Finite Group Databasebeta

← #8429439

Subgroups — #8429439

Order 512.

4872 conjugacy classes of subgroups.

The subgroup lattice has 1758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59809C212yesmaximal, complemented
3#59401C212yesmaximal, complemented
4#59314C211yesmaximal, characteristic, complemented
5#59234C211yesmaximal, characteristic, complemented
6#56697C214yesmaximal, complemented
7#55834C214yesmaximal, complemented
8#53137C212yesmaximal, complemented
9#53122C212yesmaximal, complemented
10#53094C212yesmaximal, complemented
11#53048C212yesmaximal, complemented
12#52502C214yesmaximal, complemented
13#42810C212yesmaximal, complemented
14#42806C212yesmaximal, complemented
15#42555C212yesmaximal, complemented
16#42547C212yesmaximal, complemented
17#40803C214yesmaximal, complemented
18#39690C212yesmaximal, complemented
19#39657C212yesmaximal, complemented
20#39220C212yesmaximal, complemented
21#39191C211yesmaximal, characteristic, complemented
22#39124C211yesmaximal, characteristic, complemented
23#39047C212yesmaximal, complemented
24#38976C211yesmaximal, characteristic, complemented
25#38911C211yesmaximal, characteristic, complemented
26#37631C211yesmaximal, characteristic, complemented
27#37620C211yesmaximal, characteristic, complemented
28#37521C212yesmaximal, complemented
29#37494C212yesmaximal, complemented
30#36444C211yesmaximal, characteristic, complemented
31#36274C211yesmaximal, characteristic, complemented
32#36189C211yesmaximal, characteristic, complemented
33#34976C211yesmaximal, characteristic, complemented
34#34727C211yesmaximal, characteristic, complemented
35#34724C211yesmaximal, characteristic, complemented
36C2×#554C2212yes—
37C2×D4×Q8C2212yes—
38C2×D4×Q8C2211yescharacteristic
39C2×D4×Q8C2211yescharacteristic
40C2×#548C2212yes—
41C2×#529C2211yescharacteristic
42C2×#529C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45#2859C2211yescharacteristic
46#2857C2212yes—
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2855C2212yes—
50#2838C2214yes—
51#2838C2214yes—
52#2838C2214yes—
53#2836C2214yes—
54#2836C2214yes—
55#2832C2214yes—
56#2831C2214yes—
57#2827C2214yes—
58#2826C2214yes—
59#2824C2214yes—
60#2823C2214yes—
61#2820C2214yes—
62#2820C2214yes—
63#2816C2214yes—
64#2807C2214yes—
65#2786C2214yes—
66#2778C2214yes—
67#2778C2214yes—
68#2777C2214yes—
69#2775C2214yes—
70#2766C2214yes—
71#2764C2214yes—
72#2762C2214yes—
73#2755C2214yes—
74#2753C2214yes—
75#2752C2214yes—
76#2749C2214yes—
77#2744C2214yes—
78#2743C2214yes—
79#2742C2214yes—
80#2732C2214yes—
81#2731C2214yes—
82#2730C2214yes—
83#2730C2214yes—
84#2729C2214yes—
85#2723C2214yes—
86#2720C2214yes—
87#2719C2214yes—
88#2713C2214yes—
89#2711C2214yes—
90#2711C2214yes—
91#2704C2214yes—
92#2696C2214yes—
93#2692C2214yes—
94#2692C2214yes—
95#2692C2214yes—
96#2689C2214yes—
97#2687C2214yes—
98#2683C2214yes—
99#2676C2214yes—
100#2676C2214yes—
101#2665C2214yes—
102#2653C2214yes—
103#2650C2214yes—
104#2649C2214yes—
105#2645C2212yes—
106#2645C2212yes—
107#2643C2214yes—
108#2640C2212yes—
109#2639C2214yes—
110#2638C2214yes—
111#2635C2214yes—
112#2633C2214yes—
113#2631C2214yes—
114#2629C2212yes—
115#2629C2212yes—
116#2628C2212yes—
117#2628C2212yes—
118#2625C2212yes—
119#2625C2212yes—
120#2624C2212yes—
121#2620C2212yes—
122#2620C2212yes—
123#2618C2214yes—
124#2609C2214yes—
125#2600C2214yes—
126#2589C2214yes—
127#2582C2211yescharacteristic
128#2582C2211yescharacteristic
129#2576C2214yes—
130#2573C2214yes—
131#2570C2212yes—
132#2568C2211yescharacteristic
133#2563C2212yes—
134#2556C2214yes—
135#2551C2212yes—
136#2551C2211yescharacteristic
137#2550C2212yes—
138#2549C2214yes—
139#2547C2212yes—
