Finite Group Databasebeta

← #7671089

Subgroups — #7671089

Order 512.

5140 conjugacy classes of subgroups.

The subgroup lattice has 1734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59737C214yesmaximal, complemented
2#59695C212yesmaximal, complemented
3#59659C211yesmaximal, characteristic, complemented
4#59478C212yesmaximal, complemented
5#59436C211yesmaximal, characteristic, complemented
6#59434C211yesmaximal, characteristic, complemented
7#59418C211yesmaximal, characteristic, complemented
8#59232C212yesmaximal, complemented
9#59216C212yesmaximal, complemented
10#40351C214yesmaximal, complemented
11#40329C214yesmaximal, complemented
12#39939C212yesmaximal, complemented
13#39931C212yesmaximal, complemented
14#39889C212yesmaximal, complemented
15#39883C212yesmaximal, complemented
16#36635C211yesmaximal, characteristic, complemented
17#36539C212yesmaximal, complemented
18#36513C212yesmaximal, complemented
19#36505C211yesmaximal, characteristic, complemented
20#36477C211yesmaximal, characteristic, complemented
21#36474C211yesmaximal, characteristic, complemented
22#36456C211yesmaximal, characteristic, complemented
23#36415C211yesmaximal, characteristic, complemented
24#36411C211yesmaximal, characteristic, complemented
25#36390C212yesmaximal, complemented
26#36387C212yesmaximal, complemented
27#36270C211yesmaximal, characteristic, complemented
28#36259C211yesmaximal, characteristic, complemented
29#35509C214yesmaximal, complemented
30#35107C212yesmaximal, complemented
31#35046C212yesmaximal, complemented
32#34316C212yesmaximal, complemented
33#34314C212yesmaximal, complemented
34C4×#532C211yesmaximal, characteristic, complemented
35C4×#529C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#555C2211yescharacteristic
39C2×#552C2212yes—
40C2×#547C2212yes—
41C2×#547C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#529C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46#2864C2212yes—
47#2863C2212yes—
48#2863C2212yes—
49#2862C2211yescharacteristic
50#2862C2212yes—
51#2860C2212yes—
52#2859C2211yescharacteristic
53#2857C2211yescharacteristic
54#2857C2211yescharacteristic
55#2857C2212yes—
56#2855C2212yes—
57#2855C2212yes—
58#2855C2212yes—
59#2854C2212yes—
60#2854C2212yes—
61#2851C2212yes—
62#2851C2212yes—
63#2850C2212yes—
64#2777C2214yes—
65#2766C2214yes—
66#2745C2214yes—
67#2745C2214yes—
68#2739C2214yes—
69#2737C2214yes—
70#2737C2214yes—
71#2731C2214yes—
72#2725C2214yes—
73#2707C2214yes—
74#2707C2214yes—
75#2705C2214yes—
76#2701C2214yes—
77#2701C2214yes—
78#2699C2214yes—
79#2682C2214yes—
80#2653C2214yes—
81#2650C2214yes—
82#2636C2214yes—
83#2630C2214yes—
84#2610C2214yes—
85#2609C2214yes—
86#2608C2214yes—
87#2606C2214yes—
88#2602C2214yes—
89#2602C2214yes—
90#2601C2214yes—
91#2601C2214yes—
92#2599C2214yes—
93#2594C2214yes—
94#2594C2214yes—
95#2594C2214yes—
96#2590C2214yes—
97#2589C2214yes—
98#2588C2214yes—
99#2587C2214yes—
100#2587C2214yes—
101#2579C2214yes—
102#2576C2214yes—
103#2576C2214yes—
104#2572C2214yes—
105#2570C2212yes—
106#2570C2212yes—
107#2567C2212yes—
108#2567C2211yescharacteristic
109#2566C2212yes—
110#2564C2214yes—
111#2563C2211yescharacteristic
112#2563C2212yes—
113#2562C2212yes—
114#2562C2212yes—
115#2558C2214yes—
116#2558C2214yes—
117#2557C2214yes—
118#2557C2214yes—
119#2550C2212yes—
120#2550C2212yes—
121#2550C2214yes—
122#2550C2214yes—
123#2547C2211yescharacteristic
124#2546C2211yescharacteristic
125#2546C2212yes—
126#2545C2214yes—
127#2545C2212yes—
128#2538C2211yescharacteristic
129#2538C2211yescharacteristic
130#2538C2211yescharacteristic
131#2538C2211yescharacteristic
132#2538C2212yes—
133#2536C2212yes—
134#2536C2212yes—
135#2535C2212yes—
136#2535C2212yes—
137#2529C2214yes—
