Finite Group Databasebeta

← #7674383

Subgroups — #7674383

Order 512.

4638 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45232C214yesmaximal, complemented
2#45212C214yesmaximal, complemented
3#45085C214yesmaximal, complemented
4#45058C214yesmaximal, complemented
5#39803C214yesmaximal, complemented
6#39802C214yesmaximal, complemented
7#39761C214yesmaximal, complemented
8#39758C214yesmaximal, complemented
9#38235C218yesmaximal, complemented
10#38233C218yesmaximal, complemented
11#35545C212yesmaximal, complemented
12#35519C212yesmaximal, complemented
13#35289C211yesmaximal, characteristic
14#35281C211yesmaximal, characteristic, complemented
15#35160C212yesmaximal, complemented
16#34637C211yesmaximal, characteristic
17#34252C212yesmaximal, complemented
18#34215C211yesmaximal, characteristic, complemented
19#34208C211yesmaximal, characteristic
20#34074C211yesmaximal, characteristic, complemented
21C2×#2331C211yesmaximal, characteristic, complemented
22C2×#533C2211yescharacteristic
23C2×#533C2211yescharacteristic
24C2×#532C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C2×#520C2212yes—
27#2868C2212yes—
28#2862C2212yes—
29#2862C2212yes—
30#2858C2212yes—
31#2852C2218yes—
32#2798C2218yes—
33#2798C2218yes—
34#2793C2218yes—
35#2793C2218yes—
36#2789C2218yes—
37#2786C2218yes—
38#2767C2218yes—
39#2762C2218yes—
40#2759C2218yes—
41#2759C2218yes—
42#2758C2218yes—
43#2740C2218yes—
44#2716C2218yes—
45#2716C2218yes—
46#2715C2218yes—
47#2700C2218yes—
48#2660C2214yes—
49#2643C2218yes—
50#2642C2212yes—
51#2641C2212yes—
52#2640C2212yes—
53#2640C2212yes—
54#2640C2214yes—
55#2639C2214yes—
56#2639C2214yes—
57#2605C2218yes—
58#2601C2218yes—
59#2588C2218yes—
60#2582C2214yes—
61#2581C2214yes—
62#2580C2214yes—
63#2567C2214yes—
64#2563C2214yes—
65#2560C2218yes—
66#2547C2214yes—
67#2546C2214yes—
68#2538C2214yes—
69#2528C2218yes—
70#2527C2218yes—
71#2527C2218yes—
72#2524C2218yes—
73#2523C2218yes—
74#2523C2218yes—
75#2521C2218yes—
76#2514C2214yes—
77#2514C2214yes—
78#2513C2214yes—
79#2513C2214yes—
80#2512C2214yes—
81#2512C2214yes—
82#2511C2214yes—
83#2511C2214yes—
84#2510C2218yes—
85#2504C2214yes—
86#2502C2214yes—
87#2499C2218yes—
88#2497C2214yes—
89#2497C2214yes—
90#2496C2214yes—
91#2496C2218yes—
92#2496C2214yes—
93#2495C2214yes—
94#2495C2214yes—
95#2494C2214yes—
96#2494C2214yes—
97#2492C2218yes—
98#2481C2218yes—
99#2474C2218yes—
100#2450C2218yes—
101#2449C2218yes—
102#2442C2214yes—
103#2441C2214yes—
104#2440C2214yes—
105#2439C2214yes—
106#2439C2218yes—
107#2436C2214yes—
108#2434C2214yes—
109#2398C2212yes—
110#2398C2212yes—
111#2398C2212yes—
112#2398C2212yes—
113#2368C2214yes—
114#2368C2214yes—
115#2364C2214yes—
116#2364C2214yes—
117#2357C2214yes—
118#2356C2214yes—
119#2355C2214yes—
120#2355C2214yes—
121#2355C2214yes—
122#2354C2214yes—
123#2352C2214yes—
124#2352C2214yes—
125#2347C2214yes—
126#2346C2214yes—
127#2345C2214yes—
128#2344C2214yes—
129#2331C2212yes—
130#2331C2212yes—
131#2331C2212yes—
132#2331C2214yes—
133#2331C2214yes—
134#2331C2212yes—
135#2331C2212yes—
136#2331C2212yes—
137#2331C2212yes—
138#2331C2212yes—
139#2330C2212yes—
140#2330C2212yes—
141#2329C2214yes—
142#2329C2214yes—
143#2328C2212yes—
144#2327C2212yes—
145#2318C2218yes—
146#2317C2212yes—
147#2317C2212yes—
148#2317C2212yes—
149#2311C2212yes—
150#2311C2212yes—
151#2311C2212yes—
152C4×#125C2214yes—
153C4×#124C2214yes—
