Finite Group Databasebeta

← #7681446

Subgroups — #7681446

Order 512.

4902 conjugacy classes of subgroups.

The subgroup lattice has 1508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59591C214yesmaximal, complemented
2#59576C214yesmaximal, complemented
3#59552C214yesmaximal, complemented
4#59541C214yesmaximal, complemented
5#44570C214yesmaximal, complemented
6#44562C214yesmaximal, complemented
7#44130C214yesmaximal, complemented
8#44122C214yesmaximal, complemented
9#39510C211yesmaximal, characteristic, complemented
10#39500C211yesmaximal, characteristic, complemented
11#39462C212yesmaximal, complemented
12#37975C212yesmaximal, complemented
13#37969C212yesmaximal, complemented
14#37898C211yesmaximal, characteristic, complemented
15#37893C211yesmaximal, characteristic, complemented
16#37889C211yesmaximal, characteristic, complemented
17#37883C211yesmaximal, characteristic, complemented
18#36200C212yesmaximal, complemented
19#36191C211yesmaximal, characteristic, complemented
20#36182C211yesmaximal, characteristic, complemented
21#35590C212yesmaximal, complemented
22#35589C212yesmaximal, complemented
23#35337C211yesmaximal, characteristic, complemented
24#35259C211yesmaximal, characteristic, complemented
25#35259C211yesmaximal, characteristic, complemented
26#34917C212yesmaximal, complemented
27#34319C212yesmaximal, complemented
28#34189C211yesmaximal, characteristic, complemented
29#34188C211yesmaximal, characteristic, complemented
30#34141C211yesmaximal, characteristic, complemented
31C4×#540C211yesmaximal, characteristic, complemented
32C2×#553C2212yes—
33C2×#540C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37#2862C2211yescharacteristic
38#2859C2211yescharacteristic
39#2856C2211yescharacteristic
40#2856C2211yescharacteristic
41#2854C2212yes—
42#2854C2212yes—
43#2851C2211yescharacteristic
44#2851C2212yes—
45#2851C2211yescharacteristic
46#2808C2214yes—
47#2800C2214yes—
48#2793C2214yes—
49#2791C2214yes—
50#2787C2214yes—
51#2779C2214yes—
52#2776C2214yes—
53#2763C2214yes—
54#2761C2214yes—
55#2760C2214yes—
56#2759C2214yes—
57#2753C2214yes—
58#2753C2214yes—
59#2752C2214yes—
60#2749C2214yes—
61#2733C2214yes—
62#2716C2214yes—
63#2714C2214yes—
64#2706C2214yes—
65#2703C2214yes—
66#2696C2214yes—
67#2691C2214yes—
68#2688C2214yes—
69#2673C2214yes—
70#2647C2211yescharacteristic
71#2647C2211yescharacteristic
72#2629C2211yescharacteristic
73#2629C2211yescharacteristic
74#2628C2212yes—
75#2619C2211yescharacteristic
76#2619C2211yescharacteristic
77#2615C2212yes—
78#2615C2212yes—
79#2610C2214yes—
80#2610C2214yes—
81#2598C2214yes—
82#2597C2214yes—
83#2597C2214yes—
84#2594C2214yes—
85#2594C2214yes—
86#2589C2214yes—
87#2589C2214yes—
88#2588C2214yes—
89#2588C2214yes—
90#2578C2214yes—
91#2577C2214yes—
92#2576C2214yes—
93#2576C2214yes—
94#2574C2214yes—
95#2574C2214yes—
96#2572C2214yes—
97#2570C2212yes—
98#2566C2212yes—
99#2562C2212yes—
100#2560C2214yes—
101#2557C2214yes—
102#2557C2214yes—
103#2557C2214yes—
104#2554C2214yes—
105#2543C2214yes—
106#2535C2212yes—
107#2532C2214yes—
108#2532C2214yes—
109#2529C2214yes—
110#2529C2214yes—
111#2528C2214yes—
112#2527C2214yes—
113#2526C2214yes—
114#2525C2214yes—
115#2525C2214yes—
116#2520C2214yes—
117#2515C2214yes—
118#2515C2214yes—
119#2513C2212yes—
120#2512C2212yes—
121#2512C2214yes—
122#2509C2212yes—
123#2507C2212yes—
124#2504C2212yes—
125#2500C2212yes—
126#2497C2212yes—
127#2495C2212yes—
128#2494C2212yes—
129#2494C2212yes—
130#2491C2212yes—
131#2491C2212yes—
132#2486C2212yes—
133#2485C2212yes—
134#2484C2214yes—
135#2481C2214yes—
136#2476C2214yes—
137#2474C2214yes—
138#2471C2214yes—
139#2468C2214yes—
140#2464C2214yes—
141#2464C2214yes—
142#2464C2214yes—
143#2461C2214yes—
144#2459C2214yes—
