Finite Group Databasebeta

← #7979689

Subgroups — #7979689

Order 512.

5237 conjugacy classes of subgroups.

The subgroup lattice has 1789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59813C212yesmaximal, complemented
3#59323C212yesmaximal, complemented
4#59039C211yesmaximal, characteristic, complemented
5#59036C211yesmaximal, characteristic, complemented
6#51166C214yesmaximal, complemented
7#51059C214yesmaximal, complemented
8#46014C212yesmaximal, complemented
9#45610C212yesmaximal, complemented
10#45136C212yesmaximal, complemented
11#44980C212yesmaximal, complemented
12#44156C214yesmaximal, complemented
13#42810C212yesmaximal, complemented
14#42752C212yesmaximal, complemented
15#41734C214yesmaximal, complemented
16#40198C212yesmaximal, complemented
17#40030C212yesmaximal, complemented
18#39903C212yesmaximal, complemented
19#39771C211yesmaximal, characteristic, complemented
20#39524C212yesmaximal, complemented
21#39272C212yesmaximal, complemented
22#38911C211yesmaximal, characteristic, complemented
23#36596C211yesmaximal, characteristic, complemented
24#36465C211yesmaximal, characteristic, complemented
25#36410C211yesmaximal, characteristic, complemented
26#36211C212yesmaximal, complemented
27#36186C211yesmaximal, characteristic, complemented
28#36150C211yesmaximal, characteristic, complemented
29#35238C211yesmaximal, characteristic, complemented
30#35208C211yesmaximal, characteristic, complemented
31#35044C212yesmaximal, complemented
32#34947C211yesmaximal, characteristic, complemented
33#34727C211yesmaximal, characteristic, complemented
34#34474C212yesmaximal, complemented
35C4×#554C211yesmaximal, characteristic, complemented
36C2×#554C2211yescharacteristic
37C2×#553C2212yes—
38C2×#552C2212yes—
39C2×#550C2211yescharacteristic
40C2×D4×Q8C2211yescharacteristic
41C2×#548C2212yes—
42C2×#548C2212yes—
43C2×#533C2211yescharacteristic
44C2×#532C2211yescharacteristic
45C2×#529C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47#2863C2212yes—
48#2859C2212yes—
49#2858C2211yescharacteristic
50#2858C2212yes—
51#2857C2211yescharacteristic
52#2856C2212yes—
53#2856C2211yescharacteristic
54#2856C2212yes—
55#2854C2212yes—
56#2854C2212yes—
57#2850C2212yes—
58#2829C2214yes—
59#2820C2214yes—
60#2808C2214yes—
61#2796C2214yes—
62#2796C2214yes—
63#2786C2214yes—
64#2754C2214yes—
65#2751C2214yes—
66#2748C2214yes—
67#2741C2214yes—
68#2740C2214yes—
69#2727C2214yes—
70#2724C2214yes—
71#2715C2214yes—
72#2715C2214yes—
73#2714C2214yes—
74#2710C2214yes—
75#2707C2214yes—
76#2707C2214yes—
77#2703C2214yes—
78#2701C2214yes—
79#2698C2214yes—
80#2694C2214yes—
81#2692C2214yes—
82#2692C2214yes—
83#2692C2214yes—
84#2689C2214yes—
85#2688C2214yes—
86#2687C2214yes—
87#2686C2214yes—
88#2682C2214yes—
89#2676C2214yes—
90#2676C2214yes—
91#2671C2214yes—
92#2671C2214yes—
93#2666C2214yes—
94#2662C2214yes—
95#2654C2214yes—
96#2648C2214yes—
97#2648C2214yes—
98#2640C2212yes—
99#2633C2214yes—
100#2631C2214yes—
101#2625C2212yes—
102#2597C2214yes—
103#2592C2212yes—
104#2592C2214yes—
105#2589C2214yes—
106#2582C2211yescharacteristic
107#2580C2212yes—
108#2568C2211yescharacteristic
109#2567C2211yescharacteristic
110#2567C2211yescharacteristic
111#2566C2212yes—
112#2566C2212yes—
113#2565C2212yes—
