Finite Group Databasebeta

← #7969222

Subgroups — #7969222

Order 512.

5563 conjugacy classes of subgroups.

The subgroup lattice has 1849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59418C211yesmaximal, characteristic, complemented
2#59397C212yesmaximal, complemented
3#59314C211yesmaximal, characteristic, complemented
4#59230C211yesmaximal, characteristic, complemented
5#59024C212yesmaximal, complemented
6#51687C214yesmaximal, complemented
7#48478C214yesmaximal, complemented
8#45688C212yesmaximal, complemented
9#45602C212yesmaximal, complemented
10#45103C212yesmaximal, complemented
11#45079C212yesmaximal, complemented
12#43429C214yesmaximal, complemented
13#42991C212yesmaximal, complemented
14#42633C212yesmaximal, complemented
15#41239C214yesmaximal, complemented
16#40101C212yesmaximal, complemented
17#40076C212yesmaximal, complemented
18#39910C212yesmaximal, complemented
19#39432C212yesmaximal, complemented
20#39340C211yesmaximal, characteristic, complemented
21#39193C211yesmaximal, characteristic, complemented
22#39126C212yesmaximal, complemented
23#36505C211yesmaximal, characteristic, complemented
24#36445C211yesmaximal, characteristic, complemented
25#36189C211yesmaximal, characteristic, complemented
26#36153C211yesmaximal, characteristic, complemented
27#36144C212yesmaximal, complemented
28#36114C211yesmaximal, characteristic, complemented
29#35273C211yesmaximal, characteristic, complemented
30#35170C211yesmaximal, characteristic, complemented
31#35079C212yesmaximal, complemented
32#34935C211yesmaximal, characteristic, complemented
33#34715C211yesmaximal, characteristic, complemented
34#34410C212yesmaximal, complemented
35C4×#546C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic, complemented
37C2×#554C2212yescomplemented
38C2×#547C2211yescharacteristic
39C2×#546C2211yescharacteristic
40C2×#546C2212yes—
41C2×#542C2212yes—
42C2×#537C2212yes—
43C2×#537C2212yes—
44C2×#532C2211yescharacteristic, complemented
45C2×#529C2212yescomplemented
46C2×#525C2212yes—
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2211yescharacteristic
49C22×C4×D4C2211yescharacteristic
50#2859C2211yescharacteristic, complemented
51#2857C2211yescharacteristic
52#2857C2212yescomplemented
53#2857C2212yescomplemented
54#2857C2212yescomplemented
55#2857C2211yescharacteristic, complemented
56#2856C2212yescomplemented
57#2854C2212yescomplemented
58#2851C2212yescomplemented
59#2851C2212yescomplemented
60#2847C2212yes—
61#2836C2214yescomplemented
62#2830C2214yescomplemented
63#2791C2214yescomplemented
64#2784C2214yes—
65#2781C2214yescomplemented
66#2779C2214yescomplemented
67#2771C2214yescomplemented
68#2757C2214yescomplemented
69#2750C2214yescomplemented
70#2749C2214yes—
71#2743C2214yes—
72#2743C2214yescomplemented
73#2740C2214yescomplemented
74#2720C2214yescomplemented
75#2708C2214yescomplemented
76#2708C2214yescomplemented
77#2707C2214yes—
78#2707C2214yescomplemented
79#2706C2214yes—
80#2702C2214yescomplemented
81#2702C2214yescomplemented
82#2696C2214yes—
83#2696C2214yescomplemented
84#2689C2214yescomplemented
85#2686C2214yescomplemented
86#2685C2214yes—
87#2681C2214yes—
88#2681C2214yescomplemented
89#2680C2214yes—
90#2676C2214yes—
91#2672C2214yescomplemented
92#2671C2214yes—
93#2671C2214yes—
94#2671C2214yescomplemented
95#2668C2214yes—
96#2667C2214yes—
97#2666C2214yescomplemented
98#2665C2214yes—
99#2663C2214yescomplemented
100#2649C2214yescomplemented
101#2629C2214yescomplemented
102#2625C2212yescomplemented
103#2620C2214yescomplemented
104#2616C2212yescomplemented
105#2578C2214yescomplemented
106#2577C2214yescomplemented
107#2574C2214yescomplemented
108#2570C2212yescomplemented
109#2569C2214yescomplemented
110#2563C2212yes—
111#2563C2212yescomplemented
112#2562C2214yescomplemented
113#2562C2212yescomplemented
114#2559C2214yescomplemented
115#2558C2214yescomplemented
116#2554C2214yes—
117#2553C2214yes—
118#2551C2211yescharacteristic, complemented
119#2549C2214yescomplemented
120#2547C2211yescharacteristic
121#2542C2212yes—
122#2542C2212yes—
123#2542C2211yescharacteristic, complemented
124#2539C2214yes—
125#2538C2211yescharacteristic
126#2538C2212yes—
127#2538C2211yescharacteristic
128#2538C2211yescharacteristic, complemented
129#2538C2211yescharacteristic, complemented
130#2538C2212yescomplemented
131#2537C2212yes—
132#2537C2211yescharacteristic
133#2537C2211yescharacteristic
134#2537C2214yes—
135#2537C2211yescharacteristic
136#2537C2212yescomplemented
137#2536C2212yes—
138#2536C2212yescomplemented
139#2535C2212yes—
140#2534C2214yes—
