Finite Group Databasebeta

← #7642995

Subgroups — #7642995

Order 512.

7178 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
1C2×#3520C212yesmaximal, complemented
2#39614C214yesmaximal, complemented
3#39488C212yesmaximal, complemented
4#39486C214yesmaximal, complemented
5#39484C212yesmaximal, complemented
6#39360C212yesmaximal, complemented
7#39356C212yesmaximal, complemented
8#38954C212yesmaximal, complemented
9#38951C212yesmaximal, complemented
10#38946C214yesmaximal, complemented
11#37866C218yesmaximal, complemented
12#37131C218yesmaximal, complemented
13#36645C211yesmaximal, characteristic, complemented
14#36631C211yesmaximal, characteristic, complemented
15#35606C218yesmaximal, complemented
16#35306C214yesmaximal, complemented
17#35241C212yesmaximal, complemented
18#35032C212yesmaximal, complemented
19#35011C212yesmaximal, complemented
20C2×#2293C211yesmaximal, characteristic, complemented
21#3520—232no—
22C2×#556C2212yes—
23C2×#554C2214yes—
24C2×#552C2214yes—
25C2×#551C2218yes—
26C2×D4×Q8C2212yes—
27C2×#548C2214yes—
28C2×#547C2212yes—
29C2×#547C2212yes—
30C2×#546C2214yes—
31C2×#542C2214yes—
32C2×#539C2218yes—
33C2×#536C2214yescomplemented
34C2×#533C2212yes—
35C2×#529C2212yes—
36C2×#525C2214yes—
37C22×C22⋊Q8C2214yes—
38C2×#520C2214yes—
39C22×C4×D4C2211yescharacteristic
40C22×#117C2212yes—
41#2868C2211yescharacteristic, complemented
42#2868C2211yescharacteristic, complemented
43#2862C2212yescomplemented
44#2861C2212yescomplemented
45#2860C2214yescomplemented
46#2859C2214yescomplemented
47#2859C2211yescharacteristic, complemented
48#2858C2211yescharacteristic, complemented
49#2857C2211yescharacteristic
50#2857C2214yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2214yes—
54#2856C2211yescharacteristic
55#2854C2214yes—
56#2850C2212yes—
57#2850C2214yes—
58#2726C2218yescomplemented
59#2724C2218yes—
60#2718C22116yescomplemented
61#2706C22116yescomplemented
62#2704C22116yescomplemented
63#2701C22116yes—
64#2698C22116yescomplemented
65#2683C2218yescomplemented
66#2682C2218yes—
67#2680C22116yescomplemented
68#2664C2218yescomplemented
69#2659C2218yes—
70#2621C2214yescomplemented
71#2621C2214yescomplemented
72#2620C2214yescomplemented
73#2620C2214yescomplemented
74#2617C2218yes—
75#2602C22116yescomplemented
76#2583C22116yescomplemented
77#2568C2212yescomplemented
78#2565C2214yescomplemented
79#2547C2212yescomplemented
80#2546C2212yescomplemented
81#2545C2214yescomplemented
82#2542C2212yescomplemented
83#2502C2214yescomplemented
84#2502C2214yescomplemented
85#2500C2214yescomplemented
86#2499C2214yescomplemented
87#2498C2218yes—
88#2478C22116yescomplemented
89#2474C22116yescomplemented
90#2468C22116yescomplemented
91#2461C22116yescomplemented
92#2451C2218yescomplemented
93#2447C2218yes—
94#2440C2218yescomplemented
95#2434C2214yescomplemented
96#2434C2214yescomplemented
97#2432C2218yes—
98#2432C2214yescomplemented
99#2431C2214yescomplemented
100#2429C2218yescomplemented
101#2422C2218yes—
102#2417C2218yes—
103#2417C22116yes—
