Finite Group Databasebeta

← #8424406

Subgroups — #8424406

Order 512.

5112 conjugacy classes of subgroups.

The subgroup lattice has 1747 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59681C211yesmaximal, characteristic, complemented
2#59454C212yesmaximal, complemented
3#59127C211yesmaximal, characteristic, complemented
4#59125C212yesmaximal, complemented
5#59066C211yesmaximal, characteristic, complemented
6#53626C214yesmaximal, complemented
7#53520C214yesmaximal, complemented
8#53047C212yesmaximal, complemented
9#53041C212yesmaximal, complemented
10#52989C212yesmaximal, complemented
11#52974C212yesmaximal, complemented
12#52427C214yesmaximal, complemented
13#42917C212yesmaximal, complemented
14#42857C212yesmaximal, complemented
15#42751C212yesmaximal, complemented
16#42496C212yesmaximal, complemented
17#40693C214yesmaximal, complemented
18#39767C212yesmaximal, complemented
19#39596C211yesmaximal, characteristic, complemented
20#39363C211yesmaximal, characteristic, complemented
21#39166C212yesmaximal, complemented
22#39149C211yesmaximal, characteristic, complemented
23#38987C211yesmaximal, characteristic, complemented
24#38123C212yesmaximal, complemented
25#37675C212yesmaximal, complemented
26#37628C211yesmaximal, characteristic, complemented
27#37619C211yesmaximal, characteristic, complemented
28#37505C212yesmaximal, complemented
29#37494C212yesmaximal, complemented
30#36587C211yesmaximal, characteristic, complemented
31#36576C211yesmaximal, characteristic, complemented
32#36122C211yesmaximal, characteristic, complemented
33C2×#2546C211yesmaximal, characteristic, complemented
34#34788C211yesmaximal, characteristic, complemented
35#34691C211yesmaximal, characteristic, complemented
36C2×#550C2211yescharacteristic
37C2×D4×Q8C2212yes—
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2212yes—
40C2×#548C2212yes—
41C2×#547C2212yes—
42C2×#536C2212yes—
43C2×#533C2211yescharacteristic
44C2×#532C2211yescharacteristic
45C22×C4⋊Q8C2211yescharacteristic
46C22×C4⋊Q8C2212yes—
47C22×C4×Q8C2211yescharacteristic
48#2858C2211yescharacteristic
49#2857C2211yescharacteristic
50#2856C2211yescharacteristic
51#2856C2212yes—
52#2850C2212yes—
53#2841C2214yes—
54#2838C2214yes—
55#2838C2214yes—
56#2837C2214yes—
57#2837C2214yes—
58#2836C2214yes—
59#2832C2214yes—
60#2831C2214yes—
61#2830C2214yes—
62#2829C2214yes—
63#2827C2214yes—
64#2827C2214yes—
65#2816C2214yes—
66#2814C2214yes—
67#2808C2214yes—
68#2803C2214yes—
69#2802C2214yes—
70#2800C2214yes—
71#2796C2214yes—
72#2796C2214yes—
73#2790C2214yes—
74#2790C2214yes—
75#2788C2214yes—
76#2787C2214yes—
77#2786C2214yes—
78#2780C2214yes—
79#2776C2214yes—
80#2746C2214yes—
81#2742C2214yes—
82#2740C2214yes—
83#2739C2214yes—
84#2731C2214yes—
85#2730C2214yes—
86#2729C2214yes—
87#2728C2214yes—
88#2724C2214yes—
89#2724C2214yes—
90#2720C2214yes—
91#2701C2214yes—
92#2701C2214yes—
93#2692C2214yes—
94#2681C2214yes—
95#2681C2214yes—
96#2677C2214yes—
97#2677C2214yes—
98#2677C2214yes—
99#2674C2214yes—
100#2674C2214yes—
101#2674C2214yes—
102#2674C2214yes—
103#2671C2214yes—
104#2665C2214yes—
105#2663C2214yes—
106#2658C2212yes—
107#2654C2214yes—
108#2653C2214yes—
109#2652C2214yes—
110#2651C2214yes—
111#2647C2212yes—
112#2645C2212yes—
113#2644C2212yes—
114#2644C2212yes—
