Finite Group Databasebeta

← #7968122

Subgroups — #7968122

Order 512.

5258 conjugacy classes of subgroups.

The subgroup lattice has 1820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59633C212yesmaximal, complemented
2#59421C211yesmaximal, characteristic, complemented
3#59391C212yesmaximal, complemented
4#59245C211yesmaximal, characteristic, complemented
5#59233C211yesmaximal, characteristic, complemented
6#51875C214yesmaximal, complemented
7#48460C214yesmaximal, complemented
8#45716C212yesmaximal, complemented
9#45601C212yesmaximal, complemented
10#45316C212yesmaximal, complemented
11#45093C212yesmaximal, complemented
12#44316C214yesmaximal, complemented
13#42778C212yesmaximal, complemented
14#42654C212yesmaximal, complemented
15#41253C214yesmaximal, complemented
16#40078C212yesmaximal, complemented
17#39909C212yesmaximal, complemented
18#39438C212yesmaximal, complemented
19#39343C211yesmaximal, characteristic, complemented
20#39238C212yesmaximal, complemented
21#39194C211yesmaximal, characteristic, complemented
22#39158C212yesmaximal, complemented
23#36504C211yesmaximal, characteristic, complemented
24#36444C211yesmaximal, characteristic, complemented
25#36210C211yesmaximal, characteristic, complemented
26#36203C212yesmaximal, complemented
27#36174C211yesmaximal, characteristic, complemented
28#36161C211yesmaximal, characteristic, complemented
29#35170C211yesmaximal, characteristic, complemented
30#35165C211yesmaximal, characteristic, complemented
31#35080C212yesmaximal, complemented
32#34976C211yesmaximal, characteristic, complemented
33#34715C211yesmaximal, characteristic, complemented
34#34412C212yesmaximal, complemented
35C4×#546C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic, complemented
38C2×#548C2212yes—
39C2×#546C2211yescharacteristic
40C2×#542C2212yes—
41C2×#536C2212yes—
42C2×#535C2212yes—
43C2×#532C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic, complemented
46C22×C4×D4C2211yescharacteristic
47#2859C2211yescharacteristic, complemented
48#2857C2211yescharacteristic
49#2857C2212yescomplemented
50#2857C2212yescomplemented
51#2857C2211yescharacteristic, complemented
52#2854C2212yescomplemented
53#2850C2212yes—
54#2850C2212yescomplemented
55#2848C2212yes—
56#2847C2212yes—
57#2847C2212yes—
58#2828C2214yescomplemented
59#2824C2214yes—
60#2808C2214yescomplemented
61#2804C2214yescomplemented
62#2803C2214yescomplemented
63#2803C2214yescomplemented
64#2801C2214yescomplemented
65#2800C2214yescomplemented
66#2788C2214yes—
67#2785C2214yescomplemented
68#2782C2214yescomplemented
69#2778C2214yescomplemented
70#2778C2214yescomplemented
71#2774C2214yescomplemented
72#2773C2214yescomplemented
73#2759C2214yescomplemented
74#2759C2214yescomplemented
75#2753C2214yescomplemented
76#2752C2214yescomplemented
77#2750C2214yescomplemented
78#2712C2214yescomplemented
79#2709C2214yes—
80#2703C2214yescomplemented
81#2702C2214yescomplemented
82#2700C2214yes—
83#2700C2214yescomplemented
84#2698C2214yescomplemented
85#2685C2214yes—
86#2684C2214yes—
87#2678C2214yes—
88#2674C2214yes—
89#2674C2214yescomplemented
90#2673C2214yes—
91#2672C2214yes—
92#2670C2214yes—
93#2663C2214yescomplemented
94#2653C2214yes—
95#2650C2214yescomplemented
96#2649C2214yescomplemented
97#2648C2214yes—
98#2644C2214yescomplemented
99#2624C2212yes—
100#2617C2214yes—
101#2616C2212yes—
102#2610C2214yescomplemented
103#2609C2214yescomplemented
104#2602C2214yescomplemented
105#2597C2214yescomplemented
106#2588C2214yescomplemented
107#2582C2211yescharacteristic, complemented
108#2572C2214yescomplemented
109#2568C2212yescomplemented
110#2563C2212yescomplemented
111#2563C2212yescomplemented
112#2562C2212yes—
113#2560C2214yescomplemented
114#2559C2214yescomplemented
115#2557C2214yescomplemented
116#2551C2211yescharacteristic, complemented
117#2551C2212yescomplemented
118#2547C2211yescharacteristic
119#2547C2212yes—
120#2547C2212yescomplemented
121#2544C2214yes—
122#2544C2214yes—
123#2542C2211yescharacteristic, complemented
124#2541C2212yes—
125#2540C2212yes—
126#2538C2211yescharacteristic
127#2538C2211yescharacteristic, complemented
128#2537C2211yescharacteristic
