Finite Group Databasebeta

← #7647585

Subgroups — #7647585

Order 512.

6340 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#42529C218yesmaximal, complemented
2#40540C218yesmaximal, complemented
3#39386C214yesmaximal, complemented
4#39202C214yesmaximal, complemented
5#37662C218yesmaximal, complemented
6#37626C214yesmaximal, complemented
7#37332C218yesmaximal, complemented
8#35541C212yesmaximal, complemented
9#35528C212yesmaximal, complemented
10#35274C211yesmaximal, characteristic, complemented
11#35272C212yesmaximal, complemented
12#35254C212yesmaximal, complemented
13#35171C214yesmaximal, complemented
14#35165C211yesmaximal, characteristic, complemented
15#34948C211yesmaximal, characteristic, complemented
16C2×#2541C211yesmaximal, characteristic, complemented
17#34210C211yesmaximal, characteristic, complemented
18#34141C211yesmaximal, characteristic, complemented
19#34058C211yesmaximal, characteristic, complemented
20C2×#540C2218yescomplemented
21C2×#535C2212yes—
22C2×#535C2212yes—
23C2×#535C2212yes—
24C2×#532C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#127C2212yes—
27C22×#121C2214yes—
28C2×#518C2212yes—
29C2×C4×#41C2212yes—
30C22×C4×D4C2211yescharacteristic
31#2867C2212yescomplemented
32#2858C2212yescomplemented
33#2856C2218yescomplemented
34#2854C2218yescomplemented
35#2847C2214yes—
36#2828C22116yescomplemented
37#2797C22116yescomplemented
38#2752C22116yescomplemented
39#2703C22116yescomplemented
40#2699C22116yescomplemented
41#2688C22116yescomplemented
42#2673C22116yescomplemented
43#2673C22116yescomplemented
44#2671C22116yescomplemented
45#2661C22116yescomplemented
46#2657C2214yescomplemented
47#2635C22116yescomplemented
48#2624C2218yescomplemented
49#2624C2218yescomplemented
50#2619C2218yescomplemented
51#2619C2218yescomplemented
52#2617C2214yes—
53#2571C2212yescomplemented
54#2570C2214yescomplemented
55#2569C2214yes—
56#2552C2212yescomplemented
57#2548C2218yescomplemented
58#2547C2212yescomplemented
59#2544C2214yescomplemented
60#2544C2218yescomplemented
61#2541C2214yes—
62#2541C2214yes—
63#2541C2212yes—
64#2541C2214yes—
65#2541C2212yes—
66#2541C2218yescomplemented
67#2541C2218yescomplemented
68#2541C2212yescomplemented
69#2541C2214yescomplemented
70#2541C2214yescomplemented
71#2537C2214yescomplemented
72#2535C2214yescomplemented
73#2490C2218yescomplemented
74#2464C22116yescomplemented
75#2448C2218yescomplemented
76#2447C2218yescomplemented
77#2445C2218yescomplemented
78#2445C2218yescomplemented
79#2442C2214yes—
80#2433C2214yes—
81#2433C2214yes—
82#2428C2218yescomplemented
83#2428C2218yescomplemented
84#2428C2218yescomplemented
85#2428C2218yescomplemented
86#2422C2218yescomplemented
87#2420C2218yescomplemented
88#2420C2218yescomplemented
89#2418C22116yes—
90#2412C22116yes—
91#2410C22116yes—
92#2408C22116yes—
93#2402C2214yescomplemented
94C2×#392C2214yes—
95#2367C2214yescomplemented
96#2366C2214yescomplemented
97#2366C2214yescomplemented
98#2366C2212yescomplemented
99#2365C2212yescomplemented
