Finite Group Databasebeta

← #7658971

Subgroups — #7658971

Order 512.

7008 conjugacy classes of subgroups.

The subgroup lattice has 1633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3521C212yesmaximal, complemented
2#42952C211yesmaximal, characteristic, complemented
3#42929C211yesmaximal, characteristic, complemented
4#42928C212yesmaximal, complemented
5#42803C212yesmaximal, complemented
6#42802C212yesmaximal, complemented
7#42799C212yesmaximal, complemented
8#42798C212yesmaximal, complemented
9#42167C212yesmaximal, complemented
10#41984C214yesmaximal, complemented
11#41983C212yesmaximal, complemented
12#40519C214yesmaximal, complemented
13#40518C214yesmaximal, complemented
14#40515C214yesmaximal, complemented
15#40514C214yesmaximal, complemented
16#37620C212yesmaximal, complemented
17#37620C212yesmaximal, complemented
18#37542C211yesmaximal, characteristic, complemented
19#37538C214yesmaximal, complemented
20#36684C211yesmaximal, characteristic, complemented
21C2×#2823C212yesmaximal, complemented
22#36020C211yesmaximal, characteristic, complemented
23#35821C212yesmaximal, complemented
24#35821C212yesmaximal, complemented
25#35806C212yesmaximal, complemented
26#35776C212yesmaximal, complemented
27#35761C212yesmaximal, complemented
28#35728C211yesmaximal, characteristic, complemented
29#34183C211yesmaximal, characteristic, complemented
30#3521—232no—
31C2×#556C2212yescomplemented
32C2×#556C2212yescomplemented
33C2×#554C2212yes—
34C2×#553C2214yescomplemented
35C2×#553C2212yescomplemented
36C2×#552C2214yescomplemented
37C2×#552C2212yescomplemented
38C2×#551C2214yescomplemented
39C2×#551C2214yescomplemented
40C2×#547C2212yes—
41C2×#547C2211yescharacteristic
42C2×#546C2212yes—
43C2×#546C2212yes—
44C2×#546C2212yes—
45C2×D42C2211yescharacteristic
46C2×#542C2212yescomplemented
47C2×#541C2212yescomplemented
48C2×#539C2214yescomplemented
49C2×#538C2214yescomplemented
50C2×#529C2212yescomplemented
51C2×#529C2214yescomplemented
52C2×#529C2212yescomplemented
53C22×#126C2214yescomplemented
54C2×#520C2212yes—
55C2×#520C2211yescharacteristic
56C2×#520C2211yescharacteristic
57C2×#518C2212yes—
58C2×C4×#41C2211yescharacteristic
59#2823C2214yes—
60#2823C2211yescharacteristic
61#2823C2212yes—
62#2823C2214yescomplemented
63#2823C2214yescomplemented
64#2823C2214yescomplemented
65#2823C2214yescomplemented
66#2823C2214yescomplemented
67#2823C2212yescomplemented
68#2823C2212yescomplemented
69#2823C2212yescomplemented
70#2823C2211yescharacteristic, complemented
71#2823C2212yescomplemented
72#2823C2214yescomplemented
73#2822C2211yescharacteristic, complemented
74#2820C2212yescomplemented
75#2819C2211yescharacteristic
76#2814C2212yescomplemented
77#2814C2212yescomplemented
78#2813C2212yes—
79#2813C2212yescomplemented
80#2727C2214yescomplemented
81#2726C2214yescomplemented
82#2725C2214yescomplemented
83#2725C2214yescomplemented
84#2722C2212yescomplemented
85#2715C2214yescomplemented
86#2712C2212yes—
87#2707C2214yescomplemented
88#2707C2214yescomplemented
89#2705C2214yes—
90#2705C2214yescomplemented
91#2704C2214yescomplemented
92#2704C2214yescomplemented
93#2702C2214yescomplemented
94#2702C2214yescomplemented
95#2695C2214yescomplemented
96#2693C2212yescomplemented
97#2691C2214yescomplemented
98#2683C2214yescomplemented
99#2682C2214yescomplemented
100#2681C2214yescomplemented
101#2681C2214yescomplemented
102#2676C2214yescomplemented
103#2675C2212yescomplemented
104#2672C2214yescomplemented
105#2671C2214yescomplemented
106#2664C2214yescomplemented
107#2664C2214yescomplemented
108#2662C2214yescomplemented
109#2662C2214yescomplemented
110#2637C2214yescomplemented
111#2637C2214yescomplemented
112#2636C2214yescomplemented
113#2636C2214yescomplemented
114#2630C2214yescomplemented
115#2630C2214yescomplemented
116#2629C2214yescomplemented
117#2629C2212yescomplemented
118#2629C2214yescomplemented