115#2643C2214yes—
116#2640C2212yes—
117#2639C2214yes—
118#2639C2214yes—
119#2633C2214yes—
120#2628C2212yes—
121#2627C2214yes—
122#2625C2212yes—
123#2624C2212yes—
124#2624C2212yes—
125#2621C2212yes—
126#2620C2212yes—
127#2597C2214yes—
128#2590C2214yes—
129#2589C2214yes—
130#2583C2214yes—
131#2580C2212yes—
132#2580C2212yes—
133#2580C2212yes—
134#2571C2211yescharacteristic
135#2570C2212yes—
136#2570C2212yes—
137#2567C2212yes—
138#2564C2214yes—
139#2551C2212yes—
140#2548C2211yescharacteristic
141#2548C2211yescharacteristic
142#2548C2212yes—
143#2547C2212yes—
144#2546C2212yes—
145#2546C2214yes—
146#2546C2212yes—
147#2546C2211yescharacteristic
148#2546C2211yescharacteristic
149#2546C2212yes—
150#2546C2211yescharacteristic
151#2546C2212yes—
152#2546C2211yescharacteristic
153#2546C2212yes—
154#2546C2211yescharacteristic
155#2545C2212yes—
156#2545C2212yes—
157#2543C2214yes—
158#2542C2212yes—
159#2542C2211yescharacteristic
160#2538C2212yes—
161#2538C2211yescharacteristic
162#2525C2212yes—
163#2516C2212yes—
164#2513C2212yes—
165#2513C2212yes—
166#2513C2212yes—
167#2513C2211yescharacteristic
168#2513C2212yes—
169#2511C2212yes—
170#2510C2212yes—
171#2509C2211yescharacteristic
172#2509C2212yes—
173#2509C2212yes—
174#2507C2212yes—
175#2507C2212yes—
176#2504C2211yescharacteristic
177#2504C2212yes—
178#2497C2212yes—
179#2494C2212yes—
180#2494C2211yescharacteristic
181#2492C2212yes—
182#2491C2212yes—
183#2491C2214yes—
184#2491C2212yes—
185#2490C2211yescharacteristic
186#2487C2211yescharacteristic
187#2473C2212yes—
188#2465C2212yes—
189#2462C2212yes—
190#2454C2212yes—
191#2452C2212yes—
192#2452C2212yes—
193#2452C2212yes—
194#2452C2212yes—
195#2452C2212yes—
196#2451C2211yescharacteristic
197#2450C2214yes—
198#2449C2214yes—
199#2449C2214yes—
200#2449C2212yes—
201#2449C2214yes—
202#2448C2212yes—
203#2447C2212yes—
204#2447C2212yes—
205#2446C2212yes—
206#2446C2211yescharacteristic
207#2445C2212yes—
208#2445C2212yes—
209#2445C2212yes—
210#2444C2214yes—
211#2444C2212yes—
212#2444C2214yes—
213#2443C2214yes—
214#2443C2214yes—
215#2443C2214yes—
216#2443C2214yes—
217#2443C2214yes—
218#2442C2211yescharacteristic
219#2440C2214yes—
220#2440C2212yes—
221#2440C2211yescharacteristic
222#2436C2212yes—
223#2436C2212yes—
224#2434C2211yescharacteristic
225#2434C2212yes—
226#2434C2212yes—
227#2432C2212yes—
228#2432C2212yes—
229#2432C2212yes—
230#2432C2212yes—
231#2432C2212yes—
232#2429C2212yes—
233#2429C2212yes—
234#2429C2211yescharacteristic
235#2429C2212yes—
236#2428C2212yes—
237#2427C2212yes—
238#2426C2214yes—
239#2426C2212yes—
240#2423C2211yescharacteristic
241#2422C2212yes—
242#2421C2212yes—
243#2421C2212yes—
244#2417C2211yescharacteristic
245#2416C2212yes—
246#2416C2212yes—
247#2416C2212yes—
248#2416C2214yes—
249#2416C2214yes—
250#2416C2211yescharacteristic
251#2409C2212yes—
252#2409C2211yescharacteristic
253#2409C2212yes—
254#2407C2212yes—
255#2401C2212yes—
256#2399C2212yes—
257#2396C2212yes—
258#2395C2212yes—
259C2×#398C2214yes—
260#2370C2212yes—
261#2366C2211yescharacteristic
262#2365C2212yes—
263#2365C2211yescharacteristic
264#2361C2212yes—
265#2361C2212yes—
266#2361C2212yes—
267#2361C2212yes—
268#2357C2212yes—
269#2355C2211yescharacteristic
270Q8×C4⋊C4C2211yescharacteristic
271D4×C4⋊C4C2212yes—
272D4×C4⋊C4C2214yes—
