Finite Group Databasebeta

← #7715368

Subgroups — #7715368

Order 512.

5430 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51088C214yesmaximal, complemented
2#50715C214yesmaximal, complemented
3#48007C218yesmaximal, complemented
4#47711C218yesmaximal, complemented
5#47033C214yesmaximal, complemented
6#46454C214yesmaximal, complemented
7#39808C214yesmaximal, complemented
8#39416C214yesmaximal, complemented
9#37775C214yesmaximal, complemented
10#37751C214yesmaximal, complemented
11#37614C211yesmaximal, characteristic, complemented
12#37559C211yesmaximal, characteristic, complemented
13#37432C212yesmaximal, complemented
14#37319C212yesmaximal, complemented
15#35345C211yesmaximal, characteristic, complemented
16#35343C212yesmaximal, complemented
17#35278C212yesmaximal, complemented
18#35274C211yesmaximal, characteristic, complemented
19#34402C211yesmaximal, characteristic, complemented
20#34364C211yesmaximal, characteristic, complemented
21#34081C211yesmaximal, characteristic, complemented
22C2×#540C2214yescomplemented
23C2×#535C2214yes—
24C2×#532C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C2×#529C2211yescharacteristic
27C2×#529C2214yescomplemented
28#2867C2211yescharacteristic
29#2867C2211yescharacteristic
30#2864C2212yescomplemented
31#2861C2214yescomplemented
32#2859C2212yescomplemented
33#2858C2211yescharacteristic
34#2858C2211yescharacteristic
35#2856C2214yescomplemented
36#2818C2214yes—
37#2816C2212yes—
38#2815C2212yes—
39#2803C2218yescomplemented
40#2803C2218yescomplemented
41#2797C2218yescomplemented
42#2797C2218yescomplemented
43#2786C2218yescomplemented
44#2752C2218yescomplemented
45#2740C2218yescomplemented
46#2714C2218yescomplemented
47#2710C2218yescomplemented
48#2709C2218yescomplemented
49#2709C2218yescomplemented
50#2705C2218yescomplemented
51#2701C2218yescomplemented
52#2699C2218yescomplemented
53#2697C2218yes—
54#2691C2218yescomplemented
55#2685C2218yes—
56#2682C2218yescomplemented
57#2678C2218yes—
58#2678C2218yes—
59#2673C2218yescomplemented
60#2673C2218yescomplemented
61#2673C2218yescomplemented
62#2671C2218yescomplemented
63#2661C2214yes—
64#2657C2212yes—
65#2657C2214yes—
66#2641C2212yes—
67#2641C2214yescomplemented
68#2633C2212yescomplemented
69#2631C2212yescomplemented
70#2629C2214yes—
71#2621C2212yescomplemented
72#2620C2214yescomplemented
73#2619C2212yes—
74#2619C2212yes—
75#2619C2212yescomplemented
76#2613C2214yes—
77#2608C2214yes—
78#2608C2214yes—
79#2606C2214yescomplemented
80#2606C2214yescomplemented
81#2603C2214yescomplemented
82#2602C2218yescomplemented
83#2602C2218yescomplemented
84#2602C2218yescomplemented
85#2601C2218yescomplemented
86#2601C2218yescomplemented
87#2600C2218yescomplemented
88#2592C2212yescomplemented
89#2548C2212yes—
90#2543C2218yescomplemented
91#2541C2214yes—
92#2541C2214yes—
93#2541C2212yes—
94#2540C2212yescomplemented
95#2534C2218yes—
96#2476C2218yescomplemented
97#2471C2218yescomplemented
98#2464C2218yescomplemented
99#2459C2218yescomplemented
100#2456C2218yescomplemented
101#2455C2218yescomplemented
102#2448C2214yescomplemented
103#2447C2214yescomplemented
104#2445C2218yescomplemented
105#2445C2214yescomplemented
106#2445C2214yescomplemented
107#2445C2218yescomplemented
108#2435C2212yes—
109#2433C2212yes—
110#2433C2214yes—
111#2433C2214yes—
112#2428C2218yescomplemented
113#2428C2218yescomplemented
114#2428C2218yescomplemented
115#2428C2214yescomplemented
116#2428C2214yescomplemented