138#2529C2214yes—
139#2527C2214yes—
140#2526C2214yes—
141#2525C2214yes—
142#2525C2214yes—
143#2518C2214yes—
144#2518C2214yes—
145#2515C2214yes—
146#2514C2212yes—
147#2514C2212yes—
148#2506C2212yes—
149#2499C2212yes—
150#2497C2212yes—
151#2497C2212yes—
152#2495C2212yes—
153#2494C2212yes—
154#2494C2212yes—
155#2491C2212yes—
156#2491C2212yes—
157#2490C2212yes—
158#2486C2212yes—
159#2485C2212yes—
160#2477C2214yes—
161#2475C2214yes—
162#2474C2214yes—
163#2470C2214yes—
164#2461C2214yes—
165#2461C2214yes—
166#2460C2214yes—
167#2459C2214yes—
168#2452C2212yes—
169#2452C2214yes—
170#2448C2212yes—
171#2447C2212yes—
172#2446C2212yes—
173#2445C2212yes—
174#2442C2212yes—
175#2442C2212yes—
176#2441C2212yes—
177#2439C2212yes—
178#2439C2212yes—
179#2439C2212yes—
180#2439C2214yes—
181#2432C2212yes—
182#2432C2212yes—
183#2431C2212yes—
184#2429C2212yes—
185#2429C2212yes—
186#2429C2212yes—
187#2426C2212yes—
188#2426C2212yes—
189#2426C2212yes—
190#2425C2214yes—
191#2422C2212yes—
192#2421C2212yes—
193#2416C2212yes—
194#2415C2212yes—
195#2414C2212yes—
196#2413C2214yes—
197#2407C2212yes—
198#2374C2214yes—
199#2374C2214yes—
200#2374C2214yes—
201#2373C2214yes—
202#2370C2214yes—
203#2370C2212yes—
204#2368C2214yes—
205#2367C2212yes—
206#2365C2212yes—
207#2363C2214yes—
208#2362C2212yes—
209#2362C2212yes—
210#2362C2212yes—
211#2362C2212yes—
212#2360C2212yes—
213#2359C2214yes—
214#2357C2212yes—
215#2355C2211yescharacteristic
216#2354C2212yes—
217#2354C2212yes—
218#2354C2211yescharacteristic
219#2352C2212yes—
220#2352C2212yes—
221#2352C2212yes—
222#2351C2212yes—
223#2351C2212yes—
224#2351C2212yes—
225Q8×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2211yescharacteristic
227#2347C2212yes—
228#2345C2214yes—
229#2344C2212yes—
230#2343C2214yes—
231#2341C2212yes—
232#2341C2212yes—
233#2339C2212yes—
234#2337C2214yes—
235#2336C2214yes—
236#2335C2214yes—
237#2335C2214yes—
238#2334C2214yes—
239#2324C2214yes—
240#2322C2214yes—
241C4×C4⋊Q8C2211yescharacteristic
242C4×C4⋊Q8C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×#127C2211yescharacteristic
248C4×#125C2212yes—
249C4×#125C2211yescharacteristic
250C4×#125C2211yescharacteristic
251C4×#126C2212yes—
252C4×#126C2212yes—
253C4×#124C2211yescharacteristic
254C4×#124C2211yescharacteristic
255C4×#124C2211yescharacteristic
256C4×#124C2211yescharacteristic
257C4×#124C2211yescharacteristic
258C4×#124C2211yescharacteristic
259C4×C22⋊Q8C2212yes—
260C4×C22⋊Q8C2212yes—
261C4×C22⋊Q8C2212yes—
262C4×C22⋊Q8C2212yes—
263C4×C22⋊Q8C2212yes—
264C4×C22⋊Q8C2211yescharacteristic
265C4×C22⋊Q8C2211yescharacteristic
266C4×#123C2212yes—
267C4×#123C2212yes—
268C4×#121C2211yescharacteristic
269C4×#121C2212yes—
270C4×#121C2212yes—
271C4×#121C2211yescharacteristic
272C4×#121C2212yes—
273C4×#121C2212yes—
274#2298C2212yes—
275#2297C2211yescharacteristic
276#2297C2212yes—
277#2297C2211yescharacteristic
278#2296C2212yes—
279#2295C2211yescharacteristic
280#2295C2212yes—
281#2295C2212yes—
282#2293C2212yes—
283#2293C2211yescharacteristic
284#2293C2212yes—
285#2293C2212yes—
286C2×#389C2212yes—
287#2290C2212yes—
288#2285C2211yescharacteristic
289#2283C2212yes—
290#2283C2211yescharacteristic
291#2274C2214yes—
292C42×Q8C2211yescharacteristic
293C42×D4C2212yes—
294C42×D4C2212yes—
295C42×D4C2212yes—
296C42×D4C2211yescharacteristic
297C4×#117C2212yes—
298C2×C43C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C22×#41C2311yescharacteristic
302Q82—44no—
303#557—44no—
304#555—44no—
305#552—216no—
306#547—216no—
307#547—44no—
308#532—28no—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2314yes—
317C2×#127C2311yescharacteristic
318#529—28no—
319C2×#126C2312yes—
320C2×#126C2314yes—
321C2×#125C2311yescharacteristic
322C2×#125C2312yes—