100#2364C2214yes—
101#2361C2214yes—
102D4×C22⋊C4C2214yes—
103D4×C22⋊C4C2214yes—
104#2328C2214yescomplemented
105#2324C2218yescomplemented
106#2319C2214yescomplemented
107#2319C2214yescomplemented
108#2316C2211yescharacteristic
109#2316C2211yescharacteristic
110#2312C2214yes—
111#2311C2212yes—
112#2309C2211yescharacteristic
113#2309C2211yescharacteristic
114#2309C2212yes—
115C4×#127C2214yescomplemented
116C4×#125C2214yescomplemented
117#2297C2212yes—
118#2296C2212yes—
119#2293C2214yescomplemented
120#2293C2214yescomplemented
121#2293C2212yescomplemented
122C2×#390C2212yes—
123#2290C2214yescomplemented
124#2285C2211yescharacteristic
125#2285C2212yes—
126#2280C2214yes—
127C42×D4C2212yescomplemented
128C4×#117C2211yescharacteristic
129C4×#117C2211yescharacteristic
130C2×C4×C4⋊C4C2211yescharacteristic
131C22×#41C2312yes—
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2318yes—
137C24×C4C2312yes—
138#540—432no—
139#535—48no—
140#535—48no—
141#535—48no—
142#532—28no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×#127—28no—
145C2×#127—48no—
146C2×#127C2312yes—
147C2×#127C2312yes—
148C2×#127C2312yes—
149C2×#127C2311yescharacteristic
150C2×#127C2312yes—
151C2×#127C2314yes—
152C2×#127C2318yes—
153C2×#127C2314yes—
154C2×#127C2314yes—
155C2×#127C2314yes—
156C2×#127C2318yes—
157C2×#127C2314yes—
158C2×#127C2318yes—
159C2×#125C2314yes—
160C2×#124C2312yes—
161C2×#124C2314yes—
162C2×#124C2314yes—
163C2×#124C2314yes—
164C2×#123C23116yes—
165C2×#123C23116yes—
166C2×#121—416no—
167C2×#121C2318yes—
168C2×#121C2312yes—
169C2×#121C2312yes—
170C2×#121C2318yes—
171C2×#121C2318yes—
172C2×#121C2318yes—
173C2×#121C2318yes—
174C2×#121C23116yes—
175C2×#121C2318yes—
176C2×#121C23116yes—
177C2×#121C23116yes—
178C2×#121C23116yes—
179C2×#121C23116yes—
180C2×#120C2318yes—
181C2×#120C2318yes—
182C2×#120C2318yes—
183#518—48no—
184C4×#41—48no—
185C2×C4×Q8C2314yes—
186C2×C4×D4—28no—
187C2×C4×D4C2312yes—
188C2×C4×D4C2312yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2312yes—
192C2×C4×D4C2312yes—
193C2×C4×D4C2312yes—
194C2×C4×D4C2318yes—
195C2×C4×D4C2318yes—
196C2×C4×D4C2318yes—
197C2×C4×D4C2318yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2318yes—
200C2×#117C2311yescharacteristic
201C2×#117C2312yes—
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2311yescharacteristic
205C2×#117C2318yes—
206C2×#117C2314yes—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2318yes—
211C22×C22⋊C4C2318yes—
212C22×C42C2312yes—
213C22×C42C2314yes—
214C22×C42C2311yescharacteristic
215#400C2318yes—
216#400C2318yes—
217#399C23116yes—
218#398C2318yes—
219#398C2318yes—
220#397C23116yes—
221#397C23116yes—
222#397C2318yes—
223#397C23116yes—
224#394C23116yes—
225#394C23116yes—
226#394C23116yes—
227#394C23116yes—
228#394C23116yes—
229#394C23116yes—
230#394C23116yes—
231#394C23116yes—
232#394C23116yes—
233#392C2318yes—
234#392C23116yes—
235#392C23116yes—
236#392C23116yes—
237#392C2318yes—
238#392C23116yes—
239#392C2318yes—
240#392C23116yes—
241#392C23116yes—