141#2521C2214yescomplemented
142#2511C2212yescomplemented
143#2508C2212yescomplemented
144#2507C2212yescomplemented
145#2506C2212yescomplemented
146#2504C2212yescomplemented
147#2497C2212yes—
148#2496C2212yescomplemented
149#2496C2212yescomplemented
150#2495C2212yescomplemented
151#2495C2212yescomplemented
152#2492C2212yescomplemented
153#2492C2212yescomplemented
154#2491C2212yescomplemented
155#2490C2212yescomplemented
156#2490C2212yescomplemented
157#2487C2212yes—
158#2487C2212yescomplemented
159#2486C2212yes—
160#2486C2212yes—
161#2476C2212yescomplemented
162#2475C2214yescomplemented
163#2474C2212yescomplemented
164#2472C2214yes—
165#2471C2214yes—
166#2470C2214yescomplemented
167#2467C2214yescomplemented
168#2466C2214yescomplemented
169#2460C2214yescomplemented
170#2460C2214yescomplemented
171#2459C2212yes—
172#2456C2212yes—
173#2454C2214yes—
174#2454C2212yescomplemented
175#2451C2211yescharacteristic, complemented
176#2450C2214yescomplemented
177#2449C2214yescomplemented
178#2446C2212yescomplemented
179#2445C2211yescharacteristic, complemented
180#2442C2212yescomplemented
181#2442C2212yescomplemented
182#2442C2212yescomplemented
183#2441C2212yes—
184#2441C2212yes—
185#2441C2214yescomplemented
186#2440C2212yescomplemented
187#2440C2212yescomplemented
188#2440C2212yescomplemented
189#2439C2211yescharacteristic
190#2439C2212yes—
191#2437C2214yes—
192#2437C2214yes—
193#2432C2212yes—
194#2432C2212yes—
195#2431C2211yescharacteristic
196#2429C2212yescomplemented
197#2428C2212yescomplemented
198#2427C2212yes—
199#2427C2212yes—
200#2427C2212yes—
201#2427C2214yescomplemented
202#2426C2212yescomplemented
203#2426C2211yescharacteristic, complemented
204#2425C2214yes—
205#2425C2214yescomplemented
206#2424C2214yes—
207#2424C2214yes—
208#2423C2212yes—
209#2423C2212yescomplemented
210#2422C2212yes—
211#2421C2212yescomplemented
212#2421C2212yescomplemented
213#2420C2212yescomplemented
214#2420C2211yescharacteristic, complemented
215#2417C2212yes—
216#2417C2212yes—
217#2417C2212yes—
218#2417C2212yescomplemented
219#2416C2212yes—
220#2416C2212yescomplemented
221#2416C2212yescomplemented
222#2416C2214yescomplemented
223#2416C2212yescomplemented
224#2414C2211yescharacteristic
225#2412C2214yes—
226#2408C2212yes—
227#2407C2212yes—
228#2407C2211yescharacteristic
229#2392C2214yes—
230#2392C2212yes—
231#2388C2212yes—
232#2377C2214yescomplemented
233#2377C2214yescomplemented
234#2367C2212yes—
235#2367C2211yescharacteristic
236#2364C2212yes—
237#2364C2214yescomplemented
238#2364C2214yescomplemented
239#2363C2212yes—
240#2363C2211yescharacteristic
241#2363C2214yescomplemented
242#2362C2212yescomplemented
243#2361C2212yes—
244#2361C2212yes—
245#2360C2211yescharacteristic
246#2360C2212yescomplemented
247#2360C2212yescomplemented
248#2359C2212yes—
249#2358C2212yes—
250#2355C2211yescharacteristic, complemented
251#2352C2212yes—
252#2352C2211yescharacteristic
253Q8×C4⋊C4C2211yescharacteristic, complemented
254Q8×C4⋊C4C2212yescomplemented
255#2349C2211yescharacteristic
256D4×C4⋊C4C2211yescharacteristic
257D4×C4⋊C4C2211yescharacteristic, complemented
258#2345C2212yescomplemented
259#2345C2212yescomplemented
260#2344C2212yescomplemented
261#2342C2212yes—
262#2341C2212yes—
263#2341C2212yes—
264#2339C2211yescharacteristic
265#2339C2212yes—
266D4×C22⋊C4C2211yescharacteristic
267#2333C2214yescomplemented
268#2332C2214yescomplemented
269#2329C2214yescomplemented
270#2329C2214yescomplemented
271#2324C2212yes—
272#2324C2214yescomplemented
273#2323C2212yescomplemented
274#2311C2212yescomplemented
275C4×C4⋊Q8C2211yescharacteristic, complemented
276C4×#124C2211yescharacteristic
277C4×#124C2211yescharacteristic, complemented
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2212yescomplemented
280C4×C22⋊Q8C2212yescomplemented
281C4×C22⋊Q8C2211yescharacteristic, complemented
282C4×#123C2212yes—
283C4×#123C2212yescomplemented
284C4×#121C2212yes—
285C4×#121C2211yescharacteristic
286C4×#121C2212yes—
287C4×#121C2212yes—
288C4×#121C2211yescharacteristic
289C4×#120C2212yes—
290#2297C2212yescomplemented
291#2293C2211yescharacteristic, complemented
292#2285C2211yescharacteristic
293C2×#384C2211yescharacteristic, complemented
294#2280C2212yes—
295C2×#380C2212yes—
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C22⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C22×#41C2312yes—
302C22×#41C2312yes—
303C23×D4C2311yescharacteristic
304C24×C4C2312yes—
305#557—44no—
306#554—48no—
307#547—44no—
308#546—28no—
309#546—48no—
310#542—48no—
311#537—216no—
312#537—48no—
