Finite Group Databasebeta

← #7692194

Subgroups — #7692194

Order 512.

5189 conjugacy classes of subgroups.

The subgroup lattice has 1741 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59475C212yesmaximal, complemented
2#59437C211yesmaximal, characteristic, complemented
3#59364C214yesmaximal, complemented
4#59227C211yesmaximal, characteristic, complemented
5#59217C211yesmaximal, characteristic, complemented
6#59205C212yesmaximal, complemented
7#59103C212yesmaximal, complemented
8#59044C212yesmaximal, complemented
9#45374C212yesmaximal, complemented
10#45118C212yesmaximal, complemented
11#44017C214yesmaximal, complemented
12#44008C214yesmaximal, complemented
13#39028C212yesmaximal, complemented
14#39022C212yesmaximal, complemented
15#38966C211yesmaximal, characteristic, complemented
16#38920C211yesmaximal, characteristic, complemented
17#38404C214yesmaximal, complemented
18#37857C212yesmaximal, complemented
19#36481C211yesmaximal, characteristic, complemented
20#36438C212yesmaximal, complemented
21#36392C212yesmaximal, complemented
22#36209C211yesmaximal, characteristic, complemented
23#36173C212yesmaximal, complemented
24#36153C211yesmaximal, characteristic, complemented
25#36116C211yesmaximal, characteristic, complemented
26#36114C211yesmaximal, characteristic, complemented
27#35978C212yesmaximal, complemented
28#35734C212yesmaximal, complemented
29#34932C212yesmaximal, complemented
30#34700C211yesmaximal, characteristic, complemented
31#34316C211yesmaximal, characteristic, complemented
32#34243C211yesmaximal, characteristic, complemented
33#34180C212yesmaximal, complemented
34C4×#553C211yesmaximal, characteristic, complemented
35D4×#117C211yesmaximal, characteristic, complemented
36C2×#553C2211yescharacteristic
37C2×#547C2211yescharacteristic
38C2×#546C2212yes—
39C2×#529C2211yescharacteristic
40C2×#529C2212yes—
41C2×#529C2212yes—
42C22×C4×D4C2211yescharacteristic
43C22×#117C2212yes—
44#2863C2212yescomplemented
45#2859C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic, complemented
48#2855C2212yescomplemented
49#2852C2214yescomplemented
50#2851C2212yescomplemented
51#2847C2212yes—
52#2791C2214yescomplemented
53#2790C2214yescomplemented
54#2790C2214yescomplemented
55#2787C2214yescomplemented
56#2781C2214yes—
57#2781C2214yescomplemented
58#2768C2214yescomplemented
59#2767C2214yescomplemented
60#2761C2214yescomplemented
61#2757C2214yescomplemented
62#2746C2214yes—
63#2743C2214yes—
64#2740C2214yes—
65#2739C2214yescomplemented
66#2738C2214yes—
67#2718C2214yescomplemented
68#2708C2214yes—
69#2706C2214yescomplemented
70#2697C2214yes—
71#2695C2214yes—
72#2685C2214yes—
73#2655C2214yescomplemented
74#2654C2214yescomplemented
75#2629C2212yescomplemented
76#2624C2212yescomplemented
77#2606C2214yescomplemented
78#2601C2214yescomplemented
79#2600C2214yescomplemented
80#2598C2214yescomplemented
81#2595C2214yescomplemented
82#2578C2214yescomplemented
83#2577C2214yescomplemented
84#2576C2214yescomplemented
85#2576C2214yescomplemented
86#2575C2214yescomplemented
87#2573C2214yescomplemented
88#2571C2212yescomplemented
89#2566C2212yes—
90#2562C2212yes—
91#2562C2212yescomplemented
92#2553C2214yes—
93#2553C2214yescomplemented
94#2553C2214yescomplemented
95#2552C2211yescharacteristic, complemented
96#2552C2211yescharacteristic, complemented
97#2552C2212yescomplemented
98#2547C2211yescharacteristic
99#2547C2212yes—
100#2546C2211yescharacteristic, complemented
101#2542C2212yescomplemented
102#2538C2211yescharacteristic, complemented
103#2537C2211yescharacteristic
104#2537C2212yes—
105#2536C2212yes—
106#2531C2214yescomplemented
107#2530C2214yescomplemented
108#2529C2214yescomplemented
109#2526C2214yescomplemented
110#2522C2214yes—
111#2522C2214yescomplemented
