Finite Group Databasebeta

← #7806331

Subgroups — #7806331

Order 512.

5158 conjugacy classes of subgroups.

The subgroup lattice has 1730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59821C211yesmaximal, characteristic, complemented
3#59642C211yesmaximal, characteristic, complemented
4#59639C211yesmaximal, characteristic, complemented
5#59637C212yesmaximal
6#59451C211yesmaximal, characteristic, complemented
7#59450C211yesmaximal, characteristic, complemented
8#59444C211yesmaximal, characteristic, complemented
9#59444C211yesmaximal, characteristic, complemented
10#59424C212yesmaximal, complemented
11#59321C212yesmaximal, complemented
12#59302C212yesmaximal, complemented
13#59027C212yesmaximal, complemented
14#59025C212yesmaximal, complemented
15#59016C212yesmaximal, complemented
16#59014C212yesmaximal, complemented
17#47710C214yesmaximal, complemented
18#47709C214yesmaximal, complemented
19#42704C212yesmaximal, complemented
20#42699C212yesmaximal, complemented
21#42669C212yesmaximal, complemented
22#42668C212yesmaximal, complemented
23#41974C214yesmaximal, complemented
24#37615C211yesmaximal, characteristic, complemented
25#35988C214yesmaximal, complemented
26#35934C212yesmaximal, complemented
27#35860C212yesmaximal, complemented
28#35834C212yesmaximal, complemented
29#35773C212yesmaximal, complemented
30#34966C211yesmaximal, characteristic, complemented
31#34965C211yesmaximal, characteristic
32C2×#2542C211yesmaximal, characteristic, complemented
33#34243C211yesmaximal, characteristic, complemented
34#34216C211yesmaximal, characteristic, complemented
35#34194C211yesmaximal, characteristic, complemented
36C2×#556C2212yescomplemented
37C2×#554C2212yescomplemented
38C2×#552C2212yescomplemented
39C2×#552C2212yescomplemented
40C22×C4⋊Q8C2211yescharacteristic
41C2×#529C2211yescharacteristic
42C22×C22⋊Q8C2212yes—
43C22×C22⋊Q8C2212yes—
44C22×C4×D4C2211yescharacteristic
45#2837C2214yescomplemented
46#2836C2214yescomplemented
47#2821C2214yescomplemented
48#2807C2214yescomplemented
49#2798C2214yescomplemented
50#2797C2214yes—
51#2793C2214yescomplemented
52#2793C2214yescomplemented
53#2791C2214yescomplemented
54#2791C2214yescomplemented
55#2786C2214yes—
56#2773C2214yescomplemented
57#2771C2214yescomplemented
58#2752C2214yes—
59#2740C2214yes—
60#2732C2214yescomplemented
61#2727C2214yescomplemented
62#2704C2214yescomplemented
63#2702C2214yescomplemented
64#2700C2214yescomplemented
65#2698C2214yescomplemented
66#2694C2214yescomplemented
67#2694C2214yescomplemented
68#2692C2214yescomplemented
69#2690C2214yescomplemented
70#2689C2214yescomplemented
71#2687C2214yescomplemented
72#2667C2214yescomplemented
73#2664C2214yescomplemented
74#2663C2214yescomplemented
75#2660C2212yescomplemented
76#2654C2214yescomplemented
77#2651C2214yescomplemented
78#2649C2214yescomplemented
79#2640C2212yescomplemented
80#2623C2214yes—
81#2621C2212yescomplemented
82#2621C2212yescomplemented
83#2606C2212yescomplemented
84#2605C2212yescomplemented
85#2603C2212yes—
86#2603C2212yes—
87#2602C2214yes—
88#2601C2214yes—
89#2596C2214yescomplemented
90#2596C2214yescomplemented
91#2592C2212yes—
92#2589C2214yescomplemented
93#2582C2212yescomplemented
94#2580C2212yes—
95#2575C2214yescomplemented
96#2571C2212yescomplemented
97#2570C2212yescomplemented
98#2570C2211yescharacteristic, complemented
99#2570C2211yescharacteristic, complemented
100#2570C2212yescomplemented
101#2568C2211yescharacteristic, complemented
102#2568C2211yescharacteristic, complemented
103#2566C2211yescharacteristic
104#2566C2211yescharacteristic
105#2565C2214yescomplemented
106#2560C2214yes—
107#2560C2214yescomplemented
108#2557C2214yes—
109#2556C2214yescomplemented
110#2556C2214yescomplemented
111#2553C2214yescomplemented
