Finite Group Databasebeta

← #7670617

Subgroups — #7670617

Order 512.

5758 conjugacy classes of subgroups.

The subgroup lattice has 1872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59773C214yesmaximal, complemented
2#59403C212yesmaximal, complemented
3#59381C212yesmaximal, complemented
4#59259C211yesmaximal, characteristic, complemented
5#59212C211yesmaximal, characteristic, complemented
6#59080C211yesmaximal, characteristic, complemented
7#59033C211yesmaximal, characteristic, complemented
8#59020C212yesmaximal, complemented
9#59001C212yesmaximal, complemented
10#40382C214yesmaximal, complemented
11#40194C212yesmaximal, complemented
12#40146C212yesmaximal, complemented
13#39934C212yesmaximal, complemented
14#39861C212yesmaximal, complemented
15#38713C214yesmaximal, complemented
16#36624C211yesmaximal, characteristic, complemented
17#36498C212yesmaximal, complemented
18#36472C211yesmaximal, characteristic, complemented
19#36460C211yesmaximal, characteristic, complemented
20#36455C211yesmaximal, characteristic, complemented
21#36444C211yesmaximal, characteristic, complemented
22#36410C211yesmaximal, characteristic, complemented
23#36402C212yesmaximal, complemented
24#36396C212yesmaximal, complemented
25#36381C212yesmaximal, complemented
26#36315C211yesmaximal, characteristic, complemented
27#36314C211yesmaximal, characteristic, complemented
28#36274C211yesmaximal, characteristic, complemented
29#35420C214yesmaximal, complemented
30#35038C212yesmaximal, complemented
31#35037C212yesmaximal, complemented
32#34330C212yesmaximal, complemented
33#34327C212yesmaximal, complemented
34C4×#525C211yesmaximal, characteristic, complemented
35C4×#525C211yesmaximal, characteristic, complemented
36C2×#553C2212yes—
37C2×#550C2212yes—
38C2×#550C2211yescharacteristic, complemented
39C2×D4×Q8C2211yescharacteristic, complemented
40C2×#548C2212yes—
41C2×#548C2212yes—
42C2×#532C2211yescharacteristic
43C2×#525C2211yescharacteristic
44C2×#525C2211yescharacteristic
45C2×#525C2212yes—
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic
48C23×C42C2211yescharacteristic
49#2864C2212yescomplemented
50#2861C2212yescomplemented
51#2860C2212yescomplemented
52#2860C2212yescomplemented
53#2857C2211yescharacteristic
54#2857C2211yescharacteristic
55#2857C2212yescomplemented
56#2856C2211yescharacteristic
57#2856C2211yescharacteristic
58#2856C2212yescomplemented
59#2855C2212yescomplemented
60#2854C2212yes—
61#2854C2212yes—
62#2854C2212yescomplemented
63#2850C2212yes—
64#2850C2212yes—
65#2847C2212yes—
66#2847C2212yes—
67#2781C2214yescomplemented
68#2778C2214yes—
69#2768C2214yes—
70#2761C2214yescomplemented
71#2756C2214yescomplemented
72#2751C2214yes—
73#2749C2214yes—
74#2745C2214yescomplemented
75#2709C2214yes—
76#2708C2214yes—
77#2697C2214yes—
78#2688C2214yes—
79#2676C2214yes—
80#2670C2214yes—
81#2669C2214yes—
82#2668C2214yes—
83#2653C2214yes—
84#2648C2214yes—
85#2635C2214yes—
86#2630C2214yes—
87#2603C2214yes—
88#2603C2214yescomplemented
89#2600C2214yes—
90#2597C2214yescomplemented
91#2597C2214yescomplemented
92#2595C2214yes—
93#2595C2214yescomplemented
94#2595C2214yescomplemented
95#2594C2214yescomplemented
96#2585C2214yescomplemented
97#2582C2211yescharacteristic, complemented
98#2576C2214yes—
99#2574C2214yescomplemented
100#2571C2211yescharacteristic, complemented
101#2568C2211yescharacteristic, complemented
102#2565C2212yescomplemented
103#2560C2214yescomplemented
104#2560C2214yescomplemented
105#2559C2214yes—
106#2559C2214yescomplemented
107#2557C2214yes—
108#2557C2214yes—
109#2553C2214yes—
110#2552C2211yescharacteristic, complemented
111#2548C2211yescharacteristic, complemented
112#2547C2212yes—
113#2547C2211yescharacteristic, complemented
114#2544C2212yescomplemented
115#2543C2214yes—
116#2543C2214yes—
117#2541C2212yes—
118#2541C2211yescharacteristic, complemented
119#2537C2212yes—
120#2537C2212yes—
121#2537C2211yescharacteristic, complemented
122#2535C2212yes—
123#2535C2212yes—
124#2533C2214yescomplemented
125#2531C2214yes—
126#2531C2214yescomplemented
127#2530C2214yes—
128#2529C2214yescomplemented
129#2526C2214yescomplemented
