Finite Group Databasebeta

← #7715524

Subgroups — #7715524

Order 512.

4182 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
1#51087C214yesmaximal, complemented
2#50714C214yesmaximal, complemented
3#48006C218yesmaximal, complemented
4#47777C218yesmaximal, complemented
5#47224C214yesmaximal
6#46855C214yesmaximal, complemented
7#39683C214yesmaximal, complemented
8#39547C214yesmaximal, complemented
9#37961C214yesmaximal, complemented
10#37936C214yesmaximal, complemented
11#37632C211yesmaximal, characteristic
12#37560C211yesmaximal, characteristic
13#37434C212yesmaximal, complemented
14#37320C212yesmaximal, complemented
15#35345C211yesmaximal, characteristic, complemented
16#35337C212yesmaximal, complemented
17#35294C212yesmaximal, complemented
18#35281C211yesmaximal, characteristic, complemented
19#34403C211yesmaximal, characteristic, complemented
20#34371C211yesmaximal, characteristic, complemented
21#34081C211yesmaximal, characteristic
22C2×#533C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C2×#529C2211yescharacteristic
25#2868C2211yescharacteristic
26#2868C2211yescharacteristic
27#2864C2212yes—
28#2862C2211yescharacteristic
29#2862C2211yescharacteristic
30#2859C2214yes—
31#2859C2212yes—
32#2851C2214yes—
33#2821C2214yes—
34#2817C2212yes—
35#2816C2212yes—
36#2805C2218yes—
37#2798C2218yes—
38#2798C2218yes—
39#2794C2218yes—
40#2791C2218yes—
41#2788C2218yes—
42#2786C2218yes—
43#2775C2218yes—
44#2774C2218yes—
45#2772C2218yes—
46#2770C2218yes—
47#2769C2218yes—
48#2767C2218yes—
49#2758C2218yes—
50#2758C2218yes—
51#2755C2218yes—
52#2744C2218yes—
53#2739C2218yes—
54#2721C2218yes—
55#2719C2218yes—
56#2716C2218yes—
57#2713C2218yes—
58#2707C2218yes—
59#2695C2218yes—
60#2663C2214yes—
61#2660C2212yes—
62#2660C2214yes—
63#2647C2214yes—
64#2640C2212yes—
65#2634C2212yes—
66#2632C2212yes—
67#2629C2214yes—
68#2629C2214yes—
69#2628C2212yes—
70#2628C2212yes—
71#2628C2212yes—
72#2628C2212yes—
73#2614C2214yes—
74#2608C2214yes—
75#2608C2214yes—
76#2606C2214yes—
77#2606C2214yes—
78#2606C2218yes—
79#2604C2214yes—
80#2601C2218yes—
81#2599C2218yes—
82#2589C2218yes—
83#2589C2218yes—
84#2588C2218yes—
85#2588C2218yes—
86#2588C2218yes—
87#2585C2218yes—
88#2584C2212yes—
89#2584C2218yes—
90#2573C2218yes—
91#2570C2218yes—
92#2567C2212yes—
93#2567C2214yes—
94#2563C2212yes—
95#2562C2212yes—
96#2558C2218yes—
97#2550C2218yes—
98#2546C2214yes—
99#2529C2218yes—
100#2524C2218yes—
101#2515C2218yes—
102#2509C2214yes—
103#2509C2214yes—
104#2507C2214yes—
105#2506C2218yes—
106#2506C2214yes—
107#2503C2212yes—
108#2502C2214yes—
109#2501C2212yes—
110#2497C2214yes—
111#2496C2214yes—
112#2495C2214yes—
113#2495C2214yes—
114#2486C2214yes—
115#2485C2214yes—
116#2478C2218yes—
117#2470C2218yes—
118#2469C2218yes—
119#2462C2218yes—
120#2441C2218yes—
121#2439C2218yes—
122#2434C2214yes—
123#2381C2214yes—
124#2378C2214yes—
125#2370C2214yes—
126#2365C2214yes—
127#2356C2214yes—
128#2347C2212yes—
129#2346C2212yes—
130#2345C2212yes—
131#2345C2212yes—
132Q8×C22⋊C4C2214yes—
133#2337C2212yes—
134#2336C2212yes—
135#2335C2214yes—
136#2334C2214yes—
137#2333C2212yes—
138#2332C2212yes—
139#2332C2214yes—
140#2331C2212yes—
141#2331C2212yes—
142#2331C2212yes—
143#2331C2212yes—
144#2330C2214yes—
145#2330C2214yes—
146#2327C2214yes—
