Finite Group Databasebeta

← #7688606

Subgroups — #7688606

Order 512.

5305 conjugacy classes of subgroups.

The subgroup lattice has 1749 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59655C211yesmaximal, characteristic, complemented
2#59489C212yesmaximal, complemented
3#59484C212yesmaximal, complemented
4#59421C211yesmaximal, characteristic, complemented
5#59416C212yesmaximal, complemented
6#59412C211yesmaximal, characteristic
7#59282C212yesmaximal, complemented
8#59224C212yesmaximal, complemented
9#59147C212yesmaximal, complemented
10#44099C214yesmaximal, complemented
11#43855C214yesmaximal, complemented
12#43675C214yesmaximal, complemented
13#40218C212yesmaximal, complemented
14#40049C212yesmaximal, complemented
15#40002C212yesmaximal, complemented
16#39905C212yesmaximal, complemented
17#39248C212yesmaximal, complemented
18#39020C212yesmaximal, complemented
19#36609C211yesmaximal, characteristic, complemented
20Q8×#124C211yesmaximal, characteristic, complemented
21#36534C211yesmaximal, characteristic, complemented
22#36457C211yesmaximal, characteristic, complemented
23#36419C211yesmaximal, characteristic, complemented
24#36373C212yesmaximal, complemented
25#36289C211yesmaximal, characteristic, complemented
26#36195C212yesmaximal, complemented
27D4×#124C211yesmaximal, characteristic, complemented
28#35894C214yesmaximal, complemented
29#34954C211yesmaximal, characteristic, complemented
30#34945C211yesmaximal, characteristic, complemented
31#34943C211yesmaximal, characteristic, complemented
32#34320C212yesmaximal, complemented
33#34240C212yesmaximal, complemented
34C4×#559C211yesmaximal, characteristic, complemented
35C4×#556C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×Q82C2211yescharacteristic, complemented
38C2×#556C2211yescharacteristic
39C2×#556C2211yescharacteristic, complemented
40C2×#554C2211yescharacteristic
41C2×#550C2211yescharacteristic
42C2×D4×Q8C2211yescharacteristic
43C2×#546C2212yes—
44C2×D42C2211yescharacteristic
45C22×#124C2212yes—
46#2862C2211yescharacteristic, complemented
47#2862C2212yescomplemented
48#2861C2212yescomplemented
49#2858C2211yescharacteristic
50#2858C2211yescharacteristic
51#2858C2212yescomplemented
52#2850C2212yes—
53#2850C2212yes—
54#2850C2212yescomplemented
55#2808C2214yescomplemented
56#2778C2214yescomplemented
57#2770C2214yescomplemented
58#2759C2214yescomplemented
59#2756C2214yescomplemented
60#2754C2214yescomplemented
61#2751C2214yescomplemented
62#2750C2214yescomplemented
63#2749C2214yescomplemented
64#2741C2214yescomplemented
65#2737C2214yescomplemented
66#2736C2214yescomplemented
67#2730C2214yescomplemented
68#2729C2214yescomplemented
69#2712C2214yescomplemented
70#2710C2214yescomplemented
71#2702C2214yescomplemented
72#2687C2214yescomplemented
73#2685C2214yescomplemented
74#2684C2214yescomplemented
75#2678C2214yes—
76#2653C2214yescomplemented
77#2653C2214yescomplemented
78#2648C2214yescomplemented
79#2610C2214yescomplemented
80#2593C2214yescomplemented
81#2593C2214yescomplemented
82#2592C2212yescomplemented
83#2592C2212yescomplemented
84#2589C2214yescomplemented
85#2582C2211yescharacteristic, complemented
86#2580C2212yescomplemented
87#2578C2214yescomplemented
88#2573C2214yescomplemented
89#2572C2214yescomplemented
90#2572C2214yescomplemented
91#2572C2214yescomplemented
92#2571C2211yescharacteristic, complemented
93#2568C2212yescomplemented
94#2568C2211yescharacteristic, complemented
95#2565C2212yescomplemented
96#2563C2212yes—
97#2563C2211yescharacteristic
98#2563C2212yescomplemented
99#2563C2211yescharacteristic, complemented
100#2561C2214yescomplemented
101#2560C2214yescomplemented
102#2560C2214yescomplemented
103#2560C2214yescomplemented
104#2559C2214yescomplemented
105#2559C2214yescomplemented
106#2559C2214yescomplemented
107#2557C2214yescomplemented
