Finite Group Databasebeta

← #7645368

Subgroups — #7645368

Order 512.

7504 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#553C211yesmaximal, characteristic, complemented
2C2×#3459C211yesmaximal, characteristic, complemented
3#41372C218yesmaximal, complemented
4#41368C218yesmaximal, complemented
5#38042C218yesmaximal, complemented
6#37836C218yesmaximal, complemented
7#37549C212yesmaximal, complemented
8#37439C212yesmaximal, complemented
9#36971C214yesmaximal, complemented
10#36709C214yesmaximal, complemented
11#35358C214yesmaximal, complemented
12#35263C212yesmaximal, complemented
13#35236C212yesmaximal, complemented
14#35000C212yesmaximal, complemented
15#34985C212yesmaximal, complemented
16#34984C212yesmaximal, complemented
17C2×#2487C212yesmaximal, complemented
18#34181C211yesmaximal, characteristic, complemented
19C2×#553—216no—
20C2×#553C2218yescomplemented
21C2×#553C2218yescomplemented
22#3459—216no—
23C2×#543C2211yescharacteristic
24C2×#539C2212yes—
25C2×#539C2214yescomplemented
26C2×#538C2212yes—
27C2×#538C2214yescomplemented
28C2×#534C2212yes—
29C2×#534C2211yescharacteristic
30C2×#534C2214yes—
31C2×#529C2212yes—
32C2×#529C2214yescomplemented
33C22×#126C2212yescomplemented
34C22×#125C2211yescharacteristic, complemented
35C2×#525C2212yes—
36C2×#525C2214yescomplemented
37C22×#123C2212yescomplemented
38C22×#121C2212yes—
39C22×#121C2211yescharacteristic
40C22×#121C2211yescharacteristic, complemented
41C2×#518C2212yes—
42C22×C4×D4C2212yes—
43C22×C4×D4C2212yes—
44C22×C4×D4C2211yescharacteristic
45C22×C4×D4C2211yescharacteristic, complemented
46C22×#117C2211yescharacteristic, complemented
47C23×C4⋊C4C2211yescharacteristic
48#2855C2214yescomplemented
49#2854C2214yes—
50#2854C2214yescomplemented
51#2848C2214yescomplemented
52#2847C2214yes—
53#2847C2214yescomplemented
54#2822C2214yescomplemented
55#2820C2214yescomplemented
56#2813C2218yescomplemented
57#2727C22116yescomplemented
58#2725C22116yescomplemented
59#2705C22116yescomplemented
60#2702C22116yescomplemented
61#2695C22116yescomplemented
62#2693C22116yescomplemented
63#2672C22116yescomplemented
64#2671C22116yescomplemented
65#2664C2218yescomplemented
66#2656C2214yescomplemented
67#2639C2214yescomplemented
68#2636C2218yescomplemented
69#2629C2218yescomplemented
70#2627C2214yescomplemented
71#2626C2214yescomplemented
72#2625C2214yescomplemented
73#2624C2214yescomplemented
74#2624C2214yescomplemented
75#2618C2214yes—
76#2618C2214yescomplemented
77#2617C2214yes—
78#2617C2214yescomplemented
79#2615C2214yescomplemented
80#2584C2214yescomplemented
81#2562C2214yescomplemented
82#2562C2214yescomplemented
83#2543C22116yescomplemented
84#2543C2218yescomplemented
85#2540C2214yescomplemented
86#2538C2214yescomplemented
87#2537C2214yescomplemented
88#2534C2218yescomplemented
89#2498C2218yescomplemented
90#2487C2214yescomplemented
91#2487C2218yescomplemented
92#2487C2218yescomplemented
93#2487C2218yescomplemented
94#2487C2214yescomplemented
95#2486C2214yescomplemented
96#2485C2218yescomplemented
97#2450C22116yescomplemented
98#2449C22116yescomplemented
99#2425C22116yescomplemented
100#2425C22116yescomplemented
101#2424C22116yescomplemented
