Finite Group Databasebeta

← #7671938

Subgroups — #7671938

Order 512.

6234 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59683C218yesmaximal, complemented
2#59680C214yesmaximal, complemented
3#59678C214yesmaximal, complemented
4#39548C218yesmaximal, complemented
5#39191C214yesmaximal, complemented
6#39185C214yesmaximal, complemented
7#36640C211yesmaximal, characteristic, complemented
8#36498C214yesmaximal, complemented
9#36468C214yesmaximal, complemented
10#36157C218yesmaximal, complemented
11#35557C212yesmaximal, complemented
12#35528C212yesmaximal, complemented
13#35254C212yesmaximal, complemented
14#35165C211yesmaximal, characteristic, complemented
15#35165C211yesmaximal, characteristic, complemented
16#34269C212yesmaximal, complemented
17#34186C211yesmaximal, characteristic, complemented
18#34181C211yesmaximal, characteristic, complemented
19C4×#532C211yesmaximal, characteristic, complemented
20C2×C4×#127C211yesmaximal, characteristic, complemented
21C2×#553C2218yescomplemented
22C2×#535C2212yes—
23C2×#535C2212yes—
24C2×#532C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C2×#518C2212yes—
27C2×C4×#41C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2214yes—
31#2864C2212yescomplemented
32#2864C2212yescomplemented
33#2859C2212yescomplemented
34#2859C2212yescomplemented
35#2854C2218yescomplemented
36#2851C2214yes—
37#2851C2214yes—
38#2847C2214yes—
39#2847C2214yes—
40#2796C22116yescomplemented
41#2753C22116yescomplemented
42#2714C22116yescomplemented
43#2711C22116yescomplemented
44#2624C2218yescomplemented
45#2617C2214yes—
46#2617C2214yes—
47#2602C22116yescomplemented
48#2597C22116yescomplemented
49#2562C2218yescomplemented
50#2559C22116yescomplemented
51#2547C2212yescomplemented
52#2547C2212yescomplemented
53#2544C2218yes—
54#2544C2214yescomplemented
55#2544C2214yescomplemented
56#2541C2218yes—
57#2541C2212yescomplemented
58#2541C2212yescomplemented
59#2537C2214yescomplemented
60#2537C2214yescomplemented
61#2535C2214yescomplemented
62#2535C2214yescomplemented
63#2535C2218yescomplemented
64#2512C2218yescomplemented
65#2511C2218yescomplemented
66#2497C2218yescomplemented
67#2496C2218yescomplemented
68#2487C2218yescomplemented
69#2485C2218yescomplemented
70#2481C22116yes—
71#2467C22116yescomplemented
72#2457C22116yescomplemented
73#2456C22116yescomplemented
74#2448C2218yescomplemented
75#2445C2218yescomplemented
76#2444C22116yescomplemented
77#2428C2218yes—
78#2428C2218yes—
79#2418C22116yes—
80#2416C2218yescomplemented
81#2414C2218yescomplemented
82#2410C22116yes—
83#2367C2218yescomplemented
84#2366C2218yescomplemented
85#2364C22116yescomplemented
86#2358C22116yes—
87#2357C2214yescomplemented
88#2357C2214yescomplemented
89#2354C2214yescomplemented
90#2354C2214yescomplemented
91#2352C2218yescomplemented
92#2349C2214yescomplemented
93#2349C2214yescomplemented
94D4×C4⋊C4C2214yescomplemented
95D4×C4⋊C4C2214yescomplemented
96#2324C2218yescomplemented
97#2316C2212yes—
98#2315C2214yes—
99#2312C2214yes—
100#2311C2212yes—
101#2311C2212yes—