129#2537C2211yescharacteristic
130#2537C2211yescharacteristic
131#2537C2211yescharacteristic
132#2537C2212yescomplemented
133#2536C2212yescomplemented
134#2535C2212yes—
135#2535C2212yes—
136#2534C2214yes—
137#2530C2214yescomplemented
138#2526C2214yescomplemented
139#2526C2214yescomplemented
140#2521C2214yes—
141#2521C2214yescomplemented
142#2518C2214yes—
143#2518C2214yescomplemented
144#2514C2212yescomplemented
145#2511C2212yescomplemented
146#2510C2214yescomplemented
147#2509C2212yescomplemented
148#2509C2212yescomplemented
149#2500C2212yescomplemented
150#2497C2212yes—
151#2496C2212yescomplemented
152#2495C2212yes—
153#2495C2212yescomplemented
154#2494C2212yes—
155#2494C2212yescomplemented
156#2494C2212yescomplemented
157#2494C2214yescomplemented
158#2494C2212yescomplemented
159#2492C2212yes—
160#2492C2212yescomplemented
161#2492C2212yescomplemented
162#2491C2212yes—
163#2491C2214yes—
164#2491C2212yes—
165#2491C2212yescomplemented
166#2491C2212yescomplemented
167#2490C2212yescomplemented
168#2490C2212yescomplemented
169#2489C2212yescomplemented
170#2488C2214yescomplemented
171#2485C2212yes—
172#2485C2212yes—
173#2485C2212yescomplemented
174#2485C2212yescomplemented
175#2480C2214yes—
176#2479C2214yescomplemented
177#2476C2212yes—
178#2474C2212yescomplemented
179#2472C2214yes—
180#2472C2214yes—
181#2467C2214yescomplemented
182#2466C2214yes—
183#2459C2214yescomplemented
184#2459C2212yescomplemented
185#2456C2212yes—
186#2451C2211yescharacteristic, complemented
187#2450C2214yescomplemented
188#2447C2212yes—
189#2445C2214yes—
190#2445C2212yescomplemented
191#2445C2211yescharacteristic, complemented
192#2441C2212yescomplemented
193#2439C2212yes—
194#2439C2212yescomplemented
195#2439C2211yescharacteristic, complemented
196#2436C2212yes—
197#2435C2212yes—
198#2431C2211yescharacteristic, complemented
199#2427C2212yes—
200#2427C2212yes—
201#2427C2212yescomplemented
202#2427C2214yescomplemented
203#2426C2211yescharacteristic
204#2426C2212yes—
205#2426C2212yes—
206#2423C2212yescomplemented
207#2422C2212yes—
208#2421C2212yescomplemented
209#2421C2212yescomplemented
210#2420C2212yes—
211#2420C2211yescharacteristic
212#2418C2214yes—
213#2415C2212yes—
214#2415C2212yes—
215#2415C2212yescomplemented
216#2415C2212yescomplemented
217#2415C2214yescomplemented
218#2414C2212yes—
219#2414C2211yescharacteristic
220#2414C2212yescomplemented
221#2409C2212yescomplemented
222#2407C2212yes—
223#2407C2211yescharacteristic
224#2407C2212yescomplemented
225#2407C2212yescomplemented
226#2392C2212yescomplemented
227#2392C2214yescomplemented
228#2388C2212yes—
229#2379C2214yes—
230#2376C2214yescomplemented
231#2374C2214yescomplemented
232#2372C2214yes—
233#2370C2212yescomplemented
234#2369C2212yescomplemented
235#2367C2212yes—
236#2367C2211yescharacteristic
237#2364C2212yes—
238#2363C2211yescharacteristic
239#2363C2212yes—
240#2363C2212yescomplemented
241#2363C2212yescomplemented
242#2362C2212yes—
243#2362C2212yes—
244#2360C2212yes—
245#2360C2211yescharacteristic
246#2359C2212yes—
247#2358C2212yes—
248#2355C2211yescharacteristic, complemented
249#2354C2211yescharacteristic
250#2354C2211yescharacteristic, complemented
251#2354C2212yescomplemented
252#2353C2214yescomplemented
253#2352C2211yescharacteristic
254Q8×C4⋊C4C2211yescharacteristic, complemented
255#2349C2211yescharacteristic
256#2347C2212yescomplemented
257#2346C2212yescomplemented
258#2346C2212yescomplemented
259#2346C2212yescomplemented
260#2342C2212yes—
261Q8×C22⋊C4C2212yescomplemented
262Q8×C22⋊C4C2212yescomplemented
263#2339C2211yescharacteristic
264D4×C22⋊C4C2211yescharacteristic
265#2337C2214yescomplemented
266#2335C2214yes—
267#2335C2214yes—
268#2331C2214yescomplemented
269#2331C2214yescomplemented
270#2323C2212yescomplemented
271#2323C2212yescomplemented
272#2311C2212yes—
273C4×C4⋊Q8C2211yescharacteristic, complemented
274C4×#124C2211yescharacteristic
275C4×#124C2211yescharacteristic, complemented
276C4×C22⋊Q8C2211yescharacteristic
277C4×C22⋊Q8C2211yescharacteristic
278C4×C22⋊Q8C2212yescomplemented
279C4×C22⋊Q8C2212yescomplemented
280C4×C22⋊Q8C2212yescomplemented
281C4×#123C2212yes—
