Finite Group Databasebeta

← #7715384

Subgroups — #7715384

Order 512.

4682 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51091C214yesmaximal, complemented
2#50718C214yesmaximal, complemented
3#48009C218yesmaximal, complemented
4#47743C218yesmaximal, complemented
5#47033C214yesmaximal, complemented
6#46457C214yesmaximal, complemented
7#39270C214yesmaximal, complemented
8#39046C214yesmaximal, complemented
9#38242C214yesmaximal, complemented
10#38202C214yesmaximal, complemented
11#37614C211yesmaximal, characteristic
12#37560C211yesmaximal, characteristic, complemented
13#37321C212yesmaximal, complemented
14#37321C212yesmaximal, complemented
15#35345C211yesmaximal, characteristic, complemented
16#35296C212yesmaximal, complemented
17#35285C211yesmaximal, characteristic, complemented
18#35268C212yesmaximal, complemented
19#34403C211yesmaximal, characteristic, complemented
20#34364C211yesmaximal, characteristic, complemented
21#34081C211yesmaximal, characteristic, complemented
22C2×#533C2211yescharacteristic
23C22×#127C2211yescharacteristic
24C2×#529C2211yescharacteristic
25#2864C2212yescomplemented
26#2860C2214yescomplemented
27#2859C2212yescomplemented
28#2858C2211yescharacteristic
29#2858C2211yescharacteristic
30#2858C2211yescharacteristic
31#2858C2211yescharacteristic
32#2854C2214yescomplemented
33#2818C2214yes—
34#2817C2212yes—
35#2816C2212yes—
36#2803C2218yescomplemented
37#2800C2218yescomplemented
38#2797C2218yescomplemented
39#2796C2218yescomplemented
40#2796C2218yescomplemented
41#2796C2218yescomplemented
42#2761C2218yescomplemented
43#2757C2218yescomplemented
44#2756C2218yescomplemented
45#2740C2218yescomplemented
46#2735C2218yes—
47#2735C2218yes—
48#2727C2218yescomplemented
49#2715C2218yescomplemented
50#2715C2218yescomplemented
51#2715C2218yescomplemented
52#2710C2218yescomplemented
53#2710C2218yescomplemented
54#2709C2218yescomplemented
55#2706C2218yescomplemented
56#2705C2218yescomplemented
57#2705C2218yescomplemented
58#2697C2218yes—
59#2685C2218yes—
60#2663C2214yes—
61#2657C2212yes—
62#2644C2214yescomplemented
63#2641C2214yes—
64#2641C2212yes—
65#2634C2212yescomplemented
66#2632C2212yescomplemented
67#2629C2214yes—
68#2628C2212yescomplemented
69#2628C2212yescomplemented
70#2624C2214yescomplemented
71#2619C2212yes—
72#2619C2212yes—
73#2613C2214yes—
74#2608C2214yes—
75#2608C2214yes—
76#2606C2214yescomplemented
77#2606C2214yescomplemented
78#2604C2214yescomplemented
79#2603C2218yescomplemented
80#2602C2218yescomplemented
81#2601C2218yescomplemented
82#2595C2218yescomplemented
83#2595C2218yescomplemented
84#2584C2212yescomplemented
85#2562C2212yescomplemented
86#2557C2218yescomplemented
87#2554C2218yescomplemented
88#2548C2214yes—
89#2548C2212yes—
90#2548C2214yes—
91#2541C2212yes—
92#2534C2218yes—
93#2531C2218yescomplemented
94#2521C2218yescomplemented
95#2521C2218yescomplemented
96#2516C2218yescomplemented
97#2512C2214yescomplemented
98#2512C2214yescomplemented
99#2490C2214yescomplemented
100#2490C2214yescomplemented
101#2485C2214yes—
102#2485C2218yescomplemented
103#2480C2218yes—
104#2480C2218yes—
105#2479C2218yescomplemented
106#2474C2218yescomplemented
107#2471C2218yescomplemented
108#2467C2218yescomplemented
109#2466C2218yescomplemented
110#2459C2218yescomplemented
111#2455C2218yescomplemented
112#2454C2214yescomplemented
113#2454C2214yescomplemented
