Finite Group Databasebeta

← #8461533

Subgroups — #8461533

Order 512.

4519 conjugacy classes of subgroups.

The subgroup lattice has 1697 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59655C211yesmaximal, characteristic, complemented
2#59242C211yesmaximal, characteristic, complemented
3#59235C211yesmaximal, characteristic, complemented
4#56670C214yesmaximal, complemented
5#54621C214yesmaximal, complemented
6#54122C214yesmaximal, complemented
7#53153C212yesmaximal, complemented
8#53011C212yesmaximal, complemented
9#48097C214yesmaximal, complemented
10#45667C212yesmaximal, complemented
11#45595C212yesmaximal, complemented
12#45365C212yesmaximal, complemented
13#45226C212yesmaximal, complemented
14#42955C212yesmaximal, complemented
15#42640C212yesmaximal, complemented
16#42493C212yesmaximal, complemented
17#42458C212yesmaximal, complemented
18#39597C211yesmaximal, characteristic, complemented
19#39536C212yesmaximal, complemented
20#39506C211yesmaximal, characteristic, complemented
21#39125C211yesmaximal, characteristic, complemented
22#39042C212yesmaximal
23#38977C211yesmaximal, characteristic, complemented
24#38928C212yesmaximal, complemented
25#37853C212yesmaximal, complemented
26#37637C211yesmaximal, characteristic, complemented
27#37407C212yesmaximal, complemented
28#37380C212yesmaximal, complemented
29#36544C211yesmaximal, characteristic, complemented
30#36210C211yesmaximal, characteristic, complemented
31#36154C211yesmaximal, characteristic, complemented
32#35247C211yesmaximal, characteristic, complemented
33#35172C211yesmaximal, characteristic, complemented
34#34700C211yesmaximal, characteristic
35#34691C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic, complemented
37C2×#554C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic, complemented
41C22×C4×D4C2211yescharacteristic
42#2859C2211yescharacteristic, complemented
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic, complemented
45#2855C2212yescomplemented
46#2854C2212yes—
47#2851C2212yescomplemented
48#2848C2212yes—
49#2848C2212yes—
50#2848C2212yes—
51#2843C2214yescomplemented
52#2841C2214yescomplemented
53#2838C2214yescomplemented
54#2838C2214yescomplemented
55#2838C2214yescomplemented
56#2835C2214yescomplemented
57#2831C2214yescomplemented
58#2827C2214yescomplemented
59#2807C2214yescomplemented
60#2794C2214yescomplemented
61#2790C2214yescomplemented
62#2787C2214yes—
63#2787C2214yes—
64#2787C2214yescomplemented
65#2783C2214yescomplemented
66#2783C2214yescomplemented
67#2782C2214yes—
68#2782C2214yescomplemented
69#2773C2214yescomplemented
70#2773C2214yescomplemented
71#2770C2214yescomplemented
72#2768C2214yes—
73#2768C2214yes—
74#2768C2214yescomplemented
75#2767C2214yescomplemented
76#2765C2214yescomplemented
77#2765C2214yescomplemented
78#2765C2214yescomplemented
79#2765C2214yescomplemented
80#2763C2214yes—
81#2763C2214yescomplemented
82#2757C2214yes—
83#2750C2214yes—
84#2749C2214yes—
85#2747C2214yes—
86#2746C2214yescomplemented
87#2745C2214yescomplemented
88#2745C2214yescomplemented
89#2744C2214yescomplemented
90#2742C2214yes—
91#2739C2214yescomplemented
92#2738C2214yescomplemented
93#2737C2214yes—
94#2737C2214yes—
95#2736C2214yes—
96#2735C2214yes—
97#2735C2214yes—
98#2729C2214yescomplemented
99#2729C2214yescomplemented
100#2716C2214yescomplemented
101#2716C2214yescomplemented
102#2713C2214yescomplemented
103#2695C2214yescomplemented
104#2684C2214yes—
105#2677C2214yes—
106#2674C2214yescomplemented
107#2674C2214yescomplemented
108#2666C2214yescomplemented
109#2666C2214yescomplemented
110#2647C2212yescomplemented
111#2646C2214yescomplemented
112#2645C2212yescomplemented
113#2644C2212yes—
114#2638C2214yescomplemented
115#2637C2214yescomplemented
116#2637C2214yescomplemented
117#2629C2212yescomplemented
118#2628C2212yes—
119#2628C2214yescomplemented