140#2547C2212yes—
141#2547C2211yescharacteristic
142#2542C2212yes—
143#2540C2212yes—
144#2538C2212yes—
145#2538C2211yescharacteristic
146#2538C2211yescharacteristic
147#2538C2211yescharacteristic
148#2537C2211yescharacteristic
149#2537C2211yescharacteristic
150#2537C2212yes—
151#2535C2214yes—
152#2535C2212yes—
153#2520C2214yes—
154#2514C2212yes—
155#2513C2212yes—
156#2511C2212yes—
157#2511C2212yes—
158#2508C2212yes—
159#2507C2212yes—
160#2506C2212yes—
161#2506C2212yes—
162#2506C2212yes—
163#2497C2212yes—
164#2497C2212yes—
165#2495C2212yes—
166#2494C2212yes—
167#2492C2212yes—
168#2492C2212yes—
169#2492C2212yes—
170#2492C2214yes—
171#2491C2212yes—
172#2489C2212yes—
173#2487C2212yes—
174#2487C2212yes—
175#2487C2212yes—
176#2485C2212yes—
177#2485C2212yes—
178#2485C2212yes—
179#2479C2212yes—
180#2478C2212yes—
181#2474C2214yes—
182#2471C2212yes—
183#2470C2212yes—
184#2467C2212yes—
185#2466C2212yes—
186#2464C2214yes—
187#2456C2212yes—
188#2455C2212yes—
189#2454C2211yescharacteristic
190#2454C2214yes—
191#2453C2211yescharacteristic
192#2452C2212yes—
193#2452C2214yes—
194#2452C2212yes—
195#2451C2212yes—
196#2451C2212yes—
197#2450C2214yes—
198#2450C2214yes—
199#2450C2214yes—
200#2450C2214yes—
201#2449C2214yes—
202#2448C2212yes—
203#2448C2211yescharacteristic
204#2447C2212yes—
205#2447C2211yescharacteristic
206#2446C2212yes—
207#2444C2214yes—
208#2442C2212yes—
209#2441C2212yes—
210#2441C2211yescharacteristic
211#2441C2211yescharacteristic
212#2440C2212yes—
213#2440C2212yes—
214#2439C2212yes—
215#2438C2214yes—
216#2436C2212yes—
217#2432C2211yescharacteristic
218#2431C2211yescharacteristic
219#2429C2211yescharacteristic
220#2428C2211yescharacteristic
221#2428C2212yes—
222#2427C2214yes—
223#2427C2212yes—
224#2423C2212yes—
225#2423C2212yes—
226#2423C2211yescharacteristic
227#2422C2211yescharacteristic
228#2420C2212yes—
229#2417C2212yes—
230#2417C2212yes—
231#2417C2212yes—
232#2417C2212yes—
233#2416C2212yes—
234#2416C2212yes—
235#2416C2212yes—
236#2415C2214yes—
237#2415C2212yes—
238#2415C2212yes—
239#2415C2212yes—
240#2415C2211yescharacteristic
241#2414C2212yes—
242#2414C2211yescharacteristic
243#2409C2212yes—
244#2409C2212yes—
245#2409C2212yes—
246#2409C2212yes—
247#2409C2212yes—
248#2407C2212yes—
249#2407C2212yes—
250#2407C2211yescharacteristic
251#2407C2211yescharacteristic
252#2397C2212yes—
253#2395C2212yes—
254#2392C2214yes—
255#2392C2212yes—
256#2392C2212yes—
257#2369C2212yes—
258#2366C2212yes—
259#2364C2214yes—
260#2361C2212yes—
261#2360C2212yes—
262#2355C2211yescharacteristic
263#2354C2211yescharacteristic
264#2352C2212yes—
265Q8×C4⋊C4C2211yescharacteristic
266#2349C2212yes—
267D4×C4⋊C4C2211yescharacteristic
268#2347C2212yes—
269#2345C2212yes—
270Q8×C22⋊C4C2212yes—
271#2339C2212yes—
272#2335C2214yes—
273#2324C2212yes—
274#2324C2212yes—
275#2320C2212yes—
276#2310C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2211yescharacteristic
279C4×#127C2211yescharacteristic
280C4×C22⋊Q8C2211yescharacteristic
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×#123C2212yes—
285C4×#121C2212yes—
286C4×#121C2212yes—
287C4×#121C2212yes—
288C4×#121C2212yes—
289C4×#121C2211yescharacteristic
290C4×#121C2211yescharacteristic
291#2296C2212yes—
292#2295C2211yescharacteristic
293C2×#391C2212yes—
294#2293C2211yescharacteristic
295#2290C2212yes—
296#2285C2211yescharacteristic
297C2×#384C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C23×Q8C2312yes—
302C23×Q8C2312yes—
303#554—48no—
304D4×Q8—44no—
305D4×Q8—44no—
306D4×Q8—48no—
307#548—48no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2314yes—
315C2×#127C2311yescharacteristic
316#529—44no—
317#529—44no—
318C2×#126C2312yes—