119#2629C2214yescomplemented
120#2629C2212yescomplemented
121#2627C2214yescomplemented
122#2626C2214yescomplemented
123#2621C2211yescharacteristic, complemented
124#2620C2212yes—
125#2620C2214yescomplemented
126#2620C2214yescomplemented
127#2620C2214yescomplemented
128#2620C2212yescomplemented
129#2620C2212yescomplemented
130#2619C2211yescharacteristic
131#2618C2212yes—
132#2618C2214yescomplemented
133#2618C2214yescomplemented
134#2618C2214yescomplemented
135#2618C2214yescomplemented
136#2618C2212yescomplemented
137#2617C2214yes—
138#2609C2212yescomplemented
139#2609C2212yescomplemented
140#2601C2214yescomplemented
141#2601C2214yescomplemented
142#2601C2214yescomplemented
143#2601C2214yescomplemented
144#2582C2212yescomplemented
145#2582C2212yescomplemented
146#2579C2214yescomplemented
147#2579C2214yescomplemented
148#2566C2212yescomplemented
149#2565C2212yescomplemented
150#2548C2211yescharacteristic
151#2546C2211yescharacteristic, complemented
152#2545C2212yescomplemented
153#2545C2212yescomplemented
154#2544C2212yes—
155#2543C2212yes—
156#2543C2212yescomplemented
157#2538C2214yescomplemented
158#2538C2212yescomplemented
159#2538C2212yescomplemented
160#2538C2212yescomplemented
161#2537C2212yes—
162#2537C2212yescomplemented
163#2536C2211yescharacteristic
164#2536C2211yescharacteristic, complemented
165#2534C2214yes—
166#2534C2214yescomplemented
167#2534C2214yescomplemented
168#2486C2212yescomplemented
169#2454C2212yescomplemented
170#2453C2212yescomplemented
171#2452C2212yescomplemented
172#2451C2212yescomplemented
173#2450C2214yescomplemented
174#2450C2214yescomplemented
175#2449C2214yescomplemented
176#2449C2214yescomplemented
177#2442C2212yescomplemented
178#2441C2212yescomplemented
179#2440C2212yescomplemented
180#2439C2212yescomplemented
181#2438C2214yescomplemented
182#2438C2214yescomplemented
183#2437C2214yescomplemented
184#2437C2214yescomplemented
185#2429C2212yescomplemented
186#2429C2212yescomplemented
187#2429C2212yescomplemented
188#2428C2212yes—
189#2427C2212yes—
190#2426C2212yes—
191#2426C2212yescomplemented
192#2426C2212yescomplemented
193#2425C2214yes—
194#2425C2214yescomplemented
195#2425C2214yescomplemented
196#2425C2214yescomplemented
197#2424C2214yes—
198#2424C2214yes—
199#2424C2214yescomplemented
200#2424C2214yescomplemented
201#2417C2212yescomplemented
202#2417C2214yescomplemented
203#2417C2214yescomplemented
204#2417C2214yescomplemented
205#2417C2212yescomplemented
206#2417C2212yescomplemented
207#2416C2214yes—
208#2416C2212yes—
209#2416C2212yescomplemented
210#2416C2214yescomplemented
211#2416C2214yescomplemented
212#2416C2214yescomplemented
213#2416C2212yescomplemented
214#2415C2212yes—
215#2414C2212yes—
216#2413C2214yescomplemented
217#2413C2214yescomplemented
218#2413C2214yescomplemented
219#2412C2214yes—
220#2411C2214yes—
221#2411C2214yescomplemented
222#2411C2214yescomplemented
223#2410C2214yes—
224#2408C2212yes—
225#2396C2212yescomplemented
226#2396C2212yescomplemented
227#2392C2212yes—
228#2392C2211yescharacteristic
229#2392C2212yescomplemented
230#2392C2212yescomplemented
231#2392C2211yescharacteristic, complemented
232C2×#398C2214yescomplemented
233C2×#398C2212yescomplemented
234C2×#396C2214yescomplemented
235C2×#396C2214yescomplemented
236C2×#396C2214yescomplemented
237C2×#394C2214yes—
238C2×#394C2212yes—
239Q8×C4⋊C4C2212yescomplemented
240Q8×C4⋊C4C2212yescomplemented
241#2349C2211yescharacteristic
242#2349C2211yescharacteristic
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2212yes—
245D4×C4⋊C4C2212yes—
246D4×C4⋊C4C2214yescomplemented
247D4×C4⋊C4C2214yescomplemented
248#2339C2212yes—
249#2339C2212yes—
250D4×C22⋊C4C2212yes—
251D4×C22⋊C4C2212yes—
252#2317C2212yescomplemented
253#2317C2211yescharacteristic, complemented
254#2317C2211yescharacteristic, complemented
255#2317C2212yescomplemented
