Finite Group Databasebeta

← #7643414

Subgroups — #7643414

Order 512.

4864 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40319C218yesmaximal, complemented
2#39678C214yesmaximal, complemented
3#39543C214yesmaximal, complemented
4#38703C218yesmaximal, complemented
5#37957C214yesmaximal
6#37933C214yesmaximal, complemented
7#37399C214yesmaximal, complemented
8#37354C214yesmaximal, complemented
9#36625C212yesmaximal, complemented
10#35637C214yesmaximal, complemented
11#35604C214yesmaximal, complemented
12#35310C212yesmaximal, complemented
13#35240C212yesmaximal
14#35173C211yesmaximal, characteristic, complemented
15#35104C211yesmaximal, characteristic, complemented
16#35086C212yesmaximal, complemented
17#35014C212yesmaximal, complemented
18#34221C212yesmaximal, complemented
19C2×#2290C211yesmaximal, characteristic
20C2×#541C2212yescomplemented
21C2×#533C2212yes—
22C2×#533C2212yescomplemented
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2857C2212yes—
27#2857C2212yes—
28#2857C2212yes—
29#2857C2212yescomplemented
30#2857C2212yescomplemented
31#2855C2214yescomplemented
32#2855C2214yescomplemented
33#2851C2212yes—
34#2851C2214yes—
35#2851C2214yescomplemented
36#2848C2214yes—
37#2848C2214yes—
38#2848C2214yes—
39#2799C2218yescomplemented
40#2791C2218yescomplemented
41#2791C2218yescomplemented
42#2786C2218yes—
43#2777C2218yescomplemented
44#2775C2218yescomplemented
45#2773C2218yescomplemented
46#2772C2218yescomplemented
47#2770C2218yescomplemented
48#2768C2218yescomplemented
49#2755C2218yescomplemented
50#2740C2218yes—
51#2738C2218yescomplemented
52#2715C2218yes—
53#2700C2218yes—
54#2698C2218yescomplemented
55#2659C2214yes—
56#2652C2218yescomplemented
57#2646C2214yes—
58#2633C2218yes—
59#2629C2212yescomplemented
60#2627C2214yes—
61#2626C2214yes—
62#2625C2214yescomplemented
63#2621C2212yescomplemented
64#2611C2218yescomplemented
65#2606C2214yescomplemented
66#2605C2214yescomplemented
67#2604C2218yescomplemented
68#2601C2218yes—
69#2596C2218yescomplemented
70#2589C2218yescomplemented
71#2588C2218yescomplemented
72#2587C2218yescomplemented
73#2584C2214yescomplemented
74#2584C2214yescomplemented
75#2570C2214yescomplemented
76#2567C2214yescomplemented
77#2565C2218yescomplemented
78#2560C2218yes—
79#2556C2218yescomplemented
80#2550C2214yescomplemented
81#2547C2214yes—
82#2546C2214yescomplemented
83#2542C2214yes—
84#2536C2214yes—
85#2536C2214yes—
86#2530C2218yescomplemented
87#2529C2218yescomplemented
88#2521C2218yes—
89#2520C2218yescomplemented
90#2519C2218yescomplemented
91#2506C2218yescomplemented
92#2505C2218yes—
93#2502C2214yes—
94#2497C2214yescomplemented
95#2496C2214yescomplemented
96#2492C2214yescomplemented
97#2489C2214yescomplemented
98#2482C2214yes—
99#2482C2214yes—
100#2480C2218yes—
101#2480C2218yes—
102#2478C2218yescomplemented
103#2478C2218yescomplemented
104#2475C2218yescomplemented
105#2474C2218yes—
106#2473C2218yes—
107#2435C2214yes—
108#2429C2214yescomplemented
109#2429C2214yescomplemented
110#2423C2214yescomplemented
111#2421C2214yescomplemented
112#2371C2218yescomplemented
113#2368C2218yes—
114#2356C2218yescomplemented
115#2343C2218yes—
116#2334C2218yescomplemented
117#2331C2212yescomplemented
118#2331C2212yescomplemented
119#2329C2214yes—
120#2329C2214yes—
121#2327C2212yescomplemented
122#2327C2212yescomplemented
123#2326C2218yes—