117#2427C2214yescomplemented
118#2426C2214yescomplemented
119#2425C2218yescomplemented
120#2424C2218yes—
121#2424C2218yes—
122#2414C2218yescomplemented
123#2411C2218yes—
124#2408C2214yes—
125#2407C2214yes—
126#2380C2214yes—
127#2377C2214yes—
128#2367C2214yescomplemented
129#2366C2214yes—
130#2353C2214yescomplemented
131#2341C2212yes—
132#2339C2212yes—
133D4×C22⋊C4C2212yes—
134D4×C22⋊C4C2214yes—
135D4×C22⋊C4C2212yes—
136#2337C2212yescomplemented
137#2336C2212yescomplemented
138#2335C2214yes—
139#2334C2214yescomplemented
140#2333C2212yes—
141#2333C2214yes—
142#2332C2212yes—
143#2330C2214yescomplemented
144#2328C2212yes—
145#2328C2212yes—
146#2328C2214yes—
147#2328C2212yescomplemented
148#2327C2212yescomplemented
149#2326C2214yescomplemented
150#2318C2214yescomplemented
151#2308C2214yes—
152C4×#127C2214yescomplemented
153#2298C2212yescomplemented
154#2295C2212yescomplemented
155#2293C2212yes—
156#2290C2212yes—
157#2290C2212yescomplemented
158#2283C2211yescharacteristic
159#2283C2211yescharacteristic
160#2283C2211yescharacteristic
161C4×#117C2211yescharacteristic
162C4×#117C2212yescomplemented
163C22×#41C2312yes—
164C23×D4C2312yes—
165C23×D4C2312yes—
166C23×D4C2312yes—
167#540—416no—
168#535—416no—
169#532—28no—
170C2×C4⋊Q8C2311yescharacteristic
171C2×#127—28no—
172C2×#127C2314yes—
173C2×#127C2312yes—
174C2×#127C2311yescharacteristic
175C2×#127C2311yescharacteristic
176C2×#127C2311yescharacteristic
177C2×#127C2312yes—
178C2×#127C2312yes—
179C2×#127C2314yes—
180C2×#127C2314yes—
181C2×#127C2314yes—
182C2×#127C2314yes—
183C2×#127C2314yes—
184C2×#127C2314yes—
185#529—28no—
186#529—416no—
187C2×#126C2312yes—
188C2×#126C2318yes—
189C2×#125C2314yes—
190C2×#125C2311yescharacteristic
191C2×#124C2314yes—
192C2×#124C2312yes—
193C2×#124C2311yescharacteristic
194C2×#124C2314yes—
195C2×#124C2314yes—
196C2×#123C2312yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×C22⋊Q8C2311yescharacteristic
203C2×C22⋊Q8C2314yes—
204C2×#121C2312yes—
205C2×#121C2311yescharacteristic
206C2×#121C2312yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#121C2318yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#121C2318yes—
218C2×#120C2318yes—
219C2×#120C2318yes—
220C2×#120C2318yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2314yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2318yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2318yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2318yes—
238C22×C22⋊C4C2314yes—
239C22×C22⋊C4C2314yes—
240C22×C42C2312yes—
241C22×C42C2311yescharacteristic
242#399C2314yes—
243#399C2318yes—
244#398C2314yes—
245#398C2314yes—
246#398C2318yes—
247#398C2318yes—
248#397C2314yes—
249#397C2318yes—
250#397C2314yes—
251#397C2314yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#394C2314yes—
261#394C2318yes—
262#394C2318yes—
263#394C2314yes—
264#394C2314yes—
265#394C2318yes—
266#394C2318yes—
267#394C2314yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2314yes—
273#394C2314yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#393C2314yes—
284#392C2314yes—
285#392C2318yes—
286#392C2314yes—
287#392C2318yes—
288#392C2318yes—
289#392C2314yes—
290#392C2318yes—
291#392C2314yes—
292#392C2314yes—
293#392C2314yes—
294#392C2314yes—
295#392C2318yes—
296#392C2318yes—
297#392C2318yes—
298#392C2318yes—
299#392C2318yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2318yes—
306#390C2318yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2318yes—