112#2518C2214yescomplemented
113#2517C2214yescomplemented
114#2516C2214yescomplemented
115#2515C2214yescomplemented
116#2515C2214yescomplemented
117#2514C2212yescomplemented
118#2513C2212yescomplemented
119#2508C2212yescomplemented
120#2508C2212yescomplemented
121#2508C2212yescomplemented
122#2507C2212yescomplemented
123#2505C2214yescomplemented
124#2500C2212yes—
125#2497C2212yescomplemented
126#2496C2212yescomplemented
127#2496C2212yescomplemented
128#2496C2214yescomplemented
129#2495C2212yes—
130#2495C2212yescomplemented
131#2495C2212yescomplemented
132#2494C2212yescomplemented
133#2490C2212yescomplemented
134#2489C2212yes—
135#2489C2212yescomplemented
136#2489C2212yescomplemented
137#2489C2212yescomplemented
138#2487C2212yescomplemented
139#2486C2212yes—
140#2486C2212yescomplemented
141#2485C2212yes—
142#2485C2212yes—
143#2485C2212yescomplemented
144#2480C2214yes—
145#2480C2212yes—
146#2478C2214yescomplemented
147#2476C2214yes—
148#2476C2214yes—
149#2476C2214yescomplemented
150#2470C2214yes—
151#2470C2214yes—
152#2470C2214yescomplemented
153#2468C2212yes—
154#2466C2214yescomplemented
155#2464C2214yes—
156#2457C2212yes—
157#2457C2214yes—
158#2454C2212yes—
159#2454C2211yescharacteristic
160#2453C2212yescomplemented
161#2447C2212yes—
162#2447C2211yescharacteristic
163#2446C2212yescomplemented
164#2442C2211yescharacteristic
165#2442C2212yescomplemented
166#2442C2212yescomplemented
167#2441C2212yes—
168#2441C2212yescomplemented
169#2435C2211yescharacteristic
170#2432C2212yes—
171#2429C2212yes—
172#2427C2212yes—
173#2427C2211yescharacteristic
174#2425C2214yes—
175#2424C2214yes—
176#2423C2212yes—
177#2422C2212yescomplemented
178#2422C2214yescomplemented
179#2421C2212yescomplemented
180#2420C2212yes—
181#2420C2211yescharacteristic
182#2420C2214yes—
183#2419C2214yescomplemented
184#2418C2214yes—
185#2418C2214yes—
186#2418C2212yes—
187#2417C2212yes—
188#2417C2211yescharacteristic
189#2416C2212yes—
190#2416C2212yescomplemented
191#2415C2212yes—
192#2414C2212yescomplemented
193#2412C2214yes—
194#2408C2211yescharacteristic
195#2407C2212yes—
196#2395C2212yes—
197#2395C2214yescomplemented
198#2395C2214yescomplemented
199#2392C2212yes—
200#2374C2212yes—
201#2374C2214yescomplemented
202#2373C2212yescomplemented
203#2370C2211yescharacteristic, complemented
204#2370C2212yescomplemented
205#2370C2212yescomplemented
206#2367C2212yes—
207#2367C2212yes—
208#2365C2211yescharacteristic, complemented
209#2364C2212yes—
210#2363C2212yes—
211#2363C2211yescharacteristic
212#2363C2212yescomplemented
213#2362C2212yescomplemented
214#2361C2212yescomplemented
215#2361C2211yescharacteristic, complemented
216#2359C2214yescomplemented
217#2357C2211yescharacteristic, complemented
218#2356C2212yescomplemented
219#2355C2211yescharacteristic, complemented
220#2354C2211yescharacteristic
221#2354C2211yescharacteristic
222#2354C2211yescharacteristic, complemented
223#2353C2214yescomplemented
224#2353C2212yescomplemented
225#2352C2212yes—
226#2352C2211yescharacteristic
227#2352C2212yes—
228#2352C2212yescomplemented
229Q8×C4⋊C4C2211yescharacteristic, complemented
230D4×C4⋊C4C2211yescharacteristic
231D4×C4⋊C4C2211yescharacteristic
232D4×C4⋊C4C2211yescharacteristic
233D4×C4⋊C4C2212yescomplemented
234D4×C4⋊C4C2212yescomplemented
235#2347C2212yes—
236#2347C2211yescharacteristic
237#2346C2212yes—
238#2346C2212yes—
239#2346C2212yescomplemented
240#2346C2212yescomplemented
241#2345C2212yescomplemented
242#2345C2212yescomplemented
243#2345C2212yescomplemented
244#2345C2211yescharacteristic, complemented
245#2344C2212yes—
246#2344C2212yescomplemented
247#2344C2212yescomplemented
248#2343C2214yescomplemented
249#2343C2214yescomplemented
250#2342C2214yes—
251#2342C2214yes—
252#2342C2214yes—
253#2341C2212yes—