112#2552C2212yescomplemented
113#2552C2212yescomplemented
114#2552C2212yescomplemented
115#2550C2211yescharacteristic, complemented
116#2550C2211yescharacteristic, complemented
117#2549C2214yescomplemented
118#2548C2212yes—
119#2544C2211yescharacteristic
120#2544C2211yescharacteristic
121#2542C2212yes—
122#2542C2211yescharacteristic
123#2542C2211yescharacteristic
124#2542C2211yescharacteristic
125#2542C2211yescharacteristic
126#2542C2214yes—
127#2542C2212yes—
128#2542C2212yes—
129#2542C2212yes—
130#2542C2211yescharacteristic, complemented
131#2542C2211yescharacteristic, complemented
132#2538C2212yes—
133#2538C2212yescomplemented
134#2538C2212yescomplemented
135#2538C2212yescomplemented
136#2536C2212yescomplemented
137#2536C2212yescomplemented
138#2522C2214yescomplemented
139#2521C2214yescomplemented
140#2519C2214yescomplemented
141#2516C2214yescomplemented
142#2513C2212yes—
143#2513C2212yes—
144#2512C2212yes—
145#2512C2212yes—
146#2512C2212yescomplemented
147#2512C2212yescomplemented
148#2511C2212yescomplemented
149#2511C2212yescomplemented
150#2506C2214yescomplemented
151#2504C2211yescharacteristic
152#2504C2212yes—
153#2503C2212yescomplemented
154#2502C2212yes—
155#2502C2211yescharacteristic
156#2502C2212yescomplemented
157#2499C2212yescomplemented
158#2499C2214yescomplemented
159#2499C2212yescomplemented
160#2496C2214yescomplemented
161#2492C2212yescomplemented
162#2492C2212yescomplemented
163#2489C2212yescomplemented
164#2489C2212yescomplemented
165#2488C2214yescomplemented
166#2481C2214yes—
167#2481C2214yes—
168#2480C2214yes—
169#2480C2214yes—
170#2479C2214yescomplemented
171#2479C2214yescomplemented
172#2477C2214yescomplemented
173#2473C2214yes—
174#2473C2214yes—
175#2472C2214yes—
176#2465C2214yescomplemented
177#2454C2214yescomplemented
178#2450C2214yescomplemented
179#2448C2212yes—
180#2448C2214yescomplemented
181#2447C2212yes—
182#2445C2212yes—
183#2445C2212yes—
184#2442C2211yescharacteristic
185#2442C2214yes—
186#2442C2211yescharacteristic
187#2440C2211yescharacteristic
188#2440C2211yescharacteristic
189#2438C2212yes—
190#2438C2212yes—
191#2438C2214yescomplemented
192#2437C2214yes—
193#2435C2211yescharacteristic
194#2433C2211yescharacteristic
195#2423C2212yescomplemented
196#2423C2212yescomplemented
197#2421C2212yescomplemented
198#2421C2212yescomplemented
199#2418C2214yes—
200#2417C2214yes—
201#2417C2212yescomplemented
202#2417C2212yescomplemented
203#2417C2212yescomplemented
204#2417C2212yescomplemented
205#2415C2212yescomplemented
206#2415C2212yescomplemented
207#2415C2212yescomplemented
208#2415C2212yescomplemented
209#2412C2214yes—
210#2411C2212yes—
211#2411C2212yes—
212#2409C2212yes—
213#2409C2212yes—
214#2402C2212yescomplemented
215#2399C2212yescomplemented
216#2396C2214yescomplemented
217#2395C2214yescomplemented
218C2×#399C2214yes—
219#2392C2212yes—
220#2392C2212yes—
221#2370C2212yescomplemented
222#2369C2212yescomplemented
223#2369C2212yescomplemented
224#2367C2212yes—
225#2367C2212yescomplemented
226#2366C2212yes—
227#2365C2212yescomplemented
228#2365C2212yescomplemented
229#2362C2212yescomplemented
230#2362C2212yescomplemented
231#2360C2214yes—
232#2360C2212yescomplemented
233#2360C2212yescomplemented
234#2359C2214yes—
235#2358C2214yes—
236#2357C2212yes—
237#2355C2212yescomplemented
238#2355C2211yescharacteristic, complemented
239#2355C2212yescomplemented
240#2354C2212yes—
241#2354C2211yescharacteristic
242#2354C2211yescharacteristic
243#2354C2212yescomplemented
244#2354C2211yescharacteristic, complemented
245#2352C2212yes—
246#2352C2212yes—
247#2352C2212yes—
248#2352C2214yes—
249Q8×C4⋊C4C2211yescharacteristic, complemented
250Q8×C4⋊C4C2212yescomplemented
251D4×C4⋊C4C2211yescharacteristic
252D4×C4⋊C4C2212yes—