130#2512C2212yescomplemented
131#2511C2212yescomplemented
132#2508C2212yescomplemented
133#2507C2212yescomplemented
134#2504C2212yescomplemented
135#2500C2212yes—
136#2499C2212yes—
137#2497C2212yes—
138#2497C2212yescomplemented
139#2495C2212yes—
140#2494C2212yescomplemented
141#2494C2212yescomplemented
142#2491C2212yes—
143#2490C2212yescomplemented
144#2489C2212yes—
145#2485C2212yes—
146#2485C2212yes—
147#2476C2214yescomplemented
148#2467C2214yes—
149#2466C2214yes—
150#2464C2214yes—
151#2464C2214yes—
152#2463C2214yes—
153#2463C2214yescomplemented
154#2461C2214yes—
155#2461C2214yes—
156#2457C2214yes—
157#2457C2214yescomplemented
158#2456C2214yes—
159#2456C2214yes—
160#2456C2214yes—
161#2452C2212yescomplemented
162#2451C2212yescomplemented
163#2450C2214yes—
164#2447C2212yescomplemented
165#2445C2212yescomplemented
166#2444C2214yescomplemented
167#2441C2212yes—
168#2439C2212yes—
169#2438C2214yescomplemented
170#2436C2212yescomplemented
171#2431C2212yes—
172#2431C2212yes—
173#2428C2212yes—
174#2428C2214yes—
175#2428C2212yes—
176#2428C2212yescomplemented
177#2427C2214yes—
178#2427C2212yescomplemented
179#2426C2212yes—
180#2426C2212yes—
181#2426C2212yescomplemented
182#2423C2212yes—
183#2422C2212yes—
184#2421C2212yes—
185#2420C2214yes—
186#2420C2212yes—
187#2420C2212yescomplemented
188#2419C2214yes—
189#2417C2212yes—
190#2415C2212yes—
191#2415C2214yescomplemented
192#2414C2212yes—
193#2414C2212yes—
194#2414C2212yes—
195#2414C2212yes—
196#2414C2214yescomplemented
197#2409C2212yes—
198#2407C2212yes—
199#2407C2212yes—
200#2407C2212yes—
201#2373C2214yescomplemented
202#2372C2214yes—
203#2368C2214yescomplemented
204#2367C2212yescomplemented
205#2366C2214yes—
206#2366C2212yescomplemented
207#2366C2211yescharacteristic, complemented
208#2365C2211yescharacteristic, complemented
209#2364C2214yes—
210#2364C2214yes—
211#2364C2214yescomplemented
212#2364C2214yescomplemented
213#2363C2212yes—
214#2363C2212yes—
215#2363C2212yescomplemented
216#2362C2212yes—
217#2362C2212yes—
218#2361C2212yescomplemented
219#2357C2214yescomplemented
220#2357C2212yescomplemented
221#2356C2212yescomplemented
222#2355C2212yescomplemented
223#2354C2212yes—
224#2354C2211yescharacteristic, complemented
225#2353C2214yescomplemented
226#2352C2212yes—
227Q8×C4⋊C4C2211yescharacteristic, complemented
228Q8×C4⋊C4C2211yescharacteristic, complemented
229#2349C2212yescomplemented
230D4×C4⋊C4C2211yescharacteristic, complemented
231#2346C2212yescomplemented
232#2341C2212yescomplemented
233Q8×C22⋊C4C2212yescomplemented
234#2339C2212yes—
235#2339C2212yes—
236#2339C2212yescomplemented
237#2337C2214yes—
238#2335C2214yescomplemented
239#2333C2214yes—
240#2333C2214yescomplemented
241#2332C2214yescomplemented
242#2328C2214yes—
243#2325C2214yes—
244C4×#127C2212yescomplemented
245C4×#124C2212yescomplemented
246C4×C22⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2211yescharacteristic
248C4×C22⋊Q8C2211yescharacteristic
249C4×C22⋊Q8C2211yescharacteristic
250C4×C22⋊Q8C2211yescharacteristic
251C4×C22⋊Q8C2211yescharacteristic
252C4×C22⋊Q8C2211yescharacteristic
253C4×C22⋊Q8C2211yescharacteristic
254C4×#123C2212yes—
255C4×#123C2212yes—
256C4×#123C2212yes—
257C4×#123C2212yes—
258C4×#121C2211yescharacteristic
259C4×#121C2212yes—
260C4×#121C2212yes—
261C4×#121C2212yes—
262C4×#121C2212yes—
263C4×#121C2211yescharacteristic
264C4×#121C2211yescharacteristic
265C4×#121C2211yescharacteristic
266C4×#121C2211yescharacteristic
267C4×#121C2211yescharacteristic
268C4×#121C2211yescharacteristic
269C4×#121C2211yescharacteristic
270C4×#121C2212yescomplemented
271C4×#121C2212yescomplemented
272C4×#120C2212yes—
273C4×#120C2212yes—
274C4×#120C2212yes—
275C4×#120C2212yes—
276#2297C2212yes—
277#2297C2211yescharacteristic
278#2297C2211yescharacteristic
279#2297C2212yescomplemented
280#2296C2211yescharacteristic
281#2296C2211yescharacteristic
282#2295C2212yescomplemented
283#2295C2212yescomplemented
284C2×#391C2212yescomplemented
285#2290C2212yes—
286#2290C2212yes—
287#2290C2212yes—
288#2290C2212yes—
289#2285C2211yescharacteristic
290#2280C2211yescharacteristic
