Finite Group Databasebeta

← #8466975

Subgroups — #8466975

Order 512.

5073 conjugacy classes of subgroups.

The subgroup lattice has 1782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59653C211yesmaximal, characteristic, complemented
2#59322C211yesmaximal, characteristic, complemented
3#59314C211yesmaximal, characteristic, complemented
4#57284C214yesmaximal, complemented
5#55383C214yesmaximal, complemented
6#54941C214yesmaximal, complemented
7#53016C212yesmaximal, complemented
8#52959C212yesmaximal, complemented
9#49852C214yesmaximal, complemented
10#45676C212yesmaximal, complemented
11#45501C212yesmaximal, complemented
12#45112C212yesmaximal, complemented
13#44915C212yesmaximal, complemented
14#42849C212yesmaximal, complemented
15#42794C212yesmaximal, complemented
16#42641C212yesmaximal, complemented
17#42449C212yesmaximal, complemented
18#40054C212yesmaximal, complemented
19#39691C212yesmaximal, complemented
20#39598C212yesmaximal, complemented
21#39468C211yesmaximal, characteristic, complemented
22#39377C211yesmaximal, characteristic, complemented
23#39136C211yesmaximal, characteristic, complemented
24#39127C211yesmaximal, characteristic, complemented
25#37781C212yesmaximal, complemented
26#37620C211yesmaximal, characteristic, complemented
27#37307C212yesmaximal, complemented
28#37299C212yesmaximal, complemented
29#36445C211yesmaximal, characteristic, complemented
30#36180C211yesmaximal, characteristic, complemented
31#36134C211yesmaximal, characteristic, complemented
32#35273C211yesmaximal, characteristic, complemented
33#35170C211yesmaximal, characteristic, complemented
34#34889C211yesmaximal, characteristic, complemented
35#34724C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic
37C2×#556C2211yescharacteristic
38C2×#554C2212yes—
39C2×#554C2212yes—
40C2×#542C2212yes—
41C2×#542C2212yes—
42C2×#537C2212yes—
43C2×#533C2212yes—
44C2×#532C2211yescharacteristic
45C2×#529C2211yescharacteristic
46C2×#529C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic
48#2868C2211yescharacteristic
49#2857C2212yes—
50#2857C2212yes—
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2857C2212yes—
55#2856C2212yes—
56#2854C2212yes—
57#2841C2214yes—
58#2837C2214yes—
59#2837C2214yes—
60#2836C2214yes—
61#2827C2214yes—
62#2823C2214yes—
63#2820C2214yes—
64#2814C2214yes—
65#2806C2214yes—
66#2806C2214yes—
67#2802C2214yes—
68#2797C2214yes—
69#2793C2214yes—
70#2792C2214yes—
71#2788C2214yes—
72#2788C2214yes—
73#2774C2214yes—
74#2768C2214yes—
75#2748C2214yes—
76#2748C2214yes—
77#2741C2214yes—
78#2732C2214yes—
79#2732C2214yes—
80#2730C2214yes—
81#2727C2214yes—
82#2727C2214yes—
83#2727C2214yes—
84#2725C2214yes—
85#2725C2214yes—
86#2721C2214yes—
87#2720C2214yes—
88#2718C2214yes—
89#2715C2214yes—
90#2711C2214yes—
91#2711C2214yes—
92#2707C2214yes—
93#2705C2214yes—
94#2704C2214yes—
95#2704C2214yes—
96#2704C2214yes—
97#2701C2214yes—
98#2694C2214yes—
99#2692C2214yes—
100#2691C2214yes—
101#2683C2214yes—
102#2683C2214yes—
103#2683C2214yes—
104#2683C2214yes—
105#2681C2214yes—
106#2681C2214yes—
107#2681C2214yes—
108#2674C2214yes—
109#2672C2214yes—
110#2672C2214yes—
111#2672C2214yes—
112#2672C2214yes—
113#2671C2214yes—
114#2664C2214yes—
115#2663C2214yes—
116#2651C2214yes—
117#2649C2214yes—
118#2636C2214yes—
119#2629C2212yes—
120#2629C2212yes—
121#2629C2214yes—
122#2629C2212yes—
123#2628C2212yes—
124#2620C2212yes—
125#2620C2214yes—
126#2620C2212yes—
127#2620C2212yes—
128#2618C2214yes—
129#2616C2212yes—
