Finite Group Databasebeta

← #8425213

Subgroups — #8425213

Order 512.

5220 conjugacy classes of subgroups.

The subgroup lattice has 1788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59409C212yesmaximal, complemented
3#59080C211yesmaximal, characteristic, complemented
4#59049C211yesmaximal, characteristic, complemented
5#59033C212yesmaximal, complemented
6#57272C214yesmaximal, complemented
7#54751C214yesmaximal, complemented
8#53126C212yesmaximal, complemented
9#53098C212yesmaximal, complemented
10#53021C212yesmaximal, complemented
11#52962C212yesmaximal, complemented
12#52497C214yesmaximal, complemented
13#42810C212yesmaximal, complemented
14#42536C212yesmaximal, complemented
15#42477C212yesmaximal, complemented
16#42429C212yesmaximal, complemented
17#40933C214yesmaximal, complemented
18#40068C212yesmaximal, complemented
19#39981C212yesmaximal, complemented
20#39350C211yesmaximal, characteristic, complemented
21#39167C211yesmaximal, characteristic, complemented
22#39054C212yesmaximal, complemented
23#38984C211yesmaximal, characteristic, complemented
24#38923C211yesmaximal, characteristic, complemented
25#37699C212yesmaximal, complemented
26#37629C211yesmaximal, characteristic, complemented
27#37616C211yesmaximal, characteristic, complemented
28#37501C212yesmaximal, complemented
29#37494C212yesmaximal, complemented
30#36561C211yesmaximal, characteristic, complemented
31#36274C211yesmaximal, characteristic, complemented
32#36149C211yesmaximal, characteristic, complemented
33#34937C211yesmaximal, characteristic, complemented
34#34772C211yesmaximal, characteristic, complemented
35#34727C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×#554C2212yes—
38C2×#550C2212yes—
39C2×D4×Q8C2211yescharacteristic
40C2×#548C2212yes—
41C2×#547C2212yes—
42C2×#542C2212yes—
43C2×#532C2211yescharacteristic
44C2×#532C2211yescharacteristic
45C2×#532C2212yes—
46C2×#529C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic
48#2862C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2212yes—
51#2857C2211yescharacteristic
52#2855C2212yes—
53#2841C2214yes—
54#2837C2214yes—
55#2832C2214yes—
56#2831C2214yes—
57#2830C2214yes—
58#2830C2214yes—
59#2827C2214yes—
60#2827C2214yes—
61#2825C2214yes—
62#2824C2214yes—
63#2820C2214yes—
64#2814C2214yes—
65#2813C2214yes—
66#2813C2214yes—
67#2786C2214yes—
68#2784C2214yes—
69#2783C2214yes—
70#2780C2214yes—
71#2779C2214yes—
72#2767C2214yes—
73#2762C2214yes—
74#2757C2214yes—
75#2751C2214yes—
76#2750C2214yes—
77#2746C2214yes—
78#2723C2214yes—
79#2723C2214yes—
80#2722C2214yes—
81#2717C2214yes—
82#2714C2214yes—
83#2707C2214yes—
84#2704C2214yes—
85#2703C2214yes—
86#2700C2214yes—
87#2698C2214yes—
88#2695C2214yes—
89#2692C2214yes—
90#2692C2214yes—
91#2691C2214yes—
92#2691C2214yes—
93#2691C2214yes—
94#2688C2214yes—
95#2688C2214yes—
96#2687C2214yes—
97#2683C2214yes—
98#2682C2214yes—
99#2681C2214yes—
100#2676C2214yes—
101#2676C2214yes—
102#2676C2214yes—
103#2676C2214yes—
104#2665C2214yes—
105#2653C2214yes—
106#2648C2214yes—
107#2645C2212yes—
108#2644C2212yes—
109#2644C2212yes—
110#2643C2214yes—
111#2640C2212yes—
112#2640C2212yes—
113#2640C2212yes—
114#2639C2214yes—
115#2638C2214yes—
116#2636C2214yes—
117#2633C2214yes—
118#2631C2214yes—
119#2630C2214yes—
120#2625C2212yes—
121#2625C2212yes—
122#2620C2212yes—
123#2620C2212yes—
124#2620C2212yes—
125#2619C2212yes—
126#2616C2214yes—
127#2608C2214yes—
128#2582C2211yescharacteristic
129#2581C2212yes—
