Finite Group Databasebeta

← #7652601

Subgroups — #7652601

Order 512.

4714 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42905C214yesmaximal, complemented
2#42870C214yesmaximal, complemented
3#42836C214yesmaximal, complemented
4#42827C214yesmaximal, complemented
5#42190C214yesmaximal, complemented
6#42009C214yesmaximal
7#40195C214yesmaximal, complemented
8#40101C214yesmaximal, complemented
9#39787C214yesmaximal, complemented
10#39214C214yesmaximal, complemented
11#38469C218yesmaximal, complemented
12#35672C212yesmaximal, complemented
13#35627C212yesmaximal, complemented
14#35544C212yesmaximal, complemented
15#35253C212yesmaximal, complemented
16#35154C211yesmaximal, characteristic, complemented
17C2×#2536C211yesmaximal, characteristic
18#34809C212yesmaximal
19#34249C211yesmaximal, characteristic, complemented
20#34203C212yesmaximal, complemented
21C2×#544C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C2×#519C2211yescharacteristic
24C2×#519C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2212yes—
28#2857C2214yescomplemented
29#2855C2214yes—
30#2851C2214yescomplemented
31#2839C2218yescomplemented
32#2837C2218yes—
33#2807C2218yescomplemented
34#2798C2218yescomplemented
35#2795C2214yes—
36#2794C2214yescomplemented
37#2792C2214yescomplemented
38#2791C2218yescomplemented
39#2789C2214yescomplemented
40#2787C2218yescomplemented
41#2785C2214yes—
42#2783C2218yescomplemented
43#2782C2214yes—
44#2781C2218yes—
45#2777C2218yescomplemented
46#2773C2218yescomplemented
47#2771C2218yescomplemented
48#2769C2214yescomplemented
49#2767C2218yescomplemented
50#2718C2218yes—
51#2689C2218yescomplemented
52#2680C2214yes—
53#2666C2218yescomplemented
54#2663C2218yes—
55#2655C2218yescomplemented
56#2654C2218yescomplemented
57#2650C2218yescomplemented
58#2649C2218yes—
59#2629C2214yescomplemented
60#2628C2214yescomplemented
61#2627C2214yes—
62#2596C2218yescomplemented
63#2594C2218yescomplemented
64#2585C2218yescomplemented
65#2577C2218yescomplemented
66#2575C2218yescomplemented
67#2571C2214yescomplemented
68#2571C2214yescomplemented
69#2570C2214yescomplemented
70#2570C2214yescomplemented
71#2553C2218yes—
72#2536C2214yes—
73#2536C2214yes—
74#2536C2214yes—
75#2536C2214yes—
76#2509C2214yescomplemented
77#2509C2214yescomplemented
78#2508C2214yescomplemented
79#2508C2214yescomplemented
80#2505C2218yes—
81#2505C2218yes—
82#2497C2214yescomplemented
83#2497C2214yescomplemented
84#2496C2214yescomplemented
85#2496C2214yescomplemented
86#2495C2214yescomplemented
87#2495C2214yescomplemented
88#2494C2214yescomplemented
89#2494C2214yescomplemented
90#2493C2218yes—
91#2487C2212yes—
92#2487C2212yes—
93#2486C2212yes—
94#2486C2212yes—
95#2485C2212yes—
96#2485C2212yes—
97#2485C2212yes—
98#2485C2212yes—
99#2484C2218yes—
100#2484C2214yes—
101#2483C2214yes—
102#2482C2218yes—
103#2482C2214yes—
104#2480C2218yes—
105#2453C2214yescomplemented
106#2453C2214yescomplemented
107#2451C2214yescomplemented
108#2451C2214yescomplemented
109#2442C2214yescomplemented
110#2441C2214yescomplemented
111#2440C2214yescomplemented
112#2439C2214yescomplemented
113#2438C2218yes—
114#2437C2218yes—
115#2423C2214yescomplemented
116#2423C2214yescomplemented
117#2423C2214yescomplemented
118#2423C2214yescomplemented
119#2421C2214yescomplemented
120#2421C2214yescomplemented
121#2421C2214yescomplemented
122#2421C2214yescomplemented
123#2405C2214yes—
124#2395C2214yes—
125#2395C2214yes—
126C2×#398C2212yes—
127C2×#394C2212yes—
128#2362C2214yescomplemented
129#2362C2214yescomplemented
130#2360C2214yescomplemented
131#2360C2214yescomplemented
132#2351C2214yescomplemented
133#2351C2214yescomplemented
134Q8×C4⋊C4C2214yescomplemented
135Q8×C4⋊C4C2214yescomplemented
136#2344C2218yes—
137#2342C2218yes—
138#2334C2218yescomplemented
139#2332C2218yescomplemented
140#2323C2214yescomplemented
141#2323C2214yescomplemented
142#2317C2214yes—
143#2317C2212yes—