130#2590C2214yes—
131#2584C2214yes—
132#2583C2214yes—
133#2582C2211yescharacteristic
134#2567C2212yes—
135#2567C2212yes—
136#2567C2212yes—
137#2562C2212yes—
138#2559C2212yes—
139#2557C2212yes—
140#2556C2214yes—
141#2552C2212yes—
142#2552C2212yes—
143#2552C2212yes—
144#2551C2211yescharacteristic
145#2550C2211yescharacteristic
146#2547C2211yescharacteristic
147#2545C2212yes—
148#2545C2212yes—
149#2544C2212yes—
150#2544C2211yescharacteristic
151#2542C2212yes—
152#2542C2212yes—
153#2542C2211yescharacteristic
154#2542C2212yes—
155#2540C2214yes—
156#2540C2211yescharacteristic
157#2540C2212yes—
158#2538C2211yescharacteristic
159#2538C2211yescharacteristic
160#2538C2211yescharacteristic
161#2538C2212yes—
162#2538C2212yes—
163#2538C2214yes—
164#2538C2211yescharacteristic
165#2538C2212yes—
166#2538C2212yes—
167#2538C2212yes—
168#2537C2212yes—
169#2537C2211yescharacteristic
170#2537C2211yescharacteristic
171#2535C2211yescharacteristic
172#2521C2212yes—
173#2521C2214yes—
174#2519C2214yes—
175#2507C2212yes—
176#2507C2212yes—
177#2506C2212yes—
178#2502C2212yes—
179#2502C2212yes—
180#2501C2212yes—
181#2496C2212yes—
182#2496C2212yes—
183#2492C2211yescharacteristic
184#2492C2212yes—
185#2491C2212yes—
186#2491C2212yes—
187#2490C2211yescharacteristic
188#2489C2212yes—
189#2487C2212yes—
190#2485C2212yes—
191#2478C2212yes—
192#2476C2214yes—
193#2476C2214yes—
194#2470C2212yes—
195#2467C2214yes—
196#2466C2212yes—
197#2465C2214yes—
198#2464C2212yes—
199#2464C2214yes—
200#2456C2214yes—
201#2455C2212yes—
202#2454C2212yes—
203#2454C2214yes—
204#2453C2212yes—
205#2453C2211yescharacteristic
206#2451C2212yes—
207#2449C2214yes—
208#2448C2212yes—
209#2447C2211yescharacteristic
210#2446C2212yes—
211#2441C2212yes—
212#2441C2214yes—
213#2441C2214yes—
214#2441C2212yes—
215#2441C2212yes—
216#2441C2211yescharacteristic
217#2440C2212yes—
218#2440C2212yes—
219#2440C2212yes—
220#2440C2212yes—
221#2440C2212yes—
222#2440C2212yes—
223#2440C2212yes—
224#2440C2212yes—
225#2440C2212yes—
226#2432C2211yescharacteristic
227#2429C2212yes—
228#2429C2214yes—
229#2429C2212yes—
230#2429C2211yescharacteristic
231#2428C2211yescharacteristic
232#2427C2212yes—
233#2427C2211yescharacteristic
234#2427C2212yes—
235#2426C2212yes—
236#2426C2212yes—
237#2426C2212yes—
238#2426C2214yes—
239#2423C2212yes—
240#2423C2212yes—
241#2423C2212yes—
242#2423C2212yes—
243#2422C2211yescharacteristic
244#2422C2212yes—
245#2417C2212yes—
246#2417C2212yes—
247#2417C2212yes—
248#2416C2212yes—
249#2416C2212yes—
250#2416C2212yes—
251#2416C2212yes—
252#2416C2214yes—
253#2415C2211yescharacteristic
254#2414C2212yes—
255#2407C2211yescharacteristic
256#2395C2212yes—
257#2395C2212yes—
258#2392C2212yes—
259#2388C2212yes—
260#2376C2214yes—
261#2365C2212yes—
262#2362C2212yes—
263#2361C2212yes—
264#2360C2212yes—
265#2360C2212yes—
266#2354C2212yes—
267#2351C2212yes—
268Q8×C4⋊C4C2211yescharacteristic
269Q8×C4⋊C4C2211yescharacteristic
270Q8×C4⋊C4C2212yes—
271Q8×C4⋊C4C2211yescharacteristic
272D4×C4⋊C4C2211yescharacteristic
273D4×C4⋊C4C2212yes—
274D4×C4⋊C4C2212yes—
275#2341C2212yes—
276#2324C2214yes—
277#2323C2212yes—
278#2323C2212yes—
279#2323C2212yes—
280#2311C2212yes—
281#2311C2212yes—
282C4×C4⋊Q8C2211yescharacteristic
283C4×C4⋊Q8C2211yescharacteristic
284C4×#124C2211yescharacteristic
285C4×C22⋊Q8C2212yes—
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×C22⋊Q8C2211yescharacteristic
289C4×#123C2212yes—
290C4×#121C2212yes—
291C4×#121C2211yescharacteristic