114#2445C2218yescomplemented
115#2435C2212yes—
116#2435C2214yes—
117#2435C2214yes—
118#2433C2212yes—
119#2422C2214yescomplemented
120#2422C2214yescomplemented
121#2411C2218yes—
122#2408C2214yes—
123#2380C2214yes—
124#2378C2214yes—
125#2370C2214yescomplemented
126#2366C2214yes—
127#2356C2214yescomplemented
128#2347C2212yes—
129#2346C2212yes—
130D4×C22⋊C4C2212yes—
131D4×C22⋊C4C2212yes—
132D4×C22⋊C4C2214yes—
133#2337C2212yescomplemented
134#2336C2212yescomplemented
135#2335C2214yes—
136#2334C2214yescomplemented
137#2333C2212yes—
138#2332C2212yes—
139#2332C2214yes—
140#2331C2212yescomplemented
141#2331C2212yescomplemented
142#2330C2214yescomplemented
143#2328C2214yes—
144#2328C2212yes—
145#2328C2212yes—
146#2324C2214yescomplemented
147#2320C2214yescomplemented
148#2319C2214yescomplemented
149#2309C2214yes—
150#2308C2214yes—
151C4×#121C2214yescomplemented
152#2298C2212yescomplemented
153#2295C2212yescomplemented
154#2293C2212yes—
155#2293C2214yescomplemented
156#2290C2212yes—
157#2290C2212yescomplemented
158#2283C2211yescharacteristic
159#2283C2211yescharacteristic
160#2283C2211yescharacteristic
161C4×#117C2211yescharacteristic
162C4×#117C2212yescomplemented
163C23×D4C2312yes—
164C23×D4C2312yes—
165C23×D4C2312yes—
166#533—28no—
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2311yescharacteristic
169C2×#127—28no—
170C2×#127C2312yes—
171C2×#127C2311yescharacteristic
172C2×#127C2311yescharacteristic
173C2×#127C2312yes—
174C2×#127C2312yes—
175C2×#127C2314yes—
176#529—28no—
177C2×#126C2312yes—
178C2×#126C2318yes—
179C2×#126C2318yes—
180C2×#126C2318yes—
181C2×#125C2312yes—
182C2×#125C2311yescharacteristic
183C2×#125C2314yes—
184C2×#124C2311yescharacteristic
185C2×#124C2314yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#124C2314yes—
190C2×#123C2312yes—
191C2×#123C2318yes—
192C2×#123C2318yes—
193C2×#123C2318yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2311yescharacteristic
196C2×C22⋊Q8C2312yes—
197C2×#121C2311yescharacteristic
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#120C2318yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2311yescharacteristic
203C2×C4×Q8C2312yes—
204C2×C4×D4C2311yescharacteristic
205C2×C4×D4C2312yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2318yes—
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2318yes—
215C22×C22⋊C4C2314yes—
216C22×C22⋊C4C2314yes—
217C22×C42C2312yes—
218C22×C42C2311yescharacteristic
219#400C2314yes—
220#400C2314yes—
221#400C2314yes—
222#399C2314yes—
223#399C2318yes—
224#399C2314yes—
225#399C2318yes—
226#399C2318yes—
227#398C2314yes—
228#398C2318yes—
229#398C2318yes—
230#397C2318yes—
231#397C2318yes—
232#397C2318yes—
233#397C2318yes—
234#397C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#396C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#395C2314yes—
249#395C2314yes—
250#395C2314yes—
251#394C2314yes—
252#394C2318yes—
253#394C2314yes—
254#394C2318yes—
255#394C2314yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2314yes—
262#394C2314yes—
263#394C2318yes—
264#394C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#393C2314yes—
270#393C2314yes—
271#392C2318yes—
272#392C2318yes—
273#392C2314yes—
274#392C2314yes—
275#392C2314yes—
276#392C2314yes—
277#391C2318yes—
278#391C2318yes—
279#391C2314yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#390C2314yes—
284#390C2318yes—
285#390C2318yes—
286#390C2314yes—