323C2×#125C2314yes—
324C2×#125C2312yes—
325C2×#125C2314yes—
326C2×#124C2311yescharacteristic
327C2×#124C2311yescharacteristic
328C2×#124C2311yescharacteristic
329C2×#124C2314yes—
330C2×#124C2312yes—
331C2×#124C2314yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2312yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×#121C2314yes—
348C2×#121C2311yescharacteristic
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C4×#41—44no—
355C4×#41—44no—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×#117C2314yes—
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2314yes—
395C2×#117C2312yes—
396C2×#117C2311yescharacteristic
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2311yescharacteristic
400C2×#117C2312yes—
401C2×#117C2312yes—
402C22×C4⋊C4C2314yes—
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2312yes—
405C22×C42C2311yescharacteristic
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2311yescharacteristic
409C22×C42C2312yes—
410C22×C42C2312yes—
411C22×C42C2312yes—
412C22×C42C2311yescharacteristic
413C22×C42C2311yescharacteristic
414C22×C42C2311yescharacteristic
415#401C2314yes—
416#401C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#399C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#392C2314yes—
477#392C2314yes—
478#392C2314yes—
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2311yescharacteristic
482#391C2312yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2311yescharacteristic
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2311yescharacteristic
499#391C2312yes—
500#391C2311yescharacteristic
501#390C2311yescharacteristic
502#390C2311yescharacteristic
503#390C2312yes—
504#390C2312yes—
505#390C2311yescharacteristic
506#390C2312yes—
507#390C2311yescharacteristic
508#390C2312yes—
509#390C2314yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2314yes—
514#390C2314yes—
515#390C2314yes—
516#390C2314yes—
517#390C2312yes—
518#390C2311yescharacteristic
519#390C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2311yescharacteristic
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2312yes—
526#389C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2314yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2312yes—
602#388C2312yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2312yes—
608#388C2312yes—
609#388C2314yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2314yes—
622#387C2312yes—
623#387C2312yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2312yes—
662#386C2314yes—
663#386C2314yes—
664#386C2312yes—
665#386C2312yes—
666#386C2312yes—
667#386C2312yes—
668#386C2312yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2312yes—
684#385C2312yes—
685#384C2311yescharacteristic
686#384C2311yescharacteristic
687#384C2312yes—
688#384C2311yescharacteristic
689#384C2311yescharacteristic
690#384C2312yes—
691#383C2312yes—
692#383C2314yes—
693#383C2314yes—
694#383C2314yes—
695#382C2312yes—
696#382C2311yescharacteristic
697#382C2311yescharacteristic
698#382C2312yes—
699#382C2314yes—
700#382C2312yes—
701#382C2311yescharacteristic
702#382C2312yes—
703#382C2314yes—
704#382C2314yes—
705#382C2312yes—
706#382C2311yescharacteristic
707#381C2314yes—
708#381C2314yes—
709#381C2314yes—
710#381C2314yes—
711#381C2312yes—
712#380C2311yescharacteristic
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2312yes—
722#380C2314yes—
723#380C2314yes—
724#380C2314yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2311yescharacteristic
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C22⋊C4C2312yes—
775C4×C22⋊C4C2312yes—
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807#376C2312yes—
808#376C2314yes—
809#376C2312yes—
810C2×#95C2314yes—
811C43C2311yescharacteristic
