Finite Group Databasebeta

← #7630635

Subgroups — #7630635

Order 512.

7830 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3460C212yesmaximal, complemented
2#35572C218yesmaximal, complemented
3#35571C218yesmaximal, complemented
4#35392C2116yesmaximal, complemented
5#35343C212yesmaximal, complemented
6#35331C212yesmaximal, complemented
7#35330C211yesmaximal, characteristic, complemented
8#35328C211yesmaximal, characteristic, complemented
9#35303C214yesmaximal, complemented
10#35293C212yesmaximal, complemented
11#35278C212yesmaximal, complemented
12#35276C214yesmaximal, complemented
13#35274C211yesmaximal, characteristic, complemented
14#35272C211yesmaximal, characteristic, complemented
15#35264C212yesmaximal, complemented
16#35256C212yesmaximal, complemented
17C4×#535C212yesmaximal, complemented
18#34070C211yesmaximal, characteristic, complemented
19C2×#2328C211yesmaximal, characteristic, complemented
20#33999C211yesmaximal, characteristic, complemented
21#3460—232no—
22C2×#544C2212yes—
23C2×#542C2214yescomplemented
24C2×#542C2214yescomplemented
25C2×#540C2214yescomplemented
26C2×#540C2214yescomplemented
27C2×#538C2218yes—
28C2×#537C2212yes—
29C2×#535C2212yes—
30C2×#535C2212yes—
31C2×#535C2212yes—
32C2×#532C2211yescharacteristic
33C2×#532C2214yescomplemented
34C2×#532C2214yescomplemented
35C22×#127C2211yescharacteristic
36C2×#529C2214yescomplemented
37C2×#529C2214yescomplemented
38C2×#525C2218yes—
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2212yes—
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C22×C4×D4C2212yes—
44#2867C2212yes—
45#2862C2212yescomplemented
46#2861C2214yescomplemented
47#2859C2212yescomplemented
48#2858C2212yes—
49#2858C2214yescomplemented
50#2856C2214yes—
51#2856C2214yescomplemented
52#2850C2214yescomplemented
53#2850C2214yescomplemented
54#2660C2214yescomplemented
55#2657C2214yes—
56#2641C2214yescomplemented
57#2640C2214yescomplemented
58#2621C2212yescomplemented
59#2620C2214yescomplemented
60#2619C2212yes—
61#2619C2212yes—
62#2619C2212yescomplemented
63#2619C2214yescomplemented
64#2610C22116yescomplemented
65#2603C22116yescomplemented
66#2602C22116yescomplemented
67#2601C22116yescomplemented
68#2560C22116yescomplemented
69#2557C22116yescomplemented
70#2555C22116yescomplemented
71#2554C22116yescomplemented
72#2550C2218yescomplemented
73#2549C2218yes—
74#2548C2214yes—
75#2544C22116yescomplemented
76#2543C2218yes—
77#2543C22116yescomplemented
78#2541C2214yes—
79#2541C2218yes—
80#2536C2214yescomplemented
81#2535C2214yescomplemented
82#2491C2218yescomplemented
83#2490C2218yescomplemented
84#2472C22116yes—
85#2464C22116yescomplemented
86#2461C22116yescomplemented
87#2445C22116yescomplemented
88#2433C2218yes—
89#2431C22116yescomplemented
90#2430C22116yescomplemented
91#2428C22116yescomplemented
92#2428C2218yescomplemented
93#2426C2218yescomplemented
94#2424C22116yes—
95#2408C2218yes—
96#2328C2212yes—
97#2328C2212yes—
98#2328C2212yes—
99#2328C2212yes—
100#2328C2218yes—
101#2328C2211yescharacteristic, complemented
102#2328C2211yescharacteristic, complemented
103#2328C2214yescomplemented
104#2327C2211yescharacteristic, complemented
105#2327C2211yescharacteristic, complemented