291#2280C2211yescharacteristic
292#2275C2214yescomplemented
293C42×D4C2212yes—
294C42×D4C2212yes—
295C42×D4C2212yes—
296C42×D4C2212yes—
297C4×#117C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C22×#41C2311yescharacteristic
303C23×Q8C2312yes—
304C24×C4C2311yescharacteristic
305C24×C4C2311yescharacteristic
306C24×C4C2311yescharacteristic
307#553—48no—
308#550—216no—
309#550—44no—
310D4×Q8—44no—
311#548—216no—
312#548—48no—
313#532—44no—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×#127C2312yes—
317C2×#127C2314yes—
318C2×#127C2311yescharacteristic
319C2×#127C2312yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#125C2312yes—
323C2×#124C2314yes—
324C2×#124C2312yes—
325C2×#124C2312yes—
326C2×#124C2312yes—
327C2×#124C2314yes—
328#525—28no—
329#525—28no—
330#525—48no—
331C2×#123C2312yes—
332C2×#123C2312yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2311yescharacteristic
346C2×#121C2314yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2311yescharacteristic
354C2×#121C2311yescharacteristic
355C2×#121C2311yescharacteristic
356C2×#121C2311yescharacteristic
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2314yes—
368C2×#121C2314yes—
369C2×#121C2314yes—
370C2×#120C2312yes—
371C2×#120C2312yes—
372C2×#120C2314yes—
373C4×#41—44no—
374C4×#41—44no—
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2312yes—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×C4×D4C2314yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2314yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2314yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2311yescharacteristic
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×#117C2311yescharacteristic
417C2×#117C2311yescharacteristic
418C2×#117C2311yescharacteristic
419C2×#117C2312yes—
420C2×#117C2312yes—
421C2×#117C2311yescharacteristic
422C2×#117C2311yescharacteristic
423C2×#117C2311yescharacteristic
424C2×#117C2312yes—
425C2×#117C2312yes—
426C22×C4⋊C4C2312yes—
427C22×C42—44no—
428C22×C42C2311yescharacteristic
429C22×C42C2311yescharacteristic
430C22×C42C2311yescharacteristic
431C22×C42C2311yescharacteristic
432C22×C42C2311yescharacteristic
433C22×C42C2311yescharacteristic
434C22×C42C2311yescharacteristic
435C22×C42C2312yes—
436C22×C42C2312yes—
437C22×C42C2311yescharacteristic
438C22×C42C2311yescharacteristic
439C22×C42C2311yescharacteristic
440C22×C42C2311yescharacteristic
441C22×C42C2311yescharacteristic
442#401C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2314yes—
446#400C2314yes—
447#400C2314yes—
448#400C2314yes—
449#399C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#395C2314yes—
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#393C2314yes—
494#393C2314yes—
495#393C2314yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2311yescharacteristic
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2314yes—
514#391C2312yes—
515#391C2314yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#391C2311yescharacteristic
520#391C2312yes—
521#391C2311yescharacteristic
522#391C2311yescharacteristic
523#390C2314yes—
524#390C2314yes—
525#390C2311yescharacteristic
526#390C2314yes—
527#390C2314yes—
528#390C2312yes—
529#390C2314yes—
530#390C2314yes—
531#390C2314yes—
532#390C2314yes—
533#390C2312yes—
534#390C2312yes—
535#390C2314yes—
536#390C2312yes—
537#390C2312yes—
538#390C2314yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2311yescharacteristic
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2311yescharacteristic
549#390C2311yescharacteristic
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2311yescharacteristic
563#389C2311yescharacteristic
564#389C2311yescharacteristic
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2311yescharacteristic
572#389C2311yescharacteristic
573#389C2311yescharacteristic
574#389C2311yescharacteristic
575#389C2311yescharacteristic
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2314yes—
608#388C2314yes—
609#388C2312yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2312yes—
614#388C2312yes—
615#388C2312yes—
616#388C2312yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
