Finite Group Databasebeta

← #7674583

Subgroups — #7674583

Order 512.

7446 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3494C212yesmaximal, complemented
2#43959C218yesmaximal, complemented
3#43079C218yesmaximal, complemented
4#39491C214yesmaximal, complemented
5#39483C214yesmaximal, complemented
6#37869C214yesmaximal, complemented
7#37864C214yesmaximal, complemented
8#37797C218yesmaximal, complemented
9#37792C218yesmaximal, complemented
10#35531C212yesmaximal, complemented
11#35529C212yesmaximal, complemented
12#35330C211yesmaximal, characteristic, complemented
13#35272C211yesmaximal, characteristic, complemented
14#35262C212yesmaximal, complemented
15C2×#2619C211yesmaximal, characteristic, complemented
16#34210C211yesmaximal, characteristic, complemented
17#34184C211yesmaximal, characteristic, complemented
18#34065C211yesmaximal, characteristic, complemented
19#34052C211yesmaximal, characteristic, complemented
20#3494—232no—
21C2×#555C2214yescomplemented
22C2×#553C2214yescomplemented
23C2×#553C2214yescomplemented
24C2×#551C2218yes—
25C2×#547C2214yescomplemented
26C2×#546C2218yes—
27C2×#544C2212yes—
28C2×#542C2214yescomplemented
29C2×#540C2214yescomplemented
30C2×#535C2212yes—
31C2×#532C2214yescomplemented
32C22×#127C2211yescharacteristic
33C2×#529C2214yescomplemented
34C2×#525C2211yescharacteristic
35C22×#121C2212yes—
36C2×#520C2212yes—
37C2×#518C2212yes—
38C2×C4×#41C2211yescharacteristic
39C22×#117C2211yescharacteristic
40C22×#117C2212yes—
41#2862C2212yescomplemented
42#2859C2212yescomplemented
43#2856C2214yescomplemented
44#2854C2218yescomplemented
45#2727C22116yescomplemented
46#2723C22116yescomplemented
47#2710C22116yescomplemented
48#2710C22116yescomplemented
49#2706C22116yescomplemented
50#2682C22116yescomplemented
51#2672C22116yescomplemented
52#2671C22116yescomplemented
53#2660C2214yescomplemented
54#2624C2218yescomplemented
55#2619C2214yes—
56#2619C2218yes—
57#2619C2214yes—
58#2619C2212yescomplemented
59#2619C2212yescomplemented
60#2566C2214yescomplemented
61#2566C2214yescomplemented
62#2563C2214yescomplemented
63#2550C2218yescomplemented
64#2549C2218yes—
65#2548C2214yescomplemented
66#2542C2214yescomplemented
67#2541C2214yescomplemented
68#2504C2214yescomplemented
69#2504C2214yescomplemented
70#2501C2214yescomplemented
71#2501C2214yescomplemented
72#2500C2214yescomplemented
73#2500C2214yescomplemented
74#2500C2214yescomplemented
75#2500C2214yescomplemented
76#2482C2218yes—
77#2479C22116yescomplemented
78#2461C22116yescomplemented
79#2455C22116yescomplemented
80#2455C22116yescomplemented
81#2454C2218yescomplemented
82#2452C2218yescomplemented
83#2448C2218yescomplemented
84#2445C2218yescomplemented
85#2437C22116yes—
86#2430C22116yescomplemented
87#2425C22116yescomplemented
88#2418C22116yes—
89#2415C22116yescomplemented
90#2408C2218yes—
91#2407C22116yescomplemented
92#2405C2218yes—
93C2×#394C2214yes—
94C2×#392C2214yes—
95#2366C2218yescomplemented
96#2351C2214yescomplemented
97#2349C2218yes—
98#2349C2214yescomplemented
99D4×C22⋊C4C2218yes—
100#2328C2212yescomplemented
101#2328C2212yescomplemented
