Finite Group Databasebeta

← #7644134

Subgroups — #7644134

Order 512.

6772 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3506C211yesmaximal, characteristic
2C2×#3501C211yesmaximal, characteristic, complemented
3#42682C214yesmaximal, complemented
4#42681C214yesmaximal, complemented
5#42678C214yesmaximal, complemented
6#42676C214yesmaximal, complemented
7#42485C214yesmaximal, complemented
8#42482C214yesmaximal, complemented
9#42481C214yesmaximal, complemented
10#42479C214yesmaximal, complemented
11#37447C214yesmaximal, complemented
12#37442C214yesmaximal, complemented
13#36740C218yesmaximal, complemented
14#35575C214yesmaximal, complemented
15#35541C214yesmaximal, complemented
16#35180C211yesmaximal, characteristic, complemented
17#35173C211yesmaximal, characteristic, complemented
18#34642C211yesmaximal, characteristic, complemented
19#34637C211yesmaximal, characteristic, complemented
20C2×#2319C211yesmaximal, characteristic, complemented
21#3506—216no—
22#3501—216no—
23C2×#559C2214yes—
24C2×#556C2212yes—
25C2×#555C2212yes—
26C2×#554C2214yes—
27C2×#554C2212yes—
28C2×#554C2214yes—
29C2×#554C2212yes—
30C2×#553C2214yes—
31C2×#550C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×#547C2212yes—
35C2×#544C2212yes—
36C2×#543C2214yes—
37C2×#538C2214yes—
38C2×#535C2212yes—
39C2×#533C2211yescharacteristic
40C2×#533C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#525C2214yes—
44C22×C22⋊Q8C2214yes—
45C2×#520C2212yes—
46C2×#518C2212yes—
47C22×C4×D4C2211yescharacteristic
48#2857C2214yes—
49#2850C2214yes—
50#2817C2218yescomplemented
51#2816C2218yescomplemented
52#2814C2218yescomplemented
53#2814C2218yescomplemented
54#2700C22116yescomplemented
55#2698C22116yescomplemented
56#2689C22116yescomplemented
57#2687C22116yescomplemented
58#2681C22116yescomplemented
59#2680C22116yescomplemented
60#2674C22116yescomplemented
61#2672C22116yescomplemented
62#2660C2212yescomplemented
63#2660C2212yescomplemented
64#2660C2212yescomplemented
65#2660C2212yescomplemented
66#2659C2212yes—
67#2659C2214yes—
68#2659C2212yes—
69#2659C2214yes—
70#2642C2212yescomplemented
71#2641C2212yescomplemented
72#2640C2212yescomplemented
73#2640C2212yescomplemented
74#2639C2212yes—
75#2639C2214yes—
76#2639C2212yes—
77#2639C2214yes—
78#2638C2218yescomplemented
79#2638C2218yescomplemented
80#2627C2218yescomplemented
81#2625C2218yescomplemented
82#2623C2218yescomplemented
83#2618C2218yescomplemented
84#2616C2218yescomplemented
85#2614C2218yescomplemented
86#2592C2214yescomplemented
87#2584C2214yescomplemented
88#2584C2214yescomplemented
89#2568C2212yescomplemented
90#2567C2212yescomplemented
91#2567C2212yescomplemented
92#2564C22116yes—
93#2563C2212yescomplemented
94#2562C2214yescomplemented
95#2548C2212yescomplemented
96#2547C2212yescomplemented
97#2546C2212yescomplemented
98#2546C2212yescomplemented
99#2486C2218yescomplemented
100#2484C2218yescomplemented
101#2454C2218yescomplemented
102#2453C2218yescomplemented
103#2452C2218yescomplemented
104#2451C2218yescomplemented
105#2447C2218yes—
106#2447C2218yes—
107#2445C2218yes—
108#2445C2218yes—
109#2442C2218yescomplemented
110#2441C2218yescomplemented
111#2440C2218yescomplemented
112#2439C2218yescomplemented
113#2422C2218yes—
114#2422C2218yes—
115#2420C2218yes—
116#2420C2218yes—
117#2417C22116yes—
118#2412C22116yes—
119#2412C22116yes—
120#2409C2218yescomplemented
121#2406C2218yescomplemented
122#2399C2214yescomplemented
123#2399C2214yescomplemented
124#2398C2214yescomplemented
125#2398C2214yescomplemented
126#2319C2214yes—
127#2319C2214yes—
128#2319C2214yes—