242#392C23116yes—
243#391C2314yes—
244#391C2314yes—
245#390C2318yes—
246#390C2318yes—
247#390C2318yes—
248#390C2314yes—
249#390C2314yes—
250#390C2314yes—
251#390C2314yes—
252#390C2318yes—
253#390C2314yes—
254#390C23116yes—
255#390C2318yes—
256#390C2314yes—
257#390C23116yes—
258#390C2318yes—
259#390C2314yes—
260#390C2314yes—
261#390C2314yes—
262#390C2318yes—
263#389C2314yes—
264#389C2314yes—
265#389C2314yes—
266#389C2314yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#389C2314yes—
271#389C2314yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C23116yes—
278#388C23116yes—
279#388C2318yes—
280#387C2318yes—
281#387C2318yes—
282#387C2318yes—
283#386C2318yes—
284#386C23116yes—
285#386C23116yes—
286#386C23116yes—
287#386C23116yes—
288#386C23116yes—
289#386C2318yes—
290#386C2318yes—
291#386C23116yes—
292#386C23116yes—
293#385C2318yes—
294#385C23116yes—
295#385C2318yes—
296#384C2312yes—
297#384C2314yes—
298#382C2314yes—
299#382C2312yes—
300#382C2314yes—
301#381C2318yes—
302#381C23116yes—
303#380C2318yes—
304#380C2314yes—
305#380C2314yes—
306#380C2312yes—
307#380C2318yes—
308#380C2318yes—
309#380C2318yes—
310#380C2312yes—
311#379C2314yes—
312#379C2314yes—
313#379C2318yes—
314C4×C4⋊C4C2312yes—
315C4×C4⋊C4C2312yes—
316C4×C4⋊C4C2318yes—
317C4×C4⋊C4C2318yes—
318C4×C4⋊C4C2312yes—
319C4×C4⋊C4C2312yes—
320C4×C4⋊C4C2311yescharacteristic
321C4×C4⋊C4C2312yes—
322C4×C4⋊C4C2312yes—
323C4×C4⋊C4C2314yes—
324C4×C4⋊C4C2312yes—
325C4×C4⋊C4C2312yes—
326C4×C4⋊C4C2312yes—
327C4×C4⋊C4C2311yescharacteristic
328C4×C22⋊C4C2312yes—
329C4×C22⋊C4C2312yes—
330C4×C22⋊C4C2312yes—
331C4×C22⋊C4C2318yes—
332C4×C22⋊C4C2314yes—
333C4×C22⋊C4C2318yes—
334C4×C22⋊C4C2314yes—
335C4×C22⋊C4C2312yes—
336#376C2312yes—
337#376C2312yes—
338C2×#95C2312yes—
339C43C2312yes—
340C43C2312yes—
341C25C2414yes—
342C25C2412yes—
343C2×#41—28no—
344C2×#41—28no—
345C2×#41—28no—
346C22×Q8C2412yes—
347C22×D4—24no—
348C22×D4—28no—
349C22×D4—28no—
350C22×D4—28no—
351C22×D4—28no—
352C22×D4—24no—
353C22×D4—28no—
354C22×D4—24no—
355C22×D4—48no—
356C22×D4—416no—
357C22×D4—416no—
358C22×D4—84no—
359C22×D4—88no—
360C22×D4C2412yes—
361C22×D4C2414yes—
362C22×D4C2412yes—
363C22×D4C2414yes—
364C22×D4C2414yes—
365C22×D4C2412yes—
366C22×D4C2414yes—
367C22×D4C2412yes—
368C22×D4C2414yes—
369C22×D4C2412yes—
370C22×D4C24116yes—
371C22×D4C2414yes—
372C22×D4C2414yes—
373C22×D4C24116yes—
374C22×D4C24116yes—
375C22×D4C24116yes—
376C22×D4C24116yes—
377C23×C4—28no—
378C23×C4—48no—
379C23×C4C2414yes—
380C23×C4C2414yes—
381C23×C4C2414yes—
382C23×C4C2411yescharacteristic
383C23×C4C2412yes—
384C23×C4C2418yes—
385C23×C4C2414yes—
386C23×C4C24116yes—
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C4⋊Q8—24no—
390#127—28no—
391#127—28no—
392#127—28no—
393#127—28no—
394#127—24no—
395#127—48no—
396#127—48no—
397#127—416no—
398#127—48no—
399#127—48no—
400#127—48no—
401#127—416no—
402#127—88no—
403#125—216no—
404#124—28no—
405#124—48no—
406#124—48no—
407#124—48no—
408#123—432no—
409#123—432no—
410#121—28no—