114#2564C2214yes—
115#2563C2211yescharacteristic
116#2563C2211yescharacteristic
117#2559C2214yes—
118#2557C2214yes—
119#2557C2214yes—
120#2556C2214yes—
121#2554C2214yes—
122#2552C2211yescharacteristic
123#2550C2212yes—
124#2550C2212yes—
125#2548C2212yes—
126#2548C2211yescharacteristic
127#2547C2212yes—
128#2544C2212yes—
129#2543C2214yes—
130#2542C2211yescharacteristic
131#2542C2212yes—
132#2541C2212yes—
133#2541C2211yescharacteristic
134#2540C2212yes—
135#2540C2214yes—
136#2540C2212yes—
137#2540C2212yes—
138#2540C2214yes—
139#2538C2212yes—
140#2537C2212yes—
141#2535C2214yes—
142#2522C2214yes—
143#2519C2214yes—
144#2513C2214yes—
145#2513C2212yes—
146#2513C2212yes—
147#2513C2212yes—
148#2512C2212yes—
149#2512C2212yes—
150#2511C2212yes—
151#2507C2212yes—
152#2506C2212yes—
153#2506C2212yes—
154#2498C2214yes—
155#2492C2212yes—
156#2490C2214yes—
157#2490C2214yes—
158#2490C2212yes—
159#2490C2212yes—
160#2489C2212yes—
161#2485C2212yes—
162#2485C2212yes—
163#2479C2212yes—
164#2479C2214yes—
165#2477C2214yes—
166#2476C2214yes—
167#2471C2212yes—
168#2467C2212yes—
169#2465C2214yes—
170#2464C2214yes—
171#2462C2214yes—
172#2460C2214yes—
173#2459C2214yes—
174#2456C2212yes—
175#2456C2214yes—
176#2454C2212yes—
177#2454C2212yes—
178#2454C2211yescharacteristic
179#2454C2214yes—
180#2453C2212yes—
181#2450C2214yes—
182#2448C2212yes—
183#2448C2212yes—
184#2448C2211yescharacteristic
185#2447C2212yes—
186#2447C2212yes—
187#2447C2212yes—
188#2445C2212yes—
189#2445C2212yes—
190#2445C2212yes—
191#2441C2211yescharacteristic
192#2439C2212yes—
193#2431C2212yes—
194#2431C2211yescharacteristic
195#2430C2214yes—
196#2430C2214yes—
197#2428C2211yescharacteristic
198#2428C2212yes—
199#2427C2212yes—
200#2426C2212yes—
201#2426C2212yes—
202#2423C2212yes—
203#2423C2211yescharacteristic
204#2422C2212yes—
205#2420C2212yes—
206#2420C2214yes—
207#2420C2212yes—
208#2419C2214yes—
209#2417C2212yes—
210#2417C2212yes—
211#2417C2212yes—
212#2416C2212yes—
213#2416C2212yes—
214#2416C2212yes—
215#2415C2212yes—
216#2414C2212yes—
217#2414C2212yes—
218#2414C2211yescharacteristic
219#2414C2214yes—
220#2409C2212yes—
221#2409C2212yes—
222#2407C2212yes—
223#2407C2212yes—
224#2407C2212yes—
225#2407C2211yescharacteristic
226#2397C2212yes—
227#2396C2214yes—
228#2392C2212yes—
229#2379C2214yes—
230#2377C2214yes—
231#2370C2212yes—
232#2369C2211yescharacteristic
233#2368C2212yes—
234#2368C2212yes—
235#2368C2214yes—
236#2367C2212yes—
237#2367C2212yes—
238#2366C2211yescharacteristic
239#2365C2211yescharacteristic
240#2363C2212yes—
241#2363C2212yes—
242#2363C2212yes—
243#2363C2212yes—
244#2363C2214yes—
245#2362C2212yes—
246#2360C2211yescharacteristic
247#2360C2211yescharacteristic
248#2357C2214yes—
249#2355C2211yescharacteristic
250#2355C2212yes—
251#2354C2211yescharacteristic
252#2354C2212yes—
253#2354C2211yescharacteristic
254#2349C2212yes—
255#2349C2212yes—
256D4×C4⋊C4C2211yescharacteristic
257#2345C2211yescharacteristic
258#2345C2211yescharacteristic
259#2341C2212yes—
260Q8×C22⋊C4C2212yes—
261#2339C2212yes—
262#2337C2214yes—
263#2333C2214yes—
264#2333C2214yes—
265#2332C2214yes—
266#2330C2212yes—
267#2326C2212yes—
268#2324C2212yes—
269#2324C2212yes—
270#2320C2212yes—
271#2318C2214yes—
272#2310C2212yes—