120#2628C2212yescomplemented
121#2626C2214yes—
122#2625C2212yescomplemented
123#2621C2212yescomplemented
124#2609C2214yescomplemented
125#2597C2214yes—
126#2597C2214yes—
127#2592C2212yes—
128#2584C2212yescomplemented
129#2584C2212yescomplemented
130#2582C2211yescharacteristic, complemented
131#2582C2211yescharacteristic, complemented
132#2581C2212yescomplemented
133#2580C2212yes—
134#2580C2212yes—
135#2580C2212yes—
136#2571C2212yescomplemented
137#2571C2214yescomplemented
138#2567C2211yescharacteristic, complemented
139#2566C2214yes—
140#2563C2211yescharacteristic
141#2563C2212yes—
142#2562C2212yes—
143#2562C2212yescomplemented
144#2561C2214yes—
145#2552C2211yescharacteristic, complemented
146#2551C2212yescomplemented
147#2550C2212yescomplemented
148#2550C2212yescomplemented
149#2547C2212yescomplemented
150#2546C2212yescomplemented
151#2542C2212yes—
152#2538C2211yescharacteristic
153#2538C2211yescharacteristic
154#2538C2211yescharacteristic
155#2538C2211yescharacteristic
156#2538C2211yescharacteristic
157#2536C2212yescomplemented
158#2524C2214yescomplemented
159#2517C2214yescomplemented
160#2514C2212yescomplemented
161#2514C2212yescomplemented
162#2514C2212yescomplemented
163#2513C2212yes—
164#2513C2212yes—
165#2512C2212yes—
166#2509C2212yescomplemented
167#2508C2212yescomplemented
168#2508C2212yescomplemented
169#2508C2212yescomplemented
170#2508C2212yescomplemented
171#2508C2212yescomplemented
172#2503C2212yescomplemented
173#2499C2212yes—
174#2497C2212yescomplemented
175#2496C2212yescomplemented
176#2495C2212yes—
177#2495C2212yescomplemented
178#2494C2212yes—
179#2494C2212yescomplemented
180#2494C2212yescomplemented
181#2493C2214yescomplemented
182#2492C2212yes—
183#2492C2212yescomplemented
184#2491C2212yes—
185#2489C2212yes—
186#2489C2212yescomplemented
187#2489C2212yescomplemented
188#2489C2212yescomplemented
189#2489C2212yescomplemented
190#2489C2212yescomplemented
191#2487C2212yes—
192#2486C2212yescomplemented
193#2485C2212yes—
194#2482C2214yes—
195#2480C2214yes—
196#2480C2212yes—
197#2479C2214yes—
198#2473C2212yescomplemented
199#2468C2212yes—
200#2465C2212yes—
201#2465C2214yescomplemented
202#2462C2212yescomplemented
203#2461C2214yes—
204#2457C2212yes—
205#2454C2212yes—
206#2454C2211yescharacteristic
207#2453C2212yescomplemented
208#2452C2212yes—
209#2451C2211yescharacteristic, complemented
210#2450C2214yes—
211#2449C2212yes—
212#2449C2214yescomplemented
213#2448C2212yes—
214#2447C2212yes—
215#2447C2211yescharacteristic
216#2446C2212yescomplemented
217#2446C2211yescharacteristic, complemented
218#2442C2212yes—
219#2442C2211yescharacteristic
220#2442C2212yescomplemented
221#2440C2212yescomplemented
222#2440C2211yescharacteristic, complemented
223#2438C2214yescomplemented
224#2437C2214yes—
225#2435C2211yescharacteristic
226#2434C2211yescharacteristic, complemented
227#2429C2211yescharacteristic
228#2429C2212yescomplemented
229#2429C2214yescomplemented
230#2427C2211yescharacteristic
231#2423C2212yes—
232#2423C2211yescharacteristic
233#2423C2212yescomplemented
234#2421C2212yes—
235#2421C2212yescomplemented
236#2420C2211yescharacteristic
237#2420C2212yes—
238#2418C2214yes—
239#2418C2212yes—
240#2417C2211yescharacteristic
241#2417C2212yes—
242#2417C2211yescharacteristic
243#2417C2212yescomplemented
244#2415C2212yes—
245#2413C2214yescomplemented
246#2409C2211yescharacteristic
247#2409C2212yescomplemented
248#2409C2212yescomplemented
249#2408C2211yescharacteristic
250#2399C2212yescomplemented
251#2396C2212yes—
252#2395C2212yes—
253#2392C2212yes—
254#2379C2214yescomplemented
255#2370C2212yescomplemented
256#2370C2212yescomplemented
257#2367C2212yes—
258#2362C2212yescomplemented
259#2360C2212yescomplemented
260#2360C2212yescomplemented
261#2355C2211yescharacteristic, complemented
262#2355C2211yescharacteristic, complemented
