Finite Group Databasebeta

← #8172734

Subgroups — #8172734

Order 512.

5108 conjugacy classes of subgroups.

The subgroup lattice has 1808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59214C211yesmaximal, characteristic, complemented
2#59212C211yesmaximal, characteristic, complemented
3#59127C211yesmaximal, characteristic, complemented
4#59125C211yesmaximal, characteristic, complemented
5#58074C214yesmaximal, complemented
6#55861C214yesmaximal, complemented
7#55645C214yesmaximal, complemented
8#53933C214yesmaximal, complemented
9#53137C212yesmaximal, complemented
10#53045C212yesmaximal, complemented
11#52970C212yesmaximal, complemented
12#52968C212yesmaximal, complemented
13#45267C212yesmaximal, complemented
14#45091C212yesmaximal, complemented
15#42989C212yesmaximal, complemented
16#42908C212yesmaximal, complemented
17#42844C212yesmaximal, complemented
18#42786C212yesmaximal, complemented
19#42709C212yesmaximal, complemented
20#42448C212yesmaximal, complemented
21#39343C211yesmaximal, characteristic, complemented
22#39340C211yesmaximal, characteristic, complemented
23#39156C211yesmaximal, characteristic, complemented
24#39149C211yesmaximal, characteristic, complemented
25#39146C211yesmaximal, characteristic, complemented
26#39052C212yesmaximal, complemented
27#38930C211yesmaximal, characteristic, complemented
28#38098C212yesmaximal, complemented
29#37505C212yesmaximal, complemented
30#37340C212yesmaximal, complemented
31#36444C211yesmaximal, characteristic, complemented
32#36259C211yesmaximal, characteristic, complemented
33#35279C211yesmaximal, characteristic, complemented
34#34909C211yesmaximal, characteristic, complemented
35#34609C211yesmaximal, characteristic, complemented
36C2×D4×Q8C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2212yes—
39C2×#548C2212yes—
40C2×#547C2212yes—
41C2×#547C2211yescharacteristic
42C2×#537C2212yes—
43C2×#536C2212yes—
44C2×#532C2211yescharacteristic
45C22×C4⋊Q8C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2212yes—
50#2857C2211yescharacteristic
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2854C2212yes—
54#2838C2214yes—
55#2838C2214yes—
56#2838C2214yes—
57#2837C2214yes—
58#2833C2214yes—
59#2829C2214yes—
60#2829C2214yes—
61#2826C2214yes—
62#2826C2214yes—
63#2824C2214yes—
64#2817C2214yes—
65#2814C2214yes—
66#2807C2214yes—
67#2803C2214yes—
68#2801C2214yes—
69#2795C2214yes—
70#2792C2214yes—
71#2788C2214yes—
72#2780C2214yes—
73#2779C2214yes—
74#2778C2214yes—
75#2778C2214yes—
76#2778C2214yes—
77#2777C2214yes—
78#2776C2214yes—
79#2774C2214yes—
80#2771C2214yes—
81#2770C2214yes—
82#2753C2214yes—
83#2751C2214yes—
84#2750C2214yes—
85#2746C2214yes—
86#2745C2214yes—
87#2743C2214yes—
88#2742C2214yes—
89#2740C2214yes—
90#2739C2214yes—
91#2738C2214yes—
92#2734C2214yes—
93#2731C2214yes—
94#2730C2214yes—
95#2729C2214yes—
96#2688C2214yes—
97#2688C2214yes—
98#2686C2214yes—
99#2686C2214yes—
100#2682C2214yes—
101#2677C2214yes—
102#2676C2214yes—
103#2676C2214yes—
104#2674C2214yes—
105#2674C2214yes—
106#2674C2214yes—
107#2674C2214yes—
108#2674C2214yes—
109#2672C2214yes—
110#2672C2214yes—
111#2672C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2665C2214yes—
115#2663C2214yes—
116#2653C2214yes—
117#2652C2214yes—
118#2647C2212yes—
119#2645C2212yes—
120#2645C2212yes—
121#2644C2212yes—
122#2643C2214yes—
123#2639C2214yes—
124#2635C2212yes—
125#2635C2212yes—
126#2635C2214yes—
127#2632C2212yes—
128#2631C2212yes—
129#2630C2214yes—
130#2628C2211yescharacteristic
131#2628C2211yescharacteristic
132#2628C2212yes—
133#2628C2212yes—
134#2624C2211yescharacteristic