154#2297C2212yes—
155#2297C2212yes—
156#2296C2211yescharacteristic
157#2296C2211yescharacteristic
158#2295C2214yes—
159#2295C2214yes—
160C2×#391C2214yes—
161C2×#389C2212yes—
162#2290C2218yes—
163C2×#387C2214yes—
164#2285C2211yescharacteristic
165C2×#382C2211yescharacteristic
166#2274C2212yes—
167C4×#117C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C2×C4×C4⋊C4C2212yes—
170C2×#376C2211yescharacteristic
171C22×#41C2312yes—
172C23×Q8C2312yes—
173#533—28no—
174#533—28no—
175#532—28no—
176C2×C4⋊Q8—28no—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2311yescharacteristic
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2311yescharacteristic
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2311yescharacteristic
184C2×C4⋊Q8C2312yes—
185C2×C4⋊Q8C2318yes—
186C2×#127C2311yescharacteristic
187C2×#126C2318yes—
188C2×#126C2318yes—
189C2×#125C2312yes—
190C2×#125C2312yes—
191C2×#124C2312yes—
192C2×#124C2318yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2318yes—
197C2×#121C2312yes—
198C2×#121C2312yes—
199#520—216no—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×Q8C2312yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2312yes—
208C2×#117C2311yescharacteristic
209C2×#117C2311yescharacteristic
210C2×#117C2311yescharacteristic
211C2×#117C2312yes—
212C2×#117C2314yes—
213C2×#117C2318yes—
214C2×#117C2311yescharacteristic
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2314yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2314yes—
223C22×C42C2311yescharacteristic
224#401C2318yes—
225#401C2318yes—
226#400C2318yes—
227#400C2314yes—
228#400C2318yes—
229#400C2314yes—
230#400C2318yes—
231#400C2314yes—
232#400C2314yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#399C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#397C2318yes—
243#397C2314yes—
244#397C2314yes—
245#397C2314yes—
246#397C2314yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#395C2318yes—
259#395C2318yes—
260#395C2318yes—
261#394C2314yes—
262#394C2314yes—
263#394C2314yes—
264#394C2314yes—
265#393C2318yes—
266#393C2318yes—
267#393C2318yes—
268#393C2314yes—
269#393C2314yes—
270#393C2314yes—
271#393C2314yes—
272#391C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2318yes—
277#391C2312yes—
278#391C2312yes—
279#391C2318yes—
280#391C2314yes—
281#391C2314yes—
282#391C2314yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2318yes—
287#391C2318yes—
288#391C2318yes—
289#391C2318yes—
290#391C2318yes—
291#391C2312yes—
292#391C2312yes—
293#390C2318yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2312yes—
298#390C2312yes—
299#390C2312yes—
300#390C2312yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2318yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#389C2314yes—
319#389C2314yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#387C2314yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2314yes—
367#386C2318yes—
368#386C2314yes—
369#386C2314yes—
370#386C2314yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2314yes—
375#385C2318yes—
376#385C2318yes—
377#385C2314yes—
378#384C2318yes—
379#384C2314yes—
380#384C2314yes—
381#384C2314yes—
382#384C2312yes—
383#383C2318yes—
384#383C2318yes—
385#383C2318yes—
386#382C2312yes—
387#382C2318yes—
388#382C2314yes—
389#382C2314yes—
390#382C2314yes—
391#382C2318yes—
392#382C2312yes—
393#382C2312yes—
394#382C2312yes—