130#2578C2214yes—
131#2568C2212yes—
132#2568C2211yescharacteristic
133#2567C2212yes—
134#2566C2212yes—
135#2564C2214yes—
136#2557C2214yes—
137#2556C2214yes—
138#2551C2211yescharacteristic
139#2549C2214yes—
140#2548C2211yescharacteristic
141#2548C2212yes—
142#2548C2211yescharacteristic
143#2547C2212yes—
144#2547C2212yes—
145#2547C2211yescharacteristic
146#2546C2211yescharacteristic
147#2545C2212yes—
148#2544C2212yes—
149#2544C2212yes—
150#2544C2212yes—
151#2543C2214yes—
152#2542C2211yescharacteristic
153#2541C2211yescharacteristic
154#2541C2211yescharacteristic
155#2540C2212yes—
156#2538C2212yes—
157#2537C2212yes—
158#2535C2212yes—
159#2535C2214yes—
160#2522C2212yes—
161#2520C2212yes—
162#2514C2212yes—
163#2511C2212yes—
164#2511C2211yescharacteristic
165#2507C2211yescharacteristic
166#2506C2212yes—
167#2505C2212yes—
168#2502C2211yescharacteristic
169#2497C2211yescharacteristic
170#2496C2212yes—
171#2492C2211yescharacteristic
172#2492C2212yes—
173#2491C2212yes—
174#2487C2211yescharacteristic
175#2486C2212yes—
176#2485C2212yes—
177#2479C2212yes—
178#2471C2212yes—
179#2467C2214yes—
180#2467C2212yes—
181#2466C2214yes—
182#2463C2214yes—
183#2459C2214yes—
184#2456C2212yes—
185#2454C2211yescharacteristic
186#2453C2212yes—
187#2452C2212yes—
188#2452C2212yes—
189#2452C2212yes—
190#2452C2212yes—
191#2451C2212yes—
192#2451C2212yes—
193#2451C2212yes—
194#2450C2214yes—
195#2450C2214yes—
196#2450C2212yes—
197#2448C2212yes—
198#2448C2211yescharacteristic
199#2447C2212yes—
200#2447C2212yes—
201#2447C2212yes—
202#2447C2212yes—
203#2447C2212yes—
204#2446C2212yes—
205#2445C2212yes—
206#2445C2212yes—
207#2444C2214yes—
208#2444C2214yes—
209#2441C2211yescharacteristic
210#2440C2212yes—
211#2440C2211yescharacteristic
212#2439C2212yes—
213#2438C2214yes—
214#2436C2212yes—
215#2431C2212yes—
216#2431C2211yescharacteristic
217#2430C2214yes—
218#2429C2212yes—
219#2428C2212yes—
220#2428C2211yescharacteristic
221#2427C2212yes—
222#2427C2212yes—
223#2427C2212yes—
224#2427C2212yes—
225#2426C2212yes—
226#2425C2214yes—
227#2423C2211yescharacteristic
228#2420C2212yes—
229#2420C2214yes—
230#2420C2212yes—
231#2419C2214yes—
232#2417C2212yes—
233#2417C2211yescharacteristic
234#2417C2212yes—
235#2417C2212yes—
236#2416C2212yes—
237#2416C2212yes—
238#2416C2212yes—
239#2416C2212yes—
240#2415C2212yes—
241#2415C2212yes—
242#2414C2212yes—
243#2414C2211yescharacteristic
244#2409C2212yes—
245#2409C2212yes—
246#2409C2212yes—
247#2407C2212yes—
248#2407C2212yes—
249#2407C2212yes—
250#2407C2212yes—
251#2407C2211yescharacteristic
252#2407C2212yes—
253#2407C2214yes—
254#2407C2214yes—
255#2402C2212yes—
256#2397C2212yes—
257#2396C2212yes—
258#2392C2214yes—
259#2392C2212yes—
260#2366C2212yes—
261#2365C2211yescharacteristic
262#2365C2211yescharacteristic
263#2363C2212yes—
264#2360C2212yes—
265#2349C2212yes—
266#2349C2212yes—
267D4×C4⋊C4C2211yescharacteristic
268D4×C4⋊C4C2211yescharacteristic
269#2341C2212yes—
270#2339C2212yes—
271#2339C2214yes—
272#2339C2212yes—
273#2339C2212yes—
274#2329C2214yes—
275#2326C2212yes—
276#2320C2212yes—
277#2316C2212yes—
278C4×C4⋊Q8C2211yescharacteristic
279C4×#127C2211yescharacteristic
280C4×#127C2211yescharacteristic
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2212yes—
286C4×#121C2212yes—
287C4×#121C2212yes—
288C4×#121C2211yescharacteristic
289C4×#121C2211yescharacteristic
290#2297C2212yes—
291#2295C2211yescharacteristic
292#2295C2211yescharacteristic
293C2×#391C2212yes—