102#2309C2212yes—
103C4×C4⋊Q8C2212yescomplemented
104C4×#127C2212yes—
105C4×#127C2212yes—
106C4×#127C2214yes—
107C4×#127C2214yes—
108C4×#127C2212yes—
109C4×#127C2212yes—
110C4×#127C2212yescomplemented
111C4×#125C2214yescomplemented
112C4×#125C2214yescomplemented
113C4×#124C2214yescomplemented
114C4×#121C2214yes—
115C4×#121C2214yes—
116C4×#121C2218yescomplemented
117#2297C2212yes—
118#2296C2212yes—
119#2296C2212yes—
120#2293C2212yescomplemented
121#2293C2212yescomplemented
122C2×#390C2214yes—
123C2×#390C2211yescharacteristic
124C2×#390C2211yescharacteristic
125#2285C2211yescharacteristic
126#2285C2211yescharacteristic
127#2285C2211yescharacteristic
128C2×#384C2211yescharacteristic
129#2280C2214yes—
130C2×#380C2214yes—
131#2274C2212yes—
132C42×D4C2212yescomplemented
133C42×D4C2212yescomplemented
134C2×C43C2211yescharacteristic
135C22×#41C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2314yes—
139C24×C4C2312yes—
140C24×C4C2312yes—
141#553—432no—
142#535—216no—
143#535—48no—
144#532—28no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#127—28no—
147C2×#127C2312yes—
148C2×#127C2312yes—
149C2×#127C2314yes—
150C2×#127C2311yescharacteristic
151C2×#127C2314yes—
152C2×#127C2314yes—
153C2×#126C23116yes—
154C2×#125C2314yes—
155C2×#125C2314yes—
156C2×#124C2314yes—
157C2×#124C2312yes—
158C2×#124C2314yes—
159C2×#123C23116yes—
160C2×#121C2318yes—
161C2×#121C2312yes—
162C2×#121C2312yes—
163C2×#121C2318yes—
164C2×#121C2318yes—
165C2×#121C2318yes—
166C2×#121C23116yes—
167C2×#121C23116yes—
168C2×#120C2318yes—
169C2×#120C2318yes—
170#518—48no—
171C4×#41—48no—
172C2×C4×Q8C2314yes—
173C2×C4×D4—28no—
174C2×C4×D4—28no—
175C2×C4×D4—416no—
176C2×C4×D4C2318yes—
177C2×C4×D4C2312yes—
178C2×C4×D4C2312yes—
179C2×C4×D4C2312yes—
180C2×C4×D4C2312yes—
181C2×C4×D4C2312yes—
182C2×C4×D4C2312yes—
183C2×C4×D4C2312yes—
184C2×C4×D4C2312yes—
185C2×C4×D4C2314yes—
186C2×C4×D4C2312yes—
187C2×C4×D4C2312yes—
188C2×C4×D4C2318yes—
189C2×C4×D4C2318yes—
190C2×C4×D4C2318yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C23116yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2318yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2314yes—
201C2×#117C2318yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2318yes—
205C22×C4⋊C4C2314yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2318yes—
209C22×C22⋊C4C2314yes—
210C22×C22⋊C4C2314yes—
211C22×C42C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2314yes—
216C22×C42C2311yescharacteristic
217#400C23116yes—
218#400C23116yes—
219#399C23116yes—
220#397C2318yes—
221#397C2318yes—
222#397C23116yes—
223#397C23116yes—
224#396C23116yes—
225#394C23116yes—
226#394C23116yes—
227#394C23116yes—
228#394C23116yes—
229#394C23116yes—
230#394C23116yes—
231#392C23116yes—
232#392C2318yes—
233#392C2318yes—
234#392C23116yes—
235#391C2314yes—
236#391C2314yes—
237#391C2314yes—
238#390C2312yes—
239#390C2318yes—
240#390C2312yes—
241#390C2318yes—
242#390C2314yes—
243#390C2312yes—
244#390C2314yes—
245#390C2318yes—
246#390C2318yes—
247#390C2312yes—
248#390C2314yes—