282C4×#123C2212yescomplemented
283C4×#121C2212yes—
284C4×#121C2211yescharacteristic
285C4×#121C2212yes—
286C4×#121C2212yescomplemented
287C4×#121C2211yescharacteristic, complemented
288C4×#121C2212yescomplemented
289C4×#120C2212yes—
290#2297C2212yes—
291#2293C2211yescharacteristic, complemented
292#2285C2211yescharacteristic
293#2285C2211yescharacteristic, complemented
294#2283C2212yescomplemented
295#2280C2212yes—
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C22⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2311yescharacteristic
302C23×Q8C2312yes—
303C23×D4C2311yescharacteristic
304C24×C4C2312yes—
305#556—44no—
306D4×Q8—44no—
307#548—48no—
308#546—28no—
309#542—48no—
310#536—216no—
311#535—48no—
312#532—44no—
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2314yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2311yescharacteristic
319C2×#127C2314yes—
320C2×#127C2311yescharacteristic
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#125C2312yes—
324C2×#124C2311yescharacteristic
325C2×#124C2312yes—
326C2×#124C2314yes—
327C2×#124C2314yes—
328C2×#124C2312yes—
329C2×#124C2311yescharacteristic
330C2×#124C2314yes—
331C2×#124C2314yes—
332C2×#124C2312yes—
333C2×#124C2314yes—
334C2×#123C2314yes—
335C2×#123C2312yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×#123C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×#121C2311yescharacteristic
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2311yescharacteristic
357C2×#121C2311yescharacteristic
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2311yescharacteristic
365C2×#121C2312yes—
366C2×#121C2314yes—
367C2×#120C2312yes—
368C2×#120C2314yes—
369C2×#120C2314yes—
370C4×#41—44no—
371C4×#41—44no—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2311yescharacteristic
379C2×C4×D4—44no—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2314yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2314yes—
405C2×#117C2312yes—
406C2×#117C2312yes—
407C2×#117C2312yes—
408C2×#117C2312yes—
409C2×#117C2312yes—
410C2×#117C2312yes—
411C2×#117C2311yescharacteristic
412C2×#117C2312yes—
413C2×#117C2311yescharacteristic
414C2×#117C2312yes—
415C22×C4⋊C4C2311yescharacteristic
416C22×C22⋊C4C2312yes—
417C22×C22⋊C4C2312yes—
418C22×C22⋊C4C2312yes—
419C22×C42C2311yescharacteristic
420C22×C42C2311yescharacteristic
421C22×C42C2312yes—
422C22×C42C2312yes—
423C22×C42C2312yes—
424#401C2314yes—
425#401C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#399C2314yes—
436#399C2314yes—
437#399C2314yes—
438#398C2314yes—
439#398C2312yes—
440#398C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2312yes—
462#396C2314yes—
463#396C2312yes—
464#396C2314yes—
465#396C2314yes—
466#395C2314yes—
467#395C2314yes—
468#395C2312yes—
469#395C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2312yes—
489#394C2312yes—
490#394C2312yes—
491#394C2314yes—
492#394C2312yes—
493#394C2312yes—
494#394C2312yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#393C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#393C2312yes—
508#393C2314yes—
509#392C2312yes—
510#392C2312yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2312yes—
516#392C2312yes—
517#392C2314yes—
518#391C2314yes—
519#391C2312yes—
520#391C2314yes—
521#391C2311yescharacteristic
522#391C2312yes—
523#391C2314yes—
524#391C2314yes—
525#391C2314yes—
526#391C2311yescharacteristic
527#391C2312yes—
528#391C2312yes—
529#391C2312yes—
530#391C2312yes—
531#391C2314yes—
532#391C2314yes—
533#391C2314yes—
534#391C2314yes—
535#391C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2311yescharacteristic
539#391C2311yescharacteristic
540#390C2314yes—
541#390C2314yes—
542#390C2314yes—
543#390C2314yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2311yescharacteristic
548#390C2311yescharacteristic
549#390C2312yes—
550#390C2314yes—
551#390C2311yescharacteristic
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2312yes—
556#390C2311yescharacteristic
557#390C2314yes—
558#390C2311yescharacteristic
559#390C2312yes—
560#390C2314yes—
561#390C2311yescharacteristic
562#389C2312yes—
563#389C2312yes—