102#2424C22116yescomplemented
103#2416C22116yescomplemented
104#2416C2218yescomplemented
105#2416C2218yescomplemented
106#2413C2218yescomplemented
107#2412C2218yescomplemented
108#2411C2218yescomplemented
109#2410C2218yescomplemented
110#2408C2214yescomplemented
111C2×#400C2214yescomplemented
112C2×#399C2214yescomplemented
113#2349C2218yescomplemented
114D4×C4⋊C4C2218yescomplemented
115#2324C2218yescomplemented
116#2316C2212yescomplemented
117#2316C2214yescomplemented
118#2315C2212yes—
119#2315C2212yescomplemented
120#2311C2214yescomplemented
121#2308C2214yes—
122C2×#389C2214yescomplemented
123C2×#386C2214yes—
124C2×#385C2214yes—
125#2285C2212yescomplemented
126C2×#380C2212yes—
127C2×#380C2212yescomplemented
128C2×#380C2214yescomplemented
129C22×#41C2312yes—
130C23×D4C2312yes—
131C23×D4C2312yes—
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C24×C4C2312yes—
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140#553—264no—
141#553—264no—
142#543—28no—
143#539—232no—
144#539—216no—
145#538—232no—
146#538—216no—
147#534—216no—
148#534—28no—
149#534—416no—
150#529—232no—
151#529—216no—
152C2×#126—216no—
153C2×#126C2314yes—
154C2×#126C23116yes—
155C2×#126C2314yes—
156C2×#126C2314yes—
157C2×#125—28no—
158C2×#125C2312yes—
159C2×#125C2314yes—
160C2×#125C2314yes—
161C2×#125C2314yes—
162C2×#124C2312yes—
163C2×#124C2314yes—
164#525—216no—
165#525—232no—
166C2×#123—216no—
167C2×#123C23116yes—
168C2×#123C2314yes—
169C2×#123C2314yes—
170C2×#123C2314yes—
171C2×#123C2314yes—
172C2×#123C2314yes—
173C2×#123C2314yes—
174C2×#123C2318yes—
175C2×#123C2318yes—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2312yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2318yes—
183C2×#121—216no—
184C2×#121—28no—
185C2×#121—28no—
186C2×#121C2312yes—
187C2×#121C2314yes—
188C2×#121C2312yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2312yes—
192C2×#121C2314yes—
193C2×#121C23116yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2318yes—
198C2×#121C23116yes—
199C2×#121C2318yes—
200C2×#121C23116yes—
201C2×#120C2314yes—
202C2×#120C2314yes—
203C2×#120C2314yes—
204C2×#120C2318yes—
205C2×#120C2318yes—
206#518—48no—
207C2×C4×Q8C2312yes—
208C2×C4×D4—216no—
209C2×C4×D4—216no—
210C2×C4×D4—28no—
211C2×C4×D4D4116yescomplemented
212C2×C4×D4C2312yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C23116yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C23116yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2314yes—
224C2×#117—28no—
225C2×#117C2314yes—
226C2×#117C2312yes—
227C2×#117C2314yes—
228C2×#117C2314yes—
229C2×#117C2314yes—
230C22×C4⋊C4—28no—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2314yes—
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2314yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2318yes—
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2314yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2314yes—
252C22×C22⋊C4C2318yes—
253C22×C22⋊C4C2311yescharacteristic
254C22×C22⋊C4C2311yescharacteristic
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C23116yes—
262#399C2318yes—
263#399C2318yes—
264#399C2318yes—
265#399C23116yes—
266#398C2318yes—
267#398C2318yes—
268#398C23116yes—