249#390C2314yes—
250#390C2314yes—
251#390C2318yes—
252#390C2318yes—
253#390C2314yes—
254#390C2314yes—
255#390C23116yes—
256#389C2314yes—
257#389C2314yes—
258#389C2314yes—
259#389C2314yes—
260#389C2314yes—
261#389C2314yes—
262#389C2318yes—
263#389C2318yes—
264#389C2314yes—
265#389C2314yes—
266#389C2314yes—
267#389C2314yes—
268#388C23116yes—
269#388C23116yes—
270#388C23116yes—
271#388C23116yes—
272#388C23116yes—
273#388C23116yes—
274#388C23116yes—
275#388C2318yes—
276#388C2318yes—
277#387C2318yes—
278#387C2318yes—
279#387C2318yes—
280#387C2318yes—
281#387C23116yes—
282#387C23116yes—
283#386C2318yes—
284#386C2318yes—
285#386C23116yes—
286#386C23116yes—
287#386C23116yes—
288#386C23116yes—
289#386C23116yes—
290#386C23116yes—
291#386C23116yes—
292#386C2318yes—
293#385C23116yes—
294#385C23116yes—
295#385C23116yes—
296#385C2318yes—
297#385C2318yes—
298#384C2312yes—
299#384C2312yes—
300#384C2314yes—
301#384C2312yes—
302#384C2312yes—
303#384C2312yes—
304#382C2314yes—
305#382C2314yes—
306#382C2312yes—
307#382C2312yes—
308#382C2312yes—
309#381C2318yes—
310#380C2318yes—
311#380C2318yes—
312#380C2318yes—
313#380C2318yes—
314#380C2318yes—
315#380C2318yes—
316#380C2312yes—
317#380C2312yes—
318#380C2312yes—
319#380C2318yes—
320#380C2312yes—
321#380C2312yes—
322#380C2318yes—
323#380C2312yes—
324#379C2318yes—
325C4×C4⋊C4C2312yes—
326C4×C4⋊C4C2312yes—
327C4×C4⋊C4C2312yes—
328C4×C4⋊C4C2312yes—
329C4×C4⋊C4C2318yes—
330C4×C4⋊C4C2318yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2318yes—
334C4×C4⋊C4C2312yes—
335C4×C4⋊C4C2312yes—
336C4×C4⋊C4C2318yes—
337C4×C22⋊C4C2318yes—
338C4×C22⋊C4C23116yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C2318yes—
341C4×C22⋊C4C2318yes—
342C4×C22⋊C4C2314yes—
343C4×C22⋊C4C2314yes—
344C2×#95C2318yes—
345C43C2312yes—
346C43C2312yes—
347C43C2311yescharacteristic
348C43C2311yescharacteristic
349C43C2311yescharacteristic
350C43C2311yescharacteristic
351C25C2412yes—
352C25C2412yes—
353C2×#41—28no—
354C2×#41—28no—
355C2×#41—28no—
356C22×Q8C2412yes—
357C22×D4—216no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—48no—
364C22×D4—48no—
365C22×D4#4118yes—
366C22×D4C2412yes—
367C22×D4C2414yes—
368C22×D4C2412yes—
369C22×D4C2412yes—
370C22×D4C2412yes—
371C22×D4C2418yes—
372C22×D4C2418yes—
373C22×D4C2412yes—
374C22×D4C2412yes—
375C22×D4C2412yes—
376C22×D4C24116yes—
377C22×D4C24116yes—
378C23×C4—28no—
379C23×C4—28no—
380C23×C4—48no—
381C23×C4—48no—
382C23×C4C2414yes—
383C23×C4C2412yes—
384C23×C4C2414yes—
385C23×C4C2414yes—
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2418yes—
391C23×C4C2414yes—
392C23×C4C2414yes—
393C23×C4C24116yes—
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C4⋊Q8—24no—
397#127—28no—
398#127—28no—
399#127—216no—
400#127—216no—
401#127—24no—
402#127—48no—
403#126—432no—
404#125—216no—
405#125—48no—
406#124—216no—
407#124—28no—
408#124—48no—
409#123—432no—
410#121—232no—
411#121—28no—
412#121—28no—
413#121—432no—
414#121—432no—
415#121—416no—
416#121—416no—
417#121—416no—
418#120—232no—
419#120—416no—
420C4×Q8—48no—
