Finite Group Databasebeta

← #7779552

Subgroups — #7779552

Order 512.

5217 conjugacy classes of subgroups.

The subgroup lattice has 1790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59409C212yesmaximal, complemented
2#59248C211yesmaximal, characteristic, complemented
3#59219C211yesmaximal, characteristic, complemented
4#59080C211yesmaximal, characteristic, complemented
5#59064C211yesmaximal, characteristic, complemented
6#59040C212yesmaximal, complemented
7#50088C214yesmaximal, complemented
8#48571C214yesmaximal, complemented
9#47067C214yesmaximal, complemented
10#46489C214yesmaximal, complemented
11#45687C212yesmaximal, complemented
12#45616C212yesmaximal, complemented
13#45368C212yesmaximal, complemented
14#45360C212yesmaximal, complemented
15#42605C212yesmaximal, complemented
16#42542C212yesmaximal, complemented
17#40151C212yesmaximal, complemented
18#39854C212yesmaximal, complemented
19#39726C211yesmaximal, characteristic, complemented
20#39596C211yesmaximal, characteristic, complemented
21#39004C212yesmaximal, complemented
22#38983C212yesmaximal, complemented
23#37975C212yesmaximal, complemented
24#37780C212yesmaximal, complemented
25#37287C212yesmaximal, complemented
26#36587C211yesmaximal, characteristic, complemented
27#36493C211yesmaximal, characteristic, complemented
28#36274C211yesmaximal, characteristic, complemented
29#36177C211yesmaximal, characteristic, complemented
30#36133C211yesmaximal, characteristic, complemented
31#36126C211yesmaximal, characteristic, complemented
32#35292C211yesmaximal, characteristic, complemented
33#34947C211yesmaximal, characteristic, complemented
34#34393C212yesmaximal, complemented
35C4×#537C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2212yes—
39C2×#547C2212yes—
40C2×#537C2211yescharacteristic
41C2×#533C2212yes—
42C2×#533C2211yescharacteristic
43C2×#532C2212yes—
44C2×#532C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2856C2211yescharacteristic
51#2855C2212yes—
52#2855C2212yes—
53#2855C2212yes—
54#2854C2212yes—
55#2850C2212yes—
56#2850C2212yes—
57#2838C2214yes—
58#2826C2214yes—
59#2795C2214yes—
60#2793C2214yes—
61#2790C2214yes—
62#2789C2214yes—
63#2788C2214yes—
64#2784C2214yes—
65#2775C2214yes—
66#2765C2214yes—
67#2765C2214yes—
68#2760C2214yes—
69#2760C2214yes—
70#2759C2214yes—
71#2759C2214yes—
72#2752C2214yes—
73#2749C2214yes—
74#2749C2214yes—
75#2746C2214yes—
76#2746C2214yes—
77#2746C2214yes—
78#2745C2214yes—
79#2737C2214yes—
80#2737C2214yes—
81#2720C2214yes—
82#2720C2214yes—
83#2711C2214yes—
84#2708C2214yes—
85#2707C2214yes—
86#2700C2214yes—
87#2700C2214yes—
88#2699C2214yes—
89#2696C2214yes—
90#2694C2214yes—
91#2694C2214yes—
92#2692C2214yes—
93#2692C2214yes—
94#2688C2214yes—
95#2687C2214yes—
96#2681C2214yes—
97#2676C2214yes—
98#2676C2214yes—
99#2653C2214yes—
100#2643C2214yes—
101#2638C2214yes—
102#2632C2214yes—
103#2628C2212yes—
104#2624C2212yes—
105#2620C2212yes—
106#2615C2212yes—
107#2610C2214yes—
108#2599C2214yes—
109#2598C2214yes—
110#2597C2214yes—
111#2592C2212yes—
112#2592C2212yes—
113#2582C2211yescharacteristic
114#2580C2212yes—
115#2580C2212yes—
116#2571C2211yescharacteristic
117#2568C2211yescharacteristic
118#2568C2211yescharacteristic
119#2567C2212yes—