292#2297C2212yes—
293#2296C2212yes—
294#2293C2211yescharacteristic
295C2×#384C2211yescharacteristic
296C2×#384C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301#557—44no—
302#556—44no—
303#554—48no—
304#554—48no—
305#542—48no—
306#542—48no—
307#537—48no—
308#533—48no—
309#532—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×#127C2311yescharacteristic
320#529—44no—
321#529—44no—
322C2×#126C2312yes—
323C2×#126C2312yes—
324C2×#126C2314yes—
325C2×#126C2314yes—
326C2×#126C2314yes—
327C2×#125C2312yes—
328C2×#125C2314yes—
329C2×#125C2314yes—
330C2×#125C2311yescharacteristic
331C2×#125C2311yescharacteristic
332C2×#125C2314yes—
333C2×#125C2314yes—
334C2×#124C2311yescharacteristic
335C2×#124C2314yes—
336C2×#124C2311yescharacteristic
337C2×#124C2311yescharacteristic
338C2×#124C2312yes—
339C2×#124C2312yes—
340C2×#124C2314yes—
341C2×#124C2312yes—
342C2×#123C2312yes—
343C2×#123C2314yes—
344C2×#123C2312yes—
345C2×#123C2312yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2311yescharacteristic
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2314yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2312yes—
362C2×C22⋊Q8C2311yescharacteristic
363C2×C22⋊Q8C2311yescharacteristic
364C2×C22⋊Q8C2314yes—
365C2×C22⋊Q8C2314yes—
366C2×C22⋊Q8C2314yes—
367C2×C22⋊Q8C2314yes—
368C2×C22⋊Q8C2314yes—
369C2×C22⋊Q8C2314yes—
370C2×C22⋊Q8C2314yes—
371C2×C22⋊Q8C2314yes—
372C2×C22⋊Q8C2314yes—
373C2×#121C2312yes—
374C2×#121C2311yescharacteristic
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2312yes—
378C2×#121C2314yes—
379C2×#121C2311yescharacteristic
380C2×#121C2312yes—
381C2×#121C2311yescharacteristic
382C2×#121C2311yescharacteristic
383C2×#121C2311yescharacteristic
384C2×#121C2312yes—
385C2×#121C2314yes—
386C2×#121C2314yes—
387C2×#121C2314yes—
388C2×#121C2314yes—
389C4×#41—44no—
390C2×C4×Q8C2312yes—
391C2×C4×Q8C2311yescharacteristic
392C2×C4×Q8C2311yescharacteristic
393C2×C4×Q8C2311yescharacteristic
394C2×C4×Q8C2312yes—
395C2×C4×Q8C2312yes—
396C2×C4×Q8C2312yes—
397C2×C4×Q8C2312yes—
398C2×C4×Q8C2312yes—
399C2×C4×Q8C2314yes—
400C2×C4×Q8C2311yescharacteristic
401C2×C4×Q8C2312yes—
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2311yescharacteristic
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2311yescharacteristic
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2311yescharacteristic
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2312yes—
411C2×C4×D4C2314yes—
412C2×C4×D4C2314yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2311yescharacteristic
420C2×#117C2312yes—
421C2×#117C2311yescharacteristic
422C2×#117C2312yes—
423C2×#117C2312yes—
424C2×#117C2312yes—
425C2×#117C2314yes—
426C2×#117C2312yes—
427C22×C4⋊C4C2312yes—
428C22×C4⋊C4C2312yes—
429C22×C4⋊C4C2312yes—
430C22×C4⋊C4C2312yes—
431C22×C4⋊C4C2312yes—
432C22×C4⋊C4C2312yes—
433C22×C4⋊C4C2312yes—
434C22×C42C2311yescharacteristic
435C22×C42C2311yescharacteristic
436C22×C42C2312yes—
437C22×C42C2312yes—
438#400C2314yes—
439#400C2314yes—
440#400C2312yes—
441#400C2314yes—
442#400C2312yes—
443#400C2314yes—
444#400C2314yes—
445#399C2314yes—
446#399C2314yes—
447#399C2314yes—
448#399C2314yes—
449#399C2314yes—
450#399C2314yes—
451#399C2314yes—
452#399C2314yes—
453#399C2312yes—
454#399C2312yes—
455#399C2314yes—
456#399C2314yes—
457#399C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2314yes—
470#398C2314yes—
471#398C2314yes—
472#398C2312yes—
473#398C2312yes—
474#398C2314yes—
475#398C2314yes—
476#398C2314yes—
477#398C2312yes—
