Finite Group Databasebeta

← #7631224

Subgroups — #7631224

Order 512.

8422 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3508C211yesmaximal, characteristic, complemented
3#36644C212yesmaximal, complemented
4#36639C211yesmaximal, characteristic, complemented
5#36639C212yesmaximal, complemented
6C2×#2858C211yesmaximal, characteristic, complemented
7#36597C214yesmaximal, complemented
8#36496C214yesmaximal, complemented
9#36412C214yesmaximal, complemented
10#36362C218yesmaximal, complemented
11#36125C214yesmaximal, complemented
12#36124C218yesmaximal, complemented
13#35298C212yesmaximal, complemented
14#35293C212yesmaximal, complemented
15#35281C211yesmaximal, characteristic, complemented
16#35276C218yesmaximal, complemented
17#35274C211yesmaximal, characteristic, complemented
18#35256C214yesmaximal, complemented
19#34275C214yesmaximal, complemented
20C42×#41C211yesmaximal, characteristic, complemented
21#3511—216no—
22#3508—216no—
23C2×#559C2212yes—
24C2×#559C2212yes—
25C2×#556C2212yescomplemented
26C2×#555C2212yescomplemented
27C2×#554C2212yescomplemented
28C2×#553C2214yes—
29C2×#550C2212yes—
30C2×#550C2212yes—
31C2×#548C2214yes—
32C2×#547C2212yescomplemented
33C2×#546C2214yes—
34C2×#546C2214yes—
35C2×#542C2214yescomplemented
36C2×#540C2214yes—
37C2×#537C2212yes—
38C2×#535C2212yes—
39C2×#535C2214yes—
40C2×#533C2211yescharacteristic
41C2×#533C2212yescomplemented
42C2×#532C2212yes—
43C2×#532C2211yescharacteristic
44C2×#532C2212yes—
45C2×#532C2212yescomplemented
46C2×#532C2218yescomplemented
47C22×C4⋊Q8C2211yescharacteristic
48C22×#127C2211yescharacteristic
49C22×#124C2214yes—
50C2×#520C2212yes—
51C2×#518C2212yes—
52C2×C4×#41C2212yes—
53C2×C4×#41C2211yescharacteristic
54#2868C2212yescomplemented
55#2867C2212yes—
56#2862C2211yescharacteristic, complemented
57#2862C2212yescomplemented
58#2862C2211yescharacteristic, complemented
59#2861C2218yescomplemented
60#2861C2214yescomplemented
61#2858C2214yes—
62#2858C2212yes—
63#2858C2214yes—
64#2858C2214yes—
65#2858C2212yes—
66#2858C2212yes—
67#2858C2218yescomplemented
68#2858C2211yescharacteristic, complemented
69#2858C2211yescharacteristic, complemented
70#2856C2218yescomplemented
71#2856C2218yescomplemented
72#2850C2214yes—
73#2850C2214yes—
74#2850C2218yescomplemented
75#2850C2218yescomplemented
76#2660C2214yescomplemented
77#2657C2214yes—
78#2620C2218yescomplemented
79#2619C2218yescomplemented
80#2567C2214yescomplemented
81#2566C2218yescomplemented
82#2555C22132yescomplemented
83#2554C22132yescomplemented
84#2546C2214yescomplemented
85#2545C2218yescomplemented
86#2544C2218yescomplemented
87#2544C2218yescomplemented
88#2541C2214yes—
89#2541C2214yes—
90#2502C2214yes—
91#2500C2218yescomplemented
92#2464C22132yescomplemented
93#2461C22132yescomplemented
94#2434C2214yes—
95#2433C2214yes—
96#2433C2214yes—
97#2432C2218yescomplemented
98#2431C2218yescomplemented
99#2431C2218yescomplemented
100#2428C22116yescomplemented
101#2426C22116yescomplemented
102#2424C22132yes—
103#2363C22116yescomplemented
104#2361C22116yescomplemented