319C2×#126C2312yes—
320C2×#125C2314yes—
321C2×#125C2311yescharacteristic
322C2×#125C2311yescharacteristic
323C2×#125C2314yes—
324C2×#125C2312yes—
325C2×#124C2314yes—
326C2×#124C2311yescharacteristic
327C2×#124C2311yescharacteristic
328C2×#124C2312yes—
329C2×#124C2314yes—
330C2×#123C2312yes—
331C2×#123C2312yes—
332C2×#123C2312yes—
333C2×C22⋊Q8C2311yescharacteristic
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×#121C2312yes—
353C2×#121C2311yescharacteristic
354C2×#121C2312yes—
355C2×#121C2314yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2311yescharacteristic
360C2×#121C2311yescharacteristic
361C2×#121C2311yescharacteristic
362C2×#121C2314yes—
363C2×#121C2314yes—
364C4×#41—44no—
365C4×#41—44no—
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×Q8C2311yescharacteristic
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2314yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2314yes—
398C2×#117C2312yes—
399C2×#117C2312yes—
400C2×#117C2312yes—
401C2×#117C2312yes—
402C2×#117C2312yes—
403C2×#117C2312yes—
404C2×#117C2311yescharacteristic
405C2×#117C2311yescharacteristic
406C2×#117C2312yes—
407C22×C4⋊C4C2312yes—
408C22×C4⋊C4C2312yes—
409C22×C4⋊C4C2312yes—
410C22×C4⋊C4C2312yes—
411C22×C42C2311yescharacteristic
412C22×C42C2311yescharacteristic
413C22×C42C2312yes—
414C22×C42C2312yes—
415#401C2314yes—
416#401C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2312yes—
434#399C2314yes—
435#399C2314yes—
436#399C2312yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2312yes—
441#399C2312yes—
442#399C2314yes—
443#399C2312yes—
444#399C2312yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2312yes—
460#398C2312yes—
461#398C2312yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2312yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2312yes—
472#397C2314yes—
473#397C2312yes—
474#397C2312yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2312yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2312yes—
497#396C2314yes—
498#396C2312yes—
499#396C2312yes—
500#395C2314yes—
501#395C2314yes—
502#395C2314yes—
503#395C2314yes—
504#395C2314yes—
505#395C2314yes—
506#395C2314yes—
507#395C2314yes—
508#394C2312yes—
509#394C2312yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2312yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2312yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2312yes—
523#394C2314yes—
524#394C2314yes—
525#394C2312yes—
526#394C2314yes—
527#394C2314yes—
528#394C2312yes—
529#394C2312yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2314yes—
536#393C2314yes—
537#393C2314yes—
538#393C2314yes—
539#393C2314yes—
540#392C2312yes—
541#392C2312yes—
542#392C2314yes—
543#392C2312yes—
544#392C2312yes—
545#392C2314yes—
546#392C2314yes—
547#392C2312yes—
548#392C2312yes—
549#391C2311yescharacteristic
550#391C2312yes—
551#391C2311yescharacteristic
552#391C2311yescharacteristic
553#391C2312yes—
554#391C2312yes—
555#391C2314yes—
556#391C2312yes—
557#391C2314yes—
558#391C2312yes—
559#391C2312yes—
560#391C2314yes—
561#391C2312yes—
562#391C2312yes—
563#391C2312yes—
564#391C2314yes—
565#391C2312yes—
566#391C2312yes—
567#391C2314yes—
568#391C2312yes—
569#391C2314yes—
570#391C2314yes—
571#391C2311yescharacteristic
572#391C2314yes—
573#391C2314yes—
574#391C2311yescharacteristic
575#391C2311yescharacteristic
576#390C2311yescharacteristic
577#390C2311yescharacteristic
578#390C2312yes—
579#390C2312yes—
580#390C2314yes—
581#390C2311yescharacteristic
582#390C2314yes—
583#390C2314yes—
584#390C2312yes—
585#390C2312yes—
586#390C2312yes—
587#390C2312yes—
588#390C2314yes—
589#390C2311yescharacteristic
590#390C2311yescharacteristic
591#390C2312yes—
