Finite Group Databasebeta

← #7675054

Subgroups — #7675054

Order 512.

7474 conjugacy classes of subgroups.

The subgroup lattice has 1720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C212yesmaximal, complemented
2#59118C212yesmaximal, complemented
3#59116C212yesmaximal, complemented
4#59104C212yesmaximal, complemented
5#59098C212yesmaximal, complemented
6#59025C212yesmaximal, complemented
7#59019C212yesmaximal, complemented
8#59005C212yesmaximal, complemented
9#58999C212yesmaximal, complemented
10#43929C214yesmaximal, complemented
11#43925C214yesmaximal, complemented
12#43045C214yesmaximal, complemented
13#43041C214yesmaximal, complemented
14#39487C211yesmaximal, characteristic, complemented
15#39482C212yesmaximal, complemented
16#39359C211yesmaximal, characteristic, complemented
17#39354C212yesmaximal, complemented
18#39166C212yesmaximal, complemented
19#38086C214yesmaximal, complemented
20#36576C211yesmaximal, characteristic, complemented
21Q8×#121C211yesmaximal, characteristic, complemented
22#36424C212yesmaximal, complemented
23#35366C214yesmaximal, complemented
24#35032C211yesmaximal, characteristic, complemented
25#35006C212yesmaximal, complemented
26#34737C212yesmaximal, complemented
27#34274C212yesmaximal, complemented
28C2×#2362C211yesmaximal, characteristic, complemented
29C4×#534C211yesmaximal, characteristic, complemented
30#3520—232no—
31C2×#556C2212yes—
32C2×#554C2214yescomplemented
33C2×#552C2212yes—
34C2×#552C2212yescomplemented
35C2×#551C2214yes—
36C2×#551C2214yescomplemented
37C2×#550C2211yescharacteristic, complemented
38C2×D4×Q8C2212yescomplemented
39C2×D4×Q8C2211yescharacteristic, complemented
40C2×#548C2212yes—
41C2×#548C2212yescomplemented
42C2×#547C2212yes—
43C2×#547C2212yescomplemented
44C2×#546C2214yes—
45C2×#542C2214yes—
46C2×#539C2214yes—
47C2×#539C2214yescomplemented
48C2×#537C2212yes—
49C2×#534C2211yescharacteristic
50C2×#533C2212yescomplemented
51C2×#529C2212yescomplemented
52C2×#525C2212yes—
53C2×#525C2212yescomplemented
54C2×#525C2212yescomplemented
55C22×C22⋊Q8C2211yescharacteristic
56C22×C22⋊Q8C2212yescomplemented
57C2×#520C2214yescomplemented
58C22×C4×Q8C2211yescharacteristic, complemented
59C22×C4×D4C2212yes—
60C22×#117C2211yescharacteristic
61#2857C2212yescomplemented
62#2857C2211yescharacteristic, complemented
63#2856C2212yes—
64#2856C2211yescharacteristic, complemented
65#2854C2214yescomplemented
66#2850C2212yescomplemented
67#2731C2214yescomplemented
68#2730C2214yescomplemented
69#2729C2214yescomplemented
70#2728C2214yescomplemented
71#2727C2212yescomplemented
72#2726C2212yescomplemented
73#2725C2214yescomplemented
74#2718C2214yescomplemented
75#2710C2214yes—
76#2710C2214yescomplemented
77#2703C2214yes—
78#2700C2214yes—
79#2689C2214yescomplemented
80#2689C2214yescomplemented
81#2687C2214yescomplemented
82#2685C2214yescomplemented
83#2683C2212yescomplemented
84#2682C2212yescomplemented
85#2681C2214yes—
86#2681C2214yes—
87#2681C2214yescomplemented
88#2680C2214yes—
89#2678C2214yes—
90#2678C2214yescomplemented
91#2674C2214yescomplemented
92#2669C2214yes—
93#2639C2214yescomplemented
94#2618C2212yes—
95#2618C2212yescomplemented
96#2617C2212yes—
97#2617C2212yes—
98#2602C2214yescomplemented
99#2602C2214yescomplemented
100#2564C2214yescomplemented
101#2560C2214yescomplemented
102#2560C2214yescomplemented
103#2560C2214yescomplemented
104#2558C2214yescomplemented
105#2558C2214yescomplemented
106#2558C2214yescomplemented
107#2556C2214yescomplemented
108#2554C2214yescomplemented
109#2550C2212yescomplemented
110#2548C2212yescomplemented
111#2548C2211yescharacteristic, complemented
112#2546C2212yescomplemented
113#2546C2211yescharacteristic, complemented
114#2543C2214yes—
115#2540C2212yescomplemented
116#2538C2212yescomplemented
117#2538C2212yescomplemented
118#2538C2211yescharacteristic, complemented
119#2538C2211yescharacteristic, complemented
120#2512C2214yescomplemented
121#2506C2214yescomplemented
122#2500C2212yescomplemented