294#2290C2212yes—
295#2290C2212yes—
296#2285C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2314yes—
302C22×#41C2312yes—
303C23×Q8C2312yes—
304#556—44no—
305#554—48no—
306#550—48no—
307D4×Q8—44no—
308#548—48no—
309#547—48no—
310#542—48no—
311#532—44no—
312#532—44no—
313#532—48no—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×#127C2311yescharacteristic
322C2×#127C2311yescharacteristic
323C2×#127C2312yes—
324C2×#127C2312yes—
325#529—44no—
326C2×#126C2312yes—
327C2×#126C2314yes—
328C2×#126C2314yes—
329C2×#125C2314yes—
330C2×#125C2311yescharacteristic
331C2×#124C2312yes—
332C2×#124C2314yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2311yescharacteristic
338C2×#124C2312yes—
339C2×#124C2314yes—
340C2×#123C2314yes—
341C2×#123C2312yes—
342C2×#123C2314yes—
343C2×#123C2314yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2311yescharacteristic
359C2×C22⋊Q8C2314yes—
360C2×C22⋊Q8C2314yes—
361C2×#121C2311yescharacteristic
362C2×#121C2311yescharacteristic
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2314yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2314yes—
372C2×#121C2314yes—
373C2×#121C2314yes—
374C2×#121C2314yes—
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379C4×#41—44no—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2311yescharacteristic
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2311yescharacteristic
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2312yes—
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2314yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2314yes—
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2311yescharacteristic
414C2×#117C2312yes—
415C2×#117C2312yes—
416C2×#117C2312yes—
417C2×#117C2312yes—
418C2×#117C2311yescharacteristic
419C22×C4⋊C4C2312yes—
420C22×C4⋊C4C2311yescharacteristic
421C22×C4⋊C4C2312yes—
422C22×C4⋊C4C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2311yescharacteristic
425C22×C42C2312yes—
426C22×C42C2312yes—
427#401C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2312yes—
435#400C2314yes—
436#400C2314yes—
437#400C2312yes—
438#400C2312yes—
439#400C2314yes—
440#400C2312yes—
441#400C2312yes—
442#399C2314yes—
443#399C2312yes—
444#399C2314yes—
445#399C2312yes—
446#399C2312yes—
447#399C2312yes—
448#399C2312yes—
449#398C2312yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2312yes—
457#398C2312yes—
458#398C2312yes—
459#398C2314yes—
460#398C2314yes—
461#398C2312yes—
462#398C2312yes—
463#398C2312yes—
464#398C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#397C2314yes—
486#397C2314yes—
487#396C2312yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2312yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2312yes—
504#396C2312yes—
505#395C2314yes—
506#395C2314yes—
507#395C2314yes—
508#395C2314yes—
509#395C2314yes—
510#395C2314yes—
511#395C2312yes—
512#394C2314yes—
513#394C2314yes—
514#394C2312yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2312yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2314yes—
535#394C2314yes—
536#394C2312yes—
537#394C2314yes—
538#393C2314yes—
539#393C2314yes—
540#393C2314yes—
541#393C2314yes—
542#393C2314yes—
543#393C2314yes—
544#393C2314yes—
545#393C2314yes—
546#393C2314yes—
547#393C2312yes—
548#392C2314yes—
549#392C2312yes—
550#392C2314yes—
551#392C2314yes—
552#392C2314yes—
553#392C2314yes—
554#392C2314yes—
555#392C2312yes—
556#392C2314yes—
557#392C2312yes—
558#392C2312yes—
559#392C2312yes—