135#2624C2211yescharacteristic
136#2619C2211yescharacteristic
137#2619C2211yescharacteristic
138#2616C2212yes—
139#2616C2212yes—
140#2615C2211yescharacteristic
141#2615C2211yescharacteristic
142#2602C2214yes—
143#2600C2212yes—
144#2600C2212yes—
145#2599C2212yes—
146#2598C2212yes—
147#2595C2214yes—
148#2587C2214yes—
149#2581C2211yescharacteristic
150#2580C2211yescharacteristic
151#2576C2214yes—
152#2571C2211yescharacteristic
153#2570C2212yes—
154#2568C2212yes—
155#2567C2212yes—
156#2566C2212yes—
157#2564C2214yes—
158#2563C2212yes—
159#2562C2212yes—
160#2555C2214yes—
161#2552C2211yescharacteristic
162#2551C2212yes—
163#2551C2212yes—
164#2547C2212yes—
165#2547C2211yescharacteristic
166#2546C2211yescharacteristic
167#2542C2211yescharacteristic
168#2542C2212yes—
169#2542C2211yescharacteristic
170#2538C2212yes—
171#2538C2212yes—
172#2538C2211yescharacteristic
173#2537C2211yescharacteristic
174#2537C2212yes—
175#2537C2212yes—
176#2536C2212yes—
177#2536C2211yescharacteristic
178#2535C2212yes—
179#2535C2211yescharacteristic
180#2509C2212yes—
181#2509C2212yes—
182#2505C2214yes—
183#2504C2212yes—
184#2503C2212yes—
185#2499C2212yes—
186#2497C2212yes—
187#2497C2212yes—
188#2497C2212yes—
189#2497C2212yes—
190#2494C2212yes—
191#2494C2212yes—
192#2494C2212yes—
193#2494C2212yes—
194#2491C2212yes—
195#2491C2212yes—
196#2490C2212yes—
197#2487C2212yes—
198#2487C2212yes—
199#2487C2212yes—
200#2487C2212yes—
201#2486C2212yes—
202#2485C2212yes—
203#2485C2211yescharacteristic
204#2485C2211yescharacteristic
205#2456C2214yes—
206#2456C2214yes—
207#2452C2212yes—
208#2449C2214yes—
209#2449C2214yes—
210#2449C2214yes—
211#2445C2212yes—
212#2443C2214yes—
213#2443C2214yes—
214#2442C2212yes—
215#2441C2212yes—
216#2440C2214yes—
217#2440C2212yes—
218#2440C2212yes—
219#2440C2212yes—
220#2434C2212yes—
221#2432C2212yes—
222#2429C2212yes—
223#2429C2212yes—
224#2429C2212yes—
225#2429C2212yes—
226#2428C2212yes—
227#2427C2212yes—
228#2427C2214yes—
229#2427C2212yes—
230#2425C2214yes—
231#2423C2212yes—
232#2422C2214yes—
233#2422C2212yes—
234#2421C2212yes—
235#2421C2212yes—
236#2421C2212yes—
237#2420C2212yes—
238#2417C2212yes—
239#2417C2212yes—
240#2416C2212yes—
241#2416C2212yes—
242#2416C2212yes—
243#2415C2212yes—
244#2415C2212yes—
245#2415C2212yes—
246#2415C2214yes—
247#2415C2212yes—
248#2414C2212yes—
249#2413C2214yes—
250#2409C2212yes—
251#2409C2212yes—
252#2409C2212yes—
253#2409C2212yes—
254#2409C2212yes—
255#2407C2211yescharacteristic
256#2407C2211yescharacteristic
257#2407C2212yes—
258#2398C2212yes—
259#2397C2212yes—
260#2395C2212yes—
261#2388C2212yes—
262#2388C2212yes—
263#2388C2212yes—
264#2365C2211yescharacteristic
265#2365C2211yescharacteristic
266#2363C2212yes—
267#2363C2212yes—
268#2361C2212yes—
269#2360C2212yes—
270#2354C2211yescharacteristic
271#2352C2212yes—
272Q8×C4⋊C4C2211yescharacteristic
273D4×C4⋊C4C2211yescharacteristic
274D4×C4⋊C4C2211yescharacteristic
275D4×C4⋊C4C2212yes—
276Q8×C22⋊C4C2212yes—
277#2339C2212yes—
278#2330C2212yes—
279#2327C2212yes—
280#2326C2212yes—
281#2319C2212yes—
282#2317C2212yes—
283#2311C2212yes—
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×#121C2211yescharacteristic
287C4×#121C2211yescharacteristic
288C4×#121C2211yescharacteristic
289C4×#121C2211yescharacteristic
290C4×#121C2211yescharacteristic
291C4×#121C2212yes—
292C4×#121C2211yescharacteristic
293C2×#389C2212yes—
294#2290C2212yes—
295#2290C2212yes—
296#2285C2211yescharacteristic
297#2283C2211yescharacteristic
298#2283C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C22×#41C2312yes—
302C22×#41C2312yes—