105#2358C22132yes—
106#2328C2218yescomplemented
107#2326C2218yescomplemented
108#2317C2214yes—
109C4×#127C2218yescomplemented
110C4×#127C2218yescomplemented
111C4×#124C2218yescomplemented
112C4×#124C2214yescomplemented
113C4×#124C2214yescomplemented
114C4×#124C2218yescomplemented
115#2297C2214yes—
116#2297C2218yescomplemented
117C2×#390C2214yes—
118C2×#390C2214yes—
119C42×Q8C2212yescomplemented
120C42×Q8C2212yescomplemented
121C42×D4C2214yes—
122C42×D4C2214yes—
123C42×D4C2212yescomplemented
124C42×D4C2212yescomplemented
125C4×#117C2211yescharacteristic
126C4×#117C2212yes—
127C4×#117C2214yescomplemented
128C4×#117C2212yescomplemented
129C2×C43C2211yescharacteristic
130C2×C43C2212yescomplemented
131C22×#41C2312yes—
132C22×#41C2311yescharacteristic
133C22×#41C2314yes—
134C22×#41C2314yes—
135C22×#41C2314yes—
136C23×Q8C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140#559—216no—
141#559—216no—
142#556—216no—
143#555—216no—
144#554—216no—
145#553—232no—
146#550—216no—
147#550—216no—
148#548—232no—
149#547—216no—
150#546—232no—
151#546—232no—
152#542—232no—
153#540—232no—
154#537—216no—
155#535—216no—
156#535—232no—
157#533—28no—
158#533—216no—
159#532—216no—
160#532—216no—
161#532—28no—
162#532—216no—
163#532—432no—
164C2×C4⋊Q8—28no—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2311yescharacteristic
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2318yes—
173C2×#127—28no—
174C2×#127C2318yes—
175C2×#127C2312yes—
176C2×#127C2312yes—
177C2×#127C2312yes—
178C2×#127C2312yes—
179C2×#127C2311yescharacteristic
180C2×#127C2314yes—
181C2×#127C2318yes—
182C2×#127C2318yes—
183C2×#126C2318yes—
184C2×#125C2314yes—
185C2×#125C2312yes—
186C2×#124—416no—
187C2×#124C2318yes—
188C2×#124C2314yes—
189C2×#124C2318yes—
190C2×#124C2314yes—
191C2×#124C2314yes—
192C2×#124C2312yes—
193C2×#124C2314yes—
194C2×#124C2314yes—
195C2×#124C2318yes—
196C2×#124C2314yes—
197C2×#124C2318yes—
198C2×#124C23116yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×C22⋊Q8C2312yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2318yes—
208C2×#121C2312yes—
209C2×#121C2312yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C23116yes—
217C2×#121C2318yes—
218C2×#121C2314yes—
219C2×#121C2318yes—
220C2×#121C2318yes—
221C2×#121C23132yes—
222C2×#120C23116yes—
223C2×#120C2318yes—
224#520—216no—
225#518—216no—
226C4×#41—216no—
227C4×#41D4116yescomplemented
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C23132yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2314yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2311yescharacteristic
258C2×#117C2312yes—
259C2×#117C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C22⋊C4C2318yes—
264C22×C22⋊C4C23116yes—
265C22×C42C2312yes—
266C22×C42C2314yes—
267C22×C42C2314yes—
268C22×C42C2312yes—
269C22×C42C2312yes—
270C22×C42C2314yes—
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273#398C23116yes—
274#396C23132yes—
275#395C23116yes—
276#394C23132yes—
277#394C23132yes—
278#392C23132yes—
279#392C23116yes—
280#392C23116yes—