106#2326C2214yescomplemented
107#2326C2212yescomplemented
108#2326C2212yescomplemented
109#2325C2218yes—
110#2324C2218yescomplemented
111#2321C2218yes—
112#2317C2212yes—
113#2311C2212yes—
114#2309C2212yes—
115C4×#127C2214yescomplemented
116C4×#124C2214yescomplemented
117C4×#121C2218yescomplemented
118C4×#120C2218yes—
119#2297C2212yes—
120C2×#390C2212yes—
121#2290C2218yescomplemented
122C2×#386C2218yes—
123#2285C2211yescharacteristic
124C2×#382C2211yescharacteristic
125#2276C2214yescomplemented
126#2275C2218yes—
127#2275C2214yescomplemented
128C4×#117C2211yescharacteristic
129C4×#117C2211yescharacteristic
130C4×#117C2211yescharacteristic
131C4×#117C2212yescomplemented
132C4×#117C2212yescomplemented
133C4×#117C2212yescomplemented
134C2×#376C2211yescharacteristic
135C2×#376C2212yescomplemented
136C22×#41C2312yes—
137C22×#41C2311yescharacteristic
138C22×#41C2318yes—
139C23×D4C2312yes—
140C23×D4C2314yes—
141C24×C4C2314yes—
142#544—216no—
143#542—232no—
144#542—232no—
145#540—232no—
146#540—232no—
147#538—264no—
148#537—216no—
149#535—216no—
150#535—216no—
151#535—216no—
152#532—232no—
153#532—232no—
154#532—28no—
155C2×C4⋊Q8C2311yescharacteristic
156C2×C4⋊Q8C2314yes—
157C2×C4⋊Q8C2314yes—
158C2×#127—28no—
159C2×#127C2314yes—
160C2×#127C2312yes—
161C2×#127C2312yes—
162C2×#127C2314yes—
163C2×#127C2311yescharacteristic
164C2×#127C2314yes—
165C2×#127C2314yes—
166C2×#127C23116yes—
167#529—232no—
168#529—232no—
169C2×#126C2318yes—
170C2×#126C2318yes—
171C2×#125C2314yes—
172C2×#125C2314yes—
173C2×#124C2312yes—
174C2×#124C2314yes—
175C2×#124C2314yes—
176C2×#124C2318yes—
177C2×#124C2314yes—
178C2×#124C2318yes—
179C2×#124C23116yes—
180#525—264no—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×#123C2318yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2314yes—
189C2×#121C2318yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2318yes—
195C2×#121C2318yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2318yes—
200C2×#121C2318yes—
201C2×#121C23116yes—
202C2×#121C23116yes—
203C2×#120C2318yes—
204C2×#120C2318yes—
205C2×#120C2318yes—
206C4×#41—28no—
207C4×#41—216no—
208C4×#41—28no—
209C4×#41D4116yescomplemented
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2312yes—
214C2×C4×Q8C2312yes—
215C2×C4×D4—216no—
216C2×C4×D4C2312yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2318yes—
225C2×C4×D4C2318yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C23116yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×#117C2311yescharacteristic
235C2×#117C2312yes—
236C2×#117C2314yes—
237C2×#117C2318yes—
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2311yescharacteristic
243C22×C4⋊C4C2312yes—
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2318yes—
246C22×C42C2312yes—
247C22×C42C2312yes—
248C22×C42C2314yes—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2312yes—
252C22×C42C2311yescharacteristic
253#398C2318yes—
254#398C23116yes—
255#397C23116yes—
256#397C2318yes—
257#396C23116yes—
258#395C23116yes—
259#394C2318yes—
260#394C2318yes—
261#394C23116yes—
262#394C23116yes—
263#394C23116yes—
264#394C23116yes—
265#394C2318yes—
266#393C23116yes—
267#392C2318yes—
268#392C23116yes—
269#392C23116yes—
270#392C2318yes—