263#2355C2211yescharacteristic, complemented
264#2354C2212yes—
265#2349C2212yes—
266D4×C4⋊C4C2211yescharacteristic
267D4×C4⋊C4C2212yescomplemented
268#2347C2212yes—
269#2347C2212yes—
270#2344C2212yescomplemented
271D4×C22⋊C4C2212yes—
272#2323C2212yes—
273#2323C2212yescomplemented
274#2323C2212yescomplemented
275#2323C2212yescomplemented
276#2319C2212yes—
277#2318C2214yescomplemented
278#2317C2212yes—
279#2314C2212yescomplemented
280#2309C2212yes—
281C4×C4⋊Q8C2211yescharacteristic, complemented
282C4×C4⋊Q8C2211yescharacteristic, complemented
283C4×#124C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2212yescomplemented
287C4×C22⋊Q8C2211yescharacteristic, complemented
288C4×#121C2211yescharacteristic
289C4×#121C2212yes—
290C4×#120C2212yes—
291#2295C2211yescharacteristic, complemented
292#2293C2211yescharacteristic
293#2290C2212yes—
294#2285C2211yescharacteristic
295#2285C2211yescharacteristic, complemented
296#2280C2212yes—
297C2×#380C2212yes—
298C42×D4C2211yescharacteristic
299C23×Q8C2311yescharacteristic
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302Q82—44no—
303#554—44no—
304#533—44no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2314yes—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2314yes—
313#529—44no—
314C2×#126C2312yes—
315C2×#126C2314yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2311yescharacteristic
320C2×#125C2312yes—
321C2×#124C2311yescharacteristic
322C2×#124C2311yescharacteristic
323C2×#124C2314yes—
324C2×#123C2312yes—
325C2×#123C2314yes—
326C2×C22⋊Q8C2311yescharacteristic
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2311yescharacteristic
331C2×C22⋊Q8C2311yescharacteristic
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2312yes—
344C2×#121C2311yescharacteristic
345C2×#121C2311yescharacteristic
346C2×#120C2312yes—
347C2×C4×Q8—44no—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×D4—44no—
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2314yes—
380C2×#117C2312yes—
381C22×C4⋊C4C2311yescharacteristic
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2311yescharacteristic
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C22⋊C4C2312yes—
387C22×C22⋊C4C2314yes—
388C22×C42C2311yescharacteristic
389C22×C42C2311yescharacteristic
390C22×C42C2312yes—
391#401C2314yes—
392#401C2314yes—
393#401C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2312yes—
397#400C2312yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#399C2314yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2312yes—
424#399C2312yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2312yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2312yes—
443#398C2314yes—
444#398C2312yes—
445#398C2312yes—
446#398C2312yes—
447#398C2312yes—
448#398C2312yes—
449#398C2312yes—
450#398C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2312yes—
461#397C2312yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2312yes—
470#397C2312yes—
471#397C2314yes—
472#397C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2312yes—
482#396C2314yes—
483#396C2314yes—
484#396C2312yes—
485#396C2312yes—
486#396C2312yes—
487#395C2314yes—
488#395C2312yes—
489#395C2314yes—
490#395C2314yes—
491#395C2312yes—
492#395C2312yes—
493#395C2312yes—
494#395C2314yes—
495#395C2312yes—
496#395C2314yes—
497#395C2314yes—
498#395C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2312yes—
502#394C2314yes—
503#394C2312yes—
504#394C2312yes—
505#394C2312yes—
506#394C2312yes—
507#393C2314yes—
508#393C2314yes—
509#393C2314yes—
510#393C2314yes—
511#393C2314yes—
512#393C2314yes—
513#393C2314yes—
514#393C2314yes—
515#393C2312yes—
516#392C2312yes—
517#391C2312yes—
518#391C2311yescharacteristic
519#391C2311yescharacteristic
520#391C2312yes—
521#391C2312yes—
522#391C2311yescharacteristic
523#391C2312yes—
524#391C2312yes—
525#391C2311yescharacteristic
526#391C2312yes—
527#391C2312yes—