311#390C2314yes—
312#390C2314yes—
313#390C2318yes—
314#390C2318yes—
315#390C2318yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2318yes—
322#390C2314yes—
323#390C2318yes—
324#389C2318yes—
325#389C2318yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2318yes—
331#389C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2314yes—
336#388C2314yes—
337#388C2314yes—
338#388C2318yes—
339#388C2314yes—
340#388C2314yes—
341#388C2314yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2314yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#387C2314yes—
359#387C2314yes—
360#387C2318yes—
361#387C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2314yes—
373#386C2314yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#385C2318yes—
387#385C2318yes—
388#384C2314yes—
389#383C2312yes—
390#383C2312yes—
391#383C2312yes—
392#382C2312yes—
393#382C2312yes—
394#382C2312yes—
395#381C2312yes—
396#381C2312yes—
397#381C2314yes—
398#381C2318yes—
399#381C2312yes—
400#380C2314yes—
401#380C2312yes—
402#380C2312yes—
403#380C2312yes—
404#380C2318yes—
405#379C2314yes—
406#379C2314yes—
407#379C2318yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2311yescharacteristic
425C4×C22⋊C4C2311yescharacteristic
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429#376C2312yes—
430#376C2312yes—
431#376C2312yes—
432#376C2312yes—
433#376C2312yes—
434C2×#95C2314yes—
435C43C2312yes—
436C43C2311yescharacteristic
437C43C2311yescharacteristic
438C25C2414yes—
439C2×#41—28no—
440C2×#41—48no—
441C22×Q8C2412yes—
442C22×Q8C2411yescharacteristic
443C22×D4—28no—
444C22×D4—28no—
445C22×D4—28no—
446C22×D4—48no—
447C22×D4—84no—
448C22×D4—84no—
449C22×D4C2412yes—
450C22×D4C2412yes—
451C22×D4C2412yes—
452C22×D4C2414yes—
453C22×D4C2412yes—
454C22×D4C2418yes—
455C22×D4C2418yes—
456C22×D4C2411yescharacteristic
457C22×D4C2412yes—
458C22×D4C2412yes—
459C22×D4C2414yes—
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2412yes—
463C22×D4C2412yes—
464C22×D4C2412yes—
465C22×D4C2412yes—
466C22×D4C2418yes—
467C22×D4C2418yes—
468C22×D4C2418yes—
469C22×D4C2418yes—
470C22×D4C2418yes—
471C23×C4C2412yes—
472C23×C4C2411yescharacteristic
473C23×C4C2414yes—
474C23×C4C2414yes—
475C23×C4C2418yes—
476C23×C4C2418yes—
477C23×C4C2418yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C4⋊Q8—24no—
481#127—24no—
482#127—24no—
483#127—28no—
484#127—28no—
485#127—28no—
486#127—24no—
487#127—216no—
488#127—48no—
489#127—84no—
490#127—84no—
491#127—84no—
492#127—84no—
493#127—84no—
494#126—28no—
495#126—416no—
496#125—24no—
497#125—216no—
498#124—24no—
499#124—28no—
500#124—216no—
501#124—48no—
502#124—84no—
503#123—28no—
504#123—416no—
505#123—416no—
506#123—416no—
507#123—88no—
508#123—88no—
509C22⋊Q8—24no—
510C22⋊Q8—48no—
511#121—24no—
512#121—28no—
513#121—28no—
514#121—416no—
515#121—416no—
516#121—416no—
517#121—416no—
518#121—48no—
519#121—48no—
520#121—48no—
521#121—88no—
522#121—88no—
523#121—88no—
524#121—88no—
525#120—416no—
526#120—416no—
527#120—88no—
528C4×Q8—24no—
529C4×Q8—48no—
530C4×D4—28no—
531C4×D4—24no—
532C4×D4—28no—
533C4×D4—28no—
534C4×D4—48no—
535C4×D4—48no—
536C4×D4—48no—
537C4×D4—416no—
538C4×D4—88no—
539C4×D4—88no—
540C4×D4—88no—
541#117—28no—
542#117—28no—
543#117—28no—
544#117—416no—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C22⋊C4—84no—
569C2×C22⋊C4—84no—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C42—28no—
609C2×C42#4118yes—