102#2324C2214yescomplemented
103#2323C2214yescomplemented
104#2322C2214yes—
105#2321C2214yes—
106#2317C2212yes—
107#2317C2212yes—
108#2317C2212yescomplemented
109#2317C2212yescomplemented
110#2317C2212yescomplemented
111#2317C2212yescomplemented
112#2317C2214yescomplemented
113#2316C2214yes—
114#2315C2214yes—
115#2309C2212yes—
116#2309C2212yes—
117C4×#127C2214yescomplemented
118#2297C2211yescharacteristic
119#2296C2211yescharacteristic
120#2296C2218yescomplemented
121#2293C2214yescomplemented
122C2×#390C2212yes—
123#2290C2214yescomplemented
124#2285C2211yescharacteristic
125#2285C2211yescharacteristic
126#2285C2212yes—
127#2285C2212yescomplemented
128C2×#382C2211yescharacteristic
129C2×#382C2212yescomplemented
130#2280C2211yescharacteristic
131C4×#117C2211yescharacteristic
132C22×#41C2311yescharacteristic
133C22×#41C2318yes—
134C23×D4C2312yes—
135C23×D4C2314yes—
136C23×D4C2314yes—
137C24×C4C2311yescharacteristic
138#555—232no—
139#553—232no—
140#553—232no—
141#551—264no—
142#547—232no—
143#546—264no—
144#544—216no—
145#542—232no—
146#540—232no—
147#535—216no—
148#532—232no—
149C2×C4⋊Q8C2314yes—
150C2×C4⋊Q8C2314yes—
151C2×#127—28no—
152C2×#127C2312yes—
153C2×#127C2312yes—
154C2×#127C2314yes—
155C2×#127C2314yes—
156#529—232no—
157C2×#126C2318yes—
158C2×#126C2318yes—
159C2×#125C2314yes—
160C2×#125C2314yes—
161C2×#124C2314yes—
162C2×#124C2318yes—
163C2×#124C2318yes—
164#525D4116yescomplemented
165C2×#123C2318yes—
166C2×#123C2318yes—
167C2×#123C2318yes—
168C2×#123C2318yes—
169C2×#123C23116yes—
170C2×#123C23116yes—
171C2×#123C2312yes—
172C2×C22⋊Q8C2318yes—
173C2×C22⋊Q8C2318yes—
174C2×C22⋊Q8C23116yes—
175C2×C22⋊Q8C2312yes—
176C2×#121—216no—
177C2×#121C2314yes—
178C2×#121C2314yes—
179C2×#121C2314yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2314yes—
183C2×#121C2318yes—
184C2×#121C2318yes—
185C2×#121C2318yes—
186C2×#121C23116yes—
187C2×#121C2312yes—
188C2×#120C2318yes—
189C2×#120C2312yes—
190#520—216no—
191#518—216no—
192C4×#41—28no—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2314yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2318yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C23116yes—
206C2×C4×D4C2314yes—
207C2×#117—216no—
208C2×#117—28no—
209C2×#117C2311yescharacteristic
210C2×#117C2311yescharacteristic
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2314yes—
214C2×#117C2312yes—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C2×#117C2314yes—
222C2×#117C2318yes—
223C2×#117C2311yescharacteristic
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2314yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2314yes—
231C22×C22⋊C4C2318yes—
232C22×C22⋊C4C2314yes—
233C22×C22⋊C4C2318yes—
234C22×C42C2314yes—
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#399C23116yes—
239#399C23116yes—
240#399C23116yes—
241#398C23116yes—
242#397C23116yes—
243#397C23116yes—
244#396C23116yes—
245#396C23116yes—
246#395C23116yes—
247#394C23116yes—
248#394C23116yes—
249#394C2318yes—
250#394C2318yes—
251#394C23116yes—
252#394C23116yes—
253#394C23116yes—
254#394C23116yes—
255#393C23116yes—
256#392C23116yes—