528#391C2312yes—
529#391C2312yes—
530#391C2312yes—
531#391C2312yes—
532#391C2311yescharacteristic
533#391C2314yes—
534#391C2314yes—
535#391C2311yescharacteristic
536#391C2311yescharacteristic
537#391C2314yes—
538#391C2311yescharacteristic
539#391C2312yes—
540#390C2314yes—
541#390C2312yes—
542#390C2314yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2311yescharacteristic
548#390C2311yescharacteristic
549#390C2312yes—
550#390C2311yescharacteristic
551#390C2311yescharacteristic
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2311yescharacteristic
559#389C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2314yes—
572#389C2312yes—
573#389C2312yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2314yes—
579#389C2314yes—
580#389C2314yes—
581#389C2311yescharacteristic
582#389C2312yes—
583#389C2311yescharacteristic
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2311yescharacteristic
596#389C2312yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2312yes—
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#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2312yes—
628#388C2312yes—
629#388C2314yes—
630#388C2312yes—
631#388C2312yes—
632#388C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2312yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2312yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2312yes—
658#387C2314yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2314yes—
666#386C2314yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#386C2312yes—
674#386C2314yes—
675#386C2312yes—
676#386C2312yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2312yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2312yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2314yes—
697#385C2312yes—
698#385C2314yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#385C2312yes—
703#385C2312yes—
704#385C2312yes—
705#385C2312yes—
706#384C2311yescharacteristic
707#384C2311yescharacteristic
708#384C2314yes—
709#384C2312yes—
710#384C2312yes—
711#384C2311yescharacteristic
712#384C2311yescharacteristic
713#383C2314yes—
714#383C2314yes—
715#383C2314yes—
716#382C2314yes—
717#382C2312yes—
718#382C2312yes—
719#382C2314yes—
720#382C2312yes—
721#382C2312yes—
722#382C2314yes—
723#382C2314yes—
724#382C2314yes—
725#382C2314yes—
726#382C2312yes—
727#382C2312yes—
728#382C2314yes—
729#382C2312yes—
730#382C2311yescharacteristic
731#381C2314yes—
732#381C2314yes—
733#381C2314yes—
734#381C2312yes—
735#381C2312yes—
736#381C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2311yescharacteristic
742#380C2312yes—
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2314yes—
752#380C2312yes—
753#380C2314yes—
754#380C2314yes—
755#380C2311yescharacteristic
756#380C2312yes—
757#380C2312yes—
758#380C2311yescharacteristic
759#380C2312yes—
760#380C2311yescharacteristic
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2314yes—
765#380C2312yes—
766#380C2314yes—
767#379C2312yes—
768#379C2314yes—
769#379C2314yes—
770#379C2314yes—
771#379C2312yes—
772#379C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813#376C2312yes—
814C2×#95C2314yes—
815C43C2311yescharacteristic
816C25C2412yes—
817C22×Q8—42no—
818C22×Q8—42no—
819C22×Q8—42no—
820C22×Q8C2411yescharacteristic
821C22×Q8C2411yescharacteristic
822C22×Q8C2411yescharacteristic
823C22×Q8C2411yescharacteristic
824C22×Q8C2412yes—
825C22×Q8C2412yes—
826C22×Q8C2412yes—
827C22×Q8C2414yes—
828C22×D4—24no—
829C22×D4—24no—
830C22×D4—42no—
831C22×D4C2411yescharacteristic
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C22×D4C2412yes—
835C22×D4C2411yescharacteristic
836C22×D4C2412yes—
837C23×C4—44no—
838C23×C4—44no—
839C23×C4—44no—
840C23×C4C2412yes—
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2414yes—
849C23×C4C2412yes—
850C23×C4C2414yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C4⋊Q8—24no—