478#398C2314yes—
479#398C2314yes—
480#398C2314yes—
481#397C2312yes—
482#397C2312yes—
483#397C2312yes—
484#397C2314yes—
485#397C2314yes—
486#397C2312yes—
487#397C2314yes—
488#397C2312yes—
489#397C2312yes—
490#397C2312yes—
491#397C2314yes—
492#397C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2314yes—
504#396C2314yes—
505#396C2314yes—
506#396C2314yes—
507#396C2314yes—
508#396C2314yes—
509#396C2314yes—
510#396C2314yes—
511#396C2314yes—
512#396C2314yes—
513#396C2314yes—
514#396C2314yes—
515#396C2312yes—
516#396C2312yes—
517#396C2314yes—
518#396C2314yes—
519#396C2314yes—
520#395C2314yes—
521#395C2314yes—
522#395C2314yes—
523#395C2314yes—
524#395C2314yes—
525#395C2314yes—
526#395C2314yes—
527#395C2314yes—
528#395C2314yes—
529#395C2312yes—
530#394C2314yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2314yes—
535#394C2312yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2314yes—
542#394C2314yes—
543#394C2314yes—
544#394C2314yes—
545#394C2314yes—
546#394C2312yes—
547#394C2312yes—
548#394C2312yes—
549#394C2312yes—
550#394C2312yes—
551#394C2312yes—
552#394C2312yes—
553#394C2312yes—
554#394C2312yes—
555#394C2314yes—
556#393C2314yes—
557#393C2314yes—
558#393C2312yes—
559#392C2312yes—
560#392C2312yes—
561#392C2312yes—
562#392C2312yes—
563#392C2314yes—
564#391C2311yescharacteristic
565#391C2311yescharacteristic
566#391C2312yes—
567#391C2314yes—
568#391C2314yes—
569#391C2311yescharacteristic
570#391C2311yescharacteristic
571#391C2312yes—
572#391C2312yes—
573#391C2312yes—
574#391C2312yes—
575#391C2311yescharacteristic
576#391C2312yes—
577#391C2314yes—
578#391C2314yes—
579#391C2311yescharacteristic
580#391C2312yes—
581#391C2312yes—
582#390C2314yes—
583#390C2314yes—
584#390C2314yes—
585#390C2314yes—
586#390C2314yes—
587#390C2312yes—
588#390C2312yes—
589#390C2314yes—
590#390C2314yes—
591#390C2311yescharacteristic
592#390C2312yes—
593#390C2312yes—
594#390C2312yes—
595#390C2311yescharacteristic
596#390C2314yes—
597#390C2311yescharacteristic
598#390C2311yescharacteristic
599#390C2314yes—
600#390C2312yes—
601#390C2312yes—
602#390C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2314yes—
608#389C2314yes—
609#389C2314yes—
610#389C2314yes—
611#389C2314yes—
612#389C2314yes—
613#389C2311yescharacteristic
614#389C2314yes—
615#389C2314yes—
616#389C2312yes—
617#389C2312yes—
618#389C2314yes—
619#389C2314yes—
620#389C2314yes—
621#389C2312yes—
622#389C2312yes—
623#389C2314yes—
624#389C2314yes—
625#389C2312yes—
626#389C2312yes—
627#389C2314yes—
628#389C2314yes—
629#389C2314yes—
630#389C2312yes—
631#389C2312yes—
632#389C2311yescharacteristic
633#389C2312yes—
634#389C2312yes—
635#389C2312yes—
636#389C2314yes—
637#389C2312yes—
638#389C2312yes—
639#389C2314yes—
640#389C2312yes—
641#389C2312yes—
642#389C2312yes—
643#389C2312yes—
644#389C2312yes—
645#389C2314yes—
646#389C2314yes—
647#389C2312yes—
648#389C2311yescharacteristic
649#389C2314yes—
650#389C2311yescharacteristic
651#389C2312yes—
652#389C2311yescharacteristic
653#389C2312yes—
654#389C2311yescharacteristic
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2312yes—
664#388C2314yes—
665#388C2314yes—
666#388C2312yes—
667#388C2314yes—
668#388C2314yes—
669#388C2314yes—
670#388C2314yes—
671#388C2314yes—
672#388C2312yes—
673#388C2314yes—
674#388C2312yes—
675#388C2314yes—
676#388C2312yes—
677#388C2314yes—
678#388C2312yes—
679#388C2312yes—
680#388C2312yes—
681#388C2312yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2314yes—
692#387C2314yes—