273C4×C4⋊Q8C2211yescharacteristic
274C4×C4⋊Q8C2211yescharacteristic
275C4×#127C2212yes—
276C4×#127C2211yescharacteristic
277C4×#125C2212yes—
278C4×C22⋊Q8C2212yes—
279C4×C22⋊Q8C2212yes—
280C4×C22⋊Q8C2211yescharacteristic
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2211yescharacteristic
286C4×#121C2211yescharacteristic
287C4×#121C2212yes—
288#2297C2212yes—
289#2297C2212yes—
290#2295C2211yescharacteristic
291#2290C2212yes—
292#2285C2212yes—
293#2285C2212yes—
294C42×Q8C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2212yes—
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C22×#41C2312yes—
302C23×Q8C2312yes—
303#554—28no—
304#553—48no—
305#552—48no—
306#550—44no—
307D4×Q8—44no—
308#548—216no—
309#548—48no—
310#533—44no—
311#532—44no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×#127C2311yescharacteristic
317C2×#127C2312yes—
318C2×#127C2311yescharacteristic
319C2×#127C2312yes—
320#529—44no—
321C2×#126C2312yes—
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#125C2312yes—
325C2×#125C2312yes—
326C2×#125C2312yes—
327C2×#125C2311yescharacteristic
328C2×#125C2314yes—
329C2×#125C2314yes—
330C2×#124C2314yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2314yes—
335C2×#124C2312yes—
336C2×#124C2311yescharacteristic
337C2×#124C2314yes—
338C2×#123C2314yes—
339C2×#123C2312yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2314yes—
356C2×C22⋊Q8C2314yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2312yes—
361C2×#121C2311yescharacteristic
362C2×#121C2314yes—
363C2×#121C2312yes—
364C2×#121C2311yescharacteristic
365C2×#121C2312yes—
366C2×#121C2311yescharacteristic
367C2×#121C2314yes—
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2314yes—
373C2×#121C2314yes—
374C2×#121C2312yes—
375C2×#121C2314yes—
376C2×#121C2314yes—
377C4×#41—44no—
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2311yescharacteristic
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2314yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2312yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2311yescharacteristic
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2314yes—
412C2×#117C2312yes—
413C2×#117C2312yes—
414C2×#117C2312yes—
415C2×#117C2311yescharacteristic
416C2×#117C2312yes—
417C2×#117C2314yes—
418C2×#117C2312yes—
419C22×C4⋊C4C2311yescharacteristic
420C22×C4⋊C4C2311yescharacteristic
421C22×C4⋊C4C2311yescharacteristic
422C22×C4⋊C4C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2311yescharacteristic
425C22×C42C2312yes—
426C22×C42C2312yes—
427C22×C42C2312yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#399C2314yes—
434#399C2312yes—
435#399C2314yes—
436#399C2314yes—
437#399C2314yes—
438#399C2312yes—
439#399C2312yes—
440#399C2312yes—
441#399C2314yes—
442#399C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2312yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#396C2312yes—
479#396C2314yes—
480#396C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2314yes—
484#395C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2312yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2312yes—
494#394C2312yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#393C2314yes—
508#393C2314yes—
509#393C2314yes—
510#392C2314yes—