253D4×C4⋊C4C2211yescharacteristic
254D4×C4⋊C4C2211yescharacteristic, complemented
255#2345C2212yes—
256#2345C2212yes—
257#2345C2212yes—
258#2342C2214yes—
259#2342C2214yes—
260Q8×C22⋊C4C2212yes—
261Q8×C22⋊C4C2212yes—
262D4×C22⋊C4C2212yes—
263#2334C2214yescomplemented
264#2331C2212yescomplemented
265#2331C2212yescomplemented
266#2319C2212yes—
267#2318C2214yes—
268#2316C2212yes—
269#2314C2212yescomplemented
270C4×C4⋊Q8C2211yescharacteristic, complemented
271C4×C4⋊Q8C2211yescharacteristic, complemented
272C4×C4⋊Q8C2211yescharacteristic, complemented
273C4×C4⋊Q8C2211yescharacteristic, complemented
274C4×C4⋊Q8C2211yescharacteristic, complemented
275C4×C4⋊Q8C2211yescharacteristic, complemented
276C4×#127C2211yescharacteristic
277C4×#127C2211yescharacteristic
278C4×#125C2211yescharacteristic, complemented
279C4×#125C2211yescharacteristic, complemented
280C4×#124C2211yescharacteristic
281C4×#124C2211yescharacteristic
282C4×C22⋊Q8C2212yes—
283C4×C22⋊Q8C2212yes—
284C4×C22⋊Q8C2212yes—
285C4×#121C2212yes—
286C4×#120C2212yes—
287C4×#120C2212yes—
288C2×#390C2212yes—
289#2285C2211yescharacteristic
290C2×#384C2212yes—
291#2283C2211yescharacteristic
292#2280C2212yes—
293C2×#380C2212yes—
294#2275C2212yes—
295#2274C2212yes—
296#2274C2212yescomplemented
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C23×Q8C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#556—48no—
303#554—48no—
304#552—48no—
305#552—48no—
306C2×C4⋊Q8—28no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×#127C2311yescharacteristic
315C2×#127C2311yescharacteristic
316#529—28no—
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#125C2311yescharacteristic
323C2×#125C2311yescharacteristic
324C2×#125C2311yescharacteristic
325C2×#125C2314yes—
326C2×#125C2314yes—
327C2×#125C2314yes—
328C2×#124C2311yescharacteristic
329C2×#124C2311yescharacteristic
330C2×#124C2311yescharacteristic
331C2×#124C2314yes—
332C2×#123C2312yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×C22⋊Q8—48no—
336C2×C22⋊Q8—48no—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2314yes—
355C2×C22⋊Q8C2314yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2312yes—
358C2×#121C2311yescharacteristic
359C2×#120C2312yes—
360C2×#120C2312yes—
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2314yes—
369C2×C4×Q8C2312yes—
370C2×C4×D4—28no—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2314yes—
386C2×C4×D4C2314yes—
387C2×C4×D4C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C2×#117C2311yescharacteristic
392C2×#117C2312yes—
393C2×#117C2314yes—
394C2×#117C2312yes—
395C2×#117C2312yes—
396C2×#117C2314yes—
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2311yescharacteristic
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2311yescharacteristic
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2311yescharacteristic
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2314yes—
406C22×C4⋊C4C2314yes—
407C22×C22⋊C4C2312yes—
408C22×C22⋊C4C2314yes—
409C22×C22⋊C4C2314yes—
410C22×C22⋊C4C2314yes—
411C22×C42C2312yes—
412C22×C42C2311yescharacteristic
413#400C2314yes—
414#400C2314yes—
415#400C2312yes—
416#400C2314yes—
417#400C2312yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2312yes—
424#400C2312yes—
425#400C2314yes—
426#400C2314yes—
427#399C2314yes—
428#399C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#399C2314yes—
434#399C2314yes—
435#399C2314yes—
436#399C2314yes—
437#399C2314yes—
438#399C2314yes—
439#398C2314yes—
440#398C2312yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2312yes—
447#398C2312yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2312yes—
455#398C2312yes—
456#398C2312yes—
457#398C2312yes—
458#398C2314yes—
459#398C2312yes—
460#398C2314yes—
461#398C2312yes—