123#2499C2212yescomplemented
124#2498C2214yescomplemented
125#2498C2214yescomplemented
126#2492C2212yescomplemented
127#2490C2212yescomplemented
128#2481C2214yescomplemented
129#2480C2214yescomplemented
130#2479C2214yescomplemented
131#2478C2214yescomplemented
132#2477C2214yescomplemented
133#2476C2214yes—
134#2475C2214yescomplemented
135#2473C2214yescomplemented
136#2472C2214yes—
137#2472C2214yescomplemented
138#2471C2214yescomplemented
139#2470C2214yes—
140#2470C2214yescomplemented
141#2469C2214yescomplemented
142#2467C2214yescomplemented
143#2466C2214yescomplemented
144#2466C2214yescomplemented
145#2465C2214yescomplemented
146#2464C2214yes—
147#2464C2214yes—
148#2463C2214yescomplemented
149#2462C2214yescomplemented
150#2461C2214yes—
151#2460C2214yescomplemented
152#2459C2214yescomplemented
153#2458C2214yescomplemented
154#2457C2214yes—
155#2456C2214yescomplemented
156#2455C2214yescomplemented
157#2453C2212yescomplemented
158#2452C2214yescomplemented
159#2452C2212yescomplemented
160#2449C2214yescomplemented
161#2448C2212yescomplemented
162#2446C2212yescomplemented
163#2445C2214yescomplemented
164#2443C2214yescomplemented
165#2441C2212yescomplemented
166#2440C2212yescomplemented
167#2436C2212yescomplemented
168#2432C2212yescomplemented
169#2432C2212yescomplemented
170#2431C2212yescomplemented
171#2430C2214yes—
172#2430C2214yescomplemented
173#2429C2214yescomplemented
174#2429C2212yescomplemented
175#2429C2212yescomplemented
176#2428C2212yescomplemented
177#2426C2214yescomplemented
178#2426C2212yescomplemented
179#2424C2214yes—
180#2421C2212yescomplemented
181#2421C2212yescomplemented
182#2417C2214yescomplemented
183#2417C2212yescomplemented
184#2417C2212yescomplemented
185#2416C2214yescomplemented
186#2416C2212yescomplemented
187#2416C2212yescomplemented
188#2416C2212yescomplemented
189#2415C2212yes—
190#2415C2212yes—
191#2415C2212yescomplemented
192#2414C2212yes—
193#2414C2212yes—
194#2413C2214yescomplemented
195#2412C2214yes—
196#2411C2214yescomplemented
197#2410C2214yes—
198#2409C2212yescomplemented
199#2407C2212yescomplemented
200#2392C2214yes—
201#2392C2214yes—
202#2367C2212yescomplemented
203#2363C2214yescomplemented
204#2363C2212yescomplemented
205#2363C2214yescomplemented
206#2362C2214yescomplemented
207#2362C2214yescomplemented
208#2362C2212yescomplemented
209#2362C2212yescomplemented
210#2362C2212yescomplemented
211#2362C2212yescomplemented
212#2362C2214yescomplemented
213#2362C2214yescomplemented
214#2361C2214yescomplemented
215#2361C2214yescomplemented
216#2360C2214yescomplemented
217#2360C2212yescomplemented
218#2360C2214yescomplemented
219#2352C2212yescomplemented
220Q8×C4⋊C4C2211yescharacteristic, complemented
221Q8×C4⋊C4C2211yescharacteristic, complemented
222#2341C2212yescomplemented
223Q8×C22⋊C4C2212yescomplemented
224#2325C2212yes—
225#2325C2211yescharacteristic
226#2325C2211yescharacteristic
227#2325C2212yescomplemented
228#2325C2212yescomplemented
229#2325C2214yescomplemented
230#2322C2212yes—
231#2322C2212yes—
232#2321C2212yes—
233#2321C2212yes—
234#2316C2212yescomplemented
235#2315C2211yescharacteristic
236#2308C2212yes—
237C4×#123C2212yes—
238C4×#123C2212yes—
239C4×#121C2211yescharacteristic
240C4×#121C2212yes—
241C4×#121C2211yescharacteristic
242C4×#121C2212yes—
243C4×#121C2214yescomplemented
244C4×#121C2214yescomplemented
245C4×#121C2212yescomplemented
246C4×#120C2212yes—
247C4×#120C2212yes—
248#2297C2214yescomplemented
249#2297C2212yescomplemented
250#2296C2212yescomplemented
251C2×#391C2211yescharacteristic, complemented
252C2×#389C2211yescharacteristic, complemented
253C2×#388C2212yes—
254C2×#388C2212yes—
255C2×#387C2212yescomplemented
256#2280C2212yescomplemented
257C2×C4×C4⋊C4C2211yescharacteristic, complemented
258C2×C4×C4⋊C4C2212yescomplemented
259C2×C4×C22⋊C4C2211yescharacteristic
260C22×#41C2314yes—
261C22×#41C2312yes—
262C22×#41C2312yes—
263C23×Q8C2312yes—
264C23×Q8C2311yescharacteristic
265C23×D4C2312yes—
