Finite Group Databasebeta

← #7715068

Subgroups — #7715068

Order 512.

4424 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51759C218yesmaximal, complemented
2#51553C218yesmaximal, complemented
3#46998C212yesmaximal, complemented
4#46857C214yesmaximal, complemented
5#46854C214yesmaximal, complemented
6#46837C212yesmaximal, complemented
7#46390C212yesmaximal, complemented
8#46388C212yesmaximal, complemented
9#39077C214yesmaximal, complemented
10#39076C214yesmaximal, complemented
11#39071C214yesmaximal, complemented
12#39070C214yesmaximal, complemented
13#37480C211yesmaximal, characteristic, complemented
14#37451C211yesmaximal, characteristic
15#37287C214yesmaximal, complemented
16#35311C211yesmaximal, characteristic, complemented
17#35290C214yesmaximal, complemented
18#35262C211yesmaximal, characteristic
19#34370C211yesmaximal, characteristic, complemented
20#34363C211yesmaximal, characteristic
21#34048C211yesmaximal, characteristic, complemented
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#117C2211yescharacteristic
25#2863C2214yescomplemented
26#2860C2214yescomplemented
27#2855C2212yescomplemented
28#2855C2212yescomplemented
29#2854C2212yes—
30#2854C2212yes—
31#2842C2212yes—
32#2840C2212yes—
33#2816C2214yes—
34#2793C2218yescomplemented
35#2791C2218yescomplemented
36#2775C2218yescomplemented
37#2765C2218yes—
38#2765C2218yescomplemented
39#2764C2218yes—
40#2762C2218yescomplemented
41#2759C2218yescomplemented
42#2754C2218yescomplemented
43#2754C2218yescomplemented
44#2751C2218yescomplemented
45#2746C2218yescomplemented
46#2740C2218yescomplemented
47#2740C2218yescomplemented
48#2737C2218yescomplemented
49#2737C2218yescomplemented
50#2736C2218yes—
51#2735C2218yes—
52#2721C2218yescomplemented
53#2720C2218yescomplemented
54#2695C2218yescomplemented
55#2694C2218yescomplemented
56#2687C2218yescomplemented
57#2687C2218yescomplemented
58#2665C2214yes—
59#2665C2214yescomplemented
60#2647C2214yescomplemented
61#2640C2214yescomplemented
62#2628C2214yescomplemented
63#2626C2214yes—
64#2625C2214yes—
65#2624C2214yes—
66#2620C2214yes—
67#2618C2214yes—
68#2607C2214yescomplemented
69#2607C2218yescomplemented
70#2599C2218yes—
71#2595C2218yescomplemented
72#2576C2218yescomplemented
73#2575C2218yescomplemented
74#2574C2218yescomplemented
75#2573C2218yescomplemented
76#2572C2218yescomplemented
77#2572C2218yescomplemented
78#2565C2218yescomplemented
79#2561C2218yes—
80#2560C2218yescomplemented
81#2558C2218yescomplemented
82#2553C2218yescomplemented
83#2525C2218yescomplemented
84#2524C2218yescomplemented
85#2523C2218yescomplemented
86#2516C2218yescomplemented
87#2514C2214yescomplemented
88#2513C2214yescomplemented
89#2507C2214yescomplemented
90#2506C2214yescomplemented
91#2504C2212yes—
92#2503C2212yescomplemented
93#2502C2212yes—
94#2502C2212yescomplemented
95#2501C2212yes—
96#2501C2212yes—
97#2500C2214yes—
98#2499C2214yes—
99#2484C2214yescomplemented
100#2483C2212yes—
101#2483C2212yes—
102#2482C2214yes—
103#2480C2218yes—
104#2475C2218yes—
105#2469C2218yescomplemented
106#2458C2218yescomplemented
107#2458C2218yescomplemented
108#2452C2214yescomplemented
109#2451C2214yescomplemented
110#2448C2214yescomplemented
111#2447C2214yescomplemented
112#2439C2214yes—
113#2439C2214yescomplemented
114#2436C2212yes—
115#2435C2212yes—
116#2423C2218yescomplemented
117#2405C2212yes—
118#2405C2212yes—
119#2405C2212yes—
120#2405C2212yes—
121#2378C2214yes—
122#2377C2214yes—
123#2363C2214yes—
124#2362C2214yes—
125#2345C2214yescomplemented
126#2345C2212yescomplemented
127#2344C2212yes—
128#2342C2214yes—
129Q8×C22⋊C4C2212yescomplemented
130D4×C22⋊C4C2212yes—
131#2333C2214yes—
132#2332C2214yescomplemented
133#2324C2214yes—
134#2323C2214yescomplemented
135#2320C2214yescomplemented
136#2319C2214yescomplemented
137#2317C2212yes—
138#2317C2212yescomplemented
139#2314C2214yes—
140#2314C2214yescomplemented
141#2313C2212yescomplemented
142#2313C2212yescomplemented
143#2312C2211yescharacteristic
144#2312C2211yescharacteristic
145#2312C2211yescharacteristic
146#2312C2211yescharacteristic