269#398C23116yes—
270#397C2318yes—
271#397C2318yes—
272#397C23116yes—
273#396C23116yes—
274#396C23116yes—
275#396C23116yes—
276#396C23116yes—
277#396C23116yes—
278#395C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C23116yes—
282#394C23116yes—
283#394C23116yes—
284#394C23116yes—
285#394C23116yes—
286#393C2318yes—
287#392C2318yes—
288#392C23116yes—
289#392C2318yes—
290#391C2318yes—
291#390C2318yes—
292#390C2318yes—
293#390C23116yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C23116yes—
299#389C2318yes—
300#389C23116yes—
301#389C23116yes—
302#388C23116yes—
303#388C23116yes—
304#388C23116yes—
305#388C23116yes—
306#387C23116yes—
307#386C2318yes—
308#386C2318yes—
309#386C23116yes—
310#386C23116yes—
311#386C23116yes—
312#386C2318yes—
313#386C23116yes—
314#386C2318yes—
315#386C23116yes—
316#386C23116yes—
317#385C23116yes—
318#385C23116yes—
319#385C23116yes—
320#385C2318yes—
321#385C2318yes—
322#385C23116yes—
323#384C2314yes—
324#382C2314yes—
325#381C2318yes—
326#380C2318yes—
327#380C2318yes—
328#380C2318yes—
329#380C2318yes—
330#380C2318yes—
331#380C2314yes—
332#380C2314yes—
333#380C2314yes—
334#380C23116yes—
335#380C2314yes—
336#380C2314yes—
337#380C2314yes—
338#380C2314yes—
339#380C2314yes—
340#380C23116yes—
341#379C2318yes—
342C4×C4⋊C4C2314yes—
343C4×C4⋊C4C2314yes—
344C2×#95C2314yes—
345C2×#95C2314yes—
346C2×#95C2318yes—
347C2×#95C2318yes—
348C25C2412yes—
349C25C2412yes—
350C25C2411yescharacteristic
351C25C2411yescharacteristic
352C2×#41—28no—
353C2×#41—48no—
354C22×Q8C2412yes—
355C22×Q8C2412yes—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—28no—
359C22×D4—28no—
360C22×D4—28no—
361C22×D4—28no—
362C22×D4—28no—
363C22×D4—28no—
364C22×D4—28no—
365C22×D4—24no—
366C22×D4—44no—
367C22×D4—84no—
368C22×D4C2×D418yes—
369C22×D4C2414yes—
370C22×D4C2414yes—
371C22×D4C2418yes—
372C22×D4C2412yes—
373C22×D4C2414yes—
374C22×D4C2412yes—
375C22×D4C2414yes—
376C22×D4C2412yes—
377C22×D4C2414yes—
378C22×D4C2412yes—
379C22×D4C2418yes—
380C22×D4C24116yes—
381C23×C4—28no—
382C23×C4—28no—
383C23×C4—28no—
384C23×C4—44no—
385C23×C4—44no—
386C23×C4—48no—
387C23×C4—84no—
388C23×C4—84no—
389C23×C4C2×D418yes—
390C23×C4C2×D418yes—
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2414yes—
394C23×C4C2411yescharacteristic
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2418yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2418yes—
403C23×C4C2412yes—
404C23×C4C2418yes—
405C23×C4C2414yes—
406C23×C4C2418yes—
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2412yes—
412#126—264no—
413#126—216no—
414#126—216no—
415#126—216no—
416#125—216no—
417#125—216no—
418#125—216no—
419#125—28no—
420#124—216no—
421#124—28no—
422#123—216no—
423#123—216no—
424#123—216no—
425#123—216no—
426#123—264no—
427#123—216no—
428#123—216no—
429#123—416no—
430#123—416no—
431C22⋊Q8—28no—
432C22⋊Q8—28no—
433C22⋊Q8—28no—
434C22⋊Q8—216no—
435C22⋊Q8—216no—
436C22⋊Q8—216no—
437C22⋊Q8—88no—
438#121—264no—
439#121—216no—
440#121—216no—
441#121—216no—
442#121—216no—
443#121—216no—
444#121—216no—
445#121—28no—
446#121—28no—
447#121—28no—
448#121—216no—
449#121—416no—
450#121—432no—
451#121—88no—
452#121—816no—
453#120—216no—