564#389C2314yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2314yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2311yescharacteristic
577#389C2312yes—
578#389C2311yescharacteristic
579#389C2312yes—
580#389C2314yes—
581#389C2311yescharacteristic
582#389C2312yes—
583#389C2314yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2311yescharacteristic
588#389C2312yes—
589#389C2311yescharacteristic
590#389C2314yes—
591#389C2314yes—
592#389C2311yescharacteristic
593#389C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2312yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2312yes—
618#388C2314yes—
619#388C2314yes—
620#388C2312yes—
621#388C2312yes—
622#388C2312yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2312yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2312yes—
634#388C2312yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2312yes—
640#388C2312yes—
641#388C2312yes—
642#388C2312yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2312yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2312yes—
674#386C2312yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2312yes—
679#386C2312yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2312yes—
685#386C2312yes—
686#386C2312yes—
687#386C2314yes—
688#386C2312yes—
689#386C2312yes—
690#386C2312yes—
691#386C2312yes—
692#386C2314yes—
693#386C2312yes—
694#385C2314yes—
695#385C2312yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#385C2314yes—
703#385C2314yes—
704#385C2312yes—
705#385C2314yes—
706#385C2312yes—
707#385C2312yes—
708#384C2311yescharacteristic
709#384C2311yescharacteristic
710#384C2311yescharacteristic
711#384C2312yes—
712#384C2312yes—
713#383C2314yes—
714#383C2314yes—
715#382C2314yes—
716#382C2314yes—
717#382C2312yes—
718#382C2312yes—
719#382C2314yes—
720#382C2312yes—
721#382C2311yescharacteristic
722#382C2312yes—
723#382C2311yescharacteristic
724#381C2312yes—
725#381C2314yes—
726#381C2312yes—
727#381C2314yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2311yescharacteristic
733#380C2311yescharacteristic
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2314yes—
743#380C2314yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2311yescharacteristic
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2314yes—
754#380C2314yes—
755#380C2312yes—
756#380C2312yes—
757#380C2311yescharacteristic
758#380C2312yes—
759#379C2314yes—
760#379C2312yes—
761#379C2314yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2314yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2312yes—
816#376C2314yes—
817#376C2314yes—
818C2×#95C2312yes—
819C2×#95C2312yes—
820C43C2311yescharacteristic
821C25C2412yes—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—28no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—42no—
828C2×#41—42no—
829C2×#41—42no—
830C2×#41—42no—
831C22×Q8—28no—
832C22×Q8—44no—
833C22×Q8—44no—
834C22×Q8C2412yes—
835C22×Q8C2411yescharacteristic
836C22×Q8C2411yescharacteristic
837C22×Q8C2414yes—
838C22×Q8C2412yes—
839C22×Q8C2414yes—
840C22×D4—24no—
841C22×D4—24no—
842C22×D4—42no—
843C22×D4C2411yescharacteristic
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2411yescharacteristic
849C22×D4C2411yescharacteristic
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2412yes—
857C22×D4C2412yes—
858C22×D4C2412yes—
859C22×D4C2414yes—
860C22×D4C2414yes—
861C23×C4—44no—
862C23×C4—44no—
863C23×C4—44no—
864C23×C4C2412yes—
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2412yes—
868C23×C4C2412yes—
869C23×C4C2412yes—
870C23×C4C2411yescharacteristic
871C23×C4C2412yes—
872C23×C4C2411yescharacteristic
873C23×C4C2411yescharacteristic
874C23×C4C2411yescharacteristic
875C23×C4C2412yes—
876C23×C4C2412yes—
877C23×C4C2412yes—
878C23×C4C2412yes—
879C23×C4C2414yes—
880C23×C4C2412yes—
881C23×C4C2412yes—
882C23×C4C2412yes—
883C23×C4C2412yes—
884C4⋊Q8—216no—
885C4⋊Q8—24no—
886C4⋊Q8—44no—
887C4⋊Q8—42no—
888C4⋊Q8—44no—
889C4⋊Q8—44no—
890#127—42no—
891#127—48no—
892#126—48no—
893#126—48no—
894#125—44no—
895#124—24no—
896#124—28no—
897#124—216no—
898#124—48no—
899#124—44no—
900#124—42no—
901#124—44no—
902#124—48no—
903#124—48no—
904#124—48no—
905#123—216no—
906#123—28no—
907#123—216no—
908#123—44no—
909#123—48no—