266C24×C4C2312yes—
267C24×C4C2311yescharacteristic
268#556—216no—
269#554—232no—
270#552—216no—
271#552—216no—
272#551—232no—
273#551—232no—
274#550—44no—
275D4×Q8—216no—
276D4×Q8—44no—
277#548—216no—
278#548—216no—
279#547—216no—
280#547—216no—
281#546—232no—
282#542—232no—
283#539—232no—
284#539—232no—
285#537—216no—
286#534—28no—
287#533—216no—
288C2×C4⋊Q8C2312yes—
289C2×C4⋊Q8C2312yes—
290C2×C4⋊Q8C2314yes—
291C2×C4⋊Q8C2312yes—
292C2×C4⋊Q8C2311yescharacteristic
293C2×#127C2312yes—
294C2×#127C2311yescharacteristic
295#529—216no—
296C2×#126C2314yes—
297C2×#126C2314yes—
298C2×#126C2314yes—
299C2×#126C2314yes—
300C2×#126C2314yes—
301C2×#125C2312yes—
302C2×#125C2314yes—
303C2×#125C2314yes—
304C2×#125C2314yes—
305C2×#124C2312yes—
306C2×#124C2314yes—
307C2×#124C2314yes—
308C2×#124C2314yes—
309C2×#124C2312yes—
310#525—216no—
311#525—216no—
312#525—48no—
313C2×#123C2312yes—
314C2×#123C2312yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×#123C2314yes—
325C2×C22⋊Q8—216no—
326C2×C22⋊Q8D4116yescomplemented
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2314yes—
348C2×#121C2311yescharacteristic
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2314yes—
352C2×#121C2312yes—
353C2×#121C2314yes—
354C2×#121C2314yes—
355C2×#121C2314yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2314yes—
361C2×#121C2312yes—
362C2×#121C2314yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365C2×#121C2311yescharacteristic
366C2×#120C2312yes—
367C2×#120C2312yes—
368C2×#120C2314yes—
369C2×#120C2314yes—
370C2×#120C2314yes—
371#520—232no—
372C2×C4×Q8—44no—
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2314yes—
378C2×C4×Q8C2314yes—
379C2×C4×Q8C2312yes—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2312yes—
384C2×C4×D4—216no—
385C2×C4×D4C2314yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2314yes—
392C2×C4×D4C2314yes—
393C2×C4×D4C2314yes—
394C2×C4×D4C2314yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2314yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2314yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2314yes—
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2311yescharacteristic
409C2×#117—44no—
410C2×#117C2314yes—
411C2×#117C2312yes—
412C2×#117C2312yes—
413C2×#117C2314yes—
414C2×#117C2314yes—
415C2×#117C2312yes—
416C2×#117C2314yes—
417C2×#117C2314yes—
418C2×#117C2312yes—
419C22×C4⋊C4C2312yes—
420C22×C4⋊C4C2312yes—
421C22×C4⋊C4C2312yes—
422C22×C4⋊C4C2314yes—
423C22×C4⋊C4C2314yes—
424C22×C4⋊C4C2311yescharacteristic
425C22×C4⋊C4C2311yescharacteristic
426C22×C4⋊C4C2312yes—
427C22×C4⋊C4C2312yes—
428C22×C4⋊C4C2311yescharacteristic
429C22×C22⋊C4C2312yes—
430C22×C22⋊C4C2311yescharacteristic
431C22×C22⋊C4C2312yes—
432C22×C22⋊C4C2314yes—
433C22×C22⋊C4C2311yescharacteristic
434C22×C22⋊C4C2312yes—
435C22×C22⋊C4C2312yes—
436C22×C42C2312yes—
437C22×C42C2311yescharacteristic
438C22×C42C2312yes—
439C22×C42C2312yes—
440C22×C42C2311yescharacteristic
441C22×C42C2312yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2314yes—
446#400C2314yes—
447#399C2314yes—
448#399C2314yes—
449#399C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#395C2314yes—
481#395C2314yes—
482#395C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2312yes—
517#391C2312yes—
518#391C2312yes—
519#391C2314yes—
520#391C2314yes—
521#391C2312yes—
522#391C2312yes—
523#391C2314yes—
524#391C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2314yes—
528#390C2311yescharacteristic
529#390C2311yescharacteristic
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2312yes—
534#390C2312yes—
535#390C2314yes—
536#390C2314yes—
537#390C2314yes—
538#390C2312yes—
539#390C2312yes—
540#390C2314yes—
541#390C2314yes—
542#390C2312yes—
543#390C2314yes—
544#390C2312yes—
545#390C2314yes—
546#390C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2311yescharacteristic
552#389C2311yescharacteristic
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2312yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#386C2312yes—