257#392C23116yes—
258#392C2318yes—
259#392C2318yes—
260#391C2312yes—
261#391C23116yes—
262#390C2314yes—
263#390C2314yes—
264#390C23116yes—
265#390C2314yes—
266#390C2314yes—
267#390C2314yes—
268#390C2318yes—
269#390C2318yes—
270#390C2314yes—
271#390C2318yes—
272#390C2312yes—
273#390C23116yes—
274#390C2318yes—
275#389C2318yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2318yes—
280#389C2318yes—
281#389C23116yes—
282#389C2318yes—
283#389C2314yes—
284#389C23116yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C23116yes—
289#388C23116yes—
290#388C23116yes—
291#388C23116yes—
292#387C2318yes—
293#386C2314yes—
294#386C2318yes—
295#386C23116yes—
296#386C23116yes—
297#386C23116yes—
298#386C23116yes—
299#385C23116yes—
300#385C23116yes—
301#385C2318yes—
302#385C2318yes—
303#385C2318yes—
304#385C2318yes—
305#385C2318yes—
306#385C2318yes—
307#385C23116yes—
308#385C2314yes—
309#385C2318yes—
310#384C2312yes—
311#384C2312yes—
312#384C2314yes—
313#384C2314yes—
314#384C2312yes—
315#384C2312yes—
316#382C2312yes—
317#382C2314yes—
318#382C2312yes—
319#382C2314yes—
320#382C2311yescharacteristic
321#382C2311yescharacteristic
322#382C2311yescharacteristic
323#382C2312yes—
324#382C2311yescharacteristic
325#382C2318yes—
326#382C2314yes—
327#382C2312yes—
328#381C2312yes—
329#380C23116yes—
330#380C2314yes—
331#380C2314yes—
332#380C2318yes—
333#380C2314yes—
334#380C2318yes—
335#379C2318yes—
336#379C2318yes—
337#379C2312yes—
338C4×C4⋊C4C2314yes—
339C4×C4⋊C4C2314yes—
340C4×C4⋊C4C2318yes—
341C4×C4⋊C4C2314yes—
342C4×C4⋊C4C2318yes—
343C4×C4⋊C4C2314yes—
344C4×C22⋊C4C2314yes—
345C4×C22⋊C4C2314yes—
346C4×C22⋊C4C2314yes—
347#376C2312yes—
348C2×#95C2314yes—
349C2×#95C2318yes—
350C43C2312yes—
351C25C2414yes—
352C25C2411yescharacteristic
353C2×#41—232no—
354C2×#41—24no—
355C2×#41—24no—
356C2×#41—816no—
357C2×#41C2×D418yes—
358C22×Q8C2411yescharacteristic
359C22×Q8C2418yes—
360C22×D4—216no—
361C22×D4—28no—
362C22×D4—28no—
363C22×D4—216no—
364C22×D4—28no—
365C22×D4—88no—
366C22×D4—88no—
367C22×D4C2414yes—
368C22×D4C2414yes—
369C22×D4C2412yes—
370C22×D4C2411yescharacteristic
371C22×D4C2418yes—
372C22×D4C2418yes—
373C22×D4C2418yes—
374C22×D4C2418yes—
375C22×D4C2418yes—
376C22×D4C2418yes—
377C22×D4C2414yes—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4C2×D418yes—
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2414yes—
387C23×C4C2414yes—
388C23×C4C2414yes—
389C23×C4C2418yes—
390C23×C4C2418yes—
391C23×C4C2418yes—
392C23×C4C2414yes—
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C4⋊Q8—216no—
396C4⋊Q8—216no—
397#127—216no—
398#127—28no—
399#127—28no—
400#127—216no—
401#126—232no—
402#126—232no—
403#125—216no—
404#125—216no—
405#124—216no—
406#124—232no—
407#124—232no—
408#123—232no—
409#123—232no—
410#123—232no—
411#123—232no—
412#123—816no—
413#123—816no—
414#123C2×D4116yes—
415C22⋊Q8—232no—
416C22⋊Q8—232no—
417C22⋊Q8—816no—
418C22⋊Q8C2×D4116yescomplemented
419#121—232no—
420#121—232no—
421#121—232no—
422#121—216no—
423#121—216no—
424#121—216no—
425#121—216no—
426#121—216no—
427#121—216no—
428#121—816no—
429#121C2×D4116yescomplemented
430#120—232no—