910C22⋊Q8—28no—
911C22⋊Q8—28no—
912C22⋊Q8—28no—
913C22⋊Q8—48no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—44no—
917C22⋊Q8—42no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—44no—
921C22⋊Q8—44no—
922C22⋊Q8#4118yescomplemented
923#121—28no—
924#121—28no—
925#121—24no—
926#121—28no—
927#121—44no—
928#121—48no—
929#121—42no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—44no—
934#121—42no—
935#121—42no—
936#121—44no—
937#121—44no—
938#120—28no—
939#120—48no—
940#120—48no—
941C4×Q8—24no—
942C4×Q8—24no—
943C4×Q8—42no—
944C4×Q8—42no—
945C4×Q8—44no—
946C4×Q8—44no—
947C4×Q8—44no—
948C4×D4—24no—
949C4×D4—24no—
950C4×D4—24no—
951C4×D4—24no—
952C4×D4—24no—
953C4×D4—24no—
954C4×D4—24no—
955C4×D4—44no—
956C4×D4—42no—
957C4×D4—42no—
958C4×D4—42no—
959C4×D4—42no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—48no—
964C4×D4—42no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—42no—
970C4×D4—44no—
971C4×D4—44no—
972C4×D4—48no—
973#117—28no—
974#117—44no—
975#117—44no—
976#117—44no—
977#117—44no—
978#117—44no—
979#117—42no—
980#117—42no—
981#117—44no—
982#117—44no—
983C2×C4⋊C4—42no—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2411yescharacteristic
1037C2×C4⋊C4C2412yes—
1038C2×C22⋊C4—28no—
1039C2×C22⋊C4—44no—
1040C2×C22⋊C4—44no—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2411yescharacteristic
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2411yescharacteristic
1085C2×C22⋊C4C2411yescharacteristic
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C42—24no—
1113C2×C42—24no—
1114C2×C42—44no—
1115C2×C42—44no—
1116C2×C42—44no—
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2412yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2411yescharacteristic
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2412yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2412yes—
1132C2×C42C2411yescharacteristic
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2414yes—
1136C2×C42C2414yes—
1137C2×C42C2414yes—
1138C2×C42C2414yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2411yescharacteristic
1142C2×C42C2414yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2412yes—
1145C2×C42C2414yes—
1146C2×C42C2412yes—
1147C2×C42C2411yescharacteristic
1148#95C2411yescharacteristic
1149#95C2411yescharacteristic
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2411yescharacteristic
1166#95C2414yes—
1167#95C2411yescharacteristic
1168#95C2412yes—
1169#95C2411yescharacteristic
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2411yescharacteristic
1174#95C2414yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
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#95C2412yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210C24—24no—
1211C24—24no—
1212C24—42no—
1213C24—42no—
1214C24—42no—
1215C24—42no—
1216C24—42no—
1217C24C2512yes—
1218C24C2512yes—
1219C24C2512yes—
1220C24C2511yescharacteristic
1221C24C2511yescharacteristic
1222C24C2512yes—
1223#41—416no—
1224#41—416no—
1225#41—816no—
1226C2×Q8—24no—
1227C2×Q8—28no—
1228C2×Q8—24no—
1229C2×Q8—22no—
1230C2×Q8—22no—
1231C2×Q8—22no—
1232C2×Q8—24no—
1233C2×Q8—24no—
1234C2×Q8—22no—
1235C2×Q8—22no—
1236C2×Q8—44no—
1237C2×Q8—44no—
1238C2×Q8—42no—
1239C2×Q8—42no—
1240C2×Q8—44no—
1241C2×Q8—44no—
1242C2×Q8—44no—
1243C2×Q8—816no—
1244C2×Q8C2×#4114yes—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—28no—
1251C2×D4—28no—
1252C2×D4—22no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—22no—
1256C2×D4—24no—
1257C2×D4—24no—
1258C2×D4—22no—
1259C2×D4—22no—
1260C2×D4—22no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—22no—
1264C2×D4—22no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—416no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—41no—
1272C2×D4—41no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—44no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—44no—
1291C2×D4—42no—
1292C2×D4—42no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—44no—
1299C2×D4H(5,𝔽2)14yes—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—24no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—22no—
1307C22×C4—24no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—24no—
