Finite Group Databasebeta

← #7655380

Subgroups — #7655380

Order 512.

4458 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41751C214yesmaximal, complemented
2#41391C212yesmaximal, complemented
3#41095C214yesmaximal, complemented
4#40541C212yesmaximal, complemented
5#40323C214yesmaximal, complemented
6#39811C212yesmaximal, complemented
7#39809C212yesmaximal, complemented
8#38707C214yesmaximal, complemented
9#38469C214yesmaximal, complemented
10#38241C212yesmaximal, complemented
11#38236C212yesmaximal, complemented
12#38057C212yesmaximal, complemented
13#38054C212yesmaximal
14#37581C212yesmaximal, complemented
15#37537C211yesmaximal, characteristic
16#36344C214yesmaximal, complemented
17#36293C212yesmaximal
18#36279C212yesmaximal, complemented
19#36013C212yesmaximal, complemented
20#35705C212yesmaximal, complemented
21#35248C211yesmaximal, characteristic, complemented
22#35235C211yesmaximal, characteristic, complemented
23#35188C212yesmaximal, complemented
24#35117C212yesmaximal, complemented
25#34902C212yesmaximal, complemented
26C2×#2592C211yesmaximal, characteristic
27#34240C211yesmaximal, characteristic
28#34145C211yesmaximal, characteristic, complemented
29#34128C211yesmaximal, characteristic, complemented
30C2×#533C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2866C2214yescomplemented
34#2865C2214yescomplemented
35#2863C2212yescomplemented
36#2862C2212yescomplemented
37#2861C2212yes—
38#2860C2212yes—
39#2855C2214yes—
40#2855C2212yes—
41#2855C2212yes—
42#2838C2214yescomplemented
43#2831C2214yescomplemented
44#2820C2214yes—
45#2807C2214yescomplemented
46#2798C2214yescomplemented
47#2798C2214yescomplemented
48#2798C2214yescomplemented
49#2787C2214yescomplemented
50#2783C2214yescomplemented
51#2777C2214yescomplemented
52#2773C2214yescomplemented
53#2773C2214yescomplemented
54#2771C2214yescomplemented
55#2762C2214yescomplemented
56#2762C2214yescomplemented
57#2761C2214yes—
58#2759C2214yescomplemented
59#2758C2214yescomplemented
60#2757C2214yes—
61#2755C2214yescomplemented
62#2754C2214yescomplemented
63#2754C2214yescomplemented
64#2737C2214yes—
65#2723C2214yes—
66#2716C2214yescomplemented
67#2716C2214yescomplemented
68#2689C2214yescomplemented
69#2666C2214yescomplemented
70#2665C2214yescomplemented
71#2658C2211yescharacteristic
72#2658C2211yescharacteristic
73#2654C2214yescomplemented
74#2654C2214yescomplemented
75#2652C2214yescomplemented
76#2650C2214yescomplemented
77#2650C2214yescomplemented
78#2650C2214yescomplemented
79#2645C2212yescomplemented
80#2644C2212yes—
81#2642C2212yescomplemented
82#2640C2211yescharacteristic
83#2640C2211yescharacteristic
84#2640C2212yes—
85#2637C2214yescomplemented
86#2634C2212yescomplemented
87#2634C2212yescomplemented
88#2632C2212yes—
89#2632C2212yes—
90#2626C2212yes—
91#2626C2212yes—
92#2612C2214yescomplemented
93#2607C2214yescomplemented
94#2606C2212yescomplemented
95#2605C2214yescomplemented
96#2605C2212yescomplemented
97#2597C2214yes—
98#2596C2214yescomplemented
99#2596C2214yescomplemented
100#2596C2214yescomplemented
101#2594C2214yescomplemented
102#2594C2214yescomplemented
103#2592C2212yes—
104#2592C2211yescharacteristic
105#2592C2214yes—
106#2592C2211yescharacteristic
107#2592C2212yes—
108#2592C2212yes—
109#2592C2211yescharacteristic
110#2592C2212yes—
111#2592C2211yescharacteristic
112#2589C2214yescomplemented
113#2589C2214yescomplemented
114#2586C2214yescomplemented
115#2581C2212yescomplemented
116#2581C2212yescomplemented
117#2577C2214yescomplemented
118#2577C2214yescomplemented
119#2575C2214yescomplemented
120#2575C2214yescomplemented