610C2×C42C2414yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2418yes—
616C2×C42C2414yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2412yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2412yes—
629#95C2412yes—
630#95C2414yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2412yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656C24—28no—
657C24—44no—
658C24—44no—
659C24—48no—
660C24—48no—
661C24C2514yes—
662C24C2514yes—
663C24C2512yes—
664C24C2514yes—
665C24C2511yescharacteristic
666#41—816no—
667C2×Q8—24no—
668C2×Q8—22no—
669C2×Q8—28no—
670C2×Q8—42no—
671C2×D4—24no—
672C2×D4—28no—
673C2×D4—24no—
674C2×D4—28no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—216no—
690C2×D4—216no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—816no—
724C2×D4—816no—
725C2×D4—816no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—48no—
735C22×C4—48no—
736C22×C4—48no—
737C22×C4—48no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—48no—
741C22×C4—48no—
742C22×C4—48no—
743C22×C4—48no—
744C22×C4—48no—
745C22×C4—48no—
746C22×C4C2×#4114yes—
747C22×C4C2×#4114yes—
748C22×C4C2×#4114yes—
749C22×C4C2514yes—
750C22×C4C2514yes—
751C22×C4C2514yes—
752C22×C4C2512yes—
753C22×C4C2512yes—
754C22×C4C2514yes—
755C22×C4C2518yes—
756C22×C4C2518yes—
757C22×C4C2512yes—
758C22×C4C2511yescharacteristic
759C22×C4C2511yescharacteristic
760C22×C4C2511yescharacteristic
761C22×C4C2511yescharacteristic
762C22×C4C2511yescharacteristic
763C22×C4C2514yes—
764C22×C4C2511yescharacteristic
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—22no—
770C4⋊C4—24no—
771C4⋊C4—22no—
772C4⋊C4—24no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—216no—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—216no—
779C4⋊C4—48no—
780C4⋊C4—44no—
781C4⋊C4—48no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C22⋊C4—24no—
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—24no—
794C22⋊C4—24no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—216no—
798C22⋊C4—216no—
799C22⋊C4—42no—
800C22⋊C4—42no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—44no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C42—24no—
827C42—28no—
828C42—24no—
829C42—24no—
830C42—24no—
831C42—48no—
832C42—44no—
833C42—44no—
834C42—44no—
835C42—44no—
836C42—42no—
837C42—42no—
838C42—42no—
839C42—42no—
840C42C2×#4114yes—
841C42C2×#4114yes—
842C42C2×#4114yes—
843C42C2×#4114yes—
844C42H(5,𝔽2)18yes—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—28no—
853C23—22no—
854C23—22no—
855C23—28no—
856C23—28no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—28no—
861C23—28no—
862C23—28no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—416no—
869C23—88no—
870C23—88no—
871C23—168no—
872C23—168no—
873C23C22×#4112yes—
874C23C2611yescharacteristic
875Q8—48no—
876Q8—82no—
877D4—416no—
878D4—48no—
879D4—48no—
880D4—48no—
881D4—84no—
882D4—84no—
883D4—82no—
884D4—816no—
885D4—816no—
886D4—88no—
887D4—84no—
888D4—84no—
889D4—84no—
890D4—84no—
891D4—88no—
892D4—84no—
893D4—88no—
894D4—816no—
895D4—168no—
896D4—168no—
897D4—168no—
898D4—168no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—22no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—28no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—48no—
934C2×C4—88no—
935C2×C4—88no—
936C2×C4—816no—
937C2×C4—168no—
938C2×C4—168no—
939C2×C4C22×#4112yes—
940C2×C4C22×#4112yes—
941C2×C4C22×#4112yes—
942C2×C4C22×#4112yes—
943C2×C4C22×#4112yes—
944C2×C4C22×#4112yes—