124#2323C2214yescomplemented
125#2320C2214yescomplemented
126#2316C2214yes—
127#2314C2212yescomplemented
128#2312C2214yes—
129C4×C22⋊Q8C2214yes—
130C4×C22⋊Q8C2214yes—
131C4×C22⋊Q8C2214yes—
132C4×C22⋊Q8C2214yescomplemented
133C4×C22⋊Q8C2214yescomplemented
134#2296C2214yescomplemented
135#2290C2214yes—
136#2290C2214yes—
137#2290C2214yes—
138#2290C2214yes—
139C2×#388C2212yes—
140C2×#387C2212yes—
141C2×#386C2212yes—
142C2×#385C2212yes—
143#2285C2212yescomplemented
144#2283C2212yes—
145#2280C2214yes—
146#2276C2214yescomplemented
147C2×C4×C4⋊C4C2211yescharacteristic
148C2×C4×C22⋊C4C2211yescharacteristic
149C2×C4×C22⋊C4C2211yescharacteristic
150C2×#376C2211yescharacteristic
151C23×D4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2312yes—
155#541—48no—
156#533—216no—
157#533—48no—
158C2×C4⋊Q8C2312yes—
159C2×C4⋊Q8C2312yes—
160C2×C4⋊Q8C2312yes—
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2312yes—
163C2×#126C2318yes—
164C2×#126C2318yes—
165C2×#125C2314yes—
166C2×#125C2318yes—
167C2×#125C2314yes—
168C2×#125C2312yes—
169C2×#124C2318yes—
170C2×C22⋊Q8C2314yes—
171C2×C22⋊Q8C2314yes—
172C2×C22⋊Q8C2314yes—
173C2×C22⋊Q8C2314yes—
174C2×C22⋊Q8C2314yes—
175C2×C22⋊Q8C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2314yes—
179C2×C4×Q8C2314yes—
180C2×C4×Q8C2314yes—
181C2×C4×Q8C2314yes—
182C2×C4×Q8C2314yes—
183C2×C4×Q8C2314yes—
184C2×C4×D4—28no—
185C2×C4×D4C2314yes—
186C2×C4×D4C2314yes—
187C2×#117—44no—
188C2×#117C2312yes—
189C2×#117C2314yes—
190C2×#117C2314yes—
191C2×#117C2312yes—
192C2×#117C2314yes—
193C2×#117C2314yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C42—44no—
203C22×C42C2311yescharacteristic
204C22×C42C2312yes—
205C22×C42C2311yescharacteristic
206C22×C42C2312yes—
207C22×C42C2312yes—
208C22×C42C2312yes—
209C22×C42C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213#400C2318yes—
214#400C2318yes—
215#400C2318yes—
216#400C2318yes—
217#400C2318yes—
218#400C2318yes—
219#400C2318yes—
220#399C2318yes—
221#399C2318yes—
222#399C2318yes—
223#398C2318yes—
224#398C2318yes—
225#398C2318yes—
226#398C2318yes—
227#398C2318yes—
228#398C2318yes—
229#398C2318yes—
230#398C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#397C2318yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#396C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#395C2318yes—
248#395C2318yes—
249#395C2318yes—
250#394C2318yes—
251#394C2318yes—
252#393C2318yes—
253#391C2318yes—
254#391C2318yes—
255#391C2314yes—
256#391C2314yes—
257#391C2314yes—
258#391C2314yes—
259#391C2318yes—
260#391C2318yes—
261#391C2318yes—
262#391C2314yes—
263#391C2314yes—
264#390C2318yes—
265#389C2318yes—
266#389C2318yes—
267#389C2314yes—
268#389C2314yes—
269#389C2318yes—
270#389C2318yes—
271#389C2314yes—
272#389C2314yes—
273#389C2318yes—
274#389C2314yes—
275#389C2314yes—
276#389C2318yes—
277#389C2318yes—
278#389C2318yes—
279#389C2314yes—
280#389C2318yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C2318yes—
289#388C2318yes—
290#388C2318yes—
291#388C2318yes—
292#388C2318yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2314yes—
299#388C2314yes—
300#388C2314yes—
301#388C2314yes—
302#387C2318yes—
303#387C2314yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2314yes—
326#387C2314yes—
327#387C2314yes—
328#386C2314yes—
329#386C2314yes—
330#386C2314yes—
331#386C2314yes—
332#385C2318yes—
333#385C2318yes—