108#2553C2214yescomplemented
109#2550C2212yescomplemented
110#2548C2211yescharacteristic
111#2548C2211yescharacteristic
112#2548C2212yescomplemented
113#2547C2211yescharacteristic
114#2544C2212yes—
115#2544C2212yescomplemented
116#2544C2212yescomplemented
117#2538C2211yescharacteristic
118#2537C2211yescharacteristic
119#2536C2212yescomplemented
120#2536C2212yescomplemented
121#2535C2212yes—
122#2532C2214yescomplemented
123#2532C2214yescomplemented
124#2531C2214yescomplemented
125#2530C2214yescomplemented
126#2526C2214yescomplemented
127#2523C2214yescomplemented
128#2514C2212yescomplemented
129#2513C2212yescomplemented
130#2513C2212yescomplemented
131#2513C2212yescomplemented
132#2513C2212yescomplemented
133#2504C2212yes—
134#2500C2212yescomplemented
135#2495C2212yescomplemented
136#2495C2212yescomplemented
137#2494C2212yescomplemented
138#2492C2212yescomplemented
139#2492C2212yescomplemented
140#2492C2212yescomplemented
141#2492C2214yescomplemented
142#2492C2214yescomplemented
143#2492C2212yescomplemented
144#2491C2212yes—
145#2491C2212yes—
146#2491C2214yescomplemented
147#2491C2212yescomplemented
148#2491C2214yescomplemented
149#2491C2212yescomplemented
150#2490C2212yes—
151#2490C2212yes—
152#2480C2214yescomplemented
153#2477C2214yescomplemented
154#2476C2214yescomplemented
155#2474C2214yescomplemented
156#2472C2214yes—
157#2472C2214yes—
158#2472C2214yes—
159#2472C2214yes—
160#2472C2214yescomplemented
161#2472C2214yescomplemented
162#2459C2214yescomplemented
163#2459C2214yescomplemented
164#2459C2214yescomplemented
165#2453C2212yescomplemented
166#2452C2212yes—
167#2448C2212yescomplemented
168#2448C2212yescomplemented
169#2448C2212yescomplemented
170#2448C2212yescomplemented
171#2447C2212yes—
172#2447C2212yescomplemented
173#2447C2212yescomplemented
174#2440C2212yescomplemented
175#2439C2212yescomplemented
176#2436C2212yes—
177#2436C2212yescomplemented
178#2435C2212yes—
179#2435C2212yes—
180#2433C2212yes—
181#2432C2212yescomplemented
182#2429C2212yescomplemented
183#2429C2214yescomplemented
184#2428C2212yes—
185#2427C2212yes—
186#2426C2212yescomplemented
187#2424C2214yes—
188#2422C2212yes—
189#2421C2212yescomplemented
190#2421C2212yescomplemented
191#2420C2212yes—
192#2420C2212yescomplemented
193#2418C2214yescomplemented
194#2412C2214yescomplemented
195#2408C2212yes—
196#2407C2212yes—
197#2401C2214yescomplemented
198#2398C2214yescomplemented
199#2395C2214yescomplemented
200#2374C2214yescomplemented
201#2374C2212yescomplemented
202#2374C2212yescomplemented
203#2373C2212yescomplemented
204#2373C2212yescomplemented
205#2372C2214yescomplemented
206#2372C2214yescomplemented
207#2372C2214yescomplemented
208#2367C2212yes—
209#2367C2211yescharacteristic
210#2367C2211yescharacteristic
211#2367C2211yescharacteristic
212#2367C2212yescomplemented
213#2367C2212yescomplemented
214#2367C2212yescomplemented
215#2367C2212yescomplemented
216#2367C2212yescomplemented
217#2367C2211yescharacteristic, complemented
218#2366C2211yescharacteristic
219#2365C2211yescharacteristic, complemented
220#2363C2212yes—
221#2363C2214yescomplemented
222#2362C2212yescomplemented
223#2360C2212yescomplemented
224#2358C2214yescomplemented
225#2357C2211yescharacteristic
226#2357C2212yescomplemented
227#2357C2211yescharacteristic, complemented
228#2357C2212yescomplemented
229#2356C2211yescharacteristic, complemented
230#2356C2211yescharacteristic, complemented
231#2355C2211yescharacteristic, complemented
232#2355C2211yescharacteristic, complemented
233#2355C2211yescharacteristic, complemented
234#2354C2211yescharacteristic
235#2352C2212yescomplemented
236#2352C2212yescomplemented
237#2347C2212yescomplemented
238#2342C2214yescomplemented
239#2342C2214yescomplemented
240#2342C2214yescomplemented
241#2341C2212yescomplemented