511#392C2312yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2312yes—
516#392C2314yes—
517#392C2312yes—
518#392C2312yes—
519#392C2312yes—
520#392C2314yes—
521#392C2314yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2311yescharacteristic
527#391C2312yes—
528#391C2312yes—
529#391C2314yes—
530#391C2312yes—
531#391C2314yes—
532#391C2312yes—
533#391C2312yes—
534#391C2312yes—
535#391C2314yes—
536#391C2312yes—
537#391C2314yes—
538#391C2311yescharacteristic
539#391C2314yes—
540#391C2311yescharacteristic
541#391C2311yescharacteristic
542#391C2312yes—
543#391C2312yes—
544#390C2311yescharacteristic
545#390C2312yes—
546#390C2311yescharacteristic
547#390C2312yes—
548#390C2314yes—
549#390C2312yes—
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2312yes—
555#390C2312yes—
556#390C2314yes—
557#390C2312yes—
558#390C2312yes—
559#390C2314yes—
560#390C2312yes—
561#390C2314yes—
562#390C2314yes—
563#390C2314yes—
564#390C2314yes—
565#390C2312yes—
566#390C2312yes—
567#390C2312yes—
568#390C2314yes—
569#390C2314yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2314yes—
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#390C2314yes—
578#390C2314yes—
579#390C2314yes—
580#390C2312yes—
581#390C2311yescharacteristic
582#390C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2311yescharacteristic
586#389C2311yescharacteristic
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2314yes—
600#389C2314yes—
601#389C2311yescharacteristic
602#389C2312yes—
603#389C2311yescharacteristic
604#389C2312yes—
605#389C2312yes—
606#389C2311yescharacteristic
607#389C2314yes—
608#389C2311yescharacteristic
609#389C2312yes—
610#389C2312yes—
611#389C2314yes—
612#389C2314yes—
613#389C2311yescharacteristic
614#389C2312yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2312yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2312yes—
643#388C2312yes—
644#388C2312yes—
645#388C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2314yes—
662#387C2314yes—
663#387C2312yes—
664#387C2312yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2312yes—
679#386C2312yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2312yes—
695#386C2314yes—
696#386C2312yes—
697#386C2312yes—
698#386C2312yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2312yes—
709#385C2312yes—
710#385C2312yes—
711#385C2312yes—
712#385C2312yes—
713#385C2312yes—
714#385C2312yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2312yes—
720#384C2312yes—
721#384C2311yescharacteristic
722#384C2311yescharacteristic
723#384C2311yescharacteristic
724#384C2312yes—
725#384C2312yes—
726#384C2312yes—
727#383C2314yes—
728#382C2312yes—
729#382C2312yes—
730#382C2312yes—
731#382C2314yes—
732#382C2312yes—
733#382C2314yes—
734#381C2314yes—
735#381C2314yes—
736#381C2314yes—
737#381C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2314yes—
743#380C2314yes—
744#380C2314yes—
745#380C2312yes—
746#380C2314yes—
747#380C2312yes—
748#380C2312yes—
749#380C2311yescharacteristic
750#380C2311yescharacteristic
751#380C2312yes—
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2311yescharacteristic
756#380C2311yescharacteristic
757#380C2314yes—
758#380C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815#376C2312yes—
816C2×#95C2312yes—