271#392C23116yes—
272#392C2318yes—
273#391C23116yes—
274#391C2314yes—
275#391C2312yes—
276#391C2312yes—
277#390C23116yes—
278#390C2314yes—
279#390C2314yes—
280#390C23116yes—
281#390C2318yes—
282#390C2314yes—
283#390C2312yes—
284#390C2312yes—
285#390C2314yes—
286#390C2314yes—
287#390C2318yes—
288#390C23116yes—
289#390C23116yes—
290#390C23116yes—
291#389C2318yes—
292#389C23116yes—
293#388C23116yes—
294#388C23116yes—
295#388C23116yes—
296#388C2318yes—
297#388C2318yes—
298#388C23116yes—
299#388C23116yes—
300#388C23116yes—
301#387C2318yes—
302#387C2318yes—
303#386C23116yes—
304#386C2318yes—
305#386C23116yes—
306#386C23116yes—
307#386C2318yes—
308#386C2318yes—
309#386C2318yes—
310#386C23116yes—
311#386C23116yes—
312#386C23116yes—
313#386C23116yes—
314#386C23116yes—
315#385C2318yes—
316#385C23116yes—
317#385C2318yes—
318#385C2318yes—
319#384C2314yes—
320#384C2312yes—
321#382C2314yes—
322#382C2311yescharacteristic
323#382C2311yescharacteristic
324#382C2312yes—
325#382C2312yes—
326#382C2314yes—
327#380C2318yes—
328#380C2314yes—
329#379C2318yes—
330C4×C4⋊C4C2318yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2318yes—
333C4×C4⋊C4C2318yes—
334C4×C4⋊C4C2314yes—
335C4×C4⋊C4C2314yes—
336C4×C4⋊C4C2314yes—
337C4×C22⋊C4C23116yes—
338C4×C22⋊C4C2314yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C2318yes—
341C4×C22⋊C4C2318yes—
342C4×C22⋊C4C2314yes—
343C4×C22⋊C4C2318yes—
344C4×C22⋊C4C2314yes—
345#376C2311yescharacteristic
346#376C2311yescharacteristic
347#376C2312yes—
348#376C2311yescharacteristic
349#376C2311yescharacteristic
350#376C2314yes—
351#376C2318yes—
352#376C2312yes—
353#376C2312yes—
354C2×#95C2314yes—
355C2×#95C2318yes—
356C2×#95C2314yes—
357C43C2312yes—
358C43C2312yes—
359C43C2312yes—
360C25C2414yes—
361C2×#41—28no—
362C2×#41—232no—
363C2×#41—24no—
364C2×#41—24no—
365C2×#41—28no—
366C2×#41—28no—
367C2×#41—816no—
368C2×#41C2×D418yes—
369C22×Q8C2412yes—
370C22×Q8C2411yescharacteristic
371C22×Q8C2418yes—
372C22×D4—28no—
373C22×D4—28no—
374C22×D4—28no—
375C22×D4—216no—
376C22×D4—88no—
377C22×D4C2414yes—
378C22×D4C2414yes—
379C22×D4C2414yes—
380C22×D4C2412yes—
381C22×D4C2412yes—
382C22×D4C2411yescharacteristic
383C22×D4C2418yes—
384C22×D4C2418yes—
385C22×D4C24116yes—
386C22×D4C2414yes—
387C22×D4C2418yes—
388C22×D4C2418yes—
389C22×D4C2418yes—
390C22×D4C2418yes—
391C22×D4C2418yes—
392C23×C4—216no—
393C23×C4—88no—
394C23×C4C2414yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2414yes—
398C23×C4C2418yes—
399C23×C4C2414yes—
400C23×C4C2418yes—
401C23×C4C2414yes—
402C23×C4C2414yes—
403C23×C4C2414yes—
404C23×C4C2412yes—
405C23×C4C2414yes—
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C4⋊Q8—216no—
409C4⋊Q8—216no—
410C4⋊Q8—24no—
411#127—216no—
412#127—216no—
413#127—28no—
414#127—28no—
415#127—216no—
416#127—24no—
417#127—216no—
418#127—816no—
419#126—232no—
420#126—232no—
421#125—216no—
422#125—216no—
423#124—216no—
424#124—232no—
425#124—216no—
426#124—232no—
427#124—28no—
428#124—216no—
429#124—816no—
430#123—232no—
431#123—232no—
432#123—232no—
433#123—232no—
434C22⋊Q8—216no—
435C22⋊Q8—216no—
436C22⋊Q8—232no—
437C22⋊Q8—232no—
438#121—232no—
439#121—216no—
440#121—216no—
441#121—216no—
442#121—216no—
443#121—232no—