395#382C2312yes—
396#381C2318yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2318yes—
404#380C2314yes—
405#380C2318yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436#376C2312yes—
437#376C2311yescharacteristic
438#376C2311yescharacteristic
439#376C2311yescharacteristic
440#376C2311yescharacteristic
441#376C2312yes—
442#376C2312yes—
443#376C2312yes—
444#376C2318yes—
445C2×#95C2314yes—
446C2×#95C2312yes—
447C2×#95C2312yes—
448C2×#95C2312yes—
449C2×#95C2312yes—
450C2×#95C2314yes—
451C43C2312yes—
452C43C2312yes—
453C2×#41—28no—
454C2×#41—28no—
455C2×#41—28no—
456C22×Q8—28no—
457C22×Q8—84no—
458C22×Q8C2412yes—
459C22×Q8C2414yes—
460C22×Q8C2412yes—
461C22×Q8C2412yes—
462C22×Q8C2414yes—
463C22×Q8C2414yes—
464C22×D4C2414yes—
465C22×D4C2412yes—
466C22×D4C2412yes—
467C22×D4C2412yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2412yes—
472C23×C4C2418yes—
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C4⋊Q8—28no—
478C4⋊Q8—28no—
479C4⋊Q8—28no—
480C4⋊Q8—28no—
481C4⋊Q8—28no—
482C4⋊Q8—24no—
483C4⋊Q8—24no—
484C4⋊Q8—24no—
485C4⋊Q8—88no—
486#127—24no—
487#126—88no—
488#126—88no—
489#125—28no—
490#125—28no—
491#124—28no—
492#124—88no—
493C22⋊Q8—28no—
494C22⋊Q8—28no—
495C22⋊Q8—216no—
496C22⋊Q8—88no—
497#121—28no—
498#121—28no—
499C4×Q8—216no—
500C4×Q8—216no—
501C4×Q8—28no—
502C4×Q8—28no—
503C4×D4—232no—
504C4×D4—216no—
505C4×D4—28no—
506C4×D4—28no—
507#117—24no—
508#117—28no—
509#117—24no—
510#117—24no—
511#117—216no—
512#117—88no—
513#117#4118yes—
514C2×C4⋊C4—28no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—28no—
517C2×C4⋊C4—216no—
518C2×C4⋊C4—84no—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2412yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2412yes—
577C2×C42—24no—
578C2×C42—24no—
579C2×C42—84no—
580C2×C42#4118yes—
581C2×C42C2418yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2411yescharacteristic
588C2×C42C2411yescharacteristic
589C2×C42C2411yescharacteristic
590C2×C42C2411yescharacteristic
591C2×C42C2412yes—
592C2×C42C2418yes—
593C2×C42C2418yes—
594C2×C42C2414yes—
595C2×C42C2418yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2418yes—
600C2×C42C2412yes—
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605#95C2412yes—
606#95C2412yes—
607#95C2412yes—
608#95C2412yes—
609#95C2412yes—
610#95C2412yes—
611#95C2412yes—
612#95C2412yes—
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2418yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2414yes—
644#95C2418yes—
645#95C2414yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653C24C2514yes—
654C24C2511yescharacteristic
655#41—432no—
656C2×Q8—24no—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—28no—
662C2×Q8—28no—
663C2×Q8—24no—
664C2×Q8—44no—
665C2×Q8—48no—
666C2×Q8—44no—
667C2×Q8—48no—
668C2×Q8—44no—
669C2×Q8—44no—
670C2×Q8—816no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—44no—
680C2×D4—44no—
681C22×C4—28no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—28no—
688C22×C4—216no—
689C22×C4—42no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—44no—
696C22×C4—42no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4—44no—
700C22×C4—42no—
701C22×C4C2×#4114yes—
702C22×C4C2×#4114yes—
703C22×C4C2×#4114yes—
704C22×C4C2×#4114yes—
705C22×C42−1+414yes—
706C22×C4C2514yes—
707C22×C4C2512yes—
708C22×C4C2512yes—
709C22×C4C2514yes—
710C22×C4C2512yes—
711C22×C4C2514yes—