287#390C2318yes—
288#390C2314yes—
289#390C2314yes—
290#390C2318yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2318yes—
296#390C2314yes—
297#390C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2318yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#389C2314yes—
305#389C2318yes—
306#389C2314yes—
307#389C2318yes—
308#389C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2318yes—
314#389C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2314yes—
320#388C2314yes—
321#388C2318yes—
322#388C2318yes—
323#388C2314yes—
324#388C2314yes—
325#388C2314yes—
326#388C2314yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2314yes—
346#387C2314yes—
347#387C2318yes—
348#387C2314yes—
349#387C2314yes—
350#387C2314yes—
351#387C2314yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2314yes—
365#386C2314yes—
366#386C2318yes—
367#386C2318yes—
368#385C2318yes—
369#385C2314yes—
370#385C2314yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#384C2314yes—
376#383C2312yes—
377#383C2314yes—
378#383C2312yes—
379#383C2312yes—
380#382C2312yes—
381#382C2314yes—
382#382C2312yes—
383#382C2312yes—
384#381C2312yes—
385#381C2312yes—
386#381C2318yes—
387#381C2312yes—
388#380C2314yes—
389#380C2314yes—
390#380C2318yes—
391#380C2312yes—
392#380C2312yes—
393#380C2312yes—
394#380C2318yes—
395#380C2318yes—
396#379C2314yes—
397#379C2314yes—
398#379C2318yes—
399#379C2318yes—
400#379C2318yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2311yescharacteristic
420C4×C22⋊C4C2311yescharacteristic
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2312yes—
426#376C2312yes—
427#376C2314yes—
428#376C2312yes—
429#376C2312yes—
430#376C2312yes—
431#376C2312yes—
432C43C2311yescharacteristic
433C43C2311yescharacteristic
434C43C2312yes—
435C25C2414yes—
436C22×Q8C2411yescharacteristic
437C22×Q8C2412yes—
438C22×Q8C2412yes—
439C22×D4—28no—
440C22×D4—28no—
441C22×D4—28no—
442C22×D4—48no—
443C22×D4—84no—
444C22×D4—84no—
445C22×D4C2412yes—
446C22×D4C2412yes—
447C22×D4C2414yes—
448C22×D4C2412yes—
449C22×D4C2411yescharacteristic
450C22×D4C2412yes—
451C22×D4C2412yes—
452C22×D4C2412yes—
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C2414yes—
456C22×D4C2418yes—
457C22×D4C2418yes—
458C23×C4C2412yes—
459C23×C4C2411yescharacteristic
460C23×C4C2418yes—
461C23×C4C2418yes—
462C23×C4C2414yes—
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C4⋊Q8—24no—
466C4⋊Q8—24no—
467#127—24no—
468#127—24no—
469#127—28no—
470#127—28no—
471#127—28no—
472#127—84no—
473#126—28no—
474#126—88no—
475#126—88no—
476#126—88no—
477#125—24no—
478#125—28no—
479#125—48no—
480#124—24no—
481#124—84no—
482#124—84no—
483#124—84no—
484#124—84no—
485#124—84no—
486#123—28no—
487#123—88no—
488#123—88no—
489#123—88no—
490C22⋊Q8—24no—
491C22⋊Q8—28no—
492C22⋊Q8—28no—
493#121—24no—
494#121—48no—
495#121—48no—
496#120—88no—
497C4×Q8—24no—
498C4×Q8—28no—
499C4×Q8—28no—
500C4×D4—28no—
501C4×D4—24no—
502C4×D4—48no—
503C4×D4—48no—
504C4×D4—88no—
505C4×D4—88no—
506#117—28no—
507#117—28no—
508#117—44no—
509#117—44no—
510#117—88no—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2411yescharacteristic
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2411yescharacteristic
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C22⋊C4—84no—
541C2×C22⋊C4—84no—
542C2×C22⋊C4C2412yes—
543C2×C22⋊C4C2414yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C42—44no—
