Finite Group Databasebeta

← #7644389

Subgroups — #7644389

Order 512.

4746 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42956C214yesmaximal, complemented
2#42935C214yesmaximal, complemented
3#42507C214yesmaximal, complemented
4#42501C214yesmaximal, complemented
5#42022C218yesmaximal, complemented
6#40659C218yesmaximal, complemented
7#37524C214yesmaximal, complemented
8#37522C212yesmaximal, complemented
9#37520C212yesmaximal, complemented
10#37382C212yesmaximal, complemented
11#37288C214yesmaximal, complemented
12#37286C212yesmaximal, complemented
13#35639C212yesmaximal, complemented
14#35585C212yesmaximal, complemented
15#35557C212yesmaximal, complemented
16#35517C212yesmaximal, complemented
17#35263C212yesmaximal, complemented
18#34633C211yesmaximal, characteristic
19C2×#2629C211yesmaximal, characteristic, complemented
20#34202C212yesmaximal, complemented
21#34052C211yesmaximal, characteristic, complemented
22C2×#532C2211yescharacteristic
23C22×#125C2211yescharacteristic
24C2×#525C2212yes—
25C2×#520C2212yes—
26C22×#117C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2855C2214yes—
30#2854C2214yes—
31#2839C2218yescomplemented
32#2837C2218yescomplemented
33#2827C2218yes—
34#2827C2218yes—
35#2791C2218yescomplemented
36#2790C2218yescomplemented
37#2783C2218yescomplemented
38#2781C2218yescomplemented
39#2767C2218yescomplemented
40#2744C2218yes—
41#2744C2218yescomplemented
42#2743C2218yes—
43#2740C2218yes—
44#2739C2218yes—
45#2721C2218yescomplemented
46#2718C2218yescomplemented
47#2707C2218yes—
48#2705C2218yes—
49#2695C2218yes—
50#2693C2218yes—
51#2667C2218yescomplemented
52#2664C2218yescomplemented
53#2654C2218yescomplemented
54#2652C2218yes—
55#2652C2218yes—
56#2652C2218yescomplemented
57#2636C2218yes—
58#2630C2218yes—
59#2629C2214yes—
60#2629C2212yes—
61#2629C2212yes—
62#2629C2212yes—
63#2629C2212yes—
64#2629C2214yes—
65#2625C2214yes—
66#2624C2214yes—
67#2621C2211yescharacteristic
68#2621C2211yescharacteristic
69#2620C2212yes—
70#2620C2212yes—
71#2619C2211yescharacteristic
72#2619C2211yescharacteristic
73#2618C2214yes—
74#2617C2214yes—
75#2585C2218yescomplemented
76#2579C2218yes—
77#2569C2218yes—
78#2553C2218yescomplemented
79#2512C2214yescomplemented
80#2512C2214yescomplemented
81#2511C2214yescomplemented
82#2511C2214yescomplemented
83#2509C2214yescomplemented
84#2509C2214yescomplemented
85#2508C2214yescomplemented
86#2508C2214yescomplemented
87#2507C2214yescomplemented
88#2507C2214yescomplemented
89#2506C2214yescomplemented
90#2506C2214yescomplemented
91#2498C2218yes—
92#2497C2214yescomplemented
93#2497C2214yescomplemented
94#2496C2214yescomplemented
95#2496C2214yescomplemented
96#2487C2218yes—
97#2487C2214yes—
98#2487C2214yescomplemented
99#2486C2214yes—
100#2486C2214yescomplemented
101#2485C2214yes—
102#2485C2214yes—
103#2485C2214yescomplemented
104#2485C2214yescomplemented
105#2481C2218yes—
106#2481C2218yes—
107#2466C2218yes—
108#2460C2218yes—
109#2454C2214yescomplemented
110#2454C2214yescomplemented
111#2453C2214yescomplemented
112#2453C2214yescomplemented
113#2448C2214yescomplemented
114#2447C2214yescomplemented
115#2446C2214yescomplemented
116#2445C2214yescomplemented
117#2444C2218yes—
118#2443C2218yes—
119#2442C2218yes—
120#2442C2214yescomplemented
121#2442C2214yescomplemented
122#2441C2214yescomplemented
123#2441C2214yescomplemented
124#2412C2218yes—
125#2392C2214yes—
126#2392C2214yes—
127C2×#398C2214yes—
128C2×#396C2214yes—
129#2359C2218yes—
130#2358C2218yes—
131#2354C2214yes—
132#2352C2214yes—
133#2352C2214yes—
134D4×C4⋊C4C2214yes—
