Finite Group Databasebeta

← #7979715

Subgroups — #7979715

Order 512.

5537 conjugacy classes of subgroups.

The subgroup lattice has 1812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic, complemented
2#59409C212yesmaximal, complemented
3#59145C212yesmaximal, complemented
4#59042C211yesmaximal, characteristic, complemented
5#59033C211yesmaximal, characteristic, complemented
6#51059C214yesmaximal, complemented
7#50979C214yesmaximal, complemented
8#46013C212yesmaximal, complemented
9#45675C212yesmaximal, complemented
10#45417C212yesmaximal, complemented
11#45356C212yesmaximal, complemented
12#43418C214yesmaximal, complemented
13#42810C212yesmaximal, complemented
14#42541C212yesmaximal, complemented
15#41114C214yesmaximal, complemented
16#40092C212yesmaximal, complemented
17#39980C212yesmaximal, complemented
18#39853C212yesmaximal, complemented
19#39771C211yesmaximal, characteristic, complemented
20#39524C212yesmaximal, complemented
21#39268C212yesmaximal, complemented
22#38909C211yesmaximal, characteristic, complemented
23#36561C211yesmaximal, characteristic, complemented
24#36465C211yesmaximal, characteristic, complemented
25#36274C211yesmaximal, characteristic, complemented
26#36150C211yesmaximal, characteristic, complemented
27#36149C212yesmaximal, complemented
28#36126C211yesmaximal, characteristic, complemented
29#35241C211yesmaximal, characteristic, complemented
30#35199C211yesmaximal, characteristic, complemented
31#35044C212yesmaximal, complemented
32#34937C211yesmaximal, characteristic, complemented
33#34727C211yesmaximal, characteristic, complemented
34#34472C212yesmaximal, complemented
35C4×#554C211yesmaximal, characteristic, complemented
36C2×#559C2212yes—
37C2×#554C2211yescharacteristic
38C2×#554C2212yes—
39C2×#550C2211yescharacteristic
40C2×D4×Q8C2211yescharacteristic
41C2×#548C2212yes—
42C2×#548C2212yes—
43C2×#547C2212yes—
44C2×#533C2211yescharacteristic
45C2×#532C2212yes—
46C2×#532C2212yes—
47C2×#532C2211yescharacteristic
48C2×#529C2211yescharacteristic
49C2×C4×#41C2211yescharacteristic
50#2863C2212yes—
51#2862C2212yes—
52#2858C2211yescharacteristic
53#2858C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2857C2211yescharacteristic
57#2856C2211yescharacteristic
58#2855C2212yes—
59#2854C2212yes—
60#2850C2212yes—
61#2836C2214yes—
62#2820C2214yes—
63#2808C2214yes—
64#2798C2214yes—
65#2796C2214yes—
66#2796C2214yes—
67#2786C2214yes—
68#2761C2214yes—
69#2761C2214yes—
70#2751C2214yes—
71#2748C2214yes—
72#2741C2214yes—
73#2740C2214yes—
74#2732C2214yes—
75#2732C2214yes—
76#2724C2214yes—
77#2712C2214yes—
78#2704C2214yes—
79#2703C2214yes—
80#2700C2214yes—
81#2700C2214yes—
82#2694C2214yes—
83#2694C2214yes—
84#2692C2214yes—
85#2692C2214yes—
86#2692C2214yes—
87#2691C2214yes—
88#2690C2214yes—
89#2688C2214yes—
90#2687C2214yes—
91#2676C2214yes—
92#2676C2214yes—
93#2672C2214yes—
94#2671C2214yes—
95#2671C2214yes—
96#2667C2214yes—
97#2666C2214yes—
98#2664C2214yes—
99#2648C2214yes—
100#2640C2212yes—
101#2633C2214yes—
102#2631C2214yes—
103#2630C2214yes—
104#2624C2212yes—
105#2607C2214yes—
106#2597C2214yes—
107#2592C2212yes—
108#2582C2212yes—
109#2582C2211yescharacteristic
110#2580C2212yes—
111#2568C2211yescharacteristic
112#2568C2211yescharacteristic
113#2565C2212yes—
114#2564C2214yes—
115#2557C2214yes—
116#2556C2214yes—
117#2551C2211yescharacteristic
118#2549C2214yes—
119#2548C2211yescharacteristic
120#2547C2212yes—
121#2547C2211yescharacteristic
122#2547C2211yescharacteristic
123#2546C2211yescharacteristic
124#2545C2212yes—
125#2545C2212yes—
126#2544C2212yes—
127#2544C2212yes—
128#2544C2212yes—
129#2543C2214yes—
130#2542C2212yes—
131#2542C2211yescharacteristic
132#2541C2212yes—