281#391C2318yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2318yes—
287#390C2314yes—
288#390C2314yes—
289#390C2318yes—
290#390C2318yes—
291#390C23132yes—
292#390C23132yes—
293#390C2318yes—
294#390C2318yes—
295#390C2318yes—
296#390C2314yes—
297#390C2314yes—
298#390C2318yes—
299#390C23116yes—
300#390C23116yes—
301#389C23116yes—
302#388C23132yes—
303#388C23116yes—
304#388C23116yes—
305#388C23132yes—
306#388C23132yes—
307#386C23132yes—
308#386C23132yes—
309#386C23116yes—
310#386C23132yes—
311#385C23132yes—
312#385C23116yes—
313#384C2318yes—
314#384C2318yes—
315#382C2314yes—
316#382C2318yes—
317#382C2314yes—
318C4×C4⋊C4C2314yes—
319C4×C4⋊C4C2312yes—
320C4×C4⋊C4C2314yes—
321C4×C4⋊C4C2314yes—
322C4×C4⋊C4C2318yes—
323C4×C4⋊C4C2312yes—
324C4×C4⋊C4C2314yes—
325C4×C4⋊C4C2318yes—
326C4×C22⋊C4C2318yes—
327C4×C22⋊C4C23132yes—
328C4×C22⋊C4C23116yes—
329C4×C22⋊C4C2314yes—
330C4×C22⋊C4C2314yes—
331C4×C22⋊C4C2312yes—
332C4×C22⋊C4C2312yes—
333C4×C22⋊C4C2318yes—
334C4×C22⋊C4C2318yes—
335#376C2314yes—
336#376C2312yes—
337C43C2314yes—
338C43C2314yes—
339C43C2311yescharacteristic
340C43C2311yescharacteristic
341C43C2312yes—
342C43C2312yes—
343C43C2312yes—
344C43C2312yes—
345C43C2314yes—
346C25C2414yes—
347C2×#41—28no—
348C2×#41—216no—
349C2×#41—216no—
350C2×#41—216no—
351C2×#41—28no—
352C2×#41—216no—
353C2×#41—416no—
354C2×#41—416no—
355C2×#41—416no—
356C2×#41C2×D418yes—
357C22×Q8—28no—
358C22×Q8—48no—
359C22×Q8C2412yes—
360C22×Q8C2414yes—
361C22×Q8C2412yes—
362C22×Q8C2412yes—
363C22×Q8C2411yescharacteristic
364C22×Q8C2414yes—
365C22×D4—28no—
366C22×D4—28no—
367C22×D4—28no—
368C22×D4—216no—
369C22×D4—48no—
370C22×D4—48no—
371C22×D4C2412yes—
372C22×D4C2414yes—
373C22×D4C2414yes—
374C22×D4C2414yes—
375C22×D4C2412yes—
376C22×D4C2414yes—
377C22×D4C2412yes—
378C22×D4C2414yes—
379C22×D4C2412yes—
380C22×D4C2411yescharacteristic
381C22×D4C24132yes—
382C22×D4C2418yes—
383C22×D4C2418yes—
384C22×D4C2418yes—
385C22×D4C2414yes—
386C22×D4C2414yes—
387C23×C4C2414yes—
388C23×C4C2414yes—
389C23×C4C2418yes—
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2414yes—
396C23×C4C2418yes—
397C23×C4C2418yes—
398C23×C4C2418yes—
399C23×C4C2411yescharacteristic
400C4⋊Q8—28no—
401C4⋊Q8—28no—
402C4⋊Q8—28no—
403C4⋊Q8—28no—
404C4⋊Q8—24no—
405C4⋊Q8—24no—
406C4⋊Q8—24no—
407C4⋊Q8—416no—
408#127—216no—
409#127—28no—
410#127—28no—
411#127—28no—
412#127—28no—
413#127—24no—
414#127—232no—
415#127—416no—
416#127—416no—
417#126—232no—
418#125—28no—
419#125—216no—
420#124—216no—
421#124—232no—
422#124—28no—
423#124—216no—
424#124—216no—
425#124—216no—
426#124—232no—
427#124—232no—
428#124—216no—
429#124—432no—
430#124—416no—
431#124—48no—
432#123—232no—
433#123—232no—
434#123—232no—
435C22⋊Q8—216no—
436C22⋊Q8—216no—
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439C22⋊Q8—216no—
440C22⋊Q8—232no—
441#121—216no—
442#121—232no—
443#121—216no—
444#121—216no—
445#121—216no—
446#121—216no—
447#121—216no—
448#121—28no—
449#121—28no—
450#121—216no—
451#121—264no—
452#121—232no—
453#121—232no—
454#121—464no—
455#120—232no—