273#2341C2212yes—
274#2327C2212yes—
275#2325C2214yes—
276#2324C2212yes—
277#2319C2212yes—
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2211yescharacteristic
280C4×#125C2211yescharacteristic
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2212yes—
286C4×#121C2211yescharacteristic
287C4×#121C2211yescharacteristic
288C4×#121C2212yes—
289#2295C2211yescharacteristic
290C2×#391C2212yes—
291#2293C2211yescharacteristic
292C2×#389C2212yes—
293C2×#389C2212yes—
294#2290C2212yes—
295#2290C2212yes—
296#2283C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2312yes—
301C23×Q8C2311yescharacteristic
302C23×Q8C2312yes—
303C23×Q8C2312yes—
304#550—44no—
305D4×Q8—44no—
306D4×Q8—48no—
307#548—48no—
308#548—48no—
309#547—48no—
310#536—48no—
311#533—44no—
312#532—44no—
313C2×C4⋊Q8—44no—
314C2×C4⋊Q8—48no—
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2311yescharacteristic
324C2×C4⋊Q8C2312yes—
325C2×C4⋊Q8C2314yes—
326C2×C4⋊Q8C2314yes—
327C2×C4⋊Q8C2312yes—
328C2×C4⋊Q8C2312yes—
329C2×C4⋊Q8C2312yes—
330C2×C4⋊Q8C2312yes—
331C2×C4⋊Q8C2314yes—
332C2×#127C2311yescharacteristic
333C2×#127C2312yes—
334C2×#125C2311yescharacteristic
335C2×#125C2312yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2312yes—
340C2×#124C2312yes—
341C2×#124C2314yes—
342C2×#124C2314yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2311yescharacteristic
360C2×C22⋊Q8C2311yescharacteristic
361C2×C22⋊Q8C2314yes—
362C2×C22⋊Q8C2314yes—
363C2×C22⋊Q8C2314yes—
364C2×C22⋊Q8C2314yes—
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2311yescharacteristic
369C2×#121C2312yes—
370C2×#121C2314yes—
371C2×#121C2312yes—
372C2×#121C2314yes—
373C2×#121C2312yes—
374C2×#121C2312yes—
375C2×#121C2314yes—
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379C2×C4×Q8—44no—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×Q8C2311yescharacteristic
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2311yescharacteristic
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2311yescharacteristic
390C2×C4×Q8C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2314yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2314yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2311yescharacteristic
407C2×#117C2312yes—
408C2×#117C2312yes—
409C22×C4⋊C4C2311yescharacteristic
410C22×C4⋊C4C2311yescharacteristic
411C22×C4⋊C4C2314yes—
412C22×C4⋊C4C2314yes—
413C22×C4⋊C4C2312yes—
414C22×C4⋊C4C2312yes—
415C22×C4⋊C4C2312yes—
416C22×C4⋊C4C2314yes—
417C22×C4⋊C4C2311yescharacteristic
418C22×C42C2311yescharacteristic
419C22×C42C2311yescharacteristic
420C22×C42C2312yes—
421C22×C42C2312yes—
422#401C2312yes—
423#401C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2312yes—
435#400C2312yes—
436#400C2312yes—
437#400C2312yes—
438#400C2314yes—
439#400C2312yes—
440#399C2314yes—
441#399C2314yes—
442#399C2314yes—
443#399C2314yes—
444#399C2312yes—
445#399C2314yes—
446#399C2314yes—
447#399C2312yes—
448#399C2314yes—
449#399C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2312yes—
456#398C2312yes—
457#398C2314yes—
458#398C2314yes—
459#398C2312yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2312yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2312yes—
470#398C2314yes—
471#398C2314yes—
472#398C2314yes—
473#398C2312yes—
474#398C2312yes—