121#2575C2214yescomplemented
122#2574C2214yescomplemented
123#2573C2214yescomplemented
124#2570C2212yescomplemented
125#2569C2212yes—
126#2569C2214yes—
127#2568C2212yescomplemented
128#2561C2214yes—
129#2550C2212yescomplemented
130#2549C2212yes—
131#2546C2212yescomplemented
132#2545C2212yes—
133#2545C2212yes—
134#2532C2214yescomplemented
135#2532C2214yescomplemented
136#2531C2214yes—
137#2530C2214yescomplemented
138#2529C2214yescomplemented
139#2527C2214yescomplemented
140#2527C2214yescomplemented
141#2526C2214yes—
142#2525C2214yescomplemented
143#2523C2214yescomplemented
144#2520C2214yescomplemented
145#2517C2214yescomplemented
146#2515C2214yescomplemented
147#2514C2212yescomplemented
148#2513C2212yes—
149#2512C2212yes—
150#2511C2212yescomplemented
151#2505C2214yes—
152#2505C2214yes—
153#2503C2212yes—
154#2493C2214yes—
155#2493C2214yes—
156#2492C2214yescomplemented
157#2484C2214yes—
158#2483C2214yes—
159#2482C2214yes—
160#2482C2214yes—
161#2480C2214yes—
162#2480C2214yes—
163#2479C2214yes—
164#2478C2214yescomplemented
165#2469C2214yescomplemented
166#2465C2214yescomplemented
167#2454C2212yes—
168#2453C2212yescomplemented
169#2452C2212yes—
170#2451C2212yescomplemented
171#2448C2212yes—
172#2448C2212yes—
173#2447C2212yes—
174#2447C2212yes—
175#2446C2212yescomplemented
176#2446C2212yescomplemented
177#2446C2212yescomplemented
178#2446C2212yescomplemented
179#2442C2212yes—
180#2440C2212yes—
181#2439C2214yescomplemented
182#2438C2214yes—
183#2437C2214yes—
184#2435C2212yes—
185#2434C2212yes—
186#2434C2212yes—
187#2401C2214yescomplemented
188#2396C2214yescomplemented
189C2×#397C2212yes—
190C2×#393C2212yes—
191#2372C2214yes—
192#2370C2214yescomplemented
193#2369C2212yescomplemented
194#2368C2212yes—
195#2368C2212yes—
196#2368C2214yes—
197#2367C2212yes—
198#2367C2212yes—
199#2365C2212yescomplemented
200#2360C2212yes—
201#2360C2212yes—
202#2356C2212yescomplemented
203#2356C2212yescomplemented
204#2356C2212yescomplemented
205#2351C2212yescomplemented
206#2344C2212yes—
207#2344C2211yescharacteristic
208#2344C2211yescharacteristic
209#2344C2212yes—
210#2343C2214yes—
211#2342C2212yes—
212#2342C2214yes—
213#2342C2214yes—
214#2342C2212yes—
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219D4×C22⋊C4C2211yescharacteristic
220D4×C22⋊C4C2211yescharacteristic
221#2337C2214yes—
222#2334C2214yescomplemented
223#2332C2214yescomplemented
224#2331C2212yescomplemented
225#2330C2212yescomplemented
226#2327C2214yescomplemented
227#2327C2212yescomplemented
228#2326C2212yes—
229#2320C2212yescomplemented
230#2319C2212yes—
231#2312C2212yes—
232C4×C4⋊Q8C2212yescomplemented
233C4×#126C2214yescomplemented
234C4×#124C2212yes—
235C4×#124C2212yes—
236C4×#124C2212yes—
237#2298C2214yescomplemented
238#2296C2212yes—
239#2295C2212yescomplemented
240#2295C2214yescomplemented
241#2295C2212yescomplemented
242#2295C2212yescomplemented
243#2295C2212yescomplemented
244#2295C2212yescomplemented
245C2×#391C2212yes—
246#2293C2212yes—
247C2×#390C2212yes—
248C2×#388C2214yes—
249#2283C2211yescharacteristic
250#2283C2212yes—
251#2283C2211yescharacteristic
252#2273C2212yes—
253C42×Q8C2212yescomplemented
254C42×Q8C2212yescomplemented
255C4×#117C2211yescharacteristic
256C4×#117C2212yes—
257C4×#117C2212yes—
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261C23×D4C2311yescharacteristic
262#533—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2312yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#124—28no—
274C2×#124C2312yes—
275C2×#124C2311yescharacteristic
276C2×#124C2311yescharacteristic
277C2×#124C2312yes—