254#2339C2212yes—
255D4×C22⋊C4C2212yes—
256#2335C2214yescomplemented
257#2334C2214yescomplemented
258#2324C2212yescomplemented
259#2317C2212yescomplemented
260#2317C2212yescomplemented
261#2314C2214yes—
262#2314C2214yes—
263#2314C2212yescomplemented
264C4×C4⋊Q8C2211yescharacteristic, complemented
265C4×C4⋊Q8C2212yescomplemented
266C4×#125C2211yescharacteristic, complemented
267C4×#126C2212yescomplemented
268C4×#124C2211yescharacteristic
269C4×C22⋊Q8C2211yescharacteristic
270C4×C22⋊Q8C2212yescomplemented
271C4×C22⋊Q8C2212yescomplemented
272C4×#123C2212yes—
273C4×#121C2211yescharacteristic
274C4×#121C2212yes—
275C4×#121C2211yescharacteristic
276C4×#121C2212yes—
277C4×#121C2211yescharacteristic, complemented
278C4×#121C2214yescomplemented
279C4×#120C2212yes—
280#2297C2212yes—
281#2293C2211yescharacteristic
282#2293C2212yes—
283#2290C2214yes—
284#2285C2211yescharacteristic
285#2285C2214yescomplemented
286#2285C2211yescharacteristic, complemented
287#2283C2214yescomplemented
288#2280C2212yes—
289#2280C2212yes—
290C2×#380C2212yes—
291#2274C2212yescomplemented
292#2274C2212yescomplemented
293C42×D4C2212yes—
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic, complemented
296C42×D4C2212yescomplemented
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#553—28no—
303#547—28no—
304#546—48no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2312yes—
307#529—28no—
308#529—48no—
309#529—48no—
310C2×#126C2312yes—
311C2×#126C2312yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#125C2311yescharacteristic
315C2×#125C2311yescharacteristic
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#124C2311yescharacteristic
320C2×#124C2312yes—
321C2×#124C2311yescharacteristic
322C2×#123C2314yes—
323C2×#123C2312yes—
324C2×#123C2312yes—
325C2×#123C2314yes—
326C2×#123C2314yes—
327C2×#123C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2312yes—
334C2×#121C2312yes—
335C2×#121C2311yescharacteristic
336C2×#121C2311yescharacteristic
337C2×#121C2312yes—
338C2×#121C2312yes—
339C2×#121C2311yescharacteristic
340C2×#121C2311yescharacteristic
341C2×#121C2312yes—
342C2×#121C2314yes—
343C2×#121C2314yes—
344C2×#120C2314yes—
345C2×#120C2312yes—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×D4—28no—
351C2×C4×D4C2312yes—
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2312yes—
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×#117—216no—
376C2×#117C2314yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2314yes—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2314yes—
384C2×#117C2314yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2311yescharacteristic
388C2×#117C2311yescharacteristic
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2311yescharacteristic
396C22×C22⋊C4C2314yes—
397C22×C22⋊C4C2312yes—
398C22×C22⋊C4C2314yes—
399C22×C42C2314yes—
400C22×C42C2311yescharacteristic
401C22×C42C2311yescharacteristic
402C22×C42C2312yes—
403C22×C42C2312yes—
404#401C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2312yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#399C2314yes—
418#399C2314yes—
419#399C2312yes—
420#399C2314yes—
421#399C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2312yes—
430#398C2312yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#397C2312yes—
437#397C2312yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2312yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2312yes—
459#396C2312yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#392C2314yes—
481#392C2312yes—
482#391C2311yescharacteristic
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2311yescharacteristic
491#390C2311yescharacteristic
492#390C2312yes—
493#390C2314yes—
494#390C2312yes—
495#390C2314yes—
496#390C2312yes—
497#390C2311yescharacteristic