629#387C2312yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2312yes—
639#387C2314yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2312yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2312yes—
674#386C2314yes—
675#386C2312yes—
676#386C2312yes—
677#386C2312yes—
678#386C2312yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#386C2312yes—
683#386C2312yes—
684#386C2312yes—
685#385C2314yes—
686#385C2312yes—
687#385C2312yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2312yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#385C2312yes—
703#385C2312yes—
704#384C2312yes—
705#384C2312yes—
706#384C2311yescharacteristic
707#384C2311yescharacteristic
708#384C2312yes—
709#383C2314yes—
710#382C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2312yes—
714#382C2314yes—
715#382C2314yes—
716#381C2314yes—
717#381C2314yes—
718#381C2314yes—
719#381C2314yes—
720#381C2312yes—
721#381C2312yes—
722#380C2314yes—
723#380C2314yes—
724#380C2314yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2311yescharacteristic
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2314yes—
739#380C2311yescharacteristic
740#380C2311yescharacteristic
741#380C2311yescharacteristic
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746#379C2312yes—
747#379C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814#376C2314yes—
815#376C2314yes—
816#376C2312yes—
817#376C2312yes—
818C2×#95C2314yes—
819C2×#95C2314yes—
820C2×#95C2314yes—
821C43C2312yes—
822C43C2312yes—
823C25C2411yescharacteristic
824C2×#41—24no—
825C2×#41—28no—
826C2×#41—28no—
827C2×#41—24no—
828C2×#41—42no—
829C2×#41—42no—
830C2×#41—42no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—44no—
834C2×#41—44no—
835C2×#41#4118yescomplemented
836C22×Q8—28no—
837C22×Q8—44no—
838C22×Q8—44no—
839C22×Q8C2412yes—
840C22×Q8C2411yescharacteristic
841C22×Q8C2411yescharacteristic
842C22×Q8C2414yes—
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2412yes—
851C22×D4C2411yescharacteristic
852C22×D4C2412yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2412yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C22×D4C2414yes—
861C22×D4C2412yes—
862C23×C4—24no—
863C23×C4—24no—
864C23×C4—24no—
865C23×C4—42no—
866C23×C4—42no—
867C23×C4—42no—
868C23×C4—42no—
869C23×C4—42no—
870C23×C4—42no—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2411yescharacteristic
875C23×C4C2411yescharacteristic
876C23×C4C2412yes—
877C23×C4C2411yescharacteristic
878C23×C4C2411yescharacteristic
879C23×C4C2411yescharacteristic
880C23×C4C2411yescharacteristic
881C23×C4C2411yescharacteristic
882C23×C4C2411yescharacteristic
883C23×C4C2411yescharacteristic
884C23×C4C2411yescharacteristic
885C23×C4C2411yescharacteristic
886C23×C4C2414yes—
887C23×C4C2412yes—
888C23×C4C2412yes—
889C23×C4C2414yes—
890C23×C4C2414yes—
891C23×C4C2411yescharacteristic
892C23×C4C2411yescharacteristic
893C23×C4C2411yescharacteristic
894C23×C4C2411yescharacteristic
895C23×C4C2411yescharacteristic
896C23×C4C2411yescharacteristic
897C23×C4C2414yes—
898C23×C4C2414yes—
899C23×C4C2412yes—
900C4⋊Q8—24no—
901C4⋊Q8—44no—
902#127—28no—
903#127—216no—
904#127—24no—
905#127—44no—
906#126—48no—
907#126—48no—
908#125—44no—
909#124—28no—
910#124—216no—
911#124—44no—
912#124—44no—
913#124—48no—
914#123—28no—
915#123—28no—
916#123—48no—
917#123—48no—
918#123—48no—
919C22⋊Q8—24no—
920C22⋊Q8—24no—
921C22⋊Q8—24no—
922C22⋊Q8—28no—
923C22⋊Q8—216no—
924C22⋊Q8—48no—
925C22⋊Q8—48no—
926C22⋊Q8—44no—
927C22⋊Q8—44no—
928C22⋊Q8#4118yescomplemented
929#121—24no—
930#121—24no—
931#121—28no—
932#121—216no—
933#121—24no—
934#121—28no—
935#121—216no—
936#121—28no—
937#121—24no—
938#121—28no—
939#121—216no—
940#121—48no—
941#121—44no—
942#121—44no—
943#121—48no—
944#121—48no—
945#121—48no—
946#121—44no—
947#121—44no—
948#121—44no—
949#121—44no—
950#121—44no—
951#121—44no—
952#121—44no—
953#120—28no—
954#120—28no—
955#120—48no—
956C4×Q8—28no—
957C4×Q8—28no—
958C4×Q8—24no—
959C4×Q8—24no—
960C4×Q8—42no—
961C4×Q8—42no—
962C4×Q8—44no—
963C4×D4—28no—
964C4×D4—28no—
965C4×D4—28no—
966C4×D4—28no—
967C4×D4—216no—
968C4×D4—28no—
969C4×D4—28no—
970C4×D4—216no—
971C4×D4—28no—