242#2341C2212yescomplemented
243Q8×C22⋊C4C2212yescomplemented
244Q8×C22⋊C4C2212yescomplemented
245Q8×C22⋊C4C2212yescomplemented
246D4×C22⋊C4C2212yes—
247D4×C22⋊C4C2212yes—
248D4×C22⋊C4C2212yes—
249D4×C22⋊C4C2212yes—
250D4×C22⋊C4C2212yes—
251#2337C2214yescomplemented
252#2337C2214yescomplemented
253#2335C2214yescomplemented
254#2333C2214yescomplemented
255#2321C2214yescomplemented
256#2312C2214yescomplemented
257C4×C4⋊Q8C2211yescharacteristic, complemented
258C4×C4⋊Q8C2211yescharacteristic, complemented
259C4×C4⋊Q8C2211yescharacteristic, complemented
260C4×#127C2211yescharacteristic
261C4×#127C2211yescharacteristic
262C4×#126C2212yescomplemented
263C4×#126C2212yescomplemented
264C4×#124C2211yescharacteristic
265C4×#124C2212yes—
266C4×#124C2211yescharacteristic
267C4×#124C2211yescharacteristic
268C4×#124C2212yes—
269C4×#124C2212yes—
270C4×#124C2212yescomplemented
271C4×#124C2212yescomplemented
272C4×#124C2211yescharacteristic, complemented
273C4×#124C2212yescomplemented
274C4×#124C2212yescomplemented
275C4×C22⋊Q8C2212yescomplemented
276C4×C22⋊Q8C2212yescomplemented
277C4×#123C2212yescomplemented
278C4×#123C2212yescomplemented
279C4×#121C2212yes—
280C4×#121C2212yescomplemented
281#2297C2212yescomplemented
282#2295C2212yescomplemented
283#2293C2212yescomplemented
284#2293C2212yescomplemented
285C2×#390C2212yes—
286#2283C2212yescomplemented
287#2283C2212yescomplemented
288#2283C2212yescomplemented
289#2273C2214yescomplemented
290C42×Q8C2211yescharacteristic, complemented
291C42×Q8C2211yescharacteristic, complemented
292C42×Q8C2211yescharacteristic, complemented
293C42×Q8C2211yescharacteristic, complemented
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2212yescomplemented
297C42×D4C2211yescharacteristic, complemented
298C4×#117C2212yescomplemented
299C22×#41C2312yes—
300C23×Q8C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303#559—28no—
304Q82—44no—
305#556—28no—
306#556—44no—
307#554—44no—
308#550—44no—
309D4×Q8—44no—
310#546—216no—
311D42—44no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2314yes—
319C2×#127C2311yescharacteristic
320C2×#127C2311yescharacteristic
321C2×#127C2312yes—
322C2×#126C2312yes—
323C2×#126C2312yes—
324C2×#126C2314yes—
325C2×#125C2312yes—
326C2×#124—216no—
327C2×#124C2312yes—
328C2×#124C2314yes—
329C2×#124C2311yescharacteristic
330C2×#124C2311yescharacteristic
331C2×#124C2312yes—
332C2×#124C2314yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2314yes—
339C2×#124C2312yes—
340C2×#124C2312yes—
341C2×#124C2314yes—
342C2×#124C2311yescharacteristic
343C2×#124C2311yescharacteristic
344C2×#123C2314yes—
345C2×#123C2312yes—
346C2×#123C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2314yes—
355C2×#121C2314yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2314yes—
362C2×#120C2314yes—
363C2×#120C2314yes—
364C2×#120C2314yes—
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×Q8C2311yescharacteristic
369C2×C4×Q8C2311yescharacteristic
370C2×C4×Q8C2311yescharacteristic
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2312yes—
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2312yes—
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2312yes—
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2314yes—
402C2×#117C2312yes—
403C2×#117C2312yes—
404C2×#117C2312yes—
405C2×#117C2314yes—
406C22×C4⋊C4C2312yes—
407C22×C22⋊C4C2314yes—
408C22×C22⋊C4C2314yes—
409C22×C22⋊C4C2314yes—
410C22×C22⋊C4C2314yes—
411C22×C22⋊C4C2314yes—
412C22×C42C2312yes—
413C22×C42C2312yes—
414C22×C42C2312yes—
415#401C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#399C2314yes—
425#399C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#395C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2311yescharacteristic
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2312yes—