444#121—216no—
445#121—216no—
446#121—216no—
447#121—232no—
448#121—232no—
449#121—232no—
450#121—816no—
451#121—816no—
452#120—232no—
453#120—232no—
454#120—232no—
455C4×Q8—28no—
456C4×Q8—28no—
457C4×Q8—28no—
458C4×Q8—28no—
459C4×Q8C2×D4116yescomplemented
460C4×D4—216no—
461C4×D4—216no—
462C4×D4—232no—
463C4×D4—216no—
464C4×D4—28no—
465C4×D4—216no—
466C4×D4—216no—
467C4×D4—216no—
468C4×D4—216no—
469C4×D4—216no—
470C4×D4—28no—
471C4×D4—28no—
472C4×D4—232no—
473C4×D4—28no—
474C4×D4—216no—
475C4×D4—816no—
476C4×D4C2×D4132yes—
477C4×D4C2×D4116yescomplemented
478#117—28no—
479#117—24no—
480#117—216no—
481#117—232no—
482#117—28no—
483#117—28no—
484#117C2×D418yes—
485#117C2×D4116yescomplemented
486#117#4118yescomplemented
487C2×C4⋊C4—28no—
488C2×C4⋊C4C2414yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C24116yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2412yes—
507C2×C22⋊C4—216no—
508C2×C22⋊C4—88no—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2414yes—
512C2×C22⋊C4C2414yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2412yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C24116yes—
525C2×C22⋊C4C24116yes—
526C2×C22⋊C4C24116yes—
527C2×C22⋊C4C24116yes—
528C2×C22⋊C4C24116yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C24116yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2412yes—
535C2×C42—24no—
536C2×C42—216no—
537C2×C42—28no—
538C2×C42—28no—
539C2×C42C2×D418yes—
540C2×C42C2×D4116yescomplemented
541C2×C42#4118yescomplemented
542C2×C42C2414yes—
543C2×C42C2414yes—
544C2×C42C2412yes—
545C2×C42C2411yescharacteristic
546C2×C42C2414yes—
547C2×C42C2412yes—
548C2×C42C2414yes—
549C2×C42C2414yes—
550C2×C42C2411yescharacteristic
551C2×C42C2418yes—
552C2×C42C2418yes—
553C2×C42C2418yes—
554C2×C42C2411yescharacteristic
555C2×C42C2412yes—
556C2×C42C2414yes—
557C2×C42C2412yes—
558C2×C42C2411yescharacteristic
559C2×C42C2412yes—
560C2×C42C2411yescharacteristic
561C2×C42C2412yes—
562C2×C42C2411yescharacteristic
563#95C2414yes—
564#95C2418yes—
565#95C2414yes—
566#95C2414yes—
567#95C2414yes—
568#95C2418yes—
569#95C2418yes—
570#95C2418yes—
571#95C2418yes—
572#95C24116yes—
573#95C24116yes—
574#95C2418yes—
575#95C2418yes—
576#95C2414yes—
577#95C2414yes—
578C24—28no—
579C24—28no—
580C24—28no—
581C24—48no—
582C24—48no—
583C24C2518yes—
584C24C2514yes—
585C24C2512yes—
586C24C2511yescharacteristic
587#41—232no—
588#41—432no—
589#41—864no—
590C2×Q8—24no—
591C2×Q8—216no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—24no—
595C2×Q8—24no—
596C2×Q8—416no—
597C2×Q8C22×D414yes—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—28no—
601C2×D4—28no—
602C2×D4—28no—
603C2×D4—216no—
604C2×D4—216no—
605C2×D4—216no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—24no—
609C2×D4—216no—
610C2×D4—216no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—24no—
616C2×D4—28no—
617C2×D4—28no—
618C2×D4—24no—
619C2×D4—28no—
620C2×D4—232no—
621C2×D4—216no—
622C2×D4—216no—
623C2×D4—416no—
624C2×D4—416no—
625C2×D4—416no—
626C2×D4—416no—
627C2×D4—416no—
628C2×D4—416no—
629C2×D4—416no—
630C2×D4—48no—
631C2×D4—416no—
632C2×D4—416no—
633C2×D4—432no—
634C2×D4—832no—
635C2×D4C22×D418yes—