498#390C2311yescharacteristic
499#390C2312yes—
500#390C2311yescharacteristic
501#390C2312yes—
502#390C2314yes—
503#390C2311yescharacteristic
504#390C2314yes—
505#390C2311yescharacteristic
506#389C2311yescharacteristic
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2314yes—
515#389C2311yescharacteristic
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2312yes—
539#389C2311yescharacteristic
540#389C2312yes—
541#389C2312yes—
542#389C2311yescharacteristic
543#389C2314yes—
544#389C2311yescharacteristic
545#388C2312yes—
546#388C2312yes—
547#388C2312yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2312yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
583#388C2314yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2312yes—
619#387C2314yes—
620#387C2312yes—
621#387C2314yes—
622#387C2312yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2312yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#386C2312yes—
640#386C2312yes—
641#386C2312yes—
642#386C2312yes—
643#386C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2312yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2312yes—
662#385C2314yes—
663#385C2312yes—
664#385C2312yes—
665#385C2312yes—
666#384C2312yes—
667#384C2311yescharacteristic
668#384C2314yes—
669#384C2314yes—
670#384C2312yes—
671#384C2312yes—
672#384C2311yescharacteristic
673#384C2311yescharacteristic
674#383C2312yes—
675#383C2314yes—
676#383C2314yes—
677#383C2314yes—
678#382C2311yescharacteristic
679#382C2312yes—
680#382C2314yes—
681#382C2314yes—
682#382C2312yes—
683#382C2314yes—
684#382C2312yes—
685#382C2314yes—
686#382C2312yes—
687#382C2311yescharacteristic
688#382C2314yes—
689#382C2314yes—
690#381C2314yes—
691#381C2312yes—
692#381C2314yes—
693#381C2314yes—
694#381C2314yes—
695#381C2312yes—
696#381C2314yes—
697#381C2312yes—
698#380C2311yescharacteristic
699#380C2312yes—
700#380C2312yes—
701#380C2312yes—
702#380C2311yescharacteristic
703#380C2312yes—
704#380C2312yes—
705#380C2312yes—
706#380C2314yes—
707#380C2312yes—
708#380C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2314yes—
712#380C2314yes—
713#380C2314yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2314yes—
719#380C2314yes—
720#380C2311yescharacteristic
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2311yescharacteristic
727#380C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#379C2314yes—
734#379C2312yes—
735#379C2312yes—
736#379C2312yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2311yescharacteristic
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2314yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2314yes—
811#376C2314yes—
812#376C2314yes—
813#376C2312yes—
814C2×#95C2314yes—
815C2×#95C2312yes—
816C43C2312yes—
817C43C2311yescharacteristic
818C25C2412yes—
819C2×#41—28no—
820C2×#41—44no—
821C2×#41—44no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×D4—24no—
825C22×D4—24no—
826C22×D4—42no—
827C22×D4C2411yescharacteristic
828C22×D4C2411yescharacteristic
829C22×D4C2412yes—
830C22×D4C2412yes—
831C22×D4C2412yes—
832C22×D4C2412yes—
833C22×D4C2411yescharacteristic
834C22×D4C2411yescharacteristic
835C22×D4C2412yes—
836C22×D4C2414yes—
837C22×D4C2414yes—
838C23×C4—28no—
839C23×C4—28no—
840C23×C4—44no—
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2412yes—
845C23×C4C2411yescharacteristic
846C23×C4C2414yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2414yes—
855C23×C4C2414yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2414yes—
860C23×C4C2412yes—
861C4⋊Q8—24no—
862C4⋊Q8—44no—
863#126—28no—
864#126—28no—
865#126—48no—
866#126—48no—
867#125—24no—
868#125—24no—
869#125—44no—
870#125—44no—
871#125—44no—
872#124—24no—
873#124—24no—
874#124—28no—
875#123—28no—
876#123—216no—
877#123—28no—
878#123—48no—
879#123—48no—