303C23×Q8C2312yes—
304C23×Q8C2312yes—
305D4×Q8—44no—
306D4×Q8—48no—
307#548—48no—
308#548—48no—
309#547—44no—
310#547—48no—
311#537—48no—
312#536—48no—
313#532—44no—
314C2×C4⋊Q8—44no—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2314yes—
324C2×C4⋊Q8C2314yes—
325C2×#127C2311yescharacteristic
326C2×#125C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2314yes—
330C2×#124C2314yes—
331C2×#124C2314yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2314yes—
355C2×C22⋊Q8C2314yes—
356C2×#121C2311yescharacteristic
357C2×#121C2311yescharacteristic
358C2×#121C2312yes—
359C2×#121C2311yescharacteristic
360C2×#121C2311yescharacteristic
361C2×#121C2312yes—
362C2×#121C2311yescharacteristic
363C2×#121C2311yescharacteristic
364C2×#121C2311yescharacteristic
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2314yes—
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2314yes—
371C2×#121C2314yes—
372C2×#121C2314yes—
373C2×#121C2314yes—
374C4×#41—44no—
375C4×#41—44no—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2312yes—
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2312yes—
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2314yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2312yes—
407C2×C4×D4C2314yes—
408C2×#117C2312yes—
409C2×#117C2311yescharacteristic
410C2×#117C2312yes—
411C2×#117C2312yes—
412C2×#117C2311yescharacteristic
413C2×#117C2311yescharacteristic
414C2×#117C2311yescharacteristic
415C22×C4⋊C4C2312yes—
416C22×C4⋊C4C2312yes—
417C22×C4⋊C4C2312yes—
418C22×C4⋊C4C2312yes—
419C22×C4⋊C4C2314yes—
420C22×C4⋊C4C2312yes—
421C22×C42C2311yescharacteristic
422C22×C42C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2312yes—
425#401C2314yes—
426#401C2314yes—
427#401C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2314yes—
438#400C2314yes—
439#400C2314yes—
440#400C2312yes—
441#400C2312yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2312yes—
446#400C2314yes—
447#399C2314yes—
448#399C2312yes—
449#399C2314yes—
450#399C2314yes—
451#399C2314yes—
452#399C2312yes—
453#399C2312yes—
454#399C2312yes—
455#399C2312yes—
456#399C2314yes—
457#399C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2312yes—
468#398C2314yes—
469#397C2312yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2312yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2312yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#397C2314yes—
486#397C2312yes—
487#397C2312yes—
488#397C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#395C2312yes—
502#395C2314yes—
503#395C2314yes—
504#395C2314yes—
505#395C2314yes—
506#395C2314yes—
507#395C2314yes—
508#395C2312yes—
509#395C2314yes—
510#395C2314yes—
511#395C2312yes—
512#395C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2312yes—
519#394C2312yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2312yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2312yes—
530#394C2312yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2312yes—
535#394C2312yes—
536#394C2312yes—
537#394C2312yes—
538#394C2312yes—
539#394C2312yes—
540#394C2312yes—
541#394C2312yes—
542#394C2314yes—
543#394C2314yes—
544#393C2314yes—
545#393C2314yes—
546#393C2312yes—
547#393C2314yes—
548#393C2314yes—
549#393C2312yes—
550#393C2312yes—
551#393C2312yes—
552#393C2312yes—
553#393C2314yes—
554#392C2312yes—
555#392C2312yes—
556#392C2314yes—
557#392C2312yes—
558#392C2312yes—
559#392C2312yes—
560#392C2312yes—
561#392C2312yes—
562#392C2312yes—
563#392C2312yes—
564#392C2312yes—
565#392C2312yes—
566#392C2312yes—
567#392C2312yes—
568#392C2314yes—
569#391C2314yes—
570#391C2312yes—
571#391C2312yes—