313#532—44no—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2312yes—
319C2×#127C2311yescharacteristic
320#529—48no—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#125C2312yes—
324C2×#125C2314yes—
325C2×#125C2312yes—
326C2×#125C2314yes—
327C2×#124C2312yes—
328C2×#124C2311yescharacteristic
329C2×#124C2311yescharacteristic
330C2×#124C2312yes—
331C2×#124C2314yes—
332#525—48no—
333C2×#123C2312yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×#123C2314yes—
339C2×#123C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2314yes—
356C2×C22⋊Q8C2314yes—
357C2×#121C2312yes—
358C2×#121C2314yes—
359C2×#121C2311yescharacteristic
360C2×#121C2312yes—
361C2×#121C2314yes—
362C2×#121C2312yes—
363C2×#121C2314yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2314yes—
369C2×#121C2314yes—
370C2×#121C2311yescharacteristic
371C2×#121C2312yes—
372C2×#121C2314yes—
373C2×#121C2311yescharacteristic
374C2×#121C2314yes—
375C2×#121C2314yes—
376C2×#121C2312yes—
377C2×#121C2311yescharacteristic
378C2×#120C2312yes—
379C2×#120C2314yes—
380C2×#120C2314yes—
381C4×#41—44no—
382C4×#41—44no—
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2311yescharacteristic
385C2×C4×Q8C2311yescharacteristic
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2312yes—
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2311yescharacteristic
390C2×C4×Q8C2311yescharacteristic
391C2×C4×D4—44no—
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2314yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2311yescharacteristic
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2311yescharacteristic
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2314yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2311yescharacteristic
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×#117C2311yescharacteristic
421C2×#117C2312yes—
422C2×#117C2314yes—
423C2×#117C2312yes—
424C2×#117C2312yes—
425C2×#117C2312yes—
426C2×#117C2311yescharacteristic
427C22×C4⋊C4C2312yes—
428C22×C4⋊C4C2312yes—
429C22×C4⋊C4C2312yes—
430C22×C4⋊C4C2312yes—
431C22×C4⋊C4C2311yescharacteristic
432C22×C4⋊C4C2312yes—
433C22×C4⋊C4C2312yes—
434C22×C22⋊C4C2312yes—
435C22×C22⋊C4C2312yes—
436C22×C22⋊C4C2312yes—
437C22×C22⋊C4C2314yes—
438C22×C42C2311yescharacteristic
439C22×C42C2311yescharacteristic
440C22×C42C2312yes—
441C22×C42C2312yes—
442C22×C42C2312yes—
443#400C2314yes—
444#400C2314yes—
445#400C2314yes—
446#400C2314yes—
447#400C2314yes—
448#400C2314yes—
449#400C2314yes—
450#400C2314yes—
451#400C2314yes—
452#400C2314yes—
453#399C2314yes—
454#399C2314yes—
455#399C2314yes—
456#399C2314yes—
457#399C2314yes—
458#399C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2312yes—
470#398C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2312yes—
491#396C2314yes—
492#396C2312yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#395C2314yes—
499#395C2314yes—
500#395C2314yes—
501#395C2312yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2312yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2312yes—
513#394C2312yes—
514#394C2312yes—
515#394C2314yes—
516#394C2312yes—
517#394C2314yes—
518#394C2312yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#393C2314yes—
527#393C2314yes—
528#393C2314yes—
529#393C2314yes—
530#393C2312yes—
531#392C2312yes—
532#392C2312yes—
533#392C2312yes—
534#392C2314yes—
535#392C2312yes—
536#392C2314yes—
537#391C2312yes—
538#391C2314yes—
539#391C2314yes—
540#391C2312yes—
541#391C2312yes—
542#391C2314yes—
543#391C2312yes—
544#391C2312yes—
545#391C2311yescharacteristic
546#391C2311yescharacteristic
547#391C2312yes—
548#391C2312yes—
549#391C2311yescharacteristic
550#391C2311yescharacteristic
551#390C2314yes—
552#390C2311yescharacteristic
553#390C2312yes—
554#390C2314yes—
555#390C2311yescharacteristic
556#390C2314yes—
557#390C2312yes—
558#390C2312yes—
559#390C2314yes—
560#390C2312yes—
561#390C2314yes—
562#390C2311yescharacteristic
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2314yes—
567#390C2314yes—
568#390C2311yescharacteristic
569#390C2314yes—
570#390C2312yes—
571#390C2311yescharacteristic
572#390C2311yescharacteristic
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2311yescharacteristic
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2311yescharacteristic
590#389C2312yes—
591#389C2312yes—
592#389C2311yescharacteristic
593#389C2312yes—
594#389C2314yes—
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2311yescharacteristic
601#389C2314yes—
602#389C2314yes—
603#389C2314yes—
604#389C2311yescharacteristic
605#389C2311yescharacteristic
606#389C2312yes—