278C2×#124C2311yescharacteristic
279C2×#124C2311yescharacteristic
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C4×Q8—28no—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×#117C2312yes—
304C2×#117C2311yescharacteristic
305C2×#117C2312yes—
306C2×#117C2311yescharacteristic
307C2×#117C2314yes—
308C2×#117C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2312yes—
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2312yes—
317C22×C22⋊C4C2314yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2312yes—
347#399C2314yes—
348#399C2314yes—
349#399C2312yes—
350#399C2314yes—
351#399C2312yes—
352#399C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2312yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2314yes—
379#397C2312yes—
380#397C2312yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2312yes—
407#393C2312yes—
408#393C2314yes—
409#393C2314yes—
410#393C2312yes—
411#393C2312yes—
412#393C2314yes—
413#393C2312yes—
414#393C2312yes—
415#393C2312yes—
416#393C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2314yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#386C2314yes—
586#386C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#384C2312yes—
604#383C2314yes—
605#383C2314yes—
606#383C2314yes—
607#383C2312yes—
608#383C2311yescharacteristic
609#383C2311yescharacteristic
610#383C2312yes—
611#383C2312yes—
612#382C2312yes—
613#382C2314yes—
614#382C2312yes—
615#382C2312yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2312yes—
620#382C2312yes—
621#381C2312yes—
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#381C2314yes—
626#381C2312yes—
627#381C2314yes—
628#381C2312yes—
629#381C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2311yescharacteristic
633#380C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2314yes—
637#380C2311yescharacteristic
638#380C2311yescharacteristic
639#380C2311yescharacteristic
640#380C2312yes—
641#379C2312yes—
642#379C2314yes—
643#379C2312yes—
644#379C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2311yescharacteristic
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2311yescharacteristic
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698#376C2312yes—
699#376C2312yes—
700#376C2312yes—
701#376C2311yescharacteristic
702#376C2311yescharacteristic
703#376C2314yes—
704#376C2312yes—
705#376C2312yes—
706#376C2312yes—
707#376C2314yes—
708C2×#95C2312yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C43C2314yes—
712C43C2312yes—
713C43C2312yes—
714C43C2312yes—
715C25C2412yes—
716C22×Q8—24no—
717C22×Q8—24no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×D4—24no—
730C22×D4—44no—
731C22×D4C2411yescharacteristic
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2411yescharacteristic
743C4⋊Q8—24no—
744C4⋊Q8—24no—
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8—48no—
749#126—48no—
750#126—48no—
751#125—28no—
752#125—44no—
753#124—24no—
754#124—24no—
755#124—28no—
756#124—28no—
757#124—24no—
758#124—24no—
759#124—44no—
760#124—44no—
761C22⋊Q8—28no—
762C22⋊Q8—28no—
763C22⋊Q8—48no—
764C22⋊Q8—48no—
765C4×Q8—24no—
766C4×Q8—24no—
767C4×Q8—28no—
768C4×Q8—24no—
769C4×Q8—24no—
770C4×Q8—28no—
771C4×Q8—28no—
772C4×Q8—28no—
773C4×Q8—44no—
774C4×Q8—44no—
775C4×Q8—44no—
776C4×Q8—44no—
777C4×Q8—44no—
778C4×Q8—44no—
779C4×D4—44no—
780C4×D4—44no—
781#117—28no—
782#117—24no—
783#117—28no—
784#117—48no—
785#117—42no—
786#117—44no—
787C2×C4⋊C4—24no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C22⋊C4—28no—
844C2×C22⋊C4—28no—
845C2×C22⋊C4—28no—
846C2×C22⋊C4—48no—
847C2×C22⋊C4—44no—
848C2×C22⋊C4—48no—