104#2417C2218yescomplemented
105#2415C22116yescomplemented
106#2413C22116yescomplemented
107#2412C22116yes—
108#2407C2218yes—
109#2325C2218yes—
110#2323C2218yescomplemented
111#2317C2214yescomplemented
112#2315C2218yes—
113#2311C2214yescomplemented
114#2310C2214yescomplemented
115C4×C4⋊Q8C2214yescomplemented
116C4×C4⋊Q8C2211yescharacteristic, complemented
117C4×C4⋊Q8C2212yescomplemented
118C4×C4⋊Q8C2212yescomplemented
119C4×#127C2211yescharacteristic, complemented
120C4×#124C2212yescomplemented
121C4×#121C2214yes—
122#2293C2214yes—
123#2293C2214yes—
124#2293C2212yes—
125#2293C2212yes—
126#2293C2212yes—
127#2293C2212yes—
128#2293C2214yescomplemented
129C2×#390C2212yes—
130C2×#389C2212yes—
131C2×#388C2214yes—
132#2285C2214yes—
133C2×C4×C4⋊C4C2211yescharacteristic
134C2×C4×C22⋊C4C2212yes—
135C2×C43C2211yescharacteristic
136C22×#41C2314yes—
137C22×#41C2314yes—
138C23×Q8C2314yes—
139C23×D4C2311yescharacteristic
140C24×C4C2312yes—
141#556—216no—
142#554—232no—
143#552—232no—
144#551—264no—
145D4×Q8—216no—
146#548—232no—
147#547—216no—
148#547—216no—
149#546—232no—
150#542—232no—
151#539—264no—
152#536—416no—
153#533—216no—
154C2×C4⋊Q8C2312yes—
155C2×C4⋊Q8C2312yes—
156C2×C4⋊Q8C2312yes—
157C2×C4⋊Q8C2314yes—
158C2×C4⋊Q8C2311yescharacteristic
159C2×C4⋊Q8C2314yes—
160C2×C4⋊Q8C2312yes—
161C2×C4⋊Q8C2314yes—
162C2×#127C2311yescharacteristic
163#529—216no—
164C2×#126C2314yes—
165C2×#126C2318yes—
166C2×#126C2318yes—
167C2×#125C2312yes—
168C2×#125C2314yes—
169C2×#125C2318yes—
170C2×#124C2312yes—
171C2×#124C2312yes—
172C2×#124C2314yes—
173C2×#124C2318yes—
174C2×#124C2314yes—
175#525—232no—
176C2×#123C2314yes—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×#123C23116yes—
182C2×C22⋊Q8—232no—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2312yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C23116yes—
196C2×#121C2314yes—
197C2×#121C2312yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#120C2318yes—
202#520—232no—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2314yes—
207C2×C4×D4D4116yescomplemented
208C2×C4×D4C2312yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2312yes—
219C2×#117—48no—
220C2×#117C2314yes—
221C2×#117C2314yes—
222C2×#117C2314yes—
223C2×#117C2318yes—
224C2×#117C2314yes—
225C2×#117C2314yes—
226C2×#117C2318yes—
227C22×C4⋊C4C2314yes—
228C22×C4⋊C4C2318yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2314yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C22⋊C4C2314yes—
234C22×C22⋊C4C2318yes—
235C22×C22⋊C4C2314yes—
236C22×C22⋊C4C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2312yes—
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243#400C2318yes—
244#399C2318yes—
245#398C23116yes—
246#398C23116yes—
247#398C23116yes—
248#398C23116yes—
249#398C23116yes—
250#398C2318yes—
251#397C23116yes—
252#397C23116yes—
253#397C23116yes—
254#397C2318yes—
255#396C23116yes—
256#396C23116yes—
257#396C23116yes—
258#395C23116yes—
259#395C23116yes—
260#394C23116yes—
261#394C23116yes—
262#394C23116yes—
