Finite Group Databasebeta

← #7645595

Subgroups — #7645595

Order 512.

4592 conjugacy classes of subgroups.

The subgroup lattice has 1429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42398C212yesmaximal, complemented
2#42396C212yesmaximal, complemented
3#42012C214yesmaximal, complemented
4#42010C214yesmaximal, complemented
5#41979C212yesmaximal, complemented
6#41977C212yesmaximal, complemented
7#39602C212yesmaximal, complemented
8#39474C212yesmaximal, complemented
9#39152C212yesmaximal, complemented
10#38926C212yesmaximal, complemented
11#38112C212yesmaximal, complemented
12#38110C212yesmaximal, complemented
13#37884C212yesmaximal, complemented
14#37882C212yesmaximal, complemented
15#37573C212yesmaximal, complemented
16#37571C212yesmaximal, complemented
17#36806C214yesmaximal, complemented
18#36799C214yesmaximal, complemented
19#35372C214yesmaximal, complemented
20#35218C212yesmaximal, complemented
21#35175C212yesmaximal, complemented
22#35138C211yesmaximal, characteristic, complemented
23#35104C211yesmaximal, characteristic, complemented
24#34999C214yesmaximal, complemented
25#34963C211yesmaximal, characteristic
26C2×#2566C211yesmaximal, characteristic, complemented
27#34239C211yesmaximal, characteristic, complemented
28#34126C211yesmaximal, characteristic, complemented
29#34060C211yesmaximal, characteristic, complemented
30C22×#125C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33#2857C2212yes—
34#2855C2214yescomplemented
35#2853C2214yescomplemented
36#2852C2214yescomplemented
37#2851C2212yes—
38#2851C2212yescomplemented
39#2851C2212yescomplemented
40#2851C2214yescomplemented
41#2838C2214yescomplemented
42#2836C2214yescomplemented
43#2831C2214yescomplemented
44#2829C2214yescomplemented
45#2797C2214yes—
46#2796C2214yes—
47#2794C2214yescomplemented
48#2794C2214yescomplemented
49#2793C2214yescomplemented
50#2790C2214yescomplemented
51#2786C2214yes—
52#2786C2214yescomplemented
53#2784C2214yescomplemented
54#2783C2214yescomplemented
55#2781C2214yescomplemented
56#2780C2214yescomplemented
57#2779C2214yescomplemented
58#2775C2214yescomplemented
59#2773C2214yescomplemented
60#2767C2214yescomplemented
61#2765C2214yescomplemented
62#2762C2214yescomplemented
63#2754C2214yescomplemented
64#2752C2214yes—
65#2751C2214yes—
66#2750C2214yescomplemented
67#2744C2214yescomplemented
68#2740C2214yes—
69#2730C2214yes—
70#2721C2214yescomplemented
71#2721C2214yescomplemented
72#2721C2214yescomplemented
73#2720C2214yescomplemented
74#2715C2214yescomplemented
75#2705C2214yes—
76#2695C2214yescomplemented
77#2667C2214yescomplemented
78#2665C2214yescomplemented
79#2664C2214yescomplemented
80#2662C2214yescomplemented
81#2654C2214yescomplemented
82#2653C2214yescomplemented
83#2652C2214yescomplemented
84#2652C2214yescomplemented
85#2652C2214yescomplemented
86#2650C2214yescomplemented
87#2649C2214yescomplemented
88#2648C2214yescomplemented
89#2647C2212yescomplemented
90#2647C2212yescomplemented
91#2644C2212yes—
92#2644C2212yes—
93#2634C2212yescomplemented
94#2633C2212yescomplemented
95#2629C2212yescomplemented
96#2628C2212yescomplemented
97#2627C2214yes—
98#2624C2212yes—
99#2624C2212yes—
100#2611C2214yescomplemented
101#2606C2212yescomplemented
102#2606C2212yescomplemented
103#2605C2212yescomplemented
104#2605C2212yescomplemented
105#2598C2214yes—
106#2597C2214yescomplemented
107#2595C2214yescomplemented
108#2589C2214yescomplemented
109#2587C2214yescomplemented
110#2584C2212yescomplemented
111#2580C2211yescharacteristic
112#2580C2211yescharacteristic
113#2577C2214yescomplemented
114#2575C2214yescomplemented
115#2574C2214yescomplemented
116#2574C2214yescomplemented
117#2573C2214yescomplemented
118#2573C2214yescomplemented
119#2570C2212yescomplemented
120#2570C2212yescomplemented
121#2566C2212yes—
122#2566C2212yes—
