112yes—
237#394C23112yes—
238#394C23112yes—
239#393C23112yes—
240#393C23112yes—
241#393C2316yes—
242#393C2313yes—
243#393C2316yes—
244#392C23112yes—
245#392C23112yes—
246#392C23112yes—
247#392C23112yes—
248#392C2316yes—
249#392C2316yes—
250#392C2316yes—
251#392C2316yes—
252#392C2316yes—
253#392C2313yes—
254#392C23112yes—
255#391C2313yes—
256#391C2311yescharacteristic
257#391C2312yes—
258#390C2316yes—
259#390C2316yes—
260#390C23112yes—
261#390C23112yes—
262#390C23112yes—
263#390C2313yes—
264#390C2316yes—
265#390C2316yes—
266#390C2316yes—
267#390C23112yes—
268#390C2316yes—
269#390C2316yes—
270#390C2316yes—
271#390C2316yes—
272#390C2316yes—
273#390C2316yes—
274#390C2316yes—
275#390C2316yes—
276#390C2316yes—
277#390C2316yes—
278#390C2316yes—
279#390C2316yes—
280#390C2313yes—
281#389C2316yes—
282#389C2312yes—
283#389C2316yes—
284#389C2316yes—
285#389C2316yes—
286#389C2316yes—
287#389C2316yes—
288#388C2316yes—
289#388C2316yes—
290#388C2316yes—
291#388C2316yes—
292#388C23112yes—
293#388C2316yes—
294#388C2316yes—
295#388C2316yes—
296#388C23112yes—
297#388C23112yes—
298#388C23112yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C23112yes—
304#387C2312yes—
305#387C2316yes—
306#387C2316yes—
307#387C2316yes—
308#387C2312yes—
309#386C23112yes—
310#386C2316yes—
311#386C2316yes—
312#386C23112yes—
313#386C23112yes—
314#386C2316yes—
315#386C2316yes—
316#386C23112yes—
317#386C23112yes—
318#386C2316yes—
319#385C2316yes—
320#385C23112yes—
321#384C2316yes—
322#384C2316yes—
323#383C2316yes—
324#382C2316yes—
325#382C2313yes—
326#382C2313yes—
327#381C2316yes—
328#380C2316yes—
329#380C2316yes—
330#380C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335#380C2316yes—
336#379C2316yes—
337#379C2316yes—
338#379C23112yes—
339C4×C4⋊C4C2313yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2312yes—
345C4×C4⋊C4C2313yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C4×C22⋊C4C2316yes—
357C4×C22⋊C4C2316yes—
358C4×C22⋊C4C2316yes—
359C43C2316yes—
360C25C2416yes—
361H(5,𝔽2)—464no—
362C2×#41—28no—
363C2×#41—28no—
364C2×#41—24no—
365C2×#41—24no—
366C2×#41—28no—
367C2×#41—28no—
368C2×#41—28no—
369C2×#41—28no—
370C2×#41—212no—
371C2×#41—46no—
372C2×#41—46no—
373C2×#41#4118yes—
374C22×Q8C2411yescharacteristic
375C22×Q8C2411yescharacteristic
376C22×Q8C2416yes—
377C22×Q8C2411yescharacteristic
378C22×D4—224no—
379C22×D4—212no—
380C22×D4—46no—
381C22×D4—46no—
382C22×D4—412no—
383C22×D4—412no—
384C22×D4C2416yes—
385C22×D4C2416yes—
386C22×D4C2416yes—
387C22×D4C2413yes—
388C22×D4C2416yes—
389C22×D4C24112yes—
390C22×D4C2416yes—
391C22×D4C2416yes—
392C22×D4C2413yes—
393C22×D4C2413yes—
394C22×D4C24112yes—
395C22×D4C24112yes—
396C22×D4C2416yes—
397C23×C4C2416yes—
398C23×C4C2416yes—
399C23×C4C2413yes—
400C23×C4C2416yes—
401C23×C4C2416yes—
402C23×C4C2416yes—
403C23×C4C2416yes—
404C4⋊Q8—46no—
405C4⋊Q8—412no—
406#127—224no—
407#127—412no—
408#127—46no—
409#127—412no—
410#126—224no—
411#126—424no—
412#124—424no—
413#124—424no—
414#124—412no—
415#123—224no—
416#123—424no—
417C22⋊Q8—424no—
418#121—224no—
419#121—224no—
420#121—424no—
421#121—412no—
422#121—424no—
423#121—424no—
424#121—412no—
425#121—412no—
426#121—412no—
427#121—412no—
428#121—412no—
429#120—424no—
430#120—424no—
431#120—424no—
432C4×Q8—28no—