263#394C23116yes—
264#392C23116yes—
265#391C2312yes—
266#391C2314yes—
267#391C2318yes—
268#391C2314yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C23116yes—
273#391C2318yes—
274#391C2312yes—
275#390C2312yes—
276#390C2314yes—
277#390C2314yes—
278#390C2314yes—
279#390C2314yes—
280#390C2312yes—
281#390C2314yes—
282#390C2314yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C23116yes—
292#389C23116yes—
293#389C2318yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#388C23116yes—
302#388C23116yes—
303#388C23116yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#387C23116yes—
313#387C23116yes—
314#386C23116yes—
315#386C23116yes—
316#386C23116yes—
317#386C2318yes—
318#385C23116yes—
319#385C23116yes—
320#385C23116yes—
321#385C23116yes—
322#385C23116yes—
323#385C23116yes—
324#384C2311yescharacteristic
325#384C2312yes—
326#384C2311yescharacteristic
327#384C2314yes—
328#384C2312yes—
329#384C2314yes—
330#384C2314yes—
331#384C2314yes—
332#382C2314yes—
333#382C2312yes—
334#382C2318yes—
335#381C23116yes—
336#380C23116yes—
337#380C2314yes—
338#380C2318yes—
339#380C23116yes—
340#380C2318yes—
341#380C2318yes—
342C4×C4⋊C4C2318yes—
343C4×C4⋊C4C2318yes—
344C4×C4⋊C4C2314yes—
345C4×C4⋊C4C2312yes—
346C4×C4⋊C4C2312yes—
347C4×C4⋊C4C2312yes—
348C4×C4⋊C4C2312yes—
349C4×C22⋊C4C2318yes—
350C4×C22⋊C4C2318yes—
351C4×C22⋊C4C2314yes—
352C4×C22⋊C4C2314yes—
353C2×#95C2314yes—
354C2×#95C2312yes—
355C43C2311yescharacteristic
356C43C2311yescharacteristic
357C43C2311yescharacteristic
358C43C2312yes—
359C43C2312yes—
360C43C2311yescharacteristic
361C25C2412yes—
362C2×#41—216no—
363C2×#41—216no—
364C2×#41—416no—
365C2×#41—48no—
366C2×#41—48no—
367C22×Q8—216no—
368C22×Q8—48no—
369C22×Q8—48no—
370C22×Q8C2414yes—
371C22×Q8C2412yes—
372C22×Q8C2414yes—
373C22×Q8C2418yes—
374C22×D4—44no—
375C22×D4C2×D418yes—
376C22×D4C2414yes—
377C22×D4C2412yes—
378C22×D4C2412yes—
379C22×D4C2418yes—
380C22×D4C2414yes—
381C22×D4C2418yes—
382C22×D4C2412yes—
383C23×C4—44no—
384C23×C4—44no—
385C23×C4C2×D4116yes—
386C23×C4C2414yes—
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2414yes—
391C23×C4C2411yescharacteristic
392C23×C4C2414yes—
393C23×C4C2418yes—
394C23×C4C2418yes—
395C23×C4C2418yes—
396C23×C4C2412yes—
397C23×C4C2414yes—
398C23×C4C2412yes—
399C4⋊Q8—216no—
400C4⋊Q8—28no—
401C4⋊Q8—28no—
402C4⋊Q8—28no—
403C4⋊Q8—42no—
404C4⋊Q8—48no—
405C4⋊Q8—44no—
406C4⋊Q8—48no—
407#127—42no—
408#126—232no—
409#126—232no—
410#126—216no—
411#125—232no—
412#125—28no—
413#125—216no—
414#124—216no—
415#124—232no—
416#124—28no—
417#124—28no—
418#124—48no—
419#123—232no—
420#123—232no—
421#123—216no—
422#123—232no—
423#123—232no—
424#123—432no—
425C22⋊Q8—28no—
426C22⋊Q8—216no—
427C22⋊Q8—232no—
428C22⋊Q8—216no—
429C22⋊Q8—216no—
430C22⋊Q8—232no—
431C22⋊Q8—216no—
432C22⋊Q8—216no—
433C22⋊Q8—232no—
434C22⋊Q8—216no—
435C22⋊Q8—232no—
436C22⋊Q8—432no—
437C22⋊Q8—416no—
438#121—232no—
439#121—216no—
440#121—28no—
441#121—216no—
442#121—216no—
443#120—232no—
444C4×Q8—216no—
445C4×Q8—216no—