607#388C2312yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2312yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2312yes—
623#388C2314yes—
624#388C2312yes—
625#388C2312yes—
626#388C2312yes—
627#388C2314yes—
628#388C2312yes—
629#388C2314yes—
630#388C2312yes—
631#388C2312yes—
632#388C2314yes—
633#388C2312yes—
634#388C2314yes—
635#388C2312yes—
636#388C2312yes—
637#388C2312yes—
638#387C2312yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2312yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2312yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2312yes—
659#387C2314yes—
660#387C2312yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#386C2314yes—
676#386C2312yes—
677#386C2314yes—
678#386C2312yes—
679#386C2314yes—
680#386C2312yes—
681#386C2312yes—
682#386C2312yes—
683#386C2314yes—
684#386C2312yes—
685#386C2312yes—
686#386C2314yes—
687#386C2314yes—
688#386C2312yes—
689#386C2314yes—
690#386C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2312yes—
695#385C2312yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2312yes—
704#385C2312yes—
705#385C2314yes—
706#385C2312yes—
707#385C2314yes—
708#385C2314yes—
709#385C2312yes—
710#385C2314yes—
711#385C2314yes—
712#385C2312yes—
713#384C2311yescharacteristic
714#384C2312yes—
715#384C2311yescharacteristic
716#384C2311yescharacteristic
717#384C2312yes—
718#384C2312yes—
719#384C2314yes—
720#384C2312yes—
721#384C2312yes—
722#383C2314yes—
723#382C2314yes—
724#382C2312yes—
725#382C2312yes—
726#382C2312yes—
727#382C2311yescharacteristic
728#382C2311yescharacteristic
729#381C2314yes—
730#381C2314yes—
731#381C2312yes—
732#381C2314yes—
733#381C2312yes—
734#380C2312yes—
735#380C2311yescharacteristic
736#380C2314yes—
737#380C2314yes—
738#380C2314yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2311yescharacteristic
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2314yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2314yes—
751#380C2314yes—
752#380C2314yes—
753#380C2314yes—
754#380C2312yes—
755#380C2312yes—
756#380C2311yescharacteristic
757#380C2312yes—
758#380C2312yes—
759#380C2314yes—
760#380C2312yes—
761#380C2314yes—
762#380C2312yes—
763#380C2312yes—
764#380C2314yes—
765#380C2312yes—
766#380C2311yescharacteristic
767#380C2314yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#379C2312yes—
772#379C2314yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2311yescharacteristic
817C4×C22⋊C4C2312yes—
818C4×C22⋊C4C2312yes—
819C4×C22⋊C4C2311yescharacteristic
820C2×#95C2312yes—
821C2×#95C2314yes—
822C2×#95C2312yes—
823C43C2311yescharacteristic
824C25C2412yes—
825C2×#41—24no—
826C2×#41—28no—
827C2×#41—24no—
828C2×#41—24no—
829C2×#41—28no—
830C2×#41—24no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—42no—
834C2×#41—42no—
835C2×#41—44no—
836C2×#41—44no—
837C22×Q8C2412yes—
838C22×Q8C2411yescharacteristic
839C22×Q8C2411yescharacteristic
840C22×Q8C2412yes—
841C22×Q8C2414yes—
842C22×D4—24no—
843C22×D4—24no—
844C22×D4—42no—
845C22×D4C2411yescharacteristic
846C22×D4C2411yescharacteristic
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2412yes—
851C22×D4C2411yescharacteristic
852C22×D4C2411yescharacteristic
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2412yes—
858C22×D4C2414yes—
859C22×D4C2412yes—
860C22×D4C2412yes—
861C22×D4C2412yes—
862C22×D4C2412yes—
863C23×C4—28no—
864C23×C4—44no—
865C23×C4—44no—
866C23×C4C2411yescharacteristic
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2412yes—
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2411yescharacteristic
878C23×C4C2414yes—
879C23×C4C2412yes—
880C23×C4C2412yes—
881C23×C4C2412yes—
882C23×C4C2412yes—
883C23×C4C2414yes—
884C23×C4C2412yes—
885C23×C4C2412yes—
886C23×C4C2414yes—
887C23×C4C2414yes—
888C23×C4C2412yes—
889C4⋊Q8—24no—
890C4⋊Q8—42no—
891C4⋊Q8—44no—
892C4⋊Q8—44no—
893C4⋊Q8—44no—
894#127—42no—
895#126—48no—
896#126—48no—
897#125—44no—
898#125—48no—
899#125—44no—
900#125—48no—
901#124—24no—
902#124—24no—
903#124—28no—
904#124—44no—
905#124—48no—
906#123—28no—
907#123—48no—
908#123—48no—
909#123—48no—
910#123—48no—
911#123—44no—
912#123—48no—
913C22⋊Q8—28no—
914C22⋊Q8—28no—
915C22⋊Q8—24no—
916C22⋊Q8—28no—
917C22⋊Q8—28no—
918C22⋊Q8—24no—
919C22⋊Q8—216no—
920C22⋊Q8—48no—
921C22⋊Q8—48no—
922C22⋊Q8—48no—
923C22⋊Q8—48no—
924C22⋊Q8—48no—
925C22⋊Q8—44no—
926C22⋊Q8—44no—
927C22⋊Q8—44no—
928C22⋊Q8—44no—
929C22⋊Q8—44no—
930#121—28no—
931#121—216no—
932#121—216no—
933#121—28no—
934#121—28no—
935#121—28no—
936#121—24no—
937#121—216no—
938#121—44no—
939#121—48no—
940#121—48no—
941#121—48no—
942#121—48no—
943#121—44no—
944#121—44no—