120#2567C2211yescharacteristic
121#2566C2212yes—
122#2565C2212yes—
123#2564C2212yes—
124#2564C2212yes—
125#2563C2211yescharacteristic
126#2557C2214yes—
127#2551C2211yescharacteristic
128#2549C2214yes—
129#2548C2211yescharacteristic
130#2547C2212yes—
131#2546C2211yescharacteristic
132#2545C2212yes—
133#2542C2212yes—
134#2542C2211yescharacteristic
135#2541C2211yescharacteristic
136#2540C2212yes—
137#2540C2212yes—
138#2538C2212yes—
139#2538C2214yes—
140#2538C2211yescharacteristic
141#2536C2212yes—
142#2535C2212yes—
143#2535C2212yes—
144#2533C2214yes—
145#2527C2214yes—
146#2514C2212yes—
147#2514C2212yes—
148#2514C2212yes—
149#2514C2212yes—
150#2513C2212yes—
151#2513C2212yes—
152#2510C2214yes—
153#2509C2212yes—
154#2507C2212yes—
155#2506C2212yes—
156#2504C2212yes—
157#2503C2212yes—
158#2494C2212yes—
159#2494C2212yes—
160#2494C2212yes—
161#2494C2212yes—
162#2493C2214yes—
163#2492C2212yes—
164#2492C2212yes—
165#2492C2212yes—
166#2491C2212yes—
167#2491C2212yes—
168#2486C2212yes—
169#2471C2214yes—
170#2471C2214yes—
171#2471C2214yes—
172#2470C2214yes—
173#2465C2214yes—
174#2463C2214yes—
175#2462C2214yes—
176#2461C2214yes—
177#2456C2214yes—
178#2456C2214yes—
179#2452C2212yes—
180#2452C2212yes—
181#2452C2212yes—
182#2451C2212yes—
183#2451C2212yes—
184#2450C2214yes—
185#2450C2214yes—
186#2450C2214yes—
187#2448C2212yes—
188#2447C2212yes—
189#2447C2212yes—
190#2447C2212yes—
191#2446C2212yes—
192#2445C2212yes—
193#2444C2214yes—
194#2440C2212yes—
195#2439C2212yes—
196#2438C2214yes—
197#2438C2214yes—
198#2436C2212yes—
199#2434C2212yes—
200#2432C2212yes—
201#2431C2212yes—
202#2430C2214yes—
203#2430C2214yes—
204#2428C2212yes—
205#2427C2212yes—
206#2427C2212yes—
207#2426C2212yes—
208#2426C2212yes—
209#2425C2214yes—
210#2423C2214yes—
211#2422C2212yes—
212#2420C2212yes—
213#2419C2214yes—
214#2419C2214yes—
215#2417C2211yescharacteristic
216#2417C2211yescharacteristic
217#2417C2212yes—
218#2417C2211yescharacteristic
219#2417C2211yescharacteristic
220#2416C2212yes—
221#2414C2212yes—
222#2414C2212yes—
223#2409C2212yes—
224#2409C2212yes—
225#2407C2212yes—
226#2407C2212yes—
227#2407C2212yes—
228#2407C2214yes—
229#2396C2212yes—
230#2396C2212yes—
231#2377C2214yes—
232#2377C2214yes—
233#2366C2211yescharacteristic
234#2366C2212yes—
235#2366C2212yes—
236#2365C2212yes—
237#2365C2211yescharacteristic
238#2365C2212yes—
239#2365C2212yes—
240#2363C2212yes—
241#2361C2212yes—
242#2361C2212yes—
243#2360C2212yes—
244#2360C2212yes—
245#2357C2212yes—
246#2357C2212yes—
247#2356C2212yes—
248#2355C2211yescharacteristic
249#2355C2211yescharacteristic
250Q8×C4⋊C4C2211yescharacteristic
251#2349C2212yes—
252#2349C2212yes—
253D4×C4⋊C4C2211yescharacteristic
254#2344C2212yes—
255#2341C2214yes—
256#2339C2214yes—
257#2339C2212yes—
258#2339C2212yes—
259#2326C2214yes—
260#2326C2214yes—
261#2325C2212yes—
262#2325C2212yes—
263#2324C2211yescharacteristic
264#2324C2211yescharacteristic
265#2324C2212yes—
266#2324C2212yes—
267#2324C2212yes—
268#2324C2212yes—
269#2324C2212yes—
270#2323C2211yescharacteristic
271#2323C2212yes—
272#2323C2211yescharacteristic
273#2318C2214yes—
274#2318C2214yes—
275#2316C2211yescharacteristic
276#2311C2211yescharacteristic
277#2311C2211yescharacteristic
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2211yescharacteristic