817C2×#95C2314yes—
818C2×#95C2312yes—
819C43C2312yes—
820C43C2311yescharacteristic
821C2×#41—28no—
822C2×#41—24no—
823C2×#41—44no—
824C2×#41—42no—
825C2×#41—42no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—44no—
829C2×#41—82no—
830C22×Q8—28no—
831C22×Q8—44no—
832C22×Q8—44no—
833C22×Q8C2412yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2411yescharacteristic
836C22×Q8C2412yes—
837C22×Q8C2412yes—
838C22×Q8C2414yes—
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2414yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2414yes—
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2411yescharacteristic
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2412yes—
869C23×C4C2411yescharacteristic
870C23×C4C2414yes—
871C23×C4C2414yes—
872C23×C4C2414yes—
873C23×C4C2412yes—
874C23×C4C2414yes—
875C4⋊Q8—24no—
876C4⋊Q8—24no—
877C4⋊Q8—24no—
878C4⋊Q8—44no—
879#127—24no—
880#127—44no—
881#127—42no—
882#127—44no—
883#126—44no—
884#126—48no—
885#126—48no—
886#125—28no—
887#125—28no—
888#125—42no—
889#125—44no—
890#125—48no—
891#125—84no—
892#124—216no—
893#124—28no—
894#124—48no—
895#124—44no—
896#124—42no—
897#124—44no—
898#124—44no—
899#124—84no—
900#123—44no—
901#123—48no—
902#123—48no—
903#123—84no—
904#123—84no—
905C22⋊Q8—24no—
906C22⋊Q8—24no—
907C22⋊Q8—28no—
908C22⋊Q8—216no—
909C22⋊Q8—28no—
910C22⋊Q8—28no—
911C22⋊Q8—28no—
912C22⋊Q8—48no—
913C22⋊Q8—48no—
914C22⋊Q8—42no—
915C22⋊Q8—44no—
916C22⋊Q8—44no—
917C22⋊Q8—44no—
918C22⋊Q8—44no—
919#121—28no—
920#121—24no—
921#121—28no—
922#121—216no—
923#121—28no—
924#121—48no—
925#121—48no—
926#121—44no—
927#121—48no—
928#121—42no—
929#121—42no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—48no—
934#121—44no—
935#121—48no—
936#121—82no—
937#121—84no—
938#121—84no—
939C4×Q8—24no—
940C4×Q8—24no—
941C4×Q8—24no—
942C4×Q8—44no—
943C4×Q8—42no—
944C4×Q8—44no—
945C4×Q8—44no—
946C4×Q8—44no—
947C4×Q8—82no—
948C4×Q8#4118yescomplemented
949C4×D4—24no—
950C4×D4—216no—
951C4×D4—28no—
952C4×D4—28no—
953C4×D4—24no—
954C4×D4—24no—
955C4×D4—24no—
956C4×D4—44no—
957C4×D4—42no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—48no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—48no—
971C4×D4—44no—
972C4×D4—42no—
973#117—44no—
974#117—44no—
975#117—42no—
976#117—44no—
977#117—44no—
978#117—48no—
979#117—44no—
980C2×C4⋊C4—24no—
981C2×C4⋊C4—24no—
982C2×C4⋊C4—24no—
983C2×C4⋊C4—24no—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2411yescharacteristic
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2411yescharacteristic
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2411yescharacteristic
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2411yescharacteristic
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C42—24no—
1112C2×C42—24no—
1113C2×C42—44no—
1114C2×C42—44no—
1115C2×C42—44no—
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2412yes—
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2411yescharacteristic
1129C2×C42C2412yes—
1130C2×C42C2411yescharacteristic
1131C2×C42C2412yes—
1132C2×C42C2414yes—
1133C2×C42C2412yes—
1134C2×C42C2414yes—
1135C2×C42C2414yes—
1136C2×C42C2414yes—
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2411yescharacteristic
1140C2×C42C2411yescharacteristic