579C2×C42#4118yes—
580C2×C42C2412yes—
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2418yes—
588C2×C42C2414yes—
589C2×C42C2418yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601#95C2412yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2418yes—
611#95C2414yes—
612#95C2414yes—
613#95C2412yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632C24—28no—
633C24—44no—
634C24—44no—
635C24—48no—
636C24—48no—
637C24C2514yes—
638C24C2514yes—
639C24C2512yes—
640C24C2511yescharacteristic
641C2×Q8—22no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—42no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×D4—24no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—28no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—48no—
661C2×D4—48no—
662C2×D4—44no—
663C2×D4—48no—
664C2×D4—48no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—816no—
677C2×D4—816no—
678C2×D4—816no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—44no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4C2×#4114yes—
695C22×C4C2×#4114yes—
696C22×C4C2×#4114yes—
697C22×C4C2514yes—
698C22×C4C2512yes—
699C22×C4C2514yes—
700C22×C4C2518yes—
701C22×C4C2518yes—
702C22×C4C2514yes—
703C22×C4C2512yes—
704C22×C4C2514yes—
705C22×C4C2514yes—
706C22×C4C2512yes—
707C22×C4C2514yes—
708C22×C4C2511yescharacteristic
709C22×C4C2511yescharacteristic
710C22×C4C2511yescharacteristic
711C22×C4C2511yescharacteristic
712C22×C4C2511yescharacteristic
713C22×C4C2511yescharacteristic
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—22no—
719C4⋊C4—24no—
720C4⋊C4—22no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—44no—
729C4⋊C4—44no—
730C4⋊C4—48no—
731C4⋊C4—48no—
732C4⋊C4—44no—
733C4⋊C4—48no—
734C4⋊C4—48no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—48no—
743C22⋊C4—28no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—44no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—48no—
757C22⋊C4—48no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—44no—
765C22⋊C4—48no—
766C22⋊C4—48no—
767C22⋊C4—48no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—48no—
771C22⋊C4—48no—
772C22⋊C4—48no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C42—24no—
780C42—28no—
781C42—24no—
782C42—24no—
783C42—24no—
784C42—24no—
785C42—44no—
786C42—44no—
787C42—48no—
788C42—44no—
789C42—48no—
790C42—42no—
791C42—42no—
792C42—42no—
793C42—42no—
794C42—44no—
795C42—44no—
796C42C2×#4114yes—
797C42C2×#4114yes—
798C42C2×#4114yes—
799C42C2×#4114yes—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—24no—
805C23—24no—
806C23—22no—
807C23—28no—
808C23—28no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—28no—
813C23—28no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—416no—
819C23—88no—
820C23—88no—
821C23—168no—
822C23—168no—
823C23C22×#4112yes—
824C23C2611yescharacteristic
825Q8—82no—
826Q8—84no—
827Q8—84no—
828D4—416no—
829D4—48no—
830D4—48no—
831D4—82no—
832D4—88no—
833D4—88no—
834D4—84no—
835D4—84no—
836D4—84no—
837D4—84no—
838D4—84no—
839D4—816no—
840D4—168no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—28no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—28no—
873C2×C4—28no—
874C2×C4—24no—
875C2×C4—28no—
876C2×C4—24no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—48no—
880C2×C4—88no—
881C2×C4—816no—
882C2×C4—168no—
883C2×C4C22×#4112yes—
884C2×C4C22×#4112yes—
885C2×C4C22×#4112yes—