431#120C2×D4116yes—
432C4×Q8—216no—
433C4×Q8—28no—
434C4×D4—216no—
435C4×D4—232no—
436C4×D4—216no—
437C4×D4—216no—
438C4×D4—216no—
439C4×D4—232no—
440C4×D4—232no—
441C4×D4—216no—
442C4×D4—216no—
443C4×D4—28no—
444C4×D4—816no—
445C4×D4C2×D4132yescomplemented
446#117—28no—
447#117—28no—
448#117—216no—
449#117—216no—
450#117—28no—
451#117—28no—
452#117—216no—
453#117—24no—
454#117—24no—
455#117—232no—
456#117—28no—
457#117—28no—
458#117—216no—
459#117—28no—
460#117C2×D418yes—
461C2×C4⋊C4—28no—
462C2×C4⋊C4—28no—
463C2×C4⋊C4—28no—
464C2×C4⋊C4—216no—
465C2×C4⋊C4—28no—
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2412yes—
470C2×C4⋊C4C2412yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2414yes—
476C2×C4⋊C4C2418yes—
477C2×C4⋊C4C2412yes—
478C2×C4⋊C4C2414yes—
479C2×C4⋊C4C2418yes—
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C2418yes—
483C2×C4⋊C4C2418yes—
484C2×C4⋊C4C2418yes—
485C2×C4⋊C4C2418yes—
486C2×C4⋊C4C2418yes—
487C2×C4⋊C4C24116yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C24116yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2412yes—
492C2×C22⋊C4—216no—
493C2×C22⋊C4—216no—
494C2×C22⋊C4—28no—
495C2×C22⋊C4—232no—
496C2×C22⋊C4—88no—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C2414yes—
501C2×C22⋊C4C2414yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2418yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C2412yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2412yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C24116yes—
514C2×C22⋊C4C24116yes—
515C2×C22⋊C4C24116yes—
516C2×C22⋊C4C24116yes—
517C2×C22⋊C4C24116yes—
518C2×C22⋊C4C24116yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2412yes—
522C2×C22⋊C4C2414yes—
523C2×C22⋊C4C2414yes—
524C2×C42—216no—
525C2×C42—24no—
526C2×C42—28no—
527C2×C42#4118yescomplemented
528C2×C42C2414yes—
529C2×C42C2414yes—
530C2×C42C2418yes—
531C2×C42C2414yes—
532C2×C42C2414yes—
533C2×C42C2412yes—
534C2×C42C2412yes—
535C2×C42C2412yes—
536C2×C42C2412yes—
537C2×C42C2414yes—
538C2×C42C2418yes—
539C2×C42C2412yes—
540C2×C42C2411yescharacteristic
541C2×C42C2412yes—
542C2×C42C2411yescharacteristic
543#95C2414yes—
544#95C2418yes—
545#95C24116yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2418yes—
550#95C2414yes—
551#95C2418yes—
552#95C2418yes—
553#95C2414yes—
554#95C2414yes—
555#95C2418yes—
556#95C24116yes—
557C24—22no—
558C24—22no—
559C24—28no—
560C24—28no—
561C24—28no—
562C24—44no—
563C24—48no—
564C24—48no—
565C24C22×D414yes—
566C24C2518yes—
567C24C2512yes—
568C24C2512yes—
569C24C2511yescharacteristic
570#41—232no—
571#41—864no—
572C2×Q8—216no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—416no—
576C2×Q8C22×D414yes—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—216no—
580C2×D4—216no—
581C2×D4—216no—
582C2×D4—216no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—22no—
586C2×D4—216no—
587C2×D4—28no—
588C2×D4—28no—
589C2×D4—216no—
590C2×D4—22no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—48no—
596C2×D4—416no—
597C2×D4—416no—
598C2×D4—416no—
599C2×D4—416no—
600C2×D4—432no—
601C2×D4—832no—
602C2×D4—832no—