147#2320C2214yes—
148#2317C2214yes—
149#2314C2214yes—
150#2313C2214yes—
151C4×#125C2214yes—
152#2298C2212yes—
153#2295C2212yes—
154#2293C2212yes—
155#2290C2212yes—
156#2290C2212yes—
157#2285C2214yes—
158#2283C2211yescharacteristic
159#2283C2211yescharacteristic
160#2283C2211yescharacteristic
161C4×#117C2212yes—
162C4×#117C2211yescharacteristic
163C23×Q8C2312yes—
164#533—28no—
165C2×C4⋊Q8—28no—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175#529—28no—
176C2×#126C2312yes—
177C2×#126C2318yes—
178C2×#125C2314yes—
179C2×#125C2312yes—
180C2×#125C2311yescharacteristic
181C2×#125C2318yes—
182C2×#125C2318yes—
183C2×#124C2311yescharacteristic
184C2×#123C2312yes—
185C2×#123C2318yes—
186C2×C22⋊Q8C2312yes—
187C2×C22⋊Q8C2311yescharacteristic
188C2×C22⋊Q8C2312yes—
189C2×#121C2311yescharacteristic
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2318yes—
194C2×C4×D4C2311yescharacteristic
195C2×C4×D4C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2318yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2312yes—
203C22×C42C2312yes—
204C22×C42C2311yescharacteristic
205#400C2314yes—
206#400C2314yes—
207#400C2314yes—
208#400C2314yes—
209#400C2318yes—
210#400C2318yes—
211#400C2318yes—
212#400C2314yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#399C2314yes—
222#399C2314yes—
223#399C2314yes—
224#399C2314yes—
225#398C2314yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#395C2314yes—
249#395C2314yes—
250#395C2318yes—
251#395C2318yes—
252#395C2318yes—
253#395C2314yes—
254#395C2314yes—
255#395C2314yes—
256#394C2314yes—
257#394C2318yes—
258#393C2314yes—
259#393C2318yes—
260#393C2314yes—
261#393C2314yes—
262#393C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2318yes—
267#391C2318yes—
268#391C2318yes—
269#391C2318yes—
270#391C2318yes—
271#391C2314yes—
272#391C2314yes—
273#391C2314yes—
274#390C2314yes—
275#390C2314yes—
276#389C2314yes—
277#389C2314yes—
278#389C2318yes—
279#389C2318yes—
280#389C2314yes—
281#389C2318yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2314yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2318yes—
293#389C2318yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2314yes—
302#389C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2314yes—
307#388C2318yes—
308#388C2314yes—
309#388C2318yes—
310#388C2314yes—
311#388C2314yes—
312#388C2314yes—
313#388C2314yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2314yes—
348#387C2314yes—
349#387C2314yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#386C2314yes—
354#386C2314yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2314yes—
360#385C2314yes—
361#384C2314yes—
362#384C2314yes—
363#384C2314yes—
364#384C2314yes—
365#384C2314yes—
366#384C2314yes—
367#383C2312yes—
368#383C2318yes—
369#383C2314yes—
370#383C2312yes—
371#383C2312yes—
372#383C2318yes—
373#382C2314yes—
374#382C2314yes—
375#382C2318yes—
376#382C2318yes—
377#382C2314yes—
378#382C2312yes—
379#382C2314yes—
380#382C2312yes—
381#382C2312yes—
382#381C2312yes—
383#381C2312yes—
384#381C2318yes—
385#381C2312yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2312yes—
393#380C2312yes—
394#380C2312yes—
395#380C2318yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2312yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2311yescharacteristic