462#398C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2312yes—
475#397C2312yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#396C2312yes—
482#396C2312yes—
483#396C2312yes—
484#396C2312yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#395C2314yes—
494#395C2314yes—
495#395C2312yes—
496#395C2312yes—
497#395C2312yes—
498#395C2312yes—
499#394C2312yes—
500#394C2314yes—
501#394C2312yes—
502#394C2314yes—
503#394C2314yes—
504#394C2312yes—
505#394C2314yes—
506#394C2312yes—
507#394C2312yes—
508#394C2312yes—
509#394C2314yes—
510#394C2314yes—
511#393C2314yes—
512#393C2314yes—
513#393C2314yes—
514#393C2314yes—
515#392C2312yes—
516#392C2312yes—
517#391C2312yes—
518#391C2314yes—
519#391C2312yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#391C2312yes—
528#391C2312yes—
529#391C2312yes—
530#391C2312yes—
531#391C2312yes—
532#391C2312yes—
533#391C2311yescharacteristic
534#391C2314yes—
535#391C2314yes—
536#391C2314yes—
537#391C2312yes—
538#391C2311yescharacteristic
539#391C2314yes—
540#390C2314yes—
541#390C2314yes—
542#390C2311yescharacteristic
543#390C2311yescharacteristic
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2311yescharacteristic
549#390C2311yescharacteristic
550#390C2311yescharacteristic
551#390C2311yescharacteristic
552#390C2312yes—
553#390C2312yes—
554#390C2312yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2314yes—
560#390C2312yes—
561#390C2312yes—
562#390C2314yes—
563#389C2311yescharacteristic
564#389C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2311yescharacteristic
567#389C2312yes—
568#389C2311yescharacteristic
569#389C2311yescharacteristic
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2311yescharacteristic
580#389C2311yescharacteristic
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2314yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2314yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2314yes—
594#389C2314yes—
595#389C2314yes—
596#389C2314yes—
597#389C2314yes—
598#389C2314yes—
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#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2312yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2312yes—
625#388C2312yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#386C2314yes—
662#386C2312yes—
663#386C2314yes—
664#386C2312yes—
665#386C2312yes—
666#386C2312yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2312yes—
676#385C2312yes—
677#385C2312yes—
678#385C2312yes—
679#385C2312yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2312yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2312yes—
691#385C2312yes—
692#385C2314yes—
693#385C2314yes—
694#385C2312yes—
695#385C2312yes—
696#385C2312yes—
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2311yescharacteristic
700#384C2311yescharacteristic
701#384C2311yescharacteristic
702#384C2311yescharacteristic
703#384C2314yes—
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#384C2312yes—
708#384C2312yes—
709#384C2312yes—
710#384C2312yes—
711#384C2314yes—
712#383C2312yes—
713#382C2311yescharacteristic
714#382C2311yescharacteristic
715#382C2314yes—
716#382C2311yescharacteristic
717#382C2311yescharacteristic
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2311yescharacteristic
722#382C2311yescharacteristic
723#382C2314yes—
724#382C2312yes—
725#381C2314yes—
726#381C2314yes—
727#381C2312yes—
728#381C2314yes—
729#380C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2314yes—
733#380C2314yes—
734#380C2312yes—
735#380C2312yes—
736#380C2314yes—
737#380C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2314yes—
744#380C2314yes—
745#380C2314yes—
746#380C2311yescharacteristic
747#380C2311yescharacteristic
748#380C2312yes—
749#379C2314yes—
750#379C2312yes—