280C4×C22⋊Q8C2212yes—
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×#121C2212yes—
286C4×#121C2212yes—
287C4×#121C2211yescharacteristic
288C4×#121C2211yescharacteristic
289C4×#121C2212yes—
290C4×#121C2212yes—
291C4×#121C2212yes—
292#2297C2212yes—
293C2×#391C2212yes—
294#2285C2211yescharacteristic
295#2285C2212yes—
296#2283C2212yes—
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C22×#41C2314yes—
302C22×#41C2312yes—
303C23×Q8C2312yes—
304#559—44no—
305D4×Q8—44no—
306#548—48no—
307#547—48no—
308#537—28no—
309#533—44no—
310#533—48no—
311#532—216no—
312#532—44no—
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2312yes—
320C2×#127C2311yescharacteristic
321C2×#127C2312yes—
322C2×#125C2312yes—
323C2×#125C2314yes—
324C2×#124C2314yes—
325C2×#124C2312yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2314yes—
330C2×#123C2314yes—
331C2×#123C2314yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2314yes—
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2311yescharacteristic
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2311yescharacteristic
370C4×#41—44no—
371C4×#41—44no—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2314yes—
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2314yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2314yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2312yes—
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2314yes—
407C2×#117C2311yescharacteristic
408C2×#117C2311yescharacteristic
409C2×#117C2311yescharacteristic
410C2×#117C2311yescharacteristic
411C2×#117C2312yes—
412C2×#117C2312yes—
413C2×#117C2314yes—
414C2×#117C2312yes—
415C22×C4⋊C4C2311yescharacteristic
416C22×C4⋊C4C2311yescharacteristic
417C22×C4⋊C4C2311yescharacteristic
418C22×C4⋊C4C2312yes—
419C22×C4⋊C4C2311yescharacteristic
420C22×C42C2312yes—
421C22×C42C2311yescharacteristic
422C22×C42C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2312yes—
425C22×C42C2312yes—
426#401C2314yes—
427#401C2314yes—
428#401C2314yes—
429#401C2314yes—
430#400C2312yes—
431#400C2312yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2314yes—
438#400C2314yes—
439#400C2314yes—
440#400C2314yes—
441#399C2312yes—
442#399C2312yes—
443#399C2314yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#398C2312yes—
448#398C2312yes—
449#398C2312yes—
450#398C2312yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#396C2312yes—
473#396C2312yes—
474#396C2312yes—
475#396C2312yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#395C2312yes—
485#395C2312yes—
486#395C2314yes—
487#395C2314yes—
488#395C2314yes—
489#395C2314yes—
490#395C2314yes—
491#395C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#393C2312yes—
505#393C2312yes—
506#393C2314yes—
507#393C2314yes—
508#393C2314yes—
509#393C2314yes—
510#393C2314yes—
511#393C2314yes—
512#393C2314yes—
513#393C2314yes—
514#393C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#391C2312yes—
523#391C2312yes—
524#391C2311yescharacteristic
525#391C2311yescharacteristic
526#391C2312yes—
527#391C2314yes—
528#391C2311yescharacteristic
529#391C2312yes—
530#391C2312yes—
531#391C2312yes—
532#391C2311yescharacteristic
533#391C2311yescharacteristic
534#391C2311yescharacteristic