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2411yescharacteristic
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2411yescharacteristic
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2411yescharacteristic
888C2×C42—28no—
889C2×C42—44no—
890C2×C42#4118yes—
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2411yescharacteristic
957#95C2411yescharacteristic
958#95C2412yes—
959#95C2412yes—
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006C24—24no—
1007C24—24no—
1008C24—24no—
1009C24—44no—
1010C24—44no—
1011C24C2512yes—
1012C24C2512yes—
1013C24C2511yescharacteristic
1014C2×Q8—22no—
1015C2×Q8—24no—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—22no—
1019C2×Q8—22no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—416no—
1036C2×Q8—88no—
1037C2×D4—22no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—44no—
1043C2×D4—88no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—28no—
1053C22×C4—24no—
1054C22×C4—28no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4C2×#4114yes—
1066C22×C4C2×#4114yes—
1067C22×C4C2×#4114yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2514yes—
1081C22×C4C2514yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—22no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C22⋊C4—28no—
1148C22⋊C4—24no—
1149C22⋊C4—22no—
1150C22⋊C4—24no—
1151C22⋊C4—22no—
1152C22⋊C4—24no—
1153C22⋊C4—22no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—24no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C42−1+414yes—
1186C42—24no—
1187C42—24no—
1188C42—24no—
1189C42—24no—
1190C42—28no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—42no—
1201C42—42no—
1202C42—44no—
1203C42—44no—
1204C42—42no—
1205C42—42no—
1206C42—42no—
1207C42—42no—
1208C42—42no—
1209C42—44no—
1210C42—44no—
1211C42—42no—
1212C42—42no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42C2×#4114yes—
1218C42C2×#4114yes—
1219C42C2×#4114yes—
1220C42C2×#4114yes—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—24no—
1228C23—24no—
1229C23—22no—
1230C23—22no—
1231C23—24no—
1232C23—24no—
1233C23—48no—
1234C23—84no—
1235C23—88no—
1236C23—88no—
1237C23—84no—
1238C23C22×#4112yes—
1239C23C2×2−1+412yes—
1240C23#58512yes—
1241C23C2611yescharacteristic
1242Q8—28no—
1243Q8—48no—
1244Q8—44no—
1245Q8—48no—
1246Q8—44no—
1247Q8—44no—
1248Q8—84no—
1249Q8—84no—
1250Q8—164no—
1251D4—44no—
1252D4—44no—
1253D4—84no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—28no—
1266C2×C4—28no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—44no—
1320C2×C4—48no—
1321C2×C4—48no—
1322C2×C4—88no—
1323C2×C4—88no—
1324C2×C4—84no—
1325C2×C4—164no—
1326C2×C4C22×#4112yes—
1327C2×C4C22×#4112yes—
1328C2×C4C22×#4112yes—
1329C2×C4C22×#4112yes—
1330C2×C4C22×#4112yes—
1331C2×C4C22×#4112yes—
1332C2×C4C2×2−1+414yes—
1333C2×C4#58514yes—
1334C2×C4#58514yes—
1335C22—24no—
1336C22—24no—
1337C22—22no—
1338C22—22no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—168no—
1350C22#346114yes—
1351C22C23×#4111yescharacteristic
1352C22C22×2−1+411yescharacteristic
1353C22C2×#58512yes—
1354C22C2×#58512yes—
1355C22C2×#58511yescharacteristic
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—24no—
1361C4—22no—
1362C4—22no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—44no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—44no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4#351014yes—
1382C2—24no—
1383C2—82no—
1384C2—82no—
1385C2C2×#346111yescharacteristic
1386C2C2×#351011yescharacteristic
1387C2#6281411yescharacteristic
1388C2#6302512yes—
1389C2#6303012yes—
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. #41751C2semidirect