446C4×Q8—28no—
447C4×Q8—216no—
448C4×D4—216no—
449C4×D4—232no—
450C4×D4—232no—
451C4×D4—216no—
452C4×D4—232no—
453C4×D4—28no—
454C4×D4—48no—
455C4×D4C2×D4116yes—
456C4×D4C2×D4116yes—
457C4×D4C2×D4116yes—
458C4×D4C2×D4116yes—
459#117—216no—
460#117—216no—
461#117—232no—
462#117—216no—
463#117—216no—
464#117—48no—
465#117—416no—
466C2×C4⋊C4—232no—
467C2×C4⋊C4—216no—
468C2×C4⋊C4—216no—
469C2×C4⋊C4—44no—
470C2×C4⋊C4—48no—
471C2×C4⋊C4C2×D418yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2418yes—
474C2×C4⋊C4C2412yes—
475C2×C4⋊C4C2418yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2414yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2412yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2418yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C24116yes—
496C2×C4⋊C4C24116yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C22⋊C4—232no—
504C2×C22⋊C4—216no—
505C2×C22⋊C4—48no—
506C2×C22⋊C4C2×D4116yes—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2418yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2414yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2414yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C24116yes—
526C2×C22⋊C4C24116yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2414yes—
529C2×C42—28no—
530C2×C42—24no—
531C2×C42—44no—
532C2×C42—44no—
533C2×C42—42no—
534C2×C42C2×D418yes—
535C2×C42C2412yes—
536C2×C42C2411yescharacteristic
537C2×C42C2418yes—
538C2×C42C2418yes—
539C2×C42C2414yes—
540C2×C42C2414yes—
541C2×C42C2412yes—
542C2×C42C2411yescharacteristic
543C2×C42C2412yes—
544C2×C42C2411yescharacteristic
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2412yes—
548C2×C42C2412yes—
549C2×C42C2414yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2412yes—
553C2×C42C2411yescharacteristic
554C2×C42C2411yescharacteristic
555C2×C42C2411yescharacteristic
556C2×C42C2411yescharacteristic
557C2×C42C2411yescharacteristic
558#95C2418yes—
559#95C2418yes—
560#95C2414yes—
561#95C2414yes—
562#95C2418yes—
563#95C2418yes—
564#95C24116yes—
565#95C24116yes—
566#95C2418yes—
567#95C24116yes—
568#95C24116yes—
569#95C24116yes—
570#95C24116yes—
571C24—28no—
572C24—42no—
573C24—42no—
574C24—44no—
575C24C22×D418yes—
576C24C2514yes—
577C24C2514yes—
578C24C2511yescharacteristic
579#41—464no—
580#41—832no—
581C2×Q8—28no—
582C2×Q8—24no—
583C2×Q8—28no—
584C2×Q8—216no—
585C2×Q8—24no—
586C2×Q8—28no—
587C2×Q8—216no—
588C2×Q8—24no—
589C2×Q8—28no—
590C2×Q8—48no—
591C2×Q8—48no—
592C2×Q8—832no—
593C2×D4—28no—
594C2×D4—216no—
595C2×D4—216no—
596C2×D4—216no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—28no—
600C2×D4—28no—
601C2×D4—24no—
602C2×D4—416no—
603C2×D4—44no—
604C2×D4—416no—
605C2×D4—44no—
606C2×D4—48no—
607C2×D4—44no—
608C2×D4—48no—
609C2×D4C22×D418yes—
610C2×D4C22×D418yes—
611C22×C4—24no—
612C22×C4—22no—
613C22×C4—28no—
614C22×C4—24no—
615C22×C4—22no—
616C22×C4—28no—
617C22×C4—216no—
618C22×C4—24no—
619C22×C4—216no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—24no—
623C22×C4—216no—