535#391C2314yes—
536#391C2314yes—
537#391C2312yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#391C2312yes—
545#391C2314yes—
546#391C2314yes—
547#391C2314yes—
548#390C2312yes—
549#390C2312yes—
550#390C2311yescharacteristic
551#390C2311yescharacteristic
552#390C2312yes—
553#390C2312yes—
554#390C2312yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2314yes—
559#390C2314yes—
560#390C2314yes—
561#390C2312yes—
562#390C2314yes—
563#390C2312yes—
564#390C2312yes—
565#390C2314yes—
566#390C2314yes—
567#390C2312yes—
568#390C2312yes—
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2314yes—
573#390C2312yes—
574#390C2312yes—
575#389C2311yescharacteristic
576#389C2312yes—
577#389C2312yes—
578#389C2311yescharacteristic
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2311yescharacteristic
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2311yescharacteristic
586#389C2312yes—
587#389C2311yescharacteristic
588#389C2312yes—
589#389C2311yescharacteristic
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2314yes—
604#389C2314yes—
605#389C2314yes—
606#388C2312yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2312yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#386C2312yes—
665#386C2312yes—
666#386C2312yes—
667#386C2312yes—
668#386C2312yes—
669#386C2312yes—
670#386C2312yes—
671#386C2312yes—
672#386C2312yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2312yes—
678#386C2312yes—
679#386C2312yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#385C2314yes—
703#385C2312yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2312yes—
709#385C2312yes—
710#385C2312yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#384C2312yes—
725#384C2312yes—
726#384C2314yes—
727#384C2311yescharacteristic
728#384C2311yescharacteristic
729#384C2312yes—
730#383C2314yes—
731#383C2314yes—
732#383C2314yes—
733#382C2312yes—
734#382C2312yes—
735#382C2312yes—
736#382C2312yes—
737#382C2312yes—
738#382C2312yes—
739#382C2312yes—
740#382C2312yes—
741#381C2314yes—
742#381C2314yes—
743#381C2314yes—
744#381C2314yes—
745#381C2314yes—
746#381C2314yes—
747#381C2314yes—
748#381C2314yes—
749#380C2311yescharacteristic
750#380C2311yescharacteristic
751#380C2311yescharacteristic
752#380C2311yescharacteristic
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2311yescharacteristic
758#380C2312yes—
759#380C2311yescharacteristic
760#380C2311yescharacteristic
761#380C2311yescharacteristic
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2314yes—
766#380C2314yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2312yes—
773#380C2312yes—
774#380C2314yes—
775#380C2312yes—
776#380C2314yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2312yes—
802C4×C4⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2314yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815#376C2314yes—
816C2×#95C2312yes—
817C2×#95C2314yes—
818C2×#95C2314yes—
819C2×#95C2312yes—
820C2×#95C2314yes—
821C2×#41—24no—
822C2×#41—216no—
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C2×#41—42no—
827C2×#41—42no—
828C2×#41—44no—
829C2×#41—48no—
830C2×#41—44no—
831C2×#41—44no—
832C2×#41—84no—
833C22×Q8—44no—
834C22×Q8—44no—
835C22×Q8—44no—
836C22×Q8C2411yescharacteristic
837C22×Q8C2411yescharacteristic