945#121—44no—
946#121—42no—
947#121—42no—
948#121—44no—
949#121—48no—
950#121#4118yescomplemented
951#120—28no—
952#120—48no—
953#120—48no—
954C4×Q8—28no—
955C4×Q8—24no—
956C4×Q8—24no—
957C4×Q8—42no—
958C4×Q8—42no—
959C4×Q8—44no—
960C4×Q8—44no—
961C4×Q8—44no—
962C4×D4—24no—
963C4×D4—24no—
964C4×D4—24no—
965C4×D4—24no—
966C4×D4—24no—
967C4×D4—24no—
968C4×D4—24no—
969C4×D4—24no—
970C4×D4—44no—
971C4×D4—48no—
972C4×D4—48no—
973C4×D4—42no—
974C4×D4—42no—
975C4×D4—42no—
976C4×D4—42no—
977C4×D4—44no—
978C4×D4—44no—
979C4×D4—44no—
980C4×D4—44no—
981C4×D4—44no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—44no—
985C4×D4—42no—
986C4×D4—44no—
987C4×D4—44no—
988C4×D4—48no—
989C4×D4—48no—
990#117—44no—
991#117—44no—
992#117—44no—
993#117—48no—
994#117—42no—
995#117—42no—
996#117—44no—
997C2×C4⋊C4—28no—
998C2×C4⋊C4—44no—
999C2×C4⋊C4—42no—
1000C2×C4⋊C4—44no—
1001C2×C4⋊C4—44no—
1002C2×C4⋊C4—44no—
1003C2×C4⋊C4—44no—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2411yescharacteristic
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2414yes—
1062C2×C4⋊C4C2414yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2412yes—
1065C2×C4⋊C4C2411yescharacteristic
1066C2×C22⋊C4—28no—
1067C2×C22⋊C4—44no—
1068C2×C22⋊C4—44no—
1069C2×C22⋊C4—48no—
1070C2×C22⋊C4C2411yescharacteristic
1071C2×C22⋊C4C2411yescharacteristic
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2411yescharacteristic
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2411yescharacteristic
1090C2×C22⋊C4C2411yescharacteristic
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2411yescharacteristic
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2412yes—
1130C2×C22⋊C4C2412yes—
1131C2×C22⋊C4C2412yes—
1132C2×C22⋊C4C2412yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2412yes—
1136C2×C22⋊C4C2412yes—
1137C2×C22⋊C4C2412yes—
1138C2×C42—24no—
1139C2×C42—24no—
1140C2×C42—44no—
1141C2×C42—44no—
1142C2×C42—44no—
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2414yes—
1147C2×C42C2412yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150C2×C42C2412yes—
1151C2×C42C2411yescharacteristic
1152C2×C42C2411yescharacteristic
1153C2×C42C2412yes—
1154C2×C42C2412yes—
1155C2×C42C2411yescharacteristic
1156C2×C42C2411yescharacteristic
1157C2×C42C2411yescharacteristic
1158C2×C42C2412yes—
1159C2×C42C2412yes—
1160C2×C42C2412yes—
1161C2×C42C2414yes—
1162C2×C42C2412yes—
1163C2×C42C2412yes—
1164C2×C42C2411yescharacteristic
1165C2×C42C2414yes—
1166C2×C42C2414yes—
1167C2×C42C2412yes—
1168C2×C42C2411yescharacteristic
1169C2×C42C2414yes—
1170C2×C42C2411yescharacteristic
1171#95C2411yescharacteristic
1172#95C2411yescharacteristic
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2411yescharacteristic
1185#95C2412yes—
1186#95C2411yescharacteristic
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2411yescharacteristic
1191#95C2411yescharacteristic
1192#95C2412yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2412yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2412yes—
1218#95C2412yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2412yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226#95C2414yes—
1227#95C2414yes—
1228#95C2414yes—
1229C24—24no—
1230C24—24no—
1231C24—24no—
1232C24—42no—
1233C24—42no—
1234C24—42no—
1235C24—42no—
1236C24C2512yes—
1237C24C2512yes—
1238C24C2512yes—
1239C24C2511yescharacteristic
1240C24C2512yes—
1241C24C2511yescharacteristic
1242#41—416no—
1243#41—416no—
1244#41—816no—
1245#41—816no—
1246C2×Q8—24no—
1247C2×Q8—22no—
1248C2×Q8—24no—
1249C2×Q8—22no—
1250C2×Q8—22no—
1251C2×Q8—24no—
1252C2×Q8—24no—
1253C2×Q8—22no—
1254C2×Q8—22no—
1255C2×Q8—42no—
1256C2×Q8—42no—
1257C2×Q8—44no—
1258C2×Q8—44no—
1259C2×Q8—44no—
1260C2×Q8H(5,𝔽2)14yes—
1261C2×D4—22no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—22no—
1267C2×D4—24no—
1268C2×D4—28no—
1269C2×D4—24no—
1270C2×D4—28no—
1271C2×D4—24no—
1272C2×D4—28no—
1273C2×D4—28no—
1274C2×D4—24no—
1275C2×D4—22no—
1276C2×D4—24no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—24no—
1284C2×D4—22no—
1285C2×D4—22no—
1286C2×D4—22no—
1287C2×D4—24no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—42no—
1291C2×D4—42no—
1292C2×D4—41no—
1293C2×D4—42no—
1294C2×D4—42no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—42no—
1299C2×D4—44no—
1300C2×D4—42no—
1301C2×D4—42no—
1302C2×D4—42no—
1303C2×D4—42no—
1304C2×D4—42no—
1305C2×D4—44no—
1306C2×D4—44no—
1307C2×D4—44no—
1308C2×D4—42no—
1309C2×D4—42no—
1310C2×D4—42no—
1311C2×D4—44no—
1312C2×D4—416no—
1313C2×D4C2×#4114yes—
1314C2×D4C2×#4118yes—
1315C2×D4H(5,𝔽2)14yes—