1141C2×C42C2414yes—
1142C2×C42C2412yes—
1143C2×C42C2412yes—
1144C2×C42C2412yes—
1145C2×C42C2412yes—
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2411yescharacteristic
1166#95C2412yes—
1167#95C2412yes—
1168#95C2411yescharacteristic
1169#95C2412yes—
1170#95C2411yescharacteristic
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2411yescharacteristic
1175#95C2411yescharacteristic
1176#95C2412yes—
1177#95C2411yescharacteristic
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2412yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210C24C2512yes—
1211C24C2514yes—
1212C24C2512yes—
1213C24C2511yescharacteristic
1214C24C2511yescharacteristic
1215#41—416no—
1216#41—816no—
1217#41—816no—
1218C2×Q8—24no—
1219C2×Q8—24no—
1220C2×Q8—28no—
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—22no—
1224C2×Q8—24no—
1225C2×Q8—24no—
1226C2×Q8—24no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—42no—
1230C2×Q8—42no—
1231C2×Q8—42no—
1232C2×Q8—44no—
1233C2×Q8—44no—
1234C2×Q8—42no—
1235C2×Q8—816no—
1236C2×Q8C2×#4114yes—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—28no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—28no—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—28no—
1249C2×D4—28no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—28no—
1256C2×D4—24no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—22no—
1260C2×D4—24no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—44no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—44no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—44no—
1282C2×D4—42no—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—44no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—24no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—22no—
1311C22×C4—24no—
1312C22×C4—22no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—28no—
1316C22×C4—28no—
1317C22×C4—22no—
1318C22×C4—24no—
1319C22×C4—42no—
1320C22×C4—42no—
1321C22×C4—42no—
1322C22×C4—41no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—44no—
1328C22×C4—44no—
1329C22×C4—44no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—42no—
1333C22×C4—41no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—41no—
1338C22×C4—42no—
1339C22×C4—44no—
1340C22×C4—44no—
1341C22×C4—44no—
1342C22×C4—44no—
1343C22×C4—44no—
1344C22×C42−1+414yes—
1345C22×C4C2512yes—
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2512yes—
1352C22×C4C2511yescharacteristic
1353C22×C4C2512yes—
1354C22×C4C2514yes—
1355C22×C4C2511yescharacteristic
1356C22×C4C2514yes—
1357C22×C4C2511yescharacteristic
1358C22×C4C2512yes—
1359C22×C4C2512yes—
1360C22×C4C2512yes—
1361C22×C4C2512yes—
1362C22×C4C2514yes—
1363C22×C4C2512yes—
1364C22×C4C2511yescharacteristic
1365C22×C4C2511yescharacteristic
1366C22×C4C2512yes—
1367C22×C4C2511yescharacteristic
1368C22×C4C2511yescharacteristic
1369C22×C4C2512yes—
1370C22×C4C2511yescharacteristic
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2511yescharacteristic
1374C22×C4C2511yescharacteristic
1375C4⋊C4—24no—
1376C4⋊C4—24no—
1377C4⋊C4—22no—
1378C4⋊C4—22no—
1379C4⋊C4—24no—
1380C4⋊C4—28no—
1381C4⋊C4—22no—
1382C4⋊C4—24no—
1383C4⋊C4—24no—
1384C4⋊C4—24no—
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—24no—