880#123—48no—
881C22⋊Q8—24no—
882C22⋊Q8—28no—
883C22⋊Q8—42no—
884C22⋊Q8—44no—
885C22⋊Q8—44no—
886C22⋊Q8—44no—
887#121—24no—
888#121—24no—
889#121—28no—
890#121—28no—
891#121—24no—
892#121—24no—
893#121—28no—
894#121—48no—
895#121—48no—
896#121—44no—
897#120—48no—
898#120—44no—
899C4×Q8—24no—
900C4×Q8—44no—
901C4×Q8—44no—
902C4×Q8—44no—
903C4×D4—24no—
904C4×D4—28no—
905C4×D4—28no—
906C4×D4—28no—
907C4×D4—24no—
908C4×D4—24no—
909C4×D4—24no—
910C4×D4—28no—
911C4×D4—24no—
912C4×D4—24no—
913C4×D4—28no—
914C4×D4—42no—
915C4×D4—44no—
916C4×D4—44no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—42no—
920C4×D4—44no—
921C4×D4—48no—
922C4×D4—42no—
923C4×D4—44no—
924C4×D4—48no—
925C4×D4—48no—
926C4×D4#4118yes—
927#117—28no—
928#117—28no—
929#117—28no—
930#117—28no—
931#117—216no—
932#117—216no—
933#117—44no—
934#117—44no—
935#117—48no—
936#117—48no—
937#117—42no—
938#117—44no—
939#117#4118yescomplemented
940C2×C4⋊C4—28no—
941C2×C4⋊C4—28no—
942C2×C4⋊C4—28no—
943C2×C4⋊C4—24no—
944C2×C4⋊C4—24no—
945C2×C4⋊C4—42no—
946C2×C4⋊C4—44no—
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C22⋊C4—216no—
1013C2×C22⋊C4—28no—
1014C2×C22⋊C4—48no—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2411yescharacteristic
1029C2×C22⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C42—216no—
1077C2×C42—24no—
1078C2×C42—24no—
1079C2×C42—44no—
1080C2×C42—44no—
1081C2×C42C2411yescharacteristic
1082C2×C42C2414yes—
1083C2×C42C2414yes—
1084C2×C42C2411yescharacteristic
1085C2×C42C2414yes—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2411yescharacteristic
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2414yes—
1102C2×C42C2414yes—
1103C2×C42C2412yes—
1104C2×C42C2414yes—
1105C2×C42C2414yes—
1106C2×C42C2412yes—
1107C2×C42C2411yescharacteristic
1108C2×C42C2414yes—
1109C2×C42C2414yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2411yescharacteristic
1114C2×C42C2412yes—
1115C2×C42C2411yescharacteristic
1116#95C2412yes—
1117#95C2412yes—
1118#95C2414yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2411yescharacteristic
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2411yescharacteristic
1134#95C2412yes—
1135#95C2411yescharacteristic
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2411yescharacteristic
1145#95C2412yes—
1146#95C2412yes—
1147#95C2411yescharacteristic
1148#95C2411yescharacteristic
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184C24—24no—
1185C24—24no—
1186C24—24no—
1187C24—42no—
1188C24—42no—
1189C24—42no—
1190C24—42no—
1191C24C2512yes—
1192C24C2511yescharacteristic
1193C24C2512yes—
1194C24C2512yes—
1195C24C2511yescharacteristic
1196#41—816no—
1197C2×Q8—22no—
1198C2×Q8—24no—
1199C2×Q8—22no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—22no—
1203C2×D4—24no—
1204C2×D4—22no—
1205C2×D4—24no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—24no—
1209C2×D4—22no—
1210C2×D4—24no—
1211C2×D4—24no—
1212C2×D4—24no—
1213C2×D4—28no—
1214C2×D4—28no—
1215C2×D4—22no—
1216C2×D4—24no—
1217C2×D4—22no—
1218C2×D4—22no—
1219C2×D4—22no—
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—42no—
1224C2×D4—42no—
1225C2×D4—41no—
1226C2×D4—42no—
1227C2×D4—42no—
1228C2×D4—42no—
1229C2×D4—44no—
1230C2×D4—44no—
1231C2×D4—44no—
1232C2×D4—42no—
1233C2×D4—44no—
1234C2×D4—416no—
1235C2×D4C2×#4114yes—
1236C2×D4H(5,𝔽2)14yes—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—22no—
1241C22×C4—24no—
1242C22×C4—24no—
1243C22×C4—28no—
1244C22×C4—22no—
1245C22×C4—28no—
1246C22×C4—24no—
1247C22×C4—24no—
1248C22×C4—28no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—24no—
1254C22×C4—24no—
1255C22×C4—22no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—24no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—24no—
1265C22×C4—22no—