812C43C2311yescharacteristic
813C43C2311yescharacteristic
814C43C2311yescharacteristic
815C43C2311yescharacteristic
816C43C2311yescharacteristic
817C43C2312yes—
818C43C2311yescharacteristic
819C43C2311yescharacteristic
820C2×#41—28no—
821C2×#41—24no—
822C2×#41—42no—
823C2×#41—42no—
824C2×#41—42no—
825C2×#41—42no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41#4118yes—
829C22×Q8C2412yes—
830C22×Q8C2411yescharacteristic
831C22×Q8C2411yescharacteristic
832C22×Q8C2411yescharacteristic
833C22×Q8C2412yes—
834C22×Q8C2414yes—
835C22×D4C2411yescharacteristic
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2412yes—
848C23×C4C2411yescharacteristic
849C23×C4C2414yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2414yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2411yescharacteristic
862C23×C4C2412yes—
863C4⋊Q8—24no—
864C4⋊Q8—28no—
865C4⋊Q8—24no—
866C4⋊Q8—24no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870C4⋊Q8—48no—
871#127—24no—
872#126—28no—
873#126—216no—
874#125—24no—
875#125—216no—
876#125—28no—
877#125—44no—
878#125—48no—
879#124—24no—
880#124—24no—
881#124—24no—
882#124—48no—
883#124—44no—
884#124—48no—
885#123—216no—
886#123—216no—
887#123—28no—
888#123—216no—
889#123—48no—
890#123—48no—
891C22⋊Q8—24no—
892C22⋊Q8—28no—
893C22⋊Q8—28no—
894C22⋊Q8—28no—
895C22⋊Q8—28no—
896C22⋊Q8—48no—
897C22⋊Q8—44no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900#121—28no—
901#121—28no—
902#121—216no—
903#121—24no—
904#121—44no—
905#121—44no—
906#121—44no—
907C4×Q8—24no—
908C4×Q8—24no—
909C4×Q8—24no—
910C4×Q8—24no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×Q8—44no—
914C4×Q8—42no—
915C4×Q8—42no—
916C4×Q8—44no—
917C4×Q8—44no—
918C4×Q8—44no—
919C4×Q8—44no—
920C4×Q8#4118yescomplemented
921C4×D4—28no—
922C4×D4—28no—
923C4×D4—28no—
924C4×D4—28no—
925C4×D4—24no—
926C4×D4—28no—
927C4×D4—28no—
928C4×D4—24no—
929C4×D4—24no—
930C4×D4—24no—
931C4×D4—28no—
932C4×D4—24no—
933C4×D4—44no—
934C4×D4—42no—
935C4×D4—42no—
936C4×D4—44no—
937C4×D4—44no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—44no—
941C4×D4—44no—
942#117—28no—
943#117—28no—
944#117—216no—
945#117—44no—
946#117—48no—
947#117—44no—
948#117—44no—
949#117—42no—
950#117—42no—
951#117—44no—
952#117—44no—
953C2×C4⋊C4—216no—
954C2×C4⋊C4—28no—
955C2×C4⋊C4—44no—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C42—24no—
1071C2×C42—24no—
1072C2×C42—24no—
1073C2×C42—24no—
1074C2×C42—44no—
1075C2×C42—44no—
1076C2×C42—42no—
1077C2×C42—44no—
1078C2×C42—42no—
1079C2×C42—42no—
1080C2×C42C2411yescharacteristic
1081C2×C42C2414yes—
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2414yes—
1085C2×C42C2411yescharacteristic
1086C2×C42C2412yes—
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2414yes—
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2414yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2414yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2412yes—
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131#95C2412yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195C24C2512yes—
1196C24C2512yes—
1197C24C2512yes—
1198C24C2511yescharacteristic
1199#41—416no—
1200#41—416no—
1201#41—816no—
1202C2×Q8—24no—
1203C2×Q8—22no—
1204C2×Q8—22no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—24no—
1208C2×Q8—24no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—24no—
1212C2×Q8—22no—
1213C2×Q8—42no—
1214C2×Q8—42no—
1215C2×Q8—44no—
1216C2×Q8—44no—
1217C2×Q8—44no—
1218C2×Q8C2×#4114yes—
1219C2×Q8C2×#4114yes—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—28no—
1225C2×D4—24no—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—42no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—44no—
1248C2×D4C2×#4114yes—