411#121—28no—
412#121—232no—
413#121—432no—
414#121—432no—
415#121—416no—
416#121—416no—
417#121—416no—
418#121—416no—
419#121—432no—
420#121—416no—
421#121—816no—
422#121—816no—
423#120—416no—
424#120—416no—
425#120—416no—
426C4×Q8—48no—
427C4×D4—216no—
428C4×D4—28no—
429C4×D4—28no—
430C4×D4—28no—
431C4×D4—28no—
432C4×D4—28no—
433C4×D4—28no—
434C4×D4—48no—
435C4×D4—416no—
436C4×D4—416no—
437C4×D4—416no—
438C4×D4—416no—
439C4×D4—88no—
440#117—24no—
441#117—24no—
442#117—28no—
443#117—24no—
444#117—24no—
445#117—48no—
446#117—416no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—28no—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2412yes—
460C2×C4⋊C4C2412yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2412yes—
470C2×C22⋊C4—28no—
471C2×C22⋊C4—416no—
472C2×C22⋊C4—416no—
473C2×C22⋊C4C2412yes—
474C2×C22⋊C4C2414yes—
475C2×C22⋊C4C2414yes—
476C2×C22⋊C4C2414yes—
477C2×C22⋊C4C24116yes—
478C2×C22⋊C4C2412yes—
479C2×C22⋊C4C2412yes—
480C2×C22⋊C4C2412yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C24116yes—
485C2×C22⋊C4C24116yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C24116yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C24116yes—
493C2×C22⋊C4C24116yes—
494C2×C22⋊C4C2418yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C24116yes—
498C2×C42—28no—
499C2×C42—48no—
500C2×C42#4118yes—
501C2×C42C2412yes—
502C2×C42C2414yes—
503C2×C42C2414yes—
504C2×C42C2412yes—
505C2×C42C2412yes—
506C2×C42C2414yes—
507C2×C42C2412yes—
508C2×C42C2412yes—
509C2×C42C2414yes—
510C2×C42C2412yes—
511C2×C42C2414yes—
512C2×C42C2418yes—
513C2×C42C2414yes—
514C2×C42C2411yescharacteristic
515C2×C42C2411yescharacteristic
516C2×C42C2411yescharacteristic
517C2×C42C2411yescharacteristic
518#95C2412yes—
519#95C2414yes—
520#95C2412yes—
521#95C2414yes—
522#95C2414yes—
523#95C2414yes—
524#95C2414yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2414yes—
531#95C2414yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C24116yes—
536C24—24no—
537C24—24no—
538C24—28no—
539C24—28no—
540C24—24no—
541C24—28no—
542C24—44no—
543C24—44no—
544C24—48no—
545C24—48no—
546C24C2514yes—
547C24C2518yes—
548C24C2514yes—
549C24C2511yescharacteristic
550#41—432no—
551C2×Q8—24no—
552C2×Q8—24no—
553C2×Q8—24no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—24no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—24no—
572C2×D4—216no—
573C2×D4—24no—
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—28no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—232no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—416no—
584C2×D4—416no—
585C2×D4—416no—
586C2×D4—416no—
587C2×D4—416no—
588C2×D4—44no—
589C2×D4—48no—
590C2×D4—416no—
591C2×D4—416no—
592C2×D4—416no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—416no—
596C2×D4—416no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4—432no—
601C2×D4—816no—
602C2×D4—816no—
603C2×D4—864no—
604C22×C4—24no—
605C22×C4—28no—
606C22×C4—24no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—216no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—216no—