433C4×Q8—28no—
434C4×Q8—28no—
435C4×Q8—24no—
436C4×Q8—24no—
437C4×Q8—28no—
438C4×Q8—46no—
439C4×D4—224no—
440C4×D4—224no—
441C4×D4—412no—
442C4×D4—412no—
443C4×D4—412no—
444C4×D4—412no—
445C4×D4—46no—
446C4×D4—46no—
447C4×D4—424no—
448C4×D4—412no—
449C4×D4—46no—
450C4×D4—412no—
451#117—46no—
452#117—46no—
453#117—412no—
454C2×C4⋊C4—46no—
455C2×C4⋊C4C2413yes—
456C2×C4⋊C4C2413yes—
457C2×C4⋊C4C2416yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C2416yes—
462C2×C4⋊C4C2412yes—
463C2×C4⋊C4C2416yes—
464C2×C4⋊C4C2416yes—
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C2413yes—
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C24112yes—
472C2×C4⋊C4C2416yes—
473C2×C4⋊C4C2416yes—
474C2×C4⋊C4C2413yes—
475C2×C4⋊C4C24112yes—
476C2×C4⋊C4C2412yes—
477C2×C22⋊C4—424no—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C24112yes—
492C2×C22⋊C4C24112yes—
493C2×C22⋊C4C2416yes—
494C2×C22⋊C4C2413yes—
495C2×C22⋊C4C2413yes—
496C2×C22⋊C4C24112yes—
497C2×C22⋊C4C24112yes—
498C2×C22⋊C4C2416yes—
499C2×C22⋊C4C2416yes—
500C2×C22⋊C4C2416yes—
501C2×C22⋊C4C2416yes—
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×C42—46no—
511C2×C42—412no—
512C2×C42C2413yes—
513C2×C42C2413yes—
514C2×C42C2412yes—
515C2×C42C2416yes—
516C2×C42C2416yes—
517C2×C42C2416yes—
518C2×C42C2416yes—
519C2×C42C2416yes—
520C2×C42C2416yes—
521C2×C42C2413yes—
522C2×C42C2416yes—
523C2×C42C2416yes—
524C2×C42C2411yescharacteristic
525C2×C42C2412yes—
526#95C2412yes—
527#95C2412yes—
528#95C2412yes—
529#95C2412yes—
530#95C2412yes—
531#95C2412yes—
532#95C2412yes—
533#95C2416yes—
534#95C2416yes—
535#95C2416yes—
536#95C2416yes—
537#95C2416yes—
538#95C2416yes—
539#95C2416yes—
540#95C2416yes—
541#95C2416yes—
542#95C2411yescharacteristic
543#95C24112yes—
544#95C2411yescharacteristic
545#95C2413yes—
546#95C2413yes—
547#95C2416yes—
548#95C2416yes—
549#95C2416yes—
550#95C2416yes—
551C24—212no—
552C24—46no—
553C24—46no—
554C24—412no—
555C24—412no—
556C24C2516yes—
557C24C2516yes—
558C24C2513yes—
559#41—232no—
560#41—448no—
561#41—432no—
562#41—432no—
563C2×Q8—22no—
564C2×Q8—24no—
565C2×Q8—41no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×Q8—412no—
569C2×Q8—46no—
570C2×Q8C2×#4114yes—
571C2×Q8H(5,𝔽2)14yes—
572C2×Q8H(5,𝔽2)14yes—
573C2×D4—212no—
574C2×D4—212no—
575C2×D4—224no—
576C2×D4—212no—
577C2×D4—26no—
578C2×D4—212no—
579C2×D4—26no—
580C2×D4—26no—
581C2×D4—212no—
582C2×D4—212no—
583C2×D4—212no—
584C2×D4—212no—
585C2×D4—212no—
586C2×D4—212no—
587C2×D4—212no—
588C2×D4—46no—
589C2×D4—43no—
590C2×D4—43no—
591C2×D4—46no—
592C2×D4—46no—
593C2×D4—448no—
594C2×D4—412no—
595C2×D4—46no—
596C2×D4—46no—
597C2×D4—43no—
598C2×D4—412no—
599C2×D4—46no—
600C2×D4—46no—
601C2×D4—46no—
602C2×D4—412no—
603C2×D4—412no—
604C2×D4—412no—
605C2×D4—412no—
606C2×D4—412no—
607C2×D4—412no—
608C2×D4—46no—
609C2×D4—412no—
610C2×D4—496no—
611C2×D4C2×#41112yes—
612C22×C4—26no—
613C22×C4—26no—
614C22×C4—212no—
615C22×C4—212no—
616C22×C4—212no—
617C22×C4—212no—
618C22×C4—212no—
619C22×C4—212no—
620C22×C4—212no—
621C22×C4—212no—
622C22×C4—212no—
623C22×C4—46no—
624C22×C4—46no—
625C22×C4—46no—
626C22×C4—46no—
627C22×C4—46no—
628C22×C4—46no—
629C22×C4—412no—
630C22×C4—46no—
631C22×C4C2×#41112yes—
632C22×C4C2512yes—
633C22×C4C2511yescharacteristic