972C4×D4—24no—
973C4×D4—24no—
974C4×D4—48no—
975C4×D4—48no—
976C4×D4—44no—
977C4×D4—44no—
978C4×D4—42no—
979C4×D4—42no—
980C4×D4—44no—
981C4×D4—44no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—44no—
985C4×D4—44no—
986C4×D4—44no—
987C4×D4—44no—
988C4×D4—44no—
989C4×D4—44no—
990C4×D4—44no—
991C4×D4—44no—
992C4×D4—44no—
993C4×D4—44no—
994C4×D4—48no—
995C4×D4—48no—
996C4×D4—48no—
997#117—24no—
998#117—24no—
999#117—24no—
1000#117—44no—
1001#117—44no—
1002#117—42no—
1003#117—44no—
1004#117—42no—
1005#117—42no—
1006#117—44no—
1007C2×C4⋊C4—44no—
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2411yescharacteristic
1057C2×C4⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2412yes—
1121C2×C42—24no—
1122C2×C42—24no—
1123C2×C42—24no—
1124C2×C42—44no—
1125C2×C42—44no—
1126C2×C42—42no—
1127C2×C42—42no—
1128C2×C42—42no—
1129C2×C42—42no—
1130C2×C42—42no—
1131C2×C42—42no—
1132C2×C42—42no—
1133C2×C42—42no—
1134C2×C42—42no—
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2412yes—
1143C2×C42C2412yes—
1144C2×C42C2412yes—
1145C2×C42C2411yescharacteristic
1146C2×C42C2411yescharacteristic
1147C2×C42C2412yes—
1148C2×C42C2414yes—
1149C2×C42C2412yes—
1150C2×C42C2414yes—
1151C2×C42C2411yescharacteristic
1152C2×C42C2411yescharacteristic
1153C2×C42C2412yes—
1154C2×C42C2411yescharacteristic
1155C2×C42C2411yescharacteristic
1156C2×C42C2411yescharacteristic
1157C2×C42C2412yes—
1158C2×C42C2412yes—
1159C2×C42C2414yes—
1160C2×C42C2412yes—
1161C2×C42C2414yes—
1162C2×C42C2414yes—
1163C2×C42C2412yes—
1164C2×C42C2412yes—
1165C2×C42C2412yes—
1166C2×C42C2412yes—
1167C2×C42C2411yescharacteristic
1168C2×C42C2411yescharacteristic
1169C2×C42C2411yescharacteristic
1170C2×C42C2411yescharacteristic
1171C2×C42C2411yescharacteristic
1172C2×C42C2411yescharacteristic
1173C2×C42C2411yescharacteristic
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2412yes—
1212#95C2412yes—
1213#95C2412yes—
1214#95C2412yes—
1215#95C2412yes—
1216#95C2412yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226#95C2414yes—
1227#95C2414yes—
1228#95C2414yes—
1229#95C2414yes—
1230#95C2414yes—
1231#95C2414yes—
1232C24—22no—
1233C24—22no—
1234C24—22no—
1235C24—41no—
1236C24—41no—
1237C24—41no—
1238C24—41no—
1239C24C2514yes—
1240C24C2512yes—
1241C24C2511yescharacteristic
1242C24C2511yescharacteristic
1243C24C2512yes—
1244C24C2511yescharacteristic
1245#41—416no—
1246#41—416no—
1247#41—816no—
1248#41—816no—
1249C2×Q8—24no—
1250C2×Q8—28no—
1251C2×Q8—22no—
1252C2×Q8—22no—
1253C2×Q8—22no—
1254C2×Q8—24no—
1255C2×Q8—24no—
1256C2×Q8—22no—
1257C2×Q8—44no—
1258C2×Q8—44no—
1259C2×Q8—816no—
1260C2×Q8C2×#4114yes—
1261C2×Q8C2×#4114yes—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—24no—
1267C2×D4—28no—
1268C2×D4—24no—
1269C2×D4—24no—
1270C2×D4—28no—
1271C2×D4—28no—
1272C2×D4—28no—
1273C2×D4—28no—
1274C2×D4—28no—
1275C2×D4—24no—
1276C2×D4—28no—
1277C2×D4—24no—
1278C2×D4—22no—
1279C2×D4—24no—
1280C2×D4—24no—
1281C2×D4—28no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—24no—
1285C2×D4—24no—
1286C2×D4—24no—
1287C2×D4—22no—
1288C2×D4—24no—
1289C2×D4—22no—
1290C2×D4—24no—
1291C2×D4—42no—
1292C2×D4—42no—
1293C2×D4—44no—
1294C2×D4—42no—
1295C2×D4—42no—
1296C2×D4—42no—
1297C2×D4—42no—
1298C2×D4—42no—
1299C2×D4—42no—
1300C2×D4—44no—
1301C2×D4—44no—
1302C2×D4—44no—
1303C2×D4—44no—
1304C2×D4—44no—
1305C2×D4—44no—
1306C2×D4—42no—
1307C2×D4—42no—
1308C2×D4—44no—
1309C2×D4—44no—
1310C2×D4—44no—
1311C2×D4—44no—
1312C2×D4—44no—
1313C2×D4—44no—
1314C2×D4—44no—
1315C2×D4—44no—
1316C2×D4—44no—
1317C2×D4C2×#4114yes—
1318C2×D4C2×#4118yes—
1319C22×C4—22no—
1320C22×C4—22no—
1321C22×C4—22no—
1322C22×C4—22no—
1323C22×C4—22no—
1324C22×C4—22no—
1325C22×C4—22no—
1326C22×C4—22no—
1327C22×C4—22no—
1328C22×C4—22no—
1329C22×C4—22no—
1330C22×C4—22no—
1331C22×C4—24no—
1332C22×C4—24no—
1333C22×C4—24no—
1334C22×C4—22no—
1335C22×C4—22no—
1336C22×C4—22no—
1337C22×C4—22no—
1338C22×C4—22no—
1339C22×C4—22no—
1340C22×C4—22no—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—24no—
1345C22×C4—24no—
1346C22×C4—24no—
1347C22×C4—22no—
1348C22×C4—24no—
1349C22×C4—22no—
1350C22×C4—22no—