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2314yes—
497#391C2314yes—
498#391C2312yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2314yes—
505#391C2311yescharacteristic
506#391C2311yescharacteristic
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2312yes—
512#391C2311yescharacteristic
513#391C2314yes—
514#390C2312yes—
515#390C2312yes—
516#390C2314yes—
517#390C2312yes—
518#390C2312yes—
519#390C2311yescharacteristic
520#390C2311yescharacteristic
521#390C2312yes—
522#390C2311yescharacteristic
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2314yes—
528#390C2312yes—
529#390C2312yes—
530#390C2314yes—
531#390C2314yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2314yes—
542#390C2314yes—
543#390C2312yes—
544#390C2311yescharacteristic
545#390C2311yescharacteristic
546#390C2314yes—
547#390C2311yescharacteristic
548#390C2312yes—
549#390C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2314yes—
561#389C2314yes—
562#389C2312yes—
563#389C2312yes—
564#388C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2312yes—
604#388C2314yes—
605#388C2314yes—
606#388C2312yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2312yes—
625#388C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#387C2312yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#387C2312yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2312yes—
667#386C2312yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2312yes—
675#385C2312yes—
676#385C2314yes—
677#385C2314yes—
678#385C2312yes—
679#385C2312yes—
680#384C2311yescharacteristic
681#384C2311yescharacteristic
682#384C2311yescharacteristic
683#383C2312yes—
684#383C2312yes—
685#383C2314yes—
686#383C2314yes—
687#383C2314yes—
688#382C2312yes—
689#382C2312yes—
690#382C2312yes—
691#382C2312yes—
692#382C2311yescharacteristic
693#382C2312yes—
694#382C2312yes—
695#382C2312yes—
696#382C2311yescharacteristic
697#382C2311yescharacteristic
698#382C2311yescharacteristic
699#382C2312yes—
700#381C2312yes—
701#381C2314yes—
702#381C2314yes—
703#381C2314yes—
704#381C2314yes—
705#381C2312yes—
706#380C2314yes—
707#380C2312yes—
708#380C2312yes—
709#380C2314yes—
710#380C2314yes—
711#380C2314yes—
712#380C2312yes—
713#380C2312yes—
714#380C2314yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#379C2314yes—
722#379C2314yes—
723#379C2314yes—
724#379C2314yes—
725#379C2314yes—
726C4×C4⋊C4C2312yes—
727C4×C4⋊C4C2311yescharacteristic
728C4×C4⋊C4C2311yescharacteristic
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2311yescharacteristic
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C22⋊C4C2312yes—
770C4×C22⋊C4C2312yes—
771C4×C22⋊C4C2312yes—
772C4×C22⋊C4C2312yes—
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2314yes—
775C4×C22⋊C4C2314yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810#376C2314yes—
811#376C2312yes—
812#376C2312yes—
813#376C2314yes—
814C43C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2311yescharacteristic
818C43C2311yescharacteristic
819C43C2312yes—
820C25C2414yes—
821C2×#41—28no—
822C2×#41—44no—
823C2×#41—44no—
824C22×Q8—28no—
825C22×Q8—44no—
826C22×Q8—44no—
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2411yescharacteristic
830C22×Q8C2411yescharacteristic
831C22×Q8C2411yescharacteristic
832C22×Q8C2412yes—
833C22×Q8C2414yes—
834C22×Q8C2414yes—
835C22×D4—28no—
836C22×D4—28no—
837C22×D4—44no—
838C22×D4—44no—
839C22×D4—44no—
840C22×D4—44no—
841C22×D4C2411yescharacteristic
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2411yescharacteristic
846C22×D4C2411yescharacteristic
847C22×D4C2414yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2414yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2412yes—
865C23×C4C2414yes—
866C23×C4C2412yes—
867C4⋊Q8—24no—
868C4⋊Q8—24no—
869C4⋊Q8—24no—
870C4⋊Q8—44no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—48no—
874#127—24no—