592#390C2311yescharacteristic
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2314yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2314yes—
611#389C2311yescharacteristic
612#389C2312yes—
613#389C2312yes—
614#389C2311yescharacteristic
615#389C2314yes—
616#389C2312yes—
617#389C2312yes—
618#389C2312yes—
619#389C2312yes—
620#389C2314yes—
621#389C2314yes—
622#389C2312yes—
623#389C2312yes—
624#389C2314yes—
625#389C2311yescharacteristic
626#389C2311yescharacteristic
627#389C2311yescharacteristic
628#389C2312yes—
629#389C2311yescharacteristic
630#389C2311yescharacteristic
631#389C2311yescharacteristic
632#389C2312yes—
633#389C2312yes—
634#389C2312yes—
635#388C2312yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2312yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2312yes—
645#388C2314yes—
646#388C2312yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2312yes—
655#388C2314yes—
656#388C2312yes—
657#388C2312yes—
658#388C2312yes—
659#388C2312yes—
660#388C2312yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2314yes—
668#387C2314yes—
669#387C2312yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2312yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2312yes—
682#387C2312yes—
683#387C2312yes—
684#387C2312yes—
685#387C2312yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2312yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2312yes—
704#386C2314yes—
705#386C2312yes—
706#386C2312yes—
707#386C2312yes—
708#386C2312yes—
709#386C2312yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2312yes—
717#385C2312yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2312yes—
724#385C2314yes—
725#385C2312yes—
726#385C2312yes—
727#385C2314yes—
728#385C2312yes—
729#385C2312yes—
730#385C2312yes—
731#385C2312yes—
732#384C2311yescharacteristic
733#384C2311yescharacteristic
734#384C2311yescharacteristic
735#384C2312yes—
736#384C2311yescharacteristic
737#384C2311yescharacteristic
738#384C2312yes—
739#384C2312yes—
740#384C2312yes—
741#383C2314yes—
742#383C2314yes—
743#382C2314yes—
744#382C2314yes—
745#382C2312yes—
746#382C2312yes—
747#382C2312yes—
748#382C2312yes—
749#381C2314yes—
750#381C2314yes—
751#381C2314yes—
752#381C2312yes—
753#380C2311yescharacteristic
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2314yes—
759#380C2312yes—
760#380C2312yes—
761#380C2314yes—
762#380C2312yes—
763#380C2314yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2314yes—
768#380C2312yes—
769#380C2314yes—
770#380C2312yes—
771#380C2312yes—
772#380C2312yes—
773#380C2311yescharacteristic
774#380C2311yescharacteristic
775#380C2312yes—
776#380C2312yes—
777#380C2312yes—
778#380C2311yescharacteristic
779#380C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2314yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2311yescharacteristic
814C4×C22⋊C4C2311yescharacteristic
815#376C2312yes—
816C2×#95C2314yes—
817C2×#95C2314yes—
818C43C2311yescharacteristic
819C2×#41—24no—
820C2×#41—24no—
821C2×#41—42no—
822C2×#41—42no—
823C2×#41—42no—
824C2×#41—42no—
825C22×Q8—28no—
826C22×Q8—44no—
827C22×Q8—44no—
828C22×Q8—44no—
829C22×Q8—44no—
830C22×Q8—44no—
831C22×Q8C2411yescharacteristic
832C22×Q8C2411yescharacteristic
833C22×Q8C2412yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2414yes—
836C22×Q8C2414yes—
837C22×Q8C2414yes—
838C22×D4C2411yescharacteristic
839C22×D4C2411yescharacteristic
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2411yescharacteristic
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2414yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2412yes—
865C23×C4C2414yes—
866C23×C4C2414yes—
867C23×C4C2414yes—
868C23×C4C2414yes—
869C4⋊Q8—24no—