632#386C2314yes—
633#386C2314yes—
634#386C2312yes—
635#386C2312yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#386C2312yes—
640#386C2312yes—
641#386C2312yes—
642#386C2314yes—
643#386C2314yes—
644#386C2312yes—
645#386C2312yes—
646#386C2312yes—
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#385C2314yes—
662#385C2314yes—
663#385C2312yes—
664#385C2312yes—
665#385C2312yes—
666#385C2312yes—
667#385C2312yes—
668#385C2312yes—
669#385C2312yes—
670#385C2312yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#384C2312yes—
682#384C2311yescharacteristic
683#384C2311yescharacteristic
684#384C2312yes—
685#382C2312yes—
686#381C2312yes—
687#381C2312yes—
688#381C2314yes—
689#380C2312yes—
690#380C2314yes—
691#380C2311yescharacteristic
692#380C2311yescharacteristic
693#380C2312yes—
694#380C2312yes—
695#380C2312yes—
696#380C2314yes—
697#380C2312yes—
698#380C2314yes—
699#380C2314yes—
700#380C2312yes—
701#380C2312yes—
702#379C2312yes—
703#379C2312yes—
704#379C2314yes—
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2311yescharacteristic
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2314yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2314yes—
731C4×C22⋊C4C2314yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2314yes—
734C4×C22⋊C4C2312yes—
735C4×C22⋊C4C2312yes—
736C4×C22⋊C4C2312yes—
737C2×#95C2312yes—
738C2×#95C2311yescharacteristic
739C2×#95C2311yescharacteristic
740C2×#95C2312yes—
741C2×#95C2312yes—
742C2×#95C2312yes—
743C25C2412yes—
744C25C2411yescharacteristic
745C2×#41—28no—
746C2×#41—216no—
747C2×#41—216no—
748C2×#41—28no—
749C2×#41—48no—
750C2×#41—44no—
751C2×#41—44no—
752C2×#41—44no—
753C2×#41—44no—
754C22×Q8—28no—
755C22×Q8—42no—
756C22×Q8—42no—
757C22×Q8—44no—
758C22×Q8—44no—
759C22×Q8C2×D418yes—
760C22×Q8C2412yes—
761C22×Q8C2414yes—
762C22×Q8C2411yescharacteristic
763C22×Q8C2411yescharacteristic
764C22×Q8C2414yes—
765C22×Q8C2412yes—
766C22×D4—28no—
767C22×D4—28no—
768C22×D4—44no—
769C22×D4C2414yes—
770C22×D4C2412yes—
771C22×D4C2412yes—
772C22×D4C2414yes—
773C22×D4C2412yes—
774C22×D4C2412yes—
775C22×D4C2412yes—
776C22×D4C2414yes—
777C22×D4C2411yescharacteristic
778C22×D4C2412yes—
779C22×D4C2414yes—
780C22×D4C2414yes—
781C22×D4C2412yes—
782C22×D4C2414yes—
783C22×D4C2414yes—
784C22×D4C2412yes—
785C22×D4C2411yescharacteristic
786C23×C4—28no—
787C23×C4—42no—
788C23×C4—42no—
789C23×C4—44no—
790C23×C4—44no—
791C23×C4C2×D418yes—
792C23×C4C2412yes—
793C23×C4C2412yes—
794C23×C4C2414yes—
795C23×C4C2412yes—
796C23×C4C2414yes—
797C23×C4C2412yes—
798C23×C4C2412yes—
799C23×C4C2411yescharacteristic
800C23×C4C2412yes—
801C23×C4C2412yes—
802C23×C4C2412yes—
803C23×C4C2411yescharacteristic
804C23×C4C2414yes—
805C23×C4C2412yes—
806C23×C4C2411yescharacteristic
807C23×C4C2411yescharacteristic
808C23×C4C2412yes—
809C23×C4C2414yes—
810C23×C4C2414yes—
811C23×C4C2412yes—
812C23×C4C2412yes—
813C23×C4C2412yes—
814C23×C4C2411yescharacteristic
815C23×C4C2411yescharacteristic
816C4⋊Q8—28no—
817C4⋊Q8—216no—
818C4⋊Q8—28no—
819C4⋊Q8—44no—
820C4⋊Q8—42no—
821#127—42no—
822#127—44no—
823#126—216no—
824#126—216no—
825#126—216no—
826#126—216no—
827#126—216no—
828#125—28no—
829#125—216no—
830#125—216no—
831#125—216no—
832#124—28no—
833#124—216no—
834#124—216no—
835#124—216no—
836#124—44no—
837#123—216no—
838#123—216no—
839#123—216no—
840#123—216no—
841#123—216no—
842#123—216no—
843#123—28no—
844#123—216no—
845#123—216no—
846#123—216no—
847#123—28no—
848#123—48no—
849C22⋊Q8—28no—
850C22⋊Q8—28no—
851C22⋊Q8—216no—
852C22⋊Q8—216no—
853C22⋊Q8—28no—
854C22⋊Q8—28no—
855C22⋊Q8—216no—
856C22⋊Q8—216no—
857C22⋊Q8—28no—
858C22⋊Q8—216no—
859C22⋊Q8—216no—
860C22⋊Q8—216no—
861C22⋊Q8—28no—
862C22⋊Q8—216no—
863C22⋊Q8—216no—
864C22⋊Q8—216no—
865C22⋊Q8—48no—
866C22⋊Q8—44no—
867C22⋊Q8C2×D4116yes—
868C22⋊Q8C2×D4116yes—
869C22⋊Q8C2×D4132yes—
870#121—28no—
871#121—216no—
872#121—216no—
873#121—28no—
874#121—28no—
875#121—216no—
876#121—24no—
877#121—28no—
878#121—28no—