1390C4⋊C4—22no—
1391C4⋊C4—22no—
1392C4⋊C4—24no—
1393C4⋊C4—24no—
1394C4⋊C4—28no—
1395C4⋊C4—24no—
1396C4⋊C4—28no—
1397C4⋊C4—22no—
1398C4⋊C4—24no—
1399C4⋊C4—28no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—22no—
1403C4⋊C4—24no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—22no—
1407C4⋊C4—22no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—41no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—44no—
1421C4⋊C4—44no—
1422C4⋊C4—44no—
1423C4⋊C4—42no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—42no—
1427C4⋊C4—44no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—42no—
1433C4⋊C4—42no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C4⋊C4—42no—
1437C4⋊C4C2×#4114yes—
1438C4⋊C4C2×#4118yes—
1439C4⋊C4H(5,𝔽2)14yes—
1440C22⋊C4—22no—
1441C22⋊C4—22no—
1442C22⋊C4—24no—
1443C22⋊C4—24no—
1444C22⋊C4—22no—
1445C22⋊C4—22no—
1446C22⋊C4—24no—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—28no—
1450C22⋊C4—28no—
1451C22⋊C4—28no—
1452C22⋊C4—28no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—28no—
1456C22⋊C4—28no—
1457C22⋊C4—22no—
1458C22⋊C4—28no—
1459C22⋊C4—24no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—42no—
1463C22⋊C4—44no—
1464C22⋊C4—42no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—41no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—42no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—44no—
1487C22⋊C4—42no—
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—42no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C42—22no—
1503C42—22no—
1504C42—22no—
1505C42—22no—
1506C42—22no—
1507C42—22no—
1508C42—24no—
1509C42—24no—
1510C42—24no—
1511C42—22no—
1512C42—24no—
1513C42—22no—
1514C42—24no—
1515C42—24no—
1516C42—24no—
1517C42—22no—
1518C42—42no—
1519C42—42no—
1520C42—42no—
1521C42—42no—
1522C42—42no—
1523C42—42no—
1524C42—44no—
1525C42—44no—
1526C42—44no—
1527C42—44no—
1528C42—42no—
1529C42—41no—
1530C42—41no—
1531C42—44no—
1532C42—42no—
1533C42C2×#4118yes—
1534C42C2×#4114yes—
1535C42H(5,𝔽2)14yes—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—22no—
1549C23—24no—
1550C23—22no—
1551C23—22no—
1552C23—22no—
1553C23—24no—
1554C23—22no—
1555C23—22no—
1556C23—24no—
1557C23—22no—
1558C23—24no—
1559C23—22no—
1560C23—24no—
1561C23—22no—
1562C23—22no—
1563C23—24no—
1564C23—22no—
1565C23—22no—
1566C23—22no—
1567C23—22no—
1568C23—24no—
1569C23C2×2−1+412yes—
1570C23#58512yes—
1571C23C2611yescharacteristic
1572Q8—28no—
1573Q8—48no—
1574Q8—48no—
1575Q8—44no—
1576Q8—84no—
1577Q8—88no—
1578D4—28no—
1579D4—48no—
1580D4—48no—
1581D4—44no—
1582D4—48no—
1583D4—44no—
1584D4—88no—
1585D4—84no—
1586D4—88no—
1587D4—88no—
1588D4—84no—
1589D4—84no—
1590D4—84no—
1591D4—88no—
1592D4—84no—
1593D4—88no—
1594D4—84no—
1595D4—164no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—28no—
1611C2×C4—22no—
1612C2×C4—24no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—21no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—24no—
1637C2×C4—24no—
1638C2×C4—24no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—24no—
1662C2×C4—22no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—24no—
1666C2×C4—24no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—21no—
1671C2×C4—22no—
1672C2×C4—22no—
1673C2×C4—21no—