603C2×D4C22×D418yes—
604C2×D4C22×D414yes—
605C2×D4C22×D4116yes—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—232no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—28no—
618C22×C4—216no—
619C22×C4—24no—
620C22×C4—216no—
621C22×C4—216no—
622C22×C4—28no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—416no—
628C22×C4—416no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—416no—
632C22×C4C22×D418yes—
633C22×C4C22×D414yes—
634C22×C4C22×D418yes—
635C22×C4C22×D418yes—
636C22×C4C22×D414yes—
637C22×C4C2×#4118yes—
638C22×C4C2×#4114yes—
639C22×C42−1+414yes—
640C22×C4C2514yes—
641C22×C4C2514yes—
642C22×C4C2514yes—
643C22×C4C2514yes—
644C22×C4C2514yes—
645C22×C4C2518yes—
646C22×C4C2514yes—
647C22×C4C2514yes—
648C22×C4C2512yes—
649C22×C4C2512yes—
650C22×C4C2514yes—
651C22×C4C2512yes—
652C22×C4C2512yes—
653C22×C4C2511yescharacteristic
654C22×C4C2511yescharacteristic
655C4⋊C4—24no—
656C4⋊C4—28no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—216no—
664C4⋊C4—216no—
665C4⋊C4—216no—
666C4⋊C4—216no—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—28no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—416no—
677C4⋊C4—416no—
678C4⋊C4—48no—
679C4⋊C4C22×D4116yes—
680C4⋊C4C22×D418yes—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—216no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—216no—
689C22⋊C4—216no—
690C22⋊C4—216no—
691C22⋊C4—216no—
692C22⋊C4—216no—
693C22⋊C4—216no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—416no—
698C22⋊C4—416no—
699C22⋊C4—416no—
700C22⋊C4—416no—
701C22⋊C4—416no—
702C22⋊C4—416no—
703C22⋊C4—48no—
704C22⋊C4—48no—
705C22⋊C4C22×D418yes—
706C22⋊C4C22×D4116yes—
707C22⋊C4C22×D4116yes—
708C42—28no—
709C42—28no—
710C42—28no—
711C42—28no—
712C42—216no—
713C42—24no—
714C42—24no—
715C42—24no—
716C42—28no—
717C42—24no—
718C42—48no—
719C42C22×D418yes—
720C42C2×#4114yes—
721C42C2×#4114yes—
722C42C2×#4118yes—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—28no—
730C23—24no—
731C23—28no—
732C23—28no—
733C23—28no—
734C23—28no—
735C23—216no—
736C23—216no—
737C23—48no—
738C23—416no—
739C23—84no—
740C23—84no—
741C23—88no—
742C23—816no—
743C23—88no—
744C23—816no—
745C23C23×D414yes—
746C23C23×D414yes—
747C23C23×D412yes—
748C23C22×#4112yes—
749C23C2×2−1+412yes—
750C23C2611yescharacteristic
751Q8—28no—
752Q8—816no—
753D4—216no—
754D4—28no—
755D4—416no—
756D4—432no—
757D4—432no—
758D4—416no—
759D4—416no—
760D4—816no—
761D4—816no—
762D4—816no—
763D4—816no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—216no—
773C2×C4—216no—
774C2×C4—216no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—28no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—216no—
791C2×C4—28no—
792C2×C4—48no—
793C2×C4—416no—
794C2×C4—816no—
795C2×C4—88no—
796C2×C4—816no—
797C2×C4—88no—
798C2×C4—84no—
799C2×C4—88no—
800C2×C4—816no—
801C2×C4#547116yes—
802C2×C4C23×D414yes—
803C2×C4C23×D414yes—
804C2×C4C23×D418yes—
805C2×C4C23×D412yes—
806C2×C4C23×D412yes—
807C2×C4C22×#4114yes—
808C2×C4C22×#4114yes—
809C2×C4C22×#4112yes—
810C2×C4C22×#4112yes—
811C2×C4C2×2−1+412yes—