751#379C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2314yes—
789C4×C4⋊C4C2314yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812#376C2312yes—
813#376C2311yescharacteristic
814#376C2311yescharacteristic
815C2×#95C2314yes—
816C2×#95C2312yes—
817C43C2311yescharacteristic
818C43C2311yescharacteristic
819C25C2412yes—
820C22×Q8—28no—
821C22×Q8—44no—
822C22×Q8—44no—
823C22×Q8C2411yescharacteristic
824C22×Q8C2412yes—
825C22×Q8C2412yes—
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2414yes—
829C22×D4—24no—
830C22×D4—24no—
831C22×D4—42no—
832C22×D4C2412yes—
833C22×D4C2411yescharacteristic
834C22×D4C2411yescharacteristic
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C23×C4—28no—
842C23×C4—44no—
843C23×C4—44no—
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2414yes—
853C23×C4C2412yes—
854C23×C4C2414yes—
855C23×C4C2414yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2414yes—
859C4⋊Q8—24no—
860C4⋊Q8—24no—
861C4⋊Q8—28no—
862C4⋊Q8—24no—
863C4⋊Q8—24no—
864C4⋊Q8—28no—
865C4⋊Q8—28no—
866#127—24no—
867#127—42no—
868#126—28no—
869#126—48no—
870#126—48no—
871#126—48no—
872#126—48no—
873#125—24no—
874#125—24no—
875#125—24no—
876#125—48no—
877#125—48no—
878#125—48no—
879#124—24no—
880#124—24no—
881#124—42no—
882#124—48no—
883#123—28no—
884#123—48no—
885#123—48no—
886C22⋊Q8—24no—
887C22⋊Q8—28no—
888C22⋊Q8—28no—
889C22⋊Q8—28no—
890C22⋊Q8—28no—
891C22⋊Q8—28no—
892C22⋊Q8—44no—
893C22⋊Q8—48no—
894C22⋊Q8—48no—
895C22⋊Q8—48no—
896C22⋊Q8—48no—
897C22⋊Q8—48no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900C22⋊Q8—44no—
901C22⋊Q8—44no—
902C22⋊Q8—44no—
903C22⋊Q8—44no—
904C22⋊Q8—44no—
905C22⋊Q8—48no—
906C22⋊Q8—44no—
907#121—24no—
908#120—28no—
909#120—44no—
910C4×Q8—24no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×Q8—44no—
914C4×Q8—44no—
915C4×Q8—44no—
916C4×Q8—44no—
917C4×Q8—48no—
918C4×Q8—44no—
919C4×D4—28no—
920C4×D4—28no—
921C4×D4—28no—
922C4×D4—24no—
923C4×D4—24no—
924C4×D4—24no—
925C4×D4—24no—
926C4×D4—28no—
927C4×D4—24no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—44no—
932C4×D4—44no—
933C4×D4—44no—
934C4×D4—48no—
935C4×D4—48no—
936#117—28no—
937#117—24no—
938#117—28no—
939#117—48no—
940#117—44no—
941#117—42no—
942#117—44no—
943#117—48no—
944#117—44no—
945C2×C4⋊C4—24no—
946C2×C4⋊C4—28no—
947C2×C4⋊C4—28no—
948C2×C4⋊C4—24no—
949C2×C4⋊C4—24no—
950C2×C4⋊C4—28no—
951C2×C4⋊C4—48no—
952C2×C4⋊C4—48no—
953C2×C4⋊C4—44no—
954C2×C4⋊C4—44no—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C22⋊C4—28no—
1034C2×C22⋊C4—48no—
1035C2×C22⋊C4—48no—
1036C2×C22⋊C4—48no—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2411yescharacteristic
1090C2×C42—44no—
1091C2×C42#4118yes—
1092C2×C42C2414yes—
1093C2×C42C2412yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2412yes—
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2414yes—
1109C2×C42C2414yes—
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2414yes—
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2414yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2411yescharacteristic
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2411yescharacteristic
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2411yescharacteristic
1144#95C2412yes—
1145#95C2412yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193C24—24no—
1194C24—24no—
1195C24—24no—
1196C24—24no—
1197C24—42no—
1198C24—42no—
1199C24—42no—
1200C24C2512yes—
1201C24C2512yes—
1202C24C2512yes—
1203C24C2511yescharacteristic
1204C2×Q8—22no—
1205C2×Q8—24no—
1206C2×Q8—24no—
1207C2×Q8—28no—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—24no—
1211C2×Q8—24no—
1212C2×Q8—24no—
1213C2×Q8—24no—
1214C2×Q8—24no—
1215C2×Q8—22no—
1216C2×Q8—22no—
1217C2×Q8—42no—
1218C2×Q8—42no—
1219C2×Q8—44no—
1220C2×Q8—44no—