875#127—24no—
876#127—44no—
877#126—28no—
878#126—28no—
879#126—48no—
880#125—44no—
881#124—28no—
882#124—24no—
883#124—28no—
884#124—24no—
885#124—216no—
886#124—216no—
887#124—28no—
888#124—28no—
889#124—48no—
890#124—44no—
891#124—44no—
892#124—44no—
893#124—44no—
894#124—82no—
895#124—84no—
896#124#4118yes—
897#124#4118yescomplemented
898#123—216no—
899#123—28no—
900#123—28no—
901C22⋊Q8—28no—
902C22⋊Q8—28no—
903C22⋊Q8—48no—
904C22⋊Q8—48no—
905C22⋊Q8—44no—
906C22⋊Q8—44no—
907C22⋊Q8—44no—
908C22⋊Q8—84no—
909#121—28no—
910#121—216no—
911#121—48no—
912#121—44no—
913#121—44no—
914#121—44no—
915#121—44no—
916#120—216no—
917#120—48no—
918#120—84no—
919C4×Q8—24no—
920C4×Q8—24no—
921C4×Q8—24no—
922C4×Q8—24no—
923C4×Q8—24no—
924C4×Q8—24no—
925C4×Q8—24no—
926C4×Q8—24no—
927C4×Q8—42no—
928C4×Q8—42no—
929C4×Q8—42no—
930C4×Q8—42no—
931C4×Q8—44no—
932C4×Q8—44no—
933C4×Q8—44no—
934C4×Q8—44no—
935C4×Q8—82no—
936C4×D4—24no—
937C4×D4—24no—
938C4×D4—28no—
939C4×D4—28no—
940C4×D4—28no—
941C4×D4—24no—
942C4×D4—24no—
943C4×D4—24no—
944C4×D4—24no—
945C4×D4—42no—
946C4×D4—44no—
947C4×D4—42no—
948C4×D4—42no—
949C4×D4—44no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—82no—
955C4×D4—84no—
956#117—28no—
957#117—44no—
958#117—44no—
959#117—84no—
960C2×C4⋊C4—44no—
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2412yes—
1013C2×C22⋊C4—216no—
1014C2×C22⋊C4—216no—
1015C2×C22⋊C4—216no—
1016C2×C22⋊C4—48no—
1017C2×C22⋊C4—84no—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C42—28no—
1083C2×C42—44no—
1084C2×C42—44no—
1085C2×C42C2412yes—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2414yes—
1110C2×C42C2412yes—
1111C2×C42C2411yescharacteristic
1112C2×C42C2414yes—
1113C2×C42C2412yes—
1114C2×C42C2414yes—
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2414yes—
1122C2×C42C2411yescharacteristic
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131#95C2411yescharacteristic
1132#95C2411yescharacteristic
1133#95C2412yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2412yes—
1148#95C2411yescharacteristic
1149#95C2412yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2411yescharacteristic
1184#95C2412yes—
1185#95C2411yescharacteristic
1186#95C2412yes—
1187#95C2412yes—
1188#95C2411yescharacteristic
1189#95C2412yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2414yes—
1197C24—28no—
1198C24—28no—
1199C24—44no—
1200C24—44no—
1201C24—44no—
1202C24—44no—
1203C24—44no—
1204C24C2514yes—
1205C24C2512yes—
1206C24C2512yes—
1207C24C2512yes—
1208#41—816no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—28no—
1214C2×Q8—22no—
1215C2×Q8—22no—
1216C2×Q8—22no—
1217C2×Q8—24no—
1218C2×Q8—24no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—24no—
1223C2×Q8—41no—
1224C2×Q8—42no—
1225C2×Q8—44no—
1226C2×Q8—42no—
1227C2×Q8—44no—
1228C2×Q8—44no—
1229C2×Q8—44no—
1230C2×Q8—44no—
1231C2×Q8—816no—
1232C2×Q8C2×#4114yes—
1233C2×Q8C2×#4114yes—
1234C2×D4—24no—
1235C2×D4—28no—
1236C2×D4—28no—
1237C2×D4—24no—
1238C2×D4—28no—
1239C2×D4—24no—
1240C2×D4—22no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—28no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—42no—
1256C2×D4—42no—
1257C2×D4—44no—
1258C2×D4—42no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—42no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—42no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—44no—
1270C2×D4—44no—
1271C2×D4—816no—
1272C2×D4—816no—
1273C2×D4C2×#4114yes—
1274C2×D4C2×#4114yes—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—24no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—24no—
1285C22×C4—24no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—28no—
1289C22×C4—28no—
1290C22×C4—28no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—44no—
1300C22×C4—44no—
1301C22×C4—44no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—44no—