1317C22×C4—22no—
1318C22×C4—24no—
1319C22×C4—24no—
1320C22×C4—22no—
1321C22×C4—24no—
1322C22×C4—22no—
1323C22×C4—24no—
1324C22×C4—22no—
1325C22×C4—22no—
1326C22×C4—24no—
1327C22×C4—22no—
1328C22×C4—24no—
1329C22×C4—28no—
1330C22×C4—22no—
1331C22×C4—24no—
1332C22×C4—24no—
1333C22×C4—42no—
1334C22×C4—42no—
1335C22×C4—41no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—42no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—42no—
1342C22×C4—42no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—44no—
1347C22×C4—44no—
1348C22×C4—41no—
1349C22×C4—42no—
1350C22×C4—42no—
1351C22×C4—42no—
1352C22×C4—42no—
1353C22×C4—42no—
1354C22×C4—42no—
1355C22×C4—42no—
1356C22×C4—41no—
1357C22×C4—42no—
1358C22×C4—42no—
1359C22×C4—816no—
1360C22×C4C2×#4114yes—
1361C22×C4C2511yescharacteristic
1362C22×C4C2511yescharacteristic
1363C22×C4C2511yescharacteristic
1364C22×C4C2511yescharacteristic
1365C22×C4C2512yes—
1366C22×C4C2512yes—
1367C22×C4C2511yescharacteristic
1368C22×C4C2514yes—
1369C22×C4C2514yes—
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2512yes—
1373C22×C4C2512yes—
1374C22×C4C2511yescharacteristic
1375C22×C4C2514yes—
1376C22×C4C2512yes—
1377C22×C4C2512yes—
1378C22×C4C2512yes—
1379C22×C4C2511yescharacteristic
1380C22×C4C2511yescharacteristic
1381C22×C4C2514yes—
1382C22×C4C2512yes—
1383C22×C4C2512yes—
1384C22×C4C2511yescharacteristic
1385C22×C4C2512yes—
1386C22×C4C2511yescharacteristic
1387C22×C4C2511yescharacteristic
1388C22×C4C2511yescharacteristic
1389C22×C4C2511yescharacteristic
1390C4⋊C4—24no—
1391C4⋊C4—22no—
1392C4⋊C4—28no—
1393C4⋊C4—28no—
1394C4⋊C4—28no—
1395C4⋊C4—22no—
1396C4⋊C4—22no—
1397C4⋊C4—22no—
1398C4⋊C4—22no—
1399C4⋊C4—24no—
1400C4⋊C4—22no—
1401C4⋊C4—24no—
1402C4⋊C4—24no—
1403C4⋊C4—24no—
1404C4⋊C4—24no—
1405C4⋊C4—22no—
1406C4⋊C4—22no—
1407C4⋊C4—24no—
1408C4⋊C4—22no—
1409C4⋊C4—24no—
1410C4⋊C4—22no—
1411C4⋊C4—24no—
1412C4⋊C4—24no—
1413C4⋊C4—22no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—44no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—42no—
1424C4⋊C4—42no—
1425C4⋊C4—44no—
1426C4⋊C4—41no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—42no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—42no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4C2×#4114yes—
1443C4⋊C4C2×#4118yes—
1444C22⋊C4—22no—
1445C22⋊C4—28no—
1446C22⋊C4—24no—
1447C22⋊C4—28no—
1448C22⋊C4—28no—
1449C22⋊C4—28no—
1450C22⋊C4—28no—
1451C22⋊C4—24no—
1452C22⋊C4—24no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—22no—
1456C22⋊C4—24no—
1457C22⋊C4—28no—
1458C22⋊C4—28no—
1459C22⋊C4—24no—
1460C22⋊C4—24no—
1461C22⋊C4—24no—
1462C22⋊C4—24no—
1463C22⋊C4—22no—
1464C22⋊C4—24no—
1465C22⋊C4—24no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—44no—
1481C22⋊C4—42no—
1482C22⋊C4—42no—
1483C22⋊C4—44no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—41no—
1489C22⋊C4—41no—
1490C22⋊C4—41no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—44no—
1495C22⋊C4—42no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—42no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—42no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—42no—
1509C22⋊C4—42no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4C2×#4118yes—
1515C42—28no—
1516C42—22no—
1517C42—22no—
1518C42—22no—
1519C42—22no—
1520C42—22no—
1521C42—22no—
1522C42—22no—
1523C42—24no—
1524C42—24no—
1525C42—22no—
1526C42—24no—
1527C42—22no—
1528C42—24no—
1529C42—28no—
1530C42—22no—
1531C42—42no—
1532C42—42no—
1533C42—42no—
1534C42—42no—
1535C42—42no—
1536C42—42no—
1537C42—44no—
1538C42—41no—
1539C42—44no—
1540C42—44no—
1541C42—44no—
1542C42—41no—
1543C42—44no—
1544C42—44no—
1545C42H(5,𝔽2)14yes—
1546C23—22no—
1547C23—22no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—22no—
1553C23—22no—
1554C23—21no—
1555C23—22no—
1556C23—21no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—21no—
1562C23—22no—
1563C23—22no—
1564C23—22no—
1565C23—21no—
1566C23—21no—
1567C23—22no—
1568C23—22no—
1569C23—22no—
1570C23—22no—
1571C23—22no—
1572C23—21no—
1573C23—22no—
1574C23—22no—
1575C23—22no—
1576C23—22no—
1577C23—21no—
1578C23—22no—
1579C23—22no—