123#2566C2212yes—
124#2566C2212yes—
125#2566C2212yes—
126#2566C2212yes—
127#2566C2212yes—
128#2566C2212yes—
129#2562C2212yescomplemented
130#2556C2214yescomplemented
131#2554C2214yescomplemented
132#2550C2212yescomplemented
133#2550C2212yescomplemented
134#2535C2211yescharacteristic
135#2535C2211yescharacteristic
136#2523C2214yescomplemented
137#2517C2214yescomplemented
138#2513C2212yes—
139#2512C2212yes—
140#2509C2212yescomplemented
141#2508C2212yescomplemented
142#2506C2212yescomplemented
143#2506C2212yescomplemented
144#2505C2214yescomplemented
145#2498C2214yes—
146#2496C2212yescomplemented
147#2496C2212yescomplemented
148#2495C2212yescomplemented
149#2494C2212yescomplemented
150#2493C2214yes—
151#2493C2214yescomplemented
152#2491C2212yes—
153#2490C2212yes—
154#2488C2214yes—
155#2487C2212yes—
156#2487C2212yes—
157#2486C2212yes—
158#2484C2212yes—
159#2483C2214yes—
160#2482C2212yes—
161#2482C2214yes—
162#2481C2214yes—
163#2481C2214yes—
164#2480C2214yes—
165#2479C2214yescomplemented
166#2478C2214yescomplemented
167#2475C2214yescomplemented
168#2474C2214yescomplemented
169#2473C2214yes—
170#2473C2214yes—
171#2472C2214yes—
172#2468C2214yescomplemented
173#2468C2214yescomplemented
174#2466C2214yescomplemented
175#2460C2214yescomplemented
176#2454C2212yes—
177#2454C2214yescomplemented
178#2452C2212yes—
179#2450C2214yescomplemented
180#2447C2214yescomplemented
181#2438C2214yes—
182#2437C2214yes—
183#2422C2212yes—
184#2420C2212yes—
185#2419C2214yescomplemented
186#2412C2214yes—
187#2412C2214yes—
188#2411C2214yes—
189#2408C2212yes—
190#2406C2212yes—
191#2404C2212yes—
192#2398C2212yes—
193#2397C2212yes—
194C2×#396C2214yes—
195#2371C2212yescomplemented
196#2371C2212yescomplemented
197#2370C2212yescomplemented
198#2370C2212yescomplemented
199#2357C2211yescharacteristic
200#2357C2211yescharacteristic
201#2353C2212yes—
202#2353C2212yes—
203#2349C2211yescharacteristic
204#2349C2211yescharacteristic
205#2345C2212yes—
206#2345C2212yes—
207#2344C2214yes—
208#2344C2212yes—
209#2342C2214yes—
210D4×C22⋊C4C2212yes—
211#2336C2214yescomplemented
212#2331C2212yescomplemented
213#2330C2212yescomplemented
214#2329C2214yes—
215#2324C2212yes—
216#2324C2212yes—
217#2322C2214yes—
218#2320C2211yescharacteristic, complemented
219#2320C2211yescharacteristic, complemented
220#2319C2212yes—
221#2319C2212yes—
222#2319C2211yescharacteristic, complemented
223#2319C2211yescharacteristic, complemented
224#2318C2212yes—
225#2318C2212yes—
226#2317C2212yes—
227#2314C2212yescomplemented
228#2314C2212yescomplemented
229#2314C2212yescomplemented
230#2314C2212yescomplemented
231#2313C2212yes—
232#2311C2212yes—
233C4×#125C2212yescomplemented
234C4×#125C2212yescomplemented
235C4×#121C2212yes—
236C4×#121C2212yes—
237C4×#120C2214yes—
238#2295C2212yescomplemented
239#2293C2212yes—
240#2293C2212yescomplemented
241C2×#390C2211yescharacteristic
242C2×#390C2211yescharacteristic
243#2290C2212yes—
244#2290C2212yes—
245#2290C2214yes—
246C2×#385C2214yes—
247#2285C2212yescomplemented
248C2×#384C2211yescharacteristic
249#2283C2211yescharacteristic
250#2283C2211yescharacteristic
251#2283C2212yescomplemented
252C2×#382C2211yescharacteristic
253#2280C2212yes—
254#2274C2212yes—
255C42×D4C2212yes—
256C4×#117C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C22⋊C4C2212yes—
259C22×#41C2311yescharacteristic
260C23×D4C2311yescharacteristic
261C24×C4C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#125—28no—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#124C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#120C2314yes—
282C4×#41—28no—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×D4—28no—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2312yes—
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2314yes—
299C2×C4×D4C2314yes—
