Finite Group Databasebeta

← #7715335

Subgroups — #7715335

Order 512.

4182 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51225C214yesmaximal, complemented
2#50915C214yesmaximal, complemented
3#48877C218yesmaximal, complemented
4#47738C218yesmaximal, complemented
5#47032C214yesmaximal
6#46453C214yesmaximal, complemented
7#39682C214yesmaximal, complemented
8#39546C214yesmaximal, complemented
9#37960C214yesmaximal, complemented
10#37937C214yesmaximal, complemented
11#37617C211yesmaximal, characteristic
12#37560C211yesmaximal, characteristic
13#37433C212yesmaximal, complemented
14#37320C212yesmaximal, complemented
15#35345C211yesmaximal, characteristic, complemented
16#35337C212yesmaximal, complemented
17#35294C212yesmaximal, complemented
18#35281C211yesmaximal, characteristic, complemented
19#34403C211yesmaximal, characteristic, complemented
20#34365C211yesmaximal, 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#2802C2218yes—
37#2794C2218yes—
38#2789C2218yes—
39#2789C2218yes—
40#2789C2218yes—
41#2787C2218yes—
42#2783C2218yes—
43#2777C2218yes—
44#2768C2218yes—
45#2767C2218yes—
46#2766C2218yes—
47#2765C2218yes—
48#2765C2218yes—
49#2761C2218yes—
50#2755C2218yes—
51#2754C2218yes—
52#2754C2218yes—
53#2750C2218yes—
54#2726C2218yes—
55#2721C2218yes—
56#2716C2218yes—
57#2715C2218yes—
58#2713C2218yes—
59#2713C2218yes—
60#2663C2214yes—
61#2660C2214yes—
62#2658C2212yes—
63#2647C2214yes—
64#2642C2212yes—
65#2634C2212yes—
66#2632C2212yes—
67#2629C2214yes—
68#2629C2214yes—
69#2628C2212yes—
70#2628C2212yes—
71#2628C2212yes—
72#2628C2212yes—
73#2623C2214yes—
74#2611C2218yes—
75#2609C2218yes—
76#2608C2214yes—
77#2608C2214yes—
78#2606C2214yes—
79#2606C2214yes—
80#2604C2214yes—
81#2601C2218yes—
82#2594C2218yes—
83#2590C2218yes—
84#2590C2218yes—
85#2589C2218yes—
86#2589C2218yes—
87#2588C2218yes—
88#2588C2218yes—
89#2588C2218yes—
90#2584C2212yes—
91#2570C2218yes—
92#2567C2214yes—
93#2562C2212yes—
94#2550C2218yes—
95#2550C2218yes—
96#2547C2212yes—
97#2546C2212yes—
98#2546C2214yes—
99#2528C2218yes—
100#2520C2218yes—
101#2519C2218yes—
102#2508C2214yes—
103#2508C2214yes—
104#2508C2218yes—
105#2507C2214yes—
106#2506C2214yes—
107#2502C2214yes—
108#2497C2214yes—
109#2496C2214yes—
110#2494C2214yes—
111#2494C2214yes—
112#2487C2214yes—
113#2485C2214yes—
114#2478C2218yes—
115#2475C2218yes—
116#2475C2218yes—
117#2474C2218yes—
118#2441C2218yes—
119#2439C2218yes—
120#2436C2212yes—
121#2434C2212yes—
122#2434C2214yes—
123#2381C2214yes—
124#2378C2214yes—
125#2370C2214yes—
126#2369C2214yes—
127#2356C2214yes—
128#2347C2212yes—
129#2346C2212yes—
130#2344C2212yes—
131#2344C2212yes—
132#2344C2214yes—
133#2337C2212yes—
134#2336C2212yes—
135#2335C2214yes—
136#2334C2214yes—
137#2333C2212yes—
138#2332C2212yes—
139#2332C2214yes—
140#2331C2212yes—
141#2331C2212yes—
142#2331C2212yes—
143#2331C2214yes—
144#2331C2212yes—
145#2330C2214yes—
146#2330C2214yes—
147#2320C2214yes—
148#2317C2214yes—
149#2314C2214yes—
150#2310C2214yes—
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—
175C2×C4⋊Q8C2314yes—
176#529—28no—
177C2×#126C2312yes—
178C2×#126C2318yes—
179C2×#125C2314yes—
180C2×#125C2312yes—
181C2×#125C2311yescharacteristic
182C2×#125C2318yes—
183C2×#125C2318yes—
184C2×#124C2311yescharacteristic
185C2×#124C2314yes—
186C2×#123C2312yes—
187C2×C22⋊Q8C2312yes—
188C2×C22⋊Q8C2311yescharacteristic
189C2×C22⋊Q8C2312yes—
190C2×#121C2311yescharacteristic
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2311yescharacteristic
194C2×C4×D4C2311yescharacteristic
195C2×C4×D4C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2314yes—
201C2×#117C2314yes—
202C2×#117C2318yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C42C2312yes—
206C22×C42C2311yescharacteristic
207#401C2318yes—
208#401C2318yes—
209#400C2314yes—
210#400C2314yes—
211#400C2318yes—
212#400C2314yes—
213#400C2314yes—
214#400C2314yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#399C2314yes—
223#399C2318yes—
224#399C2314yes—
225#399C2314yes—
226#399C2314yes—
227#398C2314yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#396C2318yes—