560#392C2314yes—
561#391C2312yes—
562#391C2312yes—
563#391C2312yes—
564#391C2312yes—
565#391C2311yescharacteristic
566#391C2312yes—
567#391C2314yes—
568#391C2312yes—
569#391C2312yes—
570#391C2314yes—
571#391C2312yes—
572#391C2312yes—
573#391C2312yes—
574#391C2312yes—
575#391C2312yes—
576#391C2314yes—
577#391C2314yes—
578#391C2312yes—
579#391C2312yes—
580#391C2312yes—
581#391C2312yes—
582#391C2312yes—
583#391C2311yescharacteristic
584#391C2311yescharacteristic
585#391C2311yescharacteristic
586#391C2314yes—
587#391C2311yescharacteristic
588#391C2311yescharacteristic
589#390C2312yes—
590#390C2311yescharacteristic
591#390C2311yescharacteristic
592#390C2312yes—
593#390C2312yes—
594#390C2312yes—
595#390C2312yes—
596#390C2312yes—
597#390C2312yes—
598#390C2314yes—
599#390C2312yes—
600#390C2314yes—
601#390C2314yes—
602#390C2312yes—
603#390C2314yes—
604#390C2312yes—
605#390C2312yes—
606#390C2312yes—
607#390C2311yescharacteristic
608#390C2312yes—
609#390C2314yes—
610#390C2312yes—
611#390C2311yescharacteristic
612#390C2312yes—
613#389C2311yescharacteristic
614#389C2311yescharacteristic
615#389C2312yes—
616#389C2314yes—
617#389C2314yes—
618#389C2311yescharacteristic
619#389C2312yes—
620#389C2312yes—
621#389C2312yes—
622#389C2314yes—
623#389C2314yes—
624#389C2311yescharacteristic
625#389C2312yes—
626#389C2312yes—
627#389C2312yes—
628#389C2311yescharacteristic
629#389C2312yes—
630#389C2312yes—
631#389C2312yes—
632#389C2312yes—
633#389C2314yes—
634#389C2312yes—
635#389C2312yes—
636#389C2312yes—
637#389C2312yes—
638#389C2312yes—
639#389C2312yes—
640#389C2311yescharacteristic
641#389C2311yescharacteristic
642#389C2311yescharacteristic
643#389C2311yescharacteristic
644#389C2311yescharacteristic
645#388C2314yes—
646#388C2312yes—
647#388C2312yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2312yes—
655#388C2314yes—
656#388C2312yes—
657#388C2312yes—
658#388C2312yes—
659#388C2314yes—
660#388C2312yes—
661#388C2312yes—
662#387C2314yes—
663#387C2314yes—
664#387C2312yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#387C2312yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2314yes—
673#387C2314yes—
674#387C2312yes—
675#387C2314yes—
676#387C2314yes—
677#387C2312yes—
678#387C2314yes—
679#387C2314yes—
680#387C2312yes—
681#387C2312yes—
682#387C2312yes—
683#387C2312yes—
684#387C2312yes—
685#387C2312yes—
686#386C2312yes—
687#386C2314yes—
688#386C2314yes—
689#386C2312yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2312yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2312yes—
706#386C2314yes—
707#386C2314yes—
708#386C2312yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2312yes—
714#386C2314yes—
715#386C2312yes—
716#386C2312yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2312yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2314yes—
730#385C2312yes—
731#385C2314yes—
732#385C2314yes—
733#385C2312yes—
734#385C2314yes—
735#385C2312yes—
736#385C2312yes—
737#385C2312yes—
738#385C2312yes—
739#385C2312yes—
740#384C2311yescharacteristic
741#384C2311yescharacteristic
742#384C2311yescharacteristic
743#384C2312yes—
744#384C2311yescharacteristic
745#384C2311yescharacteristic
746#383C2314yes—
747#382C2314yes—
748#382C2312yes—
749#382C2312yes—
750#382C2312yes—
751#382C2312yes—
752#381C2314yes—
753#381C2314yes—
754#381C2314yes—
755#381C2314yes—
756#381C2314yes—
757#380C2312yes—
758#380C2314yes—
759#380C2314yes—
760#380C2314yes—
761#380C2314yes—
762#380C2314yes—