133#2541C2211yescharacteristic
134#2540C2214yes—
135#2540C2212yes—
136#2540C2212yes—
137#2540C2212yes—
138#2540C2214yes—
139#2536C2212yes—
140#2535C2212yes—
141#2535C2214yes—
142#2520C2214yes—
143#2513C2212yes—
144#2508C2212yes—
145#2506C2212yes—
146#2498C2214yes—
147#2492C2212yes—
148#2492C2212yes—
149#2491C2212yes—
150#2490C2212yes—
151#2486C2212yes—
152#2486C2212yes—
153#2479C2212yes—
154#2477C2214yes—
155#2471C2212yes—
156#2467C2212yes—
157#2464C2214yes—
158#2461C2214yes—
159#2460C2214yes—
160#2459C2214yes—
161#2459C2214yes—
162#2457C2214yes—
163#2456C2214yes—
164#2456C2214yes—
165#2456C2212yes—
166#2454C2212yes—
167#2454C2212yes—
168#2454C2211yescharacteristic
169#2452C2212yes—
170#2452C2212yes—
171#2451C2212yes—
172#2451C2212yes—
173#2451C2212yes—
174#2451C2212yes—
175#2450C2214yes—
176#2448C2212yes—
177#2448C2212yes—
178#2448C2211yescharacteristic
179#2447C2212yes—
180#2447C2214yes—
181#2447C2212yes—
182#2447C2214yes—
183#2447C2212yes—
184#2447C2212yes—
185#2447C2212yes—
186#2446C2212yes—
187#2445C2212yes—
188#2444C2214yes—
189#2441C2211yescharacteristic
190#2439C2212yes—
191#2438C2214yes—
192#2431C2211yescharacteristic
193#2431C2212yes—
194#2430C2214yes—
195#2430C2214yes—
196#2428C2211yescharacteristic
197#2428C2212yes—
198#2427C2212yes—
199#2427C2214yes—
200#2427C2212yes—
201#2427C2212yes—
202#2426C2212yes—
203#2426C2212yes—
204#2425C2214yes—
205#2423C2211yescharacteristic
206#2421C2212yes—
207#2420C2214yes—
208#2420C2214yes—
209#2420C2212yes—
210#2419C2214yes—
211#2417C2212yes—
212#2417C2212yes—
213#2417C2212yes—
214#2417C2212yes—
215#2416C2212yes—
216#2416C2212yes—
217#2416C2212yes—
218#2416C2212yes—
219#2414C2212yes—
220#2414C2211yescharacteristic
221#2409C2212yes—
222#2409C2212yes—
223#2407C2212yes—
224#2407C2214yes—
225#2407C2214yes—
226#2407C2211yescharacteristic
227#2407C2212yes—
228#2407C2212yes—
229#2397C2212yes—
230#2392C2212yes—
231#2392C2214yes—
232#2379C2214yes—
233#2378C2214yes—
234#2370C2212yes—
235#2369C2211yescharacteristic
236#2368C2212yes—
237#2368C2212yes—
238#2367C2212yes—
239#2367C2212yes—
240#2366C2211yescharacteristic
241#2365C2211yescharacteristic
242#2364C2214yes—
243#2363C2212yes—
244#2361C2212yes—
245#2360C2211yescharacteristic
246#2360C2211yescharacteristic
247#2360C2212yes—
248#2355C2211yescharacteristic
249#2349C2214yes—
250#2349C2212yes—
251#2349C2212yes—
252D4×C4⋊C4C2211yescharacteristic
253D4×C4⋊C4C2211yescharacteristic
254D4×C4⋊C4C2212yes—
255D4×C4⋊C4C2211yescharacteristic
256#2345C2211yescharacteristic
257#2345C2211yescharacteristic
258#2341C2212yes—
259Q8×C22⋊C4C2212yes—
260#2339C2212yes—
261#2339C2214yes—
262#2339C2212yes—
263#2339C2212yes—
264#2337C2214yes—
265#2333C2214yes—
266#2331C2212yes—
267#2329C2214yes—
268#2326C2212yes—
269#2325C2214yes—
270#2323C2212yes—
271#2323C2212yes—
272#2320C2212yes—
273#2318C2214yes—
274#2311C2212yes—
275C4×C4⋊Q8C2211yescharacteristic
276C4×C4⋊Q8C2211yescharacteristic
277C4×#127C2212yes—
278C4×#127C2211yescharacteristic
279C4×#125C2212yes—
280C4×C22⋊Q8C2212yes—
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2212yes—
286C4×#121C2212yes—
287C4×#121C2211yescharacteristic
288C4×#121C2212yes—
289C4×#121C2211yescharacteristic
290#2297C2212yes—
291#2295C2211yescharacteristic
292C2×#391C2212yes—
293#2290C2212yes—
294C42×Q8C2211yescharacteristic
295C42×D4C2212yes—
296C42×D4C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C22×#41C2314yes—
303C23×Q8C2312yes—
304#559—48no—
305#554—28no—
306#554—48no—
307#550—44no—
308D4×Q8—44no—
309#548—216no—
310#548—48no—
311#547—48no—
312#533—44no—
313#532—44no—
314#532—48no—
315#532—48no—
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2312yes—
323C2×#127C2312yes—
324C2×#127C2311yescharacteristic