145#2459C2214yes—
146#2459C2214yes—
147#2458C2214yes—
148#2458C2214yes—
149#2457C2214yes—
150#2457C2214yes—
151#2456C2214yes—
152#2456C2214yes—
153#2456C2214yes—
154#2456C2214yes—
155#2456C2214yes—
156#2450C2214yes—
157#2447C2214yes—
158#2444C2214yes—
159#2440C2212yes—
160#2439C2212yes—
161#2427C2214yes—
162#2422C2212yes—
163#2422C2214yes—
164#2420C2212yes—
165#2419C2214yes—
166#2416C2212yes—
167#2416C2214yes—
168#2414C2212yes—
169#2413C2214yes—
170#2413C2214yes—
171#2401C2214yes—
172#2392C2214yes—
173#2374C2214yes—
174#2373C2214yes—
175#2373C2214yes—
176#2370C2212yes—
177#2368C2214yes—
178#2367C2212yes—
179#2367C2212yes—
180#2366C2212yes—
181#2365C2212yes—
182#2364C2212yes—
183#2364C2212yes—
184#2363C2212yes—
185#2363C2214yes—
186#2361C2212yes—
187#2361C2212yes—
188#2361C2214yes—
189#2361C2212yes—
190#2359C2214yes—
191#2357C2212yes—
192#2357C2214yes—
193#2357C2214yes—
194#2356C2214yes—
195#2355C2214yes—
196#2354C2214yes—
197#2353C2214yes—
198#2353C2214yes—
199#2352C2212yes—
200#2352C2214yes—
201#2352C2214yes—
202#2346C2212yes—
203#2344C2212yes—
204#2335C2214yes—
205#2334C2214yes—
206#2333C2214yes—
207#2333C2214yes—
208#2331C2212yes—
209#2330C2211yescharacteristic
210#2328C2211yescharacteristic
211#2324C2212yes—
212#2324C2212yes—
213#2324C2212yes—
214#2319C2212yes—
215#2314C2211yescharacteristic
216#2314C2211yescharacteristic
217#2314C2211yescharacteristic
218#2314C2211yescharacteristic
219#2314C2211yescharacteristic
220#2314C2211yescharacteristic
221#2314C2211yescharacteristic
222#2311C2212yes—
223#2311C2212yes—
224C4×#127C2211yescharacteristic
225C4×#125C2212yes—
226C4×#125C2211yescharacteristic
227C4×#123C2214yes—
228C4×#123C2214yes—
229C4×#123C2214yes—
230C4×#121C2212yes—
231C4×#121C2212yes—
232C4×#121C2212yes—
233C4×#121C2214yes—
234#2297C2211yescharacteristic
235#2297C2211yescharacteristic
236#2293C2211yescharacteristic
237#2293C2211yescharacteristic
238#2290C2211yescharacteristic
239#2290C2211yescharacteristic
240#2290C2211yescharacteristic
241#2290C2211yescharacteristic
242#2290C2214yes—
243#2290C2214yes—
244#2285C2211yescharacteristic
245#2285C2212yes—
246#2285C2211yescharacteristic
247#2285C2212yes—
248C2×#384C2211yescharacteristic
249#2283C2212yes—
250#2283C2212yes—
251C2×#382C2211yescharacteristic
252#2274C2212yes—
253#2274C2212yes—
254C42×D4C2212yes—
255C42×D4C2211yescharacteristic
256C42×D4C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261#553—216no—
262#540—28no—
263#532—28no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#127C2311yescharacteristic
267C2×#127C2311yescharacteristic
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#125C2312yes—
271C2×#125C2311yescharacteristic
272C2×#124C2311yescharacteristic
273C2×#124C2311yescharacteristic
274C2×#124C2314yes—
275C2×#124C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2311yescharacteristic
289C2×#121C2311yescharacteristic
290C2×#121C2311yescharacteristic
291C2×#121C2311yescharacteristic
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C4×#41—28no—
298C4×#41—28no—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2311yescharacteristic
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2311yescharacteristic
329C2×#117C2314yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2311yescharacteristic
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2314yes—
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342C22×C42C2311yescharacteristic
343C22×C42C2311yescharacteristic
344C22×C42C2314yes—
345#401C2314yes—
346#401C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2314yes—
388#395C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#393C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#390C2314yes—
427#390C2312yes—