147#2312C2212yes—
148#2312C2212yes—
149#2310C2212yescomplemented
150#2309C2212yes—
151#2309C2212yes—
152#2308C2212yes—
153C4×C4⋊Q8C2214yescomplemented
154C4×#124C2214yescomplemented
155#2298C2214yes—
156#2298C2214yescomplemented
157#2285C2212yescomplemented
158#2280C2211yescharacteristic
159#2280C2211yescharacteristic
160#2280C2211yescharacteristic
161#2280C2211yescharacteristic
162C4×#117C2212yescomplemented
163C23×Q8C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C23×D4C2312yes—
166C24×C4C2311yescharacteristic
167C2×C4⋊Q8C2314yes—
168C2×#126C2318yes—
169C2×#125C2318yes—
170C2×#124C2314yes—
171C2×#123C2314yes—
172C2×#123C2314yes—
173C2×#123C2314yes—
174C2×#123C2314yes—
175C2×C22⋊Q8—28no—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2312yes—
179C2×C22⋊Q8C2312yes—
180C2×C22⋊Q8C2318yes—
181C2×#121—28no—
182C2×#121C2312yes—
183C2×#121C2312yes—
184C2×#121C2312yes—
185C2×#121C2312yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2318yes—
188C2×C4×D4C2314yes—
189C2×#117—28no—
190C2×#117C2312yes—
191C2×#117C2312yes—
192C2×#117C2312yes—
193C2×#117C2312yes—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2314yes—
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2314yes—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211#401C2318yes—
212#400C2318yes—
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#399C2318yes—
219#399C2318yes—
220#399C2318yes—
221#399C2318yes—
222#398C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
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#396C2318yes—
241#396C2318yes—
242#396C2318yes—
243#396C2318yes—
244#396C2318yes—
245#395C2318yes—
246#395C2318yes—
247#394C2318yes—
248#394C2318yes—
249#394C2318yes—
250#394C2318yes—
251#394C2318yes—
252#393C2318yes—
253#393C2318yes—
254#393C2318yes—
255#393C2318yes—
256#393C2318yes—
257#393C2318yes—
258#393C2318yes—
259#391C2318yes—
260#391C2318yes—
261#391C2318yes—
262#391C2314yes—
263#391C2314yes—
264#391C2314yes—
265#391C2314yes—
266#391C2314yes—
267#391C2314yes—
268#391C2318yes—
269#391C2318yes—
270#390C2314yes—
271#390C2314yes—
272#390C2318yes—
273#390C2314yes—
274#390C2314yes—
275#390C2318yes—
276#390C2314yes—
277#390C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2318yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2314yes—
286#389C2318yes—
287#389C2314yes—
288#389C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2314yes—
293#388C2318yes—
294#388C2318yes—
295#388C2314yes—
296#388C2314yes—
297#388C2314yes—
298#388C2314yes—
299#388C2314yes—
300#388C2314yes—
301#388C2314yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#387C2314yes—
317#387C2314yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2314yes—
322#387C2314yes—
323#387C2314yes—
324#387C2314yes—
325#387C2314yes—
326#387C2314yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2314yes—
345#386C2314yes—
346#386C2314yes—
347#386C2314yes—
348#385C2314yes—
349#385C2314yes—
350#385C2314yes—
351#385C2314yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2314yes—
357#385C2314yes—
358#385C2314yes—
359#384C2314yes—
360#384C2314yes—
361#384C2314yes—
362#384C2314yes—
363#383C2318yes—
364#383C2318yes—
365#383C2318yes—
366#382C2318yes—
367#382C2314yes—
368#382C2314yes—
369#382C2314yes—
370#382C2314yes—
371#381C2312yes—
372#381C2318yes—
373#381C2318yes—
374#381C2314yes—
375#381C2314yes—
376#381C2314yes—
377#381C2312yes—
378#381C2314yes—
379#381C2314yes—
380#381C2312yes—
381#381C2312yes—
382#380C2312yes—
383#380C2312yes—
384#380C2312yes—
385#380C2312yes—
386#380C2314yes—
387#380C2314yes—
388#380C2312yes—
389#380C2312yes—
390#380C2312yes—
391#380C2312yes—
392#380C2318yes—
393#380C2312yes—
394#380C2312yes—
395#380C2312yes—
396#380C2312yes—
397#379C2314yes—
398#379C2314yes—
399#379C2311yescharacteristic
400#379C2312yes—
401#379C2311yescharacteristic
402#379C2314yes—
403#379C2314yes—
404#379C2311yescharacteristic
405#379C2312yes—
406#379C2311yescharacteristic
407#379C2314yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2312yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432C4×C22⋊C4C2312yes—
