Finite Group Databasebeta

← #7712354

Subgroups — #7712354

Order 512.

4578 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59664C214yesmaximal, complemented
2#59455C214yesmaximal
3#46151C218yesmaximal, complemented
4#39754C212yesmaximal, complemented
5#39686C218yesmaximal, complemented
6#39682C214yesmaximal, complemented
7#39675C214yesmaximal, complemented
8#39370C212yesmaximal, complemented
9#37687C214yesmaximal, complemented
10#37623C212yesmaximal, complemented
11#37429C214yesmaximal, complemented
12#36635C211yesmaximal, characteristic, complemented
13C2×#2859C211yesmaximal, characteristic, complemented
14#36565C211yesmaximal, characteristic, complemented
15Q8×#125C211yesmaximal, characteristic, complemented
16#36192C211yesmaximal, characteristic, complemented
17#36191C212yesmaximal, complemented
18#36165C212yesmaximal, complemented
19#36165C211yesmaximal, characteristic, complemented
20#35336C212yesmaximal, complemented
21#35330C212yesmaximal, complemented
22#34384C212yesmaximal
23C4×#529C211yesmaximal, characteristic
24C2×#544C2214yes—
25C2×#529C2211yescharacteristic
26C22×#125C2212yes—
27#2864C2212yes—
28#2863C2214yes—
29#2862C2211yescharacteristic
30#2862C2212yes—
31#2859C2212yes—
32#2859C2212yes—
33#2859C2214yes—
34#2859C2211yescharacteristic
35#2859C2212yes—
36#2859C2211yescharacteristic
37#2859C2214yes—
38#2859C2212yes—
39#2859C2211yescharacteristic
40#2857C2212yes—
41#2855C2214yes—
42#2851C2212yes—
43#2851C2212yes—
44#2851C2211yescharacteristic
45#2851C2211yescharacteristic
46#2843C2218yes—
47#2805C2218yes—
48#2802C2218yes—
49#2802C2218yes—
50#2791C2218yes—
51#2790C2218yes—
52#2788C2218yes—
53#2774C2218yes—
54#2768C2218yes—
55#2755C2218yes—
56#2742C2218yes—
57#2729C2218yes—
58#2726C2218yes—
59#2720C2218yes—
60#2713C2218yes—
61#2704C2218yes—
62#2704C2218yes—
63#2660C2214yes—
64#2660C2214yes—
65#2660C2214yes—
66#2647C2214yes—
67#2647C2214yes—
68#2629C2214yes—
69#2627C2218yes—
70#2590C2218yes—
71#2590C2218yes—
72#2587C2218yes—
73#2587C2218yes—
74#2586C2218yes—
75#2584C2214yes—
76#2581C2214yes—
77#2574C2218yes—
78#2571C2214yes—
79#2571C2212yes—
80#2570C2214yes—
81#2552C2214yes—
82#2552C2212yes—
83#2552C2212yes—
84#2551C2212yes—
85#2550C2218yes—
86#2550C2218yes—
87#2550C2214yes—
88#2549C2218yes—
89#2549C2218yes—
90#2546C2214yes—
91#2538C2214yes—
92#2522C2218yes—
93#2520C2218yes—
94#2508C2214yes—
95#2508C2214yes—
96#2508C2218yes—
97#2507C2214yes—
98#2507C2218yes—
99#2506C2214yes—
100#2505C2218yes—
101#2505C2218yes—
102#2505C2218yes—
103#2473C2218yes—
104#2454C2214yes—
105#2453C2214yes—
106#2452C2214yes—
107#2451C2214yes—
108#2450C2218yes—
109#2449C2218yes—
110#2442C2214yes—
111#2442C2214yes—
112#2442C2214yes—
113#2442C2214yes—
114#2441C2214yes—
115#2440C2218yes—
116#2440C2214yes—
117#2440C2214yes—
118#2439C2214yes—
119#2417C2218yes—
120#2383C2218yes—
121#2370C2214yes—
122#2369C2214yes—
123#2368C2218yes—
124#2361C2214yes—
125#2360C2214yes—
126#2355C2212yes—
127#2354C2212yes—
128#2352C2214yes—
129Q8×C4⋊C4C2214yes—
130Q8×C4⋊C4C2212yes—
131#2349C2218yes—
132#2349C2214yes—
133D4×C4⋊C4C2214yes—
134D4×C4⋊C4C2212yes—
135#2330C2214yes—
136#2330C2214yes—
137#2326C2214yes—
138#2322C2218yes—
139#2317C2214yes—
140#2314C2214yes—
141C4×C4⋊Q8C2212yes—
142C4×#125C2212yes—
143C4×#125C2212yes—
144C4×#125C2212yes—
145C4×#125C2211yescharacteristic
146C4×#125C2211yescharacteristic
147C4×#126C2214yes—
148C4×#124C2212yes—
149C4×C22⋊Q8C2212yes—
150C4×C22⋊Q8C2214yes—
151C4×#123C2214yes—
152C4×#121C2212yes—
153#2298C2212yes—
154#2295C2214yes—
155#2295C2211yescharacteristic
156#2293C2211yescharacteristic
157C2×#389C2214yes—
158C2×#389C2214yes—
159#2290C2212yes—
160#2285C2212yes—
161C2×#384C2212yes—
162#2283C2212yes—