870C4⋊Q8—24no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874C4⋊Q8—44no—
875C4⋊Q8—48no—
876#127—24no—
877#126—44no—
878#126—44no—
879#125—42no—
880#125—42no—
881#125—48no—
882#125—84no—
883#125—82no—
884#124—42no—
885#124—42no—
886#124—48no—
887#124—44no—
888#124—84no—
889#123—28no—
890#123—44no—
891#123—44no—
892C22⋊Q8—28no—
893C22⋊Q8—24no—
894C22⋊Q8—48no—
895C22⋊Q8—48no—
896C22⋊Q8—48no—
897C22⋊Q8—48no—
898C22⋊Q8—48no—
899C22⋊Q8—48no—
900C22⋊Q8—44no—
901C22⋊Q8—42no—
902C22⋊Q8—44no—
903C22⋊Q8—42no—
904C22⋊Q8—42no—
905C22⋊Q8—44no—
906C22⋊Q8—48no—
907C22⋊Q8—44no—
908C22⋊Q8—44no—
909C22⋊Q8—44no—
910C22⋊Q8—84no—
911#121—24no—
912#121—28no—
913#121—28no—
914#121—44no—
915#121—44no—
916#121—42no—
917#121—42no—
918#121—42no—
919#121—44no—
920#121—48no—
921#121—84no—
922#121—84no—
923C4×Q8—28no—
924C4×Q8—24no—
925C4×Q8—24no—
926C4×Q8—24no—
927C4×Q8—42no—
928C4×Q8—42no—
929C4×Q8—44no—
930C4×D4—24no—
931C4×D4—24no—
932C4×D4—24no—
933C4×D4—24no—
934C4×D4—48no—
935C4×D4—44no—
936C4×D4—42no—
937C4×D4—42no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—42no—
941C4×D4—44no—
942C4×D4—42no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—44no—
947C4×D4—48no—
948C4×D4—44no—
949C4×D4—44no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—48no—
954C4×D4—84no—
955#117—44no—
956#117—44no—
957#117—44no—
958#117—44no—
959#117—44no—
960#117—44no—
961#117—42no—
962#117—42no—
963#117—82no—
964C2×C4⋊C4—44no—
965C2×C4⋊C4—44no—
966C2×C4⋊C4—44no—
967C2×C4⋊C4—82no—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2411yescharacteristic
1079C2×C22⋊C4C2411yescharacteristic
1080C2×C22⋊C4C2411yescharacteristic
1081C2×C22⋊C4C2411yescharacteristic
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2411yescharacteristic
1100C2×C42—24no—
1101C2×C42—24no—
1102C2×C42—44no—
1103C2×C42—44no—
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2414yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2414yes—
1124C2×C42C2414yes—
1125C2×C42C2414yes—
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2414yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131#95C2412yes—
1132#95C2412yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2411yescharacteristic
1144#95C2411yescharacteristic
1145#95C2411yescharacteristic
1146#95C2411yescharacteristic
1147#95C2411yescharacteristic
1148#95C2411yescharacteristic
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197C24C2512yes—
1198C24C2512yes—
1199C24C2511yescharacteristic
1200C24C2512yes—
1201C24C2511yescharacteristic
1202#41—416no—
1203#41—416no—
1204C2×Q8—22no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—24no—
1208C2×Q8—24no—
1209C2×Q8—22no—
1210C2×Q8—28no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—22no—
1214C2×Q8—22no—
1215C2×Q8—24no—
1216C2×Q8—44no—
1217C2×Q8—44no—
1218C2×Q8—44no—
1219C2×Q8—44no—
1220C2×Q8—44no—
1221C2×Q8—44no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8—816no—
1225C2×Q8—816no—
1226C2×Q8H(5,𝔽2)14yes—
1227C2×D4—22no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—28no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—24no—
1240C2×D4—22no—
1241C2×D4—24no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—42no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—42no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C2×D4—44no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—44no—
1267C2×D4—42no—
1268C2×D42−1+414yes—
1269C22×C4—22no—
1270C22×C4—24no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—24no—
1278C22×C4—24no—
1279C22×C4—22no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—24no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—24no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—28no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—41no—