144#2317C2212yes—
145#2317C2212yes—
146#2316C2212yes—
147#2316C2211yescharacteristic
148#2310C2212yes—
149C4×C22⋊Q8C2214yescomplemented
150C4×C22⋊Q8C2214yescomplemented
151C4×#123C2214yes—
152C4×#123C2214yes—
153#2296C2212yes—
154#2296C2212yes—
155#2296C2214yes—
156C2×#388C2214yes—
157C2×#382C2211yescharacteristic
158#2280C2212yes—
159#2280C2212yes—
160#2280C2212yes—
161C2×#380C2212yes—
162#2274C2212yes—
163C23×Q8C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C24×C4C2312yes—
166#544—44no—
167C2×C4⋊Q8C2314yes—
168C2×#126C2318yes—
169C2×#125C2314yes—
170C2×#123C2314yes—
171C2×#123C2314yes—
172C2×C22⋊Q8—216no—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2318yes—
178C2×C22⋊Q8C2314yes—
179#519—28no—
180#519—44no—
181C2×C4×Q8—44no—
182C2×C4×Q8C2314yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2314yes—
187C2×C4×Q8C2314yes—
188C2×C4×D4—44no—
189C2×C4×D4C2312yes—
190C2×C4×D4C2312yes—
191C2×C4×D4C2312yes—
192C2×C4×D4C2312yes—
193C2×#117—48no—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2314yes—
199C2×#117C2314yes—
200C2×#117C2314yes—
201C2×#117C2314yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2314yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C22⋊C4C2314yes—
212C22×C22⋊C4C2314yes—
213C22×C22⋊C4C2314yes—
214C22×C22⋊C4C2312yes—
215C22×C42C2311yescharacteristic
216C22×C42C2314yes—
217C22×C42C2312yes—
218#401C2318yes—
219#400C2318yes—
220#400C2318yes—
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2314yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2314yes—
233#400C2314yes—
234#400C2314yes—
235#399C2314yes—
236#399C2318yes—
237#399C2318yes—
238#399C2318yes—
239#399C2314yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2314yes—
245#398C2314yes—
246#398C2318yes—
247#398C2318yes—
248#398C2314yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2314yes—
253#397C2318yes—
254#397C2314yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2314yes—
259#397C2314yes—
260#397C2314yes—
261#397C2314yes—
262#397C2314yes—
263#397C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#395C2314yes—
268#395C2314yes—
269#395C2318yes—
270#394C2314yes—
271#394C2314yes—
272#394C2314yes—
273#394C2318yes—
274#394C2314yes—
275#394C2314yes—
276#394C2314yes—
277#393C2318yes—
278#391C2314yes—
279#391C2314yes—
280#391C2314yes—
281#391C2314yes—
282#391C2318yes—
283#391C2318yes—
284#389C2312yes—
285#389C2312yes—
286#389C2314yes—
287#389C2314yes—
288#389C2312yes—
289#389C2312yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2318yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2318yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2312yes—
311#389C2312yes—
312#389C2312yes—
313#389C2312yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2314yes—
322#388C2318yes—
323#388C2318yes—
324#388C2314yes—
325#388C2314yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2314yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2314yes—
345#387C2314yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2314yes—
355#387C2314yes—
356#386C2314yes—
357#386C2314yes—
358#385C2314yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2314yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#384C2314yes—
372#384C2314yes—
373#384C2314yes—
374#384C2314yes—
375#384C2314yes—
376#383C2318yes—
377#382C2314yes—
378#382C2314yes—
379#382C2314yes—
380#382C2314yes—
381#382C2318yes—
382#382C2318yes—
383#382C2314yes—
384#382C2314yes—
385#382C2314yes—
386#381C2318yes—
387#381C2314yes—
388#381C2314yes—
389#381C2314yes—
390#381C2314yes—
391#381C2314yes—
392#380C2318yes—
393#380C2314yes—
394#380C2318yes—
395#380C2312yes—
396#380C2312yes—
397#380C2312yes—
398#380C2314yes—
399#380C2312yes—
400#380C2312yes—
401#380C2314yes—
402#380C2312yes—
403#380C2312yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2314yes—
408#380C2314yes—
409#380C2312yes—
410#380C2312yes—
411#379C2314yes—
412#379C2314yes—
