Finite Group Databasebeta

← #7968127

Subgroups — #7968127

Order 512.

5211 conjugacy classes of subgroups.

The subgroup lattice has 1811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59854C212yesmaximal, complemented
2#59815C211yesmaximal, characteristic, complemented
3#59810C212yesmaximal, complemented
4#59233C211yesmaximal, characteristic, complemented
5#59229C211yesmaximal, characteristic, complemented
6#52027C214yesmaximal, complemented
7#48640C214yesmaximal, complemented
8#46333C212yesmaximal, complemented
9#45717C212yesmaximal, complemented
10#45011C212yesmaximal, complemented
11#44981C212yesmaximal, complemented
12#44188C214yesmaximal, complemented
13#42885C212yesmaximal, complemented
14#42839C212yesmaximal, complemented
15#41133C214yesmaximal, complemented
16#40070C212yesmaximal, complemented
17#39961C212yesmaximal, complemented
18#39763C211yesmaximal, characteristic, complemented
19#39491C212yesmaximal, complemented
20#39275C212yesmaximal, complemented
21#39222C212yesmaximal, complemented
22#38920C211yesmaximal, characteristic, complemented
23#36404C211yesmaximal, characteristic, complemented
24#36404C211yesmaximal, characteristic, complemented
25#36392C212yesmaximal, complemented
26#36270C211yesmaximal, characteristic, complemented
27#36259C211yesmaximal, characteristic, complemented
28#36210C211yesmaximal, characteristic, complemented
29#35199C211yesmaximal, characteristic, complemented
30#35189C211yesmaximal, characteristic, complemented
31#35046C212yesmaximal, complemented
32#34976C211yesmaximal, characteristic, complemented
33#34727C211yesmaximal, characteristic, complemented
34#34465C212yesmaximal, complemented
35C4×#550C211yesmaximal, characteristic, complemented
36C2×#555C2212yes—
37C2×#552C2212yes—
38C2×#550C2211yescharacteristic
39C2×#550C2212yes—
40C2×#547C2211yescharacteristic
41C2×#547C2212yes—
42C2×#547C2211yescharacteristic
43C2×#529C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47#2863C2212yes—
48#2862C2212yes—
49#2860C2212yes—
50#2859C2211yescharacteristic
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2855C2212yes—
54#2855C2212yes—
55#2854C2212yes—
56#2851C2212yes—
57#2850C2212yes—
58#2830C2214yes—
59#2818C2214yes—
60#2803C2214yes—
61#2803C2214yes—
62#2803C2214yes—
63#2800C2214yes—
64#2800C2214yes—
65#2798C2214yes—
66#2797C2214yes—
67#2797C2214yes—
68#2797C2214yes—
69#2793C2214yes—
70#2788C2214yes—
71#2785C2214yes—
72#2783C2214yes—
73#2773C2214yes—
74#2768C2214yes—
75#2761C2214yes—
76#2751C2214yes—
77#2718C2214yes—
78#2711C2214yes—
79#2711C2214yes—
80#2710C2214yes—
81#2710C2214yes—
82#2710C2214yes—
83#2710C2214yes—
84#2709C2214yes—
85#2708C2214yes—
86#2706C2214yes—
87#2688C2214yes—
88#2686C2214yes—
89#2686C2214yes—
90#2682C2214yes—
91#2673C2214yes—
92#2673C2214yes—
93#2666C2214yes—
94#2661C2214yes—
95#2653C2214yes—
96#2651C2214yes—
97#2641C2212yes—
98#2636C2214yes—
99#2630C2214yes—
100#2624C2212yes—
101#2619C2214yes—
102#2610C2214yes—
103#2609C2214yes—
104#2602C2214yes—
105#2601C2214yes—
106#2601C2214yes—
107#2600C2214yes—
108#2598C2214yes—
109#2591C2214yes—
110#2589C2214yes—
111#2582C2211yescharacteristic
112#2578C2214yes—
113#2576C2214yes—
114#2576C2214yes—
115#2576C2214yes—
116#2575C2214yes—
117#2568C2211yescharacteristic
118#2563C2212yes—
119#2563C2212yes—
120#2562C2212yes—