838C22×Q8C2411yescharacteristic
839C22×Q8C2412yes—
840C22×Q8C2414yes—
841C22×Q8C2411yescharacteristic
842C22×Q8C2412yes—
843C22×Q8C2414yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2414yes—
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2411yescharacteristic
850C22×D4C2411yescharacteristic
851C22×D4C2411yescharacteristic
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2411yescharacteristic
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2411yescharacteristic
867C23×C4C2411yescharacteristic
868C23×C4C2412yes—
869C23×C4C2412yes—
870C23×C4C2414yes—
871C23×C4C2412yes—
872C23×C4C2411yescharacteristic
873C23×C4C2411yescharacteristic
874C23×C4C2414yes—
875C23×C4C2411yescharacteristic
876C23×C4C2412yes—
877C23×C4C2414yes—
878C23×C4C2414yes—
879C23×C4C2414yes—
880C4⋊Q8—28no—
881C4⋊Q8—28no—
882C4⋊Q8—24no—
883C4⋊Q8—42no—
884C4⋊Q8—44no—
885C4⋊Q8—42no—
886C4⋊Q8—44no—
887#127—28no—
888#127—24no—
889#125—44no—
890#125—48no—
891#124—216no—
892#124—48no—
893#124—44no—
894#124—44no—
895#124—44no—
896#124—44no—
897#123—48no—
898#123—48no—
899#123—48no—
900#123—84no—
901C22⋊Q8—24no—
902C22⋊Q8—24no—
903C22⋊Q8—24no—
904C22⋊Q8—24no—
905C22⋊Q8—28no—
906C22⋊Q8—48no—
907C22⋊Q8—48no—
908C22⋊Q8—48no—
909C22⋊Q8—48no—
910C22⋊Q8—44no—
911C22⋊Q8—42no—
912C22⋊Q8—42no—
913C22⋊Q8—44no—
914C22⋊Q8—44no—
915C22⋊Q8—44no—
916C22⋊Q8—42no—
917C22⋊Q8—42no—
918C22⋊Q8—44no—
919C22⋊Q8—84no—
920#121—216no—
921#121—24no—
922#121—28no—
923#121—28no—
924#121—28no—
925#121—28no—
926#121—28no—
927#121—28no—
928#121—48no—
929#121—44no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—44no—
934#121—82no—
935#121—82no—
936#121#4118yescomplemented
937C4×Q8—28no—
938C4×Q8—24no—
939C4×Q8—24no—
940C4×Q8—24no—
941C4×Q8—42no—
942C4×Q8—42no—
943C4×Q8—44no—
944C4×Q8—42no—
945C4×Q8—44no—
946C4×Q8—48no—
947C4×Q8—84no—
948C4×D4—28no—
949C4×D4—28no—
950C4×D4—216no—
951C4×D4—24no—
952C4×D4—42no—
953C4×D4—44no—
954C4×D4—44no—
955C4×D4—44no—
956C4×D4—48no—
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—84no—
971C4×D4—84no—
972#117—42no—
973#117—42no—
974#117—42no—
975#117—44no—
976#117—44no—
977#117—48no—
978#117—42no—
979#117—82no—
980C2×C4⋊C4—24no—
981C2×C4⋊C4—24no—
982C2×C4⋊C4—24no—
983C2×C4⋊C4—42no—
984C2×C4⋊C4—44no—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2411yescharacteristic
1051C2×C4⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C22⋊C4C2411yescharacteristic
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2411yescharacteristic
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2411yescharacteristic
1069C2×C22⋊C4C2411yescharacteristic
1070C2×C22⋊C4C2411yescharacteristic
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C42—28no—
1111C2×C42—24no—
1112C2×C42—24no—
1113C2×C42—24no—
1114C2×C42—44no—
1115C2×C42—44no—
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2414yes—
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2412yes—
1136C2×C42C2414yes—
1137C2×C42C2414yes—
1138C2×C42C2414yes—
1139C2×C42C2414yes—
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2412yes—
1143C2×C42C2411yescharacteristic
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2414yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2414yes—