693#387C2314yes—
694#387C2312yes—
695#387C2314yes—
696#387C2312yes—
697#387C2312yes—
698#387C2312yes—
699#387C2312yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2314yes—
709#386C2312yes—
710#386C2312yes—
711#386C2312yes—
712#386C2312yes—
713#386C2312yes—
714#386C2312yes—
715#386C2312yes—
716#386C2312yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2312yes—
722#385C2312yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2312yes—
730#385C2314yes—
731#385C2312yes—
732#385C2312yes—
733#385C2312yes—
734#385C2312yes—
735#385C2312yes—
736#384C2311yescharacteristic
737#384C2311yescharacteristic
738#384C2312yes—
739#384C2312yes—
740#384C2312yes—
741#384C2312yes—
742#384C2312yes—
743#384C2312yes—
744#384C2311yescharacteristic
745#384C2311yescharacteristic
746#384C2312yes—
747#384C2312yes—
748#384C2312yes—
749#384C2312yes—
750#384C2314yes—
751#384C2312yes—
752#384C2312yes—
753#384C2312yes—
754#382C2314yes—
755#382C2311yescharacteristic
756#381C2312yes—
757#380C2311yescharacteristic
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2311yescharacteristic
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2314yes—
771#380C2314yes—
772#380C2314yes—
773#380C2314yes—
774#380C2312yes—
775#380C2312yes—
776#380C2314yes—
777#380C2312yes—
778#380C2314yes—
779#380C2312yes—
780#380C2312yes—
781#380C2314yes—
782#380C2311yescharacteristic
783#380C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2314yes—
795C4×C4⋊C4C2314yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2311yescharacteristic
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2311yescharacteristic
818C4×C22⋊C4C2311yescharacteristic
819C4×C22⋊C4C2311yescharacteristic
820C4×C22⋊C4C2312yes—
821C43C2311yescharacteristic
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—28no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—42no—
828C22×Q8C2411yescharacteristic
829C22×Q8C2412yes—
830C22×Q8C2411yescharacteristic
831C22×Q8C2411yescharacteristic
832C22×Q8C2414yes—
833C22×Q8C2412yes—
834C22×Q8C2414yes—
835C22×D4C2411yescharacteristic
836C22×D4C2411yescharacteristic
837C22×D4C2411yescharacteristic
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C4⋊Q8—24no—
866C4⋊Q8—28no—
867C4⋊Q8—24no—
868C4⋊Q8—42no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—82no—
874#127—42no—
875#126—44no—
876#126—44no—
877#126—48no—
878#126—48no—
879#126—48no—
880#125—42no—
881#125—42no—
882#125—48no—
883#125—48no—
884#125—44no—
885#125—48no—
886#125—48no—
887#124—24no—
888#124—44no—
889#124—48no—
890#124—42no—
891#124—42no—
892#124—44no—
893#124—44no—
894#124—48no—
895#123—28no—
896#123—48no—
897#123—44no—
898#123—44no—
899#123—48no—
900#123—84no—
901C22⋊Q8—28no—
902C22⋊Q8—28no—
903C22⋊Q8—24no—
904C22⋊Q8—24no—
905C22⋊Q8—28no—
906C22⋊Q8—24no—
907C22⋊Q8—48no—
908C22⋊Q8—48no—
909C22⋊Q8—48no—
910C22⋊Q8—48no—
911C22⋊Q8—48no—
912C22⋊Q8—48no—
913C22⋊Q8—48no—
914C22⋊Q8—48no—
915C22⋊Q8—42no—
916C22⋊Q8—42no—
917C22⋊Q8—44no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—44no—
921C22⋊Q8—44no—
922C22⋊Q8—44no—
923C22⋊Q8—84no—
924C22⋊Q8—84no—
925C22⋊Q8—84no—
926#121—24no—
927#121—28no—
928#121—44no—
929#121—48no—
930#121—48no—
931#121—48no—
932#121—42no—
933#121—42no—
934#121—42no—
935#121—42no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—44no—
940#121—84no—
941#121—84no—
942C4×Q8—28no—
943C4×Q8—24no—
944C4×Q8—24no—
945C4×Q8—24no—
946C4×Q8—28no—
947C4×Q8—48no—
948C4×Q8—42no—
949C4×Q8—44no—
950C4×Q8—44no—
951C4×Q8—44no—