121#2562C2212yes—
122#2558C2214yes—
123#2555C2214yes—
124#2551C2211yescharacteristic
125#2547C2212yes—
126#2546C2211yescharacteristic
127#2544C2214yes—
128#2543C2214yes—
129#2542C2212yes—
130#2541C2212yes—
131#2538C2211yescharacteristic
132#2538C2211yescharacteristic
133#2538C2211yescharacteristic
134#2538C2211yescharacteristic
135#2538C2212yes—
136#2537C2211yescharacteristic
137#2537C2211yescharacteristic
138#2536C2212yes—
139#2526C2214yes—
140#2520C2214yes—
141#2518C2214yes—
142#2516C2214yes—
143#2514C2212yes—
144#2513C2212yes—
145#2513C2212yes—
146#2509C2212yes—
147#2508C2212yes—
148#2506C2212yes—
149#2504C2214yes—
150#2500C2214yes—
151#2495C2212yes—
152#2494C2212yes—
153#2494C2212yes—
154#2491C2212yes—
155#2491C2212yes—
156#2491C2212yes—
157#2489C2212yes—
158#2487C2212yes—
159#2486C2212yes—
160#2485C2212yes—
161#2485C2212yes—
162#2485C2212yes—
163#2485C2212yes—
164#2485C2212yes—
165#2485C2212yes—
166#2485C2212yes—
167#2479C2212yes—
168#2476C2214yes—
169#2474C2214yes—
170#2471C2212yes—
171#2470C2214yes—
172#2470C2214yes—
173#2467C2212yes—
174#2459C2214yes—
175#2459C2214yes—
176#2457C2214yes—
177#2457C2214yes—
178#2456C2212yes—
179#2454C2211yescharacteristic
180#2451C2212yes—
181#2451C2212yes—
182#2448C2211yescharacteristic
183#2446C2212yes—
184#2445C2214yes—
185#2445C2212yes—
186#2441C2211yescharacteristic
187#2439C2212yes—
188#2432C2212yes—
189#2431C2211yescharacteristic
190#2429C2212yes—
191#2428C2211yescharacteristic
192#2425C2214yes—
193#2423C2211yescharacteristic
194#2421C2212yes—
195#2420C2212yes—
196#2420C2212yes—
197#2420C2212yes—
198#2416C2212yes—
199#2416C2212yes—
200#2416C2212yes—
201#2416C2212yes—
202#2415C2212yes—
203#2415C2212yes—
204#2415C2212yes—
205#2415C2212yes—
206#2415C2212yes—
207#2415C2212yes—
208#2415C2212yes—
209#2414C2212yes—
210#2414C2212yes—
211#2414C2212yes—
212#2414C2212yes—
213#2414C2211yescharacteristic
214#2413C2214yes—
215#2407C2212yes—
216#2407C2212yes—
217#2407C2212yes—
218#2407C2212yes—
219#2407C2212yes—
220#2407C2212yes—
221#2407C2212yes—
222#2407C2212yes—
223#2407C2211yescharacteristic
224#2407C2212yes—
225#2407C2212yes—
226#2397C2212yes—
227#2392C2212yes—
228#2392C2214yes—
229#2383C2214yes—
230#2382C2214yes—
231#2370C2212yes—
232#2366C2211yescharacteristic
233#2366C2212yes—
234#2363C2212yes—
235#2363C2212yes—
236#2363C2211yescharacteristic
237#2363C2211yescharacteristic
238#2362C2212yes—
239#2360C2212yes—
240#2360C2212yes—
241#2359C2214yes—
242#2354C2211yescharacteristic
243#2354C2211yescharacteristic
244#2354C2211yescharacteristic
245#2354C2212yes—
246#2354C2211yescharacteristic
247#2353C2214yes—
248#2352C2212yes—
249#2352C2212yes—
250#2352C2212yes—
251Q8×C4⋊C4C2211yescharacteristic
252D4×C4⋊C4C2211yescharacteristic
253D4×C4⋊C4C2212yes—
254#2347C2212yes—
255#2346C2212yes—
256#2346C2212yes—
257#2344C2212yes—
258#2343C2214yes—
259#2341C2211yescharacteristic
260#2341C2211yescharacteristic
261#2339C2212yes—
262#2337C2214yes—
263#2334C2214yes—
264#2331C2212yes—
265#2330C2212yes—
266#2330C2214yes—
267#2324C2212yes—
268#2323C2212yes—
269#2322C2214yes—
270#2320C2212yes—
271#2317C2212yes—
272#2317C2214yes—
273C4×C4⋊Q8C2211yescharacteristic
274C4×#127C2212yes—
275C4×#127C2211yescharacteristic
276C4×#127C2211yescharacteristic
277C4×C22⋊Q8C2212yes—
278C4×C22⋊Q8C2212yes—
279C4×#121C2211yescharacteristic