712C22×C4C2518yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2512yes—
716C22×C4C2518yes—
717C22×C4C2514yes—
718C22×C4C2511yescharacteristic
719C22×C4C2511yescharacteristic
720C22×C4C2511yescharacteristic
721C22×C4C2511yescharacteristic
722C22×C4C2514yes—
723C22×C4C2511yescharacteristic
724C22×C4C2511yescharacteristic
725C4⋊C4—28no—
726C4⋊C4—216no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—28no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4C2×#4118yes—
761C22⋊C4—28no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—48no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—48no—
775C22⋊C4—44no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—44no—
780C22⋊C4—48no—
781C22⋊C4—44no—
782C22⋊C4C2×#4118yes—
783C42—24no—
784C42—22no—
785C42—22no—
786C42—216no—
787C42—28no—
788C42—24no—
789C42—24no—
790C42—22no—
791C42—22no—
792C42—24no—
793C42—24no—
794C42—48no—
795C42—48no—
796C42—44no—
797C42—44no—
798C42—48no—
799C42—48no—
800C42—44no—
801C42—44no—
802C42C2×#4114yes—
803C42C2×#4114yes—
804C42C2×#4114yes—
805C42C2×#4114yes—
806C42C2×#4118yes—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23C22×#4112yes—
817C23C22×#4112yes—
818C23C2×2−1+412yes—
819C23C2611yescharacteristic
820Q8—48no—
821Q8—84no—
822Q8—88no—
823Q8—84no—
824Q8—88no—
825Q8—88no—
826D4—416no—
827D4—48no—
828D4—84no—
829D4—84no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—28no—
843C2×C4—24no—
844C2×C4—28no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—28no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—22no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—48no—
875C2×C4—416no—
876C2×C4—416no—
877C2×C4—816no—
878C2×C4—84no—
879C2×C4—88no—
880C2×C4#556116yes—
881C2×C4C22×#4118yes—
882C2×C4C22×#4112yes—
883C2×C4C22×#4112yes—
884C2×C4C22×#4112yes—
885C2×C4C22×#4112yes—
886C2×C4C22×#4112yes—
887C2×C4C22×#4112yes—
888C2×C4C22×#4112yes—
889C2×C4C22×#4112yes—
890C2×C4C2×2−1+412yes—
891C2×C4C2×2−1+412yes—
892C22—22no—
893C22—24no—
894C22—22no—
895C22—24no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22C2×#55614yes—
904C22C23×#4111yescharacteristic
905C22C23×#4111yescharacteristic
906C22C22×2−1+411yescharacteristic
907C22H(7,𝔽2)12yes—
908C222−1+612yes—
909C4—22no—
910C4—22no—
911C4—28no—
912C4—22no—
913C4—22no—
914C4—48no—
915C4—44no—
916C4—42no—
917C4—48no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—44no—
922C4—44no—
923C4—42no—
924C4—42no—
925C4—44no—
926C4C2×#55614yes—
927C4C2×#55614yes—
928C2—24no—
929C2—84no—
930C2C22×#55611yescharacteristic
931C2#6285511yescharacteristic
932C2#6285712yes—
933C2#6286011yescharacteristic
934C2#6287712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45232C2semidirect
2. #45212C2semidirect
3. #45085C2semidirect
4. #45058C2semidirect
5. #39803C2semidirect
6. #39802C2semidirect
7. #39761C2semidirect
8. #39758C2semidirect
9. #38235C2semidirect
10. #38233C2semidirect
11. #35545C2semidirect
12. #35519C2semidirect
14. #35281C2semidirect
15. #35160C2semidirect
17. #34252C2semidirect
18. #34215C2semidirect
20. #34074C2semidirect
21. C2×#2331C2semidirect

Maximal subgroups

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

subgroupindex
#452322
#452122
#450852
#450582
#398032
#398022
#397612
#397582
#382352
#382332
#355452
#355192
#352892
#352812
#351602
#346372
#342522
#342152
#342082
#340742
C2×#23312