428#390C2314yes—
429#390C2312yes—
430#390C2312yes—
431#390C2314yes—
432#390C2314yes—
433#390C2312yes—
434#390C2314yes—
435#390C2312yes—
436#390C2312yes—
437#390C2314yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#388C2312yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2312yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2312yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2312yes—
507#388C2314yes—
508#388C2312yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2312yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
544#387C2314yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2312yes—
567#386C2314yes—
568#386C2314yes—
569#386C2312yes—
570#386C2314yes—
571#386C2312yes—
572#386C2312yes—
573#386C2314yes—
574#386C2312yes—
575#386C2312yes—
576#386C2312yes—
577#386C2312yes—
578#386C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2312yes—
590#385C2314yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
594#385C2314yes—
595#384C2311yescharacteristic
596#384C2312yes—
597#384C2311yescharacteristic
598#384C2311yescharacteristic
599#384C2312yes—
600#384C2314yes—
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#382C2311yescharacteristic
605#382C2312yes—
606#382C2312yes—
607#382C2311yescharacteristic
608#382C2311yescharacteristic
609#382C2312yes—
610#382C2314yes—
611#382C2314yes—
612#382C2312yes—
613#382C2314yes—
614#382C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#381C2314yes—
619#381C2314yes—
620#381C2314yes—
621#381C2314yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2314yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2311yescharacteristic
686C4×C22⋊C4C2311yescharacteristic
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2311yescharacteristic
697C4×C22⋊C4C2311yescharacteristic
698#376C2311yescharacteristic
699#376C2311yescharacteristic
700#376C2314yes—
701#376C2314yes—
702#376C2314yes—
703C2×#95C2314yes—
704C2×#95C2312yes—
705C43C2311yescharacteristic
706C43C2311yescharacteristic
707C2×#41—24no—
708C2×#41—24no—
709C2×#41—24no—
710C2×#41—24no—
711C2×#41—42no—
712C2×#41—42no—
713C22×Q8C2411yescharacteristic
714C22×Q8C2411yescharacteristic
715C22×Q8C2414yes—
716C22×D4C2412yes—
717C22×D4C2411yescharacteristic
718C22×D4C2411yescharacteristic
719C22×D4C2411yescharacteristic
720C22×D4C2411yescharacteristic
721C22×D4C2411yescharacteristic
722C22×D4C2411yescharacteristic
723C22×D4C2411yescharacteristic
724C22×D4C2414yes—
725C22×D4C2411yescharacteristic
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2414yes—
729C22×D4C2411yescharacteristic
730C22×D4C2414yes—
731C22×D4C2414yes—
732C22×D4C2411yescharacteristic
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2414yes—
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C4⋊Q8—24no—
752C4⋊Q8—44no—
753#127—24no—
754#127—24no—
755#126—216no—
756#126—48no—
757#125—24no—
758#125—28no—
759#124—24no—
760#124—24no—
761#124—84no—
762#124—84no—
763#123—216no—
764#123—216no—
765#123—48no—
766#123—48no—
767#123—84no—
768#123—84no—
769C22⋊Q8—48no—
770#121—24no—
771#121—216no—
772#121—28no—
773#121—28no—
774#121—28no—
775#121—24no—
776#121—24no—
777#121—24no—
778#121—216no—
779#121—48no—
780#121—44no—
781#121—44no—
782#121—84no—
783#121—84no—
784C4×Q8—28no—
785C4×Q8—28no—
786C4×D4—24no—
787C4×D4—24no—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—28no—
794C4×D4—216no—
795C4×D4—24no—
796C4×D4—28no—
797C4×D4—28no—
798C4×D4—44no—
799C4×D4—48no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—84no—
803C4×D4—84no—
804C4×D4—84no—
805C4×D4—84no—
806C4×D4#4118yes—
807#117—28no—
808#117—24no—
809#117—24no—
810#117—24no—
811#117—24no—
812#117—42no—
813#117—44no—
814#117—84no—
815#117—84no—
816#117—84no—
817#117#4118yes—