280C4×#121C2212yes—
281C4×#121C2212yes—
282C4×#121C2211yescharacteristic
283C4×#121C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2211yescharacteristic
286C4×#121C2212yes—
287C4×#121C2212yes—
288#2297C2212yes—
289#2297C2212yes—
290#2295C2211yescharacteristic
291#2293C2212yes—
292C2×#389C2212yes—
293#2290C2212yes—
294#2285C2211yescharacteristic
295#2285C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×D4C2212yes—
298C42×D4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C22×#41C2311yescharacteristic
302C22×#41C2311yescharacteristic
303C22×#41C2312yes—
304#555—48no—
305#552—216no—
306#550—28no—
307#550—48no—
308#547—44no—
309#547—44no—
310#547—48no—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×#127C2312yes—
316C2×#127C2311yescharacteristic
317C2×#127C2311yescharacteristic
318C2×#127C2314yes—
319#529—44no—
320C2×#126C2314yes—
321C2×#126C2312yes—
322C2×#125C2312yes—
323C2×#125C2314yes—
324C2×#125C2311yescharacteristic
325C2×#124C2314yes—
326C2×#124C2311yescharacteristic
327C2×#124C2314yes—
328C2×#124C2314yes—
329C2×#123C2314yes—
330C2×#123C2314yes—
331C2×#123C2314yes—
332C2×#123C2312yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2312yes—
344C2×#121C2311yescharacteristic
345C2×#121C2311yescharacteristic
346C2×#121C2312yes—
347C2×#121C2312yes—
348C2×#121C2311yescharacteristic
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2314yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2314yes—
355C2×#121C2314yes—
356C2×#121C2312yes—
357C2×#121C2311yescharacteristic
358C2×#121C2311yescharacteristic
359C2×#121C2312yes—
360C2×#121C2314yes—
361C2×#121C2312yes—
362C4×#41—44no—
363C4×#41—44no—
364C4×#41—44no—
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2311yescharacteristic
369C2×C4×Q8C2311yescharacteristic
370C2×C4×Q8C2311yescharacteristic
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2312yes—
394C2×C4×D4C2314yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×#117C2314yes—
404C2×#117C2312yes—
405C2×#117C2312yes—
406C2×#117C2314yes—
407C2×#117C2312yes—
408C2×#117C2312yes—
409C2×#117C2312yes—
410C2×#117C2311yescharacteristic
411C2×#117C2311yescharacteristic
412C2×#117C2312yes—
413C2×#117C2312yes—
414C2×#117C2312yes—
415C2×#117C2312yes—
416C2×#117C2311yescharacteristic
417C22×C4⋊C4C2312yes—
418C22×C4⋊C4C2314yes—
419C22×C4⋊C4C2312yes—
420C22×C4⋊C4C2312yes—
421C22×C42C2311yescharacteristic
422C22×C42C2311yescharacteristic
423C22×C42C2312yes—
424C22×C42C2312yes—
425C22×C42C2312yes—
426#401C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#399C2312yes—
434#399C2312yes—
435#399C2314yes—
436#399C2314yes—
437#399C2312yes—
438#399C2312yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2312yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2312yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#396C2312yes—
462#396C2314yes—
463#396C2312yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#395C2314yes—
472#395C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2312yes—
498#394C2312yes—
499#394C2312yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#392C2312yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2312yes—
515#392C2312yes—
516#392C2314yes—
517#392C2314yes—
518#392C2312yes—
519#392C2312yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2312yes—
531#391C2312yes—
532#391C2312yes—