456#120—264no—
457C4×Q8—216no—
458C4×Q8—216no—
459C4×Q8—216no—
460C4×Q8—28no—
461C4×Q8—28no—
462C4×Q8C2×D418yes—
463C4×Q8C2×D418yes—
464C4×D4—216no—
465C4×D4—216no—
466C4×D4—216no—
467C4×D4—232no—
468C4×D4—232no—
469C4×D4—216no—
470C4×D4—216no—
471C4×D4—216no—
472C4×D4—216no—
473C4×D4—216no—
474C4×D4—28no—
475C4×D4—216no—
476C4×D4—28no—
477C4×D4—464no—
478C4×D4C2×D4116yes—
479C4×D4C2×D4116yes—
480C4×D4C2×D418yes—
481C4×D4C2×D418yes—
482#117—28no—
483#117—216no—
484#117—216no—
485#117—216no—
486#117C2×D418yes—
487#117C2×D4116yes—
488#117#41116yescomplemented
489C2×C4⋊C4—28no—
490C2×C4⋊C4—28no—
491C2×C4⋊C4—216no—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2418yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C24132yes—
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2411yescharacteristic
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C22⋊C4—232no—
514C2×C22⋊C4—432no—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C24132yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C24116yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2414yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C24132yes—
529C2×C22⋊C4C24132yes—
530C2×C22⋊C4C24116yes—
531C2×C22⋊C4C2412yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2412yes—
534C2×C22⋊C4C2414yes—
535C2×C42—28no—
536C2×C42—216no—
537C2×C42—28no—
538C2×C42—216no—
539C2×C42—44no—
540C2×C42—48no—
541C2×C42C2×D418yes—
542C2×C42C2×D4116yes—
543C2×C42C2418yes—
544C2×C42C2412yes—
545C2×C42C2414yes—
546C2×C42C2418yes—
547C2×C42C2414yes—
548C2×C42C2418yes—
549C2×C42C2414yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2414yes—
553C2×C42C2414yes—
554C2×C42C2412yes—
555C2×C42C2412yes—
556C2×C42C2418yes—
557C2×C42C2414yes—
558C2×C42C2412yes—
559C2×C42C2411yescharacteristic
560C2×C42C2412yes—
561C2×C42C2412yes—
562C2×C42C2411yescharacteristic
563C2×C42C2411yescharacteristic
564C2×C42C2411yescharacteristic
565C2×C42C2414yes—
566C2×C42C2412yes—
567#95C2418yes—
568#95C2418yes—
569#95C2414yes—
570#95C2414yes—
571#95C24116yes—
572#95C24116yes—
573#95C24132yes—
574C24—28no—
575C24—216no—
576C24—48no—
577C24—48no—
578C24C2518yes—
579C24C2514yes—
580C24C2512yes—
581C24C2511yescharacteristic
582#41—232no—
583#41—432no—
584#41—832no—
585#41—832no—
586#41—832no—
587C2×Q8—24no—
588C2×Q8—24no—
589C2×Q8—24no—
590C2×Q8—28no—
591C2×Q8—28no—
592C2×Q8—24no—
593C2×Q8—28no—
594C2×Q8—216no—
595C2×Q8—28no—
596C2×Q8—28no—
597C2×Q8—48no—
598C2×Q8—816no—
599C2×Q8C22×D414yes—
600C2×D4—28no—
601C2×D4—28no—
602C2×D4—216no—
603C2×D4—216no—
604C2×D4—216no—
605C2×D4—216no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—24no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—24no—
616C2×D4—216no—
617C2×D4—216no—
618C2×D4—28no—
619C2×D4—264no—
620C2×D4—216no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—216no—
624C2×D4—432no—
625C2×D4—416no—
626C2×D4—416no—
627C2×D4—48no—
628C2×D4—432no—
629C2×D4—48no—
630C2×D4—416no—
631C2×D4—432no—
632C2×D4—816no—
633C2×D4—816no—
634C2×D4C22×D418yes—
635C2×D4C22×D414yes—
636C22×C4—28no—