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—
1210C24C2511yescharacteristic
1211C24C2514yes—
1212C24C2512yes—
1213C24C2511yescharacteristic
1214C24C2511yescharacteristic
1215#41—416no—
1216#41—416no—
1217#41—832no—
1218#41—816no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—28no—
1222C2×Q8—22no—
1223C2×Q8—22no—
1224C2×Q8—22no—
1225C2×Q8—24no—
1226C2×Q8—22no—
1227C2×Q8—28no—
1228C2×Q8—22no—
1229C2×Q8—24no—
1230C2×Q8—22no—
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—24no—
1235C2×Q8—41no—
1236C2×Q8—44no—
1237C2×Q8—42no—
1238C2×Q8—44no—
1239C2×Q8—44no—
1240C2×Q8—42no—
1241C2×Q8—44no—
1242C2×Q8—42no—
1243C2×Q8—816no—
1244C2×D4—22no—
1245C2×D4—24no—
1246C2×D4—22no—
1247C2×D4—28no—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—24no—
1251C2×D4—28no—
1252C2×D4—24no—
1253C2×D4—28no—
1254C2×D4—28no—
1255C2×D4—24no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—28no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—22no—
1264C2×D4—24no—
1265C2×D4—22no—
1266C2×D4—24no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—41no—
1270C2×D4—42no—
1271C2×D4—42no—
1272C2×D4—44no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—42no—
1282C2×D4—44no—
1283C2×D4—42no—
1284C2×D4—42no—
1285C2×D4—44no—
1286C2×D4—44no—
1287C2×D4C2×#4114yes—
1288C2×D4C2×#4118yes—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—24no—
1294C22×C4—24no—
1295C22×C4—24no—
1296C22×C4—24no—
1297C22×C4—28no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—24no—
1306C22×C4—22no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—22no—
1310C22×C4—24no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—24no—
1315C22×C4—22no—
1316C22×C4—24no—
1317C22×C4—28no—
1318C22×C4—22no—
1319C22×C4—22no—
1320C22×C4—42no—
1321C22×C4—42no—
1322C22×C4—41no—
1323C22×C4—41no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—44no—
1329C22×C4—42no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—44no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—44no—
1338C22×C4—41no—
1339C22×C4—41no—
1340C22×C4—44no—
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×C4—44no—
1350C22×C4C2×#4114yes—
1351C22×C42−1+414yes—
1352C22×C4C2512yes—
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2514yes—
1357C22×C4C2512yes—
1358C22×C4C2512yes—
1359C22×C4C2512yes—
1360C22×C4C2511yescharacteristic
1361C22×C4C2512yes—
1362C22×C4C2511yescharacteristic
1363C22×C4C2511yescharacteristic
1364C22×C4C2512yes—
1365C22×C4C2512yes—
1366C22×C4C2514yes—
1367C22×C4C2514yes—
1368C22×C4C2511yescharacteristic
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2512yes—
1374C22×C4C2511yescharacteristic
1375C22×C4C2511yescharacteristic
1376C22×C4C2512yes—
1377C22×C4C2511yescharacteristic
1378C22×C4C2512yes—
1379C22×C4C2511yescharacteristic
1380C22×C4C2511yescharacteristic
1381C22×C4C2511yescharacteristic
1382C4⋊C4—24no—
1383C4⋊C4—22no—
1384C4⋊C4—28no—
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—22no—
1389C4⋊C4—24no—
1390C4⋊C4—24no—
1391C4⋊C4—22no—
1392C4⋊C4—22no—
1393C4⋊C4—24no—
1394C4⋊C4—28no—
1395C4⋊C4—22no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—28no—
1400C4⋊C4—24no—
1401C4⋊C4—22no—
1402C4⋊C4—24no—
1403C4⋊C4—24no—
1404C4⋊C4—24no—
1405C4⋊C4—22no—
1406C4⋊C4—22no—
1407C4⋊C4—24no—