1316C22×C4—22no—
1317C22×C4—22no—
1318C22×C4—22no—
1319C22×C4—22no—
1320C22×C4—24no—
1321C22×C4—28no—
1322C22×C4—24no—
1323C22×C4—24no—
1324C22×C4—24no—
1325C22×C4—24no—
1326C22×C4—22no—
1327C22×C4—24no—
1328C22×C4—22no—
1329C22×C4—22no—
1330C22×C4—22no—
1331C22×C4—24no—
1332C22×C4—24no—
1333C22×C4—24no—
1334C22×C4—22no—
1335C22×C4—24no—
1336C22×C4—24no—
1337C22×C4—24no—
1338C22×C4—24no—
1339C22×C4—24no—
1340C22×C4—22no—
1341C22×C4—24no—
1342C22×C4—22no—
1343C22×C4—24no—
1344C22×C4—24no—
1345C22×C4—24no—
1346C22×C4—22no—
1347C22×C4—24no—
1348C22×C4—28no—
1349C22×C4—22no—
1350C22×C4—24no—
1351C22×C4—24no—
1352C22×C4—24no—
1353C22×C4—42no—
1354C22×C4—42no—
1355C22×C4—41no—
1356C22×C4—42no—
1357C22×C4—42no—
1358C22×C4—42no—
1359C22×C4—42no—
1360C22×C4—42no—
1361C22×C4—44no—
1362C22×C4—42no—
1363C22×C4—44no—
1364C22×C4—44no—
1365C22×C4—42no—
1366C22×C4—42no—
1367C22×C4—42no—
1368C22×C4—42no—
1369C22×C4—41no—
1370C22×C4—42no—
1371C22×C4—42no—
1372C22×C4—41no—
1373C22×C4—42no—
1374C22×C4—44no—
1375C22×C4—42no—
1376C22×C4—42no—
1377C22×C4—44no—
1378C22×C4—44no—
1379C22×C4—44no—
1380C22×C4—44no—
1381C22×C4—44no—
1382C22×C4—44no—
1383C22×C4—816no—
1384C22×C4C2×#4114yes—
1385C22×C42−1+414yes—
1386C22×C4C2511yescharacteristic
1387C22×C4C2511yescharacteristic
1388C22×C4C2512yes—
1389C22×C4C2511yescharacteristic
1390C22×C4C2511yescharacteristic
1391C22×C4C2512yes—
1392C22×C4C2514yes—
1393C22×C4C2512yes—
1394C22×C4C2512yes—
1395C22×C4C2512yes—
1396C22×C4C2512yes—
1397C22×C4C2512yes—
1398C22×C4C2511yescharacteristic
1399C22×C4C2512yes—
1400C22×C4C2512yes—
1401C22×C4C2512yes—
1402C22×C4C2514yes—
1403C22×C4C2514yes—
1404C22×C4C2511yescharacteristic
1405C22×C4C2514yes—
1406C22×C4C2511yescharacteristic
1407C22×C4C2512yes—
1408C22×C4C2511yescharacteristic
1409C22×C4C2512yes—
1410C22×C4C2511yescharacteristic
1411C22×C4C2511yescharacteristic
1412C22×C4C2511yescharacteristic
1413C22×C4C2511yescharacteristic
1414C22×C4C2511yescharacteristic
1415C4⋊C4—24no—
1416C4⋊C4—28no—
1417C4⋊C4—22no—
1418C4⋊C4—28no—
1419C4⋊C4—28no—
1420C4⋊C4—24no—
1421C4⋊C4—22no—
1422C4⋊C4—24no—
1423C4⋊C4—22no—
1424C4⋊C4—22no—
1425C4⋊C4—24no—
1426C4⋊C4—22no—
1427C4⋊C4—24no—
1428C4⋊C4—24no—
1429C4⋊C4—24no—
1430C4⋊C4—22no—
1431C4⋊C4—22no—
1432C4⋊C4—24no—
1433C4⋊C4—24no—
1434C4⋊C4—22no—
1435C4⋊C4—24no—
1436C4⋊C4—28no—
1437C4⋊C4—22no—
1438C4⋊C4—28no—
1439C4⋊C4—28no—
1440C4⋊C4—24no—
1441C4⋊C4—24no—
1442C4⋊C4—22no—
1443C4⋊C4—22no—
1444C4⋊C4—28no—
1445C4⋊C4—22no—
1446C4⋊C4—24no—
1447C4⋊C4—42no—
1448C4⋊C4—42no—
1449C4⋊C4—42no—
1450C4⋊C4—44no—
1451C4⋊C4—44no—
1452C4⋊C4—44no—
1453C4⋊C4—44no—
1454C4⋊C4—42no—
1455C4⋊C4—42no—
1456C4⋊C4—42no—
1457C4⋊C4—42no—
1458C4⋊C4—42no—
1459C4⋊C4—44no—
1460C4⋊C4—42no—
1461C4⋊C4—42no—
1462C4⋊C4—42no—
1463C4⋊C4—42no—
1464C4⋊C4—44no—
1465C4⋊C4—44no—
1466C4⋊C4—44no—
1467C4⋊C4—44no—
1468C4⋊C4—44no—
1469C4⋊C4—44no—
1470C4⋊C4—44no—
1471C4⋊C4—44no—
1472C4⋊C4—44no—
1473C4⋊C4—44no—
1474C4⋊C4—44no—
1475C4⋊C4—44no—
1476C4⋊C4C2×#4114yes—
1477C22⋊C4—24no—
1478C22⋊C4—22no—
1479C22⋊C4—24no—
1480C22⋊C4—28no—
1481C22⋊C4—28no—
1482C22⋊C4—28no—
1483C22⋊C4—28no—
1484C22⋊C4—24no—
1485C22⋊C4—28no—
1486C22⋊C4—28no—
1487C22⋊C4—22no—
1488C22⋊C4—22no—
1489C22⋊C4—24no—
1490C22⋊C4—24no—
1491C22⋊C4—28no—
1492C22⋊C4—24no—
1493C22⋊C4—24no—
1494C22⋊C4—24no—
1495C22⋊C4—24no—
1496C22⋊C4—24no—
1497C22⋊C4—28no—
1498C22⋊C4—28no—
1499C22⋊C4—24no—
1500C22⋊C4—24no—
1501C22⋊C4—22no—
1502C22⋊C4—24no—
1503C22⋊C4—22no—
1504C22⋊C4—24no—
1505C22⋊C4—42no—
1506C22⋊C4—42no—
1507C22⋊C4—42no—
1508C22⋊C4—42no—
1509C22⋊C4—42no—
1510C22⋊C4—44no—
1511C22⋊C4—42no—
1512C22⋊C4—42no—
1513C22⋊C4—42no—
1514C22⋊C4—42no—
1515C22⋊C4—44no—
1516C22⋊C4—42no—
1517C22⋊C4—42no—
1518C22⋊C4—42no—
1519C22⋊C4—42no—
1520C22⋊C4—44no—
1521C22⋊C4—44no—
1522C22⋊C4—42no—
1523C22⋊C4—42no—
1524C22⋊C4—41no—
1525C22⋊C4—44no—
1526C22⋊C4—42no—
1527C22⋊C4—44no—
1528C22⋊C4—44no—
1529C22⋊C4—42no—
1530C22⋊C4—42no—
1531C22⋊C4—42no—
1532C22⋊C4—42no—
1533C22⋊C4—44no—
1534C22⋊C4—44no—
1535C22⋊C4—44no—
1536C22⋊C4—44no—
1537C22⋊C4—44no—
1538C22⋊C4—44no—
1539C22⋊C4—44no—
1540C22⋊C4—44no—
1541C22⋊C4—42no—
1542C22⋊C4—42no—
1543C22⋊C4—42no—
1544C22⋊C4C2×#4118yes—
1545C42—22no—
1546C42—22no—
1547C42—22no—
1548C42—22no—
1549C42—22no—
1550C42—22no—
1551C42—22no—
1552C42—22no—
1553C42—24no—
1554C42—24no—
1555C42—24no—
1556C42—22no—
1557C42—28no—
1558C42—24no—
1559C42—22no—
1560C42—42no—
1561C42—42no—
1562C42—42no—
1563C42—42no—
1564C42—42no—
1565C42—42no—
1566C42—41no—
1567C42—44no—
1568C42—44no—
1569C42—41no—
1570C42—44no—
1571C42—44no—
1572C42H(5,𝔽2)14yes—