325C2×#127C2311yescharacteristic
326C2×#127C2312yes—
327#529—44no—
328C2×#126C2312yes—
329C2×#125C2312yes—
330C2×#125C2311yescharacteristic
331C2×#125C2312yes—
332C2×#125C2314yes—
333C2×#124C2314yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2314yes—
340C2×#124C2311yescharacteristic
341C2×#124C2314yes—
342C2×#124C2312yes—
343C2×#124C2314yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2312yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2311yescharacteristic
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2314yes—
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2314yes—
364C2×C22⋊Q8C2314yes—
365C2×C22⋊Q8C2314yes—
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2311yescharacteristic
369C2×#121C2311yescharacteristic
370C2×#121C2312yes—
371C2×#121C2314yes—
372C2×#121C2311yescharacteristic
373C2×#121C2312yes—
374C2×#121C2312yes—
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2312yes—
378C2×#121C2314yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2314yes—
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C4×#41—44no—
386C2×C4×Q8C2311yescharacteristic
387C2×C4×Q8C2311yescharacteristic
388C2×C4×Q8C2311yescharacteristic
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2312yes—
391C2×C4×Q8C2312yes—
392C2×C4×Q8C2312yes—
393C2×C4×Q8C2312yes—
394C2×C4×Q8C2311yescharacteristic
395C2×C4×Q8C2311yescharacteristic
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2314yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2314yes—
411C2×C4×D4C2314yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2314yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2311yescharacteristic
418C2×C4×D4C2311yescharacteristic
419C2×C4×D4C2314yes—
420C2×C4×D4C2312yes—
421C2×C4×D4C2312yes—
422C2×C4×D4C2312yes—
423C2×C4×D4C2312yes—
424C2×C4×D4C2312yes—
425C2×C4×D4C2312yes—
426C2×#117C2312yes—
427C2×#117C2312yes—
428C2×#117C2312yes—
429C2×#117C2311yescharacteristic
430C22×C4⋊C4C2311yescharacteristic
431C22×C4⋊C4C2311yescharacteristic
432C22×C4⋊C4C2311yescharacteristic
433C22×C4⋊C4C2311yescharacteristic
434C22×C4⋊C4C2312yes—
435C22×C4⋊C4C2312yes—
436C22×C42C2311yescharacteristic
437C22×C42C2311yescharacteristic
438C22×C42C2312yes—
439C22×C42C2312yes—
440C22×C42C2312yes—
441#400C2314yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2314yes—
446#399C2314yes—
447#399C2312yes—
448#399C2314yes—
449#399C2314yes—
450#399C2314yes—
451#399C2314yes—
452#399C2314yes—
453#399C2312yes—
454#399C2312yes—
455#399C2312yes—
456#398C2314yes—
457#398C2314yes—
458#398C2312yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2312yes—
492#396C2312yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#395C2314yes—
497#395C2314yes—
498#395C2314yes—
499#395C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2312yes—
505#394C2314yes—
506#394C2314yes—
507#394C2312yes—
508#394C2314yes—
509#394C2312yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#393C2314yes—
518#393C2314yes—
519#393C2314yes—
520#393C2314yes—
521#393C2314yes—
522#393C2314yes—
523#392C2314yes—
524#392C2312yes—
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2312yes—
530#392C2314yes—
531#392C2312yes—
532#392C2312yes—
533#392C2312yes—
534#392C2314yes—
535#391C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2312yes—
539#391C2311yescharacteristic
540#391C2312yes—
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#391C2312yes—
545#391C2312yes—
546#391C2312yes—
547#391C2312yes—
548#391C2314yes—
549#391C2312yes—
550#391C2314yes—
551#391C2314yes—
552#391C2314yes—
553#391C2314yes—
554#391C2311yescharacteristic
555#391C2314yes—
556#391C2311yescharacteristic
557#391C2314yes—
558#391C2314yes—
559#391C2312yes—