637C22×C4—24no—
638C22×C4—28no—
639C22×C4—24no—
640C22×C4—28no—
641C22×C4—28no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—216no—
645C22×C4—216no—
646C22×C4—28no—
647C22×C4—216no—
648C22×C4—216no—
649C22×C4—216no—
650C22×C4—216no—
651C22×C4—48no—
652C22×C4—44no—
653C22×C4—48no—
654C22×C4—416no—
655C22×C4—416no—
656C22×C4—416no—
657C22×C4C22×D414yes—
658C22×C4C22×D418yes—
659C22×C4C22×D418yes—
660C22×C4C22×D414yes—
661C22×C4C22×D418yes—
662C22×C4C22×D414yes—
663C22×C4C2×#4118yes—
664C22×C4C2514yes—
665C22×C4C2514yes—
666C22×C4C2514yes—
667C22×C4C2518yes—
668C22×C4C2514yes—
669C22×C4C2512yes—
670C22×C4C2511yescharacteristic
671C22×C4C2512yes—
672C22×C4C2511yescharacteristic
673C22×C4C2512yes—
674C22×C4C2518yes—
675C22×C4C2514yes—
676C22×C4C2511yescharacteristic
677C22×C4C2511yescharacteristic
678C22×C4C2511yescharacteristic
679C22×C4C2511yescharacteristic
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—216no—
684C4⋊C4—28no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—28no—
692C4⋊C4—28no—
693C4⋊C4—216no—
694C4⋊C4—216no—
695C4⋊C4—432no—
696C4⋊C4C22×D414yes—
697C4⋊C4C22×D414yes—
698C4⋊C4C22×D418yes—
699C4⋊C4C22×D418yes—
700C4⋊C4C2×#41116yes—
701C22⋊C4—28no—
702C22⋊C4—216no—
703C22⋊C4—216no—
704C22⋊C4—216no—
705C22⋊C4—216no—
706C22⋊C4—216no—
707C22⋊C4—216no—
708C22⋊C4—216no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—216no—
712C22⋊C4—264no—
713C22⋊C4—264no—
714C22⋊C4—232no—
715C22⋊C4—432no—
716C22⋊C4—416no—
717C22⋊C4C22×D418yes—
718C22⋊C4C22×D418yes—
719C22⋊C4C22×D418yes—
720C22⋊C4C2×#41116yes—
721C42—216no—
722C42—28no—
723C42—24no—
724C42—24no—
725C42—216no—
726C42—28no—
727C42—216no—
728C42—28no—
729C42—24no—
730C42—28no—
731C42—24no—
732C42—24no—
733C42—28no—
734C42—48no—
735C42—44no—
736C42C22×D414yes—
737C42C22×D418yes—
738C42C22×D414yes—
739C42C22×D418yes—
740C42C22×D418yes—
741C42C22×D414yes—
742C42C22×D414yes—
743C42C2×#41116yes—
744C42H(5,𝔽2)18yes—
745C23—22no—
746C23—22no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—28no—
752C23—216no—
753C23—28no—
754C23—216no—
755C23—28no—
756C23—28no—
757C23—216no—
758C23—416no—
759C23—88no—
760C23—88no—
761C23—832no—
762C23C23×D414yes—
763C23C23×D412yes—
764C23C22×#4114yes—
765C23C2611yescharacteristic
766Q8—28no—
767Q8—48no—
768Q8—416no—
769Q8—48no—
770Q8—48no—
771Q8—88no—
772D4—216no—
773D4—28no—
774D4—416no—
775D4—416no—
776D4—416no—
777D4—48no—
778D4—416no—
779D4—48no—
780D4—48no—
781D4—416no—
782D4—864no—
783D4—88no—
784D4—88no—
785D4—816no—
786D4—816no—
787D4—816no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—28no—
799C2×C4—216no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—216no—
810C2×C4—28no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—432no—
814C2×C4—416no—
815C2×C4—416no—
816C2×C4—816no—
817C2×C4—816no—
818C2×C4—816no—
819C2×C4—88no—
820C2×C4#532116yescomplemented
821C2×C4C23×D414yes—
822C2×C4C23×D414yes—
823C2×C4C23×D412yes—
824C2×C4C23×D414yes—
825C2×C4C23×D412yes—
826C2×C4C23×D412yes—
827C2×C4C23×D412yes—
828C2×C4C23×D412yes—
829C2×C4C23×D412yes—