818C2×C4⋊C4—28no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4—84no—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2411yescharacteristic
920C2×C22⋊C4C2411yescharacteristic
921C2×C42—24no—
922C2×C42—24no—
923C2×C42—24no—
924C2×C42—24no—
925C2×C42—24no—
926C2×C42—24no—
927C2×C42—24no—
928C2×C42—84no—
929C2×C42C2411yescharacteristic
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2414yes—
933C2×C42C2411yescharacteristic
934C2×C42C2411yescharacteristic
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961C2×C42C2411yescharacteristic
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2414yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019C24C2514yes—
1020C24C2511yescharacteristic
1021C24C2511yescharacteristic
1022C24C2511yescharacteristic
1023C24C2511yescharacteristic
1024C24C2511yescharacteristic
1025#41—416no—
1026#41—416no—
1027C2×Q8—22no—
1028C2×Q8—22no—
1029C2×Q8—22no—
1030C2×Q8—22no—
1031C2×Q8—41no—
1032C2×Q8—41no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×D4—22no—
1037C2×D4—22no—
1038C2×D4—22no—
1039C2×D4—22no—
1040C2×D4—22no—
1041C2×D4—22no—
1042C2×D4—22no—
1043C2×D4—22no—
1044C2×D4—28no—
1045C2×D4—22no—
1046C2×D4—22no—
1047C2×D4—28no—
1048C2×D4—28no—
1049C2×D4—22no—
1050C2×D4—22no—
1051C2×D4—24no—
1052C2×D4—22no—
1053C2×D4—24no—
1054C2×D4—22no—
1055C2×D4—22no—
1056C2×D4—28no—
1057C2×D4—24no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—41no—
1065C2×D4—41no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—42no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—42no—
1082C2×D4C2×#4114yes—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—22no—
1086C22×C4—22no—
1087C22×C4—22no—
1088C22×C4—22no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—28no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—24no—
1105C22×C4—24no—
1106C22×C4—22no—
1107C22×C4—28no—
1108C22×C4—28no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—42no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4C2×#4114yes—
1133C22×C4C2×#4114yes—
1134C22×C4C2×#4114yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2512yes—
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2514yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2514yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2514yes—
1150C22×C4C2514yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2512yes—
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2511yescharacteristic
1156C22×C4C2511yescharacteristic
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2511yescharacteristic
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—22no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—28no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4C2×#4118yes—
1203C4⋊C4C2×#4114yes—
1204C22⋊C4—28no—
1205C22⋊C4—22no—
1206C22⋊C4—22no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—28no—
1212C22⋊C4—22no—
1213C22⋊C4—22no—
1214C22⋊C4—22no—
1215C22⋊C4—22no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—28no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—42no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C22⋊C4—42no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4C2×#4118yes—
1257C22⋊C4C2×#4114yes—
1258C22⋊C4C2×#4114yes—
1259C42—22no—
1260C42—22no—
1261C42—22no—
1262C42—22no—
1263C42—22no—
1264C42—24no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—24no—
1269C42—24no—
1270C42—22no—
1271C42—22no—
1272C42—28no—
1273C42—22no—
1274C42—22no—
1275C42—42no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—42no—
1285C42—44no—
1286C42—42no—
1287C42—42no—
1288C42—44no—
1289C42C2×#4114yes—
1290C42C2×#4114yes—
1291C42C2×#4114yes—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—22no—
1296C23—21no—