433#376C2314yes—
434C43C2314yes—
435C25C2412yes—
436C25C2411yescharacteristic
437C22×Q8—24no—
438C22×Q8—44no—
439C22×Q8C2412yes—
440C22×Q8C2412yes—
441C22×Q8C2418yes—
442C22×D4—28no—
443C22×D4—24no—
444C22×D4—44no—
445C22×D4—84no—
446C22×D4C2412yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C22×D4C2412yes—
450C23×C4—44no—
451C23×C4#4118yes—
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2418yes—
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C4⋊Q8—48no—
467#126—88no—
468#125—88no—
469#124—48no—
470#123—84no—
471#123—84no—
472#123—84no—
473#123—84no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—28no—
477C22⋊Q8—28no—
478C22⋊Q8—88no—
479#121—28no—
480#121—28no—
481#121—28no—
482#121—28no—
483C4×Q8—48no—
484C4×Q8—88no—
485C4×D4—48no—
486#117—28no—
487#117—28no—
488#117—28no—
489#117—28no—
490#117—44no—
491#117—44no—
492#117—44no—
493#117—44no—
494#117—84no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—28no—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—28no—
533C2×C22⋊C4—28no—
534C2×C22⋊C4—84no—
535C2×C22⋊C4C2412yes—
536C2×C22⋊C4C2412yes—
537C2×C22⋊C4C2412yes—
538C2×C22⋊C4C2412yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2412yes—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2412yes—
547C2×C22⋊C4C2412yes—
548C2×C22⋊C4C2412yes—
549C2×C22⋊C4C2412yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C42—24no—
573C2×C42—24no—
574C2×C42C2412yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2414yes—
579C2×C42C2414yes—
580C2×C42C2418yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2418yes—
585C2×C42C2418yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589#95C2414yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C2414yes—
595#95C2414yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2414yes—
600#95C2414yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625C24—24no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24C2×#4114yes—
633C24C2514yes—
634C24C2511yescharacteristic
635C24C2511yescharacteristic
636C24C2511yescharacteristic
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—28no—
640C2×Q8—48no—
641C2×Q8—48no—
642C2×Q8—44no—
643C2×Q8—48no—
644C2×Q8—88no—
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—28no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—88no—
656C2×D4—816no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—416no—
668C22×C4—44no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—44no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—44no—
678C22×C4—48no—
679C22×C4—48no—
680C22×C4—48no—
681C22×C4C2×#4114yes—
682C22×C4C2×#4114yes—
683C22×C4C2×#4114yes—
684C22×C4C2×#4114yes—
685C22×C4C2×#4114yes—
686C22×C4C2×#4114yes—
687C22×C4C2512yes—
688C22×C4C2512yes—
689C22×C4C2514yes—
690C22×C4C2514yes—
691C22×C4C2514yes—
692C22×C4C2518yes—
693C22×C4C2518yes—
694C22×C4C2514yes—
695C22×C4C2514yes—
696C22×C4C2514yes—
697C22×C4C2512yes—
698C22×C4C2512yes—
699C22×C4C2514yes—
700C22×C4C2511yescharacteristic
701C22×C4C2511yescharacteristic
702C22×C4C2511yescharacteristic
703C22×C4C2511yescharacteristic
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—24no—
712C4⋊C4—28no—
713C4⋊C4—28no—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C4⋊C4—48no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—44no—
727C4⋊C4—48no—
728C4⋊C4—48no—
729C4⋊C4—48no—
730C4⋊C4—48no—
731C4⋊C4—44no—
732C4⋊C4—48no—
733C4⋊C4—48no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—28no—
739C22⋊C4—28no—
740C22⋊C4—28no—
741C22⋊C4—28no—
742C22⋊C4—42no—
743C22⋊C4—44no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—42no—
747C22⋊C4—48no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—44no—
752C22⋊C4—48no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C22⋊C4—42no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—42no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—48no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C42—24no—
772C42—24no—
773C42—24no—
774C42—24no—
775C42—28no—
776C42—28no—
777C42—44no—