1573C23—21no—
1574C23—22no—
1575C23—21no—
1576C23—22no—
1577C23—22no—
1578C23—22no—
1579C23—22no—
1580C23—21no—
1581C23—21no—
1582C23—21no—
1583C23—21no—
1584C23—22no—
1585C23—21no—
1586C23—21no—
1587C23—22no—
1588C23—22no—
1589C23—22no—
1590C23—21no—
1591C23—21no—
1592C23—22no—
1593C23—22no—
1594C23—21no—
1595C23—22no—
1596C23—21no—
1597C23—22no—
1598C23—22no—
1599C23—22no—
1600C23—22no—
1601C23—22no—
1602C23—22no—
1603C23—22no—
1604C23—22no—
1605C23—22no—
1606C23—22no—
1607C23—22no—
1608C23—22no—
1609C23—22no—
1610C23—22no—
1611C23—48no—
1612C23—48no—
1613C23—48no—
1614C23—84no—
1615C23—84no—
1616C23—84no—
1617C23—84no—
1618C23C22×#4112yes—
1619C23C22×#4114yes—
1620C23C2×H(5,𝔽2)14yes—
1621C23C2×2−1+412yes—
1622C23C2611yescharacteristic
1623Q8—28no—
1624Q8—44no—
1625Q8—48no—
1626Q8—84no—
1627Q8—164no—
1628D4—28no—
1629D4—28no—
1630D4—48no—
1631D4—48no—
1632D4—44no—
1633D4—48no—
1634D4—48no—
1635D4—44no—
1636D4—44no—
1637D4—84no—
1638D4—84no—
1639D4—88no—
1640D4—88no—
1641D4—88no—
1642D4—84no—
1643D4—84no—
1644D4—84no—
1645D4—88no—
1646C2×C4—22no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—22no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—22no—
1657C2×C4—21no—
1658C2×C4—28no—
1659C2×C4—28no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—22no—
1663C2×C4—24no—
1664C2×C4—22no—
1665C2×C4—24no—
1666C2×C4—21no—
1667C2×C4—22no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—22no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—21no—
1681C2×C4—24no—
1682C2×C4—22no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—24no—
1686C2×C4—24no—
1687C2×C4—24no—
1688C2×C4—24no—
1689C2×C4—24no—
1690C2×C4—22no—
1691C2×C4—22no—
1692C2×C4—22no—
1693C2×C4—24no—
1694C2×C4—22no—
1695C2×C4—22no—
1696C2×C4—22no—
1697C2×C4—22no—
1698C2×C4—22no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—21no—
1702C2×C4—21no—
1703C2×C4—21no—
1704C2×C4—22no—
1705C2×C4—22no—
1706C2×C4—22no—
1707C2×C4—21no—
1708C2×C4—21no—
1709C2×C4—22no—
1710C2×C4—22no—
1711C2×C4—22no—
1712C2×C4—21no—
1713C2×C4—24no—
1714C2×C4—22no—
1715C2×C4—24no—
1716C2×C4—22no—
1717C2×C4—22no—
1718C2×C4—21no—
1719C2×C4—21no—
1720C2×C4—24no—
1721C2×C4—22no—
1722C2×C4—21no—
1723C2×C4—44no—
1724C2×C4—48no—
1725C2×C4—48no—
1726C2×C4—44no—
1727C2×C4—48no—
1728C2×C4—48no—
1729C2×C4—44no—
1730C2×C4—48no—
1731C2×C4—48no—
1732C2×C4—84no—
1733C2×C4—88no—
1734C2×C4—84no—
1735C2×C4—82no—
1736C2×C4—84no—
1737C2×C4—84no—
1738C2×C4—84no—
1739C2×C4—84no—
1740C2×C4—88no—
1741C2×C4—84no—
1742C2×C4—164no—
1743C2×C4—164no—
1744C2×C4C22×#4114yes—
1745C2×C4C22×#4112yes—
1746C2×C4C22×#4112yes—
1747C2×C4C2×H(5,𝔽2)12yes—
1748C2×C4C2×H(5,𝔽2)14yes—
1749C2×C4C2×H(5,𝔽2)12yes—
1750C2×C4C2×H(5,𝔽2)12yes—
1751C2×C4C2×H(5,𝔽2)12yes—
1752C2×C4C2×H(5,𝔽2)12yes—
1753C2×C4C2×2−1+412yes—
1754C2×C4C2×2−1+412yes—
1755C2×C4#58512yes—
1756C22—22no—
1757C22—22no—
1758C22—24no—
1759C22—24no—
1760C22—22no—
1761C22—24no—
1762C22—24no—
1763C22—22no—
1764C22—22no—
1765C22—24no—
1766C22—22no—
1767C22—24no—
1768C22—42no—
1769C22—42no—
1770C22—41no—
1771C22—42no—
1772C22—41no—
1773C22—41no—
1774C22—42no—
1775C22—41no—
1776C22—41no—
1777C22—42no—
1778C22—41no—
1779C22—42no—
1780C22—41no—
1781C22—42no—
1782C22—41no—
1783C22—42no—
1784C22—42no—
1785C22—42no—
1786C22—42no—
1787C22—42no—
1788C22—42no—
1789C22—42no—
1790C22—42no—
1791C22—42no—
1792C22—42no—
1793C22—42no—
1794C22—42no—
1795C22—42no—
1796C22—42no—
1797C22—42no—
1798C22—816no—
1799C22C23×#4111yescharacteristic
1800C22C22×H(5,𝔽2)11yescharacteristic
1801C22C22×H(5,𝔽2)11yescharacteristic
1802C22C22×H(5,𝔽2)11yescharacteristic
1803C22C22×2−1+411yescharacteristic
1804C22C2×#58511yescharacteristic
1805C222−1+611yescharacteristic
1806C4—22no—
1807C4—24no—
1808C4—24no—
1809C4—22no—
1810C4—22no—
1811C4—22no—
1812C4—41no—
1813C4—42no—
1814C4—42no—
1815C4—41no—
1816C4—44no—
1817C4—41no—
1818C4—42no—
1819C4—44no—
1820C4—42no—
1821C4—44no—
1822C4—42no—
1823C4—41no—
1824C4—42no—
1825C4—42no—
1826C4—44no—
1827C4—41no—
1828C4—41no—
1829C4—42no—
1830C4—42no—
1831C4—42no—
1832C4—41no—
1833C4#351914yes—
1834C4#353614yes—
1835C2—42no—
1836C2—44no—
1837C2—44no—
1838C2—42no—
1839C2—82no—
1840C2—82no—
1841C2C2×#353611yescharacteristic
1842C2C2×#351911yescharacteristic
1843C2#6280511yescharacteristic
1844C2#6291511yescharacteristic
1845C2#6292711yescharacteristic
1846C2#6298411yescharacteristic
1847C2#6301411yescharacteristic
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. #59418C2semidirect
2. #59397C2semidirect
3. #59314C2semidirect
4. #59230C2semidirect
5. #59024C2semidirect