163#2283C2211yescharacteristic
164C2×#382C2212yes—
165C2×#382C2212yes—
166C42×Q8C2211yescharacteristic
167C42×D4C2212yes—
168C42×D4C2211yescharacteristic
169C4×#117C2212yes—
170C2×C43C2211yescharacteristic
171#544—416no—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2318yes—
176#529Q8116yescomplemented
177C2×#126C2312yes—
178C2×#125—48no—
179C2×#125C2311yescharacteristic
180C2×#125C2311yescharacteristic
181C2×#125C2314yes—
182C2×#125C2314yes—
183C2×#125C2312yes—
184C2×#125C2312yes—
185C2×#125C2318yes—
186C2×#125C2314yes—
187C2×#125C2318yes—
188C2×#125C2311yescharacteristic
189C2×#124C2311yescharacteristic
190C2×#123C2312yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2311yescharacteristic
196C2×#121C2311yescharacteristic
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2312yes—
200C2×C4×Q8C2311yescharacteristic
201C2×C4×D4C2318yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2311yescharacteristic
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2312yes—
210C22×C4⋊C4C2314yes—
211C22×C4⋊C4C2314yes—
212C22×C4⋊C4C2314yes—
213C22×C4⋊C4C2314yes—
214C22×C4⋊C4C2318yes—
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221#400C2318yes—
222#400C2318yes—
223#400C2318yes—
224#400C2318yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#399C2318yes—
231#398C2318yes—
232#398C2318yes—
233#398C2318yes—
234#398C2318yes—
235#398C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#396C2318yes—
250#396C2318yes—
251#396C2318yes—
252#396C2318yes—
253#395C2318yes—
254#395C2318yes—
255#395C2318yes—
256#395C2318yes—
257#395C2318yes—
258#395C2318yes—
259#395C2318yes—
260#393C2318yes—
261#391C2314yes—
262#391C2318yes—
263#391C2312yes—
264#391C2314yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2314yes—
269#391C2314yes—
270#391C2318yes—
271#390C2314yes—
272#390C2312yes—
273#389C2312yes—
274#389C2312yes—
275#389C2312yes—
276#389C2314yes—
277#389C2314yes—
278#389C2312yes—
279#389C2312yes—
280#389C2312yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2318yes—
285#389C2314yes—
286#389C2318yes—
287#389C2318yes—
288#389C2318yes—
289#389C2314yes—
290#389C2314yes—
291#389C2318yes—
292#389C2314yes—
293#389C2318yes—
294#389C2314yes—
295#389C2318yes—
296#389C2314yes—
297#389C2318yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2318yes—
309#389C2314yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C2314yes—
314#389C2318yes—
315#389C2314yes—
316#389C2318yes—
317#388C2314yes—
318#388C2314yes—
319#388C2314yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2314yes—
325#387C2314yes—
326#387C2314yes—
327#387C2314yes—
328#387C2314yes—
329#387C2318yes—
330#387C2318yes—
331#387C2314yes—
332#387C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2314yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#387C2314yes—
349#387C2318yes—
350#387C2318yes—
351#386C2318yes—
352#386C2314yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2314yes—
361#385C2314yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#384C2312yes—
368#384C2314yes—
369#384C2314yes—
370#384C2314yes—
371#384C2312yes—
372#384C2314yes—
373#384C2314yes—
374#384C2312yes—
375#384C2314yes—
376#384C2318yes—
377#383C2312yes—
378#383C2314yes—
379#382C2312yes—
380#382C2312yes—
381#382C2311yescharacteristic
382#382C2311yescharacteristic
383#382C2312yes—
384#382C2312yes—
385#382C2314yes—
386#382C2314yes—
387#382C2314yes—
388#382C2314yes—
389#382C2318yes—
390#382C2312yes—
391#382C2318yes—
392#382C2318yes—
393#381C2314yes—
394#381C2312yes—
395#380C2314yes—
396#380C2314yes—
397#380C2318yes—
398#380C2312yes—
399#380C2312yes—
400#380C2314yes—
401#380C2318yes—
402#380C2318yes—
403#380C2318yes—
404#380C2312yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2312yes—