634C22×C4C2516yes—
635C22×C4C2512yes—
636C22×C4C2511yescharacteristic
637C22×C4C2516yes—
638C22×C4C2516yes—
639C22×C4C2516yes—
640C22×C4C2513yes—
641C22×C4C2513yes—
642C22×C4C2511yescharacteristic
643C22×C4C2512yes—
644C22×C4C2512yes—
645C22×C4C2512yes—
646C22×C4C2512yes—
647C22×C4C2513yes—
648C4⋊C4—24no—
649C4⋊C4—212no—
650C4⋊C4—26no—
651C4⋊C4—26no—
652C4⋊C4—212no—
653C4⋊C4—212no—
654C4⋊C4—212no—
655C4⋊C4—212no—
656C4⋊C4—212no—
657C4⋊C4—212no—
658C4⋊C4—24no—
659C4⋊C4—43no—
660C4⋊C4—41no—
661C4⋊C4—46no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—41no—
665C4⋊C4—412no—
666C4⋊C4—46no—
667C4⋊C4—43no—
668C4⋊C4—412no—
669C4⋊C4H(5,𝔽2)18yescomplemented
670C22⋊C4—212no—
671C22⋊C4—212no—
672C22⋊C4—212no—
673C22⋊C4—212no—
674C22⋊C4—212no—
675C22⋊C4—212no—
676C22⋊C4—212no—
677C22⋊C4—212no—
678C22⋊C4—212no—
679C22⋊C4—212no—
680C22⋊C4—212no—
681C22⋊C4—212no—
682C22⋊C4—212no—
683C22⋊C4—412no—
684C22⋊C4—412no—
685C22⋊C4—43no—
686C22⋊C4—43no—
687C22⋊C4—46no—
688C22⋊C4—412no—
689C22⋊C4—412no—
690C22⋊C4—46no—
691C22⋊C4—46no—
692C22⋊C4—46no—
693C22⋊C4—46no—
694C22⋊C4—46no—
695C22⋊C4—412no—
696C22⋊C4—412no—
697C22⋊C4—412no—
698C22⋊C4—46no—
699C22⋊C4—412no—
700C22⋊C4—46no—
701C22⋊C4—46no—
702C42—212no—
703C42—212no—
704C42—212no—
705C42—26no—
706C42—26no—
707C42—212no—
708C42—212no—
709C42—212no—
710C42—24no—
711C42—41no—
712C42—42no—
713C42—43no—
714C42—46no—
715C42—46no—
716C23—26no—
717C23—23no—
718C23—23no—
719C23—26no—
720C23—26no—
721C23—26no—
722C23—26no—
723C23—26no—
724C23—26no—
725C23—26no—
726C23—26no—
727C23—26no—
728C23—26no—
729C23—26no—
730C23—26no—
731C23—26no—
732C23—26no—
733C23—26no—
734C23—424no—
735C23—824no—
736C23—1612no—
737C23—166no—
738C23—166no—
739C23C22×#4116yes—
740C23C2611yescharacteristic
741Q8—44no—
742Q8—44no—
743Q8—166no—
744Q8#538116yescomplemented
745D4—224no—
746D4—424no—
747D4—412no—
748D4—424no—
749D4—424no—
750D4—424no—
751D4—812no—
752D4—812no—
753D4—824no—
754D4—86no—
755D4—1612no—
756D4—166no—
757D4—1612no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—224no—
769C2×C4—26no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—26no—
775C2×C4—26no—
776C2×C4—26no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—26no—
780C2×C4—23no—
781C2×C4—26no—
782C2×C4—23no—
783C2×C4—22no—
784C2×C4—26no—
785C2×C4—26no—
786C2×C4—26no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—26no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—424no—
796C2×C4—424no—
797C2×C4—812no—
798C2×C4—812no—
799C2×C4—812no—
800C2×C4—166no—
801C2×C4C22×#4112yes—
802C2×C4C22×#4116yes—
803C2×C4C2×H(5,𝔽2)14yes—
804C2×C4C2×H(5,𝔽2)14yes—
805C2×C4C2×H(5,𝔽2)14yes—
806C2×C4C2×H(5,𝔽2)16yes—
807C2×C4C2×H(5,𝔽2)16yes—
808C2×C4#58514yes—
809C22—212no—
810C22—26no—
811C22—46no—
812C22—43no—
813C22—43no—
814C22—46no—
815C22—46no—
816C22—46no—
817C22—46no—
818C22—46no—
819C22—46no—
820C22—46no—
821C22—46no—
822C22—46no—
823C22—46no—
824C22—46no—
825C22—46no—
826C22—46no—
827C22—46no—
828C22—1624no—
829C22C23×#4111yescharacteristic
830C22C22×H(5,𝔽2)11yescharacteristic
831C22C22×H(5,𝔽2)12yes—
832C22C22×H(5,𝔽2)11yescharacteristic
833C22C2×#58512yes—
834C4—24no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—22no—
839C4—46no—
840C4—46no—
841C4—41no—
842C4—41no—