879#121—28no—
880#121—216no—
881#121—216no—
882#121—216no—
883#121—48no—
884#121—44no—
885#121—48no—
886#121—44no—
887#121#4118yescomplemented
888#120—216no—
889#120—28no—
890#120—216no—
891#120—28no—
892#120—48no—
893C4×Q8—28no—
894C4×Q8—28no—
895C4×Q8—216no—
896C4×Q8—216no—
897C4×Q8—28no—
898C4×Q8—24no—
899C4×Q8—24no—
900C4×Q8—44no—
901C4×Q8—44no—
902C4×Q8—42no—
903C4×Q8—42no—
904C4×D4—28no—
905C4×D4—28no—
906C4×D4—28no—
907C4×D4—28no—
908C4×D4—28no—
909C4×D4—28no—
910C4×D4—28no—
911C4×D4—28no—
912C4×D4—216no—
913C4×D4—216no—
914C4×D4—216no—
915C4×D4—216no—
916C4×D4—216no—
917C4×D4—216no—
918C4×D4—28no—
919C4×D4—216no—
920C4×D4—216no—
921C4×D4—48no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—48no—
925C4×D4—44no—
926C4×D4—42no—
927C4×D4—42no—
928#117—216no—
929#117—28no—
930#117—216no—
931#117—216no—
932#117—28no—
933#117—28no—
934#117—216no—
935#117—48no—
936#117—44no—
937C2×C4⋊C4—28no—
938C2×C4⋊C4—28no—
939C2×C4⋊C4—216no—
940C2×C4⋊C4—216no—
941C2×C4⋊C4—28no—
942C2×C4⋊C4—24no—
943C2×C4⋊C4—42no—
944C2×C4⋊C4—44no—
945C2×C4⋊C4C2×D4116yes—
946C2×C4⋊C4C2×D418yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C22⋊C4—28no—
1004C2×C22⋊C4—28no—
1005C2×C22⋊C4—24no—
1006C2×C22⋊C4—216no—
1007C2×C22⋊C4—44no—
1008C2×C22⋊C4—42no—
1009C2×C22⋊C4C2×D4116yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C42—28no—
1070C2×C42—44no—
1071C2×C42—42no—
1072C2×C42—44no—
1073C2×C42—42no—
1074C2×C42—44no—
1075C2×C42C2412yes—
1076C2×C42C2414yes—
1077C2×C42C2414yes—
1078C2×C42C2414yes—
1079C2×C42C2414yes—
1080C2×C42C2414yes—
1081C2×C42C2414yes—
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2412yes—
1085C2×C42C2411yescharacteristic
1086C2×C42C2412yes—
1087C2×C42C2411yescharacteristic
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2414yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2412yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2412yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2414yes—
1114#95C2412yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2412yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140C24—22no—
1141C24—22no—
1142C24—24no—
1143C24—24no—
1144C24—41no—
1145C24—41no—
1146C24—42no—
1147C24—41no—
1148C24—41no—
1149C24—42no—
1150C24—42no—
1151C24—42no—
1152C24—42no—
1153C24C22×D414yes—
1154C24C2512yes—
1155C24C2514yes—
1156C24C2512yes—
1157C24C2512yes—
1158C24C2511yescharacteristic
1159#41—464no—
1160#41—816no—
1161#41—816no—
1162C2×Q8—28no—
1163C2×Q8—24no—
1164C2×Q8—28no—
1165C2×Q8—28no—
1166C2×Q8—22no—
1167C2×Q8—22no—
1168C2×Q8—24no—
1169C2×Q8—22no—
1170C2×Q8—22no—
1171C2×Q8—24no—
1172C2×Q8—42no—
1173C2×Q8—42no—
1174C2×Q8—44no—
1175C2×Q8—44no—
1176C2×Q8—44no—
1177C2×Q8—416no—
1178C2×Q8—816no—
1179C2×Q8C22×D414yes—
1180C2×Q8C22×D414yes—
1181C2×Q8C22×D418yes—
1182C2×D4—24no—
1183C2×D4—24no—
1184C2×D4—28no—
1185C2×D4—28no—
1186C2×D4—24no—
1187C2×D4—24no—
1188C2×D4—24no—
1189C2×D4—24no—
1190C2×D4—24no—
1191C2×D4—28no—
1192C2×D4—28no—
1193C2×D4—24no—
1194C2×D4—28no—
1195C2×D4—28no—
1196C2×D4—24no—
1197C2×D4—28no—
1198C2×D4—28no—
1199C2×D4—24no—
1200C2×D4—28no—
1201C2×D4—24no—
1202C2×D4—22no—
1203C2×D4—24no—
1204C2×D4—24no—
1205C2×D4—28no—
1206C2×D4—24no—
1207C2×D4—41no—
1208C2×D4—42no—
1209C2×D4—42no—
1210C2×D4—41no—
1211C2×D4—44no—
1212C2×D4—44no—
1213C2×D4—44no—
1214C2×D4—44no—
1215C2×D4—42no—
1216C2×D4—41no—
1217C2×D4—42no—
1218C2×D4—44no—
1219C2×D4—44no—
1220C2×D4—44no—
1221C2×D4—44no—
1222C2×D4—41no—
1223C2×D4—42no—
1224C2×D4—42no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4—44no—
1228C2×D4—42no—
1229C2×D4—42no—
1230C2×D4—42no—
1231C2×D4—432no—
1232C2×D4C2×#4118yes—
1233C2×D4C2×#4114yes—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—22no—
1237C22×C4—24no—
1238C22×C4—22no—
1239C22×C4—24no—
1240C22×C4—24no—
1241C22×C4—24no—
1242C22×C4—28no—
1243C22×C4—22no—
1244C22×C4—24no—
1245C22×C4—24no—
1246C22×C4—22no—
1247C22×C4—24no—
1248C22×C4—22no—
1249C22×C4—28no—