1221C2×Q8—42no—
1222C2×Q8—816no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—22no—
1230C2×D4—24no—
1231C2×D4—22no—
1232C2×D4—22no—
1233C2×D4—24no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—24no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—416no—
1241C2×D4—42no—
1242C2×D4—42no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D42−1+414yes—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—24no—
1260C22×C4—28no—
1261C22×C4—28no—
1262C22×C4—24no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—28no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—44no—
1279C22×C4—44no—
1280C22×C4—44no—
1281C22×C4—42no—
1282C22×C4—42no—
1283C22×C4—44no—
1284C22×C4—44no—
1285C22×C4—44no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—44no—
1291C22×C4—44no—
1292C22×C4—44no—
1293C22×C4—816no—
1294C22×C4C2×#4114yes—
1295C22×C4C2×#4114yes—
1296C22×C4C2×#4114yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2512yes—
1301C22×C4C2511yescharacteristic
1302C22×C4C2512yes—
1303C22×C4C2514yes—
1304C22×C4C2512yes—
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2514yes—
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C22×C4C2511yescharacteristic
1312C22×C4C2512yes—
1313C22×C4C2512yes—
1314C22×C4C2514yes—
1315C22×C4C2514yes—
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2511yescharacteristic
1320C22×C4C2511yescharacteristic
1321C22×C4C2511yescharacteristic
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C4⋊C4—24no—
1329C4⋊C4—22no—
1330C4⋊C4—22no—
1331C4⋊C4—28no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—28no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—24no—
1339C4⋊C4—22no—
1340C4⋊C4—24no—
1341C4⋊C4—22no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—28no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—24no—
1352C4⋊C4—28no—
1353C4⋊C4—28no—
1354C4⋊C4—28no—
1355C4⋊C4—28no—
1356C4⋊C4—22no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—24no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—24no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—24no—
1370C4⋊C4—24no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—41no—
1378C4⋊C4—41no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4H(5,𝔽2)14yes—
1405C4⋊C4H(5,𝔽2)14yes—
1406C22⋊C4—24no—
1407C22⋊C4—22no—
1408C22⋊C4—28no—
1409C22⋊C4—24no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—28no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—28no—
1425C22⋊C4—28no—
1426C22⋊C4—28no—
1427C22⋊C4—28no—
1428C22⋊C4—28no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—42no—
1446C22⋊C4—42no—
1447C22⋊C4—44no—
1448C22⋊C4—42no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C42−1+414yes—
1459C42—24no—
1460C42—28no—
1461C42—22no—
1462C42—22no—
1463C42—22no—
1464C42—22no—
1465C42—22no—
1466C42—22no—
1467C42—24no—
1468C42—22no—
1469C42—22no—
1470C42—24no—
1471C42—24no—
1472C42—24no—
1473C42—22no—
1474C42—22no—
1475C42—42no—
1476C42—42no—
1477C42—44no—
1478C42—41no—
1479C42—41no—
1480C42—44no—
1481C42—44no—
1482C42—44no—
1483C42—44no—
1484C42—44no—
1485C42—44no—
1486C42—44no—
1487C42—44no—
1488C42C2×#4114yes—
1489C42C2×#4114yes—
1490C42C2×#4114yes—
1491C42C2×#4114yes—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—22no—
1497C23—22no—
1498C23—22no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—22no—
1503C23—22no—
1504C23—22no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23—22no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—48no—
1517C23—48no—
1518C23—48no—
1519C23—48no—
1520C23—84no—
1521C23—84no—
1522C23—84no—
1523C23C22×#4112yes—
1524C23C2×2−1+414yes—
1525C23C2×2−1+412yes—
1526C23#58512yes—
1527C23C2611yescharacteristic
1528Q8—48no—
1529Q8—44no—
1530Q8—48no—
1531Q8—48no—
1532Q8—84no—
1533Q8—88no—