1351C22×C4—24no—
1352C22×C4—22no—
1353C22×C4—22no—
1354C22×C4—22no—
1355C22×C4—22no—
1356C22×C4—22no—
1357C22×C4—22no—
1358C22×C4—22no—
1359C22×C4—22no—
1360C22×C4—28no—
1361C22×C4—28no—
1362C22×C4—28no—
1363C22×C4—24no—
1364C22×C4—24no—
1365C22×C4—41no—
1366C22×C4—41no—
1367C22×C4—41no—
1368C22×C4—41no—
1369C22×C4—41no—
1370C22×C4—41no—
1371C22×C4—41no—
1372C22×C4—41no—
1373C22×C4—41no—
1374C22×C4—42no—
1375C22×C4—42no—
1376C22×C4—41no—
1377C22×C4—41no—
1378C22×C4—41no—
1379C22×C4—41no—
1380C22×C4—41no—
1381C22×C4—41no—
1382C22×C4—41no—
1383C22×C4—41no—
1384C22×C4—41no—
1385C22×C4—42no—
1386C22×C4—416no—
1387C22×C4—42no—
1388C22×C4—42no—
1389C22×C4—44no—
1390C22×C4—44no—
1391C22×C4—44no—
1392C22×C4—44no—
1393C22×C4—44no—
1394C22×C4—42no—
1395C22×C4—42no—
1396C22×C4—44no—
1397C22×C4—44no—
1398C22×C4—44no—
1399C22×C4—44no—
1400C22×C4—44no—
1401C22×C4—44no—
1402C22×C4—44no—
1403C22×C4—416no—
1404C22×C4—416no—
1405C22×C4C2×#4114yes—
1406C22×C4C2×#4114yes—
1407C22×C4C2×#4118yes—
1408C22×C4H(5,𝔽2)14yes—
1409C22×C4C2512yes—
1410C22×C4C2512yes—
1411C22×C4C2511yescharacteristic
1412C22×C4C2511yescharacteristic
1413C22×C4C2511yescharacteristic
1414C22×C4C2512yes—
1415C22×C4C2512yes—
1416C22×C4C2512yes—
1417C22×C4C2514yes—
1418C22×C4C2512yes—
1419C22×C4C2512yes—
1420C22×C4C2512yes—
1421C22×C4C2514yes—
1422C22×C4C2514yes—
1423C22×C4C2511yescharacteristic
1424C22×C4C2512yes—
1425C22×C4C2512yes—
1426C22×C4C2512yes—
1427C22×C4C2512yes—
1428C22×C4C2511yescharacteristic
1429C22×C4C2511yescharacteristic
1430C22×C4C2512yes—
1431C22×C4C2512yes—
1432C22×C4C2511yescharacteristic
1433C22×C4C2511yescharacteristic
1434C22×C4C2511yescharacteristic
1435C22×C4C2511yescharacteristic
1436C22×C4C2511yescharacteristic
1437C22×C4C2511yescharacteristic
1438C4⋊C4—22no—
1439C4⋊C4—22no—
1440C4⋊C4—22no—
1441C4⋊C4—24no—
1442C4⋊C4—24no—
1443C4⋊C4—24no—
1444C4⋊C4—24no—
1445C4⋊C4—24no—
1446C4⋊C4—28no—
1447C4⋊C4—24no—
1448C4⋊C4—28no—
1449C4⋊C4—22no—
1450C4⋊C4—24no—
1451C4⋊C4—22no—
1452C4⋊C4—22no—
1453C4⋊C4—22no—
1454C4⋊C4—24no—
1455C4⋊C4—22no—
1456C4⋊C4—24no—
1457C4⋊C4—22no—
1458C4⋊C4—24no—
1459C4⋊C4—24no—
1460C4⋊C4—24no—
1461C4⋊C4—28no—
1462C4⋊C4—24no—
1463C4⋊C4—22no—
1464C4⋊C4—22no—
1465C4⋊C4—24no—
1466C4⋊C4—24no—
1467C4⋊C4—24no—
1468C4⋊C4—44no—
1469C4⋊C4—42no—
1470C4⋊C4—42no—
1471C4⋊C4—44no—
1472C4⋊C4—42no—
1473C4⋊C4—42no—
1474C4⋊C4—42no—
1475C4⋊C4—44no—
1476C4⋊C4—44no—
1477C4⋊C4—44no—
1478C4⋊C4—42no—
1479C4⋊C4—42no—
1480C4⋊C4—44no—
1481C4⋊C4—44no—
1482C4⋊C4—44no—
1483C4⋊C4—44no—
1484C4⋊C4—44no—
1485C4⋊C4—44no—
1486C4⋊C4C2×#4114yes—
1487C4⋊C4C2×#4118yes—
1488C22⋊C4—24no—
1489C22⋊C4—24no—
1490C22⋊C4—28no—
1491C22⋊C4—24no—
1492C22⋊C4—24no—
1493C22⋊C4—24no—
1494C22⋊C4—24no—
1495C22⋊C4—24no—
1496C22⋊C4—28no—
1497C22⋊C4—24no—
1498C22⋊C4—24no—
1499C22⋊C4—24no—
1500C22⋊C4—24no—
1501C22⋊C4—24no—
1502C22⋊C4—24no—
1503C22⋊C4—28no—
1504C22⋊C4—24no—
1505C22⋊C4—24no—
1506C22⋊C4—28no—
1507C22⋊C4—28no—
1508C22⋊C4—28no—
1509C22⋊C4—24no—
1510C22⋊C4—24no—
1511C22⋊C4—24no—
1512C22⋊C4—28no—
1513C22⋊C4—24no—
1514C22⋊C4—24no—
1515C22⋊C4—28no—
1516C22⋊C4—28no—
1517C22⋊C4—42no—
1518C22⋊C4—44no—
1519C22⋊C4—42no—
1520C22⋊C4—42no—
1521C22⋊C4—42no—
1522C22⋊C4—42no—
1523C22⋊C4—44no—
1524C22⋊C4—42no—
1525C22⋊C4—42no—
1526C22⋊C4—44no—
1527C22⋊C4—44no—
1528C22⋊C4—42no—
1529C22⋊C4—42no—
1530C22⋊C4—42no—
1531C22⋊C4—42no—
1532C22⋊C4—42no—
1533C22⋊C4—42no—
1534C22⋊C4—44no—
1535C22⋊C4—44no—
1536C22⋊C4—44no—
1537C22⋊C4—44no—
1538C22⋊C4—44no—
1539C22⋊C4—44no—
1540C22⋊C4—44no—
1541C22⋊C4—44no—
1542C22⋊C4—44no—
1543C22⋊C4—44no—
1544C22⋊C4—44no—
1545C22⋊C4—44no—
1546C22⋊C4—44no—
1547C22⋊C4—44no—
1548C22⋊C4—44no—
1549C22⋊C4—44no—
1550C22⋊C4C2×#4118yes—
1551C42—24no—
1552C42—24no—
1553C42—24no—
1554C42—28no—
1555C42—28no—
1556C42—24no—
1557C42—22no—
1558C42—22no—
1559C42—22no—
1560C42—22no—
1561C42—22no—
1562C42—22no—
1563C42—22no—
1564C42—22no—
1565C42—22no—
1566C42—24no—
1567C42—24no—
1568C42—24no—
1569C42—24no—
1570C42—24no—
1571C42—24no—
1572C42—24no—
1573C42—41no—
1574C42—41no—
1575C42—41no—
1576C42—41no—
1577C42—41no—
1578C42—41no—
1579C42—42no—
1580C42—42no—
1581C42—42no—
1582C42—42no—