560#391C2311yescharacteristic
561#391C2312yes—
562#391C2312yes—
563#391C2312yes—
564#391C2314yes—
565#390C2311yescharacteristic
566#390C2312yes—
567#390C2311yescharacteristic
568#390C2314yes—
569#390C2314yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2312yes—
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#390C2314yes—
578#390C2312yes—
579#390C2312yes—
580#390C2312yes—
581#390C2314yes—
582#390C2314yes—
583#390C2314yes—
584#390C2312yes—
585#390C2312yes—
586#390C2312yes—
587#390C2312yes—
588#390C2314yes—
589#390C2312yes—
590#390C2311yescharacteristic
591#390C2312yes—
592#390C2311yescharacteristic
593#389C2312yes—
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2311yescharacteristic
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2314yes—
603#389C2312yes—
604#389C2314yes—
605#389C2311yescharacteristic
606#389C2312yes—
607#389C2314yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2314yes—
613#389C2312yes—
614#389C2311yescharacteristic
615#389C2311yescharacteristic
616#389C2312yes—
617#389C2312yes—
618#389C2311yescharacteristic
619#389C2312yes—
620#389C2312yes—
621#389C2312yes—
622#389C2311yescharacteristic
623#389C2311yescharacteristic
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#388C2312yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2312yes—
644#388C2312yes—
645#388C2314yes—
646#388C2312yes—
647#388C2312yes—
648#388C2312yes—
649#387C2312yes—
650#387C2312yes—
651#387C2312yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2312yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2312yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#386C2312yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2312yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2312yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2312yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2312yes—
705#386C2312yes—
706#385C2314yes—
707#385C2314yes—
708#385C2312yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2312yes—
718#385C2312yes—
719#385C2314yes—
720#385C2312yes—
721#385C2312yes—
722#385C2312yes—
723#385C2312yes—
724#385C2312yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#384C2312yes—
730#384C2311yescharacteristic
731#384C2311yescharacteristic
732#384C2311yescharacteristic
733#383C2314yes—
734#382C2312yes—
735#382C2314yes—
736#382C2312yes—
737#382C2312yes—
738#382C2314yes—
739#381C2314yes—
740#381C2314yes—
741#381C2314yes—
742#381C2314yes—
743#381C2314yes—
744#381C2314yes—
745#380C2312yes—
746#380C2314yes—
747#380C2314yes—
748#380C2314yes—
749#380C2312yes—
750#380C2312yes—
751#380C2314yes—
752#380C2311yescharacteristic
753#380C2312yes—
754#380C2314yes—
755#380C2312yes—
756#380C2314yes—
757#380C2311yescharacteristic
758#380C2312yes—
759#380C2311yescharacteristic
760#380C2311yescharacteristic
761#380C2312yes—
762#380C2312yes—
763#380C2314yes—
764#380C2312yes—
765#380C2314yes—
766#380C2312yes—
767#380C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2311yescharacteristic
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2312yes—
816#376C2312yes—
817C2×#95C2312yes—
818C2×#95C2314yes—
819C2×#95C2314yes—
820C2×#95C2314yes—
821C2×#95C2312yes—
822C43C2312yes—
823C43C2311yescharacteristic
824C2×#41—28no—
825C2×#41—24no—
826C2×#41—24no—
827C2×#41—28no—
828C2×#41—48no—
829C2×#41—48no—
830C2×#41—42no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—48no—
834C2×#41—44no—
835C2×#41—44no—
836C22×Q8—28no—
837C22×Q8—44no—
838C22×Q8—44no—
839C22×Q8C2412yes—
840C22×Q8C2411yescharacteristic
841C22×Q8C2412yes—
842C22×Q8C2411yescharacteristic
843C22×Q8C2412yes—
844C22×Q8C2414yes—
845C22×Q8C2414yes—
846C22×D4C2411yescharacteristic
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2414yes—