300C2×#117C2312yes—
301C2×#117C2311yescharacteristic
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2312yes—
305C2×#117C2314yes—
306C2×#117C2314yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2314yes—
314C22×C22⋊C4C2312yes—
315C22×C22⋊C4C2314yes—
316C22×C22⋊C4C2314yes—
317C22×C22⋊C4C2314yes—
318C22×C42C2312yes—
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2314yes—
322C22×C42C2311yescharacteristic
323#401C2314yes—
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#399C2314yes—
343#399C2314yes—
344#399C2312yes—
345#399C2312yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
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#397C2312yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#393C2312yes—
416#393C2314yes—
417#393C2312yes—
418#393C2314yes—
419#393C2314yes—
420#392C2312yes—
421#392C2314yes—
422#392C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2312yes—
480#388C2312yes—
481#388C2312yes—
482#388C2312yes—
483#388C2312yes—
484#388C2312yes—
485#388C2312yes—
486#388C2312yes—
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#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2312yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
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#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#386C2312yes—
558#386C2312yes—
559#386C2312yes—
560#386C2312yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2312yes—
581#385C2312yes—
582#385C2312yes—
583#385C2312yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
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#384C2312yes—
602#384C2312yes—
603#384C2312yes—
604#384C2312yes—
605#384C2312yes—
606#384C2312yes—
607#384C2312yes—
608#383C2312yes—
609#383C2314yes—
610#383C2312yes—
611#383C2312yes—
612#383C2312yes—
613#382C2311yescharacteristic
614#382C2311yescharacteristic
615#382C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2312yes—
622#382C2311yescharacteristic
623#382C2312yes—
624#382C2312yes—
625#382C2314yes—
626#382C2311yescharacteristic
627#381C2314yes—
628#381C2312yes—
629#381C2314yes—
630#381C2312yes—
631#381C2312yes—
632#381C2314yes—
633#381C2314yes—
634#381C2312yes—
635#381C2314yes—
636#381C2312yes—
637#381C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2312yes—
660#379C2314yes—
661#379C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C22⋊C4C2311yescharacteristic
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704#376C2312yes—
705#376C2312yes—
706#376C2311yescharacteristic
707#376C2311yescharacteristic
708#376C2312yes—
709#376C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2314yes—
714C43C2312yes—
715C25C2412yes—
716C2×#41—24no—
717C2×#41—44no—
718C22×Q8C2411yescharacteristic
719C22×Q8C2414yes—
720C22×D4—24no—
721C22×D4—24no—
722C22×D4—42no—
723C22×D4C2412yes—
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C22×D4C2414yes—
729C22×D4C2414yes—
730C23×C4—28no—
731C23×C4—84no—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2414yes—
748C23×C4C2411yescharacteristic
749C4⋊Q8—44no—
750#126—84no—
751#126—84no—
752#126—84no—
753#125—28no—
754#125—28no—
755#125—28no—
756#125—28no—
757#125—44no—
758#125—84no—
759#125—84no—
760#124—84no—
761#123—48no—
762#123—84no—
763C22⋊Q8—48no—
764C22⋊Q8—84no—
765#121—28no—
766#121—44no—
767#120—48no—
768C4×Q8—24no—
769C4×Q8—24no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—24no—
774C4×D4—24no—
775C4×D4—28no—
776C4×D4—24no—
777C4×D4—24no—
778C4×D4—28no—
779C4×D4—24no—
780C4×D4—24no—
781C4×D4—44no—
782C4×D4—84no—
783C4×D4—84no—
784#117—24no—
785#117—28no—
786#117—44no—
787#117—44no—
788#117—44no—
789#117—48no—
790#117—84no—
791C2×C4⋊C4—24no—
792C2×C4⋊C4—24no—
793C2×C4⋊C4—28no—
794C2×C4⋊C4—28no—
795C2×C4⋊C4—24no—
796C2×C4⋊C4—44no—
797C2×C4⋊C4—84no—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C22⋊C4—28no—