1583C42—42no—
1584C42—44no—
1585C42—44no—
1586C42—42no—
1587C42—42no—
1588C42—44no—
1589C42H(5,𝔽2)14yes—
1590C23—21no—
1591C23—21no—
1592C23—21no—
1593C23—21no—
1594C23—22no—
1595C23—22no—
1596C23—22no—
1597C23—21no—
1598C23—21no—
1599C23—21no—
1600C23—21no—
1601C23—21no—
1602C23—22no—
1603C23—21no—
1604C23—21no—
1605C23—21no—
1606C23—21no—
1607C23—21no—
1608C23—21no—
1609C23—22no—
1610C23—22no—
1611C23—21no—
1612C23—21no—
1613C23—21no—
1614C23—24no—
1615C23—22no—
1616C23—22no—
1617C23—24no—
1618C23—24no—
1619C23—22no—
1620C23—22no—
1621C23—24no—
1622C23—24no—
1623C23—24no—
1624C23—22no—
1625C23—22no—
1626C23—22no—
1627C23—24no—
1628C23—44no—
1629C23—44no—
1630C23—44no—
1631C23—44no—
1632C23—44no—
1633C23—44no—
1634C23—44no—
1635C23C22×#4112yes—
1636C23C22×#4114yes—
1637C23C22×#4112yes—
1638C23C2×H(5,𝔽2)12yes—
1639C23C2611yescharacteristic
1640Q8—28no—
1641Q8—28no—
1642Q8—48no—
1643Q8—88no—
1644D4—28no—
1645D4—48no—
1646D4—416no—
1647D4—48no—
1648D4—48no—
1649D4—48no—
1650D4—48no—
1651D4—48no—
1652D4—48no—
1653D4—44no—
1654D4—48no—
1655D4—84no—
1656D4—88no—
1657D4—88no—
1658D4—88no—
1659D4—88no—
1660D4—88no—
1661D4—88no—
1662D4—164no—
1663C2×C4—22no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—21no—
1673C2×C4—22no—
1674C2×C4—22no—
1675C2×C4—21no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—21no—
1679C2×C4—21no—
1680C2×C4—22no—
1681C2×C4—28no—
1682C2×C4—28no—
1683C2×C4—28no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—22no—
1690C2×C4—24no—
1691C2×C4—24no—
1692C2×C4—22no—
1693C2×C4—22no—
1694C2×C4—21no—
1695C2×C4—21no—
1696C2×C4—21no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—22no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—22no—
1705C2×C4—22no—
1706C2×C4—22no—
1707C2×C4—24no—
1708C2×C4—22no—
1709C2×C4—22no—
1710C2×C4—24no—
1711C2×C4—22no—
1712C2×C4—24no—
1713C2×C4—21no—
1714C2×C4—24no—
1715C2×C4—22no—
1716C2×C4—22no—
1717C2×C4—22no—
1718C2×C4—22no—
1719C2×C4—22no—
1720C2×C4—22no—
1721C2×C4—22no—
1722C2×C4—22no—
1723C2×C4—22no—
1724C2×C4—22no—
1725C2×C4—22no—
1726C2×C4—24no—
1727C2×C4—22no—
1728C2×C4—24no—
1729C2×C4—24no—
1730C2×C4—21no—
1731C2×C4—22no—
1732C2×C4—22no—
1733C2×C4—21no—
1734C2×C4—21no—
1735C2×C4—21no—
1736C2×C4—22no—
1737C2×C4—22no—
1738C2×C4—48no—
1739C2×C4—44no—
1740C2×C4—44no—
1741C2×C4—44no—
1742C2×C4—44no—
1743C2×C4—48no—
1744C2×C4—44no—
1745C2×C4—44no—
1746C2×C4—44no—
1747C2×C4—44no—
1748C2×C4—44no—
1749C2×C4—44no—
1750C2×C4—44no—
1751C2×C4—44no—
1752C2×C4—44no—
1753C2×C4—44no—
1754C2×C4—48no—
1755C2×C4—44no—
1756C2×C4—48no—
1757C2×C4—84no—
1758C2×C4—84no—
1759C2×C4—88no—
1760C2×C4—88no—
1761C2×C4—88no—
1762C2×C4—164no—
1763C2×C4—164no—
1764C2×C4C22×#4114yes—
1765C2×C4C22×#4112yes—
1766C2×C4C22×#4114yes—
1767C2×C4C22×#4114yes—
1768C2×C4C22×#4112yes—
1769C2×C4C22×#4112yes—
1770C2×C4C22×#4112yes—
1771C2×C4C2×H(5,𝔽2)12yes—
1772C2×C4C2×H(5,𝔽2)12yes—
1773C2×C4C2×H(5,𝔽2)12yes—
1774C2×C4C2×H(5,𝔽2)12yes—
1775C2×C4C2×H(5,𝔽2)12yes—
1776C2×C4#58512yes—
1777C2×C4#58512yes—
1778C2×C4#58512yes—
1779C22—22no—
1780C22—24no—
1781C22—22no—
1782C22—22no—
1783C22—22no—
1784C22—22no—
1785C22—24no—
1786C22—22no—
1787C22—22no—
1788C22—24no—
1789C22—22no—
1790C22—22no—
1791C22—416no—
1792C22—41no—
1793C22—41no—
1794C22—41no—
1795C22—42no—
1796C22—42no—
1797C22—41no—
1798C22—41no—
1799C22—41no—
1800C22—41no—
1801C22—41no—
1802C22—41no—
1803C22—42no—
1804C22—42no—
1805C22—41no—
1806C22—41no—
1807C22—41no—
1808C22—42no—
1809C22—44no—
1810C22—42no—
1811C22—44no—
1812C22—42no—
1813C22—44no—
1814C22—44no—
1815C22—42no—
1816C22—42no—
1817C22—44no—
1818C22—44no—
1819C22—42no—
1820C22—44no—
1821C22—42no—
1822C22C23×#4111yescharacteristic
1823C22C23×#4111yescharacteristic
1824C22C22×H(5,𝔽2)11yescharacteristic
1825C22C22×H(5,𝔽2)11yescharacteristic
1826C22C2×#58511yescharacteristic
1827C22C2×#58511yescharacteristic
1828C22C2×#58511yescharacteristic
1829C4—22no—
1830C4—24no—
1831C4—22no—
1832C4—22no—
1833C4—24no—
1834C4—22no—
1835C4—22no—
1836C4—22no—
1837C4—24no—
1838C4—41no—
1839C4—41no—
1840C4—42no—
1841C4—41no—
1842C4—42no—
1843C4—44no—
1844C4—42no—
1845C4—42no—