854C22×D4C2412yes—
855C22×D4C2411yescharacteristic
856C22×D4C2412yes—
857C22×D4C2412yes—
858C22×D4C2412yes—
859C22×D4C2412yes—
860C22×D4C2414yes—
861C22×D4C2414yes—
862C22×D4C2414yes—
863C22×D4C2414yes—
864C23×C4C2411yescharacteristic
865C23×C4C2411yescharacteristic
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C23×C4C2412yes—
870C23×C4C2411yescharacteristic
871C23×C4C2412yes—
872C23×C4C2411yescharacteristic
873C23×C4C2412yes—
874C23×C4C2414yes—
875C23×C4C2412yes—
876C23×C4C2412yes—
877C23×C4C2414yes—
878C23×C4C2414yes—
879C23×C4C2411yescharacteristic
880C23×C4C2414yes—
881C23×C4C2414yes—
882C23×C4C2414yes—
883C23×C4C2412yes—
884C4⋊Q8—28no—
885C4⋊Q8—24no—
886C4⋊Q8—24no—
887C4⋊Q8—24no—
888C4⋊Q8—44no—
889C4⋊Q8—44no—
890C4⋊Q8—44no—
891#127—28no—
892#127—24no—
893#127—24no—
894#127—44no—
895#126—44no—
896#125—28no—
897#125—42no—
898#125—44no—
899#125—48no—
900#124—28no—
901#124—216no—
902#124—28no—
903#124—48no—
904#124—42no—
905#124—44no—
906#124—44no—
907#124—44no—
908#124—44no—
909#124—48no—
910#124—48no—
911#123—48no—
912#123—44no—
913#123—48no—
914#123—48no—
915#123—48no—
916C22⋊Q8—24no—
917C22⋊Q8—24no—
918C22⋊Q8—28no—
919C22⋊Q8—216no—
920C22⋊Q8—28no—
921C22⋊Q8—28no—
922C22⋊Q8—28no—
923C22⋊Q8—48no—
924C22⋊Q8—48no—
925C22⋊Q8—48no—
926C22⋊Q8—48no—
927C22⋊Q8—42no—
928C22⋊Q8—44no—
929C22⋊Q8—44no—
930C22⋊Q8—44no—
931C22⋊Q8—44no—
932C22⋊Q8—48no—
933#121—24no—
934#121—24no—
935#121—28no—
936#121—216no—
937#121—28no—
938#121—48no—
939#121—48no—
940#121—44no—
941#121—48no—
942#121—48no—
943#121—48no—
944#121—48no—
945#121—42no—
946#121—44no—
947#121—44no—
948#121—44no—
949#121—44no—
950#121—44no—
951#121—44no—
952C4×Q8—24no—
953C4×Q8—24no—
954C4×Q8—24no—
955C4×Q8—44no—
956C4×Q8—42no—
957C4×Q8—44no—
958C4×Q8—44no—
959C4×Q8—44no—
960C4×Q8—44no—
961C4×Q8#4118yescomplemented
962C4×D4—28no—
963C4×D4—24no—
964C4×D4—216no—
965C4×D4—28no—
966C4×D4—28no—
967C4×D4—24no—
968C4×D4—24no—
969C4×D4—24no—
970C4×D4—42no—
971C4×D4—44no—
972C4×D4—44no—
973C4×D4—44no—
974C4×D4—44no—
975C4×D4—48no—
976C4×D4—44no—
977C4×D4—44no—
978C4×D4—44no—
979C4×D4—44no—
980C4×D4—44no—
981C4×D4—44no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—44no—
985C4×D4—48no—
986C4×D4—42no—
987C4×D4—44no—
988C4×D4—48no—
989C4×D4—48no—
990C4×D4—48no—
991C4×D4—48no—
992#117—44no—
993#117—44no—
994#117—42no—
995#117—44no—
996C2×C4⋊C4—24no—
997C2×C4⋊C4—24no—
998C2×C4⋊C4—24no—
999C2×C4⋊C4—24no—
1000C2×C4⋊C4—44no—
1001C2×C4⋊C4—44no—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2411yescharacteristic
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2411yescharacteristic
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2412yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2411yescharacteristic
1064C2×C4⋊C4C2412yes—
1065C2×C4⋊C4C2411yescharacteristic
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2411yescharacteristic
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2411yescharacteristic
1079C2×C22⋊C4C2411yescharacteristic
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2411yescharacteristic
1083C2×C22⋊C4C2411yescharacteristic
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2411yescharacteristic
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2412yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C42—24no—
1127C2×C42—24no—
1128C2×C42—44no—
1129C2×C42—44no—
1130C2×C42—44no—
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2411yescharacteristic
1140C2×C42C2411yescharacteristic
1141C2×C42C2412yes—
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2414yes—
1149C2×C42C2412yes—
1150C2×C42C2412yes—
1151C2×C42C2412yes—
1152C2×C42C2414yes—
1153C2×C42C2414yes—
1154C2×C42C2412yes—