572#391C2312yes—
573#391C2312yes—
574#391C2314yes—
575#391C2311yescharacteristic
576#391C2311yescharacteristic
577#391C2312yes—
578#391C2314yes—
579#391C2312yes—
580#391C2312yes—
581#391C2312yes—
582#390C2314yes—
583#390C2311yescharacteristic
584#390C2312yes—
585#390C2314yes—
586#390C2311yescharacteristic
587#390C2312yes—
588#390C2311yescharacteristic
589#390C2311yescharacteristic
590#390C2314yes—
591#390C2314yes—
592#390C2312yes—
593#390C2312yes—
594#390C2311yescharacteristic
595#390C2311yescharacteristic
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2311yescharacteristic
608#389C2311yescharacteristic
609#389C2311yescharacteristic
610#389C2311yescharacteristic
611#389C2314yes—
612#389C2314yes—
613#389C2314yes—
614#389C2311yescharacteristic
615#389C2314yes—
616#389C2314yes—
617#389C2314yes—
618#389C2314yes—
619#389C2314yes—
620#389C2312yes—
621#389C2314yes—
622#389C2314yes—
623#389C2312yes—
624#389C2312yes—
625#389C2314yes—
626#389C2312yes—
627#389C2312yes—
628#389C2312yes—
629#389C2312yes—
630#389C2312yes—
631#389C2311yescharacteristic
632#389C2311yescharacteristic
633#389C2311yescharacteristic
634#389C2314yes—
635#389C2312yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2312yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2312yes—
650#388C2312yes—
651#388C2312yes—
652#388C2314yes—
653#388C2312yes—
654#388C2314yes—
655#388C2312yes—
656#388C2312yes—
657#388C2312yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2312yes—
662#388C2312yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2314yes—
673#387C2314yes—
674#387C2312yes—
675#387C2312yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2312yes—
682#387C2314yes—
683#387C2312yes—
684#387C2312yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#386C2312yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2312yes—
702#386C2312yes—
703#386C2312yes—
704#386C2312yes—
705#386C2312yes—
706#386C2314yes—
707#386C2314yes—
708#386C2312yes—
709#386C2312yes—
710#386C2312yes—
711#386C2312yes—
712#386C2314yes—
713#386C2314yes—
714#386C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2312yes—
724#385C2312yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2312yes—
729#385C2312yes—
730#385C2312yes—
731#385C2312yes—
732#385C2314yes—
733#385C2314yes—
734#385C2314yes—
735#385C2314yes—
736#385C2314yes—
737#384C2312yes—
738#384C2314yes—
739#384C2311yescharacteristic
740#384C2312yes—
741#384C2312yes—
742#384C2311yescharacteristic
743#384C2312yes—
744#383C2312yes—
745#383C2312yes—
746#382C2314yes—
747#382C2312yes—
748#382C2311yescharacteristic
749#382C2312yes—
750#382C2312yes—
751#382C2311yescharacteristic
752#382C2311yescharacteristic
753#382C2311yescharacteristic
754#381C2314yes—
755#381C2314yes—
756#381C2312yes—
757#381C2312yes—
758#381C2314yes—
759#380C2311yescharacteristic
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2314yes—
768#380C2314yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2314yes—
773#380C2312yes—
774#380C2312yes—
775#380C2314yes—
776#380C2312yes—
777#380C2311yescharacteristic
778#380C2312yes—
779#380C2311yescharacteristic
780#380C2312yes—
781#380C2311yescharacteristic
782#380C2311yescharacteristic
783#380C2311yescharacteristic
784#380C2311yescharacteristic
785#380C2311yescharacteristic
786#380C2311yescharacteristic
787#380C2311yescharacteristic
788#380C2311yescharacteristic
789#380C2311yescharacteristic
790#380C2312yes—
791#380C2314yes—
792#380C2312yes—
793#380C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2311yescharacteristic
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2312yes—