334#385C2318yes—
335#385C2318yes—
336#385C2318yes—
337#385C2318yes—
338#385C2318yes—
339#385C2318yes—
340#385C2318yes—
341#385C2318yes—
342#385C2318yes—
343#385C2314yes—
344#385C2314yes—
345#385C2314yes—
346#385C2314yes—
347#384C2318yes—
348#384C2312yes—
349#384C2312yes—
350#384C2312yes—
351#383C2318yes—
352#383C2314yes—
353#382C2318yes—
354#382C2312yes—
355#382C2312yes—
356#382C2318yes—
357#382C2312yes—
358#382C2314yes—
359#381C2314yes—
360#381C2318yes—
361#380C2314yes—
362#380C2314yes—
363#380C2314yes—
364#380C2314yes—
365#380C2318yes—
366#380C2314yes—
367#380C2314yes—
368#380C2314yes—
369#380C2314yes—
370#380C2314yes—
371#380C2314yes—
372#380C2314yes—
373#380C2314yes—
374#379C2318yes—
375#379C2318yes—
376C4×C4⋊C4C2318yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2314yes—
379C4×C4⋊C4C2314yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2312yes—
382C4×C4⋊C4C2312yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2318yes—
389C4×C22⋊C4C2318yes—
390C4×C22⋊C4C2318yes—
391C4×C22⋊C4C2314yes—
392C4×C22⋊C4C2312yes—
393C4×C22⋊C4C2312yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2318yes—
396C4×C22⋊C4C2314yes—
397C4×C22⋊C4C2314yes—
398#376C2312yes—
399#376C2314yes—
400#376C2312yes—
401#376C2318yes—
402#376C2314yes—
403C2×#95C2312yes—
404C2×#95C2312yes—
405C2×#95C2312yes—
406C2×#95C2312yes—
407C2×#95C2312yes—
408C25C2411yescharacteristic
409C25C2411yescharacteristic
410C22×Q8C2414yes—
411C22×Q8C2414yes—
412C22×Q8C2414yes—
413C22×D4—24no—
414C22×D4—44no—
415C22×D4C2414yes—
416C23×C4—24no—
417C23×C4—24no—
418C23×C4—28no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—44no—
424C23×C4—44no—
425C23×C4C2412yes—
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2412yes—
442C4⋊Q8—28no—
443C4⋊Q8—28no—
444C4⋊Q8—44no—
445C4⋊Q8—44no—
446C4⋊Q8—44no—
447#126—416no—
448#126—416no—
449#125—216no—
450#125—48no—
451#125—44no—
452#125—416no—
453#124—416no—
454C22⋊Q8—216no—
455C22⋊Q8—216no—
456C22⋊Q8—216no—
457C22⋊Q8—48no—
458C22⋊Q8—48no—
459C22⋊Q8—48no—
460C22⋊Q8—48no—
461C22⋊Q8—48no—
462C22⋊Q8—48no—
463C4×Q8—216no—
464C4×Q8—216no—
465C4×Q8—216no—
466C4×Q8—48no—
467C4×Q8—48no—
468C4×D4—216no—
469C4×D4—216no—
470#117—216no—
471#117—28no—
472#117—44no—
473#117—48no—
474#117—48no—
475#117—48no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—28no—
478C2×C4⋊C4—44no—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2414yes—
485C2×C4⋊C4C2414yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2418yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2418yes—
490C2×C4⋊C4C2414yes—
491C2×C4⋊C4C2414yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—28no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4—44no—
517C2×C22⋊C4C2414yes—
518C2×C22⋊C4C2414yes—
519C2×C22⋊C4C2414yes—
520C2×C22⋊C4C2414yes—
521C2×C22⋊C4C2414yes—
522C2×C22⋊C4C2414yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C42—24no—
536C2×C42—28no—
537C2×C42—42no—
538C2×C42—44no—
539C2×C42—44no—
540C2×C42—44no—
541C2×C42—44no—
542C2×C42—42no—
543C2×C42—42no—
544C2×C42#4118yes—
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2411yescharacteristic
548C2×C42C2418yes—
549C2×C42C2418yes—
550C2×C42C2412yes—
551C2×C42C2412yes—
552C2×C42C2412yes—
553C2×C42C2412yes—
554C2×C42C2412yes—
555C2×C42C2418yes—
556C2×C42C2418yes—
557C2×C42C2418yes—
558C2×C42C2418yes—
559C2×C42C2412yes—