763#380C2312yes—
764#380C2312yes—
765#380C2314yes—
766#380C2311yescharacteristic
767#380C2314yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2314yes—
772#380C2311yescharacteristic
773#380C2311yescharacteristic
774#380C2311yescharacteristic
775#380C2311yescharacteristic
776#380C2312yes—
777#380C2312yes—
778#380C2311yescharacteristic
779#380C2312yes—
780#380C2312yes—
781#380C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2311yescharacteristic
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2311yescharacteristic
814C4×C22⋊C4C2311yescharacteristic
815#376C2312yes—
816#376C2312yes—
817C2×#95C2312yes—
818C2×#95C2314yes—
819C2×#95C2314yes—
820C2×#95C2314yes—
821C43C2311yescharacteristic
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—28no—
825C2×#41—48no—
826C2×#41—42no—
827C2×#41—44no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—48no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—48no—
834C22×Q8—44no—
835C22×Q8—44no—
836C22×Q8—44no—
837C22×Q8C2411yescharacteristic
838C22×Q8C2412yes—
839C22×Q8C2411yescharacteristic
840C22×Q8C2412yes—
841C22×Q8C2412yes—
842C22×Q8C2414yes—
843C22×Q8C2414yes—
844C22×D4C2411yescharacteristic
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2414yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2411yescharacteristic
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2411yescharacteristic
854C22×D4C2412yes—
855C22×D4C2414yes—
856C22×D4C2412yes—
857C22×D4C2414yes—
858C22×D4C2412yes—
859C22×D4C2414yes—
860C22×D4C2414yes—
861C22×D4C2414yes—
862C23×C4C2411yescharacteristic
863C23×C4C2412yes—
864C23×C4C2412yes—
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C23×C4C2412yes—
870C23×C4C2414yes—
871C23×C4C2414yes—
872C23×C4C2414yes—
873C23×C4C2411yescharacteristic
874C23×C4C2414yes—
875C23×C4C2411yescharacteristic
876C23×C4C2412yes—
877C23×C4C2414yes—
878C23×C4C2414yes—
879C23×C4C2412yes—
880C4⋊Q8—24no—
881C4⋊Q8—24no—
882C4⋊Q8—24no—
883C4⋊Q8—44no—
884C4⋊Q8—44no—
885C4⋊Q8—44no—
886C4⋊Q8—44no—
887#127—28no—
888#127—24no—
889#127—24no—
890#127—44no—
891#126—44no—
892#126—48no—
893#126—48no—
894#125—42no—
895#125—48no—
896#124—28no—
897#124—48no—
898#124—42no—
899#124—44no—
900#124—44no—
901#124—44no—
902#124—44no—
903#124—44no—
904#124—48no—
905#123—44no—
906#123—48no—
907#123—48no—
908#123—48no—
909C22⋊Q8—24no—
910C22⋊Q8—48no—
911C22⋊Q8—48no—
912C22⋊Q8—48no—
913C22⋊Q8—44no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—48no—
917C22⋊Q8—48no—
918C22⋊Q8—44no—
919C22⋊Q8—42no—
920C22⋊Q8—42no—
921C22⋊Q8—44no—
922C22⋊Q8—44no—
923C22⋊Q8—44no—
924C22⋊Q8—44no—
925C22⋊Q8—44no—
926#121—24no—
927#121—24no—
928#121—28no—
929#121—44no—
930#121—48no—
931#121—48no—
932#121—48no—
933#121—48no—
934#121—48no—
935#121—44no—
936#121—44no—
937#121—42no—
938#121—44no—
939#121—44no—
940#121—44no—
941#121—44no—
942#121—44no—
943#121—48no—
944C4×Q8—28no—
945C4×Q8—24no—
946C4×Q8—24no—
947C4×Q8—44no—
948C4×Q8—42no—
949C4×Q8—44no—
950C4×Q8—44no—
951C4×D4—28no—
952C4×D4—24no—
953C4×D4—24no—
954C4×D4—24no—
955C4×D4—42no—
956C4×D4—42no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—48no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—42no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—44no—
971C4×D4—44no—
972C4×D4—44no—
973C4×D4—48no—
974C4×D4—44no—
975C4×D4—44no—
976C4×D4—48no—
977C4×D4—48no—
978#117—44no—
979#117—44no—
980#117—44no—
981#117—42no—
982#117—44no—
983C2×C4⋊C4—28no—
984C2×C4⋊C4—24no—