1155C2×C42C2411yescharacteristic
1156C2×C42C2412yes—
1157C2×C42C2412yes—
1158C2×C42C2411yescharacteristic
1159C2×C42C2412yes—
1160C2×C42C2412yes—
1161C2×C42C2411yescharacteristic
1162C2×C42C2411yescharacteristic
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2411yescharacteristic
1186#95C2411yescharacteristic
1187#95C2412yes—
1188#95C2412yes—
1189#95C2411yescharacteristic
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2411yescharacteristic
1194#95C2411yescharacteristic
1195#95C2411yescharacteristic
1196#95C2412yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2412yes—
1215#95C2412yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225C24C2512yes—
1226C24C2514yes—
1227C24C2512yes—
1228C24C2511yescharacteristic
1229C24C2511yescharacteristic
1230#41—416no—
1231#41—816no—
1232#41—832no—
1233#41—816no—
1234C2×Q8—24no—
1235C2×Q8—24no—
1236C2×Q8—28no—
1237C2×Q8—22no—
1238C2×Q8—22no—
1239C2×Q8—22no—
1240C2×Q8—24no—
1241C2×Q8—24no—
1242C2×Q8—24no—
1243C2×Q8—24no—
1244C2×Q8—22no—
1245C2×Q8—28no—
1246C2×Q8—22no—
1247C2×Q8—24no—
1248C2×Q8—42no—
1249C2×Q8—44no—
1250C2×Q8—44no—
1251C2×Q8—44no—
1252C2×Q8—42no—
1253C2×Q8—44no—
1254C2×Q8—816no—
1255C2×Q8C2×#4114yes—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—28no—
1259C2×D4—24no—
1260C2×D4—28no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—24no—
1267C2×D4—28no—
1268C2×D4—24no—
1269C2×D4—28no—
1270C2×D4—22no—
1271C2×D4—24no—
1272C2×D4—28no—
1273C2×D4—24no—
1274C2×D4—28no—
1275C2×D4—22no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—28no—
1279C2×D4—24no—
1280C2×D4—24no—
1281C2×D4—24no—
1282C2×D4—24no—
1283C2×D4—24no—
1284C2×D4—22no—
1285C2×D4—22no—
1286C2×D4—24no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—44no—
1291C2×D4—42no—
1292C2×D4—42no—
1293C2×D4—44no—
1294C2×D4—42no—
1295C2×D4—42no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—44no—
1299C2×D4—44no—
1300C2×D4—44no—
1301C2×D4—44no—
1302C2×D4—42no—
1303C2×D4—42no—
1304C2×D4—42no—
1305C2×D4—42no—
1306C2×D4—44no—
1307C2×D4—44no—
1308C2×D4—44no—
1309C2×D4H(5,𝔽2)14yes—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—24no—
1313C22×C4—22no—
1314C22×C4—24no—
1315C22×C4—28no—
1316C22×C4—22no—
1317C22×C4—22no—
1318C22×C4—24no—
1319C22×C4—24no—
1320C22×C4—22no—
1321C22×C4—22no—
1322C22×C4—22no—
1323C22×C4—22no—
1324C22×C4—22no—
1325C22×C4—24no—
1326C22×C4—22no—
1327C22×C4—22no—
1328C22×C4—24no—
1329C22×C4—24no—
1330C22×C4—24no—
1331C22×C4—24no—
1332C22×C4—22no—
1333C22×C4—24no—
1334C22×C4—24no—
1335C22×C4—24no—
1336C22×C4—28no—
1337C22×C4—28no—
1338C22×C4—22no—
1339C22×C4—24no—
1340C22×C4—28no—
1341C22×C4—42no—
1342C22×C4—42no—
1343C22×C4—41no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—42no—
1347C22×C4—42no—
1348C22×C4—44no—
1349C22×C4—44no—
1350C22×C4—44no—
1351C22×C4—44no—
1352C22×C4—44no—
1353C22×C4—44no—
1354C22×C4—44no—
1355C22×C4—44no—
1356C22×C4—44no—
1357C22×C4—41no—
1358C22×C4—42no—
1359C22×C4—42no—
1360C22×C4—42no—
1361C22×C4—42no—
1362C22×C4—41no—
1363C22×C4—42no—
1364C22×C4—44no—
1365C22×C4—44no—
1366C22×C4—44no—
1367C22×C4—44no—
1368C22×C4—44no—
1369C22×C42−1+414yes—
1370C22×C4C2511yescharacteristic
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2512yes—
1374C22×C4C2512yes—
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2512yes—
1378C22×C4C2514yes—
1379C22×C4C2512yes—
1380C22×C4C2512yes—
1381C22×C4C2511yescharacteristic
1382C22×C4C2514yes—
1383C22×C4C2511yescharacteristic
1384C22×C4C2512yes—
1385C22×C4C2512yes—
1386C22×C4C2514yes—
1387C22×C4C2512yes—
1388C22×C4C2511yescharacteristic
1389C22×C4C2511yescharacteristic
1390C22×C4C2511yescharacteristic
1391C22×C4C2512yes—
1392C22×C4C2511yescharacteristic
1393C22×C4C2511yescharacteristic