1266C22×C4—24no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—28no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—42no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—41no—
1276C22×C4—44no—
1277C22×C4—432no—
1278C22×C4—42no—
1279C22×C4—42no—
1280C22×C4—42no—
1281C22×C4—42no—
1282C22×C4—44no—
1283C22×C4—42no—
1284C22×C4—44no—
1285C22×C4—41no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—44no—
1289C22×C4—41no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4C2×#4118yes—
1297C22×C4C2×#4114yes—
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2511yescharacteristic
1303C22×C4C2514yes—
1304C22×C4C2511yescharacteristic
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2512yes—
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C22×C4C2512yes—
1312C22×C4C2514yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2512yes—
1316C22×C4C2514yes—
1317C22×C4C2514yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2512yes—
1323C22×C4C2511yescharacteristic
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C4⋊C4—22no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—28no—
1332C4⋊C4—28no—
1333C4⋊C4—24no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—24no—
1337C4⋊C4—28no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—22no—
1344C4⋊C4—22no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—24no—
1354C4⋊C4—22no—
1355C4⋊C4—24no—
1356C4⋊C4—22no—
1357C4⋊C4—44no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—41no—
1375C4⋊C4—41no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—42no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4C2×#4114yes—
1391C4⋊C4C2×#4114yes—
1392C4⋊C4C2×#4114yes—
1393C22⋊C4—28no—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—24no—
1397C22⋊C4—22no—
1398C22⋊C4—24no—
1399C22⋊C4—28no—
1400C22⋊C4—28no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—24no—
1405C22⋊C4—28no—
1406C22⋊C4—28no—
1407C22⋊C4—22no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—22no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—24no—
1417C22⋊C4—28no—
1418C22⋊C4—24no—
1419C22⋊C4—42no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—44no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—42no—
1431C22⋊C4—41no—
1432C22⋊C4—41no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—41no—
1440C22⋊C4—42no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—42no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—42no—
1452C22⋊C4C2×#4118yes—
1453C22⋊C4C2×#4118yes—
1454C42—28no—
1455C42—28no—
1456C42—28no—
1457C42—22no—
1458C42—22no—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—22no—
1463C42—24no—
1464C42—22no—
1465C42—24no—
1466C42—22no—
1467C42—24no—
1468C42—22no—
1469C42—24no—
1470C42—24no—
1471C42—22no—
1472C42—42no—
1473C42—42no—
1474C42—42no—
1475C42—42no—
1476C42—41no—
1477C42—42no—
1478C42—42no—
1479C42—44no—
1480C42—44no—
1481C42—44no—
1482C42—44no—
1483C42—41no—
1484C42—42no—
1485C42—44no—
1486C42—44no—
1487C42C2×#4118yes—
1488C42C2×#4114yes—
1489C23—22no—
1490C23—21no—
1491C23—22no—
1492C23—21no—
1493C23—22no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—22no—
1498C23—21no—
1499C23—21no—
1500C23—22no—
1501C23—21no—
1502C23—22no—
1503C23—21no—
1504C23—21no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23—22no—
1511C23—21no—
1512C23—21no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—22no—
1517C23—22no—
1518C23—22no—
1519C23—22no—
1520C23—48no—
1521C23—48no—
1522C23—48no—
1523C23—84no—
1524C23—84no—
1525C23—84no—
1526C23—84no—
1527C23C22×#4112yes—
1528C23C22×#4114yes—
1529C23C2×H(5,𝔽2)14yes—
1530C23#58512yes—
1531C23C2611yescharacteristic
1532Q8—44no—
1533Q8—48no—
1534D4—28no—
1535D4—28no—
1536D4—48no—
1537D4—48no—
1538D4—48no—
1539D4—44no—
1540D4—48no—
1541D4—44no—
1542D4—84no—