812C2×C4C2×2−1+412yes—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—28no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—48no—
826C22—48no—
827C22—416no—
828C22—416no—
829C22—48no—
830C22—88no—
831C22—1616no—
832C22C2×#54714yes—
833C22C24×D411yescharacteristic
834C22C23×#4111yescharacteristic
835C22C22×2−1+411yescharacteristic
836C22H(7,𝔽2)14yes—
837C4—28no—
838C4—24no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—44no—
843C4—44no—
844C4—44no—
845C4—48no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—44no—
850C4C2×#54714yes—
851C4C2×#54714yes—
852C2—24no—
853C2—44no—
854C2—44no—
855C2—88no—
856C2C22×#54711yescharacteristic
857C2#6285212yes—
858C2#6285512yes—
859C2#6288112yes—
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×#3494C2semidirect
2. #43959C2semidirect
3. #43079C2semidirect
4. #39491C2semidirect
5. #39483C2semidirect
6. #37869C2semidirect
7. #37864C2semidirect
8. #37797C2semidirect
9. #37792C2semidirect
10. #35531C2semidirect
11. #35529C2semidirect
12. #35330C2semidirect
13. #35272C2semidirect
14. #35262C2semidirect
15. C2×#2619C2semidirect
16. #34210C2semidirect
17. #34184C2semidirect
18. #34065C2semidirect
19. #34052C2semidirect
21. C2×#555C22semidirect
22. C2×#553C22semidirect
23. C2×#553C22semidirect
25. C2×#547C22semidirect
28. C2×#542C22semidirect
29. C2×#540C22semidirect
31. C2×#532C22semidirect
33. C2×#529C22semidirect
41. #2862C22semidirect
42. #2859C22semidirect
43. #2856C22semidirect
44. #2854C22semidirect
45. #2727C22semidirect
46. #2723C22semidirect
47. #2710C22semidirect
48. #2710C22semidirect
49. #2706C22semidirect
50. #2682C22semidirect
51. #2672C22semidirect
52. #2671C22semidirect
53. #2660C22semidirect
54. #2624C22semidirect
58. #2619C22semidirect
59. #2619C22semidirect
60. #2566C22semidirect
61. #2566C22semidirect
62. #2563C22semidirect
63. #2550C22semidirect
65. #2548C22semidirect
66. #2542C22semidirect
67. #2541C22semidirect
68. #2504C22semidirect
69. #2504C22semidirect
70. #2501C22semidirect
71. #2501C22semidirect
72. #2500C22semidirect
73. #2500C22semidirect
74. #2500C22semidirect
75. #2500C22semidirect
77. #2479C22semidirect
78. #2461C22semidirect
79. #2455C22semidirect
80. #2455C22semidirect
81. #2454C22semidirect
82. #2452C22semidirect
83. #2448C22semidirect
84. #2445C22semidirect
86. #2430C22semidirect
87. #2425C22semidirect
89. #2415C22semidirect
91. #2407C22semidirect
95. #2366C22semidirect
96. #2351C22semidirect
98. #2349C22semidirect
100. #2328C22semidirect
101. #2328C22semidirect
102. #2324C22semidirect
103. #2323C22semidirect
108. #2317C22semidirect
109. #2317C22semidirect
110. #2317C22semidirect
111. #2317C22semidirect
112. #2317C22semidirect
117. C4×#127C22semidirect
120. #2296C22semidirect
121. #2293C22semidirect
123. #2290C22semidirect
127. #2285C22semidirect
129. C2×#382C22semidirect
164. #525D4semidirect
418. C22⋊Q8C2×D4semidirect
429. #121C2×D4semidirect
445. C4×D4C2×D4semidirect
527. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34942
#439592
#430792
#394912
#394832
#378692
#378642
#377972
#377922
#355312
#355292
#353302
#352722
#352622
C2×#26192
#342102
#341842
#340652
#340522