475#397C2312yes—
476#397C2312yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#397C2314yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2314yes—
490#397C2314yes—
491#397C2312yes—
492#397C2314yes—
493#397C2314yes—
494#397C2314yes—
495#397C2314yes—
496#397C2312yes—
497#397C2312yes—
498#397C2312yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2314yes—
504#396C2314yes—
505#396C2314yes—
506#396C2314yes—
507#396C2314yes—
508#396C2314yes—
509#396C2314yes—
510#396C2312yes—
511#396C2312yes—
512#396C2312yes—
513#396C2314yes—
514#395C2314yes—
515#395C2314yes—
516#395C2312yes—
517#395C2314yes—
518#395C2312yes—
519#395C2314yes—
520#395C2314yes—
521#395C2314yes—
522#395C2312yes—
523#395C2312yes—
524#395C2312yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2312yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2314yes—
542#394C2312yes—
543#394C2314yes—
544#394C2314yes—
545#393C2314yes—
546#393C2314yes—
547#393C2314yes—
548#393C2314yes—
549#393C2314yes—
550#393C2314yes—
551#393C2314yes—
552#393C2314yes—
553#393C2314yes—
554#393C2312yes—
555#392C2314yes—
556#391C2311yescharacteristic
557#391C2312yes—
558#391C2311yescharacteristic
559#391C2314yes—
560#391C2314yes—
561#391C2311yescharacteristic
562#391C2312yes—
563#391C2312yes—
564#391C2312yes—
565#391C2312yes—
566#391C2312yes—
567#391C2312yes—
568#391C2311yescharacteristic
569#391C2312yes—
570#391C2314yes—
571#391C2312yes—
572#391C2311yescharacteristic
573#391C2312yes—
574#391C2311yescharacteristic
575#390C2314yes—
576#390C2314yes—
577#390C2312yes—
578#390C2312yes—
579#390C2312yes—
580#390C2311yescharacteristic
581#390C2312yes—
582#390C2312yes—
583#390C2312yes—
584#390C2312yes—
585#390C2312yes—
586#390C2314yes—
587#390C2312yes—
588#390C2312yes—
589#390C2312yes—
590#390C2314yes—
591#390C2312yes—
592#390C2312yes—
593#390C2312yes—
594#390C2312yes—
595#390C2312yes—
596#390C2312yes—
597#390C2311yescharacteristic
598#390C2311yescharacteristic
599#390C2311yescharacteristic
600#390C2312yes—
601#389C2311yescharacteristic
602#389C2311yescharacteristic
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2311yescharacteristic
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2312yes—
617#389C2312yes—
618#389C2312yes—
619#389C2312yes—
620#389C2314yes—
621#389C2314yes—
622#389C2314yes—
623#389C2312yes—
624#389C2314yes—
625#389C2314yes—
626#389C2314yes—
627#389C2314yes—
628#389C2314yes—
629#389C2312yes—
630#389C2312yes—
631#389C2312yes—
632#389C2312yes—
633#389C2314yes—
634#389C2311yescharacteristic
635#389C2311yescharacteristic
636#389C2311yescharacteristic
637#389C2314yes—
638#389C2311yescharacteristic
639#389C2311yescharacteristic
640#389C2312yes—
641#389C2311yescharacteristic
642#389C2312yes—
643#389C2314yes—
644#389C2311yescharacteristic
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2312yes—
650#388C2314yes—
651#388C2312yes—
652#388C2314yes—
653#388C2314yes—
654#388C2312yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2314yes—
664#388C2312yes—
665#388C2312yes—
666#388C2314yes—
667#388C2312yes—
668#388C2314yes—
669#388C2312yes—
670#388C2312yes—
671#388C2312yes—
672#388C2312yes—
673#387C2312yes—
674#387C2312yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2312yes—
685#387C2312yes—
686#387C2312yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2312yes—