803C4×C4⋊C4C2311yescharacteristic
804C4×C4⋊C4C2312yes—
805C4×C4⋊C4C2311yescharacteristic
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2312yes—
818C4×C22⋊C4C2312yes—
819#376C2312yes—
820#376C2312yes—
821C2×#95C2314yes—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—28no—
825C2×#41—24no—
826C2×#41—42no—
827C2×#41—42no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—42no—
832C2×#41—44no—
833C2×#41—44no—
834C22×Q8—28no—
835C22×Q8—44no—
836C22×Q8—44no—
837C22×Q8—44no—
838C22×Q8—44no—
839C22×Q8—44no—
840C22×Q8C2412yes—
841C22×Q8C2412yes—
842C22×Q8C2411yescharacteristic
843C22×Q8C2411yescharacteristic
844C22×Q8C2414yes—
845C22×Q8C2414yes—
846C22×Q8C2412yes—
847C22×D4C2411yescharacteristic
848C22×D4C2411yescharacteristic
849C22×D4C2412yes—
850C22×D4C2412yes—
851C22×D4C2411yescharacteristic
852C22×D4C2412yes—
853C22×D4C2411yescharacteristic
854C22×D4C2411yescharacteristic
855C22×D4C2411yescharacteristic
856C22×D4C2412yes—
857C22×D4C2414yes—
858C22×D4C2412yes—
859C22×D4C2414yes—
860C22×D4C2412yes—
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2412yes—
864C22×D4C2412yes—
865C22×D4C2412yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C23×C4C2412yes—
870C23×C4C2411yescharacteristic
871C23×C4C2411yescharacteristic
872C23×C4C2411yescharacteristic
873C23×C4C2411yescharacteristic
874C23×C4C2412yes—
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2414yes—
878C23×C4C2411yescharacteristic
879C23×C4C2414yes—
880C23×C4C2411yescharacteristic
881C23×C4C2414yes—
882C23×C4C2414yes—
883C23×C4C2414yes—
884C23×C4C2412yes—
885C4⋊Q8—28no—
886C4⋊Q8—24no—
887C4⋊Q8—24no—
888C4⋊Q8—44no—
889C4⋊Q8—44no—
890C4⋊Q8—42no—
891C4⋊Q8—44no—
892C4⋊Q8—44no—
893C4⋊Q8—48no—
894C4⋊Q8—48no—
895#127—42no—
896#125—44no—
897#124—28no—
898#124—44no—
899#124—48no—
900#124—48no—
901#124—48no—
902#123—48no—
903#123—48no—
904#123—48no—
905#123—48no—
906#123—48no—
907C22⋊Q8—24no—
908C22⋊Q8—28no—
909C22⋊Q8—24no—
910C22⋊Q8—48no—
911C22⋊Q8—48no—
912C22⋊Q8—48no—
913C22⋊Q8—48no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—44no—
917C22⋊Q8—44no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—44no—
921C22⋊Q8—44no—
922C22⋊Q8—44no—
923C22⋊Q8—44no—
924C22⋊Q8—44no—
925C22⋊Q8—44no—
926#121—24no—
927#121—28no—
928#121—24no—
929#121—24no—
930#121—24no—
931#121—44no—
932#121—48no—
933#121—48no—
934#121—48no—
935#121—48no—
936#121—48no—
937#121—42no—
938#121—44no—
939#121—42no—
940#121—42no—
941#121—42no—
942#121—44no—
943#121—48no—
944C4×Q8—24no—
945C4×Q8—42no—
946C4×Q8—42no—
947C4×Q8—42no—
948C4×Q8—44no—
949C4×Q8—44no—
950C4×Q8—44no—
951C4×D4—28no—
952C4×D4—24no—
953C4×D4—24no—
954C4×D4—24no—
955C4×D4—44no—
956C4×D4—42no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—42no—
961C4×D4—42no—
962C4×D4—42no—
963C4×D4—42no—
964C4×D4—42no—
965C4×D4—42no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—44no—
971C4×D4—44no—
972C4×D4—44no—
973C4×D4—48no—
974C4×D4—48no—
975C4×D4—48no—
976#117—42no—
977#117—42no—
978#117—42no—
979#117—44no—
980#117—44no—
981#117—42no—
982#117—44no—
983C2×C4⋊C4—44no—
984C2×C4⋊C4—44no—
985C2×C4⋊C4—44no—
986C2×C4⋊C4—44no—
987C2×C4⋊C4—44no—
988C2×C4⋊C4—48no—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2411yescharacteristic
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2411yescharacteristic
1072C2×C22⋊C4C2411yescharacteristic
1073C2×C22⋊C4C2411yescharacteristic
1074C2×C22⋊C4C2411yescharacteristic
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2411yescharacteristic
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C42—24no—
1122C2×C42—24no—
1123C2×C42—24no—