129#2319C2214yes—
130#2316C2214yes—
131#2311C2214yes—
132#2297C2214yes—
133C2×#390C2212yes—
134C2×#389C2212yes—
135C2×#388C2214yes—
136#2285C2214yes—
137C2×#381C2212yes—
138C2×#380C2212yes—
139C2×C4×C4⋊C4C2211yescharacteristic
140C2×#376C2211yescharacteristic
141C22×#41C2312yes—
142C22×#41C2314yes—
143C23×Q8C2314yes—
144C23×D4C2311yescharacteristic
145C24×C4C2312yes—
146#559—232no—
147#556—216no—
148#555—216no—
149#554—232no—
150#554—232no—
151#554—216no—
152#554—216no—
153#553—232no—
154#550—216no—
155D4×Q8—216no—
156D4×Q8—216no—
157#547—216no—
158#544—216no—
159#543—232no—
160#538—232no—
161#535—216no—
162#533—28no—
163#533—28no—
164#533—28no—
165#532—28no—
166C2×C4⋊Q8C2311yescharacteristic
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2311yescharacteristic
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2314yes—
176C2×#127C2311yescharacteristic
177C2×#127C2314yes—
178C2×#126C2318yes—
179C2×#125C2312yes—
180C2×#125C2312yes—
181C2×#125C2312yes—
182C2×#125C2314yes—
183C2×#125C2314yes—
184C2×#124C2312yes—
185C2×#124C2318yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188#525—232no—
189C2×#123C2318yes—
190C2×#123C2318yes—
191C2×#123C23116yes—
192C2×#123C23116yes—
193C2×C22⋊Q8—232no—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2312yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2318yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C23116yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2312yes—
213C2×#121C2318yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#120C2318yes—
217#520—216no—
218#518—216no—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×D4D4116yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2318yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4C2318yes—
252C22×C22⋊C4C2314yes—
253C22×C22⋊C4C2314yes—
254C22×C22⋊C4C2312yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258#400C2314yes—
259#400C2318yes—
260#400C23116yes—
261#400C2314yes—
262#400C2318yes—
263#399C23116yes—
264#398C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2314yes—
268#398C2314yes—
269#398C23116yes—
270#398C23116yes—
271#398C2318yes—
272#398C2318yes—
273#398C2314yes—
274#397C23116yes—
275#397C23116yes—
276#397C2318yes—
277#397C2314yes—
278#397C23116yes—
279#397C23116yes—
280#397C2318yes—
281#397C2314yes—
282#396C23116yes—
283#396C23116yes—
284#395C2314yes—
285#395C23116yes—
286#395C2318yes—
287#395C2318yes—
288#395C2314yes—
289#395C2314yes—
290#395C2314yes—
291#395C2318yes—
292#395C2318yes—
293#394C2314yes—
294#394C2318yes—
295#394C23116yes—
296#394C23116yes—
297#394C2314yes—
298#394C23116yes—
299#394C23116yes—
300#394C2318yes—
301#393C23116yes—
302#393C2318yes—
303#393C2314yes—
304#393C2314yes—
305#393C2318yes—
306#391C2318yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C23116yes—
311#391C2314yes—
312#391C2314yes—
313#390C2314yes—
314#390C2318yes—
315#390C2318yes—
316#390C2318yes—
317#390C2314yes—
318#390C2314yes—
319#389C2318yes—
320#389C2318yes—
321#389C2318yes—
322#389C2318yes—
323#389C2318yes—
324#389C2318yes—
325#389C23116yes—
326#389C23116yes—
327#388C23116yes—
328#388C23116yes—
329#388C23116yes—
330#387C23116yes—
331#387C23116yes—
332#386C2318yes—
333#386C23116yes—
334#386C23116yes—
335#386C23116yes—
336#386C2318yes—
337#385C23116yes—
338#385C23116yes—
339#385C23116yes—
340#385C23116yes—
341#384C2314yes—
342#384C2314yes—
343#384C2314yes—
344#382C2314yes—
345#382C2314yes—
346#382C2314yes—
347#381C2318yes—
348#381C2318yes—
349#381C23116yes—
350#381C23116yes—
351#380C2318yes—
352#380C2318yes—