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2312yes—
426#376C2314yes—
427#376C2312yes—
428#376C2312yes—
429#376C2312yes—
430#376C2312yes—
431#376C2312yes—
432C43C2312yes—
433C43C2311yescharacteristic
434C43C2311yescharacteristic
435C22×Q8—28no—
436C22×Q8—84no—
437C22×Q8C2414yes—
438C22×Q8C2411yescharacteristic
439C22×Q8C2412yes—
440C22×Q8C2412yes—
441C22×Q8C2412yes—
442C22×Q8C2412yes—
443C22×D4C2412yes—
444C22×D4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2414yes—
448C23×C4C2414yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C4⋊Q8—24no—
452C4⋊Q8—24no—
453C4⋊Q8—28no—
454C4⋊Q8—28no—
455C4⋊Q8—28no—
456C4⋊Q8—24no—
457C4⋊Q8—24no—
458C4⋊Q8—84no—
459C4⋊Q8—84no—
460#126—28no—
461#126—88no—
462#125—24no—
463#125—28no—
464#125—216no—
465#125—88no—
466#125—88no—
467#124—24no—
468#123—28no—
469#123—88no—
470C22⋊Q8—24no—
471C22⋊Q8—28no—
472C22⋊Q8—28no—
473#121—24no—
474C4×Q8—24no—
475C4×Q8—28no—
476C4×Q8—28no—
477C4×Q8—88no—
478C4×D4—28no—
479C4×D4—24no—
480#117—28no—
481#117—28no—
482#117—28no—
483#117—28no—
484#117—88no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—28no—
487C2×C4⋊C4C2412yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2411yescharacteristic
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2411yescharacteristic
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C22⋊C4C2412yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2414yes—
535C2×C22⋊C4C2412yes—
536C2×C22⋊C4C2412yes—
537C2×C22⋊C4C2412yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2418yes—
548C2×C42—28no—
549C2×C42#4118yes—
550C2×C42C2412yes—
551C2×C42C2414yes—
552C2×C42C2412yes—
553C2×C42C2412yes—
554C2×C42C2412yes—
555C2×C42C2414yes—
556C2×C42C2418yes—
557C2×C42C2418yes—
558C2×C42C2414yes—
559C2×C42C2418yes—
560C2×C42C2414yes—
561C2×C42C2412yes—
562C2×C42C2412yes—
563C2×C42C2412yes—
564C2×C42C2414yes—
565C2×C42C2412yes—
566C2×C42C2414yes—
567C2×C42C2418yes—
568C2×C42C2411yescharacteristic
569C2×C42C2411yescharacteristic
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572C2×C42C2412yes—
573#95C2412yes—
574#95C2414yes—
575#95C2414yes—
576#95C2414yes—
577#95C2414yes—
578#95C2414yes—
579#95C2414yes—
580#95C2414yes—
581#95C2414yes—
582#95C2414yes—
583#95C2414yes—
584#95C2418yes—
585#95C2412yes—
586#95C2414yes—
587#95C2418yes—
588#95C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2418yes—
592#95C2414yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2414yes—
599#95C2414yes—
600#95C2418yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2414yes—
606#95C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616C24C2512yes—
617C24C2511yescharacteristic
618C2×Q8—28no—
619C2×Q8—22no—
620C2×Q8—24no—
621C2×Q8—24no—
622C2×Q8—24no—
623C2×Q8—24no—
624C2×Q8—48no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8—42no—
629C2×Q8—44no—
630C2×Q8—816no—
631C2×D4—24no—
632C2×D4—22no—
633C2×D4—44no—
634C2×D4—42no—
635C22×C4—24no—
636C22×C4—28no—
637C22×C4—24no—
638C22×C4—28no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—48no—
646C22×C4C2×#4114yes—
647C22×C4C2×#4114yes—
648C22×C4C2×#4114yes—
649C22×C4C2512yes—
650C22×C4C2514yes—
651C22×C4C2512yes—
652C22×C4C2514yes—
653C22×C4C2514yes—
654C22×C4C2514yes—
655C22×C4C2518yes—
656C22×C4C2518yes—