636C2×D4C22×D414yes—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—28no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—216no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—216no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—44no—
651C22×C4—416no—
652C22×C4—44no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—44no—
656C22×C4—48no—
657C22×C4—48no—
658C22×C4—416no—
659C22×C4—48no—
660C22×C4—48no—
661C22×C4—832no—
662C22×C4C22×D418yes—
663C22×C4C22×D418yes—
664C22×C4C22×D4116yes—
665C22×C4C22×D414yes—
666C22×C4C2×#4118yes—
667C22×C4C2×#4114yes—
668C22×C4C2×#4114yes—
669C22×C4C2512yes—
670C22×C4C2512yes—
671C22×C4C2514yes—
672C22×C4C2514yes—
673C22×C4C2514yes—
674C22×C4C2518yes—
675C22×C4C2514yes—
676C22×C4C2512yes—
677C22×C4C2512yes—
678C22×C4C2514yes—
679C22×C4C2512yes—
680C22×C4C2512yes—
681C22×C4C2512yes—
682C22×C4C2514yes—
683C22×C4C2511yescharacteristic
684C22×C4C2511yescharacteristic
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—216no—
692C4⋊C4—216no—
693C4⋊C4—216no—
694C4⋊C4—216no—
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—24no—
698C4⋊C4—28no—
699C4⋊C4—416no—
700C4⋊C4—48no—
701C4⋊C4C22×D418yes—
702C4⋊C4C22×D4116yes—
703C4⋊C4C2×#4118yes—
704C22⋊C4—28no—
705C22⋊C4—216no—
706C22⋊C4—24no—
707C22⋊C4—216no—
708C22⋊C4—216no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—216no—
712C22⋊C4—216no—
713C22⋊C4—216no—
714C22⋊C4—216no—
715C22⋊C4—216no—
716C22⋊C4—28no—
717C22⋊C4—28no—
718C22⋊C4—216no—
719C22⋊C4—232no—
720C22⋊C4—416no—
721C22⋊C4—416no—
722C22⋊C4—416no—
723C22⋊C4—416no—
724C22⋊C4—48no—
725C22⋊C4—416no—
726C22⋊C4—48no—
727C22⋊C4C22×D418yes—
728C22⋊C4C22×D4116yes—
729C22⋊C4C2×#4118yes—
730C42—28no—
731C42—28no—
732C42—28no—
733C42—22no—
734C42—22no—
735C42—24no—
736C42—28no—
737C42—28no—
738C42—24no—
739C42—48no—
740C42—48no—
741C42—48no—
742C42C22×D418yes—
743C42C22×D414yes—
744C42C22×D414yes—
745C42C22×D4116yes—
746C42C22×D418yes—
747C42C2×#4114yes—
748C42C2×#4118yes—
749C42C2×#4114yes—
750C42C2×#4118yes—
751C23—24no—
752C23—22no—
753C23—22no—
754C23—28no—
755C23—28no—
756C23—24no—
757C23—24no—
758C23—28no—
759C23—24no—
760C23—28no—
761C23—28no—
762C23—216no—
763C23—216no—
764C23—28no—
765C23—432no—
766C23—416no—
767C23—88no—
768C23—88no—
769C23—816no—
770C23C23×D414yes—
771C23C23×D412yes—
772C23C22×#4112yes—
773C23C22×#4112yes—
774C23C2611yescharacteristic
775Q8—28no—
776Q8—48no—
777Q8—816no—
778D4—216no—
779D4—28no—
780D4—416no—
781D4—416no—
782D4—416no—
783D4—48no—
784D4—816no—
785D4—88no—
786D4—832no—
787D4—816no—
788D4—816no—
789D4—816no—
790D4—816no—
791D4—816no—
792D4—816no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—28no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—216no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—216no—
816C2×C4—28no—
817C2×C4—48no—
818C2×C4—416no—
819C2×C4—48no—
820C2×C4—432no—
821C2×C4—416no—
822C2×C4—416no—
823C2×C4—88no—
824C2×C4—88no—
825C2×C4—88no—
826C2×C4—816no—
827C2×C4—84no—
828C2×C4—88no—
829C2×C4#532116yes—
830C2×C4C23×D414yes—
831C2×C4C23×D414yes—
832C2×C4C23×D414yes—
833C2×C4C23×D418yes—
834C2×C4C23×D412yes—
835C2×C4C23×D412yes—
836C2×C4C22×#4114yes—
837C2×C4C22×#4118yes—
838C2×C4C22×#4114yes—
839C2×C4C22×#4112yes—
840C2×C4C22×#4112yes—