985C2×C4⋊C4—42no—
986C2×C4⋊C4—44no—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2411yescharacteristic
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2411yescharacteristic
1095C2×C22⋊C4C2411yescharacteristic
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C42—24no—
1116C2×C42—24no—
1117C2×C42—44no—
1118C2×C42—44no—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2414yes—
1129C2×C42C2412yes—
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2412yes—
1134C2×C42C2411yescharacteristic
1135C2×C42C2412yes—
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2414yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2414yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145#95C2411yescharacteristic
1146#95C2412yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2411yescharacteristic
1171#95C2411yescharacteristic
1172#95C2411yescharacteristic
1173#95C2411yescharacteristic
1174#95C2411yescharacteristic
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2414yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211C24C2511yescharacteristic
1212C24C2512yes—
1213C24C2514yes—
1214C24C2512yes—
1215C24C2511yescharacteristic
1216#41—416no—
1217#41—816no—
1218#41—816no—
1219#41—832no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—24no—
1223C2×Q8—24no—
1224C2×Q8—24no—
1225C2×Q8—22no—
1226C2×Q8—24no—
1227C2×Q8—24no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—24no—
1231C2×Q8—22no—
1232C2×Q8—24no—
1233C2×Q8—24no—
1234C2×Q8—42no—
1235C2×Q8—44no—
1236C2×Q8—44no—
1237C2×Q8—44no—
1238C2×Q8—44no—
1239C2×Q8—44no—
1240C2×Q8—44no—
1241C2×Q8—816no—
1242C2×D4—28no—
1243C2×D4—24no—
1244C2×D4—24no—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—28no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—28no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—24no—
1255C2×D4—22no—
1256C2×D4—28no—
1257C2×D4—24no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—41no—
1270C2×D4—41no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—44no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—42no—
1285C2×D4—42no—
1286C2×D4—44no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—44no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4H(5,𝔽2)14yes—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—24no—
1299C22×C4—28no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—22no—
1306C22×C4—24no—
1307C22×C4—24no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—24no—
1312C22×C4—22no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—22no—
1318C22×C4—24no—
1319C22×C4—28no—
1320C22×C4—28no—
1321C22×C4—28no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—44no—
1327C22×C4—42no—
1328C22×C4—44no—
1329C22×C4—44no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—44no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4—44no—
1336C22×C4—44no—
1337C22×C4—41no—
1338C22×C4—41no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—41no—
1342C22×C4—41no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—44no—
1346C22×C4—44no—
1347C22×C4—44no—
1348C22×C4—44no—
1349C22×C42−1+414yes—
1350C22×C4C2511yescharacteristic
1351C22×C4C2511yescharacteristic
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2511yescharacteristic
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2512yes—
1358C22×C4C2512yes—
1359C22×C4C2514yes—
1360C22×C4C2511yescharacteristic
1361C22×C4C2512yes—
1362C22×C4C2514yes—
1363C22×C4C2512yes—
1364C22×C4C2511yescharacteristic