533#391C2311yescharacteristic
534#391C2311yescharacteristic
535#390C2311yescharacteristic
536#390C2311yescharacteristic
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2311yescharacteristic
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2311yescharacteristic
548#390C2312yes—
549#390C2314yes—
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2314yes—
554#390C2312yes—
555#390C2311yescharacteristic
556#390C2311yescharacteristic
557#390C2312yes—
558#390C2312yes—
559#390C2312yes—
560#390C2312yes—
561#390C2314yes—
562#390C2312yes—
563#390C2312yes—
564#390C2312yes—
565#390C2311yescharacteristic
566#390C2311yescharacteristic
567#390C2314yes—
568#389C2312yes—
569#389C2312yes—
570#389C2311yescharacteristic
571#389C2312yes—
572#389C2314yes—
573#389C2314yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#389C2312yes—
579#389C2312yes—
580#389C2314yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2311yescharacteristic
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2311yescharacteristic
604#389C2314yes—
605#389C2311yescharacteristic
606#389C2312yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2312yes—
624#388C2314yes—
625#388C2312yes—
626#388C2314yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2312yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2312yes—
640#388C2312yes—
641#388C2312yes—
642#388C2312yes—
643#388C2314yes—
644#388C2314yes—
645#388C2312yes—
646#388C2312yes—
647#388C2312yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
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#387C2314yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2312yes—
675#387C2312yes—
676#387C2312yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2312yes—
684#386C2314yes—
685#386C2314yes—
686#386C2312yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2312yes—
694#386C2312yes—
695#386C2312yes—
696#386C2312yes—
697#386C2312yes—
698#386C2312yes—
699#386C2312yes—
700#386C2312yes—
701#386C2314yes—
702#386C2314yes—
703#386C2312yes—
704#386C2314yes—
705#386C2312yes—
706#385C2312yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2312yes—
720#385C2314yes—
721#385C2314yes—
722#384C2312yes—
723#384C2311yescharacteristic
724#384C2311yescharacteristic
725#384C2311yescharacteristic
726#384C2314yes—
727#384C2311yescharacteristic
728#384C2311yescharacteristic
729#383C2314yes—
730#383C2314yes—
731#382C2314yes—
732#382C2314yes—
733#382C2312yes—
734#382C2314yes—
735#382C2314yes—
736#382C2314yes—
737#382C2312yes—
738#382C2312yes—
739#382C2312yes—
740#381C2314yes—
741#381C2314yes—
742#381C2314yes—
743#381C2314yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2311yescharacteristic
753#380C2311yescharacteristic
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#380C2311yescharacteristic
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2314yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2314yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2311yescharacteristic
816#376C2312yes—
817#376C2314yes—
818C2×#95C2314yes—
819C43C2311yescharacteristic
820C43C2312yes—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—28no—
825C2×#41—42no—
826C2×#41—42no—
827C2×#41—42no—
828C2×#41—42no—
829C2×#41—42no—
830C2×#41—42no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—44no—
834C2×#41—44no—
835C2×#41—44no—