1302C22×C4—41no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—42no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—42no—
1311C22×C4—42no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4—44no—
1315C22×C4—44no—
1316C22×C4—44no—
1317C22×C4—44no—
1318C22×C4—44no—
1319C22×C4—44no—
1320C22×C4C2511yescharacteristic
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2514yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2514yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2511yescharacteristic
1336C22×C4C2512yes—
1337C22×C4C2514yes—
1338C22×C4C2511yescharacteristic
1339C22×C4C2514yes—
1340C22×C4C2512yes—
1341C22×C4C2512yes—
1342C22×C4C2511yescharacteristic
1343C22×C4C2511yescharacteristic
1344C22×C4C2512yes—
1345C22×C4C2511yescharacteristic
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2511yescharacteristic
1349C22×C4C2511yescharacteristic
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—22no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—28no—
1363C4⋊C4—22no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—28no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—22no—
1378C4⋊C4—24no—
1379C4⋊C4—22no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—42no—
1394C4⋊C4—42no—
1395C4⋊C4—41no—
1396C4⋊C4—41no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—44no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—44no—
1404C4⋊C4—42no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—44no—
1408C4⋊C4—44no—
1409C4⋊C4—42no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—42no—
1416C4⋊C4—44no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4—42no—
1420C4⋊C4—44no—
1421C22⋊C4—28no—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—24no—
1425C22⋊C4—24no—
1426C22⋊C4—24no—
1427C22⋊C4—28no—
1428C22⋊C4—24no—
1429C22⋊C4—22no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C22⋊C4—41no—
1445C22⋊C4—41no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—41no—
1450C22⋊C4—41no—
1451C22⋊C4—42no—
1452C22⋊C4—44no—
1453C22⋊C4—42no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—44no—
1458C22⋊C4—44no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—44no—
1462C22⋊C4—42no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—42no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—44no—
1472C22⋊C4—44no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C42−1+414yes—
1482C42—22no—
1483C42—22no—
1484C42—22no—
1485C42—22no—
1486C42—22no—
1487C42—22no—
1488C42—24no—
1489C42—24no—
1490C42—24no—
1491C42—28no—
1492C42—24no—
1493C42—22no—
1494C42—22no—
1495C42—22no—
1496C42—22no—
1497C42—24no—
1498C42—22no—
1499C42—42no—
1500C42—42no—
1501C42—42no—
1502C42—42no—
1503C42—44no—
1504C42—44no—
1505C42—44no—
1506C42—44no—
1507C42—41no—
1508C42H(5,𝔽2)14yes—
1509C23—21no—
1510C23—22no—
1511C23—22no—
1512C23—21no—
1513C23—21no—
1514C23—22no—
1515C23—21no—
1516C23—22no—
1517C23—21no—
1518C23—22no—
1519C23—22no—
1520C23—21no—
1521C23—22no—
1522C23—22no—
1523C23—22no—
1524C23—21no—
1525C23—21no—
1526C23—22no—
1527C23—21no—
1528C23—22no—
1529C23—22no—
1530C23—21no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—22no—
1535C23—21no—
1536C23—22no—
1537C23—22no—
1538C23—21no—
1539C23—21no—
1540C23—22no—
1541C23—22no—
1542C23C2×2−1+414yes—
1543C23C2×2−1+412yes—
1544C23C2611yescharacteristic
1545Q8—28no—
1546Q8—44no—
1547Q8—44no—
1548Q8—48no—
1549Q8—88no—
1550Q8—88no—
1551Q8—164no—
1552D4—28no—
1553D4—48no—
1554D4—48no—
1555D4—48no—
1556D4—44no—
1557D4—48no—
1558D4—44no—
1559D4—44no—
1560D4—84no—
1561D4—84no—
1562D4—88no—
1563D4—84no—
1564D4—88no—