353#380C2318yes—
354#380C23116yes—
355#380C2318yes—
356#380C2318yes—
357#380C23116yes—
358#380C2318yes—
359C4×C4⋊C4C2312yes—
360C4×C4⋊C4C2312yes—
361C4×C4⋊C4C2312yes—
362C4×C4⋊C4C2312yes—
363C4×C4⋊C4C2318yes—
364C4×C4⋊C4C2318yes—
365C4×C22⋊C4C2318yes—
366C4×C22⋊C4C2318yes—
367#376C2312yes—
368#376C2312yes—
369#376C2312yes—
370#376C2312yes—
371C2×#95C2314yes—
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2312yes—
375C2×#95C2312yes—
376C25C2412yes—
377C2×#41—28no—
378C2×#41—216no—
379C2×#41—216no—
380C2×#41—88no—
381C22×Q8—216no—
382C22×Q8—88no—
383C22×Q8C2412yes—
384C22×Q8C2412yes—
385C22×Q8C2412yes—
386C22×Q8C2412yes—
387C22×Q8C2412yes—
388C22×Q8C2412yes—
389C22×Q8C2412yes—
390C22×Q8C2418yes—
391C22×D4—28no—
392C22×D4C2×D418yes—
393C22×D4C2414yes—
394C22×D4C2412yes—
395C22×D4C2412yes—
396C22×D4C2412yes—
397C22×D4C2418yes—
398C22×D4C2412yes—
399C22×D4C2412yes—
400C22×D4C2418yes—
401C23×C4—84no—
402C23×C4C2×D4116yes—
403C23×C4C2414yes—
404C23×C4C2412yes—
405C23×C4C2414yes—
406C23×C4C2412yes—
407C23×C4C2418yes—
408C23×C4C2418yes—
409C23×C4C2418yes—
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2414yes—
413C23×C4C2414yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C4⋊Q8—216no—
417C4⋊Q8—216no—
418C4⋊Q8—24no—
419C4⋊Q8—24no—
420C4⋊Q8—24no—
421C4⋊Q8—24no—
422C4⋊Q8—24no—
423C4⋊Q8—24no—
424C4⋊Q8—24no—
425C4⋊Q8—84no—
426#127—216no—
427#127—24no—
428#126—232no—
429#125—216no—
430#125—216no—
431#125—28no—
432#125—28no—
433#125—28no—
434#124—216no—
435#124—232no—
436#124—28no—
437#124—84no—
438#123—232no—
439#123—232no—
440#123—816no—
441#123—816no—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8—232no—
445C22⋊Q8—216no—
446C22⋊Q8—216no—
447C22⋊Q8—232no—
448C22⋊Q8—28no—
449C22⋊Q8—216no—
450C22⋊Q8—28no—
451C22⋊Q8—28no—
452C22⋊Q8—28no—
453C22⋊Q8—232no—
454C22⋊Q8—232no—
455C22⋊Q8—232no—
456C22⋊Q8—232no—
457C22⋊Q8—816no—
458#121—216no—
459#121—216no—
460#121—28no—
461#121—216no—
462#121—28no—
463#121—232no—
464#120—232no—
465C4×Q8—216no—
466C4×Q8—28no—
467C4×Q8—28no—
468C4×Q8—28no—
469C4×Q8—28no—
470C4×Q8—28no—
471C4×Q8—28no—
472C4×D4—216no—
473C4×D4—216no—
474C4×D4—216no—
475C4×D4—216no—
476C4×D4—232no—
477C4×D4—232no—
478C4×D4—216no—
479C4×D4—28no—
480C4×D4—28no—
481C4×D4C2×D4116yes—
482C4×D4C2×D4116yes—
483C4×D4C2×D4116yes—
484C4×D4C2×D4116yes—
485#117—28no—
486#117—28no—
487#117—28no—
488#117—216no—
489#117—216no—
490C2×C4⋊C4—232no—
491C2×C4⋊C4—216no—
492C2×C4⋊C4—28no—
493C2×C4⋊C4—216no—
494C2×C4⋊C4—84no—
495C2×C4⋊C4C2×D418yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2412yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2412yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C24116yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C24116yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C24116yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C22⋊C4—232no—
532C2×C22⋊C4—84no—
533C2×C22⋊C4—84no—
534C2×C22⋊C4C2×D4116yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C24116yes—
546C2×C22⋊C4C24116yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C24116yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C24116yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C42—28no—
556C2×C42—82no—
557C2×C42C2×D418yes—
558C2×C42C2418yes—
559C2×C42C2414yes—
560C2×C42C2414yes—
561C2×C42C2414yes—
562C2×C42C2414yes—
563C2×C42C2414yes—
564C2×C42C2414yes—
565C2×C42C2414yes—
566C2×C42C2411yescharacteristic
567C2×C42C2411yescharacteristic
568C2×C42C2411yescharacteristic
569C2×C42C2411yescharacteristic
570#95C2412yes—
571#95C2412yes—
572#95C2412yes—