135#2324C2214yes—
136#2323C2214yes—
137#2317C2212yes—
138#2317C2212yes—
139#2317C2212yes—
140#2317C2214yes—
141#2316C2212yes—
142#2316C2212yes—
143#2316C2212yes—
144#2316C2212yes—
145#2315C2214yes—
146#2311C2212yes—
147#2311C2212yes—
148#2311C2212yes—
149C4×C22⋊Q8C2214yes—
150C4×#121C2214yes—
151#2297C2212yes—
152#2296C2212yes—
153#2296C2212yes—
154#2296C2212yes—
155#2296C2212yes—
156C2×#389C2212yes—
157#2285C2211yescharacteristic
158#2285C2212yes—
159#2285C2212yes—
160C2×#384C2211yescharacteristic
161C2×#380C2212yes—
162#2274C2212yes—
163C22×#41C2312yes—
164C24×C4C2311yescharacteristic
165#532—44no—
166C2×C4⋊Q8C2311yescharacteristic
167C2×#127C2311yescharacteristic
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#125—44no—
171C2×#125C2314yes—
172C2×#125C2312yes—
173C2×#125C2312yes—
174C2×#125C2318yes—
175C2×#124C2312yes—
176#525—216no—
177C2×#123C2314yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×C22⋊Q8C2312yes—
181C2×C22⋊Q8C2312yes—
182C2×#121C2312yes—
183C2×#121C2312yes—
184C2×#121C2314yes—
185C2×#120C2314yes—
186#520—48no—
187C2×C4×Q8C2314yes—
188C2×C4×D4C2314yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2318yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2314yes—
193C2×C4×D4C2318yes—
194C2×#117—28no—
195C2×#117—44no—
196C2×#117—44no—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2311yescharacteristic
205C2×#117C2311yescharacteristic
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2314yes—
211C2×#117C2311yescharacteristic
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2314yes—
223C22×C4⋊C4C2314yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2314yes—
228C22×C42C2312yes—
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#399C2318yes—
245#399C2318yes—
246#399C2318yes—
247#399C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2314yes—
256#398C2318yes—
257#398C2318yes—
258#398C2314yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2314yes—
271#397C2314yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2314yes—
278#396C2314yes—
279#396C2314yes—
280#396C2314yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#394C2314yes—
285#394C2314yes—
286#394C2318yes—
287#394C2318yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2314yes—
292#394C2314yes—
293#394C2314yes—
294#392C2314yes—
295#392C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2312yes—
300#391C2312yes—
301#390C2314yes—
302#390C2314yes—
303#390C2314yes—
304#390C2318yes—
305#390C2312yes—
306#390C2312yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#389C2312yes—
315#389C2312yes—
316#389C2312yes—
317#389C2312yes—
318#389C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2318yes—
330#389C2318yes—
331#389C2318yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2318yes—
337#389C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2314yes—
369#386C2318yes—
370#386C2318yes—
371#386C2314yes—
372#386C2318yes—
373#385C2314yes—
374#385C2318yes—
375#385C2314yes—
376#385C2314yes—
377#385C2314yes—
378#385C2314yes—
379#385C2314yes—
380#385C2314yes—
381#385C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#384C2314yes—
389#384C2314yes—
390#384C2314yes—
391#384C2312yes—
392#384C2314yes—
393#384C2312yes—
394#384C2312yes—
395#382C2314yes—
396#382C2314yes—
397#382C2314yes—
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2318yes—
401#381C2318yes—
402#381C2318yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2318yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2318yes—
421#380C2318yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C25C2411yescharacteristic