836C22×Q8C2411yescharacteristic
837C22×Q8C2412yes—
838C22×Q8C2411yescharacteristic
839C22×Q8C2414yes—
840C22×D4C2411yescharacteristic
841C22×D4C2411yescharacteristic
842C22×D4C2411yescharacteristic
843C22×D4C2412yes—
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2414yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2414yes—
857C22×D4C2412yes—
858C22×D4C2412yes—
859C22×D4C2414yes—
860C22×D4C2414yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2414yes—
870C23×C4C2411yescharacteristic
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2412yes—
874C23×C4C2412yes—
875C23×C4C2412yes—
876C23×C4C2412yes—
877C23×C4C2411yescharacteristic
878C23×C4C2414yes—
879C23×C4C2412yes—
880C4⋊Q8—24no—
881C4⋊Q8—44no—
882C4⋊Q8—44no—
883C4⋊Q8—44no—
884#127—24no—
885#127—28no—
886#127—24no—
887#127—48no—
888#126—216no—
889#126—44no—
890#125—216no—
891#125—28no—
892#125—42no—
893#124—48no—
894#124—42no—
895#124—48no—
896#124—48no—
897#123—216no—
898#123—48no—
899#123—48no—
900#123—44no—
901#123—48no—
902#123—48no—
903C22⋊Q8—28no—
904C22⋊Q8—28no—
905C22⋊Q8—44no—
906C22⋊Q8—44no—
907C22⋊Q8—42no—
908C22⋊Q8—44no—
909C22⋊Q8—44no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912#121—28no—
913#121—24no—
914#121—24no—
915#121—24no—
916#121—28no—
917#121—28no—
918#121—44no—
919#121—48no—
920#121—42no—
921#121—44no—
922#121—44no—
923#121—42no—
924#121—44no—
925#121—44no—
926#121—44no—
927#121—48no—
928#121—48no—
929#121—48no—
930C4×Q8—24no—
931C4×Q8—24no—
932C4×Q8—42no—
933C4×Q8—42no—
934C4×Q8—42no—
935C4×Q8—42no—
936C4×Q8—44no—
937C4×Q8#4118yescomplemented
938C4×D4—28no—
939C4×D4—28no—
940C4×D4—24no—
941C4×D4—28no—
942C4×D4—24no—
943C4×D4—24no—
944C4×D4—24no—
945C4×D4—24no—
946C4×D4—42no—
947C4×D4—42no—
948C4×D4—42no—
949C4×D4—48no—
950C4×D4—44no—
951C4×D4—42no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—44no—
955C4×D4—44no—
956C4×D4—44no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—42no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—48no—
968#117—28no—
969#117—216no—
970#117—44no—
971#117—44no—
972#117—44no—
973#117—44no—
974#117—44no—
975#117—48no—
976#117—44no—
977#117—42no—
978#117—42no—
979#117—42no—
980#117—44no—
981#117—44no—
982C2×C4⋊C4—28no—
983C2×C4⋊C4—44no—
984C2×C4⋊C4—44no—
985C2×C4⋊C4—48no—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2411yescharacteristic
1046C2×C4⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2411yescharacteristic
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2411yescharacteristic
1094C2×C22⋊C4C2411yescharacteristic
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2411yescharacteristic
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C42—24no—
1117C2×C42—24no—
1118C2×C42—44no—
1119C2×C42—44no—
1120C2×C42—44no—
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2414yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2412yes—
1126C2×C42C2414yes—
1127C2×C42C2412yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2414yes—
1137C2×C42C2414yes—
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2414yes—
1142C2×C42C2414yes—
1143C2×C42C2412yes—
1144C2×C42C2412yes—
1145C2×C42C2412yes—
1146C2×C42C2412yes—
1147C2×C42C2411yescharacteristic
1148C2×C42C2412yes—
1149C2×C42C2412yes—
1150C2×C42C2411yescharacteristic
1151C2×C42C2412yes—
1152C2×C42C2411yescharacteristic