843C4—43no—
844C4—43no—
845C4—46no—
846C4—46no—
847C4—42no—
848C4—42no—
849C4C2×#538112yes—
850C2—46no—
851C2—86no—
852C2—86no—
853C2C22×#53811yescharacteristic
854C2#6280012yes—
855C2#6301412yes—
856C2#6302011yescharacteristic
857C2#6304011yescharacteristic
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. #42977C2semidirect
2. #42975C2semidirect
3. #42923C2semidirect
4. #40173C2semidirect
5. #40164C2semidirect
6. #39405C2semidirect
7. #39401C2semidirect
8. #37513C2semidirect
9. #36458C2semidirect
10. #36457C2semidirect
11. #36455C2semidirect
12. #36433C2semidirect
13. #36091C2semidirect
14. #36029C2semidirect
15. #35748C2semidirect
16. #35007C2semidirect
17. #34962C2semidirect
18. #34258C2semidirect
19. C4×#550C2semidirect
21. C2×Q82C22semidirect
25. C2×#550C22semidirect
26. C2×#538C22semidirect
29. C2×C4×#41C22semidirect
30. #2860C22semidirect
31. #2858C22semidirect
32. #2856C22semidirect
33. #2854C22semidirect
34. #2832C22semidirect
35. #2828C22semidirect
36. #2753C22semidirect
37. #2736C22semidirect
38. #2714C22semidirect
39. #2696C22semidirect
40. #2685C22semidirect
41. #2678C22semidirect
42. #2676C22semidirect
43. #2670C22semidirect
44. #2670C22semidirect
45. #2668C22semidirect
46. #2662C22semidirect
47. #2661C22semidirect
48. #2635C22semidirect
49. #2631C22semidirect
50. #2628C22semidirect
51. #2619C22semidirect
53. #2593C22semidirect
54. #2586C22semidirect
55. #2580C22semidirect
56. #2574C22semidirect
57. #2572C22semidirect
58. #2563C22semidirect
59. #2555C22semidirect
60. #2555C22semidirect
61. #2554C22semidirect
62. #2548C22semidirect
63. #2542C22semidirect
64. #2541C22semidirect
65. #2541C22semidirect
66. #2537C22semidirect
67. #2535C22semidirect
68. #2518C22semidirect
69. #2513C22semidirect
70. #2512C22semidirect
71. #2512C22semidirect
72. #2500C22semidirect
73. #2497C22semidirect
74. #2496C22semidirect
75. #2495C22semidirect
76. #2491C22semidirect
77. #2491C22semidirect
78. #2491C22semidirect
79. #2491C22semidirect
80. #2485C22semidirect
81. #2472C22semidirect
82. #2467C22semidirect
83. #2459C22semidirect
84. #2456C22semidirect
85. #2452C22semidirect
86. #2445C22semidirect
87. #2445C22semidirect
88. #2440C22semidirect
92. #2428C22semidirect
93. #2428C22semidirect
94. #2428C22semidirect
95. #2424C22semidirect
96. #2422C22semidirect
97. #2420C22semidirect
98. #2416C22semidirect
99. #2414C22semidirect
100. #2414C22semidirect
104. #2396C22semidirect
105. #2392C22semidirect
107. #2366C22semidirect
108. #2363C22semidirect
109. #2363C22semidirect
110. #2354C22semidirect
111. #2351C22semidirect
112. #2351C22semidirect
113. Q8×C4⋊C4C22semidirect
114. Q8×C4⋊C4C22semidirect
120. #2341C22semidirect
121. #2341C22semidirect
124. #2321C22semidirect
127. C4×#127C22semidirect
128. C4×#126C22semidirect
129. C4×#124C22semidirect
130. C4×#123C22semidirect
131. C4×#121C22semidirect
132. C4×#121C22semidirect
133. C4×#121C22semidirect
136. C42×Q8C22semidirect
137. C42×D4C22semidirect
669. C4⋊C4H(5,𝔽2)semidirect
744. Q8#538semidirect

Maximal subgroups

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

subgroupindex
#429772
#429752
#429232
#401732
#401642
#394052
#394012
#375132
#364582
#364572
#364552
#364332
#360912
#360292
#357482
#350072
#349622
#342582
C4×#5502