454#120—216no—
455#120—216no—
456#120—416no—
457#120—416no—
458C4×Q8—28no—
459C4×D4—216no—
460C4×D4—216no—
461C4×D4—216no—
462C4×D4—216no—
463C4×D4—216no—
464C4×D4—264no—
465C4×D4—216no—
466C4×D4—216no—
467C4×D4—28no—
468C4×D4—432no—
469C4×D4C2×D4132yes—
470C4×D4C2×D4132yes—
471#117—216no—
472#117—216no—
473#117—28no—
474#117—216no—
475#117—48no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—216no—
480C2×C4⋊C4—216no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—28no—
483C2×C4⋊C4—28no—
484C2×C4⋊C4—28no—
485C2×C4⋊C4—48no—
486C2×C4⋊C4—48no—
487C2×C4⋊C4—88no—
488C2×C4⋊C4C2×D418yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2418yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C24116yes—
510C2×C4⋊C4C24116yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C24116yes—
516C2×C4⋊C4C2414yes—
517C2×C22⋊C4—28no—
518C2×C22⋊C4—28no—
519C2×C22⋊C4—216no—
520C2×C22⋊C4—28no—
521C2×C22⋊C4—28no—
522C2×C22⋊C4—28no—
523C2×C22⋊C4—28no—
524C2×C22⋊C4—48no—
525C2×C22⋊C4—88no—
526C2×C22⋊C4C2×D418yes—
527C2×C22⋊C4C2×D418yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C24116yes—
546C2×C22⋊C4C24116yes—
547C2×C22⋊C4C24116yes—
548C2×C22⋊C4C24116yes—
549C2×C22⋊C4C24116yes—
550C2×C22⋊C4C24116yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C42—28no—
554C2×C42—28no—
555C2×C42C2×D418yes—
556C2×C42C2414yes—
557C2×C42C2418yes—
558C2×C42C2414yes—
559C2×C42C2418yes—
560C2×C42C2412yes—
561C2×C42C2412yes—
562#95C2418yes—
563#95C24116yes—
564#95C2418yes—
565#95C24116yes—
566#95C2418yes—
567#95C24116yes—
568#95C24116yes—
569#95C2418yes—
570#95C24116yes—
571#95C24116yes—
572C24—22no—
573C24—22no—
574C24—24no—
575C24—24no—
576C24—24no—
577C24—24no—
578C24—24no—
579C24—24no—
580C24—42no—
581C24—42no—
582C24—44no—
583C24—44no—
584C24—42no—
585C24—44no—
586C24—44no—
587C24—42no—
588C24C22×D414yes—
589C24C22×D414yes—
590C24H(5,𝔽2)14yes—
591C242−1+414yes—
592C24C2514yes—
593C24C2514yes—
594C24C2512yes—
595C24C2511yescharacteristic
596C24C2512yes—
597#41—816no—
598C2×Q8—24no—
599C2×Q8—24no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×D4—232no—
603C2×D4—28no—
604C2×D4—28no—
605C2×D4—28no—
606C2×D4—28no—
607C2×D4—216no—
608C2×D4—28no—
609C2×D4—216no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—216no—
614C2×D4—28no—
615C2×D4—28no—
616C2×D4—216no—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—28no—
622C2×D4—44no—
623C2×D4—416no—
624C2×D4—44no—
625C2×D4—48no—
626C2×D4—416no—
627C2×D4—44no—
628C2×D4—48no—
629C2×D4—416no—
630C2×D4—416no—
631C2×D4—416no—
632C2×D4—432no—
633C2×D4—432no—
634C2×D4—816no—
635C2×D4C22×D4116yes—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—216no—
652C22×C4—216no—
653C22×C4—28no—
654C22×C4—216no—
655C22×C4—216no—
656C22×C4—28no—
657C22×C4—416no—
658C22×C4—416no—
659C22×C4—42no—
660C22×C4—44no—
661C22×C4—42no—
662C22×C4—44no—
663C22×C4—42no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—44no—
670C22×C4—48no—
671C22×C4—48no—
672C22×C4—48no—
673C22×C4—48no—
674C22×C4—44no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—48no—
678C22×C4—816no—
679C22×C4—816no—
680C22×C4—816no—
681C22×C4C22×D418yes—
682C22×C4C22×D414yes—
683C22×C4C22×D414yes—
684C22×C4C22×D418yes—