857C2×C22⋊C4—48no—
858C2×C22⋊C4—48no—
859C2×C22⋊C4—84no—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C42—28no—
906C2×C42—42no—
907C2×C42—42no—
908C2×C42—84no—
909C2×C42#4118yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2411yescharacteristic
937#95C2411yescharacteristic
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2411yescharacteristic
952#95C2411yescharacteristic
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
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—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009C24—24no—
1010C24—24no—
1011C24—28no—
1012C24—44no—
1013C24—42no—
1014C24C2512yes—
1015C24C2512yes—
1016C24C2512yes—
1017C24C2511yescharacteristic
1018#41—416no—
1019C2×Q8—22no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—28no—
1029C2×D4—22no—
1030C2×D4—24no—
1031C2×D4—22no—
1032C2×D4—22no—
1033C2×D4—22no—
1034C2×D4—22no—
1035C2×D4—22no—
1036C2×D4—416no—
1037C2×D4—42no—
1038C2×D4—42no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D42−1+414yes—
1045C22×C4—24no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—28no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—28no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—816no—
1085C22×C4C2×#4114yes—
1086C22×C4C2×#4114yes—
1087C22×C4C2×#4114yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C22⋊C4—24no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—28no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—42no—
1213C22⋊C4—44no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C42—24no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—41no—
1224C42—41no—
1225C42—41no—
1226C42—41no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42—44no—
1235C42—42no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42C2×#4114yes—
1240C42C2×#4114yes—
1241C42C2×#4114yes—
1242C42C2×#4114yes—
1243C23—21no—
1244C23—21no—
1245C23—22no—
1246C23—22no—
1247C23—24no—
1248C23—22no—
1249C23—24no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—22no—
1254C23—24no—
1255C23—22no—
1256C23—22no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—24no—
1262C23—48no—
1263C23—416no—
1264C23—48no—
1265C23—84no—
1266C23—88no—
1267C23C22×#4112yes—
1268C23C2×2−1+414yes—
1269C23#58514yes—
1270C23C2611yescharacteristic
1271Q8—44no—
1272Q8—164no—
1273D4—28no—
1274D4—48no—
1275D4—44no—
1276D4—48no—
1277D4—44no—
1278D4—88no—
1279D4—88no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—28no—
1287C2×C4—28no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—44no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—48no—
1347C2×C4—48no—
1348C2×C4—48no—
1349C2×C4—48no—
1350C2×C4—84no—
1351C2×C4—84no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—84no—
1355C2×C4—88no—
1356C2×C4—84no—
1357C2×C4—88no—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4C2×2−1+412yes—
1365C2×C4#58512yes—
1366C22—22no—
1367C22—22no—
1368C22—24no—
1369C22—24no—
1370C22—24no—
1371C22—28no—
1372C22—42no—
1373C22—44no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—44no—
1381C22—42no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—44no—
1387C22—816no—
1388C22#345514yes—
1389C22C23×#4111yescharacteristic
1390C22C22×2−1+411yescharacteristic
1391C22C2×#58511yescharacteristic
1392C22C2×#58512yes—
1393C22H(7,𝔽2)12yes—
1394C4—22no—
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—22no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—42no—
1411C4—44no—
1412C4—44no—
1413C4—42no—
1414C4—42no—
1415C4—44no—
1416C4—42no—
1417C4—44no—
1418C4#349514yes—
1419C2—24no—
1420C2—44no—
1421C2—82no—
1422C2—82no—
1423C2C2×#345511yescharacteristic
1424C2C2×#349511yescharacteristic
1425C2#6285511yescharacteristic
1426C2#6293512yes—
1427C2#6294812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34963C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42398C2semidirect