1580C23—22no—
1581C23—21no—
1582C23—22no—
1583C23—22no—
1584C23—22no—
1585C23—21no—
1586C23—48no—
1587C23—48no—
1588C23—84no—
1589C23—84no—
1590C23—84no—
1591C23—84no—
1592C23—84no—
1593C23C22×#4112yes—
1594C23C2×H(5,𝔽2)14yes—
1595C23C2611yescharacteristic
1596Q8—28no—
1597Q8—48no—
1598Q8—44no—
1599Q8—88no—
1600Q8—84no—
1601Q8—164no—
1602D4—28no—
1603D4—48no—
1604D4—48no—
1605D4—44no—
1606D4—48no—
1607D4—44no—
1608D4—44no—
1609D4—44no—
1610D4—84no—
1611D4—84no—
1612D4—88no—
1613D4—88no—
1614D4—84no—
1615D4—84no—
1616D4—84no—
1617D4—84no—
1618D4—164no—
1619D4—164no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—28no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—24no—
1635C2×C4—21no—
1636C2×C4—24no—
1637C2×C4—22no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—21no—
1649C2×C4—24no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—24no—
1653C2×C4—22no—
1654C2×C4—24no—
1655C2×C4—24no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—22no—
1664C2×C4—24no—
1665C2×C4—21no—
1666C2×C4—24no—
1667C2×C4—21no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—21no—
1672C2×C4—21no—
1673C2×C4—24no—
1674C2×C4—22no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—21no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—24no—
1682C2×C4—24no—
1683C2×C4—21no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—21no—
1689C2×C4—21no—
1690C2×C4—22no—
1691C2×C4—21no—
1692C2×C4—21no—
1693C2×C4—24no—
1694C2×C4—22no—
1695C2×C4—22no—
1696C2×C4—21no—
1697C2×C4—44no—
1698C2×C4—48no—
1699C2×C4—48no—
1700C2×C4—48no—
1701C2×C4—44no—
1702C2×C4—48no—
1703C2×C4—48no—
1704C2×C4—48no—
1705C2×C4—44no—
1706C2×C4—44no—
1707C2×C4—84no—
1708C2×C4—84no—
1709C2×C4—84no—
1710C2×C4—82no—
1711C2×C4—88no—
1712C2×C4—84no—
1713C2×C4—84no—
1714C2×C4—84no—
1715C2×C4—84no—
1716C2×C4C22×#4114yes—
1717C2×C4C22×#4114yes—
1718C2×C4C22×#4112yes—
1719C2×C4C22×#4112yes—
1720C2×C4C2×H(5,𝔽2)12yes—
1721C2×C4C2×H(5,𝔽2)12yes—
1722C2×C4C2×H(5,𝔽2)12yes—
1723C2×C4C2×H(5,𝔽2)12yes—
1724C2×C4#58512yes—
1725C2×C4#58512yes—
1726C2×C4#58512yes—
1727C22—22no—
1728C22—24no—
1729C22—22no—
1730C22—24no—
1731C22—22no—
1732C22—24no—
1733C22—41no—
1734C22—42no—
1735C22—42no—
1736C22—41no—
1737C22—42no—
1738C22—41no—
1739C22—42no—
1740C22—41no—
1741C22—42no—
1742C22—42no—
1743C22—41no—
1744C22—42no—
1745C22—41no—
1746C22—42no—
1747C22—42no—
1748C22—42no—
1749C22—42no—
1750C22—42no—
1751C22—42no—
1752C22—41no—
1753C22—42no—
1754C22—41no—
1755C22—42no—
1756C22—42no—
1757C22—41no—
1758C22—42no—
1759C22—42no—
1760C22—42no—
1761C22—42no—
1762C22—41no—
1763C22—42no—
1764C22—42no—
1765C22—41no—
1766C22—42no—
1767C22—42no—
1768C22—42no—
1769C22—816no—
1770C22C23×#4111yescharacteristic
1771C22C22×H(5,𝔽2)11yescharacteristic
1772C22C22×H(5,𝔽2)11yescharacteristic
1773C22C2×#58511yescharacteristic
1774C22C2×#58511yescharacteristic
1775C22C2×#58511yescharacteristic
1776C222−1+611yescharacteristic
1777C4—24no—
1778C4—22no—
1779C4—24no—
1780C4—22no—
1781C4—22no—
1782C4—41no—
1783C4—42no—
1784C4—42no—
1785C4—41no—
1786C4—42no—
1787C4—41no—
1788C4—41no—
1789C4—42no—
1790C4—44no—
1791C4—42no—
1792C4—41no—
1793C4—42no—
1794C4—42no—
1795C4—44no—
1796C4—44no—
1797C4—41no—
1798C4—41no—
1799C4—42no—
1800C4—44no—
1801C4—42no—
1802C4—42no—
1803C4—41no—
1804C4#351914yes—
1805C4#354014yes—
1806C2—44no—
1807C2—42no—
1808C2—81no—
1809C2—82no—
1810C2—82no—
1811C2—82no—
1812C2C2×#354011yescharacteristic
1813C2C2×#351911yescharacteristic
1814C2#6279311yescharacteristic
1815C2#6292111yescharacteristic
1816C2#6292711yescharacteristic
1817C2#6299511yescharacteristic
1818C2#6302411yescharacteristic
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. #59633C2semidirect
2. #59421C2semidirect
3. #59391C2semidirect
4. #59245C2semidirect
5. #59233C2semidirect
6. #51875C2semidirect
7. #48460C2semidirect
8. #45716C2semidirect
9. #45601C2semidirect
10. #45316C2semidirect
11. #45093C2semidirect
12. #44316C2semidirect
13. #42778C2semidirect
14. #42654C2semidirect
15. #41253C2semidirect
16. #40078C2semidirect
17. #39909C2semidirect
18. #39438C2semidirect
19. #39343C2semidirect
20. #39238C2semidirect
21. #39194C2semidirect