856C4⋊Q8—42no—
857C4⋊Q8—44no—
858C4⋊Q8—44no—
859C4⋊Q8—42no—
860C4⋊Q8—42no—
861C4⋊Q8—48no—
862C4⋊Q8—84no—
863#126—44no—
864#126—84no—
865#125—44no—
866#125—44no—
867#125—42no—
868#125—44no—
869#125—44no—
870#124—24no—
871#124—42no—
872#124—48no—
873#123—44no—
874#123—84no—
875C22⋊Q8—24no—
876C22⋊Q8—44no—
877C22⋊Q8—44no—
878C22⋊Q8—48no—
879C22⋊Q8—44no—
880C22⋊Q8—42no—
881C22⋊Q8—44no—
882C22⋊Q8—44no—
883C22⋊Q8—44no—
884C22⋊Q8—44no—
885C22⋊Q8—44no—
886C22⋊Q8—42no—
887C22⋊Q8—42no—
888C22⋊Q8—42no—
889C22⋊Q8—42no—
890C22⋊Q8—44no—
891C22⋊Q8—82no—
892C22⋊Q8—84no—
893#121—24no—
894#121—42no—
895#120—44no—
896C4×Q8—24no—
897C4×Q8—24no—
898C4×Q8—24no—
899C4×Q8—24no—
900C4×Q8—44no—
901C4×Q8—44no—
902C4×Q8—44no—
903C4×Q8—42no—
904C4×Q8—42no—
905C4×Q8—44no—
906C4×Q8—44no—
907C4×Q8—82no—
908C4×D4—28no—
909C4×D4—24no—
910C4×D4—24no—
911C4×D4—24no—
912C4×D4—44no—
913C4×D4—42no—
914C4×D4—42no—
915C4×D4—44no—
916C4×D4—44no—
917C4×D4—44no—
918C4×D4—42no—
919C4×D4—44no—
920C4×D4—42no—
921C4×D4—48no—
922#117—28no—
923#117—44no—
924#117—44no—
925#117—44no—
926#117—82no—
927#117—84no—
928C2×C4⋊C4—44no—
929C2×C4⋊C4—42no—
930C2×C4⋊C4—42no—
931C2×C4⋊C4—44no—
932C2×C4⋊C4—44no—
933C2×C4⋊C4C2411yescharacteristic
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2411yescharacteristic
936C2×C4⋊C4C2411yescharacteristic
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C22⋊C4—44no—
1011C2×C22⋊C4—84no—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2411yescharacteristic
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2411yescharacteristic
1018C2×C22⋊C4C2411yescharacteristic
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C42—24no—
1065C2×C42—24no—
1066C2×C42—44no—
1067C2×C42C2411yescharacteristic
1068C2×C42C2411yescharacteristic
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2414yes—
1074C2×C42C2411yescharacteristic
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2412yes—
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2412yes—
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2414yes—
1085C2×C42C2414yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2414yes—
1088C2×C42C2414yes—
1089C2×C42C2411yescharacteristic
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2414yes—
1093C2×C42C2414yes—
1094C2×C42C2411yescharacteristic
1095#95C2412yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2412yes—
1102#95C2412yes—
1103#95C2411yescharacteristic
1104#95C2411yescharacteristic
1105#95C2411yescharacteristic
1106#95C2412yes—
1107#95C2411yescharacteristic
1108#95C2411yescharacteristic
1109#95C2411yescharacteristic
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2414yes—
1118#95C2412yes—
1119#95C2414yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2414yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2414yes—
1129#95C2412yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171C24—24no—
1172C24—24no—
1173C24—42no—
1174C24—42no—
1175C24—42no—
1176C24—42no—
1177C24—42no—
1178C24C2512yes—
1179C24C2511yescharacteristic
1180C24C2512yes—
1181C24C2511yescharacteristic
1182C2×Q8—22no—
1183C2×Q8—22no—
1184C2×Q8—22no—
1185C2×Q8—22no—
1186C2×Q8—24no—
1187C2×Q8—22no—
1188C2×Q8—22no—
1189C2×Q8—22no—
1190C2×Q8—22no—
1191C2×Q8—22no—
1192C2×Q8—22no—
1193C2×Q8—22no—
1194C2×Q8—22no—
1195C2×Q8—42no—
1196C2×Q8—42no—
1197C2×Q8—42no—
1198C2×Q8—42no—
1199C2×Q8—42no—
1200C2×Q8—42no—
1201C2×Q8—42no—
1202C2×Q8—42no—
1203C2×Q8—44no—
1204C2×Q8—44no—
1205C2×Q8—44no—
1206C2×Q8—416no—
1207C2×D4—22no—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—24no—
1211C2×D4—22no—
1212C2×D4—24no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—24no—
1217C2×D4—22no—
1218C2×D4—22no—
1219C2×D4—416no—
1220C2×D4—42no—
1221C2×D4—42no—
1222C2×D4—41no—
1223C2×D4—42no—
1224C2×D4—42no—
1225C2×D42−1+414yes—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—28no—