624C22×C4—216no—
625C22×C4—432no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—42no—
633C22×C4—416no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—48no—
640C22×C4C22×D414yes—
641C22×C4C22×D414yes—
642C22×C4C22×D414yes—
643C22×C4C22×D4116yes—
644C22×C4C22×D418yes—
645C22×C4C22×D4116yes—
646C22×C42−1+418yes—
647C22×C4C2512yes—
648C22×C4C2514yes—
649C22×C4C2518yes—
650C22×C4C2518yes—
651C22×C4C2514yes—
652C22×C4C2518yes—
653C22×C4C2514yes—
654C22×C4C2511yescharacteristic
655C22×C4C2511yescharacteristic
656C22×C4C2514yes—
657C22×C4C2511yescharacteristic
658C22×C4C2511yescharacteristic
659C22×C4C2512yes—
660C22×C4C2512yes—
661C22×C4C2512yes—
662C22×C4C2511yescharacteristic
663C22×C4C2511yescharacteristic
664C4⋊C4—28no—
665C4⋊C4—216no—
666C4⋊C4—24no—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—216no—
670C4⋊C4—216no—
671C4⋊C4—216no—
672C4⋊C4—28no—
673C4⋊C4—24no—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—216no—
677C4⋊C4—28no—
678C4⋊C4—216no—
679C4⋊C4—28no—
680C4⋊C4—216no—
681C4⋊C4—216no—
682C4⋊C4—28no—
683C4⋊C4—28no—
684C4⋊C4—44no—
685C4⋊C4—48no—
686C4⋊C4—44no—
687C4⋊C4—416no—
688C4⋊C4—416no—
689C4⋊C4—48no—
690C4⋊C4—48no—
691C4⋊C4—48no—
692C4⋊C4—44no—
693C4⋊C4C22×D418yes—
694C4⋊C4C22×D418yes—
695C22⋊C4—28no—
696C22⋊C4—216no—
697C22⋊C4—216no—
698C22⋊C4—216no—
699C22⋊C4—216no—
700C22⋊C4—216no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—28no—
704C22⋊C4—216no—
705C22⋊C4—28no—
706C22⋊C4—216no—
707C22⋊C4—216no—
708C22⋊C4—216no—
709C22⋊C4—216no—
710C22⋊C4—216no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—416no—
714C22⋊C4—416no—
715C22⋊C4C22×D4116yes—
716C22⋊C4C22×D4116yes—
717C42—216no—
718C42—216no—
719C42—28no—
720C42—24no—
721C42—22no—
722C42—28no—
723C42—24no—
724C42—24no—
725C42—24no—
726C42—24no—
727C42—24no—
728C42—22no—
729C42—24no—
730C42—22no—
731C42—42no—
732C42—42no—
733C42—42no—
734C42—44no—
735C42C22×D414yes—
736C42C22×D414yes—
737C42C22×D414yes—
738C42C22×D414yes—
739C42H(5,𝔽2)14yes—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—24no—
744C23—28no—
745C23—24no—
746C23—28no—
747C23—216no—
748C23—24no—
749C23—24no—
750C23—28no—
751C23—28no—
752C23—24no—
753C23—48no—
754C23—48no—
755C23—88no—
756C23—88no—
757C23C23×D418yes—
758C23C23×D412yes—
759C23C2×2−1+414yes—
760C23C2611yescharacteristic
761Q8—416no—
762Q8—48no—
763Q8—416no—
764Q8—816no—
765D4—216no—
766D4—48no—
767D4—432no—
768D4—416no—
769D4—48no—
770D4—88no—
771D4—816no—
772C2×C4—21no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—28no—
788C2×C4—232no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—28no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—28no—
803C2×C4—28no—
804C2×C4—216no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—416no—
808C2×C4—48no—
809C2×C4—48no—
810C2×C4—48no—
811C2×C4—432no—
812C2×C4—416no—
813C2×C4—816no—
814C2×C4—88no—
815C2×C4—816no—
816C2×C4C23×D412yes—
817C2×C4C23×D418yes—
818C2×C4C23×D412yes—
819C2×C4C23×D412yes—
820C2×C4C23×D412yes—
821C2×C4C23×D412yes—