945C2×C4C2×H(5,𝔽2)18yes—
946C2×C4C2×H(5,𝔽2)14yes—
947C22—22no—
948C22—22no—
949C22—22no—
950C22—44no—
951C22—42no—
952C22—44no—
953C22—44no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—42no—
960C22—44no—
961C22—44no—
962C22—42no—
963C22—44no—
964C22—48no—
965C22—48no—
966C22—48no—
967C22—48no—
968C22—48no—
969C22—48no—
970C22—44no—
971C22—1616no—
972C22C23×#4111yescharacteristic
973C22C22×H(5,𝔽2)12yes—
974C22H(7,𝔽2)12yes—
975C22H(7,𝔽2)12yes—
976C4—22no—
977C4—22no—
978C4—22no—
979C4—22no—
980C4—22no—
981C4—28no—
982C4—42no—
983C4—44no—
984C4—42no—
985C4—42no—
986C4—44no—
987C4—48no—
988C4—44no—
989C4—48no—
990C4—44no—
991C4#350814yes—
992C2—42no—
993C2—82no—
994C2—84no—
995C2—84no—
996C2—84no—
997C2C2×#350811yescharacteristic
998C2#6285511yescharacteristic
999C2#6285511yescharacteristic
1000C2#6288014yes—
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. #51088C2semidirect
2. #50715C2semidirect
3. #48007C2semidirect
4. #47711C2semidirect
5. #47033C2semidirect
6. #46454C2semidirect
7. #39808C2semidirect
8. #39416C2semidirect
9. #37775C2semidirect
10. #37751C2semidirect
11. #37614C2semidirect
12. #37559C2semidirect
13. #37432C2semidirect
14. #37319C2semidirect
15. #35345C2semidirect
16. #35343C2semidirect
17. #35278C2semidirect
18. #35274C2semidirect
19. #34402C2semidirect
20. #34364C2semidirect
21. #34081C2semidirect
22. C2×#540C22semidirect
27. C2×#529C22semidirect
30. #2864C22semidirect
31. #2861C22semidirect
32. #2859C22semidirect
35. #2856C22semidirect
39. #2803C22semidirect
40. #2803C22semidirect
41. #2797C22semidirect
42. #2797C22semidirect
43. #2786C22semidirect
44. #2752C22semidirect
45. #2740C22semidirect
46. #2714C22semidirect
47. #2710C22semidirect
48. #2709C22semidirect
49. #2709C22semidirect
50. #2705C22semidirect
51. #2701C22semidirect
52. #2699C22semidirect
54. #2691C22semidirect
56. #2682C22semidirect
59. #2673C22semidirect
60. #2673C22semidirect
61. #2673C22semidirect
62. #2671C22semidirect
67. #2641C22semidirect
68. #2633C22semidirect
69. #2631C22semidirect
71. #2621C22semidirect
72. #2620C22semidirect
75. #2619C22semidirect
79. #2606C22semidirect
80. #2606C22semidirect
81. #2603C22semidirect
82. #2602C22semidirect
83. #2602C22semidirect
84. #2602C22semidirect
85. #2601C22semidirect
86. #2601C22semidirect
87. #2600C22semidirect
88. #2592C22semidirect
90. #2543C22semidirect
94. #2540C22semidirect
96. #2476C22semidirect
97. #2471C22semidirect
98. #2464C22semidirect
99. #2459C22semidirect
100. #2456C22semidirect
101. #2455C22semidirect
102. #2448C22semidirect
103. #2447C22semidirect
104. #2445C22semidirect
105. #2445C22semidirect
106. #2445C22semidirect
107. #2445C22semidirect
112. #2428C22semidirect
113. #2428C22semidirect
114. #2428C22semidirect
115. #2428C22semidirect
116. #2428C22semidirect
117. #2427C22semidirect
118. #2426C22semidirect
119. #2425C22semidirect
122. #2414C22semidirect
128. #2367C22semidirect
130. #2353C22semidirect
136. #2337C22semidirect
137. #2336C22semidirect
139. #2334C22semidirect
143. #2330C22semidirect
147. #2328C22semidirect
148. #2327C22semidirect
149. #2326C22semidirect
150. #2318C22semidirect
152. C4×#127C22semidirect
153. #2298C22semidirect
154. #2295C22semidirect
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
#510882
#507152
#480072
#477112
#470332
#464542
#398082
#394162
#377752
#377512
#376142
#375592
#374322
#373192
#353452
#353432
#352782
#352742
#344022
#343642
#340812