615C22×C4—42no—
616C22×C4—44no—
617C22×C4—48no—
618C22×C4—44no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—416no—
622C22×C4—416no—
623C22×C4—416no—
624C22×C4—816no—
625C22×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4H(5,𝔽2)14yes—
629C22×C4H(5,𝔽2)14yes—
630C22×C4C2514yes—
631C22×C4C2514yes—
632C22×C4C2514yes—
633C22×C4C2514yes—
634C22×C4C2514yes—
635C22×C4C2518yes—
636C22×C4C2514yes—
637C22×C4C2514yes—
638C22×C4C2511yescharacteristic
639C22×C4C2511yescharacteristic
640C22×C4C2511yescharacteristic
641C22×C4C2514yes—
642C22×C4C2511yescharacteristic
643C22×C4C2511yescharacteristic
644C22×C4C2511yescharacteristic
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—28no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—28no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—28no—
657C4⋊C4—216no—
658C4⋊C4—216no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—44no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4H(5,𝔽2)18yes—
666C22⋊C4—24no—
667C22⋊C4—28no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—232no—
676C22⋊C4—216no—
677C22⋊C4—416no—
678C22⋊C4—416no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—416no—
683C22⋊C4—416no—
684C22⋊C4—416no—
685C22⋊C4—416no—
686C22⋊C4—416no—
687C22⋊C4—416no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C42—24no—
692C42—24no—
693C42—28no—
694C42—24no—
695C42—24no—
696C42—28no—
697C42—24no—
698C42—24no—
699C42—28no—
700C42—28no—
701C42—48no—
702C42—44no—
703C42—44no—
704C42C2×#4114yes—
705C42C2×#4114yes—
706C42C2×#4114yes—
707C42C2×#4114yes—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—24no—
712C23—28no—
713C23—28no—
714C23—216no—
715C23—28no—
716C23—24no—
717C23—24no—
718C23—28no—
719C23—28no—
720C23—24no—
721C23—24no—
722C23—28no—
723C23—28no—
724C23—216no—
725C23—416no—
726C23—48no—
727C23—416no—
728C23—84no—
729C23—84no—
730C23—88no—
731C23—88no—
732C23—88no—
733C23—816no—
734C23—816no—
735C23C22×#4112yes—
736C23C2×H(5,𝔽2)12yes—
737C23C2×H(5,𝔽2)12yes—
738C23C2611yescharacteristic
739Q8—48no—
740D4—416no—
741D4—416no—
742D4—48no—
743D4—416no—
744D4—48no—
745D4—416no—
746D4—48no—
747D4—48no—
748D4—416no—
749D4—84no—
750D4—88no—
751D4—88no—
752D4—832no—
753D4—832no—
754D4—1616no—
755D4—1616no—
756D4—1616no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—28no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—44no—
787C2×C4—416no—
788C2×C4—416no—
789C2×C4—416no—
790C2×C4—816no—
791C2×C4—88no—
792C2×C4—84no—
793C2×C4—1616no—
794C2×C4#540116yescomplemented
795C2×C4C22×#4112yes—
796C2×C4C22×#4112yes—
797C2×C4C22×#4112yes—
798C2×C4C22×#4112yes—
799C2×C4C22×#4112yes—
800C2×C4C22×#4112yes—
801C2×C4C2×H(5,𝔽2)18yes—
802C2×C4C2×H(5,𝔽2)12yes—
803C2×C4C2×H(5,𝔽2)12yes—
804C2×C4C2×H(5,𝔽2)12yes—
805C2×C4C2×H(5,𝔽2)12yes—
806C2×C4C2×H(5,𝔽2)14yes—
807C22—22no—
808C22—22no—
809C22—24no—
810C22—24no—
811C22—44no—
812C22—48no—
813C22—44no—
814C22—48no—
815C22—44no—
816C22—44no—