1846C4—42no—
1847C4—42no—
1848C4—44no—
1849C4—41no—
1850C4—42no—
1851C4—42no—
1852C4—42no—
1853C4—42no—
1854C4—44no—
1855C4—42no—
1856C4#350514yes—
1857C4#351914yes—
1858C2—44no—
1859C2—42no—
1860C2—42no—
1861C2—42no—
1862C2—82no—
1863C2—84no—
1864C2#41211yescharacteristic
1865C2C2×#350511yescharacteristic
1866C2C2×#351911yescharacteristic
1867C2#6279311yescharacteristic
1868C2#6280011yescharacteristic
1869C2#6282111yescharacteristic
1870C2#6283611yescharacteristic
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. #59773C2semidirect
2. #59403C2semidirect
3. #59381C2semidirect
4. #59259C2semidirect
5. #59212C2semidirect
6. #59080C2semidirect
7. #59033C2semidirect
8. #59020C2semidirect
9. #59001C2semidirect
10. #40382C2semidirect
11. #40194C2semidirect
12. #40146C2semidirect
13. #39934C2semidirect
14. #39861C2semidirect
15. #38713C2semidirect
16. #36624C2semidirect
17. #36498C2semidirect
18. #36472C2semidirect
19. #36460C2semidirect
20. #36455C2semidirect
21. #36444C2semidirect
22. #36410C2semidirect
23. #36402C2semidirect
24. #36396C2semidirect
25. #36381C2semidirect
26. #36315C2semidirect
27. #36314C2semidirect
28. #36274C2semidirect
29. #35420C2semidirect
30. #35038C2semidirect
31. #35037C2semidirect
32. #34330C2semidirect
33. #34327C2semidirect
34. C4×#525C2semidirect
35. C4×#525C2semidirect
38. C2×#550C22semidirect
39. C2×D4×Q8C22semidirect
49. #2864C22semidirect
50. #2861C22semidirect
51. #2860C22semidirect
52. #2860C22semidirect
55. #2857C22semidirect
58. #2856C22semidirect
59. #2855C22semidirect
62. #2854C22semidirect
67. #2781C22semidirect
70. #2761C22semidirect
71. #2756C22semidirect
74. #2745C22semidirect
88. #2603C22semidirect
90. #2597C22semidirect
91. #2597C22semidirect
93. #2595C22semidirect
94. #2595C22semidirect
95. #2594C22semidirect
96. #2585C22semidirect
97. #2582C22semidirect
99. #2574C22semidirect
100. #2571C22semidirect
101. #2568C22semidirect
102. #2565C22semidirect
103. #2560C22semidirect
104. #2560C22semidirect
106. #2559C22semidirect
110. #2552C22semidirect
111. #2548C22semidirect
113. #2547C22semidirect
114. #2544C22semidirect
118. #2541C22semidirect
121. #2537C22semidirect
124. #2533C22semidirect
126. #2531C22semidirect
128. #2529C22semidirect
129. #2526C22semidirect
130. #2512C22semidirect
131. #2511C22semidirect
132. #2508C22semidirect
133. #2507C22semidirect
134. #2504C22semidirect
138. #2497C22semidirect
140. #2494C22semidirect
141. #2494C22semidirect
143. #2490C22semidirect
147. #2476C22semidirect
153. #2463C22semidirect
157. #2457C22semidirect
161. #2452C22semidirect
162. #2451C22semidirect
164. #2447C22semidirect
165. #2445C22semidirect
166. #2444C22semidirect
169. #2438C22semidirect
170. #2436C22semidirect
176. #2428C22semidirect
178. #2427C22semidirect
181. #2426C22semidirect
187. #2420C22semidirect
191. #2415C22semidirect
196. #2414C22semidirect
201. #2373C22semidirect
203. #2368C22semidirect
204. #2367C22semidirect
206. #2366C22semidirect
207. #2366C22semidirect
208. #2365C22semidirect
211. #2364C22semidirect
212. #2364C22semidirect
215. #2363C22semidirect
218. #2361C22semidirect
219. #2357C22semidirect
220. #2357C22semidirect
221. #2356C22semidirect
222. #2355C22semidirect
224. #2354C22semidirect
225. #2353C22semidirect
227. Q8×C4⋊C4C22semidirect
228. Q8×C4⋊C4C22semidirect
229. #2349C22semidirect
230. D4×C4⋊C4C22semidirect
231. #2346C22semidirect
232. #2341C22semidirect
233. Q8×C22⋊C4C22semidirect
236. #2339C22semidirect
238. #2335C22semidirect
240. #2333C22semidirect
241. #2332C22semidirect
244. C4×#127C22semidirect
245. C4×#124C22semidirect
270. C4×#121C22semidirect
271. C4×#121C22semidirect
279. #2297C22semidirect
282. #2295C22semidirect
283. #2295C22semidirect
284. C2×#391C22semidirect
292. #2275C22semidirect
835. C2×#41#41semidirect
928. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#597732
#594032
#593812
#592592
#592122
#590802
#590332
#590202
#590012
#403822
#401942
#401462
#399342
#398612
#387132
#366242
#364982
#364722
#364602
#364552
#364442
#364102
#364022
#363962
#363812
#363152
#363142
#362742
#354202
#350382
#350372
#343302
#343272
C4×#5252