421C4×D4—28no—
422C4×D4—28no—
423C4×D4—28no—
424C4×D4—28no—
425C4×D4—28no—
426C4×D4—28no—
427C4×D4—28no—
428C4×D4—28no—
429C4×D4—28no—
430C4×D4—28no—
431C4×D4—232no—
432C4×D4—216no—
433C4×D4—416no—
434C4×D4—48no—
435C4×D4—416no—
436C4×D4—48no—
437C4×D4—416no—
438C4×D4—416no—
439C4×D4—416no—
440C4×D4—432no—
441C4×D4—416no—
442#117—28no—
443#117—28no—
444#117—28no—
445#117—48no—
446#117—416no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—48no—
450C2×C4⋊C4—416no—
451C2×C4⋊C4C2414yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2418yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2412yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2412yes—
464C2×C4⋊C4C2412yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C24116yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2418yes—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—28no—
476C2×C22⋊C4—48no—
477C2×C22⋊C4—48no—
478C2×C22⋊C4—416no—
479C2×C22⋊C4C2414yes—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2414yes—
487C2×C22⋊C4C2414yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C24116yes—
493C2×C22⋊C4C24116yes—
494C2×C22⋊C4C2418yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C24116yes—
498C2×C22⋊C4C24116yes—
499C2×C22⋊C4C24116yes—
500C2×C22⋊C4C24116yes—
501C2×C22⋊C4C24116yes—
502C2×C42—24no—
503C2×C42—24no—
504C2×C42—28no—
505C2×C42—48no—
506C2×C42—44no—
507C2×C42#4118yes—
508C2×C42C2411yescharacteristic
509C2×C42C2414yes—
510C2×C42C2414yes—
511C2×C42C2414yes—
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2412yes—
515C2×C42C2412yes—
516C2×C42C2412yes—
517C2×C42C2412yes—
518C2×C42C2411yescharacteristic
519C2×C42C2411yescharacteristic
520C2×C42C2412yes—
521C2×C42C2411yescharacteristic
522C2×C42C24116yes—
523C2×C42C2418yes—
524C2×C42C2412yes—
525C2×C42C2412yes—
526C2×C42C2411yescharacteristic
527C2×C42C2411yescharacteristic
528C2×C42C2411yescharacteristic
529C2×C42C2411yescharacteristic
530C2×C42C2412yes—
531#95C2414yes—
532#95C2414yes—
533#95C24116yes—
534#95C2414yes—
535#95C2414yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C24116yes—
540#95C24116yes—
541#95C2414yes—
542#95C2414yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C24116yes—
547C24—24no—
548C24—24no—
549C24—24no—
550C24—24no—
551C24—24no—
552C24—44no—
553C24—44no—
554C24—44no—
555C24—44no—
556C24C2×#4118yes—
557C24C2514yes—
558C24C2514yes—
559C24C2514yes—
560C24C2511yescharacteristic
561#41—432no—
562C2×Q8—24no—
563C2×Q8—24no—
564C2×Q8—24no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—216no—
568C2×D4—216no—
569C2×D4—28no—
570C2×D4—232no—
571C2×D4—232no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—216no—
585C2×D4—28no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—216no—
590C2×D4—48no—
591C2×D4—44no—
592C2×D4—48no—
593C2×D4—464no—
594C2×D4—416no—
595C2×D4—416no—
596C2×D4—416no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4C2×#4118yes—
601C2×D4C2×#4118yes—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—28no—
612C22×C4—28no—
613C22×C4—24no—
614C22×C4—28no—