1153C2×C42C2411yescharacteristic
1154#95C2412yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2411yescharacteristic
1166#95C2411yescharacteristic
1167#95C2411yescharacteristic
1168#95C2412yes—
1169#95C2412yes—
1170#95C2411yescharacteristic
1171#95C2411yescharacteristic
1172#95C2412yes—
1173#95C2411yescharacteristic
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2412yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210C24C2512yes—
1211C24C2512yes—
1212C24C2512yes—
1213C24C2511yescharacteristic
1214C24C2511yescharacteristic
1215C24C2512yes—
1216#41—416no—
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—22no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—24no—
1229C2×Q8—44no—
1230C2×Q8—44no—
1231C2×Q8—44no—
1232C2×Q8C2×#4114yes—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—28no—
1237C2×D4—24no—
1238C2×D4—28no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—22no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—42no—
1259C2×D4—42no—
1260C2×D4—42no—
1261C2×D4—41no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—41no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—44no—
1276C2×D4—42no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—44no—
1284C2×D4—42no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4H(5,𝔽2)14yes—
1296C22×C4—24no—
1297C22×C4—28no—
1298C22×C4—28no—
1299C22×C4—28no—
1300C22×C4—24no—
1301C22×C4—24no—
1302C22×C4—24no—
1303C22×C4—24no—
1304C22×C4—22no—
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—22no—
1316C22×C4—24no—
1317C22×C4—24no—
1318C22×C4—22no—
1319C22×C4—22no—
1320C22×C4—24no—
1321C22×C4—24no—
1322C22×C4—24no—
1323C22×C4—22no—
1324C22×C4—22no—
1325C22×C4—22no—
1326C22×C4—22no—
1327C22×C4—24no—
1328C22×C4—22no—
1329C22×C4—24no—
1330C22×C4—24no—
1331C22×C4—42no—
1332C22×C4—42no—
1333C22×C4—42no—
1334C22×C4—41no—
1335C22×C4—44no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—42no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—42no—
1342C22×C4—44no—
1343C22×C4—44no—
1344C22×C4—44no—
1345C22×C4—41no—
1346C22×C4—42no—
1347C22×C4—41no—
1348C22×C4—42no—
1349C22×C4—42no—
1350C22×C4—42no—
1351C22×C4—44no—
1352C22×C4—44no—
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2511yescharacteristic
1356C22×C4C2512yes—
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2512yes—
1360C22×C4C2514yes—
1361C22×C4C2512yes—
1362C22×C4C2514yes—
1363C22×C4C2514yes—
1364C22×C4C2512yes—
1365C22×C4C2511yescharacteristic
1366C22×C4C2514yes—
1367C22×C4C2511yescharacteristic
1368C22×C4C2512yes—
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2512yes—
1373C22×C4C2511yescharacteristic
1374C22×C4C2511yescharacteristic
1375C22×C4C2511yescharacteristic
1376C22×C4C2512yes—
1377C22×C4C2512yes—
1378C22×C4C2511yescharacteristic
1379C22×C4C2511yescharacteristic
1380C22×C4C2511yescharacteristic
1381C22×C4C2511yescharacteristic
1382C4⋊C4—24no—
1383C4⋊C4—28no—
1384C4⋊C4—28no—
1385C4⋊C4—24no—
1386C4⋊C4—28no—
1387C4⋊C4—22no—
1388C4⋊C4—24no—
1389C4⋊C4—28no—
1390C4⋊C4—28no—
1391C4⋊C4—22no—
1392C4⋊C4—22no—
1393C4⋊C4—24no—
1394C4⋊C4—24no—
1395C4⋊C4—24no—
1396C4⋊C4—22no—
1397C4⋊C4—22no—
1398C4⋊C4—22no—
1399C4⋊C4—22no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—22no—
1403C4⋊C4—24no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—22no—
1407C4⋊C4—22no—
1408C4⋊C4—24no—