413#379C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2318yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2318yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C2×#95C2312yes—
436C2×#95C2314yes—
437C2×#95C2312yes—
438C25C2412yes—
439C22×Q8—24no—
440C22×Q8—24no—
441C22×Q8#4118yes—
442C22×Q8C2414yes—
443C22×Q8C2414yes—
444C22×D4—42no—
445C22×D4—44no—
446C22×D4C2411yescharacteristic
447C22×D4C2412yes—
448C22×D4C2411yescharacteristic
449C23×C4—28no—
450C23×C4—28no—
451C23×C4—28no—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2414yes—
460C23×C4C2411yescharacteristic
461C23×C4C2414yes—
462C23×C4C2411yescharacteristic
463C23×C4C2414yes—
464C23×C4C2411yescharacteristic
465C4⋊Q8—48no—
466#126—416no—
467#125—48no—
468#123—48no—
469#123—48no—
470C22⋊Q8—216no—
471C22⋊Q8—216no—
472C22⋊Q8—216no—
473C22⋊Q8—216no—
474C22⋊Q8—416no—
475C22⋊Q8—48no—
476C4×Q8—216no—
477C4×Q8—216no—
478C4×Q8—48no—
479C4×Q8—48no—
480C4×Q8—48no—
481C4×Q8—48no—
482C4×D4—44no—
483C4×D4—44no—
484C4×D4—44no—
485C4×D4—44no—
486#117—216no—
487#117—28no—
488#117—28no—
489#117—28no—
490#117—28no—
491#117—48no—
492#117—48no—
493#117—48no—
494#117—44no—
495#117—44no—
496C2×C4⋊C4—216no—
497C2×C4⋊C4—28no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—44no—
500C2×C4⋊C4—44no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—44no—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2412yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2411yescharacteristic
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C22⋊C4—216no—
546C2×C22⋊C4—48no—
547C2×C22⋊C4—48no—
548C2×C22⋊C4—44no—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C42—24no—
576C2×C42—48no—
577C2×C42—44no—
578C2×C42C2414yes—
579C2×C42C2414yes—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2418yes—
589C2×C42C2418yes—
590C2×C42C2418yes—
591C2×C42C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2414yes—
595#95C2418yes—
596#95C2414yes—
597#95C2414yes—
598#95C2414yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2414yes—
616#95C2414yes—
617#95C2418yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2418yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633C24—24no—
634C24—24no—
635C24—24no—
636C24—24no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24C2512yes—
641C24C2512yes—
642C24C2511yescharacteristic
643C2×Q8—232no—
644C2×Q8—28no—
645C2×Q8—28no—
646C2×Q8—44no—
647C2×Q8—48no—
648C2×Q8C2×#41116yes—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—41no—
652C2×D4—42no—
653C2×D4—41no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—416no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—28no—
665C22×C4—24no—
666C22×C4—28no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—432no—
690C22×C4C2×#4118yes—
691C22×C4C2×#4114yes—
692C22×C4H(5,𝔽2)14yes—
693C22×C42−1+414yes—
694C22×C4C2512yes—
695C22×C4C2514yes—
696C22×C4C2514yes—
697C22×C4C2512yes—
698C22×C4C2518yes—
699C22×C4C2512yes—
700C22×C4C2514yes—
701C22×C4C2514yes—
702C22×C4C2514yes—
703C22×C4C2514yes—
704C22×C4C2514yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2514yes—
710C22×C4C2512yes—
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—216no—
714C4⋊C4—216no—
715C4⋊C4—216no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—28no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—41no—
728C4⋊C4—42no—
729C4⋊C4—41no—
730C4⋊C4—44no—
731C4⋊C4—44no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—48no—
735C4⋊C4—48no—
736C4⋊C4—48no—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—216no—
758C22⋊C4—28no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—216no—
762C22⋊C4—216no—
763C22⋊C4—48no—
764C22⋊C4—44no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C42—28no—
780C42—28no—
781C42—28no—
782C42—24no—
783C42—24no—
784C42—28no—
785C42—28no—
786C42—28no—
787C42—44no—
788C42—44no—
789C42—48no—
790C42—48no—
791C42—48no—