952C4×Q8—44no—
953C4×Q8—44no—
954C4×D4—24no—
955C4×D4—24no—
956C4×D4—24no—
957C4×D4—24no—
958C4×D4—24no—
959C4×D4—24no—
960C4×D4—24no—
961C4×D4—24no—
962C4×D4—48no—
963C4×D4—42no—
964C4×D4—44no—
965C4×D4—48no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—44no—
971C4×D4—44no—
972#117—28no—
973#117—44no—
974#117—44no—
975#117—44no—
976#117—48no—
977#117—42no—
978#117—44no—
979C2×C4⋊C4—44no—
980C2×C4⋊C4—44no—
981C2×C4⋊C4—44no—
982C2×C4⋊C4—44no—
983C2×C4⋊C4—44no—
984C2×C4⋊C4—82no—
985C2×C4⋊C4—82no—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2414yes—
1062C2×C4⋊C4C2414yes—
1063C2×C4⋊C4C2414yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2411yescharacteristic
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2411yescharacteristic
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2411yescharacteristic
1078C2×C22⋊C4C2411yescharacteristic
1079C2×C22⋊C4C2411yescharacteristic
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2412yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2411yescharacteristic
1128C2×C42—24no—
1129C2×C42—24no—
1130C2×C42—44no—
1131C2×C42—44no—
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2412yes—
1136C2×C42C2412yes—
1137C2×C42C2414yes—
1138C2×C42C2412yes—
1139C2×C42C2411yescharacteristic
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2414yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2411yescharacteristic
1147C2×C42C2411yescharacteristic
1148C2×C42C2411yescharacteristic
1149C2×C42C2412yes—
1150C2×C42C2414yes—
1151C2×C42C2414yes—
1152C2×C42C2412yes—
1153C2×C42C2414yes—
1154C2×C42C2412yes—
1155C2×C42C2414yes—
1156C2×C42C2412yes—
1157C2×C42C2411yescharacteristic
1158C2×C42C2411yescharacteristic
1159C2×C42C2411yescharacteristic
1160#95C2412yes—
1161#95C2411yescharacteristic
1162#95C2411yescharacteristic
1163#95C2411yescharacteristic
1164#95C2411yescharacteristic
1165#95C2411yescharacteristic
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2411yescharacteristic
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2412yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216C24C2512yes—
1217C24C2512yes—
1218C24C2512yes—
1219C24C2511yescharacteristic
1220C24C2511yescharacteristic
1221#41—416no—
1222#41—816no—
1223C2×Q8—22no—
1224C2×Q8—22no—
1225C2×Q8—24no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—24no—
1230C2×Q8—28no—
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—24no—
1234C2×Q8—22no—
1235C2×Q8—24no—
1236C2×Q8—44no—
1237C2×Q8—42no—
1238C2×Q8—44no—
1239C2×Q8—42no—
1240C2×Q8—44no—
1241C2×Q8—44no—
1242C2×Q8—44no—
1243C2×Q8H(5,𝔽2)14yes—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—22no—
1260C2×D4—22no—
1261C2×D4—24no—
1262C2×D4—22no—
1263C2×D4—22no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—22no—
1294C22×C4—24no—
1295C22×C4—24no—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—22no—
1299C22×C4—24no—
1300C22×C4—24no—
1301C22×C4—24no—
1302C22×C4—24no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—24no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—42no—
1317C22×C4—42no—
1318C22×C4—41no—
1319C22×C4—41no—
1320C22×C4—42no—
1321C22×C4—42no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—44no—
1325C22×C4—44no—
1326C22×C4—44no—
1327C22×C4—44no—
1328C22×C4—44no—
1329C22×C4—44no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—44no—
1333C22×C42−1+414yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2511yescharacteristic
1341C22×C4C2512yes—
1342C22×C4C2514yes—