1124C2×C42—44no—
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2411yescharacteristic
1129C2×C42C2412yes—
1130C2×C42C2411yescharacteristic
1131C2×C42C2412yes—
1132C2×C42C2411yescharacteristic
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2411yescharacteristic
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2414yes—
1141C2×C42C2414yes—
1142C2×C42C2414yes—
1143C2×C42C2414yes—
1144C2×C42C2414yes—
1145C2×C42C2412yes—
1146C2×C42C2411yescharacteristic
1147#95C2412yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211C24C2511yescharacteristic
1212C24C2512yes—
1213C24C2512yes—
1214C24C2511yescharacteristic
1215C24C2512yes—
1216C24C2511yescharacteristic
1217#41—416no—
1218#41—416no—
1219#41—816no—
1220#41—816no—
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—24no—
1224C2×Q8—24no—
1225C2×Q8—24no—
1226C2×Q8—24no—
1227C2×Q8—24no—
1228C2×Q8—24no—
1229C2×Q8—28no—
1230C2×Q8—22no—
1231C2×Q8—41no—
1232C2×Q8—41no—
1233C2×Q8—42no—
1234C2×Q8—44no—
1235C2×Q8—44no—
1236C2×Q8—44no—
1237C2×Q8—44no—
1238C2×Q8—42no—
1239C2×Q8—44no—
1240C2×Q8—42no—
1241C2×Q8—816no—
1242C2×Q8—816no—
1243C2×Q8H(5,𝔽2)14yes—
1244C2×D4—24no—
1245C2×D4—24no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—28no—
1251C2×D4—24no—
1252C2×D4—28no—
1253C2×D4—24no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—22no—
1260C2×D4—22no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—22no—
1264C2×D4—42no—
1265C2×D4—41no—
1266C2×D4—42no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—41no—
1272C2×D4—41no—
1273C2×D4—41no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C2×D4—44no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—42no—
1291C2×D4—42no—
1292C2×D4—42no—
1293C2×D4—42no—
1294C2×D4—42no—
1295C2×D4—42no—
1296C2×D4—42no—
1297C2×D4—42no—
1298C2×D4—44no—
1299C2×D4—42no—
1300C2×D4H(5,𝔽2)14yes—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—24no—
1304C22×C4—28no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—24no—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—24no—
1317C22×C4—22no—
1318C22×C4—22no—
1319C22×C4—22no—
1320C22×C4—22no—
1321C22×C4—24no—
1322C22×C4—24no—
1323C22×C4—22no—
1324C22×C4—22no—
1325C22×C4—24no—
1326C22×C4—22no—
1327C22×C4—22no—
1328C22×C4—24no—
1329C22×C4—22no—
1330C22×C4—22no—
1331C22×C4—22no—
1332C22×C4—22no—
1333C22×C4—28no—
1334C22×C4—42no—
1335C22×C4—41no—
1336C22×C4—41no—
1337C22×C4—42no—
1338C22×C4—44no—
1339C22×C4—44no—
1340C22×C4—44no—
1341C22×C4—44no—
1342C22×C4—44no—
1343C22×C4—44no—
1344C22×C4—44no—
1345C22×C4—44no—
1346C22×C4—44no—
1347C22×C4—41no—
1348C22×C4—41no—
1349C22×C4—41no—
1350C22×C4—41no—
1351C22×C4—42no—
1352C22×C4—44no—
1353C22×C4—42no—
1354C22×C4—44no—
1355C22×C4—44no—
1356C22×C4—44no—
1357C22×C42−1+414yes—
1358C22×C4C2511yescharacteristic
1359C22×C4C2511yescharacteristic
1360C22×C4C2511yescharacteristic
1361C22×C4C2511yescharacteristic
1362C22×C4C2512yes—
1363C22×C4C2512yes—
1364C22×C4C2512yes—
1365C22×C4C2512yes—
1366C22×C4C2512yes—
1367C22×C4C2512yes—
1368C22×C4C2511yescharacteristic
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2514yes—
1372C22×C4C2512yes—
1373C22×C4C2514yes—
1374C22×C4C2512yes—
1375C22×C4C2511yescharacteristic
1376C22×C4C2512yes—
1377C22×C4C2511yescharacteristic
1378C22×C4C2514yes—
1379C22×C4C2514yes—
1380C22×C4C2512yes—
1381C22×C4C2511yescharacteristic
1382C22×C4C2511yescharacteristic
1383C22×C4C2512yes—
1384C22×C4C2511yescharacteristic
1385C22×C4C2511yescharacteristic
1386C22×C4C2511yescharacteristic
1387C4⋊C4—22no—
1388C4⋊C4—22no—
1389C4⋊C4—24no—
1390C4⋊C4—24no—
1391C4⋊C4—24no—
1392C4⋊C4—28no—