778C42—44no—
779C42—44no—
780C42—44no—
781C42—48no—
782C42—48no—
783C42—44no—
784C42—48no—
785C42—44no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—28no—
797C23—24no—
798C23—24no—
799C23—28no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—48no—
804C23—84no—
805C23—84no—
806C23—88no—
807C23—168no—
808C23C22×#4112yes—
809C23C22×#4112yes—
810C23C22×#4112yes—
811C23C2611yescharacteristic
812Q8—48no—
813Q8—84no—
814Q8—816no—
815D4—48no—
816D4—84no—
817D4—88no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—28no—
823C2×C4—28no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—28no—
837C2×C4—28no—
838C2×C4—28no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—28no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—48no—
862C2×C4—82no—
863C2×C4—82no—
864C2×C4—84no—
865C2×C4—82no—
866C2×C4—82no—
867C2×C4—84no—
868C2×C4—168no—
869C2×C4C22×#4112yes—
870C2×C4C22×#4112yes—
871C2×C4C22×#4112yes—
872C2×C4C22×#4112yes—
873C2×C4#58514yes—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—48no—
890C22—48no—
891C22—88no—
892C22—168no—
893C22C23×#4111yescharacteristic
894C22C2×#58512yes—
895C22H(7,𝔽2)12yes—
896C222−1+612yes—
897C4—22no—
898C4—22no—
899C4—22no—
900C4—44no—
901C4—44no—
902C4—42no—
903C4—42no—
904C4—44no—
905C4—42no—
906C4—42no—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—48no—
911C4—48no—
912C4—44no—
913C4#349114yes—
914C2—42no—
915C2—42no—
916C2—42no—
917C2—84no—
918C2C2×#349111yescharacteristic
919C2#6285511yescharacteristic
920C2#6286011yescharacteristic
921C2#6288214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51759C2semidirect
2. #51553C2semidirect
3. #46998C2semidirect
4. #46857C2semidirect
5. #46854C2semidirect
6. #46837C2semidirect
7. #46390C2semidirect
8. #46388C2semidirect
9. #39077C2semidirect
10. #39076C2semidirect
11. #39071C2semidirect
12. #39070C2semidirect
13. #37480C2semidirect
15. #37287C2semidirect
16. #35311C2semidirect
17. #35290C2semidirect
19. #34370C2semidirect
21. #34048C2semidirect
25. #2863C22semidirect
26. #2860C22semidirect
27. #2855C22semidirect
28. #2855C22semidirect
34. #2793C22semidirect
35. #2791C22semidirect
36. #2775C22semidirect
38. #2765C22semidirect
40. #2762C22semidirect
41. #2759C22semidirect
42. #2754C22semidirect
43. #2754C22semidirect
44. #2751C22semidirect
45. #2746C22semidirect
46. #2740C22semidirect
47. #2740C22semidirect
48. #2737C22semidirect
49. #2737C22semidirect
52. #2721C22semidirect
53. #2720C22semidirect
54. #2695C22semidirect
55. #2694C22semidirect
56. #2687C22semidirect
57. #2687C22semidirect
59. #2665C22semidirect
60. #2647C22semidirect
61. #2640C22semidirect
62. #2628C22semidirect
68. #2607C22semidirect
69. #2607C22semidirect
71. #2595C22semidirect
72. #2576C22semidirect
73. #2575C22semidirect
74. #2574C22semidirect
75. #2573C22semidirect
76. #2572C22semidirect
77. #2572C22semidirect
78. #2565C22semidirect
80. #2560C22semidirect
81. #2558C22semidirect
82. #2553C22semidirect
83. #2525C22semidirect
84. #2524C22semidirect
85. #2523C22semidirect
86. #2516C22semidirect
87. #2514C22semidirect
88. #2513C22semidirect
89. #2507C22semidirect
90. #2506C22semidirect
92. #2503C22semidirect
94. #2502C22semidirect
99. #2484C22semidirect
105. #2469C22semidirect
106. #2458C22semidirect
107. #2458C22semidirect
108. #2452C22semidirect
109. #2451C22semidirect
110. #2448C22semidirect
111. #2447C22semidirect
113. #2439C22semidirect
116. #2423C22semidirect
125. #2345C22semidirect
126. #2345C22semidirect
129. Q8×C22⋊C4C22semidirect
132. #2332C22semidirect
134. #2323C22semidirect
135. #2320C22semidirect
136. #2319C22semidirect
138. #2317C22semidirect
140. #2314C22semidirect
141. #2313C22semidirect
142. #2313C22semidirect
149. #2310C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#124C22semidirect
156. #2298C22semidirect
157. #2285C22semidirect
162. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#517592
#515532
#469982
#468572
#468542
#468372
#463902
#463882
#390772
#390762
#390712
#390702
#374802
#374512
#372872
#353112
#352902
#352622
#343702
#343632
#340482