817C22—48no—
818C22—48no—
819C22—416no—
820C22—416no—
821C22—48no—
822C22—48no—
823C22—44no—
824C22—44no—
825C22—48no—
826C22—816no—
827C22—1616no—
828C22C2×#54014yes—
829C22C23×#4111yescharacteristic
830C22C22×H(5,𝔽2)12yes—
831C22C22×H(5,𝔽2)11yescharacteristic
832C22C22×H(5,𝔽2)11yescharacteristic
833C22H(7,𝔽2)12yes—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—28no—
838C4—44no—
839C4—44no—
840C4—44no—
841C4—44no—
842C4—44no—
843C4—48no—
844C4—44no—
845C4—44no—
846C4C2×#54014yes—
847C4C2×#54014yes—
848C4#350814yes—
849C2—24no—
850C2—84no—
851C2—84no—
852C2—88no—
853C2C22×#54011yescharacteristic
854C2C2×#350811yescharacteristic
855C2#6285511yescharacteristic
856C2#6291212yes—
857C2#6291612yes—
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. #42529C2semidirect
2. #40540C2semidirect
3. #39386C2semidirect
4. #39202C2semidirect
5. #37662C2semidirect
6. #37626C2semidirect
7. #37332C2semidirect
8. #35541C2semidirect
9. #35528C2semidirect
10. #35274C2semidirect
11. #35272C2semidirect
12. #35254C2semidirect
13. #35171C2semidirect
14. #35165C2semidirect
15. #34948C2semidirect
16. C2×#2541C2semidirect
17. #34210C2semidirect
18. #34141C2semidirect
19. #34058C2semidirect
20. C2×#540C22semidirect
31. #2867C22semidirect
32. #2858C22semidirect
33. #2856C22semidirect
34. #2854C22semidirect
36. #2828C22semidirect
37. #2797C22semidirect
38. #2752C22semidirect
39. #2703C22semidirect
40. #2699C22semidirect
41. #2688C22semidirect
42. #2673C22semidirect
43. #2673C22semidirect
44. #2671C22semidirect
45. #2661C22semidirect
46. #2657C22semidirect
47. #2635C22semidirect
48. #2624C22semidirect
49. #2624C22semidirect
50. #2619C22semidirect
51. #2619C22semidirect
53. #2571C22semidirect
54. #2570C22semidirect
56. #2552C22semidirect
57. #2548C22semidirect
58. #2547C22semidirect
59. #2544C22semidirect
60. #2544C22semidirect
66. #2541C22semidirect
67. #2541C22semidirect
68. #2541C22semidirect
69. #2541C22semidirect
70. #2541C22semidirect
71. #2537C22semidirect
72. #2535C22semidirect
73. #2490C22semidirect
74. #2464C22semidirect
75. #2448C22semidirect
76. #2447C22semidirect
77. #2445C22semidirect
78. #2445C22semidirect
82. #2428C22semidirect
83. #2428C22semidirect
84. #2428C22semidirect
85. #2428C22semidirect
86. #2422C22semidirect
87. #2420C22semidirect
88. #2420C22semidirect
93. #2402C22semidirect
95. #2367C22semidirect
96. #2366C22semidirect
97. #2366C22semidirect
98. #2366C22semidirect
99. #2365C22semidirect
104. #2328C22semidirect
105. #2324C22semidirect
106. #2319C22semidirect
107. #2319C22semidirect
115. C4×#127C22semidirect
116. C4×#125C22semidirect
119. #2293C22semidirect
120. #2293C22semidirect
121. #2293C22semidirect
123. #2290C22semidirect
127. C42×D4C22semidirect
794. C2×C4#540semidirect

Maximal subgroups

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

subgroupindex
#425292
#405402
#393862
#392022
#376622
#376262
#373322
#355412
#355282
#352742
#352722
#352542
#351712
#351652
#349482
C2×#25412
#342102
#341412
#340582