1343C22×C4C2512yes—
1344C22×C4C2512yes—
1345C22×C4C2511yescharacteristic
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2514yes—
1351C22×C4C2512yes—
1352C22×C4C2514yes—
1353C22×C4C2514yes—
1354C22×C4C2511yescharacteristic
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2512yes—
1360C22×C4C2511yescharacteristic
1361C22×C4C2511yescharacteristic
1362C22×C4C2511yescharacteristic
1363C22×C4C2511yescharacteristic
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—22no—
1368C4⋊C4—24no—
1369C4⋊C4—24no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—22no—
1374C4⋊C4—24no—
1375C4⋊C4—22no—
1376C4⋊C4—24no—
1377C4⋊C4—22no—
1378C4⋊C4—24no—
1379C4⋊C4—22no—
1380C4⋊C4—22no—
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—28no—
1384C4⋊C4—22no—
1385C4⋊C4—28no—
1386C4⋊C4—28no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—24no—
1390C4⋊C4—28no—
1391C4⋊C4—28no—
1392C4⋊C4—24no—
1393C4⋊C4—24no—
1394C4⋊C4—22no—
1395C4⋊C4—22no—
1396C4⋊C4—24no—
1397C4⋊C4—22no—
1398C4⋊C4—24no—
1399C4⋊C4—28no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—24no—
1403C4⋊C4—44no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—44no—
1408C4⋊C4—42no—
1409C4⋊C4—44no—
1410C4⋊C4—44no—
1411C4⋊C4—42no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—44no—
1443C4⋊C42−1+414yes—
1444C22⋊C4—22no—
1445C22⋊C4—24no—
1446C22⋊C4—24no—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—28no—
1451C22⋊C4—24no—
1452C22⋊C4—24no—
1453C22⋊C4—22no—
1454C22⋊C4—22no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—28no—
1458C22⋊C4—24no—
1459C22⋊C4—24no—
1460C22⋊C4—24no—
1461C22⋊C4—22no—
1462C22⋊C4—22no—
1463C22⋊C4—24no—
1464C22⋊C4—24no—
1465C22⋊C4—24no—
1466C22⋊C4—28no—
1467C22⋊C4—24no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—42no—
1474C22⋊C4—42no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—42no—
1483C22⋊C4—42no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—42no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—44no—
1503C22⋊C4—42no—
1504C22⋊C4—42no—
1505C22⋊C42−1+414yes—
1506C42—22no—
1507C42—22no—
1508C42—22no—
1509C42—22no—
1510C42—22no—
1511C42—22no—
1512C42—22no—
1513C42—24no—
1514C42—24no—
1515C42—24no—
1516C42—24no—
1517C42—28no—
1518C42—24no—
1519C42—28no—
1520C42—22no—
1521C42—22no—
1522C42—22no—
1523C42—42no—
1524C42—42no—
1525C42—42no—
1526C42—42no—
1527C42—44no—
1528C42—44no—
1529C42—44no—
1530C42—44no—
1531C42—41no—
1532C42H(5,𝔽2)14yes—
1533C42H(5,𝔽2)14yes—
1534C23—21no—
1535C23—21no—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—22no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—22no—
1553C23—22no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—22no—
1562C23—22no—
1563C23—22no—
1564C23—22no—
1565C23—22no—
1566C23—22no—
1567C23C2×2−1+412yes—
1568C23C2×2−1+412yes—
1569C23C2611yescharacteristic
1570Q8—28no—
1571Q8—44no—
1572Q8—48no—
1573Q8—44no—
1574Q8—88no—
1575Q8—84no—
1576Q8—164no—
1577D4—28no—
1578D4—48no—
1579D4—48no—
1580D4—44no—
1581D4—44no—
1582D4—44no—
1583D4—84no—
1584D4—84no—
1585D4—84no—
1586D4—84no—
1587D4—84no—
1588D4—84no—
1589D4—164no—
1590D4—164no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—28no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—24no—
1620C2×C4—22no—
1621C2×C4—24no—
1622C2×C4—24no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—22no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—24no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—24no—
1652C2×C4—22no—