1394C22×C4C2512yes—
1395C22×C4C2511yescharacteristic
1396C22×C4C2512yes—
1397C22×C4C2511yescharacteristic
1398C22×C4C2511yescharacteristic
1399C22×C4C2511yescharacteristic
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—22no—
1403C4⋊C4—22no—
1404C4⋊C4—24no—
1405C4⋊C4—28no—
1406C4⋊C4—22no—
1407C4⋊C4—24no—
1408C4⋊C4—24no—
1409C4⋊C4—24no—
1410C4⋊C4—22no—
1411C4⋊C4—22no—
1412C4⋊C4—24no—
1413C4⋊C4—24no—
1414C4⋊C4—24no—
1415C4⋊C4—22no—
1416C4⋊C4—22no—
1417C4⋊C4—24no—
1418C4⋊C4—24no—
1419C4⋊C4—24no—
1420C4⋊C4—22no—
1421C4⋊C4—24no—
1422C4⋊C4—22no—
1423C4⋊C4—24no—
1424C4⋊C4—24no—
1425C4⋊C4—28no—
1426C4⋊C4—28no—
1427C4⋊C4—24no—
1428C4⋊C4—24no—
1429C4⋊C4—22no—
1430C4⋊C4—22no—
1431C4⋊C4—22no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—42no—
1439C4⋊C4—42no—
1440C4⋊C4—41no—
1441C4⋊C4—42no—
1442C4⋊C4—42no—
1443C4⋊C4—44no—
1444C4⋊C4—44no—
1445C4⋊C4—44no—
1446C4⋊C4—42no—
1447C4⋊C4—42no—
1448C4⋊C4—42no—
1449C4⋊C4—42no—
1450C4⋊C4—44no—
1451C4⋊C4—44no—
1452C4⋊C4—44no—
1453C4⋊C4—42no—
1454C4⋊C4—42no—
1455C4⋊C4—44no—
1456C4⋊C4—42no—
1457C4⋊C4—44no—
1458C4⋊C4—42no—
1459C4⋊C4—44no—
1460C4⋊C4—44no—
1461C4⋊C4C2×#4114yes—
1462C4⋊C4C2×#4118yes—
1463C4⋊C4H(5,𝔽2)14yes—
1464C22⋊C4—28no—
1465C22⋊C4—24no—
1466C22⋊C4—28no—
1467C22⋊C4—28no—
1468C22⋊C4—22no—
1469C22⋊C4—22no—
1470C22⋊C4—24no—
1471C22⋊C4—24no—
1472C22⋊C4—22no—
1473C22⋊C4—22no—
1474C22⋊C4—24no—
1475C22⋊C4—24no—
1476C22⋊C4—24no—
1477C22⋊C4—28no—
1478C22⋊C4—28no—
1479C22⋊C4—28no—
1480C22⋊C4—28no—
1481C22⋊C4—24no—
1482C22⋊C4—24no—
1483C22⋊C4—28no—
1484C22⋊C4—28no—
1485C22⋊C4—22no—
1486C22⋊C4—24no—
1487C22⋊C4—42no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—42no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—44no—
1494C22⋊C4—42no—
1495C22⋊C4—41no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—42no—
1507C22⋊C4—42no—
1508C22⋊C4—44no—
1509C22⋊C4—42no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C22⋊C4—44no—
1516C22⋊C4—42no—
1517C22⋊C4—42no—
1518C22⋊C4—44no—
1519C22⋊C4—42no—
1520C22⋊C4—44no—
1521C22⋊C4—44no—
1522C22⋊C4—44no—
1523C22⋊C4—44no—
1524C42—22no—
1525C42—22no—
1526C42—22no—
1527C42—22no—
1528C42—22no—
1529C42—22no—
1530C42—24no—
1531C42—24no—
1532C42—24no—
1533C42—24no—
1534C42—24no—
1535C42—24no—
1536C42—22no—
1537C42—24no—
1538C42—22no—
1539C42—22no—
1540C42—42no—
1541C42—42no—
1542C42—42no—
1543C42—42no—
1544C42—42no—
1545C42—42no—
1546C42—41no—
1547C42—42no—
1548C42—44no—
1549C42—41no—
1550C42—42no—
1551C42—44no—
1552C42—44no—
1553C42C2×#4118yes—
1554C42C2×#4114yes—
1555C42H(5,𝔽2)14yes—
1556C23—21no—
1557C23—21no—
1558C23—22no—
1559C23—22no—
1560C23—21no—
1561C23—21no—
1562C23—21no—
1563C23—21no—
1564C23—22no—
1565C23—21no—
1566C23—21no—
1567C23—21no—
1568C23—22no—
1569C23—21no—
1570C23—22no—
1571C23—22no—
1572C23—21no—
1573C23—21no—
1574C23—22no—
1575C23—24no—
1576C23—22no—
1577C23—24no—
1578C23—22no—
1579C23—22no—
1580C23—24no—
1581C23—24no—
1582C23—22no—
1583C23—24no—
1584C23—24no—
1585C23—22no—
1586C23—24no—
1587C23—22no—
1588C23C2×H(5,𝔽2)14yes—
1589C23C2×2−1+412yes—
1590C23#58512yes—
1591C23C2611yescharacteristic
1592Q8—28no—
1593Q8—48no—
1594Q8—44no—
1595Q8—48no—
1596Q8—84no—
1597Q8—88no—
1598Q8—88no—
1599D4—28no—
1600D4—28no—
1601D4—416no—
1602D4—48no—
1603D4—416no—
1604D4—48no—
1605D4—48no—
1606D4—48no—
1607D4—48no—
1608D4—44no—
1609D4—48no—
1610D4—84no—
1611D4—88no—
1612D4—84no—
1613D4—84no—
1614D4—88no—
1615D4—88no—
1616D4—164no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—28no—
1632C2×C4—22no—
1633C2×C4—24no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—21no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—24no—
1660C2×C4—24no—
1661C2×C4—24no—
1662C2×C4—24no—