1230C22×C4—24no—
1231C22×C4—22no—
1232C22×C4—22no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—24no—
1236C22×C4—24no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—24no—
1240C22×C4—24no—
1241C22×C4—22no—
1242C22×C4—24no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—24no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—42no—
1249C22×C4—41no—
1250C22×C4—42no—
1251C22×C4—42no—
1252C22×C4—42no—
1253C22×C4—42no—
1254C22×C4—44no—
1255C22×C4—44no—
1256C22×C4—42no—
1257C22×C4—42no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—42no—
1261C22×C4—42no—
1262C22×C4—42no—
1263C22×C4—42no—
1264C22×C4—42no—
1265C22×C4—42no—
1266C22×C4—42no—
1267C22×C4—44no—
1268C22×C4—44no—
1269C22×C4—44no—
1270C22×C4—816no—
1271C22×C42−1+414yes—
1272C22×C4C2511yescharacteristic
1273C22×C4C2512yes—
1274C22×C4C2511yescharacteristic
1275C22×C4C2512yes—
1276C22×C4C2511yescharacteristic
1277C22×C4C2512yes—
1278C22×C4C2511yescharacteristic
1279C22×C4C2512yes—
1280C22×C4C2514yes—
1281C22×C4C2514yes—
1282C22×C4C2511yescharacteristic
1283C22×C4C2511yescharacteristic
1284C22×C4C2514yes—
1285C22×C4C2512yes—
1286C22×C4C2511yescharacteristic
1287C22×C4C2512yes—
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2512yes—
1291C22×C4C2512yes—
1292C22×C4C2512yes—
1293C22×C4C2512yes—
1294C22×C4C2511yescharacteristic
1295C22×C4C2514yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2511yescharacteristic
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2511yescharacteristic
1303C4⋊C4—22no—
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—24no—
1307C4⋊C4—24no—
1308C4⋊C4—22no—
1309C4⋊C4—24no—
1310C4⋊C4—24no—
1311C4⋊C4—22no—
1312C4⋊C4—24no—
1313C4⋊C4—22no—
1314C4⋊C4—24no—
1315C4⋊C4—24no—
1316C4⋊C4—24no—
1317C4⋊C4—22no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—22no—
1321C4⋊C4—24no—
1322C4⋊C4—22no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—22no—
1327C4⋊C4—44no—
1328C4⋊C4—42no—
1329C4⋊C4—42no—
1330C4⋊C4—42no—
1331C4⋊C4—42no—
1332C4⋊C4—44no—
1333C4⋊C4—42no—
1334C4⋊C4—42no—
1335C4⋊C4—42no—
1336C4⋊C4—42no—
1337C4⋊C4—42no—
1338C4⋊C4—42no—
1339C4⋊C4—42no—
1340C4⋊C4—42no—
1341C4⋊C4—42no—
1342C4⋊C4—44no—
1343C4⋊C4—42no—
1344C4⋊C4—41no—
1345C4⋊C4—44no—
1346C4⋊C4—41no—
1347C4⋊C4—42no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—42no—
1351C4⋊C4—44no—
1352C4⋊C4—44no—
1353C4⋊C4—44no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—44no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—42no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—42no—
1366C4⋊C4—44no—
1367C4⋊C4—42no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C22⋊C4—28no—
1381C22⋊C4—22no—
1382C22⋊C4—28no—
1383C22⋊C4—24no—
1384C22⋊C4—24no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—22no—
1388C22⋊C4—28no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—22no—
1393C22⋊C4—42no—
1394C22⋊C4—42no—
1395C22⋊C4—42no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—42no—
1400C22⋊C4—42no—
1401C22⋊C4—42no—
1402C22⋊C4—42no—
1403C22⋊C4—42no—
1404C22⋊C4—42no—
1405C22⋊C4—42no—
1406C22⋊C4—44no—
1407C22⋊C4—44no—
1408C22⋊C4—42no—
1409C22⋊C4—42no—
1410C22⋊C4—41no—
1411C22⋊C4—41no—
1412C22⋊C4—44no—
1413C22⋊C4—41no—
1414C22⋊C4—44no—
1415C22⋊C4—42no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C42—22no—
1433C42—22no—
1434C42—22no—
1435C42—22no—
1436C42—22no—
1437C42—22no—
1438C42—24no—
1439C42—24no—
1440C42—24no—
1441C42—24no—
1442C42—28no—
1443C42—22no—
1444C42—24no—
1445C42—22no—
1446C42—22no—
1447C42—24no—
1448C42—22no—
1449C42—42no—
1450C42—42no—
1451C42—44no—
1452C42—44no—
1453C42—41no—
1454C42—44no—
1455C42—44no—
1456C42—41no—
1457C42—44no—
1458C42—44no—
1459C42H(5,𝔽2)14yes—
1460C23—22no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—22no—
1467C23—21no—
1468C23—22no—
1469C23—22no—
1470C23—21no—
1471C23—22no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—22no—