1305C22×C4—42no—
1306C22×C4—42no—
1307C22×C4—42no—
1308C22×C4—42no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4C2512yes—
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2512yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C22×C4C2512yes—
1324C22×C4C2514yes—
1325C22×C4C2514yes—
1326C22×C4C2512yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2514yes—
1330C22×C4C2511yescharacteristic
1331C22×C4C2512yes—
1332C22×C4C2511yescharacteristic
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C22×C4C2511yescharacteristic
1338C22×C4C2511yescharacteristic
1339C22×C4C2512yes—
1340C22×C4C2512yes—
1341C22×C4C2511yescharacteristic
1342C22×C4C2511yescharacteristic
1343C22×C4C2511yescharacteristic
1344C22×C4C2511yescharacteristic
1345C4⋊C4—22no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—28no—
1360C4⋊C4—24no—
1361C4⋊C4—22no—
1362C4⋊C4—24no—
1363C4⋊C4—24no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—22no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—22no—
1373C4⋊C4—24no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—22no—
1377C4⋊C4—22no—
1378C4⋊C4—24no—
1379C4⋊C4—44no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—41no—
1388C4⋊C4—44no—
1389C4⋊C4—42no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—42no—
1397C22⋊C4—28no—
1398C22⋊C4—28no—
1399C22⋊C4—28no—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—28no—
1406C22⋊C4—28no—
1407C22⋊C4—28no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—28no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—28no—
1420C22⋊C4—24no—
1421C22⋊C4—44no—
1422C22⋊C4—44no—
1423C22⋊C4—42no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—42no—
1456C22⋊C4—44no—
1457C22⋊C4C2×#4118yes—
1458C22⋊C4C2×#4118yes—
1459C22⋊C4C2×#4118yes—
1460C22⋊C4C2×#4118yes—
1461C42—24no—
1462C42—24no—
1463C42—24no—
1464C42—24no—
1465C42—24no—
1466C42—24no—
1467C42—22no—
1468C42—22no—
1469C42—22no—
1470C42—22no—
1471C42—24no—
1472C42—24no—
1473C42—24no—
1474C42—22no—
1475C42—22no—
1476C42—24no—
1477C42—24no—
1478C42—22no—
1479C42—22no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—42no—
1484C42—42no—
1485C42—42no—
1486C42—42no—
1487C42—42no—
1488C42—44no—
1489C42—42no—
1490C42—42no—
1491C42—42no—
1492C42—41no—
1493C42—44no—
1494C42—42no—
1495C42—44no—
1496C42—42no—
1497C42—41no—
1498C42—41no—
1499C42—42no—
1500C42—44no—
1501C42—41no—
1502C42—41no—
1503C42—42no—
1504C42C2×#4114yes—
1505C42C2×#4114yes—
1506C42H(5,𝔽2)14yes—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23—22no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—22no—
1517C23—22no—
1518C23—22no—
1519C23—24no—
1520C23—22no—
1521C23—24no—
1522C23—22no—
1523C23—22no—
1524C23—24no—
1525C23—24no—
1526C23—22no—
1527C23—22no—
1528C23—24no—
1529C23—24no—
1530C23—22no—
1531C23—24no—
1532C23—22no—
1533C23—416no—
1534C23—88no—
1535C23—88no—
1536C23—88no—
1537C23—88no—
1538C23—164no—
1539C23—164no—
1540C23C22×#4114yes—
1541C23C22×#4114yes—
1542C23C2611yescharacteristic
1543Q8—28no—
1544Q8—28no—
1545Q8—44no—
1546Q8—44no—
1547Q8—48no—
1548Q8—84no—
1549Q8—88no—
1550Q8—164no—
1551D4—28no—
1552D4—28no—
1553D4—48no—
1554D4—44no—
1555D4—48no—
1556D4—48no—
1557D4—84no—
1558D4—88no—
1559D4—84no—
1560D4—88no—
1561D4—88no—
1562D4—88no—
1563D4—164no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—24no—
1602C2×C4—24no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—21no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—24no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—21no—
1642C2×C4—24no—
1643C2×C4—48no—
1644C2×C4—48no—
1645C2×C4—48no—
1646C2×C4—48no—
1647C2×C4—84no—
1648C2×C4—84no—
1649C2×C4—88no—
1650C2×C4—84no—
1651C2×C4—88no—
1652C2×C4—88no—
1653C2×C4—84no—
1654C2×C4—84no—
1655C2×C4—164no—
1656C2×C4C22×#4112yes—
1657C2×C4C22×#4112yes—