692#387C2314yes—
693#387C2312yes—
694#387C2312yes—
695#387C2312yes—
696#387C2312yes—
697#387C2312yes—
698#387C2312yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2312yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2312yes—
712#386C2312yes—
713#386C2312yes—
714#386C2314yes—
715#386C2314yes—
716#386C2312yes—
717#386C2312yes—
718#386C2312yes—
719#386C2312yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2314yes—
730#385C2314yes—
731#385C2314yes—
732#385C2314yes—
733#385C2314yes—
734#385C2314yes—
735#385C2312yes—
736#385C2314yes—
737#385C2314yes—
738#385C2312yes—
739#385C2312yes—
740#385C2314yes—
741#385C2314yes—
742#385C2312yes—
743#385C2312yes—
744#385C2312yes—
745#385C2312yes—
746#385C2312yes—
747#384C2311yescharacteristic
748#384C2311yescharacteristic
749#384C2314yes—
750#384C2312yes—
751#384C2312yes—
752#383C2312yes—
753#382C2311yescharacteristic
754#382C2311yescharacteristic
755#382C2312yes—
756#382C2312yes—
757#382C2312yes—
758#382C2311yescharacteristic
759#381C2312yes—
760#381C2314yes—
761#381C2314yes—
762#380C2312yes—
763#380C2312yes—
764#380C2314yes—
765#380C2312yes—
766#380C2314yes—
767#380C2312yes—
768#380C2314yes—
769#380C2312yes—
770#380C2314yes—
771#380C2311yescharacteristic
772#380C2311yescharacteristic
773#380C2311yescharacteristic
774#380C2311yescharacteristic
775#380C2311yescharacteristic
776#380C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2314yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2311yescharacteristic
801C4×C4⋊C4C2311yescharacteristic
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816#376C2312yes—
817#376C2312yes—
818C2×#95C2314yes—
819C2×#95C2314yes—
820C2×#95C2312yes—
821C43C2311yescharacteristic
822C2×#41—28no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C22×Q8—24no—
829C22×Q8—24no—
830C22×Q8—28no—
831C22×Q8—42no—
832C22×Q8—44no—
833C22×Q8—44no—
834C22×Q8—44no—
835C22×Q8—44no—
836C22×Q8—44no—
837C22×Q8C2411yescharacteristic
838C22×Q8C2411yescharacteristic
839C22×Q8C2412yes—
840C22×Q8C2412yes—
841C22×Q8C2412yes—
842C22×Q8C2411yescharacteristic
843C22×Q8C2414yes—
844C22×Q8C2412yes—
845C22×Q8C2414yes—
846C22×D4C2412yes—
847C22×D4C2411yescharacteristic
848C22×D4C2414yes—
849C22×D4C2411yescharacteristic
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C23×C4C2411yescharacteristic
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2411yescharacteristic
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2414yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2411yescharacteristic
871C23×C4C2414yes—
872C23×C4C2414yes—
873C4⋊Q8—28no—
874C4⋊Q8—28no—
875C4⋊Q8—24no—
876C4⋊Q8—24no—
877C4⋊Q8—24no—
878C4⋊Q8—44no—
879C4⋊Q8—44no—
880C4⋊Q8—42no—
881C4⋊Q8—44no—
882C4⋊Q8—44no—
883C4⋊Q8—44no—
884C4⋊Q8—44no—
885C4⋊Q8—42no—
886C4⋊Q8—44no—
887C4⋊Q8—48no—
888C4⋊Q8—48no—
889C4⋊Q8—48no—
890#127—24no—
891#127—44no—
892#125—24no—
893#125—44no—
894#124—44no—
895#124—44no—
896#124—44no—
897#124—44no—
898#124—44no—
899#124—48no—
900#124—48no—
901#123—48no—
902#123—48no—
903#123—48no—
904#123—48no—
905C22⋊Q8—24no—
906C22⋊Q8—24no—
907C22⋊Q8—44no—
908C22⋊Q8—48no—
909C22⋊Q8—48no—
910C22⋊Q8—48no—
911C22⋊Q8—48no—
912C22⋊Q8—48no—
913C22⋊Q8—44no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—42no—