436C4×C22⋊C4C2312yes—
437#376C2314yes—
438#376C2312yes—
439#376C2312yes—
440C2×#95C2318yes—
441C2×#95C2318yes—
442C43C2312yes—
443C43C2311yescharacteristic
444C43C2312yes—
445C43C2312yes—
446C43C2311yescharacteristic
447C43C2311yescharacteristic
448C43C2311yescharacteristic
449C22×Q8C2411yescharacteristic
450C22×Q8C2414yes—
451C22×Q8C2418yes—
452C22×D4C2412yes—
453C22×D4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2418yes—
461C23×C4C2414yes—
462C23×C4C2418yes—
463C4⋊Q8—28no—
464C4⋊Q8—48no—
465C4⋊Q8—48no—
466C4⋊Q8—416no—
467#126C2×Q8116yes—
468#125—216no—
469#125—24no—
470#125—24no—
471#125—44no—
472#125—44no—
473#125—416no—
474#125—48no—
475#125—48no—
476#125—416no—
477#125C2×Q818yes—
478#124C2×Q818yes—
479#123C2×Q8116yes—
480C22⋊Q8—48no—
481C22⋊Q8—416no—
482C22⋊Q8—416no—
483C22⋊Q8—416no—
484C22⋊Q8C2×Q818yes—
485#121C2×Q818yes—
486C4×Q8—48no—
487C4×Q8—44no—
488C4×Q8—48no—
489C4×Q8C2×Q818yes—
490C4×D4—44no—
491C4×D4—48no—
492C4×D4—416no—
493C4×D4—48no—
494C4×D4C2×Q818yes—
495C4×D4C2×Q8116yes—
496#117—28no—
497#117—48no—
498#117C2×Q8116yes—
499C2×C4⋊C4—48no—
500C2×C4⋊C4—48no—
501C2×C4⋊C4—416no—
502C2×C4⋊C4—48no—
503C2×C4⋊C4—48no—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2414yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
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×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2411yescharacteristic
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2411yescharacteristic
552C2×C4⋊C4C2412yes—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2412yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2412yes—
567C2×C42—24no—
568C2×C42—24no—
569C2×C42—28no—
570C2×C42—44no—
571C2×C42—44no—
572C2×C42C2×Q818yes—
573C2×C42C2412yes—
574C2×C42C2414yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2411yescharacteristic
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2411yescharacteristic
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2418yes—
585C2×C42C2414yes—
586C2×C42C2418yes—
587C2×C42C2414yes—
588C2×C42C2418yes—
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2411yescharacteristic
596C2×C42C2412yes—
597C2×C42C2411yescharacteristic
598C2×C42C2411yescharacteristic
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602#95C2414yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2414yes—
612#95C2414yes—
613#95C2414yes—
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2412yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2414yes—
627#95C2412yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643C24C2512yes—
644C24C2511yescharacteristic
645C2×Q8—28no—
646C2×Q8—24no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—48no—
650C2×Q8—48no—
651C2×Q8—48no—
652C2×Q8C22×Q814yes—
653C2×D4—28no—
654C2×D4—24no—
655C2×D4C22×Q818yes—
656C2×D4C22×Q814yes—
657C22×C4—24no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—216no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—28no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—48no—
672C22×C4—48no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—48no—
678C22×C4C22×Q814yes—
679C22×C4C22×Q814yes—
680C22×C4C22×Q814yes—
681C22×C4C22×Q818yes—
682C22×C4C2512yes—
683C22×C4C2514yes—
684C22×C4C2514yes—
685C22×C4C2514yes—
686C22×C4C2514yes—
687C22×C4C2518yes—
688C22×C4C2514yes—
689C22×C4C2514yes—
690C22×C4C2512yes—
691C22×C4C2518yes—
692C22×C4C2512yes—
693C22×C4C2512yes—
694C22×C4C2511yescharacteristic
695C22×C4C2512yes—
696C22×C4C2511yescharacteristic
697C22×C4C2511yescharacteristic
698C22×C4C2511yescharacteristic
699C22×C4C2512yes—
700C22×C4C2512yes—
701C22×C4C2511yescharacteristic
702C22×C4C2511yescharacteristic
703C4⋊C4—28no—