615C22×C4—216no—
616C22×C4—216no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—216no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—48no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—416no—
629C22×C4—416no—
630C22×C4—416no—
631C22×C4—816no—
632C22×C4—816no—
633C22×C4C2×#4114yes—
634C22×C4C2×#4114yes—
635C22×C4C2×#4114yes—
636C22×C4C2×#4114yes—
637C22×C4H(5,𝔽2)14yes—
638C22×C4C2514yes—
639C22×C4C2518yes—
640C22×C4C2518yes—
641C22×C4C2514yes—
642C22×C4C2518yes—
643C22×C4C2514yes—
644C22×C4C2512yes—
645C22×C4C2511yescharacteristic
646C22×C4C2511yescharacteristic
647C22×C4C2511yescharacteristic
648C22×C4C2512yes—
649C22×C4C2512yes—
650C22×C4C2512yes—
651C22×C4C2511yescharacteristic
652C22×C4C2511yescharacteristic
653C22×C4C2511yescharacteristic
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—28no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—216no—
664C4⋊C4—28no—
665C4⋊C4—28no—
666C4⋊C4—28no—
667C4⋊C4—216no—
668C4⋊C4—216no—
669C4⋊C4—216no—
670C4⋊C4—48no—
671C4⋊C4—416no—
672C4⋊C4—48no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—48no—
677C22⋊C4—28no—
678C22⋊C4—232no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—216no—
688C22⋊C4—216no—
689C22⋊C4—216no—
690C22⋊C4—216no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4—416no—
694C22⋊C4—48no—
695C22⋊C4—416no—
696C22⋊C4—416no—
697C22⋊C4—416no—
698C22⋊C4—416no—
699C22⋊C4—416no—
700C42—24no—
701C42—22no—
702C42—22no—
703C42—28no—
704C42—22no—
705C42—22no—
706C42—24no—
707C42—24no—
708C42—24no—
709C42—24no—
710C42—28no—
711C42—28no—
712C42—24no—
713C42—24no—
714C42—42no—
715C42—42no—
716C42—48no—
717C42—416no—
718C42C2×#4114yes—
719C42C2×#4114yes—
720C42C2×#4114yes—
721C42C2×#4114yes—
722C42H(5,𝔽2)18yes—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—28no—
727C23—24no—
728C23—28no—
729C23—216no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—28no—
735C23—28no—
736C23—24no—
737C23—24no—
738C23—28no—
739C23—28no—
740C23—416no—
741C23—416no—
742C23—48no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—88no—
748C23—88no—
749C23C22×#4118yes—
750C23C22×#4112yes—
751C23C22×#4112yes—
752C23C2×H(5,𝔽2)12yes—
753C23C2611yescharacteristic
754Q8—48no—
755D4—216no—
756D4—216no—
757D4—432no—
758D4—432no—
759D4—48no—
760D4—416no—
761D4—48no—
762D4—48no—
763D4—48no—
764D4—48no—
765D4—832no—
766D4—1616no—
767C2×C4—216no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—44no—
798C2×C4—48no—
799C2×C4—416no—
800C2×C4—416no—
801C2×C4—416no—
802C2×C4—816no—
803C2×C4—88no—
804C2×C4—88no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—1616no—
808C2×C4#553116yescomplemented
809C2×C4C22×#4112yes—
810C2×C4C22×#4112yes—
811C2×C4C22×#4112yes—
812C2×C4C22×#4112yes—
813C2×C4C22×#4112yes—
814C2×C4C22×#4112yes—
815C2×C4C22×#4112yes—
816C2×C4C22×#4112yes—
817C2×C4C2×H(5,𝔽2)14yes—
818C2×C4C2×H(5,𝔽2)14yes—
819C2×C4C2×H(5,𝔽2)12yes—
820C2×C4C2×H(5,𝔽2)12yes—
821C2×C4C2×H(5,𝔽2)14yes—
822C2×C4#58514yes—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—24no—
827C22—216no—
828C22—28no—