792C42—48no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—48no—
809C23—48no—
810C23—48no—
811C23—48no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23C22×#4112yes—
816C23C2×H(5,𝔽2)12yes—
817C23C2×2−1+412yes—
818C23#58514yes—
819C23C2611yescharacteristic
820Q8—232no—
821Q8—164no—
822D4—44no—
823D4—48no—
824D4—44no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—216no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—28no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—48no—
873C2×C4—48no—
874C2×C4—48no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—88no—
878C2×C4—88no—
879C2×C4—84no—
880C2×C4—88no—
881C2×C4#539116yes—
882C2×C4C22×#4118yes—
883C2×C4C22×#4114yes—
884C2×C4C2×H(5,𝔽2)14yes—
885C2×C4C2×2−1+414yes—
886C22—24no—
887C22—22no—
888C22—22no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—24no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—816no—
905C22C2×#53914yes—
906C22C23×#4111yescharacteristic
907C22C22×H(5,𝔽2)11yescharacteristic
908C22C22×2−1+411yescharacteristic
909C22C2×#58512yes—
910C222−1+612yes—
911C4—28no—
912C4—44no—
913C4—44no—
914C4—48no—
915C4—41no—
916C4—41no—
917C4—44no—
918C4—44no—
919C4—44no—
920C4—42no—
921C4—44no—
922C4—44no—
923C4—42no—
924C4—42no—
925C4—44no—
926C4—44no—
927C4C2×#53918yes—
928C2—24no—
929C2—44no—
930C2—82no—
931C2C22×#53911yescharacteristic
932C2#6282111yescharacteristic
933C2#6288611yescharacteristic
934C2#6292812yes—
935C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42905C2semidirect
2. #42870C2semidirect
3. #42836C2semidirect
4. #42827C2semidirect
5. #42190C2semidirect
7. #40195C2semidirect
8. #40101C2semidirect
9. #39787C2semidirect
10. #39214C2semidirect
11. #38469C2semidirect
12. #35672C2semidirect
13. #35627C2semidirect
14. #35544C2semidirect
15. #35253C2semidirect
16. #35154C2semidirect
19. #34249C2semidirect
20. #34203C2semidirect
28. #2857C22semidirect
30. #2851C22semidirect
31. #2839C22semidirect
33. #2807C22semidirect
34. #2798C22semidirect
36. #2794C22semidirect
37. #2792C22semidirect
38. #2791C22semidirect
39. #2789C22semidirect
40. #2787C22semidirect
42. #2783C22semidirect
45. #2777C22semidirect
46. #2773C22semidirect
47. #2771C22semidirect
48. #2769C22semidirect
49. #2767C22semidirect
51. #2689C22semidirect
53. #2666C22semidirect
55. #2655C22semidirect
56. #2654C22semidirect
57. #2650C22semidirect
59. #2629C22semidirect
60. #2628C22semidirect
62. #2596C22semidirect
63. #2594C22semidirect
64. #2585C22semidirect
65. #2577C22semidirect
66. #2575C22semidirect
67. #2571C22semidirect
68. #2571C22semidirect
69. #2570C22semidirect
70. #2570C22semidirect
76. #2509C22semidirect
77. #2509C22semidirect
78. #2508C22semidirect
79. #2508C22semidirect
82. #2497C22semidirect
83. #2497C22semidirect
84. #2496C22semidirect
85. #2496C22semidirect
86. #2495C22semidirect
87. #2495C22semidirect
88. #2494C22semidirect
89. #2494C22semidirect
105. #2453C22semidirect
106. #2453C22semidirect
107. #2451C22semidirect
108. #2451C22semidirect
109. #2442C22semidirect
110. #2441C22semidirect
111. #2440C22semidirect
112. #2439C22semidirect
115. #2423C22semidirect
116. #2423C22semidirect
117. #2423C22semidirect
118. #2423C22semidirect
119. #2421C22semidirect
120. #2421C22semidirect
121. #2421C22semidirect
122. #2421C22semidirect
128. #2362C22semidirect
129. #2362C22semidirect
130. #2360C22semidirect
131. #2360C22semidirect
132. #2351C22semidirect
133. #2351C22semidirect
134. Q8×C4⋊C4C22semidirect
135. Q8×C4⋊C4C22semidirect
138. #2334C22semidirect
139. #2332C22semidirect
140. #2323C22semidirect
141. #2323C22semidirect
149. C4×C22⋊Q8C22semidirect
150. C4×C22⋊Q8C22semidirect

Maximal subgroups

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

subgroupindex
#429052
#428702
#428362
#428272
#421902
#420092
#401952
#401012
#397872
#392142
#384692
#356722
#356272
#355442
#352532
#351542
C2×#25362
#348092
#342492
#342032