1408C4⋊C4—22no—
1409C4⋊C4—22no—
1410C4⋊C4—24no—
1411C4⋊C4—42no—
1412C4⋊C4—44no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—41no—
1416C4⋊C4—41no—
1417C4⋊C4—41no—
1418C4⋊C4—41no—
1419C4⋊C4—41no—
1420C4⋊C4—41no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—42no—
1424C4⋊C4—44no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—42no—
1430C4⋊C4—44no—
1431C4⋊C4—42no—
1432C4⋊C4—42no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—42no—
1439C4⋊C4—44no—
1440C4⋊C4—42no—
1441C4⋊C4—44no—
1442C4⋊C4—44no—
1443C4⋊C4—42no—
1444C4⋊C4—44no—
1445C4⋊C4—42no—
1446C4⋊C4—44no—
1447C4⋊C4C2×#4114yes—
1448C4⋊C4H(5,𝔽2)14yes—
1449C22⋊C4—28no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—28no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—28no—
1458C22⋊C4—24no—
1459C22⋊C4—28no—
1460C22⋊C4—44no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—41no—
1469C22⋊C4—41no—
1470C22⋊C4—41no—
1471C22⋊C4—41no—
1472C22⋊C4—41no—
1473C22⋊C4—42no—
1474C22⋊C4—41no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—42no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—42no—
1490C22⋊C4—44no—
1491C22⋊C4—42no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
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—42no—
1506C22⋊C4C2×#4118yes—
1507C42—24no—
1508C42—24no—
1509C42—24no—
1510C42—24no—
1511C42—22no—
1512C42—22no—
1513C42—22no—
1514C42—22no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—22no—
1519C42—22no—
1520C42—24no—
1521C42—24no—
1522C42—24no—
1523C42—28no—
1524C42—24no—
1525C42—24no—
1526C42—42no—
1527C42—42no—
1528C42—42no—
1529C42—42no—
1530C42—44no—
1531C42—44no—
1532C42—44no—
1533C42—44no—
1534C42H(5,𝔽2)14yes—
1535C23—21no—
1536C23—21no—
1537C23—22no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—22no—
1542C23—21no—
1543C23—22no—
1544C23—21no—
1545C23—22no—
1546C23—21no—
1547C23—22no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—22no—
1553C23—24no—
1554C23—21no—
1555C23—21no—
1556C23—24no—
1557C23—24no—
1558C23—21no—
1559C23—24no—
1560C23—21no—
1561C23—21no—
1562C23—24no—
1563C23—21no—
1564C23—24no—
1565C23—21no—
1566C23—24no—
1567C23C22×#4114yes—
1568C23C22×#4112yes—
1569C23C2×2−1+412yes—
1570C23C2611yescharacteristic
1571Q8—44no—
1572Q8—416no—
1573Q8—44no—
1574Q8—44no—
1575Q8—44no—
1576Q8—48no—
1577Q8—84no—
1578Q8—88no—
1579D4—28no—
1580D4—48no—
1581D4—44no—
1582D4—44no—
1583D4—416no—
1584D4—44no—
1585D4—48no—
1586D4—48no—
1587D4—48no—
1588D4—84no—
1589D4—84no—
1590D4—88no—
1591D4—88no—
1592D4—88no—
1593D4—88no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—28no—
1605C2×C4—28no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—24no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—21no—
1637C2×C4—24no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—24no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—21no—
1644C2×C4—22no—
1645C2×C4—21no—
1646C2×C4—24no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—24no—
1652C2×C4—22no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—24no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—24no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—21no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—21no—
1673C2×C4—22no—
1674C2×C4—21no—
1675C2×C4—48no—