1297C23—22no—
1298C23—21no—
1299C23—22no—
1300C23—21no—
1301C23—22no—
1302C23—22no—
1303C23—22no—
1304C23—24no—
1305C23—21no—
1306C23—21no—
1307C23—24no—
1308C23—21no—
1309C23—21no—
1310C23—24no—
1311C23—22no—
1312C23—24no—
1313C23—22no—
1314C23—24no—
1315C23—21no—
1316C23—21no—
1317C23—22no—
1318C23—22no—
1319C23—24no—
1320C23—24no—
1321C23C22×#4112yes—
1322C23C22×#4112yes—
1323C23C22×#4112yes—
1324C23C2611yescharacteristic
1325Q8—44no—
1326Q8—44no—
1327Q8—164no—
1328D4—44no—
1329D4—44no—
1330D4—44no—
1331D4—44no—
1332D4—44no—
1333D4—44no—
1334D4—44no—
1335D4—44no—
1336D4—48no—
1337D4—88no—
1338D4—88no—
1339D4—88no—
1340D4—88no—
1341D4—82no—
1342D4—82no—
1343D4—88no—
1344D4—88no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—28no—
1360C2×C4—28no—
1361C2×C4—28no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—24no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—24no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—22no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—48no—
1409C2×C4—48no—
1410C2×C4—48no—
1411C2×C4—44no—
1412C2×C4—44no—
1413C2×C4—44no—
1414C2×C4—84no—
1415C2×C4—88no—
1416C2×C4—84no—
1417C2×C4—88no—
1418C2×C4—82no—
1419C2×C4—84no—
1420C2×C4—88no—
1421C2×C4—88no—
1422C2×C4—164no—
1423C2×C4C22×#4112yes—
1424C2×C4C22×#4112yes—
1425C2×C4C22×#4114yes—
1426C2×C4C22×#4114yes—
1427C2×C4C22×#4112yes—
1428C2×C4C22×#4112yes—
1429C2×C4C22×#4112yes—
1430C2×C4C22×#4112yes—
1431C2×C4C22×#4112yes—
1432C2×C4#58514yes—
1433C2×C4#58512yes—
1434C22—24no—
1435C22—22no—
1436C22—22no—
1437C22—22no—
1438C22—22no—
1439C22—22no—
1440C22—22no—
1441C22—22no—
1442C22—42no—
1443C22—42no—
1444C22—41no—
1445C22—41no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—44no—
1451C22—42no—
1452C22—44no—
1453C22—41no—
1454C22—41no—
1455C22—44no—
1456C22—44no—
1457C22—41no—
1458C22—41no—
1459C22—44no—
1460C22—42no—
1461C22—42no—
1462C22—44no—
1463C22—41no—
1464C22—41no—
1465C22—44no—
1466C22C23×#4111yescharacteristic
1467C22C23×#4111yescharacteristic
1468C22C2×#58512yes—
1469C22C2×#58511yescharacteristic
1470C22H(7,𝔽2)12yes—
1471C4—24no—
1472C4—24no—
1473C4—24no—
1474C4—22no—
1475C4—22no—
1476C4—22no—
1477C4—22no—
1478C4—22no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—44no—
1483C4—41no—
1484C4—44no—
1485C4—44no—
1486C4—44no—
1487C4—41no—
1488C4—42no—
1489C4—44no—
1490C4—44no—
1491C4—44no—
1492C4—42no—
1493C4—41no—
1494C4—41no—
1495C4#347514yes—
1496C2—42no—
1497C2—42no—
1498C2—42no—
1499C2—81no—
1500C2—84no—
1501C2—81no—
1502C2C2×#347511yescharacteristic
1503C2#6281511yescharacteristic
1504C2#6285811yescharacteristic
1505C2#6293812yes—
1506C2#6300812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59591C2semidirect
2. #59576C2semidirect
3. #59552C2semidirect
4. #59541C2semidirect
5. #44570C2semidirect
6. #44562C2semidirect
7. #44130C2semidirect
8. #44122C2semidirect
9. #39510C2semidirect
10. #39500C2semidirect
11. #39462C2semidirect
12. #37975C2semidirect
13. #37969C2semidirect
14. #37898C2semidirect
15. #37893C2semidirect
16. #37889C2semidirect
17. #37883C2semidirect
18. #36200C2semidirect
19. #36191C2semidirect
20. #36182C2semidirect
21. #35590C2semidirect
22. #35589C2semidirect
23. #35337C2semidirect
24. #35259C2semidirect
25. #35259C2semidirect
26. #34917C2semidirect
27. #34319C2semidirect
28. #34189C2semidirect
29. #34188C2semidirect
30. #34141C2semidirect
31. C4×#540C2semidirect

Maximal subgroups

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

subgroupindex
#595912
#595762
#595522
#595412
#445702
#445622
#441302
#441222
#395102
#395002
#394622
#379752
#379692
#378982
#378932
#378892
#378832
#362002
#361912
#361822
#355902
#355892
#353372
#352592
#349172
#343192
#341892
#341882
#341412
C4×#5402