1250C22×C4—28no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—28no—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—24no—
1260C22×C4—28no—
1261C22×C4—24no—
1262C22×C4—28no—
1263C22×C4—28no—
1264C22×C4—24no—
1265C22×C4—416no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—42no—
1269C22×C4—41no—
1270C22×C4—42no—
1271C22×C4—42no—
1272C22×C4—41no—
1273C22×C4—41no—
1274C22×C4—42no—
1275C22×C4—41no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—42no—
1279C22×C4—42no—
1280C22×C4—44no—
1281C22×C4—44no—
1282C22×C4—42no—
1283C22×C4—41no—
1284C22×C4—41no—
1285C22×C4—42no—
1286C22×C4—42no—
1287C22×C4—44no—
1288C22×C4—44no—
1289C22×C4—44no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—41no—
1295C22×C4—42no—
1296C22×C4—41no—
1297C22×C4—44no—
1298C22×C4—44no—
1299C22×C4—44no—
1300C22×C4—816no—
1301C22×C4C22×D418yes—
1302C22×C4C22×D418yes—
1303C22×C4C22×D414yes—
1304C22×C4C22×D418yes—
1305C22×C4C22×D418yes—
1306C22×C4C22×D414yes—
1307C22×C4C2×#4114yes—
1308C22×C4C2512yes—
1309C22×C4C2512yes—
1310C22×C4C2511yescharacteristic
1311C22×C4C2514yes—
1312C22×C4C2512yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2512yes—
1315C22×C4C2514yes—
1316C22×C4C2512yes—
1317C22×C4C2514yes—
1318C22×C4C2512yes—
1319C22×C4C2512yes—
1320C22×C4C2514yes—
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2514yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2511yescharacteristic
1330C22×C4C2512yes—
1331C22×C4C2511yescharacteristic
1332C4⋊C4—24no—
1333C4⋊C4—28no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—28no—
1339C4⋊C4—28no—
1340C4⋊C4—28no—
1341C4⋊C4—28no—
1342C4⋊C4—28no—
1343C4⋊C4—24no—
1344C4⋊C4—28no—
1345C4⋊C4—28no—
1346C4⋊C4—28no—
1347C4⋊C4—28no—
1348C4⋊C4—28no—
1349C4⋊C4—28no—
1350C4⋊C4—28no—
1351C4⋊C4—28no—
1352C4⋊C4—28no—
1353C4⋊C4—28no—
1354C4⋊C4—28no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—22no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—28no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—41no—
1368C4⋊C4—42no—
1369C4⋊C4—44no—
1370C4⋊C4—41no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—42no—
1375C4⋊C4—41no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—41no—
1379C4⋊C4—44no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4C22×D418yes—
1383C4⋊C4C22×D4116yes—
1384C4⋊C4C22×D4116yes—
1385C4⋊C4C22×D418yes—
1386C4⋊C4C2×#4114yes—
1387C4⋊C4H(5,𝔽2)14yes—
1388C22⋊C4—24no—
1389C22⋊C4—28no—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—28no—
1394C22⋊C4—28no—
1395C22⋊C4—24no—
1396C22⋊C4—28no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—28no—
1404C22⋊C4—28no—
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—28no—
1416C22⋊C4—28no—
1417C22⋊C4—28no—
1418C22⋊C4—28no—
1419C22⋊C4—28no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—42no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—44no—
1436C22⋊C4—42no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4C22×D4116yes—
1445C22⋊C4C22×D4116yes—
1446C22⋊C4C2×#4118yes—
1447C42—24no—
1448C42—24no—
1449C42—24no—
1450C42—24no—
1451C42—28no—
1452C42—28no—
1453C42—28no—
1454C42—28no—
1455C42—28no—
1456C42—28no—
1457C42—24no—
1458C42—22no—
1459C42—24no—
1460C42—22no—
1461C42—24no—
1462C42—44no—
1463C42—44no—
1464C42—42no—
1465C42—44no—
1466C42—42no—
1467C42—41no—
1468C42—42no—
1469C42—41no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—22no—
1475C23—22no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—22no—
1482C23—22no—
1483C23—22no—
1484C23—22no—
1485C23—22no—
1486C23—28no—
1487C23—22no—
1488C23—24no—
1489C23—24no—
1490C23—22no—
1491C23—24no—
1492C23—22no—
1493C23—24no—
1494C23—24no—
1495C23—22no—
1496C23—22no—
1497C23—22no—
1498C23—24no—
1499C23—24no—
1500C23—22no—
1501C23—44no—
1502C23—44no—
1503C23—48no—
1504C23—48no—
1505C23—84no—
1506C23—82no—
1507C23—82no—
1508C23—82no—
1509C23—82no—
1510C23—84no—
1511C23—84no—
1512C23—84no—
1513C23—84no—
1514C23C23×D414yes—
1515C23C23×D412yes—
1516C23C22×#4114yes—
1517C23C22×#4112yes—
1518C23#58512yes—
1519C23C2611yescharacteristic