560C2×C42C2411yescharacteristic
561C2×C42C2411yescharacteristic
562C2×C42C2412yes—
563C2×C42C2412yes—
564C2×C42C2412yes—
565C2×C42C2412yes—
566C2×C42C2411yescharacteristic
567#95C2414yes—
568#95C2414yes—
569#95C2414yes—
570#95C2414yes—
571#95C2414yes—
572#95C2414yes—
573#95C2414yes—
574#95C2414yes—
575#95C2414yes—
576#95C2414yes—
577#95C2418yes—
578#95C2418yes—
579#95C2418yes—
580#95C2418yes—
581#95C2414yes—
582#95C2414yes—
583#95C2418yes—
584#95C2418yes—
585#95C2418yes—
586#95C2418yes—
587#95C2414yes—
588#95C2414yes—
589#95C2418yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602C24—22no—
603C24—24no—
604C24—22no—
605C24—24no—
606C24—24no—
607C24—41no—
608C24—41no—
609C24—41no—
610C24—41no—
611C24—42no—
612C24C2512yes—
613C24C2512yes—
614C24C2511yescharacteristic
615C2×Q8—28no—
616C2×Q8—28no—
617C2×Q8—28no—
618C2×Q8—28no—
619C2×Q8—28no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—48no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—44no—
626C2×D4—416no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—22no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—432no—
673C22×C4—416no—
674C22×C4—416no—
675C22×C4C2×#4114yes—
676C22×C4C2×#4114yes—
677C22×C4C2×#4114yes—
678C22×C42−1+418yes—
679C22×C4C2514yes—
680C22×C4C2512yes—
681C22×C4C2518yes—
682C22×C4C2512yes—
683C22×C4C2518yes—
684C22×C4C2518yes—
685C22×C4C2514yes—
686C22×C4C2512yes—
687C22×C4C2518yes—
688C22×C4C2512yes—
689C22×C4C2512yes—
690C22×C4C2511yescharacteristic
691C22×C4C2512yes—
692C22×C4C2512yes—
693C22×C4C2512yes—
694C22×C4C2511yescharacteristic
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—216no—
699C4⋊C4—216no—
700C4⋊C4—28no—
701C4⋊C4—28no—
702C4⋊C4—28no—
703C4⋊C4—28no—
704C4⋊C4—216no—
705C4⋊C4—28no—
706C4⋊C4—28no—
707C4⋊C4—28no—
708C4⋊C4—216no—
709C4⋊C4—28no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—44no—
718C4⋊C4—44no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—48no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—48no—
727C4⋊C4—48no—
728C22⋊C4—216no—
729C22⋊C4—216no—
730C22⋊C4—28no—
731C22⋊C4—216no—
732C22⋊C4—216no—
733C22⋊C4—28no—
734C22⋊C4—28no—
735C22⋊C4—28no—
736C22⋊C4—28no—
737C22⋊C4—28no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C42—216no—
747C42—24no—
748C42—22no—
749C42—24no—
750C42—24no—
751C42—24no—
752C42—24no—
753C42—216no—
754C42—24no—
755C42—41no—
756C42—41no—
757C42—42no—
758C42—42no—
759C42—42no—
760C42—42no—
761C42—48no—
762C42—48no—
763C42—48no—
764C42—48no—
765C42C2×#4118yes—
766C42C2×#4118yes—
767C42H(5,𝔽2)14yes—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—28no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—24no—
781C23—22no—
782C23—24no—
783C23—48no—
784C23—48no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—44no—
789C23—44no—
790C23—84no—
791C23—84no—
792C23C22×#4112yes—
793C23C2×2−1+414yes—
794C23#58514yes—
795C23C2611yescharacteristic
796Q8—416no—
797Q8—88no—
798Q8—88no—
799D4—416no—
800C2×C4—216no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—28no—
812C2×C4—28no—
813C2×C4—28no—
814C2×C4—28no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—28no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—28no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—24no—
836C2×C4—28no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—48no—
841C2×C4—44no—
842C2×C4—48no—
843C2×C4—48no—