685C22×C4C22×D414yes—
686C22×C4C22×D414yes—
687C22×C4C22×D414yes—
688C22×C4C22×D418yes—
689C22×C4C22×D418yes—
690C22×C4C2514yes—
691C22×C4C25116yes—
692C22×C4C2514yes—
693C22×C4C2514yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2514yes—
697C22×C4C2511yescharacteristic
698C22×C4C2512yes—
699C22×C4C2512yes—
700C22×C4C2512yes—
701C22×C4C2512yes—
702C22×C4C2511yescharacteristic
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—216no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—216no—
713C4⋊C4—216no—
714C4⋊C4—24no—
715C4⋊C4—28no—
716C4⋊C4—24no—
717C4⋊C4—28no—
718C4⋊C4—28no—
719C4⋊C4—24no—
720C4⋊C4—28no—
721C4⋊C4—24no—
722C4⋊C4—216no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—416no—
726C4⋊C4—416no—
727C4⋊C4—48no—
728C4⋊C4—416no—
729C4⋊C4—48no—
730C4⋊C4C22×D4116yes—
731C22⋊C4—216no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—216no—
737C22⋊C4—216no—
738C22⋊C4—216no—
739C22⋊C4—216no—
740C22⋊C4—28no—
741C22⋊C4—28no—
742C22⋊C4—216no—
743C22⋊C4—28no—
744C22⋊C4—28no—
745C22⋊C4—28no—
746C22⋊C4—28no—
747C22⋊C4—48no—
748C22⋊C4—416no—
749C22⋊C4—416no—
750C22⋊C4—416no—
751C22⋊C4—416no—
752C22⋊C4—416no—
753C22⋊C4—416no—
754C22⋊C4C22×D4116yes—
755C22⋊C4C22×D4116yes—
756C42—28no—
757C42—216no—
758C42—28no—
759C42—48no—
760C42C22×D418yes—
761C42C22×D418yes—
762C23—24no—
763C23—22no—
764C23—24no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—24no—
769C23—24no—
770C23—28no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—28no—
778C23—28no—
779C23—28no—
780C23—28no—
781C23—44no—
782C23—44no—
783C23—48no—
784C23—48no—
785C23—44no—
786C23—44no—
787C23—48no—
788C23—48no—
789C23—416no—
790C23—48no—
791C23—48no—
792C23—84no—
793C23—84no—
794C23—84no—
795C23—88no—
796C23—88no—
797C23—84no—
798C23—88no—
799C23#537116yes—
800C23C23×D414yes—
801C23C23×D412yes—
802C23C23×D414yes—
803C23C2×H(5,𝔽2)12yes—
804C23C2×H(5,𝔽2)14yes—
805C23C2×2−1+412yes—
806C23C2×2−1+414yes—
807C23C2611yescharacteristic
808Q8—84no—
809Q8—84no—
810D4—232no—
811D4—48no—
812D4—416no—
813D4—416no—
814D4—432no—
815D4—48no—
816D4—84no—
817D4—84no—
818D4—88no—
819D4—816no—
820D4—88no—
821D4—1616no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—216no—
831C2×C4—216no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—216no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—216no—
845C2×C4—24no—
846C2×C4—216no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—24no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—48no—
856C2×C4—48no—
857C2×C4—48no—
858C2×C4—48no—
859C2×C4—416no—
860C2×C4—88no—
861C2×C4—816no—
862C2×C4—84no—
863C2×C4—816no—
864C2×C4—84no—
865C2×C4—816no—
866C2×C4—168no—
867C2×C4C23×D414yes—
868C2×C4C23×D414yes—
869C2×C4C23×D414yes—
870C2×C4C23×D412yes—
871C2×C4C23×D414yes—
872C2×C4C23×D412yes—
873C2×C4#58514yes—
874C22—22no—
875C22—24no—
876C22—22no—
877C22—24no—
878C22—28no—
879C22—24no—
880C22—28no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—416no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—48no—
893C22—48no—
894C22—48no—
895C22—48no—
896C22—44no—
897C22—44no—
898C22—88no—
899C22—816no—
900C22—816no—
901C22C2×#53714yes—
902C22C2×#53718yes—