1249C2×D4C2×#4118yes—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—28no—
1255C22×C4—28no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—28no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—24no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—42no—
1282C22×C4—42no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—42no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—42no—
1291C22×C4—44no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—44no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—44no—
1302C22×C4C2×#4114yes—
1303C22×C4C2×#4118yes—
1304C22×C4C2511yescharacteristic
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2511yescharacteristic
1309C22×C4C2511yescharacteristic
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2514yes—
1313C22×C4C2514yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2514yes—
1319C22×C4C2514yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2511yescharacteristic
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2512yes—
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2511yescharacteristic
1332C22×C4C2511yescharacteristic
1333C22×C4C2511yescharacteristic
1334C22×C4C2511yescharacteristic
1335C4⋊C4—24no—
1336C4⋊C4—28no—
1337C4⋊C4—28no—
1338C4⋊C4—28no—
1339C4⋊C4—24no—
1340C4⋊C4—28no—
1341C4⋊C4—28no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—28no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—24no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—28no—
1353C4⋊C4—28no—
1354C4⋊C4—28no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—22no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—22no—
1370C4⋊C4—24no—
1371C4⋊C4—22no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—28no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—42no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4C2×#4114yes—
1397C4⋊C4C2×#4118yes—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—28no—
1401C22⋊C4—24no—
1402C22⋊C4—28no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—28no—
1406C22⋊C4—24no—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—28no—
1416C22⋊C4—28no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—24no—
1425C22⋊C4—24no—
1426C22⋊C4—24no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C42—22no—
1450C42—22no—
1451C42—22no—
1452C42—22no—
1453C42—22no—
1454C42—22no—
1455C42—22no—
1456C42—28no—
1457C42—24no—
1458C42—22no—
1459C42—22no—
1460C42—22no—
1461C42—24no—
1462C42—24no—
1463C42—24no—
1464C42—22no—
1465C42—22no—
1466C42—22no—
1467C42—24no—
1468C42—22no—
1469C42—22no—
1470C42—22no—
1471C42—22no—
1472C42—22no—
1473C42—22no—
1474C42—24no—
1475C42—28no—
1476C42—41no—
1477C42—41no—
1478C42—41no—
1479C42—42no—
1480C42—42no—
1481C42—41no—
1482C42—41no—
1483C42—41no—
1484C42—42no—
1485C42—42no—
1486C42—42no—
1487C42—42no—
1488C42—42no—
1489C42—44no—
1490C42—44no—
1491C42—42no—
1492C42—44no—
1493C42—44no—
1494C42—44no—
1495C42—44no—
1496C42C2×#4114yes—
1497C42C2×#4118yes—
1498C42H(5,𝔽2)14yes—
1499C422−1+414yes—
1500C23—22no—
1501C23—21no—
1502C23—22no—
1503C23—21no—
1504C23—22no—
1505C23—21no—
1506C23—22no—
1507C23—22no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—22no—
1517C23—22no—
1518C23—22no—
1519C23—22no—
1520C23—22no—
1521C23—22no—
1522C23—22no—
1523C23—22no—
1524C23—22no—
1525C23—22no—
1526C23C22×#4112yes—
1527C23C22×#4114yes—
1528C23C2611yescharacteristic
1529Q8—28no—
1530Q8—28no—
1531Q8—44no—
1532Q8—48no—
1533Q8—84no—
1534Q8—164no—
1535D4—28no—
1536D4—48no—
1537D4—48no—
1538D4—48no—
1539D4—48no—
1540D4—48no—
1541D4—44no—
1542D4—44no—
1543D4—88no—
1544D4—164no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—28no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—24no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—24no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—24no—