248#396C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#395C2314yes—
253#395C2314yes—
254#395C2314yes—
255#395C2314yes—
256#395C2318yes—
257#395C2318yes—
258#395C2314yes—
259#394C2314yes—
260#394C2318yes—
261#393C2314yes—
262#393C2314yes—
263#393C2314yes—
264#393C2314yes—
265#391C2318yes—
266#391C2318yes—
267#391C2318yes—
268#391C2318yes—
269#391C2314yes—
270#391C2314yes—
271#391C2318yes—
272#391C2318yes—
273#391C2314yes—
274#391C2314yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#390C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2318yes—
282#389C2318yes—
283#389C2318yes—
284#389C2318yes—
285#389C2318yes—
286#389C2314yes—
287#389C2318yes—
288#389C2318yes—
289#389C2314yes—
290#389C2318yes—
291#389C2314yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2318yes—
299#389C2314yes—
300#389C2318yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#389C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2314yes—
309#388C2314yes—
310#388C2318yes—
311#388C2318yes—
312#388C2314yes—
313#388C2314yes—
314#388C2314yes—
315#388C2314yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
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#387C2318yes—
335#387C2314yes—
336#387C2314yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2314yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#386C2314yes—
356#386C2314yes—
357#386C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2314yes—
363#385C2314yes—
364#385C2318yes—
365#384C2314yes—
366#384C2314yes—
367#384C2314yes—
368#384C2314yes—
369#384C2314yes—
370#383C2312yes—
371#383C2314yes—
372#383C2312yes—
373#383C2312yes—
374#382C2314yes—
375#382C2318yes—
376#382C2318yes—
377#382C2314yes—
378#382C2312yes—
379#382C2314yes—
380#382C2312yes—
381#382C2312yes—
382#382C2318yes—
383#382C2318yes—
384#381C2312yes—
385#381C2312yes—
386#381C2314yes—
387#381C2314yes—
388#381C2312yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2312yes—
393#380C2312yes—
394#380C2312yes—
395#380C2314yes—
396#380C2318yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2311yescharacteristic
422C4×C22⋊C4C2311yescharacteristic
423C4×C22⋊C4C2312yes—
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×Q8C2411yescharacteristic
438C22×Q8C2412yes—
439C22×Q8C2412yes—
440C22×Q8C2414yes—
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—
460C4⋊Q8—84no—
461#126—28no—
462#126—88no—
463#125—24no—
464#125—28no—
465#125—216no—
466#125—88no—
467#125—88no—
468#124—24no—
469#124—84no—
470#123—28no—
471C22⋊Q8—24no—
472C22⋊Q8—28no—
473C22⋊Q8—28no—
474#121—24no—
475C4×Q8—24no—
476C4×Q8—28no—
477C4×Q8—28no—
478C4×D4—28no—
479C4×D4—24no—
480#117—28no—
481#117—28no—
482#117—28no—
483#117—28no—
484#117—84no—
485#117—88no—
486#117—84no—
487C2×C4⋊C4—28no—
488C2×C4⋊C4—28no—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2412yes—
496C2×C4⋊C4C2412yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2411yescharacteristic
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2411yescharacteristic
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2414yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2412yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2418yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2412yes—
538C2×C22⋊C4C2412yes—
539C2×C22⋊C4C2412yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2418yes—
550C2×C42—28no—
551C2×C42#4118yes—
552C2×C42C2412yes—
553C2×C42C2414yes—
554C2×C42C2412yes—
555C2×C42C2412yes—
556C2×C42C2412yes—
557C2×C42C2414yes—
558C2×C42C2418yes—
559C2×C42C2418yes—
560C2×C42C2418yes—
561C2×C42C2414yes—
562C2×C42C2414yes—
563C2×C42C2412yes—
564C2×C42C2412yes—
565C2×C42C2412yes—
566C2×C42C2414yes—
567C2×C42C2412yes—
568C2×C42C2414yes—
569C2×C42C2418yes—
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572C2×C42C2411yescharacteristic
573C2×C42C2411yescharacteristic
574C2×C42C2412yes—
575#95C2412yes—
576#95C2414yes—
577#95C2414yes—
578#95C2414yes—
579#95C2414yes—
580#95C2414yes—
581#95C2414yes—
582#95C2414yes—
583#95C2414yes—
584#95C2414yes—