903C22C24×D411yescharacteristic
904C22C22×H(5,𝔽2)11yescharacteristic
905C22C22×2−1+411yescharacteristic
906C22C2×#58512yes—
907C22H(7,𝔽2)12yes—
908C4—22no—
909C4—24no—
910C4—24no—
911C4—24no—
912C4—24no—
913C4—44no—
914C4—44no—
915C4—44no—
916C4—44no—
917C4—416no—
918C4—44no—
919C4—44no—
920C4#348514yes—
921C2—24no—
922C2—28no—
923C2—44no—
924C2—84no—
925C2—84no—
926C2C22×#53711yescharacteristic
927C2C2×#348511yescharacteristic
928C2#6285211yescharacteristic
929C2#6290212yes—
930C2#6290512yes—
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. C22×#553C2semidirect
2. C2×#3459C2semidirect
3. #41372C2semidirect
4. #41368C2semidirect
5. #38042C2semidirect
6. #37836C2semidirect
7. #37549C2semidirect
8. #37439C2semidirect
9. #36971C2semidirect
10. #36709C2semidirect
11. #35358C2semidirect
12. #35263C2semidirect
13. #35236C2semidirect
14. #35000C2semidirect
15. #34985C2semidirect
16. #34984C2semidirect
17. C2×#2487C2semidirect
18. #34181C2semidirect
20. C2×#553C22semidirect
21. C2×#553C22semidirect
25. C2×#539C22semidirect
27. C2×#538C22semidirect
32. C2×#529C22semidirect
33. C22×#126C22semidirect
34. C22×#125C22semidirect
36. C2×#525C22semidirect
37. C22×#123C22semidirect
40. C22×#121C22semidirect
45. C22×C4×D4C22semidirect
46. C22×#117C22semidirect
48. #2855C22semidirect
50. #2854C22semidirect
51. #2848C22semidirect
53. #2847C22semidirect
54. #2822C22semidirect
55. #2820C22semidirect
56. #2813C22semidirect
57. #2727C22semidirect
58. #2725C22semidirect
59. #2705C22semidirect
60. #2702C22semidirect
61. #2695C22semidirect
62. #2693C22semidirect
63. #2672C22semidirect
64. #2671C22semidirect
65. #2664C22semidirect
66. #2656C22semidirect
67. #2639C22semidirect
68. #2636C22semidirect
69. #2629C22semidirect
70. #2627C22semidirect
71. #2626C22semidirect
72. #2625C22semidirect
73. #2624C22semidirect
74. #2624C22semidirect
76. #2618C22semidirect
78. #2617C22semidirect
79. #2615C22semidirect
80. #2584C22semidirect
81. #2562C22semidirect
82. #2562C22semidirect
83. #2543C22semidirect
84. #2543C22semidirect
85. #2540C22semidirect
86. #2538C22semidirect
87. #2537C22semidirect
88. #2534C22semidirect
89. #2498C22semidirect
90. #2487C22semidirect
91. #2487C22semidirect
92. #2487C22semidirect
93. #2487C22semidirect
94. #2487C22semidirect
95. #2486C22semidirect
96. #2485C22semidirect
97. #2450C22semidirect
98. #2449C22semidirect
99. #2425C22semidirect
100. #2425C22semidirect
101. #2424C22semidirect
102. #2424C22semidirect
103. #2416C22semidirect
104. #2416C22semidirect
105. #2416C22semidirect
106. #2413C22semidirect
107. #2412C22semidirect
108. #2411C22semidirect
109. #2410C22semidirect
110. #2408C22semidirect
111. C2×#400C22semidirect
112. C2×#399C22semidirect
113. #2349C22semidirect
114. D4×C4⋊C4C22semidirect
115. #2324C22semidirect
116. #2316C22semidirect
117. #2316C22semidirect
119. #2315C22semidirect
120. #2311C22semidirect
122. C2×#389C22semidirect
125. #2285C22semidirect
127. C2×#380C22semidirect
128. C2×#380C22semidirect
211. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5532
C2×#34592
#413722
#413682
#380422
#378362
#375492
#374392
#369712
#367092
#353582
#352632
#352362
#350002
#349852
#349842
C2×#24872
#341812