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—28no—
443C22×Q8C2412yes—
444C22×D4C2414yes—
445C22×D4C2412yes—
446C22×D4C2414yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4#4118yes—
452C23×C4C2414yes—
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2412yes—
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2412yes—
462C23×C4C2414yes—
463C23×C4C2414yes—
464C23×C4C2418yes—
465C23×C4C2411yescharacteristic
466C4⋊Q8—42no—
467#127—42no—
468#126—88no—
469#126—88no—
470#125—48no—
471#125—44no—
472#125—44no—
473#125—88no—
474#124—44no—
475#123—216no—
476#123—88no—
477#123—88no—
478C22⋊Q8—28no—
479C22⋊Q8—28no—
480#121—28no—
481#121—28no—
482#121—48no—
483#120—216no—
484C4×Q8—48no—
485C4×D4—216no—
486C4×D4—216no—
487C4×D4—48no—
488C4×D4—48no—
489C4×D4—416no—
490C4×D4—88no—
491#117—24no—
492#117—24no—
493#117—28no—
494#117—28no—
495#117—28no—
496#117—28no—
497#117—28no—
498#117—44no—
499#117—44no—
500#117—42no—
501#117—42no—
502#117—42no—
503#117—42no—
504#117—44no—
505#117—44no—
506#117—42no—
507#117—42no—
508#117—48no—
509C2×C4⋊C4—28no—
510C2×C4⋊C4—28no—
511C2×C4⋊C4—28no—
512C2×C4⋊C4—44no—
513C2×C4⋊C4—48no—
514C2×C4⋊C4—44no—
515C2×C4⋊C4—48no—
516C2×C4⋊C4—84no—
517C2×C4⋊C4—84no—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C22⋊C4—28no—
561C2×C22⋊C4—44no—
562C2×C22⋊C4—44no—
563C2×C22⋊C4—84no—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2418yes—
594C2×C42—28no—
595C2×C42—24no—
596C2×C42—24no—
597C2×C42—44no—
598C2×C42C2412yes—
599C2×C42C2414yes—
600C2×C42C2411yescharacteristic
601C2×C42C2412yes—
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2418yes—
612C2×C42C2418yes—
613C2×C42C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646C24—22no—
647C24—22no—
648C24—42no—
649C24—42no—
650C24C2×#4114yes—
651C24C2514yes—
652C24C2511yescharacteristic
653C24C2511yescharacteristic
654C24C2511yescharacteristic
655#41—432no—
656C2×Q8—24no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—232no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—24no—
686C22×C4—28no—
687C22×C4—24no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—42no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—42no—
706C22×C4—48no—
707C22×C4—48no—
708C22×C4—48no—
709C22×C4C2×#4114yes—
710C22×C4C2×#4114yes—
711C22×C4C2×#4114yes—
712C22×C4C2×#4114yes—
713C22×C4C2×#4114yes—
714C22×C4C2×#4114yes—
715C22×C4H(5,𝔽2)14yes—
716C22×C42−1+414yes—
717C22×C4C2514yes—
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2514yes—
721C22×C4C2514yes—
722C22×C4C2514yes—
723C22×C4C2518yes—
724C22×C4C2512yes—
725C22×C4C2518yes—
726C22×C4C2514yes—
727C22×C4C2512yes—
728C22×C4C2512yes—
729C22×C4C2512yes—
730C22×C4C2511yescharacteristic
731C22×C4C2511yescharacteristic
732C22×C4C2511yescharacteristic
733C22×C4C2511yescharacteristic
734C4⋊C4—28no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—42no—
748C4⋊C4—42no—
749C4⋊C4—42no—
750C4⋊C4—42no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C4⋊C4—48no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—48no—
768C4⋊C4—44no—
769C4⋊C4—48no—
770C4⋊C4—48no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C22⋊C4—24no—
777C22⋊C4—24no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C22⋊C4—42no—
789C22⋊C4—42no—
790C22⋊C4—42no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C42—24no—
807C42—24no—
808C42—28no—
809C42—28no—
810C42—24no—
811C42—22no—
812C42—22no—
813C42—22no—
814C42—24no—
815C42—22no—
816C42—28no—
817C42—42no—
818C42—42no—
819C42—48no—
820C42—48no—
821C42—48no—
822C23—22no—