1543D4—88no—
1544D4—88no—
1545C2×C4—22no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—28no—
1556C2×C4—216no—
1557C2×C4—21no—
1558C2×C4—24no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—24no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—24no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—24no—
1585C2×C4—24no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—22no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—24no—
1597C2×C4—22no—
1598C2×C4—24no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—24no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—24no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—21no—
1613C2×C4—24no—
1614C2×C4—22no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—24no—
1625C2×C4—22no—
1626C2×C4—48no—
1627C2×C4—416no—
1628C2×C4—44no—
1629C2×C4—48no—
1630C2×C4—48no—
1631C2×C4—44no—
1632C2×C4—48no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—48no—
1636C2×C4—84no—
1637C2×C4—84no—
1638C2×C4—82no—
1639C2×C4—88no—
1640C2×C4—84no—
1641C2×C4—88no—
1642C2×C4—84no—
1643C2×C4—164no—
1644C2×C4C22×#4112yes—
1645C2×C4C22×#4112yes—
1646C2×C4C22×#4114yes—
1647C2×C4C22×#4114yes—
1648C2×C4C22×#4114yes—
1649C2×C4C22×#4112yes—
1650C2×C4C22×#4112yes—
1651C2×C4C22×#4112yes—
1652C2×C4C2×H(5,𝔽2)12yes—
1653C2×C4#58512yes—
1654C2×C4#58512yes—
1655C22—24no—
1656C22—22no—
1657C22—22no—
1658C22—24no—
1659C22—22no—
1660C22—24no—
1661C22—24no—
1662C22—24no—
1663C22—22no—
1664C22—22no—
1665C22—22no—
1666C22—24no—
1667C22—41no—
1668C22—42no—
1669C22—41no—
1670C22—42no—
1671C22—42no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—42no—
1676C22—42no—
1677C22—41no—
1678C22—42no—
1679C22—42no—
1680C22—41no—
1681C22—42no—
1682C22—41no—
1683C22—42no—
1684C22—42no—
1685C22—42no—
1686C22—42no—
1687C22—42no—
1688C22—42no—
1689C22—42no—
1690C22—816no—
1691C22C23×#4111yescharacteristic
1692C22C23×#4111yescharacteristic
1693C22C22×H(5,𝔽2)11yescharacteristic
1694C22C2×#58511yescharacteristic
1695C22C2×#58511yescharacteristic
1696C22C2×#58511yescharacteristic
1697C222−1+611yescharacteristic
1698C4—24no—
1699C4—22no—
1700C4—24no—
1701C4—22no—
1702C4—24no—
1703C4—44no—
1704C4—41no—
1705C4—42no—
1706C4—41no—
1707C4—41no—
1708C4—42no—
1709C4—41no—
1710C4—42no—
1711C4—42no—
1712C4—44no—
1713C4—42no—
1714C4—41no—
1715C4—42no—
1716C4—41no—
1717C4—44no—
1718C4—42no—
1719C4—44no—
1720C4—41no—
1721C4—41no—
1722C4—42no—
1723C4—42no—
1724C4—41no—
1725C4—42no—
1726C4#347514yes—
1727C4#349414yes—
1728C2—42no—
1729C2—44no—
1730C2—44no—
1731C2—42no—
1732C2—82no—
1733C2C2×#347511yescharacteristic
1734C2C2×#349411yescharacteristic
1735C2#6281611yescharacteristic
1736C2#6293911yescharacteristic
1737C2#6298511yescharacteristic
1738C2#6299311yescharacteristic
1739C2#6301811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59475C2semidirect
2. #59437C2semidirect
3. #59364C2semidirect
4. #59227C2semidirect
5. #59217C2semidirect
6. #59205C2semidirect
7. #59103C2semidirect
8. #59044C2semidirect
9. #45374C2semidirect
10. #45118C2semidirect
11. #44017C2semidirect
12. #44008C2semidirect
13. #39028C2semidirect
14. #39022C2semidirect
15. #38966C2semidirect
16. #38920C2semidirect
17. #38404C2semidirect
18. #37857C2semidirect
19. #36481C2semidirect
20. #36438C2semidirect
21. #36392C2semidirect
22. #36209C2semidirect
23. #36173C2semidirect
24. #36153C2semidirect
25. #36116C2semidirect
26. #36114C2semidirect
27. #35978C2semidirect
28. #35734C2semidirect
29. #34932C2semidirect
30. #34700C2semidirect
31. #34316C2semidirect
32. #34243C2semidirect
33. #34180C2semidirect
34. C4×#553C2semidirect
35. D4×#117C2semidirect
44. #2863C22semidirect
45. #2859C22semidirect
47. #2857C22semidirect
48. #2855C22semidirect
49. #2852C22semidirect
50. #2851C22semidirect