704C4⋊C4—24no—
705C4⋊C4—28no—
706C4⋊C4—216no—
707C4⋊C4—216no—
708C4⋊C4—28no—
709C4⋊C4—24no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—28no—
716C4⋊C4—28no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—48no—
720C4⋊C4—44no—
721C4⋊C4—48no—
722C4⋊C4—44no—
723C4⋊C4—48no—
724C4⋊C4—48no—
725C4⋊C4—48no—
726C4⋊C4—48no—
727C4⋊C4—44no—
728C4⋊C4—48no—
729C4⋊C4—44no—
730C4⋊C4—44no—
731C4⋊C4—48no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—48no—
738C4⋊C4—48no—
739C4⋊C4—48no—
740C4⋊C4—48no—
741C4⋊C4—48no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4C22×Q818yes—
747C4⋊C4C22×Q818yes—
748C4⋊C4C22×Q814yes—
749C4⋊C4C22×Q818yes—
750C4⋊C4C22×Q814yes—
751C4⋊C4C22×Q818yes—
752C22⋊C4—28no—
753C22⋊C4—28no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—48no—
757C22⋊C4—48no—
758C22⋊C4—44no—
759C22⋊C4—48no—
760C22⋊C4—44no—
761C22⋊C4C22×Q818yes—
762C22⋊C4C22×Q818yes—
763C22⋊C4C22×Q818yes—
764C22⋊C4C22×Q818yes—
765C22⋊C4C22×Q818yes—
766C42—24no—
767C42—22no—
768C42—24no—
769C42—24no—
770C42—28no—
771C42—22no—
772C42—24no—
773C42—24no—
774C42—24no—
775C42—28no—
776C42—28no—
777C42—42no—
778C42—42no—
779C42—42no—
780C42—42no—
781C42—42no—
782C42—42no—
783C42—48no—
784C42—44no—
785C42—48no—
786C42—44no—
787C42—48no—
788C42C22×Q814yes—
789C42C22×Q814yes—
790C42C22×Q814yes—
791C42C22×Q814yes—
792C42C22×Q818yes—
793C42H(5,𝔽2)14yes—
794C422−1+414yes—
795C23—21no—
796C23—21no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23C23×Q814yes—
803C23C23×Q812yes—
804C23#58514yes—
805C23C2611yescharacteristic
806Q8—28no—
807Q8—88no—
808Q8—168no—
809D4—216no—
810D4—28no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—28no—
825C2×C4—28no—
826C2×C4—216no—
827C2×C4—28no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—28no—
849C2×C4—24no—
850C2×C4—28no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—28no—
858C2×C4—48no—
859C2×C4—48no—
860C2×C4—88no—
861C2×C4—816no—
862C2×C4—168no—
863C2×C4C23×Q812yes—
864C2×C4C23×Q812yes—
865C2×C4C23×Q812yes—
866C2×C4C23×Q812yes—
867C2×C4C23×Q814yes—
868C2×C4C23×Q814yes—
869C2×C4C23×Q814yes—
870C2×C4C23×Q812yes—
871C2×C4C23×Q812yes—
872C2×C4C2×H(5,𝔽2)14yes—
873C2×C4C2×H(5,𝔽2)12yes—
874C2×C4C2×2−1+414yes—
875C2×C4C2×2−1+412yes—
876C2×C4#58514yes—
877C22—24no—
878C22—22no—
879C22—22no—
880C22—24no—
881C22—24no—
882C22—24no—
883C22—24no—
884C22—44no—
885C22—44no—
886C22#350414yes—
887C22C24×Q811yescharacteristic
888C22C22×H(5,𝔽2)11yescharacteristic
889C22C22×2−1+411yescharacteristic
890C22C2×#58512yes—
891C22C2×#58512yes—
892C4—24no—
893C4—22no—
894C4—24no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—24no—
899C4—24no—
900C4—24no—
901C4—44no—
902C4—44no—
903C4—42no—
904C4—44no—
905C4—42no—
906C4—48no—
907C4—48no—
908C4—44no—
909C4—44no—
910C4—44no—
911C4#350314yes—
912C4#350414yes—
913C2—24no—
914C2—44no—
915C2#6275212yes—
916C2C2×#350311yescharacteristic
917C2C2×#350411yescharacteristic
918C2C2×#350411yescharacteristic
919C2#6283012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59664C2semidirect
3. #46151C2semidirect
4. #39754C2semidirect
5. #39686C2semidirect
6. #39682C2semidirect
7. #39675C2semidirect
8. #39370C2semidirect
9. #37687C2semidirect
10. #37623C2semidirect
11. #37429C2semidirect
12. #36635C2semidirect
13. C2×#2859C2semidirect
14. #36565C2semidirect
15. Q8×#125C2semidirect
16. #36192C2semidirect
17. #36191C2semidirect
18. #36165C2semidirect
19. #36165C2semidirect
20. #35336C2semidirect
21. #35330C2semidirect
176. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#596642
#594552
#461512
#397542
#396862
#396822
#396752
#393702
#376872
#376232
#374292
#366352
C2×#28592
#365652
Q8×#1252
#361922
#361912
#361652
#353362
#353302
#343842
C4×#5292