2. #41391C2semidirect
3. #41095C2semidirect
4. #40541C2semidirect
5. #40323C2semidirect
6. #39811C2semidirect
7. #39809C2semidirect
8. #38707C2semidirect
9. #38469C2semidirect
10. #38241C2semidirect
11. #38236C2semidirect
12. #38057C2semidirect
14. #37581C2semidirect
16. #36344C2semidirect
18. #36279C2semidirect
19. #36013C2semidirect
20. #35705C2semidirect
21. #35248C2semidirect
22. #35235C2semidirect
23. #35188C2semidirect
24. #35117C2semidirect
25. #34902C2semidirect
28. #34145C2semidirect
29. #34128C2semidirect
33. #2866C22semidirect
34. #2865C22semidirect
35. #2863C22semidirect
36. #2862C22semidirect
42. #2838C22semidirect
43. #2831C22semidirect
45. #2807C22semidirect
46. #2798C22semidirect
47. #2798C22semidirect
48. #2798C22semidirect
49. #2787C22semidirect
50. #2783C22semidirect
51. #2777C22semidirect
52. #2773C22semidirect
53. #2773C22semidirect
54. #2771C22semidirect
55. #2762C22semidirect
56. #2762C22semidirect
58. #2759C22semidirect
59. #2758C22semidirect
61. #2755C22semidirect
62. #2754C22semidirect
63. #2754C22semidirect
66. #2716C22semidirect
67. #2716C22semidirect
68. #2689C22semidirect
69. #2666C22semidirect
70. #2665C22semidirect
73. #2654C22semidirect
74. #2654C22semidirect
75. #2652C22semidirect
76. #2650C22semidirect
77. #2650C22semidirect
78. #2650C22semidirect
79. #2645C22semidirect
81. #2642C22semidirect
85. #2637C22semidirect
86. #2634C22semidirect
87. #2634C22semidirect
92. #2612C22semidirect
93. #2607C22semidirect
94. #2606C22semidirect
95. #2605C22semidirect
96. #2605C22semidirect
98. #2596C22semidirect
99. #2596C22semidirect
100. #2596C22semidirect
101. #2594C22semidirect
102. #2594C22semidirect
112. #2589C22semidirect
113. #2589C22semidirect
114. #2586C22semidirect
115. #2581C22semidirect
116. #2581C22semidirect
117. #2577C22semidirect
118. #2577C22semidirect
119. #2575C22semidirect
120. #2575C22semidirect
121. #2575C22semidirect
122. #2574C22semidirect
123. #2573C22semidirect
124. #2570C22semidirect
127. #2568C22semidirect
129. #2550C22semidirect
131. #2546C22semidirect
134. #2532C22semidirect
135. #2532C22semidirect
137. #2530C22semidirect
138. #2529C22semidirect
139. #2527C22semidirect
140. #2527C22semidirect
142. #2525C22semidirect
143. #2523C22semidirect
144. #2520C22semidirect
145. #2517C22semidirect
146. #2515C22semidirect
147. #2514C22semidirect
150. #2511C22semidirect
156. #2492C22semidirect
164. #2478C22semidirect
165. #2469C22semidirect
166. #2465C22semidirect
168. #2453C22semidirect
170. #2451C22semidirect
175. #2446C22semidirect
176. #2446C22semidirect
177. #2446C22semidirect
178. #2446C22semidirect
181. #2439C22semidirect
187. #2401C22semidirect
188. #2396C22semidirect
192. #2370C22semidirect
193. #2369C22semidirect
199. #2365C22semidirect
202. #2356C22semidirect
203. #2356C22semidirect
204. #2356C22semidirect
205. #2351C22semidirect
222. #2334C22semidirect
223. #2332C22semidirect
224. #2331C22semidirect
225. #2330C22semidirect
226. #2327C22semidirect
227. #2327C22semidirect
229. #2320C22semidirect
232. C4×C4⋊Q8C22semidirect
233. C4×#126C22semidirect
237. #2298C22semidirect
239. #2295C22semidirect
240. #2295C22semidirect
241. #2295C22semidirect
242. #2295C22semidirect
243. #2295C22semidirect
244. #2295C22semidirect
253. C42×Q8C22semidirect
254. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#417512
#413912
#410952
#405412
#403232
#398112
#398092
#387072
#384692
#382412
#382362
#380572
#380542
#375812
#375372
#363442
#362932
#362792
#360132
#357052
#352482
#352352
#351882
#351172
#349022
C2×#25922
#342402
#341452
#341282