823C23—22no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—28no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—48no—
841C23—84no—
842C23—82no—
843C23—82no—
844C23C22×#4112yes—
845C23C22×#4112yes—
846C23C22×#4112yes—
847C23C2×H(5,𝔽2)12yes—
848C23C2×2−1+412yes—
849C23C2611yescharacteristic
850Q8—48no—
851D4—416no—
852D4—416no—
853D4—48no—
854D4—88no—
855D4—88no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—24no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—48no—
905C2×C4—416no—
906C2×C4—88no—
907C2×C4—84no—
908C2×C4—88no—
909C2×C4—88no—
910C2×C4—88no—
911C2×C4—168no—
912C2×C4#539116yes—
913C2×C4C22×#4112yes—
914C2×C4C22×#4112yes—
915C2×C4C22×#4112yes—
916C2×C4C22×#4112yes—
917C2×C4C2×H(5,𝔽2)12yes—
918C2×C4C2×H(5,𝔽2)12yes—
919C2×C4C2×2−1+412yes—
920C2×C4C2×2−1+412yes—
921C22—24no—
922C22—24no—
923C22—22no—
924C22—22no—
925C22—24no—
926C22—24no—
927C22—22no—
928C22—22no—
929C22—42no—
930C22—42no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—44no—
939C22—44no—
940C22—44no—
941C22—44no—
942C22—88no—
943C22C2×#53914yes—
944C22C23×#4111yescharacteristic
945C22C22×H(5,𝔽2)11yescharacteristic
946C22C22×2−1+411yescharacteristic
947C22H(7,𝔽2)12yes—
948C222−1+612yes—
949C4—22no—
950C4—22no—
951C4—44no—
952C4—44no—
953C4—44no—
954C4—44no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—44no—
959C4—48no—
960C4—44no—
961C4—42no—
962C4—48no—
963C4—44no—
964C4C2×#53914yes—
965C4C2×#53914yes—
966C2—24no—
967C2—42no—
968C2—42no—
969C2—84no—
970C2C22×#53911yescharacteristic
971C2#6285612yes—
972C2#6287512yes—
973C2#6288111yescharacteristic
974C2#6288911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34633C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42956C2semidirect
2. #42935C2semidirect
3. #42507C2semidirect
4. #42501C2semidirect
5. #42022C2semidirect
6. #40659C2semidirect
7. #37524C2semidirect
8. #37522C2semidirect
9. #37520C2semidirect
10. #37382C2semidirect
11. #37288C2semidirect
12. #37286C2semidirect
13. #35639C2semidirect
14. #35585C2semidirect
15. #35557C2semidirect
16. #35517C2semidirect
17. #35263C2semidirect
19. C2×#2629C2semidirect
20. #34202C2semidirect
21. #34052C2semidirect
31. #2839C22semidirect
32. #2837C22semidirect
35. #2791C22semidirect
36. #2790C22semidirect
37. #2783C22semidirect
38. #2781C22semidirect
39. #2767C22semidirect
41. #2744C22semidirect
45. #2721C22semidirect
46. #2718C22semidirect
51. #2667C22semidirect
52. #2664C22semidirect
53. #2654C22semidirect
56. #2652C22semidirect
75. #2585C22semidirect
78. #2553C22semidirect
79. #2512C22semidirect
80. #2512C22semidirect
81. #2511C22semidirect
82. #2511C22semidirect
83. #2509C22semidirect
84. #2509C22semidirect
85. #2508C22semidirect
86. #2508C22semidirect
87. #2507C22semidirect
88. #2507C22semidirect
89. #2506C22semidirect
90. #2506C22semidirect
92. #2497C22semidirect
93. #2497C22semidirect
94. #2496C22semidirect
95. #2496C22semidirect
98. #2487C22semidirect
100. #2486C22semidirect
103. #2485C22semidirect
104. #2485C22semidirect
109. #2454C22semidirect
110. #2454C22semidirect
111. #2453C22semidirect
112. #2453C22semidirect
113. #2448C22semidirect
114. #2447C22semidirect
115. #2446C22semidirect
116. #2445C22semidirect
120. #2442C22semidirect
121. #2442C22semidirect
122. #2441C22semidirect
123. #2441C22semidirect

Maximal subgroups

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

subgroupindex
#429562
#429352
#425072
#425012
#420222
#406592
#375242
#375222
#375202
#373822
#372882
#372862
#356392
#355852
#355572
#355172
#352632
#346332
C2×#26292
#342022
#340522