2. #42396C2semidirect
3. #42012C2semidirect
4. #42010C2semidirect
5. #41979C2semidirect
6. #41977C2semidirect
7. #39602C2semidirect
8. #39474C2semidirect
9. #39152C2semidirect
10. #38926C2semidirect
11. #38112C2semidirect
12. #38110C2semidirect
13. #37884C2semidirect
14. #37882C2semidirect
15. #37573C2semidirect
16. #37571C2semidirect
17. #36806C2semidirect
18. #36799C2semidirect
19. #35372C2semidirect
20. #35218C2semidirect
21. #35175C2semidirect
22. #35138C2semidirect
23. #35104C2semidirect
24. #34999C2semidirect
26. C2×#2566C2semidirect
27. #34239C2semidirect
28. #34126C2semidirect
29. #34060C2semidirect
34. #2855C22semidirect
35. #2853C22semidirect
36. #2852C22semidirect
38. #2851C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
41. #2838C22semidirect
42. #2836C22semidirect
43. #2831C22semidirect
44. #2829C22semidirect
47. #2794C22semidirect
48. #2794C22semidirect
49. #2793C22semidirect
50. #2790C22semidirect
52. #2786C22semidirect
53. #2784C22semidirect
54. #2783C22semidirect
55. #2781C22semidirect
56. #2780C22semidirect
57. #2779C22semidirect
58. #2775C22semidirect
59. #2773C22semidirect
60. #2767C22semidirect
61. #2765C22semidirect
62. #2762C22semidirect
63. #2754C22semidirect
66. #2750C22semidirect
67. #2744C22semidirect
70. #2721C22semidirect
71. #2721C22semidirect
72. #2721C22semidirect
73. #2720C22semidirect
74. #2715C22semidirect
76. #2695C22semidirect
77. #2667C22semidirect
78. #2665C22semidirect
79. #2664C22semidirect
80. #2662C22semidirect
81. #2654C22semidirect
82. #2653C22semidirect
83. #2652C22semidirect
84. #2652C22semidirect
85. #2652C22semidirect
86. #2650C22semidirect
87. #2649C22semidirect
88. #2648C22semidirect
89. #2647C22semidirect
90. #2647C22semidirect
93. #2634C22semidirect
94. #2633C22semidirect
95. #2629C22semidirect
96. #2628C22semidirect
100. #2611C22semidirect
101. #2606C22semidirect
102. #2606C22semidirect
103. #2605C22semidirect
104. #2605C22semidirect
106. #2597C22semidirect
107. #2595C22semidirect
108. #2589C22semidirect
109. #2587C22semidirect
110. #2584C22semidirect
113. #2577C22semidirect
114. #2575C22semidirect
115. #2574C22semidirect
116. #2574C22semidirect
117. #2573C22semidirect
118. #2573C22semidirect
119. #2570C22semidirect
120. #2570C22semidirect
129. #2562C22semidirect
130. #2556C22semidirect
131. #2554C22semidirect
132. #2550C22semidirect
133. #2550C22semidirect
136. #2523C22semidirect
137. #2517C22semidirect
140. #2509C22semidirect
141. #2508C22semidirect
142. #2506C22semidirect
143. #2506C22semidirect
144. #2505C22semidirect
146. #2496C22semidirect
147. #2496C22semidirect
148. #2495C22semidirect
149. #2494C22semidirect
151. #2493C22semidirect
165. #2479C22semidirect
166. #2478C22semidirect
167. #2475C22semidirect
168. #2474C22semidirect
172. #2468C22semidirect
173. #2468C22semidirect
174. #2466C22semidirect
175. #2460C22semidirect
177. #2454C22semidirect
179. #2450C22semidirect
180. #2447C22semidirect
185. #2419C22semidirect
195. #2371C22semidirect
196. #2371C22semidirect
197. #2370C22semidirect
198. #2370C22semidirect
211. #2336C22semidirect
212. #2331C22semidirect
213. #2330C22semidirect
218. #2320C22semidirect
219. #2320C22semidirect
222. #2319C22semidirect
223. #2319C22semidirect
227. #2314C22semidirect
228. #2314C22semidirect
229. #2314C22semidirect
230. #2314C22semidirect
233. C4×#125C22semidirect
234. C4×#125C22semidirect
238. #2295C22semidirect
240. #2293C22semidirect
247. #2285C22semidirect
251. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#423982
#423962
#420122
#420102
#419792
#419772
#396022
#394742
#391522
#389262
#381122
#381102
#378842
#378822
#375732
#375712
#368062
#367992
#353722
#352182
#351752
#351382
#351042
#349992
#349632
C2×#25662
#342392
#341262
#340602