917C22⋊Q8—42no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—44no—
921C22⋊Q8—44no—
922C22⋊Q8—44no—
923#121—28no—
924#121—28no—
925#121—24no—
926#121—24no—
927#121—48no—
928#121—48no—
929#121—44no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—44no—
934#121—48no—
935#121—48no—
936#121—48no—
937C4×Q8—24no—
938C4×Q8—24no—
939C4×Q8—24no—
940C4×Q8—44no—
941C4×Q8—44no—
942C4×Q8—44no—
943C4×Q8—42no—
944C4×Q8—42no—
945C4×Q8—44no—
946C4×Q8—44no—
947C4×Q8—44no—
948C4×D4—24no—
949C4×D4—28no—
950C4×D4—24no—
951C4×D4—28no—
952C4×D4—24no—
953C4×D4—44no—
954C4×D4—44no—
955C4×D4—44no—
956C4×D4—44no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—48no—
960C4×D4—42no—
961C4×D4—48no—
962C4×D4—48no—
963C4×D4—48no—
964#117—44no—
965#117—44no—
966C2×C4⋊C4—24no—
967C2×C4⋊C4—24no—
968C2×C4⋊C4—44no—
969C2×C4⋊C4—42no—
970C2×C4⋊C4—48no—
971C2×C4⋊C4—44no—
972C2×C4⋊C4—44no—
973C2×C4⋊C4—48no—
974C2×C4⋊C4—48no—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2411yescharacteristic
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2411yescharacteristic
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2414yes—
1104C2×C42—24no—
1105C2×C42—24no—
1106C2×C42—44no—
1107C2×C42—44no—
1108C2×C42C2411yescharacteristic
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2412yes—
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2414yes—
1126C2×C42C2414yes—
1127C2×C42C2414yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2414yes—
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2412yes—
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2411yescharacteristic
1159#95C2411yescharacteristic
1160#95C2411yescharacteristic
1161#95C2411yescharacteristic
1162#95C2411yescharacteristic
1163#95C2411yescharacteristic
1164#95C2412yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206C24C2511yescharacteristic
1207C24C2512yes—
1208C24C2514yes—
1209C24C2511yescharacteristic
1210#41—816no—
1211#41—816no—
1212C2×Q8—22no—
1213C2×Q8—22no—
1214C2×Q8—22no—
1215C2×Q8—22no—
1216C2×Q8—24no—
1217C2×Q8—24no—
1218C2×Q8—22no—
1219C2×Q8—24no—
1220C2×Q8—22no—
1221C2×Q8—24no—
1222C2×Q8—24no—
1223C2×Q8—22no—
1224C2×Q8—24no—
1225C2×Q8—24no—
1226C2×Q8—24no—
1227C2×Q8—22no—
1228C2×Q8—28no—
1229C2×Q8—42no—
1230C2×Q8—42no—
1231C2×Q8—44no—
1232C2×Q8—44no—
1233C2×Q8—44no—
1234C2×Q8—42no—
1235C2×Q8—44no—
1236C2×Q8—44no—
1237C2×Q8—42no—
1238C2×Q8—416no—
1239C2×Q8—816no—
1240C2×Q8—816no—
1241C2×Q8H(5,𝔽2)14yes—
1242C2×D4—24no—
1243C2×D4—22no—
1244C2×D4—28no—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—28no—
1248C2×D4—22no—
1249C2×D4—28no—
1250C2×D4—24no—
1251C2×D4—22no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—28no—
1258C2×D4—24no—
1259C2×D4—22no—
1260C2×D4—22no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—42no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—28no—
1284C22×C4—24no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—24no—
1291C22×C4—24no—
1292C22×C4—22no—
1293C22×C4—22no—
1294C22×C4—24no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—28no—
1299C22×C4—28no—
1300C22×C4—42no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—41no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4—44no—
1315C22×C4—44no—
1316C22×C4—44no—
1317C22×C4—41no—
1318C22×C4—44no—
1319C22×C4—41no—