1477C23—21no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—22no—
1482C23—22no—
1483C23—22no—
1484C23—22no—
1485C23—48no—
1486C23—48no—
1487C23—84no—
1488C23—84no—
1489C23—84no—
1490C23—84no—
1491C23—84no—
1492C23C2×2−1+412yes—
1493C23C2×2−1+414yes—
1494C23#58512yes—
1495C23C2611yescharacteristic
1496Q8—48no—
1497Q8—44no—
1498Q8—44no—
1499Q8—44no—
1500Q8—44no—
1501Q8—84no—
1502Q8—84no—
1503Q8—164no—
1504D4—28no—
1505D4—48no—
1506D4—48no—
1507D4—44no—
1508D4—44no—
1509D4—84no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—28no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—24no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—24no—
1536C2×C4—24no—
1537C2×C4—21no—
1538C2×C4—22no—
1539C2×C4—21no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—21no—
1543C2×C4—24no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—21no—
1552C2×C4—22no—
1553C2×C4—24no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—21no—
1562C2×C4—22no—
1563C2×C4—24no—
1564C2×C4—24no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—24no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—24no—
1586C2×C4—24no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—24no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—44no—
1597C2×C4—48no—
1598C2×C4—44no—
1599C2×C4—48no—
1600C2×C4—48no—
1601C2×C4—44no—
1602C2×C4—44no—
1603C2×C4—82no—
1604C2×C4—88no—
1605C2×C4—84no—
1606C2×C4—84no—
1607C2×C4—84no—
1608C2×C4—84no—
1609C2×C4—164no—
1610C2×C4C2×H(5,𝔽2)12yes—
1611C2×C4C2×H(5,𝔽2)12yes—
1612C2×C4C2×H(5,𝔽2)12yes—
1613C2×C4C2×2−1+412yes—
1614C2×C4C2×2−1+412yes—
1615C2×C4C2×2−1+412yes—
1616C2×C4#58512yes—
1617C2×C4#58512yes—
1618C22—22no—
1619C22—24no—
1620C22—22no—
1621C22—24no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—24no—
1626C22—22no—
1627C22—41no—
1628C22—41no—
1629C22—41no—
1630C22—42no—
1631C22—41no—
1632C22—42no—
1633C22—41no—
1634C22—42no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—42no—
1639C22—42no—
1640C22—42no—
1641C22—42no—
1642C22—42no—
1643C22—42no—
1644C22—42no—
1645C22—42no—
1646C22—816no—
1647C22C22×H(5,𝔽2)11yescharacteristic
1648C22C22×2−1+411yescharacteristic
1649C22C22×2−1+411yescharacteristic
1650C22C2×#58511yescharacteristic
1651C22C2×#58511yescharacteristic
1652C22C2×#58511yescharacteristic
1653C22H(7,𝔽2)11yescharacteristic
1654C4—22no—
1655C4—22no—
1656C4—41no—
1657C4—42no—
1658C4—42no—
1659C4—42no—
1660C4—41no—
1661C4—41no—
1662C4—42no—
1663C4—42no—
1664C4—42no—
1665C4—41no—
1666C4—42no—
1667C4—42no—
1668C4—44no—
1669C4—41no—
1670C4—41no—
1671C4—44no—
1672C4—42no—
1673C4—41no—
1674C4—44no—
1675C4—42no—
1676C4—41no—
1677C4—42no—
1678C4—42no—
1679C4—41no—
1680C4—44no—
1681C4—42no—
1682C4—42no—
1683C4#353814yes—
1684C4#354014yes—
1685C2—42no—
1686C2—44no—
1687C2—42no—
1688C2—82no—
1689C2C2×#353811yescharacteristic
1690C2C2×#354011yescharacteristic
1691C2#6283111yescharacteristic
1692C2#6292611yescharacteristic
1693C2#6295111yescharacteristic
1694C2#6295711yescharacteristic
1695C2#6302311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2408C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59655C2semidirect
2. #59242C2semidirect
3. #59235C2semidirect
4. #56670C2semidirect
5. #54621C2semidirect
6. #54122C2semidirect
7. #53153C2semidirect
8. #53011C2semidirect
9. #48097C2semidirect
10. #45667C2semidirect
11. #45595C2semidirect
12. #45365C2semidirect
13. #45226C2semidirect
14. #42955C2semidirect
15. #42640C2semidirect
16. #42493C2semidirect
17. #42458C2semidirect
18. #39597C2semidirect
19. #39536C2semidirect
20. #39506C2semidirect
21. #39125C2semidirect
23. #38977C2semidirect
24. #38928C2semidirect
25. #37853C2semidirect
26. #37637C2semidirect
27. #37407C2semidirect
28. #37380C2semidirect
29. #36544C2semidirect
30. #36210C2semidirect
31. #36154C2semidirect
32. #35247C2semidirect