1520Q8—28no—
1521Q8—28no—
1522Q8—48no—
1523Q8—416no—
1524Q8—48no—
1525Q8—88no—
1526D4—216no—
1527D4—44no—
1528D4—48no—
1529D4—416no—
1530D4—48no—
1531D4—416no—
1532D4—48no—
1533D4—416no—
1534D4—48no—
1535D4—84no—
1536D4—82no—
1537D4—88no—
1538D4—88no—
1539D4—88no—
1540D4—84no—
1541D4—88no—
1542D4—162no—
1543C2×C4—22no—
1544C2×C4—24no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—24no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—21no—
1561C2×C4—216no—
1562C2×C4—216no—
1563C2×C4—28no—
1564C2×C4—22no—
1565C2×C4—24no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—24no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—24no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—24no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—24no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—24no—
1600C2×C4—24no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—44no—
1607C2×C4—48no—
1608C2×C4—48no—
1609C2×C4—44no—
1610C2×C4—416no—
1611C2×C4—48no—
1612C2×C4—48no—
1613C2×C4—416no—
1614C2×C4—48no—
1615C2×C4—44no—
1616C2×C4—48no—
1617C2×C4—48no—
1618C2×C4—84no—
1619C2×C4—84no—
1620C2×C4—88no—
1621C2×C4—88no—
1622C2×C4—88no—
1623C2×C4—84no—
1624C2×C4—82no—
1625C2×C4—82no—
1626C2×C4—84no—
1627C2×C4C23×D414yes—
1628C2×C4C23×D414yes—
1629C2×C4C23×D418yes—
1630C2×C4C23×D414yes—
1631C2×C4C23×D412yes—
1632C2×C4C23×D412yes—
1633C2×C4C22×#4112yes—
1634C2×C4C22×#4114yes—
1635C2×C4C22×#4112yes—
1636C2×C4C2×H(5,𝔽2)14yes—
1637C2×C4C2×H(5,𝔽2)12yes—
1638C2×C4#58512yes—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—24no—
1646C22—24no—
1647C22—24no—
1648C22—24no—
1649C22—24no—
1650C22—24no—
1651C22—42no—
1652C22—42no—
1653C22—42no—
1654C22—42no—
1655C22—42no—
1656C22—42no—
1657C22—42no—
1658C22—42no—
1659C22—44no—
1660C22—42no—
1661C22—42no—
1662C22—44no—
1663C22—42no—
1664C22—44no—
1665C22—44no—
1666C22—42no—
1667C22—42no—
1668C22—44no—
1669C22—44no—
1670C22—42no—
1671C22—44no—
1672C22—42no—
1673C22—88no—
1674C22—816no—
1675C22D4×#4114yes—
1676C22C24×D411yescharacteristic
1677C22C23×#4111yescharacteristic
1678C22C22×H(5,𝔽2)11yescharacteristic
1679C22C2×#58511yescharacteristic
1680C22C2×#58511yescharacteristic
1681C222−1+611yescharacteristic
1682C222−1+611yescharacteristic
1683C4—22no—
1684C4—22no—
1685C4—24no—
1686C4—22no—
1687C4—24no—
1688C4—24no—
1689C4—24no—
1690C4—28no—
1691C4—24no—
1692C4—44no—
1693C4—42no—
1694C4—42no—
1695C4—42no—
1696C4—44no—
1697C4—42no—
1698C4—42no—
1699C4—44no—
1700C4—42no—
1701C4—41no—
1702C4—41no—
1703C4—42no—
1704C4—42no—
1705C4—44no—
1706C4#349614yes—
1707C2—24no—
1708C2—44no—
1709C2—44no—
1710C2—84no—
1711C2—82no—
1712C2C2×D4×#4111yescharacteristic
1713C2C2×#349611yescharacteristic
1714C2#6284811yescharacteristic
1715C2#6289811yescharacteristic
1716C2#6290711yescharacteristic
1717C2#6298411yescharacteristic
1718C2#6299511yescharacteristic
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. C2×#3520C2semidirect
2. #59118C2semidirect
3. #59116C2semidirect
4. #59104C2semidirect
5. #59098C2semidirect
6. #59025C2semidirect
7. #59019C2semidirect
8. #59005C2semidirect
9. #58999C2semidirect
10. #43929C2semidirect
11. #43925C2semidirect
12. #43045C2semidirect
13. #43041C2semidirect
14. #39487C2semidirect
15. #39482C2semidirect
16. #39359C2semidirect
17. #39354C2semidirect
18. #39166C2semidirect
19. #38086C2semidirect
20. #36576C2semidirect
21. Q8×#121C2semidirect
22. #36424C2semidirect
23. #35366C2semidirect
24. #35032C2semidirect
25. #35006C2semidirect
26. #34737C2semidirect
27. #34274C2semidirect
28. C2×#2362C2semidirect
29. C4×#534C2semidirect
32. C2×#554C22semidirect
34. C2×#552C22semidirect
36. C2×#551C22semidirect
37. C2×#550C22semidirect
38. C2×D4×Q8C22semidirect
39. C2×D4×Q8C22semidirect
41. C2×#548C22semidirect
43. C2×#547C22semidirect
47. C2×#539C22semidirect
50. C2×#533C22semidirect
51. C2×#529C22semidirect
53. C2×#525C22semidirect
54. C2×#525C22semidirect
56. C22×C22⋊Q8C22semidirect
57. C2×#520C22semidirect