1393C4⋊C4—28no—
1394C4⋊C4—24no—
1395C4⋊C4—24no—
1396C4⋊C4—22no—
1397C4⋊C4—22no—
1398C4⋊C4—24no—
1399C4⋊C4—22no—
1400C4⋊C4—24no—
1401C4⋊C4—22no—
1402C4⋊C4—28no—
1403C4⋊C4—22no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—24no—
1408C4⋊C4—22no—
1409C4⋊C4—22no—
1410C4⋊C4—22no—
1411C4⋊C4—24no—
1412C4⋊C4—24no—
1413C4⋊C4—22no—
1414C4⋊C4—42no—
1415C4⋊C4—44no—
1416C4⋊C4—44no—
1417C4⋊C4—44no—
1418C4⋊C4—44no—
1419C4⋊C4—44no—
1420C4⋊C4—44no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—42no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—42no—
1427C4⋊C4—44no—
1428C4⋊C4—41no—
1429C4⋊C4—41no—
1430C4⋊C4—42no—
1431C4⋊C4—41no—
1432C4⋊C4—41no—
1433C4⋊C4—41no—
1434C4⋊C4—41no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—42no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—42no—
1442C4⋊C4—44no—
1443C4⋊C4—44no—
1444C4⋊C4—44no—
1445C4⋊C4—44no—
1446C4⋊C4—44no—
1447C4⋊C4—44no—
1448C4⋊C4—44no—
1449C4⋊C4—44no—
1450C4⋊C4—44no—
1451C4⋊C4—44no—
1452C4⋊C4—44no—
1453C22⋊C4—28no—
1454C22⋊C4—28no—
1455C22⋊C4—24no—
1456C22⋊C4—28no—
1457C22⋊C4—24no—
1458C22⋊C4—24no—
1459C22⋊C4—24no—
1460C22⋊C4—24no—
1461C22⋊C4—24no—
1462C22⋊C4—24no—
1463C22⋊C4—28no—
1464C22⋊C4—24no—
1465C22⋊C4—24no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—41no—
1484C22⋊C4—41no—
1485C22⋊C4—41no—
1486C22⋊C4—41no—
1487C22⋊C4—41no—
1488C22⋊C4—41no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—42no—
1494C22⋊C4—42no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—42no—
1499C22⋊C4—44no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—42no—
1505C22⋊C4—42no—
1506C22⋊C4—42no—
1507C22⋊C4—42no—
1508C22⋊C4—44no—
1509C22⋊C4—42no—
1510C22⋊C4—42no—
1511C22⋊C4—44no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C22⋊C4—44no—
1516C22⋊C4—44no—
1517C22⋊C4—44no—
1518C22⋊C4—44no—
1519C42—22no—
1520C42—22no—
1521C42—22no—
1522C42—22no—
1523C42—22no—
1524C42—22no—
1525C42—22no—
1526C42—22no—
1527C42—22no—
1528C42—24no—
1529C42—24no—
1530C42—24no—
1531C42—24no—
1532C42—24no—
1533C42—42no—
1534C42—42no—
1535C42—44no—
1536C42—44no—
1537C42—44no—
1538C42—44no—
1539C42—44no—
1540C42H(5,𝔽2)14yes—
1541C23—21no—
1542C23—22no—
1543C23—21no—
1544C23—22no—
1545C23—21no—
1546C23—22no—
1547C23—21no—
1548C23—22no—
1549C23—21no—
1550C23—22no—
1551C23—22no—
1552C23—21no—
1553C23—21no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—21no—
1558C23—21no—
1559C23—22no—
1560C23—21no—
1561C23—21no—
1562C23—22no—
1563C23—22no—
1564C23—21no—
1565C23—22no—
1566C23—22no—
1567C23—21no—
1568C23—21no—
1569C23—22no—
1570C23—22no—
1571C23—21no—
1572C23—21no—
1573C23—21no—
1574C23—22no—
1575C23—22no—
1576C23—21no—
1577C23—21no—
1578C23—21no—
1579C23—22no—
1580C23—22no—
1581C23C2×H(5,𝔽2)14yes—
1582C23C2×2−1+412yes—
1583C23C2611yescharacteristic
1584Q8—28no—
1585Q8—44no—
1586Q8—48no—
1587Q8—48no—
1588Q8—88no—
1589Q8—88no—
1590Q8—84no—
1591D4—28no—
1592D4—48no—
1593D4—44no—
1594D4—48no—
1595D4—48no—
1596D4—44no—
1597D4—44no—
1598D4—44no—
1599D4—44no—
1600D4—84no—
1601D4—84no—
1602D4—88no—
1603D4—88no—
1604D4—84no—
1605D4—84no—
1606D4—84no—
1607D4—84no—
1608D4—84no—
1609D4—84no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—28no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—24no—
1636C2×C4—24no—
1637C2×C4—24no—
1638C2×C4—24no—
1639C2×C4—21no—
1640C2×C4—24no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—24no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—24no—
1652C2×C4—24no—
1653C2×C4—22no—
1654C2×C4—21no—
1655C2×C4—22no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—24no—
1665C2×C4—24no—
1666C2×C4—21no—