1658C2×C4C22×#4112yes—
1659C2×C4C22×#4114yes—
1660C2×C4C22×#4114yes—
1661C2×C4C22×#4112yes—
1662C2×C4C22×#4112yes—
1663C2×C4C22×#4112yes—
1664C2×C4C2×H(5,𝔽2)12yes—
1665C2×C4C2×H(5,𝔽2)12yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4#58512yes—
1668C2×C4#58512yes—
1669C2×C4#58512yes—
1670C22—24no—
1671C22—24no—
1672C22—24no—
1673C22—24no—
1674C22—24no—
1675C22—24no—
1676C22—42no—
1677C22—42no—
1678C22—42no—
1679C22—42no—
1680C22—42no—
1681C22—42no—
1682C22—42no—
1683C22—42no—
1684C22—42no—
1685C22—44no—
1686C22—44no—
1687C22—42no—
1688C22—42no—
1689C22—44no—
1690C22—42no—
1691C22—44no—
1692C22—44no—
1693C22—42no—
1694C22—44no—
1695C22—42no—
1696C22—42no—
1697C22—44no—
1698C22—1616no—
1699C22C23×#4111yescharacteristic
1700C22C23×#4111yescharacteristic
1701C22C22×H(5,𝔽2)11yescharacteristic
1702C22C2×#58511yescharacteristic
1703C22C2×#58511yescharacteristic
1704C22C2×#58511yescharacteristic
1705C22H(7,𝔽2)11yescharacteristic
1706C4—22no—
1707C4—22no—
1708C4—22no—
1709C4—24no—
1710C4—24no—
1711C4—22no—
1712C4—22no—
1713C4—22no—
1714C4—42no—
1715C4—42no—
1716C4—41no—
1717C4—41no—
1718C4—41no—
1719C4—41no—
1720C4—44no—
1721C4—41no—
1722C4—41no—
1723C4—42no—
1724C4—42no—
1725C4—42no—
1726C4—42no—
1727C4—44no—
1728C4—42no—
1729C4—42no—
1730C4—44no—
1731C4—42no—
1732C4—42no—
1733C4—42no—
1734C4—41no—
1735C4#351414yes—
1736C4#351414yes—
1737C2—44no—
1738C2—44no—
1739C2—82no—
1740C2—84no—
1741C2#41211yescharacteristic
1742C2C2×#351411yescharacteristic
1743C2C2×#351411yescharacteristic
1744C2#6296111yescharacteristic
1745C2#6299411yescharacteristic
1746C2#6301011yescharacteristic
1747C2#6302911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#59412C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59655C2semidirect
2. #59489C2semidirect
3. #59484C2semidirect
4. #59421C2semidirect
5. #59416C2semidirect
7. #59282C2semidirect
8. #59224C2semidirect
9. #59147C2semidirect
10. #44099C2semidirect
11. #43855C2semidirect
12. #43675C2semidirect
13. #40218C2semidirect
14. #40049C2semidirect
15. #40002C2semidirect
16. #39905C2semidirect
17. #39248C2semidirect
18. #39020C2semidirect
19. #36609C2semidirect
20. Q8×#124C2semidirect
21. #36534C2semidirect
22. #36457C2semidirect
23. #36419C2semidirect
24. #36373C2semidirect
25. #36289C2semidirect
26. #36195C2semidirect
27. D4×#124C2semidirect
28. #35894C2semidirect
29. #34954C2semidirect
30. #34945C2semidirect
31. #34943C2semidirect
32. #34320C2semidirect
33. #34240C2semidirect
34. C4×#559C2semidirect
35. C4×#556C2semidirect
37. C2×Q82C22semidirect
39. C2×#556C22semidirect
46. #2862C22semidirect
47. #2862C22semidirect
48. #2861C22semidirect
51. #2858C22semidirect
54. #2850C22semidirect
55. #2808C22semidirect
56. #2778C22semidirect
57. #2770C22semidirect
58. #2759C22semidirect
59. #2756C22semidirect
60. #2754C22semidirect
61. #2751C22semidirect
62. #2750C22semidirect
63. #2749C22semidirect
64. #2741C22semidirect
65. #2737C22semidirect
66. #2736C22semidirect
67. #2730C22semidirect
68. #2729C22semidirect
69. #2712C22semidirect
70. #2710C22semidirect
71. #2702C22semidirect
72. #2687C22semidirect
73. #2685C22semidirect
74. #2684C22semidirect
76. #2653C22semidirect
77. #2653C22semidirect
78. #2648C22semidirect
79. #2610C22semidirect
80. #2593C22semidirect
81. #2593C22semidirect
82. #2592C22semidirect
83. #2592C22semidirect
84. #2589C22semidirect
85. #2582C22semidirect
86. #2580C22semidirect
87. #2578C22semidirect
88. #2573C22semidirect
89. #2572C22semidirect
90. #2572C22semidirect
91. #2572C22semidirect
92. #2571C22semidirect
93. #2568C22semidirect
94. #2568C22semidirect
95. #2565C22semidirect
98. #2563C22semidirect
99. #2563C22semidirect
100. #2561C22semidirect
101. #2560C22semidirect
102. #2560C22semidirect
103. #2560C22semidirect
104. #2559C22semidirect
105. #2559C22semidirect