1320C22×C4—42no—
1321C22×C4H(5,𝔽2)14yes—
1322C22×C42−1+414yes—
1323C22×C4C2511yescharacteristic
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2511yescharacteristic
1330C22×C4C2512yes—
1331C22×C4C2511yescharacteristic
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2514yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2511yescharacteristic
1339C22×C4C2512yes—
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C22×C4C2512yes—
1343C22×C4C2514yes—
1344C22×C4C2514yes—
1345C22×C4C2512yes—
1346C22×C4C2512yes—
1347C22×C4C2511yescharacteristic
1348C22×C4C2511yescharacteristic
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2511yescharacteristic
1352C22×C4C2511yescharacteristic
1353C22×C4C2511yescharacteristic
1354C4⋊C4—28no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—28no—
1365C4⋊C4—28no—
1366C4⋊C4—28no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—24no—
1370C4⋊C4—22no—
1371C4⋊C4—24no—
1372C4⋊C4—22no—
1373C4⋊C4—24no—
1374C4⋊C4—22no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—24no—
1379C4⋊C4—24no—
1380C4⋊C4—22no—
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—22no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—44no—
1409C4⋊C4—41no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—44no—
1422C4⋊C4—42no—
1423C4⋊C4—42no—
1424C4⋊C4—42no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C4⋊C42−1+414yes—
1429C22⋊C4—22no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—22no—
1433C22⋊C4—24no—
1434C22⋊C4—22no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—22no—
1438C22⋊C4—28no—
1439C22⋊C4—24no—
1440C22⋊C4—22no—
1441C22⋊C4—28no—
1442C22⋊C4—24no—
1443C22⋊C4—28no—
1444C22⋊C4—24no—
1445C22⋊C4—42no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—44no—
1458C22⋊C4—41no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—44no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C42—22no—
1484C42—22no—
1485C42—22no—
1486C42—22no—
1487C42—22no—
1488C42—22no—
1489C42—24no—
1490C42—24no—
1491C42—24no—
1492C42—24no—
1493C42—22no—
1494C42—24no—
1495C42—22no—
1496C42—24no—
1497C42—22no—
1498C42—24no—
1499C42—22no—
1500C42—42no—
1501C42—42no—
1502C42—42no—
1503C42—42no—
1504C42—41no—
1505C42—44no—
1506C42—41no—
1507C42—44no—
1508C42—44no—
1509C42—44no—
1510C42H(5,𝔽2)14yes—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—22no—
1517C23—21no—
1518C23—24no—
1519C23—22no—
1520C23—22no—
1521C23—24no—
1522C23—21no—
1523C23—24no—
1524C23—21no—
1525C23—24no—
1526C23—22no—
1527C23—24no—
1528C23—22no—
1529C23—21no—
1530C23—24no—
1531C23—21no—
1532C23—22no—
1533C23—21no—
1534C23—24no—
1535C23—22no—
1536C23C2×H(5,𝔽2)12yes—
1537C23C2×2−1+412yes—
1538C23#58512yes—
1539C23C2611yescharacteristic
1540Q8—28no—
1541Q8—48no—
1542Q8—44no—
1543Q8—44no—
1544Q8—48no—
1545Q8—48no—
1546Q8—88no—
1547Q8—84no—
1548Q8—88no—
1549D4—48no—
1550D4—44no—
1551D4—416no—
1552D4—48no—
1553D4—44no—
1554D4—48no—
1555D4—84no—
1556D4—84no—
1557D4—88no—
1558D4—88no—
1559D4—164no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—28no—
1571C2×C4—28no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—24no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—24no—
1603C2×C4—24no—
1604C2×C4—24no—