573#95C2412yes—
574#95C2414yes—
575#95C2414yes—
576#95C2414yes—
577#95C2414yes—
578#95C24116yes—
579#95C2418yes—
580#95C2418yes—
581#95C2418yes—
582#95C2418yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2418yes—
587#95C24116yes—
588#95C24116yes—
589#95C24116yes—
590#95C24116yes—
591C24—28no—
592C24—42no—
593C24—44no—
594C24—42no—
595C24C22×D418yes—
596C24C2514yes—
597C24C2514yes—
598C24C2511yescharacteristic
599#41—432no—
600#41—832no—
601C2×Q8—24no—
602C2×Q8—24no—
603C2×Q8—24no—
604C2×Q8—24no—
605C2×Q8—24no—
606C2×Q8—24no—
607C2×Q8—24no—
608C2×Q8—216no—
609C2×Q8—28no—
610C2×Q8—44no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—416no—
614C2×Q8—42no—
615C2×Q8—42no—
616C2×Q8—42no—
617C2×Q8—42no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—832no—
621C2×D4—28no—
622C2×D4—216no—
623C2×D4—216no—
624C2×D4—216no—
625C2×D4—232no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—28no—
630C2×D4—28no—
631C2×D4—28no—
632C2×D4—44no—
633C2×D4—48no—
634C2×D4—416no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—48no—
638C2×D4C22×D418yes—
639C2×D4C22×D418yes—
640C22×C4—216no—
641C22×C4—216no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—28no—
645C22×C4—28no—
646C22×C4—216no—
647C22×C4—216no—
648C22×C4—41no—
649C22×C4—44no—
650C22×C4—42no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—41no—
654C22×C4—44no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—44no—
658C22×C4—42no—
659C22×C4—416no—
660C22×C4—48no—
661C22×C4—416no—
662C22×C4—42no—
663C22×C4—48no—
664C22×C4—816no—
665C22×C4C22×D414yes—
666C22×C4C22×D414yes—
667C22×C4C22×D418yes—
668C22×C4C22×D4116yes—
669C22×C4C22×D4116yes—
670C22×C4C22×D414yes—
671C22×C42−1+418yes—
672C22×C4C2514yes—
673C22×C4C2514yes—
674C22×C4C2514yes—
675C22×C4C2518yes—
676C22×C4C2514yes—
677C22×C4C2514yes—
678C22×C4C2514yes—
679C22×C4C2514yes—
680C22×C4C2514yes—
681C22×C4C2514yes—
682C22×C4C2511yescharacteristic
683C22×C4C2511yescharacteristic
684C22×C4C2511yescharacteristic
685C22×C4C2511yescharacteristic
686C22×C4C2514yes—
687C22×C4C2511yescharacteristic
688C22×C4C2511yescharacteristic
689C4⋊C4—24no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—24no—
693C4⋊C4—24no—
694C4⋊C4—216no—
695C4⋊C4—216no—
696C4⋊C4—216no—
697C4⋊C4—216no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—28no—
706C4⋊C4—24no—
707C4⋊C4—28no—
708C4⋊C4—28no—
709C4⋊C4—28no—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—24no—
713C4⋊C4—28no—
714C4⋊C4—28no—
715C4⋊C4—416no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—416no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—416no—
722C4⋊C4C22×D418yes—
723C4⋊C4C22×D418yes—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—216no—
727C22⋊C4—216no—
728C22⋊C4—28no—
729C22⋊C4—216no—
730C22⋊C4—216no—
731C22⋊C4—216no—
732C22⋊C4—28no—
733C22⋊C4—28no—
734C22⋊C4—416no—
735C22⋊C4—416no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—416no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—416no—
742C22⋊C4C22×D4116yes—
743C22⋊C4C22×D4116yes—
744C42—216no—
745C42—28no—
746C42—28no—
747C42—28no—
748C42—28no—
749C42—28no—
750C42—44no—
751C42—44no—
752C42C22×D414yes—
753C42C22×D414yes—
754C42C22×D414yes—
755C42C22×D414yes—
756C23—22no—
757C23—21no—
758C23—21no—
759C23—28no—
760C23—24no—
761C23—28no—
762C23—24no—
763C23—216no—
764C23—24no—
765C23—28no—
766C23—24no—
767C23—28no—
768C23—24no—
769C23—48no—
770C23—48no—
771C23—88no—
772C23—88no—
773C23C23×D418yes—
774C23C23×D412yes—
775C23C2×2−1+414yes—
776C23C2611yescharacteristic
777Q8—48no—
778Q8—48no—
779Q8—48no—
780Q8—48no—