1409C4⋊C4—42no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—42no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—41no—
1428C4⋊C4—42no—
1429C4⋊C4—42no—
1430C4⋊C4—44no—
1431C4⋊C4—42no—
1432C4⋊C4—42no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—44no—
1436C4⋊C4—42no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4C2×#4114yes—
1442C4⋊C4C2×#4118yes—
1443C22⋊C4—24no—
1444C22⋊C4—28no—
1445C22⋊C4—28no—
1446C22⋊C4—24no—
1447C22⋊C4—28no—
1448C22⋊C4—28no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—22no—
1452C22⋊C4—22no—
1453C22⋊C4—24no—
1454C22⋊C4—28no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—24no—
1459C22⋊C4—22no—
1460C22⋊C4—24no—
1461C22⋊C4—24no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—42no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C4—41no—
1482C22⋊C4—41no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—42no—
1487C22⋊C4—42no—
1488C22⋊C4—42no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C4—41no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—44no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—42no—
1499C22⋊C4—42no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C42—28no—
1513C42—22no—
1514C42—22no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—22no—
1519C42—24no—
1520C42—24no—
1521C42—24no—
1522C42—22no—
1523C42—28no—
1524C42—22no—
1525C42—22no—
1526C42—24no—
1527C42—42no—
1528C42—42no—
1529C42—42no—
1530C42—42no—
1531C42—42no—
1532C42—42no—
1533C42—41no—
1534C42—42no—
1535C42—44no—
1536C42—44no—
1537C42—44no—
1538C42—41no—
1539C42—42no—
1540C42—44no—
1541C42—42no—
1542C42C2×#4118yes—
1543C42C2×#4114yes—
1544C42H(5,𝔽2)14yes—
1545C23—22no—
1546C23—22no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—21no—
1553C23—21no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—21no—
1563C23—22no—
1564C23—22no—
1565C23—22no—
1566C23—22no—
1567C23—22no—
1568C23—21no—
1569C23—21no—
1570C23—21no—
1571C23—22no—
1572C23—22no—
1573C23—22no—
1574C23—21no—
1575C23—22no—
1576C23—21no—
1577C23—22no—
1578C23—22no—
1579C23—21no—
1580C23—22no—
1581C23—22no—
1582C23—22no—
1583C23—22no—
1584C23—21no—
1585C23—21no—
1586C23C2×H(5,𝔽2)14yes—
1587C23C2611yescharacteristic
1588Q8—28no—
1589Q8—44no—
1590Q8—48no—
1591Q8—164no—
1592D4—28no—
1593D4—48no—
1594D4—48no—
1595D4—44no—
1596D4—48no—
1597D4—48no—
1598D4—48no—
1599D4—44no—
1600D4—44no—
1601D4—44no—
1602D4—84no—
1603D4—84no—
1604D4—84no—
1605D4—84no—
1606D4—88no—
1607D4—84no—
1608D4—88no—
1609D4—84no—
1610D4—84no—
1611D4—88no—
1612D4—164no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—24no—
1630C2×C4—22no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—22no—
1643C2×C4—24no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—24no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—24no—
1653C2×C4—21no—
1654C2×C4—22no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—24no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—24no—
1661C2×C4—21no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—21no—
1666C2×C4—24no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—21no—
1673C2×C4—21no—
1674C2×C4—24no—
1675C2×C4—22no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—21no—
1680C2×C4—22no—
1681C2×C4—24no—
1682C2×C4—21no—
1683C2×C4—22no—
1684C2×C4—24no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—44no—