1674C2×C4—48no—
1675C2×C4—44no—
1676C2×C4—48no—
1677C2×C4—44no—
1678C2×C4—44no—
1679C2×C4—48no—
1680C2×C4—48no—
1681C2×C4—44no—
1682C2×C4—84no—
1683C2×C4—84no—
1684C2×C4—84no—
1685C2×C4—82no—
1686C2×C4—88no—
1687C2×C4—88no—
1688C2×C4—84no—
1689C2×C4—88no—
1690C2×C4—164no—
1691C2×C4C22×#4112yes—
1692C2×C4C22×#4112yes—
1693C2×C4C22×#4114yes—
1694C2×C4C22×#4114yes—
1695C2×C4C22×#4112yes—
1696C2×C4C2×H(5,𝔽2)12yes—
1697C2×C4C2×H(5,𝔽2)14yes—
1698C2×C4C2×H(5,𝔽2)12yes—
1699C2×C4C2×H(5,𝔽2)12yes—
1700C2×C4C2×H(5,𝔽2)12yes—
1701C2×C4C2×2−1+412yes—
1702C2×C4C2×2−1+412yes—
1703C2×C4#58512yes—
1704C22—22no—
1705C22—22no—
1706C22—22no—
1707C22—22no—
1708C22—22no—
1709C22—22no—
1710C22—41no—
1711C22—41no—
1712C22—41no—
1713C22—41no—
1714C22—41no—
1715C22—41no—
1716C22—41no—
1717C22—41no—
1718C22—42no—
1719C22—42no—
1720C22—44no—
1721C22—42no—
1722C22—44no—
1723C22—42no—
1724C22—44no—
1725C22—42no—
1726C22—42no—
1727C22—44no—
1728C22—42no—
1729C22—42no—
1730C22—42no—
1731C22—42no—
1732C22—44no—
1733C22—44no—
1734C22—42no—
1735C22—42no—
1736C22—44no—
1737C22—42no—
1738C22—42no—
1739C22C23×#4111yescharacteristic
1740C22C22×H(5,𝔽2)11yescharacteristic
1741C22C22×H(5,𝔽2)11yescharacteristic
1742C22C22×2−1+411yescharacteristic
1743C22C2×#58511yescharacteristic
1744C22C2×#58511yescharacteristic
1745C22H(7,𝔽2)11yescharacteristic
1746C4—22no—
1747C4—24no—
1748C4—22no—
1749C4—24no—
1750C4—22no—
1751C4—24no—
1752C4—22no—
1753C4—41no—
1754C4—42no—
1755C4—42no—
1756C4—42no—
1757C4—42no—
1758C4—42no—
1759C4—42no—
1760C4—41no—
1761C4—41no—
1762C4—41no—
1763C4—42no—
1764C4—42no—
1765C4—44no—
1766C4—41no—
1767C4—42no—
1768C4—44no—
1769C4—41no—
1770C4—41no—
1771C4—42no—
1772C4—44no—
1773C4—42no—
1774C4#350814yes—
1775C4#354114yes—
1776C2—42no—
1777C2—42no—
1778C2—82no—
1779C2—82no—
1780C2—84no—
1781C2C2×#354111yescharacteristic
1782C2#6278811yescharacteristic
1783C2C2×#350811yescharacteristic
1784C2#6291711yescharacteristic
1785C2#6292411yescharacteristic
1786C2#6299411yescharacteristic
1787C2#6301811yescharacteristic
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. #59863C2semidirect
2. #59813C2semidirect
3. #59323C2semidirect
4. #59039C2semidirect
5. #59036C2semidirect
6. #51166C2semidirect
7. #51059C2semidirect
8. #46014C2semidirect
9. #45610C2semidirect
10. #45136C2semidirect
11. #44980C2semidirect
12. #44156C2semidirect
13. #42810C2semidirect
14. #42752C2semidirect
15. #41734C2semidirect
16. #40198C2semidirect
17. #40030C2semidirect
18. #39903C2semidirect
19. #39771C2semidirect
20. #39524C2semidirect
21. #39272C2semidirect
22. #38911C2semidirect
23. #36596C2semidirect
24. #36465C2semidirect
25. #36410C2semidirect
26. #36211C2semidirect
27. #36186C2semidirect
28. #36150C2semidirect
29. #35238C2semidirect
30. #35208C2semidirect
31. #35044C2semidirect
32. #34947C2semidirect
33. #34727C2semidirect
34. #34474C2semidirect
35. C4×#554C2semidirect
948. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598632
#598132
#593232
#590392
#590362
#511662
#510592
#460142
#456102
#451362
#449802
#441562
#428102
#427522
#417342
#401982
#400302
#399032
#397712
#395242
#392722
#389112
#365962
#364652
#364102
#362112
#361862
#361502
#352382
#352082
#350442
#349472
#347272
#344742
C4×#5542