1653C2×C4—21no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—21no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—21no—
1663C2×C4—24no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—24no—
1667C2×C4—24no—
1668C2×C4—48no—
1669C2×C4—44no—
1670C2×C4—48no—
1671C2×C4—44no—
1672C2×C4—44no—
1673C2×C4—48no—
1674C2×C4—48no—
1675C2×C4—44no—
1676C2×C4—44no—
1677C2×C4—48no—
1678C2×C4—84no—
1679C2×C4—84no—
1680C2×C4—164no—
1681C2×C4—164no—
1682C2×C4—164no—
1683C2×C4C2×H(5,𝔽2)12yes—
1684C2×C4C2×H(5,𝔽2)12yes—
1685C2×C4C2×H(5,𝔽2)14yes—
1686C2×C4C2×H(5,𝔽2)12yes—
1687C2×C4C2×H(5,𝔽2)12yes—
1688C2×C4C2×H(5,𝔽2)12yes—
1689C2×C4C2×H(5,𝔽2)12yes—
1690C2×C4C2×H(5,𝔽2)12yes—
1691C2×C4C2×2−1+412yes—
1692C2×C4C2×2−1+414yes—
1693C2×C4C2×2−1+412yes—
1694C2×C4C2×2−1+412yes—
1695C2×C4C2×2−1+412yes—
1696C2×C4C2×2−1+412yes—
1697C22—22no—
1698C22—22no—
1699C22—22no—
1700C22—22no—
1701C22—22no—
1702C22—22no—
1703C22—41no—
1704C22—41no—
1705C22—41no—
1706C22—41no—
1707C22—41no—
1708C22—41no—
1709C22—41no—
1710C22—41no—
1711C22—42no—
1712C22—42no—
1713C22—42no—
1714C22—42no—
1715C22—42no—
1716C22—42no—
1717C22—42no—
1718C22—42no—
1719C22—42no—
1720C22—42no—
1721C22—42no—
1722C22—42no—
1723C22—42no—
1724C22—42no—
1725C22—42no—
1726C22—42no—
1727C22—42no—
1728C22—42no—
1729C22—42no—
1730C22—42no—
1731C22—42no—
1732C22C22×H(5,𝔽2)11yescharacteristic
1733C22C22×H(5,𝔽2)11yescharacteristic
1734C22C22×H(5,𝔽2)11yescharacteristic
1735C22C22×2−1+411yescharacteristic
1736C22C22×2−1+411yescharacteristic
1737C22C22×2−1+411yescharacteristic
1738C22H(7,𝔽2)11yescharacteristic
1739C4—22no—
1740C4—24no—
1741C4—22no—
1742C4—24no—
1743C4—22no—
1744C4—22no—
1745C4—22no—
1746C4—22no—
1747C4—41no—
1748C4—42no—
1749C4—42no—
1750C4—42no—
1751C4—41no—
1752C4—41no—
1753C4—42no—
1754C4—44no—
1755C4—42no—
1756C4—42no—
1757C4—42no—
1758C4—44no—
1759C4—44no—
1760C4—42no—
1761C4—44no—
1762C4—41no—
1763C4—41no—
1764C4—42no—
1765C4—42no—
1766C4—42no—
1767C4#353614yes—
1768C4#354814yes—
1769C2—42no—
1770C2—42no—
1771C2—82no—
1772C2—82no—
1773C2—82no—
1774C2C2×#353611yescharacteristic
1775C2C2×#354811yescharacteristic
1776C2#6283311yescharacteristic
1777C2#6291611yescharacteristic
1778C2#6294311yescharacteristic
1779C2#6294411yescharacteristic
1780C2#6301611yescharacteristic
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. #59653C2semidirect
2. #59322C2semidirect
3. #59314C2semidirect
4. #57284C2semidirect
5. #55383C2semidirect
6. #54941C2semidirect
7. #53016C2semidirect
8. #52959C2semidirect
9. #49852C2semidirect
10. #45676C2semidirect
11. #45501C2semidirect
12. #45112C2semidirect
13. #44915C2semidirect
14. #42849C2semidirect
15. #42794C2semidirect
16. #42641C2semidirect
17. #42449C2semidirect
18. #40054C2semidirect
19. #39691C2semidirect
20. #39598C2semidirect
21. #39468C2semidirect
22. #39377C2semidirect
23. #39136C2semidirect
24. #39127C2semidirect
25. #37781C2semidirect
26. #37620C2semidirect
27. #37307C2semidirect
28. #37299C2semidirect
29. #36445C2semidirect
30. #36180C2semidirect
31. #36134C2semidirect
32. #35273C2semidirect
33. #35170C2semidirect
34. #34889C2semidirect
35. #34724C2semidirect

Maximal subgroups

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

subgroupindex
#596532
#593222
#593142
#572842
#553832
#549412
#530162
#529592
#498522
#456762
#455012
#451122
#449152
#428492
#427942
#426412
#424492
#400542
#396912
#395982
#394682
#393772
#391362
#391272
#377812
#376202
#373072
#372992
#364452
#361802
#361342
#352732
#351702
#348892
#347242