585#95C2414yes—
586#95C2418yes—
587#95C2412yes—
588#95C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2414yes—
599#95C2414yes—
600#95C2418yes—
601#95C2418yes—
602#95C2414yes—
603#95C2414yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618C24C2512yes—
619C24C2511yescharacteristic
620C2×Q8—22no—
621C2×Q8—24no—
622C2×Q8—24no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—28no—
626C2×Q8—44no—
627C2×Q8—42no—
628C2×Q8—44no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—816no—
634C2×D4—24no—
635C2×D4—22no—
636C2×D4—42no—
637C2×D4—44no—
638C22×C4—24no—
639C22×C4—28no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—42no—
648C22×C4—44no—
649C22×C4—42no—
650C22×C4C2×#4114yes—
651C22×C4C2×#4114yes—
652C22×C4C2×#4114yes—
653C22×C4C2512yes—
654C22×C4C2514yes—
655C22×C4C2514yes—
656C22×C4C2512yes—
657C22×C4C2514yes—
658C22×C4C2514yes—
659C22×C4C2518yes—
660C22×C4C2518yes—
661C22×C4C2514yes—
662C22×C4C2514yes—
663C22×C4C2512yes—
664C22×C4C2514yes—
665C22×C4C2511yescharacteristic
666C22×C4C2511yescharacteristic
667C22×C4C2511yescharacteristic
668C22×C4C2511yescharacteristic
669C22×C4C2511yescharacteristic
670C22×C4C2514yes—
671C22×C4C2511yescharacteristic
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—22no—
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—216no—
693C4⋊C4—216no—
694C4⋊C4—28no—
695C4⋊C4—28no—
696C4⋊C4—44no—
697C4⋊C4—48no—
698C4⋊C4—44no—
699C4⋊C4—48no—
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—
711C4⋊C4—48no—
712C4⋊C4—48no—
713C4⋊C4—48no—
714C4⋊C4—48no—
715C22⋊C4—28no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—28no—
722C22⋊C4—28no—
723C22⋊C4—48no—
724C22⋊C4—44no—
725C22⋊C4—44no—
726C22⋊C4—42no—
727C22⋊C4—42no—
728C22⋊C4—44no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—44no—
733C42—24no—
734C42—28no—
735C42—28no—
736C42—24no—
737C42—24no—
738C42—24no—
739C42—42no—
740C42—44no—
741C42—44no—
742C42—42no—
743C42—48no—
744C42—48no—
745C42—48no—
746C42—48no—
747C42—44no—
748C42—44no—
749C42—42no—
750C42—42no—
751C42C2×#4114yes—
752C42C2×#4114yes—
753C42C2×#4114yes—
754C42C2×#4114yes—
755C422−1+418yes—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—24no—
763C23—24no—
764C23C22×#4112yes—
765C23C2611yescharacteristic
766Q8—82no—
767Q8—84no—
768Q8—84no—
769Q8—88no—
770Q8—84no—
771Q8—84no—
772D4—82no—
773D4—84no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—28no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—24no—
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—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—28no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—416no—
818C2×C4—416no—
819C2×C4—48no—
820C2×C4C22×#4112yes—
821C2×C4C22×#4112yes—
822C2×C4C22×#4112yes—
823C2×C4C22×#4112yes—
824C2×C4C22×#4112yes—
825C2×C4C22×#4112yes—
826C2×C4C2×2−1+418yes—
827C2×C4C2×2−1+414yes—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—44no—
836C22—44no—
837C22C23×#4111yescharacteristic
838C22C22×2−1+412yes—
839C22H(7,𝔽2)12yes—
840C222−1+612yes—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—28no—
847C4—42no—
848C4—44no—
849C4—44no—
850C4—42no—
851C4—44no—
852C4—42no—
853C4—44no—
854C4—44no—
855C4—44no—
856C4—48no—
857C4—48no—
858C4—44no—
859C4#350914yes—
860C2—42no—
861C2—82no—
862C2C2×#350911yescharacteristic
863C2#6285511yescharacteristic
864C2#6286011yescharacteristic
865C2#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. #51225C2semidirect
2. #50915C2semidirect
3. #48877C2semidirect
4. #47738C2semidirect
6. #46453C2semidirect
7. #39682C2semidirect
8. #39546C2semidirect
9. #37960C2semidirect
10. #37937C2semidirect
13. #37433C2semidirect
14. #37320C2semidirect
15. #35345C2semidirect
16. #35337C2semidirect
17. #35294C2semidirect
18. #35281C2semidirect
19. #34403C2semidirect
20. #34365C2semidirect

Maximal subgroups

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

subgroupindex
#512252
#509152
#488772
#477382
#470322
#464532
#396822
#395462
#379602
#379372
#376172
#375602
#374332
#373202
#353452
#353372
#352942
#352812
#344032
#343652
#340812