58. C22×C4×Q8C22semidirect
61. #2857C22semidirect
62. #2857C22semidirect
64. #2856C22semidirect
65. #2854C22semidirect
66. #2850C22semidirect
67. #2731C22semidirect
68. #2730C22semidirect
69. #2729C22semidirect
70. #2728C22semidirect
71. #2727C22semidirect
72. #2726C22semidirect
73. #2725C22semidirect
74. #2718C22semidirect
76. #2710C22semidirect
79. #2689C22semidirect
80. #2689C22semidirect
81. #2687C22semidirect
82. #2685C22semidirect
83. #2683C22semidirect
84. #2682C22semidirect
87. #2681C22semidirect
90. #2678C22semidirect
91. #2674C22semidirect
93. #2639C22semidirect
95. #2618C22semidirect
98. #2602C22semidirect
99. #2602C22semidirect
100. #2564C22semidirect
101. #2560C22semidirect
102. #2560C22semidirect
103. #2560C22semidirect
104. #2558C22semidirect
105. #2558C22semidirect
106. #2558C22semidirect
107. #2556C22semidirect
108. #2554C22semidirect
109. #2550C22semidirect
110. #2548C22semidirect
111. #2548C22semidirect
112. #2546C22semidirect
113. #2546C22semidirect
115. #2540C22semidirect
116. #2538C22semidirect
117. #2538C22semidirect
118. #2538C22semidirect
119. #2538C22semidirect
120. #2512C22semidirect
121. #2506C22semidirect
122. #2500C22semidirect
123. #2499C22semidirect
124. #2498C22semidirect
125. #2498C22semidirect
126. #2492C22semidirect
127. #2490C22semidirect
128. #2481C22semidirect
129. #2480C22semidirect
130. #2479C22semidirect
131. #2478C22semidirect
132. #2477C22semidirect
134. #2475C22semidirect
135. #2473C22semidirect
137. #2472C22semidirect
138. #2471C22semidirect
140. #2470C22semidirect
141. #2469C22semidirect
142. #2467C22semidirect
143. #2466C22semidirect
144. #2466C22semidirect
145. #2465C22semidirect
148. #2463C22semidirect
149. #2462C22semidirect
151. #2460C22semidirect
152. #2459C22semidirect
153. #2458C22semidirect
155. #2456C22semidirect
156. #2455C22semidirect
157. #2453C22semidirect
158. #2452C22semidirect
159. #2452C22semidirect
160. #2449C22semidirect
161. #2448C22semidirect
162. #2446C22semidirect
163. #2445C22semidirect
164. #2443C22semidirect
165. #2441C22semidirect
166. #2440C22semidirect
167. #2436C22semidirect
168. #2432C22semidirect
169. #2432C22semidirect
170. #2431C22semidirect
172. #2430C22semidirect
173. #2429C22semidirect
174. #2429C22semidirect
175. #2429C22semidirect
176. #2428C22semidirect
177. #2426C22semidirect
178. #2426C22semidirect
180. #2421C22semidirect
181. #2421C22semidirect
182. #2417C22semidirect
183. #2417C22semidirect
184. #2417C22semidirect
185. #2416C22semidirect
186. #2416C22semidirect
187. #2416C22semidirect
188. #2416C22semidirect
191. #2415C22semidirect
194. #2413C22semidirect
196. #2411C22semidirect
198. #2409C22semidirect
199. #2407C22semidirect
202. #2367C22semidirect
203. #2363C22semidirect
204. #2363C22semidirect
205. #2363C22semidirect
206. #2362C22semidirect
207. #2362C22semidirect
208. #2362C22semidirect
209. #2362C22semidirect
210. #2362C22semidirect
211. #2362C22semidirect
212. #2362C22semidirect
213. #2362C22semidirect
214. #2361C22semidirect
215. #2361C22semidirect
216. #2360C22semidirect
217. #2360C22semidirect
218. #2360C22semidirect
219. #2352C22semidirect
220. Q8×C4⋊C4C22semidirect
221. Q8×C4⋊C4C22semidirect
222. #2341C22semidirect
223. Q8×C22⋊C4C22semidirect
227. #2325C22semidirect
228. #2325C22semidirect
229. #2325C22semidirect
234. #2316C22semidirect
243. C4×#121C22semidirect
244. C4×#121C22semidirect
245. C4×#121C22semidirect
248. #2297C22semidirect
249. #2297C22semidirect
250. #2296C22semidirect
251. C2×#391C22semidirect
252. C2×#389C22semidirect
255. C2×#387C22semidirect
256. #2280C22semidirect
257. C2×C4×C4⋊C4C22semidirect
258. C2×C4×C4⋊C4C22semidirect
326. C2×C22⋊Q8D4semidirect
887. #121#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
#591182
#591162
#591042
#590982
#590252
#590192
#590052
#589992
#439292
#439252
#430452
#430412
#394872
#394822
#393592
#393542
#391662
#380862
#365762
Q8×#1212
#364242
#353662
#350322
#350062
#347372
#342742
C2×#23622
C4×#5342