830C2×C4C22×#41116yes—
831C2×C4C22×#4114yes—
832C2×C4C22×#4114yes—
833C2×C4C2×H(5,𝔽2)18yes—
834C2×C4C2×H(5,𝔽2)14yes—
835C2×C4#58514yes—
836C22—22no—
837C22—28no—
838C22—22no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—48no—
843C22—44no—
844C22—48no—
845C22—416no—
846C22—432no—
847C22—48no—
848C22—44no—
849C22—44no—
850C22—48no—
851C22—1616no—
852C22C2×#53214yes—
853C22C24×D411yescharacteristic
854C22C23×#4112yes—
855C22C22×H(5,𝔽2)12yes—
856C22C2×#58512yes—
857C4—24no—
858C4—22no—
859C4—28no—
860C4—216no—
861C4—24no—
862C4—22no—
863C4—24no—
864C4—44no—
865C4—48no—
866C4—44no—
867C4—44no—
868C4—44no—
869C4C2×#53214yes—
870C4C2×#53214yes—
871C4#349814yes—
872C4#350014yes—
873C2—24no—
874C2—44no—
875C2—84no—
876C2—88no—
877C2C22×#53211yescharacteristic
878C2C2×#349811yescharacteristic
879C2#6280014yes—
880C2C2×#350011yescharacteristic
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×#3511C2semidirect
2. C2×#3508C2semidirect
3. #36644C2semidirect
4. #36639C2semidirect
5. #36639C2semidirect
6. C2×#2858C2semidirect
7. #36597C2semidirect
8. #36496C2semidirect
9. #36412C2semidirect
10. #36362C2semidirect
11. #36125C2semidirect
12. #36124C2semidirect
13. #35298C2semidirect
14. #35293C2semidirect
15. #35281C2semidirect
16. #35276C2semidirect
17. #35274C2semidirect
18. #35256C2semidirect
19. #34275C2semidirect
20. C42×#41C2semidirect
25. C2×#556C22semidirect
26. C2×#555C22semidirect
27. C2×#554C22semidirect
32. C2×#547C22semidirect
35. C2×#542C22semidirect
41. C2×#533C22semidirect
45. C2×#532C22semidirect
46. C2×#532C22semidirect
54. #2868C22semidirect
56. #2862C22semidirect
57. #2862C22semidirect
58. #2862C22semidirect
59. #2861C22semidirect
60. #2861C22semidirect
67. #2858C22semidirect
68. #2858C22semidirect
69. #2858C22semidirect
70. #2856C22semidirect
71. #2856C22semidirect
74. #2850C22semidirect
75. #2850C22semidirect
76. #2660C22semidirect
78. #2620C22semidirect
79. #2619C22semidirect
80. #2567C22semidirect
81. #2566C22semidirect
82. #2555C22semidirect
83. #2554C22semidirect
84. #2546C22semidirect
85. #2545C22semidirect
86. #2544C22semidirect
87. #2544C22semidirect
91. #2500C22semidirect
92. #2464C22semidirect
93. #2461C22semidirect
97. #2432C22semidirect
98. #2431C22semidirect
99. #2431C22semidirect
100. #2428C22semidirect
101. #2426C22semidirect
103. #2363C22semidirect
104. #2361C22semidirect
106. #2328C22semidirect
107. #2326C22semidirect
109. C4×#127C22semidirect
110. C4×#127C22semidirect
111. C4×#124C22semidirect
112. C4×#124C22semidirect
113. C4×#124C22semidirect
114. C4×#124C22semidirect
116. #2297C22semidirect
119. C42×Q8C22semidirect
120. C42×Q8C22semidirect
123. C42×D4C22semidirect
124. C42×D4C22semidirect
127. C4×#117C22semidirect
128. C4×#117C22semidirect
130. C2×C43C22semidirect
227. C4×#41D4semidirect
488. #117#41semidirect
820. C2×C4#532semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#35082
#366442
#366392
C2×#28582
#365972
#364962
#364122
#363622
#361252
#361242
#352982
#352932
#352812
#352762
#352742
#352562
#342752
C42×#412