1592C2×C4—24no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—24no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—24no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—24no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—24no—
1615C2×C4—22no—
1616C2×C4—24no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—24no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—48no—
1623C2×C4—44no—
1624C2×C4—44no—
1625C2×C4—44no—
1626C2×C4—416no—
1627C2×C4—44no—
1628C2×C4—44no—
1629C2×C4—48no—
1630C2×C4—48no—
1631C2×C4—48no—
1632C2×C4—44no—
1633C2×C4—48no—
1634C2×C4—48no—
1635C2×C4—84no—
1636C2×C4—84no—
1637C2×C4—84no—
1638C2×C4—88no—
1639C2×C4C22×#4114yes—
1640C2×C4C22×#4112yes—
1641C2×C4C22×#4112yes—
1642C2×C4C22×#4112yes—
1643C2×C4C22×#4114yes—
1644C2×C4C22×#4114yes—
1645C2×C4C22×#4112yes—
1646C2×C4C22×#4112yes—
1647C2×C4C2×H(5,𝔽2)12yes—
1648C2×C4C2×H(5,𝔽2)12yes—
1649C2×C4C2×H(5,𝔽2)12yes—
1650C2×C4C2×2−1+412yes—
1651C2×C4C2×2−1+412yes—
1652C2×C4C2×2−1+412yes—
1653C2×C4#58512yes—
1654C2×C4#58512yes—
1655C2×C4#58512yes—
1656C22—22no—
1657C22—24no—
1658C22—22no—
1659C22—24no—
1660C22—24no—
1661C22—22no—
1662C22—41no—
1663C22—42no—
1664C22—42no—
1665C22—41no—
1666C22—41no—
1667C22—42no—
1668C22—41no—
1669C22—42no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—42no—
1674C22—42no—
1675C22—42no—
1676C22—42no—
1677C22—42no—
1678C22—42no—
1679C22—42no—
1680C22—42no—
1681C22—42no—
1682C22—42no—
1683C22—42no—
1684C22C23×#4111yescharacteristic
1685C22C23×#4111yescharacteristic
1686C22C22×H(5,𝔽2)11yescharacteristic
1687C22C22×2−1+411yescharacteristic
1688C22C2×#58511yescharacteristic
1689C22C2×#58511yescharacteristic
1690C22C2×#58511yescharacteristic
1691C4—22no—
1692C4—24no—
1693C4—22no—
1694C4—24no—
1695C4—22no—
1696C4—22no—
1697C4—22no—
1698C4—22no—
1699C4—22no—
1700C4—24no—
1701C4—22no—
1702C4—42no—
1703C4—42no—
1704C4—44no—
1705C4—44no—
1706C4—41no—
1707C4—42no—
1708C4—41no—
1709C4—42no—
1710C4—42no—
1711C4—42no—
1712C4—41no—
1713C4—42no—
1714C4—42no—
1715C4—44no—
1716C4—42no—
1717C4—42no—
1718C4—41no—
1719C4—44no—
1720C4#350514yes—
1721C4#351114yes—
1722C2—42no—
1723C2—44no—
1724C2—82no—
1725C2—82no—
1726C2#41211yescharacteristic
1727C2C2×#350511yescharacteristic
1728C2#6279311yescharacteristic
1729C2C2×#351111yescharacteristic
1730C2#6280511yescharacteristic
1731C2#6283011yescharacteristic
1732C2#6283111yescharacteristic
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. #59737C2semidirect
2. #59695C2semidirect
3. #59659C2semidirect
4. #59478C2semidirect
5. #59436C2semidirect
6. #59434C2semidirect
7. #59418C2semidirect
8. #59232C2semidirect
9. #59216C2semidirect
10. #40351C2semidirect
11. #40329C2semidirect
12. #39939C2semidirect
13. #39931C2semidirect
14. #39889C2semidirect
15. #39883C2semidirect
16. #36635C2semidirect
17. #36539C2semidirect
18. #36513C2semidirect
19. #36505C2semidirect
20. #36477C2semidirect
21. #36474C2semidirect
22. #36456C2semidirect
23. #36415C2semidirect
24. #36411C2semidirect
25. #36390C2semidirect
26. #36387C2semidirect
27. #36270C2semidirect
28. #36259C2semidirect
29. #35509C2semidirect
30. #35107C2semidirect
31. #35046C2semidirect
32. #34316C2semidirect
33. #34314C2semidirect
34. C4×#532C2semidirect
35. C4×#529C2semidirect
920. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#597372
#596952
#596592
#594782
#594362
#594342
#594182
#592322
#592162
#403512
#403292
#399392
#399312
#398892
#398832
#366352
#365392
#365132
#365052
#364772
#364742
#364562
#364152
#364112
#363902
#363872
#362702
#362592
#355092
#351072
#350462
#343162
#343142
C4×#5322
C4×#5292