841C2×C4C22×#4112yes—
842C2×C4C22×#4112yes—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—28no—
847C22—24no—
848C22—44no—
849C22—44no—
850C22—48no—
851C22—44no—
852C22—44no—
853C22—48no—
854C22—416no—
855C22—48no—
856C22—48no—
857C22—416no—
858C22—44no—
859C22—48no—
860C22—832no—
861C22C2×#53214yes—
862C22C24×D411yescharacteristic
863C22C23×#4111yescharacteristic
864C22C23×#4111yescharacteristic
865C22H(7,𝔽2)14yes—
866C4—24no—
867C4—24no—
868C4—28no—
869C4—24no—
870C4—24no—
871C4—28no—
872C4—24no—
873C4—48no—
874C4—44no—
875C4—44no—
876C4—44no—
877C4—42no—
878C4—42no—
879C4—44no—
880C4C2×#53214yes—
881C4C2×#53214yes—
882C2—24no—
883C2—44no—
884C2—84no—
885C2—88no—
886C2C22×#53211yescharacteristic
887C2#6285212yes—
888C2#6285512yes—
889C2#6285812yes—
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. C2×#3460C2semidirect
2. #35572C2semidirect
3. #35571C2semidirect
4. #35392C2semidirect
5. #35343C2semidirect
6. #35331C2semidirect
7. #35330C2semidirect
8. #35328C2semidirect
9. #35303C2semidirect
10. #35293C2semidirect
11. #35278C2semidirect
12. #35276C2semidirect
13. #35274C2semidirect
14. #35272C2semidirect
15. #35264C2semidirect
16. #35256C2semidirect
17. C4×#535C2semidirect
18. #34070C2semidirect
19. C2×#2328C2semidirect
20. #33999C2semidirect
23. C2×#542C22semidirect
24. C2×#542C22semidirect
25. C2×#540C22semidirect
26. C2×#540C22semidirect
33. C2×#532C22semidirect
34. C2×#532C22semidirect
36. C2×#529C22semidirect
37. C2×#529C22semidirect
45. #2862C22semidirect
46. #2861C22semidirect
47. #2859C22semidirect
49. #2858C22semidirect
51. #2856C22semidirect
52. #2850C22semidirect
53. #2850C22semidirect
54. #2660C22semidirect
56. #2641C22semidirect
57. #2640C22semidirect
58. #2621C22semidirect
59. #2620C22semidirect
62. #2619C22semidirect
63. #2619C22semidirect
64. #2610C22semidirect
65. #2603C22semidirect
66. #2602C22semidirect
67. #2601C22semidirect
68. #2560C22semidirect
69. #2557C22semidirect
70. #2555C22semidirect
71. #2554C22semidirect
72. #2550C22semidirect
75. #2544C22semidirect
77. #2543C22semidirect
80. #2536C22semidirect
81. #2535C22semidirect
82. #2491C22semidirect
83. #2490C22semidirect
85. #2464C22semidirect
86. #2461C22semidirect
87. #2445C22semidirect
89. #2431C22semidirect
90. #2430C22semidirect
91. #2428C22semidirect
92. #2428C22semidirect
93. #2426C22semidirect
101. #2328C22semidirect
102. #2328C22semidirect
103. #2328C22semidirect
104. #2327C22semidirect
105. #2327C22semidirect
106. #2326C22semidirect
107. #2326C22semidirect
108. #2326C22semidirect
110. #2324C22semidirect
115. C4×#127C22semidirect
116. C4×#124C22semidirect
117. C4×#121C22semidirect
121. #2290C22semidirect
125. #2276C22semidirect
127. #2275C22semidirect
131. C4×#117C22semidirect
132. C4×#117C22semidirect
133. C4×#117C22semidirect
135. C2×#376C22semidirect
209. C4×#41D4semidirect
459. C4×Q8C2×D4semidirect
477. C4×D4C2×D4semidirect
485. #117C2×D4semidirect
486. #117#41semidirect
540. C2×C42C2×D4semidirect
541. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34602
#355722
#355712
#353922
#353432
#353312
#353302
#353282
#353032
#352932
#352782
#352762
#352742
#352722
#352642
#352562
C4×#5352
#340702
C2×#23282
#339992