822C2×C4C23×D412yes—
823C2×C4C2×H(5,𝔽2)14yes—
824C2×C4C2×H(5,𝔽2)12yes—
825C2×C4C2×2−1+414yes—
826C2×C4C2×2−1+414yes—
827C2×C4#58514yes—
828C2×C4#58512yes—
829C22—22no—
830C22—24no—
831C22—24no—
832C22—22no—
833C22—28no—
834C22—28no—
835C22—28no—
836C22—48no—
837C22—48no—
838C22—44no—
839C22—44no—
840C22—48no—
841C22—48no—
842C22—44no—
843C22—816no—
844C22#349914yes—
845C22C24×D411yescharacteristic
846C22C22×H(5,𝔽2)11yescharacteristic
847C22C22×2−1+412yes—
848C22C2×#58511yescharacteristic
849C22C2×#58512yes—
850C4—22no—
851C4—28no—
852C4—22no—
853C4—22no—
854C4—24no—
855C4—24no—
856C4—24no—
857C4—22no—
858C4—48no—
859C4—44no—
860C4—44no—
861C4—42no—
862C4—48no—
863C4—44no—
864C4—48no—
865C4#344914yes—
866C4#349614yes—
867C2—24no—
868C2—48no—
869C2—84no—
870C2C2×#344911yescharacteristic
871C2C2×#349611yescharacteristic
872C2C2×#349911yescharacteristic
873C2#6282312yes—
874C2#6283512yes—
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×#3520C2semidirect
2. #39614C2semidirect
3. #39488C2semidirect
4. #39486C2semidirect
5. #39484C2semidirect
6. #39360C2semidirect
7. #39356C2semidirect
8. #38954C2semidirect
9. #38951C2semidirect
10. #38946C2semidirect
11. #37866C2semidirect
12. #37131C2semidirect
13. #36645C2semidirect
14. #36631C2semidirect
15. #35606C2semidirect
16. #35306C2semidirect
17. #35241C2semidirect
18. #35032C2semidirect
19. #35011C2semidirect
20. C2×#2293C2semidirect
33. C2×#536C22semidirect
41. #2868C22semidirect
42. #2868C22semidirect
43. #2862C22semidirect
44. #2861C22semidirect
45. #2860C22semidirect
46. #2859C22semidirect
47. #2859C22semidirect
48. #2858C22semidirect
58. #2726C22semidirect
60. #2718C22semidirect
61. #2706C22semidirect
62. #2704C22semidirect
64. #2698C22semidirect
65. #2683C22semidirect
67. #2680C22semidirect
68. #2664C22semidirect
70. #2621C22semidirect
71. #2621C22semidirect
72. #2620C22semidirect
73. #2620C22semidirect
75. #2602C22semidirect
76. #2583C22semidirect
77. #2568C22semidirect
78. #2565C22semidirect
79. #2547C22semidirect
80. #2546C22semidirect
81. #2545C22semidirect
82. #2542C22semidirect
83. #2502C22semidirect
84. #2502C22semidirect
85. #2500C22semidirect
86. #2499C22semidirect
88. #2478C22semidirect
89. #2474C22semidirect
90. #2468C22semidirect
91. #2461C22semidirect
92. #2451C22semidirect
94. #2440C22semidirect
95. #2434C22semidirect
96. #2434C22semidirect
98. #2432C22semidirect
99. #2431C22semidirect
100. #2429C22semidirect
104. #2417C22semidirect
105. #2415C22semidirect
106. #2413C22semidirect
110. #2323C22semidirect
111. #2317C22semidirect
113. #2311C22semidirect
114. #2310C22semidirect
115. C4×C4⋊Q8C22semidirect
116. C4×C4⋊Q8C22semidirect
117. C4×C4⋊Q8C22semidirect
118. C4×C4⋊Q8C22semidirect
119. C4×#127C22semidirect
120. C4×#124C22semidirect
128. #2293C22semidirect
207. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
#396142
#394882
#394862
#394842
#393602
#393562
#389542
#389512
#389462
#378662
#371312
#366452
#366312
#356062
#353062
#352412
#350322
#350112
C2×#22932