781Q8—84no—
782Q8—84no—
783Q8—84no—
784Q8—816no—
785D4—216no—
786D4—216no—
787D4—48no—
788D4—416no—
789D4—48no—
790D4—84no—
791D4—816no—
792D4—816no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—28no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—24no—
821C2×C4—28no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—44no—
827C2×C4—48no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—44no—
831C2×C4—416no—
832C2×C4—816no—
833C2×C4—816no—
834C2×C4—84no—
835C2×C4—84no—
836C2×C4—88no—
837C2×C4—816no—
838C2×C4#536116yes—
839C2×C4C23×D418yes—
840C2×C4C23×D412yes—
841C2×C4C23×D412yes—
842C2×C4C23×D412yes—
843C2×C4C23×D412yes—
844C2×C4C23×D412yes—
845C2×C4C23×D412yes—
846C2×C4C2×2−1+414yes—
847C2×C4C2×2−1+414yes—
848C22—22no—
849C22—22no—
850C22—24no—
851C22—24no—
852C22—28no—
853C22—28no—
854C22—28no—
855C22—48no—
856C22—48no—
857C22—44no—
858C22—44no—
859C22—48no—
860C22—48no—
861C22—44no—
862C22—816no—
863C22C2×#53614yes—
864C22C24×D411yescharacteristic
865C22C22×2−1+412yes—
866C22H(7,𝔽2)12yes—
867C22H(7,𝔽2)11yescharacteristic
868C222−1+611yescharacteristic
869C4—22no—
870C4—22no—
871C4—28no—
872C4—22no—
873C4—22no—
874C4—44no—
875C4—44no—
876C4—44no—
877C4—44no—
878C4—44no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4—48no—
883C4—44no—
884C4C2×#53614yes—
885C4C2×#53614yes—
886C2—24no—
887C2—48no—
888C2—84no—
889C2C22×#53611yescharacteristic
890C2#6284211yescharacteristic
891C2#6285311yescharacteristic
892C2#6287912yes—
893C2#6288112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3506C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#3501C2semidirect
3. #42682C2semidirect
4. #42681C2semidirect
5. #42678C2semidirect
6. #42676C2semidirect
7. #42485C2semidirect
8. #42482C2semidirect
9. #42481C2semidirect
10. #42479C2semidirect
11. #37447C2semidirect
12. #37442C2semidirect
13. #36740C2semidirect
14. #35575C2semidirect
15. #35541C2semidirect
16. #35180C2semidirect
17. #35173C2semidirect
18. #34642C2semidirect
19. #34637C2semidirect
20. C2×#2319C2semidirect
50. #2817C22semidirect
51. #2816C22semidirect
52. #2814C22semidirect
53. #2814C22semidirect
54. #2700C22semidirect
55. #2698C22semidirect
56. #2689C22semidirect
57. #2687C22semidirect
58. #2681C22semidirect
59. #2680C22semidirect
60. #2674C22semidirect
61. #2672C22semidirect
62. #2660C22semidirect
63. #2660C22semidirect
64. #2660C22semidirect
65. #2660C22semidirect
70. #2642C22semidirect
71. #2641C22semidirect
72. #2640C22semidirect
73. #2640C22semidirect
78. #2638C22semidirect
79. #2638C22semidirect
80. #2627C22semidirect
81. #2625C22semidirect
82. #2623C22semidirect
83. #2618C22semidirect
84. #2616C22semidirect
85. #2614C22semidirect
86. #2592C22semidirect
87. #2584C22semidirect
88. #2584C22semidirect
89. #2568C22semidirect
90. #2567C22semidirect
91. #2567C22semidirect
93. #2563C22semidirect
94. #2562C22semidirect
95. #2548C22semidirect
96. #2547C22semidirect
97. #2546C22semidirect
98. #2546C22semidirect
99. #2486C22semidirect
100. #2484C22semidirect
101. #2454C22semidirect
102. #2453C22semidirect
103. #2452C22semidirect
104. #2451C22semidirect
109. #2442C22semidirect
110. #2441C22semidirect
111. #2440C22semidirect
112. #2439C22semidirect
120. #2409C22semidirect
121. #2406C22semidirect
122. #2399C22semidirect
123. #2399C22semidirect
124. #2398C22semidirect
125. #2398C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35062
C2×#35012
#426822
#426812
#426782
#426762
#424852
#424822
#424812
#424792
#374472
#374422
#367402
#355752
#355412
#351802
#351732
#346422
#346372
C2×#23192