1365C22×C4C2512yes—
1366C22×C4C2514yes—
1367C22×C4C2512yes—
1368C22×C4C2512yes—
1369C22×C4C2511yescharacteristic
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2512yes—
1374C22×C4C2511yescharacteristic
1375C22×C4C2512yes—
1376C22×C4C2511yescharacteristic
1377C22×C4C2511yescharacteristic
1378C22×C4C2511yescharacteristic
1379C22×C4C2511yescharacteristic
1380C4⋊C4—24no—
1381C4⋊C4—28no—
1382C4⋊C4—24no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—22no—
1388C4⋊C4—24no—
1389C4⋊C4—24no—
1390C4⋊C4—24no—
1391C4⋊C4—22no—
1392C4⋊C4—24no—
1393C4⋊C4—24no—
1394C4⋊C4—24no—
1395C4⋊C4—24no—
1396C4⋊C4—28no—
1397C4⋊C4—24no—
1398C4⋊C4—22no—
1399C4⋊C4—24no—
1400C4⋊C4—22no—
1401C4⋊C4—22no—
1402C4⋊C4—22no—
1403C4⋊C4—22no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—42no—
1408C4⋊C4—44no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—41no—
1421C4⋊C4—41no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—44no—
1430C4⋊C4—42no—
1431C4⋊C4—42no—
1432C4⋊C4—42no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—44no—
1438C4⋊C4—42no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—44no—
1443C4⋊C4—44no—
1444C4⋊C4—44no—
1445C4⋊C4H(5,𝔽2)14yes—
1446C22⋊C4—28no—
1447C22⋊C4—28no—
1448C22⋊C4—28no—
1449C22⋊C4—24no—
1450C22⋊C4—22no—
1451C22⋊C4—24no—
1452C22⋊C4—24no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—22no—
1456C22⋊C4—24no—
1457C22⋊C4—22no—
1458C22⋊C4—22no—
1459C22⋊C4—44no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—41no—
1474C22⋊C4—41no—
1475C22⋊C4—42no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—42no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C4—42no—
1492C22⋊C4—44no—
1493C22⋊C4—42no—
1494C22⋊C4—44no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—42no—
1503C22⋊C4—42no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C42—22no—
1509C42—22no—
1510C42—22no—
1511C42—22no—
1512C42—22no—
1513C42—22no—
1514C42—24no—
1515C42—24no—
1516C42—24no—
1517C42—24no—
1518C42—22no—
1519C42—28no—
1520C42—24no—
1521C42—22no—
1522C42—24no—
1523C42—22no—
1524C42—22no—
1525C42—22no—
1526C42—42no—
1527C42—42no—
1528C42—42no—
1529C42—42no—
1530C42—41no—
1531C42—44no—
1532C42—44no—
1533C42H(5,𝔽2)14yes—
1534C23—22no—
1535C23—21no—
1536C23—21no—
1537C23—22no—
1538C23—21no—
1539C23—22no—
1540C23—21no—
1541C23—21no—
1542C23—22no—
1543C23—22no—
1544C23—22no—
1545C23—21no—
1546C23—21no—
1547C23—22no—
1548C23—24no—
1549C23—21no—
1550C23—22no—
1551C23—24no—
1552C23—24no—
1553C23—21no—
1554C23—22no—
1555C23—21no—
1556C23—22no—
1557C23—24no—
1558C23—21no—
1559C23—22no—
1560C23—24no—
1561C23—24no—
1562C23—21no—
1563C23—22no—
1564C23—21no—
1565C23—24no—
1566C23—22no—
1567C23C2×H(5,𝔽2)14yes—
1568C23C2×2−1+412yes—
1569C23C2611yescharacteristic
1570Q8—48no—
1571Q8—44no—
1572Q8—48no—
1573Q8—44no—
1574Q8—48no—
1575Q8—88no—
1576Q8—164no—
1577D4—28no—
1578D4—416no—
1579D4—48no—
1580D4—48no—
1581D4—48no—
1582D4—44no—
1583D4—48no—
1584D4—44no—
1585D4—48no—
1586D4—48no—
1587D4—84no—
1588D4—88no—
1589D4—84no—
1590D4—88no—
1591D4—84no—
1592D4—88no—
1593D4—88no—
1594D4—164no—
1595C2×C4—21no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—28no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—24no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—24no—
1628C2×C4—22no—
1629C2×C4—21no—
1630C2×C4—22no—
1631C2×C4—24no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—24no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—24no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—21no—