1565D4—84no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—24no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—24no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—22no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—24no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—24no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—24no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—24no—
1635C2×C4—22no—
1636C2×C4—24no—
1637C2×C4—22no—
1638C2×C4—24no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—44no—
1647C2×C4—44no—
1648C2×C4—48no—
1649C2×C4—48no—
1650C2×C4—44no—
1651C2×C4—48no—
1652C2×C4—44no—
1653C2×C4—44no—
1654C2×C4—48no—
1655C2×C4—48no—
1656C2×C4—44no—
1657C2×C4—84no—
1658C2×C4—84no—
1659C2×C4—88no—
1660C2×C4—88no—
1661C2×C4—164no—
1662C2×C4—164no—
1663C2×C4C2×H(5,𝔽2)12yes—
1664C2×C4C2×H(5,𝔽2)14yes—
1665C2×C4C2×H(5,𝔽2)12yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4C2×H(5,𝔽2)12yes—
1668C2×C4C2×2−1+412yes—
1669C2×C4C2×2−1+412yes—
1670C2×C4C2×2−1+412yes—
1671C2×C4#58512yes—
1672C2×C4#58512yes—
1673C22—24no—
1674C22—24no—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—24no—
1679C22—41no—
1680C22—42no—
1681C22—41no—
1682C22—42no—
1683C22—42no—
1684C22—41no—
1685C22—42no—
1686C22—41no—
1687C22—41no—
1688C22—42no—
1689C22—42no—
1690C22—42no—
1691C22—41no—
1692C22—42no—
1693C22—41no—
1694C22—42no—
1695C22—42no—
1696C22—42no—
1697C22—42no—
1698C22—41no—
1699C22—41no—
1700C22—42no—
1701C22—42no—
1702C22—42no—
1703C22—42no—
1704C22—41no—
1705C22—42no—
1706C22—42no—
1707C22—41no—
1708C22C22×H(5,𝔽2)11yescharacteristic
1709C22C22×H(5,𝔽2)11yescharacteristic
1710C22C22×2−1+411yescharacteristic
1711C22C22×2−1+411yescharacteristic
1712C22C2×#58511yescharacteristic
1713C22C2×#58511yescharacteristic
1714C22H(7,𝔽2)11yescharacteristic
1715C4—22no—
1716C4—22no—
1717C4—22no—
1718C4—24no—
1719C4—41no—
1720C4—42no—
1721C4—41no—
1722C4—42no—
1723C4—42no—
1724C4—42no—
1725C4—41no—
1726C4—41no—
1727C4—44no—
1728C4—42no—
1729C4—44no—
1730C4—42no—
1731C4—41no—
1732C4—42no—
1733C4—42no—
1734C4—42no—
1735C4—44no—
1736C4—41no—
1737C4—41no—
1738C4—41no—
1739C4—42no—
1740C4—42no—
1741C4—42no—
1742C4—44no—
1743C4#354114yes—
1744C4#354214yes—
1745C2—44no—
1746C2—42no—
1747C2—81no—
1748C2—82no—
1749C2—82no—
1750C2C2×#354211yescharacteristic
1751C2C2×#354111yescharacteristic
1752C2#6276111yescharacteristic
1753C2#6292311yescharacteristic
1754C2#6294411yescharacteristic
1755C2#6295111yescharacteristic
1756C2#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. #59817C2semidirect
2. #59809C2semidirect
3. #59401C2semidirect
4. #59314C2semidirect
5. #59234C2semidirect
6. #56697C2semidirect
7. #55834C2semidirect
8. #53137C2semidirect
9. #53122C2semidirect
10. #53094C2semidirect
11. #53048C2semidirect
12. #52502C2semidirect
13. #42810C2semidirect
14. #42806C2semidirect
15. #42555C2semidirect
16. #42547C2semidirect
17. #40803C2semidirect
18. #39690C2semidirect
19. #39657C2semidirect
20. #39220C2semidirect
21. #39191C2semidirect
22. #39124C2semidirect
23. #39047C2semidirect
24. #38976C2semidirect
25. #38911C2semidirect
26. #37631C2semidirect
27. #37620C2semidirect
28. #37521C2semidirect
29. #37494C2semidirect
30. #36444C2semidirect
31. #36274C2semidirect
32. #36189C2semidirect
33. #34976C2semidirect
34. #34727C2semidirect
35. #34724C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#598092
#594012
#593142
#592342
#566972
#558342
#531372
#531222
#530942
#530482
#525022
#428102
#428062
#425552
#425472
#408032
#396902
#396572
#392202
#391912
#391242
#390472
#389762
#389112
#376312
#376202
#375212
#374942
#364442
#362742
#361892
#349762
#347272
#347242