22. #39158C2semidirect
23. #36504C2semidirect
24. #36444C2semidirect
25. #36210C2semidirect
26. #36203C2semidirect
27. #36174C2semidirect
28. #36161C2semidirect
29. #35170C2semidirect
30. #35165C2semidirect
31. #35080C2semidirect
32. #34976C2semidirect
33. #34715C2semidirect
34. #34412C2semidirect
35. C4×#546C2semidirect
37. C2×D4×Q8C22semidirect
45. C2×C4×#41C22semidirect
47. #2859C22semidirect
49. #2857C22semidirect
50. #2857C22semidirect
51. #2857C22semidirect
52. #2854C22semidirect
54. #2850C22semidirect
58. #2828C22semidirect
60. #2808C22semidirect
61. #2804C22semidirect
62. #2803C22semidirect
63. #2803C22semidirect
64. #2801C22semidirect
65. #2800C22semidirect
67. #2785C22semidirect
68. #2782C22semidirect
69. #2778C22semidirect
70. #2778C22semidirect
71. #2774C22semidirect
72. #2773C22semidirect
73. #2759C22semidirect
74. #2759C22semidirect
75. #2753C22semidirect
76. #2752C22semidirect
77. #2750C22semidirect
78. #2712C22semidirect
80. #2703C22semidirect
81. #2702C22semidirect
83. #2700C22semidirect
84. #2698C22semidirect
89. #2674C22semidirect
93. #2663C22semidirect
95. #2650C22semidirect
96. #2649C22semidirect
98. #2644C22semidirect
102. #2610C22semidirect
103. #2609C22semidirect
104. #2602C22semidirect
105. #2597C22semidirect
106. #2588C22semidirect
107. #2582C22semidirect
108. #2572C22semidirect
109. #2568C22semidirect
110. #2563C22semidirect
111. #2563C22semidirect
113. #2560C22semidirect
114. #2559C22semidirect
115. #2557C22semidirect
116. #2551C22semidirect
117. #2551C22semidirect
120. #2547C22semidirect
123. #2542C22semidirect
127. #2538C22semidirect
132. #2537C22semidirect
133. #2536C22semidirect
137. #2530C22semidirect
138. #2526C22semidirect
139. #2526C22semidirect
141. #2521C22semidirect
143. #2518C22semidirect
144. #2514C22semidirect
145. #2511C22semidirect
146. #2510C22semidirect
147. #2509C22semidirect
148. #2509C22semidirect
149. #2500C22semidirect
151. #2496C22semidirect
153. #2495C22semidirect
155. #2494C22semidirect
156. #2494C22semidirect
157. #2494C22semidirect
158. #2494C22semidirect
160. #2492C22semidirect
161. #2492C22semidirect
165. #2491C22semidirect
166. #2491C22semidirect
167. #2490C22semidirect
168. #2490C22semidirect
169. #2489C22semidirect
170. #2488C22semidirect
173. #2485C22semidirect
174. #2485C22semidirect
176. #2479C22semidirect
178. #2474C22semidirect
181. #2467C22semidirect
183. #2459C22semidirect
184. #2459C22semidirect
186. #2451C22semidirect
187. #2450C22semidirect
190. #2445C22semidirect
191. #2445C22semidirect
192. #2441C22semidirect
194. #2439C22semidirect
195. #2439C22semidirect
198. #2431C22semidirect
201. #2427C22semidirect
202. #2427C22semidirect
206. #2423C22semidirect
208. #2421C22semidirect
209. #2421C22semidirect
215. #2415C22semidirect
216. #2415C22semidirect
217. #2415C22semidirect
220. #2414C22semidirect
221. #2409C22semidirect
224. #2407C22semidirect
225. #2407C22semidirect
226. #2392C22semidirect
227. #2392C22semidirect
230. #2376C22semidirect
231. #2374C22semidirect
233. #2370C22semidirect
234. #2369C22semidirect
240. #2363C22semidirect
241. #2363C22semidirect
248. #2355C22semidirect
250. #2354C22semidirect
251. #2354C22semidirect
252. #2353C22semidirect
254. Q8×C4⋊C4C22semidirect
256. #2347C22semidirect
257. #2346C22semidirect
258. #2346C22semidirect
259. #2346C22semidirect
261. Q8×C22⋊C4C22semidirect
262. Q8×C22⋊C4C22semidirect
265. #2337C22semidirect
268. #2331C22semidirect
269. #2331C22semidirect
270. #2323C22semidirect
271. #2323C22semidirect
273. C4×C4⋊Q8C22semidirect
275. C4×#124C22semidirect
278. C4×C22⋊Q8C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
282. C4×#123C22semidirect
286. C4×#121C22semidirect
287. C4×#121C22semidirect
288. C4×#121C22semidirect
291. #2293C22semidirect
293. #2285C22semidirect
294. #2283C22semidirect
922. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#596332
#594212
#593912
#592452
#592332
#518752
#484602
#457162
#456012
#453162
#450932
#443162
#427782
#426542
#412532
#400782
#399092
#394382
#393432
#392382
#391942
#391582
#365042
#364442
#362102
#362032
#361742
#361612
#351702
#351652
#350802
#349762
#347152
#344122
C4×#5462