886C2×C4C22×#4112yes—
887C2×C4C22×#4112yes—
888C2×C4C22×#4112yes—
889C2×C4#58514yes—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—42no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—44no—
904C22—48no—
905C22—48no—
906C22—44no—
907C22—48no—
908C22—48no—
909C22—1616no—
910C22C23×#4111yescharacteristic
911C22C2×#58512yes—
912C22H(7,𝔽2)12yes—
913C22H(7,𝔽2)12yes—
914C4—22no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—42no—
920C4—42no—
921C4—42no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4—48no—
928C4—44no—
929C4—48no—
930C4#351014yes—
931C2—42no—
932C2—82no—
933C2—84no—
934C2—84no—
935C2C2×#351011yescharacteristic
936C2#6285511yescharacteristic
937C2#6285511yescharacteristic
938C2#6288314yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37614C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51091C2semidirect
2. #50718C2semidirect
3. #48009C2semidirect
4. #47743C2semidirect
5. #47033C2semidirect
6. #46457C2semidirect
7. #39270C2semidirect
8. #39046C2semidirect
9. #38242C2semidirect
10. #38202C2semidirect
12. #37560C2semidirect
13. #37321C2semidirect
14. #37321C2semidirect
15. #35345C2semidirect
16. #35296C2semidirect
17. #35285C2semidirect
18. #35268C2semidirect
19. #34403C2semidirect
20. #34364C2semidirect
21. #34081C2semidirect
25. #2864C22semidirect
26. #2860C22semidirect
27. #2859C22semidirect
32. #2854C22semidirect
36. #2803C22semidirect
37. #2800C22semidirect
38. #2797C22semidirect
39. #2796C22semidirect
40. #2796C22semidirect
41. #2796C22semidirect
42. #2761C22semidirect
43. #2757C22semidirect
44. #2756C22semidirect
45. #2740C22semidirect
48. #2727C22semidirect
49. #2715C22semidirect
50. #2715C22semidirect
51. #2715C22semidirect
52. #2710C22semidirect
53. #2710C22semidirect
54. #2709C22semidirect
55. #2706C22semidirect
56. #2705C22semidirect
57. #2705C22semidirect
62. #2644C22semidirect
65. #2634C22semidirect
66. #2632C22semidirect
68. #2628C22semidirect
69. #2628C22semidirect
70. #2624C22semidirect
76. #2606C22semidirect
77. #2606C22semidirect
78. #2604C22semidirect
79. #2603C22semidirect
80. #2602C22semidirect
81. #2601C22semidirect
82. #2595C22semidirect
83. #2595C22semidirect
84. #2584C22semidirect
85. #2562C22semidirect
86. #2557C22semidirect
87. #2554C22semidirect
93. #2531C22semidirect
94. #2521C22semidirect
95. #2521C22semidirect
96. #2516C22semidirect
97. #2512C22semidirect
98. #2512C22semidirect
99. #2490C22semidirect
100. #2490C22semidirect
102. #2485C22semidirect
105. #2479C22semidirect
106. #2474C22semidirect
107. #2471C22semidirect
108. #2467C22semidirect
109. #2466C22semidirect
110. #2459C22semidirect
111. #2455C22semidirect
112. #2454C22semidirect
113. #2454C22semidirect
114. #2445C22semidirect
119. #2422C22semidirect
120. #2422C22semidirect
125. #2370C22semidirect
127. #2356C22semidirect
133. #2337C22semidirect
134. #2336C22semidirect
136. #2334C22semidirect
140. #2331C22semidirect
141. #2331C22semidirect
142. #2330C22semidirect
146. #2324C22semidirect
147. #2320C22semidirect
148. #2319C22semidirect
151. C4×#121C22semidirect
152. #2298C22semidirect
153. #2295C22semidirect
155. #2293C22semidirect
157. #2290C22semidirect
162. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#510912
#507182
#480092
#477432
#470332
#464572
#392702
#390462
#382422
#382022
#376142
#375602
#373212
#353452
#352962
#352852
#352682
#344032
#343642
#340812