106. #2559C22semidirect
107. #2557C22semidirect
108. #2553C22semidirect
109. #2550C22semidirect
112. #2548C22semidirect
115. #2544C22semidirect
116. #2544C22semidirect
119. #2536C22semidirect
120. #2536C22semidirect
122. #2532C22semidirect
123. #2532C22semidirect
124. #2531C22semidirect
125. #2530C22semidirect
126. #2526C22semidirect
127. #2523C22semidirect
128. #2514C22semidirect
129. #2513C22semidirect
130. #2513C22semidirect
131. #2513C22semidirect
132. #2513C22semidirect
134. #2500C22semidirect
135. #2495C22semidirect
136. #2495C22semidirect
137. #2494C22semidirect
138. #2492C22semidirect
139. #2492C22semidirect
140. #2492C22semidirect
141. #2492C22semidirect
142. #2492C22semidirect
143. #2492C22semidirect
146. #2491C22semidirect
147. #2491C22semidirect
148. #2491C22semidirect
149. #2491C22semidirect
152. #2480C22semidirect
153. #2477C22semidirect
154. #2476C22semidirect
155. #2474C22semidirect
160. #2472C22semidirect
161. #2472C22semidirect
162. #2459C22semidirect
163. #2459C22semidirect
164. #2459C22semidirect
165. #2453C22semidirect
167. #2448C22semidirect
168. #2448C22semidirect
169. #2448C22semidirect
170. #2448C22semidirect
172. #2447C22semidirect
173. #2447C22semidirect
174. #2440C22semidirect
175. #2439C22semidirect
177. #2436C22semidirect
181. #2432C22semidirect
182. #2429C22semidirect
183. #2429C22semidirect
186. #2426C22semidirect
189. #2421C22semidirect
190. #2421C22semidirect
192. #2420C22semidirect
193. #2418C22semidirect
194. #2412C22semidirect
197. #2401C22semidirect
198. #2398C22semidirect
199. #2395C22semidirect
200. #2374C22semidirect
201. #2374C22semidirect
202. #2374C22semidirect
203. #2373C22semidirect
204. #2373C22semidirect
205. #2372C22semidirect
206. #2372C22semidirect
207. #2372C22semidirect
212. #2367C22semidirect
213. #2367C22semidirect
214. #2367C22semidirect
215. #2367C22semidirect
216. #2367C22semidirect
217. #2367C22semidirect
219. #2365C22semidirect
221. #2363C22semidirect
222. #2362C22semidirect
223. #2360C22semidirect
224. #2358C22semidirect
226. #2357C22semidirect
227. #2357C22semidirect
228. #2357C22semidirect
229. #2356C22semidirect
230. #2356C22semidirect
231. #2355C22semidirect
232. #2355C22semidirect
233. #2355C22semidirect
235. #2352C22semidirect
236. #2352C22semidirect
237. #2347C22semidirect
238. #2342C22semidirect
239. #2342C22semidirect
240. #2342C22semidirect
241. #2341C22semidirect
242. #2341C22semidirect
243. Q8×C22⋊C4C22semidirect
244. Q8×C22⋊C4C22semidirect
245. Q8×C22⋊C4C22semidirect
251. #2337C22semidirect
252. #2337C22semidirect
253. #2335C22semidirect
254. #2333C22semidirect
255. #2321C22semidirect
256. #2312C22semidirect
257. C4×C4⋊Q8C22semidirect
258. C4×C4⋊Q8C22semidirect
259. C4×C4⋊Q8C22semidirect
262. C4×#126C22semidirect
263. C4×#126C22semidirect
270. C4×#124C22semidirect
271. C4×#124C22semidirect
272. C4×#124C22semidirect
273. C4×#124C22semidirect
274. C4×#124C22semidirect
275. C4×C22⋊Q8C22semidirect
276. C4×C22⋊Q8C22semidirect
277. C4×#123C22semidirect
278. C4×#123C22semidirect
280. C4×#121C22semidirect
281. #2297C22semidirect
282. #2295C22semidirect
283. #2293C22semidirect
284. #2293C22semidirect
286. #2283C22semidirect
287. #2283C22semidirect
288. #2283C22semidirect
289. #2273C22semidirect
290. C42×Q8C22semidirect
291. C42×Q8C22semidirect
292. C42×Q8C22semidirect
293. C42×Q8C22semidirect
296. C42×D4C22semidirect
297. C42×D4C22semidirect
298. C4×#117C22semidirect
897. #124#41semidirect

Maximal subgroups

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

subgroupindex
#596552
#594892
#594842
#594212
#594162
#594122
#592822
#592242
#591472
#440992
#438552
#436752
#402182
#400492
#400022
#399052
#392482
#390202
#366092
Q8×#1242
#365342
#364572
#364192
#363732
#362892
#361952
D4×#1242
#358942
#349542
#349452
#349432
#343202
#342402
C4×#5592
C4×#5562