52. #2791C22semidirect
53. #2790C22semidirect
54. #2790C22semidirect
55. #2787C22semidirect
57. #2781C22semidirect
58. #2768C22semidirect
59. #2767C22semidirect
60. #2761C22semidirect
61. #2757C22semidirect
65. #2739C22semidirect
67. #2718C22semidirect
69. #2706C22semidirect
73. #2655C22semidirect
74. #2654C22semidirect
75. #2629C22semidirect
76. #2624C22semidirect
77. #2606C22semidirect
78. #2601C22semidirect
79. #2600C22semidirect
80. #2598C22semidirect
81. #2595C22semidirect
82. #2578C22semidirect
83. #2577C22semidirect
84. #2576C22semidirect
85. #2576C22semidirect
86. #2575C22semidirect
87. #2573C22semidirect
88. #2571C22semidirect
91. #2562C22semidirect
93. #2553C22semidirect
94. #2553C22semidirect
95. #2552C22semidirect
96. #2552C22semidirect
97. #2552C22semidirect
100. #2546C22semidirect
101. #2542C22semidirect
102. #2538C22semidirect
106. #2531C22semidirect
107. #2530C22semidirect
108. #2529C22semidirect
109. #2526C22semidirect
111. #2522C22semidirect
112. #2518C22semidirect
113. #2517C22semidirect
114. #2516C22semidirect
115. #2515C22semidirect
116. #2515C22semidirect
117. #2514C22semidirect
118. #2513C22semidirect
119. #2508C22semidirect
120. #2508C22semidirect
121. #2508C22semidirect
122. #2507C22semidirect
123. #2505C22semidirect
125. #2497C22semidirect
126. #2496C22semidirect
127. #2496C22semidirect
128. #2496C22semidirect
130. #2495C22semidirect
131. #2495C22semidirect
132. #2494C22semidirect
133. #2490C22semidirect
135. #2489C22semidirect
136. #2489C22semidirect
137. #2489C22semidirect
138. #2487C22semidirect
140. #2486C22semidirect
143. #2485C22semidirect
146. #2478C22semidirect
149. #2476C22semidirect
152. #2470C22semidirect
154. #2466C22semidirect
160. #2453C22semidirect
163. #2446C22semidirect
165. #2442C22semidirect
166. #2442C22semidirect
168. #2441C22semidirect
177. #2422C22semidirect
178. #2422C22semidirect
179. #2421C22semidirect
183. #2419C22semidirect
190. #2416C22semidirect
192. #2414C22semidirect
197. #2395C22semidirect
198. #2395C22semidirect
201. #2374C22semidirect
202. #2373C22semidirect
203. #2370C22semidirect
204. #2370C22semidirect
205. #2370C22semidirect
208. #2365C22semidirect
212. #2363C22semidirect
213. #2362C22semidirect
214. #2361C22semidirect
215. #2361C22semidirect
216. #2359C22semidirect
217. #2357C22semidirect
218. #2356C22semidirect
219. #2355C22semidirect
222. #2354C22semidirect
223. #2353C22semidirect
224. #2353C22semidirect
228. #2352C22semidirect
229. Q8×C4⋊C4C22semidirect
233. D4×C4⋊C4C22semidirect
234. D4×C4⋊C4C22semidirect
239. #2346C22semidirect
240. #2346C22semidirect
241. #2345C22semidirect
242. #2345C22semidirect
243. #2345C22semidirect
244. #2345C22semidirect
246. #2344C22semidirect
247. #2344C22semidirect
248. #2343C22semidirect
249. #2343C22semidirect
256. #2335C22semidirect
257. #2334C22semidirect
258. #2324C22semidirect
259. #2317C22semidirect
260. #2317C22semidirect
263. #2314C22semidirect
264. C4×C4⋊Q8C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×#125C22semidirect
267. C4×#126C22semidirect
270. C4×C22⋊Q8C22semidirect
271. C4×C22⋊Q8C22semidirect
277. C4×#121C22semidirect
278. C4×#121C22semidirect
285. #2285C22semidirect
286. #2285C22semidirect
287. #2283C22semidirect
291. #2274C22semidirect
292. #2274C22semidirect
295. C42×D4C22semidirect
296. C42×D4C22semidirect
298. C2×C4×C4⋊C4C22semidirect
939. #117#41semidirect

Maximal subgroups

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

subgroupindex
#594752
#594372
#593642
#592272
#592172
#592052
#591032
#590442
#453742
#451182
#440172
#440082
#390282
#390222
#389662
#389202
#384042
#378572
#364812
#364382
#363922
#362092
#361732
#361532
#361162
#361142
#359782
#357342
#349322
#347002
#343162
#342432
#341802
C4×#5532
D4×#1172