1534D4—28no—
1535D4—48no—
1536D4—48no—
1537D4—48no—
1538D4—44no—
1539D4—44no—
1540D4—84no—
1541D4—84no—
1542D4—84no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—21no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—22no—
1559C2×C4—28no—
1560C2×C4—28no—
1561C2×C4—28no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—24no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—24no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—24no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—24no—
1584C2×C4—24no—
1585C2×C4—24no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—21no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—24no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—21no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—24no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—24no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—24no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—48no—
1626C2×C4—48no—
1627C2×C4—48no—
1628C2×C4—48no—
1629C2×C4—48no—
1630C2×C4—88no—
1631C2×C4—84no—
1632C2×C4—84no—
1633C2×C4—88no—
1634C2×C4—84no—
1635C2×C4—88no—
1636C2×C4—164no—
1637C2×C4C22×#4112yes—
1638C2×C4C22×#4112yes—
1639C2×C4C22×#4112yes—
1640C2×C4C22×#4112yes—
1641C2×C4C22×#4112yes—
1642C2×C4C22×#4112yes—
1643C2×C4C2×H(5,𝔽2)14yes—
1644C2×C4C2×H(5,𝔽2)14yes—
1645C2×C4C2×H(5,𝔽2)12yes—
1646C2×C4C2×H(5,𝔽2)12yes—
1647C2×C4C2×2−1+412yes—
1648C2×C4C2×2−1+412yes—
1649C2×C4C2×2−1+412yes—
1650C2×C4#58512yes—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—22no—
1656C22—22no—
1657C22—24no—
1658C22—24no—
1659C22—24no—
1660C22—42no—
1661C22—42no—
1662C22—42no—
1663C22—42no—
1664C22—42no—
1665C22—42no—
1666C22—42no—
1667C22—42no—
1668C22—42no—
1669C22—42no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—42no—
1674C22—42no—
1675C22—42no—
1676C22—42no—
1677C22—42no—
1678C22—816no—
1679C22#350714yes—
1680C22C23×#4111yescharacteristic
1681C22C22×H(5,𝔽2)11yescharacteristic
1682C22C22×H(5,𝔽2)11yescharacteristic
1683C22C22×2−1+411yescharacteristic
1684C22C22×2−1+411yescharacteristic
1685C22C2×#58511yescharacteristic
1686C22C2×#58511yescharacteristic
1687C4—24no—
1688C4—22no—
1689C4—22no—
1690C4—24no—
1691C4—22no—
1692C4—22no—
1693C4—22no—
1694C4—22no—
1695C4—41no—
1696C4—42no—
1697C4—42no—
1698C4—41no—
1699C4—44no—
1700C4—42no—
1701C4—41no—
1702C4—41no—
1703C4—42no—
1704C4—42no—
1705C4—44no—
1706C4—42no—
1707C4—41no—
1708C4—41no—
1709C4—42no—
1710C4—42no—
1711C4—42no—
1712C4—42no—
1713C4—44no—
1714C4—44no—
1715C4—42no—
1716C4#349514yes—
1717C4#350814yes—
1718C2—24no—
1719C2—44no—
1720C2—82no—
1721C2—82no—
1722C2C2×#350711yescharacteristic
1723C2C2×#350811yescharacteristic
1724C2C2×#349511yescharacteristic
1725C2#6301311yescharacteristic
1726C2#6301511yescharacteristic
1727C2#6301611yescharacteristic
1728C2#6301811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2433C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59823C2semidirect
2. #59821C2semidirect
3. #59642C2semidirect
4. #59639C2semidirect
6. #59451C2semidirect
7. #59450C2semidirect
8. #59444C2semidirect
9. #59444C2semidirect
10. #59424C2semidirect
11. #59321C2semidirect
12. #59302C2semidirect
13. #59027C2semidirect
14. #59025C2semidirect
15. #59016C2semidirect
16. #59014C2semidirect
17. #47710C2semidirect
18. #47709C2semidirect
19. #42704C2semidirect
20. #42699C2semidirect
21. #42669C2semidirect
22. #42668C2semidirect
23. #41974C2semidirect
24. #37615C2semidirect
25. #35988C2semidirect
26. #35934C2semidirect
27. #35860C2semidirect
28. #35834C2semidirect
29. #35773C2semidirect
30. #34966C2semidirect
32. C2×#2542C2semidirect
33. #34243C2semidirect
34. #34216C2semidirect
35. #34194C2semidirect
36. C2×#556C22semidirect
37. C2×#554C22semidirect