6. #51687C2semidirect
7. #48478C2semidirect
8. #45688C2semidirect
9. #45602C2semidirect
10. #45103C2semidirect
11. #45079C2semidirect
12. #43429C2semidirect
13. #42991C2semidirect
14. #42633C2semidirect
15. #41239C2semidirect
16. #40101C2semidirect
17. #40076C2semidirect
18. #39910C2semidirect
19. #39432C2semidirect
20. #39340C2semidirect
21. #39193C2semidirect
22. #39126C2semidirect
23. #36505C2semidirect
24. #36445C2semidirect
25. #36189C2semidirect
26. #36153C2semidirect
27. #36144C2semidirect
28. #36114C2semidirect
29. #35273C2semidirect
30. #35170C2semidirect
31. #35079C2semidirect
32. #34935C2semidirect
33. #34715C2semidirect
34. #34410C2semidirect
35. C4×#546C2semidirect
36. C2×#557C22semidirect
37. C2×#554C22semidirect
44. C2×#532C22semidirect
45. C2×#529C22semidirect
50. #2859C22semidirect
52. #2857C22semidirect
53. #2857C22semidirect
54. #2857C22semidirect
55. #2857C22semidirect
56. #2856C22semidirect
57. #2854C22semidirect
58. #2851C22semidirect
59. #2851C22semidirect
61. #2836C22semidirect
62. #2830C22semidirect
63. #2791C22semidirect
65. #2781C22semidirect
66. #2779C22semidirect
67. #2771C22semidirect
68. #2757C22semidirect
69. #2750C22semidirect
72. #2743C22semidirect
73. #2740C22semidirect
74. #2720C22semidirect
75. #2708C22semidirect
76. #2708C22semidirect
78. #2707C22semidirect
80. #2702C22semidirect
81. #2702C22semidirect
83. #2696C22semidirect
84. #2689C22semidirect
85. #2686C22semidirect
88. #2681C22semidirect
91. #2672C22semidirect
94. #2671C22semidirect
97. #2666C22semidirect
99. #2663C22semidirect
100. #2649C22semidirect
101. #2629C22semidirect
102. #2625C22semidirect
103. #2620C22semidirect
104. #2616C22semidirect
105. #2578C22semidirect
106. #2577C22semidirect
107. #2574C22semidirect
108. #2570C22semidirect
109. #2569C22semidirect
111. #2563C22semidirect
112. #2562C22semidirect
113. #2562C22semidirect
114. #2559C22semidirect
115. #2558C22semidirect
118. #2551C22semidirect
119. #2549C22semidirect
123. #2542C22semidirect
128. #2538C22semidirect
129. #2538C22semidirect
130. #2538C22semidirect
136. #2537C22semidirect
138. #2536C22semidirect
141. #2521C22semidirect
142. #2511C22semidirect
143. #2508C22semidirect
144. #2507C22semidirect
145. #2506C22semidirect
146. #2504C22semidirect
148. #2496C22semidirect
149. #2496C22semidirect
150. #2495C22semidirect
151. #2495C22semidirect
152. #2492C22semidirect
153. #2492C22semidirect
154. #2491C22semidirect
155. #2490C22semidirect
156. #2490C22semidirect
158. #2487C22semidirect
161. #2476C22semidirect
162. #2475C22semidirect
163. #2474C22semidirect
166. #2470C22semidirect
167. #2467C22semidirect
168. #2466C22semidirect
169. #2460C22semidirect
170. #2460C22semidirect
174. #2454C22semidirect
175. #2451C22semidirect
176. #2450C22semidirect
177. #2449C22semidirect
178. #2446C22semidirect
179. #2445C22semidirect
180. #2442C22semidirect
181. #2442C22semidirect
182. #2442C22semidirect
185. #2441C22semidirect
186. #2440C22semidirect
187. #2440C22semidirect
188. #2440C22semidirect
196. #2429C22semidirect
197. #2428C22semidirect
201. #2427C22semidirect
202. #2426C22semidirect
203. #2426C22semidirect
205. #2425C22semidirect
209. #2423C22semidirect
211. #2421C22semidirect
212. #2421C22semidirect
213. #2420C22semidirect
214. #2420C22semidirect
218. #2417C22semidirect
220. #2416C22semidirect
221. #2416C22semidirect
222. #2416C22semidirect
223. #2416C22semidirect
232. #2377C22semidirect
233. #2377C22semidirect
237. #2364C22semidirect
238. #2364C22semidirect
241. #2363C22semidirect
242. #2362C22semidirect
246. #2360C22semidirect
247. #2360C22semidirect
250. #2355C22semidirect
253. Q8×C4⋊C4C22semidirect
254. Q8×C4⋊C4C22semidirect
257. D4×C4⋊C4C22semidirect
258. #2345C22semidirect
259. #2345C22semidirect
260. #2344C22semidirect
267. #2333C22semidirect
268. #2332C22semidirect
269. #2329C22semidirect
270. #2329C22semidirect
272. #2324C22semidirect
273. #2323C22semidirect
274. #2311C22semidirect
275. C4×C4⋊Q8C22semidirect
277. C4×#124C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
281. C4×C22⋊Q8C22semidirect
283. C4×#123C22semidirect
290. #2297C22semidirect
291. #2293C22semidirect
293. C2×#384C22semidirect
950. #121#41semidirect

Maximal subgroups

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

subgroupindex
#594182
#593972
#593142
#592302
#590242
#516872
#484782
#456882
#456022
#451032
#450792
#434292
#429912
#426332
#412392
#401012
#400762
#399102
#394322
#393402
#391932
#391262
#365052
#364452
#361892
#361532
#361442
#361142
#352732
#351702
#350792
#349352
#347152
#344102
C4×#5462