1661C2×C4—24no—
1662C2×C4—21no—
1663C2×C4—22no—
1664C2×C4—24no—
1665C2×C4—22no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—21no—
1672C2×C4—22no—
1673C2×C4—22no—
1674C2×C4—22no—
1675C2×C4—21no—
1676C2×C4—48no—
1677C2×C4—44no—
1678C2×C4—44no—
1679C2×C4—48no—
1680C2×C4—48no—
1681C2×C4—44no—
1682C2×C4—84no—
1683C2×C4—82no—
1684C2×C4—82no—
1685C2×C4—88no—
1686C2×C4—88no—
1687C2×C4—88no—
1688C2×C4—88no—
1689C2×C4—84no—
1690C2×C4—84no—
1691C2×C4—88no—
1692C2×C4—88no—
1693C2×C4C2×H(5,𝔽2)12yes—
1694C2×C4C2×H(5,𝔽2)14yes—
1695C2×C4C2×H(5,𝔽2)12yes—
1696C2×C4C2×H(5,𝔽2)12yes—
1697C2×C4C2×H(5,𝔽2)12yes—
1698C2×C4C2×H(5,𝔽2)12yes—
1699C2×C4C2×2−1+412yes—
1700C2×C4C2×2−1+412yes—
1701C2×C4#58512yes—
1702C2×C4#58512yes—
1703C22—22no—
1704C22—24no—
1705C22—24no—
1706C22—22no—
1707C22—22no—
1708C22—24no—
1709C22—42no—
1710C22—41no—
1711C22—41no—
1712C22—42no—
1713C22—42no—
1714C22—41no—
1715C22—41no—
1716C22—42no—
1717C22—41no—
1718C22—44no—
1719C22—42no—
1720C22—41no—
1721C22—42no—
1722C22—44no—
1723C22—42no—
1724C22—44no—
1725C22—41no—
1726C22—41no—
1727C22—42no—
1728C22—44no—
1729C22—42no—
1730C22—41no—
1731C22—44no—
1732C22—42no—
1733C22—44no—
1734C22—41no—
1735C22—41no—
1736C22—44no—
1737C22—42no—
1738C22C22×H(5,𝔽2)11yescharacteristic
1739C22C22×H(5,𝔽2)11yescharacteristic
1740C22C22×H(5,𝔽2)11yescharacteristic
1741C22C22×2−1+411yescharacteristic
1742C22C2×#58511yescharacteristic
1743C22C2×#58511yescharacteristic
1744C222−1+611yescharacteristic
1745C4—22no—
1746C4—22no—
1747C4—24no—
1748C4—22no—
1749C4—41no—
1750C4—42no—
1751C4—44no—
1752C4—41no—
1753C4—42no—
1754C4—41no—
1755C4—42no—
1756C4—44no—
1757C4—42no—
1758C4—44no—
1759C4—42no—
1760C4—42no—
1761C4—42no—
1762C4—41no—
1763C4—41no—
1764C4—42no—
1765C4—42no—
1766C4—42no—
1767C4—41no—
1768C4—42no—
1769C4—42no—
1770C4—41no—
1771C4—41no—
1772C4—42no—
1773C4#353614yes—
1774C4#354614yes—
1775C2—42no—
1776C2—44no—
1777C2—81no—
1778C2—84no—
1779C2—82no—
1780C2C2×#353611yescharacteristic
1781C2C2×#354611yescharacteristic
1782C2#6276111yescharacteristic
1783C2#6291311yescharacteristic
1784C2#6292111yescharacteristic
1785C2#6292511yescharacteristic
1786C2#6301211yescharacteristic
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. #59815C2semidirect
2. #59409C2semidirect
3. #59080C2semidirect
4. #59049C2semidirect
5. #59033C2semidirect
6. #57272C2semidirect
7. #54751C2semidirect
8. #53126C2semidirect
9. #53098C2semidirect
10. #53021C2semidirect
11. #52962C2semidirect
12. #52497C2semidirect
13. #42810C2semidirect
14. #42536C2semidirect
15. #42477C2semidirect
16. #42429C2semidirect
17. #40933C2semidirect
18. #40068C2semidirect
19. #39981C2semidirect
20. #39350C2semidirect
21. #39167C2semidirect
22. #39054C2semidirect
23. #38984C2semidirect
24. #38923C2semidirect
25. #37699C2semidirect
26. #37629C2semidirect
27. #37616C2semidirect
28. #37501C2semidirect
29. #37494C2semidirect
30. #36561C2semidirect
31. #36274C2semidirect
32. #36149C2semidirect
33. #34937C2semidirect
34. #34772C2semidirect
35. #34727C2semidirect

Maximal subgroups

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

subgroupindex
#598152
#594092
#590802
#590492
#590332
#572722
#547512
#531262
#530982
#530212
#529622
#524972
#428102
#425362
#424772
#424292
#409332
#400682
#399812
#393502
#391672
#390542
#389842
#389232
#376992
#376292
#376162
#375012
#374942
#365612
#362742
#361492
#349372
#347722
#347272