256#2285C2211yescharacteristic, complemented
257#2285C2212yescomplemented
258C2×#384C2212yescomplemented
259C2×#384C2211yescharacteristic, complemented
260C22×#41C2312yes—
261C22×#41C2311yescharacteristic
262C23×D4C2312yes—
263C23×D4C2312yes—
264#556—216no—
265#556—216no—
266#554—216no—
267#553—232no—
268#553—216no—
269#552—216no—
270#552—232no—
271#551—232no—
272#551—232no—
273#547—216no—
274#547—44no—
275#546—216no—
276#546—216no—
277#546—48no—
278D42—44no—
279#542—216no—
280#541—216no—
281#539—232no—
282#538—232no—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2312yes—
285C2×C4⋊Q8C2311yescharacteristic
286C2×#127C2311yescharacteristic
287#529—232no—
288#529—216no—
289#529—216no—
290C2×#126—232no—
291C2×#126C2312yes—
292C2×#126C2314yes—
293C2×#126C2314yes—
294C2×#126C2314yes—
295C2×#126C2314yes—
296C2×#126C2312yes—
297C2×#126C2314yes—
298C2×#126C2314yes—
299C2×#126C2314yes—
300C2×#126C2314yes—
301C2×#126C2314yes—
302C2×#126C2314yes—
303C2×#125C2312yes—
304C2×#125C2312yes—
305C2×#125C2314yes—
306C2×#125C2314yes—
307C2×#125C2312yes—
308C2×#125C2314yes—
309C2×#124C2312yes—
310C2×#124C2312yes—
311C2×#124C2314yes—
312C2×#124C2314yes—
313C2×#124C2312yes—
314C2×#124C2312yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2312yes—
319C2×#123C2312yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×#123C2314yes—
325C2×#123C2314yes—
326C2×#123C2314yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×#121C2314yes—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2314yes—
346C2×#121C2312yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2312yes—
350C2×#121C2314yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2314yes—
355C2×#121C2314yes—
356C2×#121C2314yes—
357C2×#121C2314yes—
358C2×#121C2314yes—
359C2×#120C2314yes—
360C2×#120C2314yes—
361C2×#120C2314yes—
362C2×#120C2314yes—
363#520—216no—
364#520—44no—
365#520—44no—
366#518—216no—
367C4×#41D4116yescomplemented
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2314yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2314yes—
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2314yes—
385C2×C4×D4C2314yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2314yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2314yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2314yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2312yes—
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2312yes—
399C2×C4×D4C2314yes—
400C2×#117C2314yes—
401C2×#117C2314yes—
402C2×#117C2314yes—
403C2×#117C2312yes—
404C2×#117C2312yes—
405C2×#117C2312yes—
406C2×#117C2314yes—
407C2×#117C2311yescharacteristic
408C2×#117C2311yescharacteristic
409C2×#117C2312yes—
410C2×#117C2312yes—
411C2×#117C2312yes—
412C2×#117C2311yescharacteristic
413C22×C4⋊C4C2314yes—
414C22×C4⋊C4C2314yes—
415C22×C4⋊C4C2314yes—
416C22×C4⋊C4C2312yes—
417C22×C4⋊C4C2312yes—
418C22×C4⋊C4C2312yes—
419C22×C4⋊C4C2311yescharacteristic
420C22×C4⋊C4C2311yescharacteristic
421C22×C4⋊C4C2312yes—
422C22×C4⋊C4C2314yes—
423C22×C4⋊C4C2314yes—
424C22×C4⋊C4C2314yes—
425C22×C4⋊C4C2314yes—
426C22×C22⋊C4C2314yes—
427C22×C22⋊C4C2314yes—
428C22×C22⋊C4C2314yes—
429C22×C22⋊C4C2314yes—
430C22×C22⋊C4C2314yes—
431C22×C22⋊C4C2314yes—
432C22×C22⋊C4C2314yes—
433C22×C42C2312yes—
434C22×C42C2311yescharacteristic
435#400C2312yes—
436#400C2312yes—
437#400C2314yes—
438#400C2314yes—
439#399C2312yes—
440#399C2312yes—
441#399C2314yes—
442#399C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2311yescharacteristic
446#398C2311yescharacteristic
447#398C2312yes—
448#398C2312yes—
449#398C2312yes—
450#398C2312yes—
451#398C2312yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2312yes—
461#398C2312yes—
462#398C2312yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2312yes—
467#398C2312yes—
468#398C2312yes—
469#398C2312yes—
470#398C2314yes—
471#398C2314yes—
472#398C2312yes—
473#398C2314yes—
474#398C2314yes—