1667C2×C4—22no—
1668C2×C4—21no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—21no—
1672C2×C4—22no—
1673C2×C4—22no—
1674C2×C4—22no—
1675C2×C4—22no—
1676C2×C4—21no—
1677C2×C4—24no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—21no—
1686C2×C4—22no—
1687C2×C4—24no—
1688C2×C4—21no—
1689C2×C4—48no—
1690C2×C4—44no—
1691C2×C4—44no—
1692C2×C4—48no—
1693C2×C4—44no—
1694C2×C4—48no—
1695C2×C4—44no—
1696C2×C4—48no—
1697C2×C4—44no—
1698C2×C4—44no—
1699C2×C4—82no—
1700C2×C4—82no—
1701C2×C4—88no—
1702C2×C4—88no—
1703C2×C4—84no—
1704C2×C4—88no—
1705C2×C4—88no—
1706C2×C4—164no—
1707C2×C4C2×H(5,𝔽2)12yes—
1708C2×C4C2×H(5,𝔽2)14yes—
1709C2×C4C2×H(5,𝔽2)12yes—
1710C2×C4C2×H(5,𝔽2)12yes—
1711C2×C4C2×H(5,𝔽2)12yes—
1712C2×C4C2×H(5,𝔽2)12yes—
1713C2×C4C2×2−1+412yes—
1714C2×C4C2×2−1+412yes—
1715C2×C4#58512yes—
1716C22—22no—
1717C22—24no—
1718C22—22no—
1719C22—22no—
1720C22—24no—
1721C22—24no—
1722C22—42no—
1723C22—41no—
1724C22—41no—
1725C22—42no—
1726C22—42no—
1727C22—41no—
1728C22—42no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—42no—
1733C22—42no—
1734C22—42no—
1735C22—41no—
1736C22—42no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—42no—
1741C22—42no—
1742C22—42no—
1743C22—41no—
1744C22—42no—
1745C22—41no—
1746C22—42no—
1747C22—41no—
1748C22—41no—
1749C22—42no—
1750C22—42no—
1751C22—42no—
1752C22—41no—
1753C22—41no—
1754C22—41no—
1755C22—42no—
1756C22—41no—
1757C22—42no—
1758C22C22×H(5,𝔽2)11yescharacteristic
1759C22C22×H(5,𝔽2)11yescharacteristic
1760C22C22×H(5,𝔽2)11yescharacteristic
1761C22C22×2−1+411yescharacteristic
1762C22C2×#58511yescharacteristic
1763C222−1+611yescharacteristic
1764C222−1+611yescharacteristic
1765C4—22no—
1766C4—24no—
1767C4—22no—
1768C4—42no—
1769C4—41no—
1770C4—41no—
1771C4—41no—
1772C4—42no—
1773C4—41no—
1774C4—42no—
1775C4—41no—
1776C4—44no—
1777C4—44no—
1778C4—41no—
1779C4—42no—
1780C4—41no—
1781C4—41no—
1782C4—42no—
1783C4—42no—
1784C4—42no—
1785C4—42no—
1786C4—42no—
1787C4—44no—
1788C4—42no—
1789C4—42no—
1790C4—44no—
1791C4—42no—
1792C4#353714yes—
1793C4#354114yes—
1794C2—42no—
1795C2—44no—
1796C2—81no—
1797C2—81no—
1798C2—82no—
1799C2—82no—
1800C2C2×#354111yescharacteristic
1801C2C2×#353711yescharacteristic
1802C2#6288611yescharacteristic
1803C2#6291311yescharacteristic
1804C2#6291511yescharacteristic
1805C2#6292111yescharacteristic
1806C2#6292211yescharacteristic
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. #59214C2semidirect
2. #59212C2semidirect
3. #59127C2semidirect
4. #59125C2semidirect
5. #58074C2semidirect
6. #55861C2semidirect
7. #55645C2semidirect
8. #53933C2semidirect
9. #53137C2semidirect
10. #53045C2semidirect
11. #52970C2semidirect
12. #52968C2semidirect
13. #45267C2semidirect
14. #45091C2semidirect
15. #42989C2semidirect
16. #42908C2semidirect
17. #42844C2semidirect
18. #42786C2semidirect
19. #42709C2semidirect
20. #42448C2semidirect
21. #39343C2semidirect
22. #39340C2semidirect
23. #39156C2semidirect
24. #39149C2semidirect
25. #39146C2semidirect
26. #39052C2semidirect
27. #38930C2semidirect
28. #38098C2semidirect
29. #37505C2semidirect
30. #37340C2semidirect
31. #36444C2semidirect
32. #36259C2semidirect
33. #35279C2semidirect
34. #34909C2semidirect
35. #34609C2semidirect

Maximal subgroups

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

subgroupindex
#592142
#592122
#591272
#591252
#580742
#558612
#556452
#539332
#531372
#530452
#529702
#529682
#452672
#450912
#429892
#429082
#428442
#427862
#427092
#424482
#393432
#393402
#391562
#391492
#391462
#390522
#389302
#380982
#375052
#373402
#364442
#362592
#352792
#349092
#346092