657C22×C4C2514yes—
658C22×C4C2514yes—
659C22×C4C2514yes—
660C22×C4C2512yes—
661C22×C4C2511yescharacteristic
662C22×C4C2511yescharacteristic
663C22×C4C2511yescharacteristic
664C22×C4C2511yescharacteristic
665C22×C4C2511yescharacteristic
666C22×C4C2514yes—
667C22×C4C2511yescharacteristic
668C4⋊C4—28no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—28no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—22no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—24no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—28no—
687C4⋊C4—28no—
688C4⋊C4—216no—
689C4⋊C4—216no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—48no—
693C4⋊C4—48no—
694C4⋊C4—48no—
695C4⋊C4—44no—
696C4⋊C4—48no—
697C4⋊C4—48no—
698C4⋊C4—48no—
699C4⋊C4—44no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—48no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—48no—
706C4⋊C4—44no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—48no—
710C4⋊C4—48no—
711C22⋊C4—28no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—42no—
720C22⋊C4—44no—
721C22⋊C4—48no—
722C22⋊C4—44no—
723C22⋊C4—42no—
724C22⋊C4—48no—
725C22⋊C4—48no—
726C22⋊C4—44no—
727C22⋊C4—48no—
728C22⋊C4—44no—
729C42—24no—
730C42—28no—
731C42—28no—
732C42—24no—
733C42—24no—
734C42—24no—
735C42—42no—
736C42—44no—
737C42—44no—
738C42—42no—
739C42—48no—
740C42—48no—
741C42—48no—
742C42—44no—
743C42—48no—
744C42—44no—
745C42—42no—
746C42—42no—
747C42C2×#4114yes—
748C42C2×#4114yes—
749C42C2×#4114yes—
750C42C2×#4114yes—
751C422−1+418yes—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—24no—
759C23—24no—
760C23C22×#4112yes—
761C23C2611yescharacteristic
762Q8—416no—
763Q8—84no—
764Q8—82no—
765Q8—84no—
766Q8—84no—
767Q8—84no—
768D4—82no—
769D4—84no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—24no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—416no—
812C2×C4—48no—
813C2×C4—88no—
814C2×C4C22×#4112yes—
815C2×C4C22×#4112yes—
816C2×C4C22×#4112yes—
817C2×C4C22×#4112yes—
818C2×C4C22×#4112yes—
819C2×C4C22×#4112yes—
820C2×C4C2×2−1+418yes—
821C2×C4C2×2−1+414yes—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22C23×#4111yescharacteristic
832C22C22×2−1+412yes—
833C22H(7,𝔽2)12yes—
834C222−1+612yes—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—28no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—42no—
845C4—44no—
846C4—42no—
847C4—44no—
848C4—44no—
849C4—44no—
850C4—48no—
851C4—48no—
852C4—44no—
853C4#350914yes—
854C2—42no—
855C2—82no—
856C2C2×#350911yescharacteristic
857C2#6285511yescharacteristic
858C2#6286011yescharacteristic
859C2#6287714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51087C2semidirect
2. #50714C2semidirect
3. #48006C2semidirect
4. #47777C2semidirect
6. #46855C2semidirect
7. #39683C2semidirect
8. #39547C2semidirect
9. #37961C2semidirect
10. #37936C2semidirect
13. #37434C2semidirect
14. #37320C2semidirect
15. #35345C2semidirect
16. #35337C2semidirect
17. #35294C2semidirect
18. #35281C2semidirect
19. #34403C2semidirect
20. #34371C2semidirect

Maximal subgroups

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

subgroupindex
#510872
#507142
#480062
#477772
#472242
#468552
#396832
#395472
#379612
#379362
#376322
#375602
#374342
#373202
#353452
#353372
#352942
#352812
#344032
#343712
#340812