1663C2×C4—24no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—21no—
1668C2×C4—22no—
1669C2×C4—21no—
1670C2×C4—22no—
1671C2×C4—24no—
1672C2×C4—22no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—24no—
1678C2×C4—21no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—22no—
1684C2×C4—24no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—22no—
1689C2×C4—22no—
1690C2×C4—21no—
1691C2×C4—22no—
1692C2×C4—22no—
1693C2×C4—22no—
1694C2×C4—21no—
1695C2×C4—44no—
1696C2×C4—48no—
1697C2×C4—48no—
1698C2×C4—44no—
1699C2×C4—44no—
1700C2×C4—48no—
1701C2×C4—48no—
1702C2×C4—44no—
1703C2×C4—84no—
1704C2×C4—84no—
1705C2×C4—84no—
1706C2×C4—82no—
1707C2×C4—88no—
1708C2×C4—88no—
1709C2×C4—88no—
1710C2×C4—88no—
1711C2×C4—84no—
1712C2×C4—88no—
1713C2×C4—164no—
1714C2×C4C22×#4112yes—
1715C2×C4C22×#4112yes—
1716C2×C4C22×#4114yes—
1717C2×C4C22×#4114yes—
1718C2×C4C22×#4112yes—
1719C2×C4C2×H(5,𝔽2)12yes—
1720C2×C4C2×H(5,𝔽2)14yes—
1721C2×C4C2×H(5,𝔽2)12yes—
1722C2×C4C2×H(5,𝔽2)12yes—
1723C2×C4C2×H(5,𝔽2)12yes—
1724C2×C4C2×H(5,𝔽2)12yes—
1725C2×C4C2×2−1+412yes—
1726C2×C4C2×2−1+412yes—
1727C22—22no—
1728C22—24no—
1729C22—24no—
1730C22—22no—
1731C22—24no—
1732C22—22no—
1733C22—22no—
1734C22—22no—
1735C22—22no—
1736C22—41no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—42no—
1741C22—42no—
1742C22—41no—
1743C22—41no—
1744C22—41no—
1745C22—42no—
1746C22—41no—
1747C22—42no—
1748C22—44no—
1749C22—42no—
1750C22—42no—
1751C22—44no—
1752C22—44no—
1753C22—42no—
1754C22—42no—
1755C22—44no—
1756C22—42no—
1757C22—44no—
1758C22—42no—
1759C22—44no—
1760C22—42no—
1761C22—44no—
1762C22C23×#4111yescharacteristic
1763C22C22×H(5,𝔽2)11yescharacteristic
1764C22C22×H(5,𝔽2)11yescharacteristic
1765C22C22×H(5,𝔽2)11yescharacteristic
1766C22C22×2−1+411yescharacteristic
1767C22C2×#58511yescharacteristic
1768C222−1+611yescharacteristic
1769C4—22no—
1770C4—24no—
1771C4—22no—
1772C4—24no—
1773C4—22no—
1774C4—24no—
1775C4—22no—
1776C4—41no—
1777C4—42no—
1778C4—44no—
1779C4—42no—
1780C4—42no—
1781C4—42no—
1782C4—42no—
1783C4—42no—
1784C4—44no—
1785C4—41no—
1786C4—41no—
1787C4—41no—
1788C4—42no—
1789C4—42no—
1790C4—44no—
1791C4—41no—
1792C4—42no—
1793C4—41no—
1794C4—41no—
1795C4—42no—
1796C4—42no—
1797C4#350814yes—
1798C4#353614yes—
1799C2—42no—
1800C2—44no—
1801C2—42no—
1802C2—84no—
1803C2—82no—
1804C2C2×#353611yescharacteristic
1805C2#6278811yescharacteristic
1806C2C2×#350811yescharacteristic
1807C2#6291311yescharacteristic
1808C2#6295411yescharacteristic
1809C2#6298511yescharacteristic
1810C2#6301211yescharacteristic
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. #59827C2semidirect
2. #59409C2semidirect
3. #59145C2semidirect
4. #59042C2semidirect
5. #59033C2semidirect
6. #51059C2semidirect
7. #50979C2semidirect
8. #46013C2semidirect
9. #45675C2semidirect
10. #45417C2semidirect
11. #45356C2semidirect
12. #43418C2semidirect
13. #42810C2semidirect
14. #42541C2semidirect
15. #41114C2semidirect
16. #40092C2semidirect
17. #39980C2semidirect
18. #39853C2semidirect
19. #39771C2semidirect
20. #39524C2semidirect
21. #39268C2semidirect
22. #38909C2semidirect
23. #36561C2semidirect
24. #36465C2semidirect
25. #36274C2semidirect
26. #36150C2semidirect
27. #36149C2semidirect
28. #36126C2semidirect
29. #35241C2semidirect
30. #35199C2semidirect
31. #35044C2semidirect
32. #34937C2semidirect
33. #34727C2semidirect
34. #34472C2semidirect
35. C4×#554C2semidirect
961. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598272
#594092
#591452
#590422
#590332
#510592
#509792
#460132
#456752
#454172
#453562
#434182
#428102
#425412
#411142
#400922
#399802
#398532
#397712
#395242
#392682
#389092
#365612
#364652
#362742
#361502
#361492
#361262
#352412
#351992
#350442
#349372
#347272
#344722
C4×#5542