844C2×C4—48no—
845C2×C4—48no—
846C2×C4—48no—
847C2×C4—48no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—48no—
851C2×C4—48no—
852C2×C4—84no—
853C2×C4—84no—
854C2×C4C22×#4114yes—
855C2×C4C22×#4112yes—
856C2×C4C22×#4114yes—
857C2×C4C22×#4112yes—
858C2×C4C2×H(5,𝔽2)14yes—
859C2×C4C2×H(5,𝔽2)12yes—
860C2×C4C2×2−1+414yes—
861C2×C4C2×2−1+414yes—
862C2×C4#58512yes—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—22no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—416no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—88no—
881C22#350914yes—
882C22C23×#4111yescharacteristic
883C22C22×H(5,𝔽2)11yescharacteristic
884C22C22×2−1+412yes—
885C22C2×#58512yes—
886C22C2×#58511yescharacteristic
887C4—24no—
888C4—24no—
889C4—24no—
890C4—24no—
891C4—24no—
892C4—22no—
893C4—48no—
894C4—42no—
895C4—44no—
896C4—48no—
897C4—48no—
898C4—44no—
899C4—42no—
900C4—42no—
901C4—48no—
902C4#346014yes—
903C2—24no—
904C2—44no—
905C2—82no—
906C2C2×#346011yescharacteristic
907C2C2×#350911yescharacteristic
908C2#6281411yescharacteristic
909C2#6281912yes—
910C2#6283112yes—
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. #40319C2semidirect
2. #39678C2semidirect
3. #39543C2semidirect
4. #38703C2semidirect
6. #37933C2semidirect
7. #37399C2semidirect
8. #37354C2semidirect
9. #36625C2semidirect
10. #35637C2semidirect
11. #35604C2semidirect
12. #35310C2semidirect
14. #35173C2semidirect
15. #35104C2semidirect
16. #35086C2semidirect
17. #35014C2semidirect
18. #34221C2semidirect
20. C2×#541C22semidirect
22. C2×#533C22semidirect
29. #2857C22semidirect
30. #2857C22semidirect
31. #2855C22semidirect
32. #2855C22semidirect
35. #2851C22semidirect
39. #2799C22semidirect
40. #2791C22semidirect
41. #2791C22semidirect
43. #2777C22semidirect
44. #2775C22semidirect
45. #2773C22semidirect
46. #2772C22semidirect
47. #2770C22semidirect
48. #2768C22semidirect
49. #2755C22semidirect
51. #2738C22semidirect
54. #2698C22semidirect
56. #2652C22semidirect
59. #2629C22semidirect
62. #2625C22semidirect
63. #2621C22semidirect
64. #2611C22semidirect
65. #2606C22semidirect
66. #2605C22semidirect
67. #2604C22semidirect
69. #2596C22semidirect
70. #2589C22semidirect
71. #2588C22semidirect
72. #2587C22semidirect
73. #2584C22semidirect
74. #2584C22semidirect
75. #2570C22semidirect
76. #2567C22semidirect
77. #2565C22semidirect
79. #2556C22semidirect
80. #2550C22semidirect
82. #2546C22semidirect
86. #2530C22semidirect
87. #2529C22semidirect
89. #2520C22semidirect
90. #2519C22semidirect
91. #2506C22semidirect
94. #2497C22semidirect
95. #2496C22semidirect
96. #2492C22semidirect
97. #2489C22semidirect
102. #2478C22semidirect
103. #2478C22semidirect
104. #2475C22semidirect
108. #2429C22semidirect
109. #2429C22semidirect
110. #2423C22semidirect
111. #2421C22semidirect
112. #2371C22semidirect
114. #2356C22semidirect
116. #2334C22semidirect
117. #2331C22semidirect
118. #2331C22semidirect
121. #2327C22semidirect
122. #2327C22semidirect
124. #2323C22semidirect
125. #2320C22semidirect
127. #2314C22semidirect
132. C4×C22⋊Q8C22semidirect
133. C4×C22⋊Q8C22semidirect
134. #2296C22semidirect
143. #2285C22semidirect
146. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#403192
#396782
#395432
#387032
#379572
#379332
#373992
#373542
#366252
#356372
#356042
#353102
#352402
#351732
#351042
#350862
#350142
#342212
C2×#22902