33. #35172C2semidirect
35. #34691C2semidirect
36. C2×Q82C22semidirect
40. C22×C4×Q8C22semidirect
42. #2859C22semidirect
44. #2857C22semidirect
45. #2855C22semidirect
47. #2851C22semidirect
51. #2843C22semidirect
52. #2841C22semidirect
53. #2838C22semidirect
54. #2838C22semidirect
55. #2838C22semidirect
56. #2835C22semidirect
57. #2831C22semidirect
58. #2827C22semidirect
59. #2807C22semidirect
60. #2794C22semidirect
61. #2790C22semidirect
64. #2787C22semidirect
65. #2783C22semidirect
66. #2783C22semidirect
68. #2782C22semidirect
69. #2773C22semidirect
70. #2773C22semidirect
71. #2770C22semidirect
74. #2768C22semidirect
75. #2767C22semidirect
76. #2765C22semidirect
77. #2765C22semidirect
78. #2765C22semidirect
79. #2765C22semidirect
81. #2763C22semidirect
86. #2746C22semidirect
87. #2745C22semidirect
88. #2745C22semidirect
89. #2744C22semidirect
91. #2739C22semidirect
92. #2738C22semidirect
98. #2729C22semidirect
99. #2729C22semidirect
100. #2716C22semidirect
101. #2716C22semidirect
102. #2713C22semidirect
103. #2695C22semidirect
106. #2674C22semidirect
107. #2674C22semidirect
108. #2666C22semidirect
109. #2666C22semidirect
110. #2647C22semidirect
111. #2646C22semidirect
112. #2645C22semidirect
114. #2638C22semidirect
115. #2637C22semidirect
116. #2637C22semidirect
117. #2629C22semidirect
119. #2628C22semidirect
120. #2628C22semidirect
122. #2625C22semidirect
123. #2621C22semidirect
124. #2609C22semidirect
128. #2584C22semidirect
129. #2584C22semidirect
130. #2582C22semidirect
131. #2582C22semidirect
132. #2581C22semidirect
136. #2571C22semidirect
137. #2571C22semidirect
138. #2567C22semidirect
143. #2562C22semidirect
145. #2552C22semidirect
146. #2551C22semidirect
147. #2550C22semidirect
148. #2550C22semidirect
149. #2547C22semidirect
150. #2546C22semidirect
157. #2536C22semidirect
158. #2524C22semidirect
159. #2517C22semidirect
160. #2514C22semidirect
161. #2514C22semidirect
162. #2514C22semidirect
166. #2509C22semidirect
167. #2508C22semidirect
168. #2508C22semidirect
169. #2508C22semidirect
170. #2508C22semidirect
171. #2508C22semidirect
172. #2503C22semidirect
174. #2497C22semidirect
175. #2496C22semidirect
177. #2495C22semidirect
179. #2494C22semidirect
180. #2494C22semidirect
181. #2493C22semidirect
183. #2492C22semidirect
186. #2489C22semidirect
187. #2489C22semidirect
188. #2489C22semidirect
189. #2489C22semidirect
190. #2489C22semidirect
192. #2486C22semidirect
198. #2473C22semidirect
201. #2465C22semidirect
202. #2462C22semidirect
207. #2453C22semidirect
209. #2451C22semidirect
212. #2449C22semidirect
216. #2446C22semidirect
217. #2446C22semidirect
220. #2442C22semidirect
221. #2440C22semidirect
222. #2440C22semidirect
223. #2438C22semidirect
226. #2434C22semidirect
228. #2429C22semidirect
229. #2429C22semidirect
233. #2423C22semidirect
235. #2421C22semidirect
243. #2417C22semidirect
245. #2413C22semidirect
247. #2409C22semidirect
248. #2409C22semidirect
250. #2399C22semidirect
254. #2379C22semidirect
255. #2370C22semidirect
256. #2370C22semidirect
258. #2362C22semidirect
259. #2360C22semidirect
260. #2360C22semidirect
261. #2355C22semidirect
262. #2355C22semidirect
263. #2355C22semidirect
267. D4×C4⋊C4C22semidirect
270. #2344C22semidirect
273. #2323C22semidirect
274. #2323C22semidirect
275. #2323C22semidirect
277. #2318C22semidirect
279. #2314C22semidirect
281. C4×C4⋊Q8C22semidirect
282. C4×C4⋊Q8C22semidirect
286. C4×C22⋊Q8C22semidirect
287. C4×C22⋊Q8C22semidirect
291. #2295C22semidirect
295. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#596552
#592422
#592352
#566702
#546212
#541222
#531532
#530112
#480972
#456672
#455952
#453652
#452262
#429552
#426402
#424932
#424582
#395972
#395362
#395062
#391252
#390422
#389772
#389282
#378532
#376372
#374072
#373802
#365442
#362102
#361542
#352472
#351722
#347002
#346912