1689C2×C4—416no—
1690C2×C4—48no—
1691C2×C4—48no—
1692C2×C4—48no—
1693C2×C4—48no—
1694C2×C4—48no—
1695C2×C4—44no—
1696C2×C4—44no—
1697C2×C4—44no—
1698C2×C4—44no—
1699C2×C4—48no—
1700C2×C4—48no—
1701C2×C4—84no—
1702C2×C4—84no—
1703C2×C4—82no—
1704C2×C4—88no—
1705C2×C4—84no—
1706C2×C4—88no—
1707C2×C4C22×#4114yes—
1708C2×C4C22×#4112yes—
1709C2×C4C22×#4114yes—
1710C2×C4C22×#4112yes—
1711C2×C4C22×#4112yes—
1712C2×C4C2×H(5,𝔽2)12yes—
1713C2×C4C2×H(5,𝔽2)12yes—
1714C2×C4C2×H(5,𝔽2)12yes—
1715C2×C4C2×H(5,𝔽2)12yes—
1716C2×C4#58512yes—
1717C2×C4#58512yes—
1718C2×C4#58512yes—
1719C22—24no—
1720C22—24no—
1721C22—24no—
1722C22—42no—
1723C22—42no—
1724C22—42no—
1725C22—42no—
1726C22—42no—
1727C22—41no—
1728C22—41no—
1729C22—42no—
1730C22—42no—
1731C22—41no—
1732C22—42no—
1733C22—42no—
1734C22—42no—
1735C22—41no—
1736C22—42no—
1737C22—42no—
1738C22—41no—
1739C22—41no—
1740C22—42no—
1741C22—42no—
1742C22—41no—
1743C22—41no—
1744C22—42no—
1745C22—42no—
1746C22—41no—
1747C22—41no—
1748C22—42no—
1749C22—42no—
1750C22—42no—
1751C22—41no—
1752C22—42no—
1753C22—41no—
1754C22—42no—
1755C22—42no—
1756C22—41no—
1757C22—42no—
1758C22—42no—
1759C22—41no—
1760C22—42no—
1761C22C23×#4111yescharacteristic
1762C22C22×H(5,𝔽2)11yescharacteristic
1763C22C22×H(5,𝔽2)11yescharacteristic
1764C22C2×#58511yescharacteristic
1765C22C2×#58511yescharacteristic
1766C22C2×#58511yescharacteristic
1767C222−1+611yescharacteristic
1768C4—24no—
1769C4—22no—
1770C4—24no—
1771C4—22no—
1772C4—22no—
1773C4—22no—
1774C4—44no—
1775C4—41no—
1776C4—44no—
1777C4—42no—
1778C4—42no—
1779C4—42no—
1780C4—42no—
1781C4—41no—
1782C4—41no—
1783C4—44no—
1784C4—42no—
1785C4—41no—
1786C4—42no—
1787C4—41no—
1788C4—42no—
1789C4—41no—
1790C4—41no—
1791C4—42no—
1792C4—42no—
1793C4—42no—
1794C4—44no—
1795C4#350614yes—
1796C4#354214yes—
1797C2—44no—
1798C2—82no—
1799C2—81no—
1800C2—82no—
1801C2—82no—
1802C2—81no—
1803C2C2×#354211yescharacteristic
1804C2C2×#350611yescharacteristic
1805C2#6279311yescharacteristic
1806C2#6292711yescharacteristic
1807C2#6293911yescharacteristic
1808C2#6298511yescharacteristic
1809C2#6302411yescharacteristic
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. #59854C2semidirect
2. #59815C2semidirect
3. #59810C2semidirect
4. #59233C2semidirect
5. #59229C2semidirect
6. #52027C2semidirect
7. #48640C2semidirect
8. #46333C2semidirect
9. #45717C2semidirect
10. #45011C2semidirect
11. #44981C2semidirect
12. #44188C2semidirect
13. #42885C2semidirect
14. #42839C2semidirect
15. #41133C2semidirect
16. #40070C2semidirect
17. #39961C2semidirect
18. #39763C2semidirect
19. #39491C2semidirect
20. #39275C2semidirect
21. #39222C2semidirect
22. #38920C2semidirect
23. #36404C2semidirect
24. #36404C2semidirect
25. #36392C2semidirect
26. #36270C2semidirect
27. #36259C2semidirect
28. #36210C2semidirect
29. #35199C2semidirect
30. #35189C2semidirect
31. #35046C2semidirect
32. #34976C2semidirect
33. #34727C2semidirect
34. #34465C2semidirect
35. C4×#550C2semidirect
937. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598542
#598152
#598102
#592332
#592292
#520272
#486402
#463332
#457172
#450112
#449812
#441882
#428852
#428392
#411332
#400702
#399612
#397632
#394912
#392752
#392222
#389202
#364042
#363922
#362702
#362592
#362102
#351992
#351892
#350462
#349762
#347272
#344652
C4×#5502