1676C2×C4—48no—
1677C2×C4—44no—
1678C2×C4—48no—
1679C2×C4—44no—
1680C2×C4—44no—
1681C2×C4—44no—
1682C2×C4—48no—
1683C2×C4—44no—
1684C2×C4—84no—
1685C2×C4—82no—
1686C2×C4—82no—
1687C2×C4—88no—
1688C2×C4—84no—
1689C2×C4—88no—
1690C2×C4—84no—
1691C2×C4—88no—
1692C2×C4—88no—
1693C2×C4—164no—
1694C2×C4C22×#4112yes—
1695C2×C4C22×#4114yes—
1696C2×C4C22×#4112yes—
1697C2×C4C2×H(5,𝔽2)12yes—
1698C2×C4C2×H(5,𝔽2)14yes—
1699C2×C4C2×H(5,𝔽2)12yes—
1700C2×C4C2×H(5,𝔽2)12yes—
1701C2×C4C2×H(5,𝔽2)12yes—
1702C2×C4C2×2−1+412yes—
1703C2×C4C2×2−1+412yes—
1704C2×C4#58512yes—
1705C22—22no—
1706C22—24no—
1707C22—22no—
1708C22—24no—
1709C22—22no—
1710C22—22no—
1711C22—24no—
1712C22—22no—
1713C22—22no—
1714C22—41no—
1715C22—42no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—42no—
1722C22—41no—
1723C22—42no—
1724C22—41no—
1725C22—42no—
1726C22—44no—
1727C22—41no—
1728C22—41no—
1729C22—44no—
1730C22—44no—
1731C22—41no—
1732C22—41no—
1733C22—44no—
1734C22—41no—
1735C22—44no—
1736C22—41no—
1737C22—44no—
1738C22—44no—
1739C22—41no—
1740C22C23×#4111yescharacteristic
1741C22C22×H(5,𝔽2)11yescharacteristic
1742C22C22×H(5,𝔽2)11yescharacteristic
1743C22C22×2−1+411yescharacteristic
1744C22C2×#58511yescharacteristic
1745C22H(7,𝔽2)11yescharacteristic
1746C222−1+611yescharacteristic
1747C4—24no—
1748C4—24no—
1749C4—22no—
1750C4—22no—
1751C4—22no—
1752C4—42no—
1753C4—42no—
1754C4—44no—
1755C4—41no—
1756C4—41no—
1757C4—41no—
1758C4—42no—
1759C4—44no—
1760C4—42no—
1761C4—42no—
1762C4—42no—
1763C4—42no—
1764C4—41no—
1765C4—42no—
1766C4—41no—
1767C4—41no—
1768C4—42no—
1769C4—41no—
1770C4—42no—
1771C4—42no—
1772C4—42no—
1773C4—42no—
1774C4—44no—
1775C4#352014yes—
1776C4#354614yes—
1777C2—42no—
1778C2—44no—
1779C2—42no—
1780C2—84no—
1781C2—81no—
1782C2C2×#354611yescharacteristic
1783C2C2×#352011yescharacteristic
1784C2#6287511yescharacteristic
1785C2#6291311yescharacteristic
1786C2#6296211yescharacteristic
1787C2#6298311yescharacteristic
1788C2#6300911yescharacteristic
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. #59409C2semidirect
2. #59248C2semidirect
3. #59219C2semidirect
4. #59080C2semidirect
5. #59064C2semidirect
6. #59040C2semidirect
7. #50088C2semidirect
8. #48571C2semidirect
9. #47067C2semidirect
10. #46489C2semidirect
11. #45687C2semidirect
12. #45616C2semidirect
13. #45368C2semidirect
14. #45360C2semidirect
15. #42605C2semidirect
16. #42542C2semidirect
17. #40151C2semidirect
18. #39854C2semidirect
19. #39726C2semidirect
20. #39596C2semidirect
21. #39004C2semidirect
22. #38983C2semidirect
23. #37975C2semidirect
24. #37780C2semidirect
25. #37287C2semidirect
26. #36587C2semidirect
27. #36493C2semidirect
28. #36274C2semidirect
29. #36177C2semidirect
30. #36133C2semidirect
31. #36126C2semidirect
32. #35292C2semidirect
33. #34947C2semidirect
34. #34393C2semidirect
35. C4×#537C2semidirect
936. #121#41semidirect

Maximal subgroups

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

subgroupindex
#594092
#592482
#592192
#590802
#590642
#590402
#500882
#485712
#470672
#464892
#456872
#456162
#453682
#453602
#426052
#425422
#401512
#398542
#397262
#395962
#390042
#389832
#379752
#377802
#372872
#365872
#364932
#362742
#361772
#361332
#361262
#352922
#349472
#343932
C4×#5372