38. C2×#552C22semidirect
39. C2×#552C22semidirect
45. #2837C22semidirect
46. #2836C22semidirect
47. #2821C22semidirect
48. #2807C22semidirect
49. #2798C22semidirect
51. #2793C22semidirect
52. #2793C22semidirect
53. #2791C22semidirect
54. #2791C22semidirect
56. #2773C22semidirect
57. #2771C22semidirect
60. #2732C22semidirect
61. #2727C22semidirect
62. #2704C22semidirect
63. #2702C22semidirect
64. #2700C22semidirect
65. #2698C22semidirect
66. #2694C22semidirect
67. #2694C22semidirect
68. #2692C22semidirect
69. #2690C22semidirect
70. #2689C22semidirect
71. #2687C22semidirect
72. #2667C22semidirect
73. #2664C22semidirect
74. #2663C22semidirect
75. #2660C22semidirect
76. #2654C22semidirect
77. #2651C22semidirect
78. #2649C22semidirect
79. #2640C22semidirect
81. #2621C22semidirect
82. #2621C22semidirect
83. #2606C22semidirect
84. #2605C22semidirect
89. #2596C22semidirect
90. #2596C22semidirect
92. #2589C22semidirect
93. #2582C22semidirect
95. #2575C22semidirect
96. #2571C22semidirect
97. #2570C22semidirect
98. #2570C22semidirect
99. #2570C22semidirect
100. #2570C22semidirect
101. #2568C22semidirect
102. #2568C22semidirect
105. #2565C22semidirect
107. #2560C22semidirect
109. #2556C22semidirect
110. #2556C22semidirect
111. #2553C22semidirect
112. #2552C22semidirect
113. #2552C22semidirect
114. #2552C22semidirect
115. #2550C22semidirect
116. #2550C22semidirect
117. #2549C22semidirect
130. #2542C22semidirect
131. #2542C22semidirect
133. #2538C22semidirect
134. #2538C22semidirect
135. #2538C22semidirect
136. #2536C22semidirect
137. #2536C22semidirect
138. #2522C22semidirect
139. #2521C22semidirect
140. #2519C22semidirect
141. #2516C22semidirect
146. #2512C22semidirect
147. #2512C22semidirect
148. #2511C22semidirect
149. #2511C22semidirect
150. #2506C22semidirect
153. #2503C22semidirect
156. #2502C22semidirect
157. #2499C22semidirect
158. #2499C22semidirect
159. #2499C22semidirect
160. #2496C22semidirect
161. #2492C22semidirect
162. #2492C22semidirect
163. #2489C22semidirect
164. #2489C22semidirect
165. #2488C22semidirect
170. #2479C22semidirect
171. #2479C22semidirect
172. #2477C22semidirect
176. #2465C22semidirect
177. #2454C22semidirect
178. #2450C22semidirect
180. #2448C22semidirect
191. #2438C22semidirect
195. #2423C22semidirect
196. #2423C22semidirect
197. #2421C22semidirect
198. #2421C22semidirect
201. #2417C22semidirect
202. #2417C22semidirect
203. #2417C22semidirect
204. #2417C22semidirect
205. #2415C22semidirect
206. #2415C22semidirect
207. #2415C22semidirect
208. #2415C22semidirect
214. #2402C22semidirect
215. #2399C22semidirect
216. #2396C22semidirect
217. #2395C22semidirect
221. #2370C22semidirect
222. #2369C22semidirect
223. #2369C22semidirect
225. #2367C22semidirect
227. #2365C22semidirect
228. #2365C22semidirect
229. #2362C22semidirect
230. #2362C22semidirect
232. #2360C22semidirect
233. #2360C22semidirect
237. #2355C22semidirect
238. #2355C22semidirect
239. #2355C22semidirect
243. #2354C22semidirect
244. #2354C22semidirect
249. Q8×C4⋊C4C22semidirect
250. Q8×C4⋊C4C22semidirect
254. D4×C4⋊C4C22semidirect
263. #2334C22semidirect
264. #2331C22semidirect
265. #2331C22semidirect
269. #2314C22semidirect
270. C4×C4⋊Q8C22semidirect
271. C4×C4⋊Q8C22semidirect
272. C4×C4⋊Q8C22semidirect
273. C4×C4⋊Q8C22semidirect
274. C4×C4⋊Q8C22semidirect
275. C4×C4⋊Q8C22semidirect
278. C4×#125C22semidirect
279. C4×#125C22semidirect
296. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#598232
#598212
#596422
#596392
#596372
#594512
#594502
#594442
#594242
#593212
#593022
#590272
#590252
#590162
#590142
#477102
#477092
#427042
#426992
#426692
#426682
#419742
#376152
#359882
#359342
#358602
#358342
#357732
#349662
#349652
C2×#25422
#342432
#342162
#341942