829C22—44no—
830C22—44no—
831C22—48no—
832C22—48no—
833C22—48no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—48no—
839C22—48no—
840C22—44no—
841C22—44no—
842C22—816no—
843C22—816no—
844C22C2×#55314yes—
845C22C23×#4111yescharacteristic
846C22C23×#4111yescharacteristic
847C22C22×H(5,𝔽2)12yes—
848C22C22×H(5,𝔽2)11yescharacteristic
849C22C2×#58512yes—
850C4—24no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—24no—
856C4—48no—
857C4—44no—
858C4—44no—
859C4—42no—
860C4—48no—
861C4—48no—
862C4—44no—
863C4C2×#55314yes—
864C4C2×#55314yes—
865C4#350814yes—
866C2—24no—
867C2—48no—
868C2—84no—
869C2—84no—
870C2C22×#55311yescharacteristic
871C2#6277312yes—
872C2C2×#350811yescharacteristic
873C2#6281511yescharacteristic
874C2#6283412yes—
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. #59683C2semidirect
2. #59680C2semidirect
3. #59678C2semidirect
4. #39548C2semidirect
5. #39191C2semidirect
6. #39185C2semidirect
7. #36640C2semidirect
8. #36498C2semidirect
9. #36468C2semidirect
10. #36157C2semidirect
11. #35557C2semidirect
12. #35528C2semidirect
13. #35254C2semidirect
14. #35165C2semidirect
15. #35165C2semidirect
16. #34269C2semidirect
17. #34186C2semidirect
18. #34181C2semidirect
19. C4×#532C2semidirect
20. C2×C4×#127C2semidirect
21. C2×#553C22semidirect
31. #2864C22semidirect
32. #2864C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
35. #2854C22semidirect
40. #2796C22semidirect
41. #2753C22semidirect
42. #2714C22semidirect
43. #2711C22semidirect
44. #2624C22semidirect
47. #2602C22semidirect
48. #2597C22semidirect
49. #2562C22semidirect
50. #2559C22semidirect
51. #2547C22semidirect
52. #2547C22semidirect
54. #2544C22semidirect
55. #2544C22semidirect
57. #2541C22semidirect
58. #2541C22semidirect
59. #2537C22semidirect
60. #2537C22semidirect
61. #2535C22semidirect
62. #2535C22semidirect
63. #2535C22semidirect
64. #2512C22semidirect
65. #2511C22semidirect
66. #2497C22semidirect
67. #2496C22semidirect
68. #2487C22semidirect
69. #2485C22semidirect
71. #2467C22semidirect
72. #2457C22semidirect
73. #2456C22semidirect
74. #2448C22semidirect
75. #2445C22semidirect
76. #2444C22semidirect
80. #2416C22semidirect
81. #2414C22semidirect
83. #2367C22semidirect
84. #2366C22semidirect
85. #2364C22semidirect
87. #2357C22semidirect
88. #2357C22semidirect
89. #2354C22semidirect
90. #2354C22semidirect
91. #2352C22semidirect
92. #2349C22semidirect
93. #2349C22semidirect
94. D4×C4⋊C4C22semidirect
95. D4×C4⋊C4C22semidirect
96. #2324C22semidirect
103. C4×C4⋊Q8C22semidirect
110. C4×#127C22semidirect
111. C4×#125C22semidirect
112. C4×#125C22semidirect
113. C4×#124C22semidirect
116. C4×#121C22semidirect
120. #2293C22semidirect
121. #2293C22semidirect
132. C42×D4C22semidirect
133. C42×D4C22semidirect
808. C2×C4#553semidirect

Maximal subgroups

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

subgroupindex
#596832
#596802
#596782
#395482
#391912
#391852
#366402
#364982
#364682
#361572
#355572
#355282
#352542
#351652
#342692
#341862
#341812
C4×#5322
C2×C4×#1272