1605C2×C4—24no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—21no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—24no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—24no—
1626C2×C4—22no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—48no—
1645C2×C4—44no—
1646C2×C4—48no—
1647C2×C4—48no—
1648C2×C4—48no—
1649C2×C4—44no—
1650C2×C4—44no—
1651C2×C4—88no—
1652C2×C4—82no—
1653C2×C4—88no—
1654C2×C4—84no—
1655C2×C4—88no—
1656C2×C4—88no—
1657C2×C4—88no—
1658C2×C4C2×H(5,𝔽2)12yes—
1659C2×C4C2×H(5,𝔽2)12yes—
1660C2×C4C2×H(5,𝔽2)14yes—
1661C2×C4C2×H(5,𝔽2)12yes—
1662C2×C4C2×H(5,𝔽2)12yes—
1663C2×C4C2×H(5,𝔽2)12yes—
1664C2×C4C2×H(5,𝔽2)12yes—
1665C2×C4C2×2−1+412yes—
1666C2×C4C2×2−1+414yes—
1667C2×C4C2×2−1+412yes—
1668C2×C4C2×2−1+412yes—
1669C22—22no—
1670C22—22no—
1671C22—22no—
1672C22—22no—
1673C22—22no—
1674C22—22no—
1675C22—42no—
1676C22—41no—
1677C22—44no—
1678C22—41no—
1679C22—42no—
1680C22—44no—
1681C22—42no—
1682C22—41no—
1683C22—44no—
1684C22—44no—
1685C22—41no—
1686C22—42no—
1687C22—41no—
1688C22—42no—
1689C22—44no—
1690C22—42no—
1691C22—41no—
1692C22—44no—
1693C22—41no—
1694C22—44no—
1695C22—42no—
1696C22#355414yes—
1697C22C22×H(5,𝔽2)11yescharacteristic
1698C22C22×H(5,𝔽2)11yescharacteristic
1699C22C22×H(5,𝔽2)11yescharacteristic
1700C22C22×2−1+411yescharacteristic
1701C22C22×2−1+411yescharacteristic
1702C22C2×#58511yescharacteristic
1703C222−1+611yescharacteristic
1704C4—22no—
1705C4—24no—
1706C4—22no—
1707C4—24no—
1708C4—22no—
1709C4—41no—
1710C4—42no—
1711C4—42no—
1712C4—44no—
1713C4—42no—
1714C4—44no—
1715C4—41no—
1716C4—42no—
1717C4—41no—
1718C4—44no—
1719C4—41no—
1720C4—42no—
1721C4—42no—
1722C4—41no—
1723C4—42no—
1724C4—42no—
1725C4—41no—
1726C4—42no—
1727C4—42no—
1728C4—41no—
1729C4—42no—
1730C4—42no—
1731C4—41no—
1732C4—42no—
1733C4#353714yes—
1734C4#355214yes—
1735C2—24no—
1736C2—82no—
1737C2—81no—
1738C2—84no—
1739C2C2×#353711yescharacteristic
1740C2C2×#355211yescharacteristic
1741C2C2×#355411yescharacteristic
1742C2#6291311yescharacteristic
1743C2#6294611yescharacteristic
1744C2#6295411yescharacteristic
1745C2#6301511yescharacteristic
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. #59681C2semidirect
2. #59454C2semidirect
3. #59127C2semidirect
4. #59125C2semidirect
5. #59066C2semidirect
6. #53626C2semidirect
7. #53520C2semidirect
8. #53047C2semidirect
9. #53041C2semidirect
10. #52989C2semidirect
11. #52974C2semidirect
12. #52427C2semidirect
13. #42917C2semidirect
14. #42857C2semidirect
15. #42751C2semidirect
16. #42496C2semidirect
17. #40693C2semidirect
18. #39767C2semidirect
19. #39596C2semidirect
20. #39363C2semidirect
21. #39166C2semidirect
22. #39149C2semidirect
23. #38987C2semidirect
24. #38123C2semidirect
25. #37675C2semidirect
26. #37628C2semidirect
27. #37619C2semidirect
28. #37505C2semidirect
29. #37494C2semidirect
30. #36587C2semidirect
31. #36576C2semidirect
32. #36122C2semidirect
33. C2×#2546C2semidirect
34. #34788C2semidirect
35. #34691C2semidirect

Maximal subgroups

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

subgroupindex
#596812
#594542
#591272
#591252
#590662
#536262
#535202
#530472
#530412
#529892
#529742
#524272
#429172
#428572
#427512
#424962
#406932
#397672
#395962
#393632
#391662
#391492
#389872
#381232
#376752
#376282
#376192
#375052
#374942
#365872
#365762
#361222
C2×#25462
#347882
#346912