475#398C2314yes—
476#397C2312yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2312yes—
481#397C2312yes—
482#397C2311yescharacteristic
483#397C2312yes—
484#397C2311yescharacteristic
485#396C2312yes—
486#396C2312yes—
487#396C2312yes—
488#396C2312yes—
489#396C2314yes—
490#396C2314yes—
491#396C2312yes—
492#396C2312yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2314yes—
504#396C2314yes—
505#396C2314yes—
506#396C2314yes—
507#396C2314yes—
508#396C2314yes—
509#396C2314yes—
510#396C2314yes—
511#396C2314yes—
512#396C2314yes—
513#396C2312yes—
514#396C2314yes—
515#396C2312yes—
516#396C2312yes—
517#396C2314yes—
518#396C2314yes—
519#396C2314yes—
520#396C2314yes—
521#396C2314yes—
522#396C2314yes—
523#396C2314yes—
524#396C2312yes—
525#396C2312yes—
526#396C2312yes—
527#396C2314yes—
528#396C2314yes—
529#396C2314yes—
530#396C2314yes—
531#396C2314yes—
532#396C2314yes—
533#396C2314yes—
534#396C2314yes—
535#395C2312yes—
536#395C2312yes—
537#395C2314yes—
538#395C2314yes—
539#394C2311yescharacteristic
540#394C2311yescharacteristic
541#394C2312yes—
542#394C2312yes—
543#394C2312yes—
544#394C2312yes—
545#394C2312yes—
546#394C2314yes—
547#394C2314yes—
548#394C2312yes—
549#394C2314yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2312yes—
557#394C2312yes—
558#394C2314yes—
559#394C2314yes—
560#394C2312yes—
561#394C2314yes—
562#394C2312yes—
563#394C2314yes—
564#394C2312yes—
565#394C2312yes—
566#394C2314yes—
567#394C2314yes—
568#394C2314yes—
569#394C2312yes—
570#394C2314yes—
571#394C2314yes—
572#394C2314yes—
573#394C2314yes—
574#394C2312yes—
575#394C2312yes—
576#394C2312yes—
577#394C2312yes—
578#393C2312yes—
579#393C2312yes—
580#393C2314yes—
581#393C2314yes—
582#392C2312yes—
583#392C2312yes—
584#392C2314yes—
585#392C2314yes—
586#392C2312yes—
587#392C2312yes—
588#392C2311yescharacteristic
589#392C2311yescharacteristic
590#392C2312yes—
591#391C2312yes—
592#391C2312yes—
593#391C2312yes—
594#391C2312yes—
595#391C2314yes—
596#391C2314yes—
597#391C2314yes—
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2314yes—
603#390C2314yes—
604#390C2314yes—
605#390C2314yes—
606#390C2314yes—
607#390C2314yes—
608#390C2314yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2312yes—
613#389C2314yes—
614#389C2314yes—
615#389C2314yes—
616#389C2314yes—
617#389C2312yes—
618#389C2312yes—
619#389C2314yes—
620#389C2314yes—
621#389C2314yes—
622#389C2314yes—
623#389C2314yes—
624#389C2314yes—
625#389C2314yes—
626#389C2312yes—
627#389C2312yes—
628#389C2314yes—
629#389C2314yes—
630#389C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2312yes—
676#385C2314yes—
677#385C2312yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#384C2312yes—
687#384C2311yescharacteristic
688#384C2312yes—
689#384C2314yes—
690#384C2312yes—
691#384C2311yescharacteristic
692#384C2312yes—
693#384C2314yes—
694#384C2312yes—
695#384C2312yes—
696#384C2312yes—
697#382C2311yescharacteristic
698#382C2311yescharacteristic
699#382C2311yescharacteristic
700#382C2311yescharacteristic
701#382C2312yes—
702#382C2312yes—
703#381C2314yes—
704#381C2314yes—
705#380C2314yes—
706#380C2314yes—
707#380C2312yes—
708#380C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2314yes—
712#380C2312yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2314yes—
717#380C2314yes—
718#380C2314yes—
719#380C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2314yes—
724#379C2314yes—
725#379C2314yes—
726C4×C4⋊C4C2312yes—
727C4×C4⋊C4C2312yes—
728C4×C4⋊C4C2314yes—
729C4×C4⋊C4C2314yes—
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2311yescharacteristic
732C4×C4⋊C4C2311yescharacteristic
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2312yes—
735C4×C22⋊C4C2312yes—
736C4×C22⋊C4C2312yes—
737C2×#95C2314yes—
738C2×#95C2314yes—
739C2×#95C2312yes—
740C2×#95C2312yes—
741C25C2414yes—
742C2×#41—28no—
743C2×#41—24no—
744C2×#41—28no—
745C2×#41—24no—
746C2×#41—28no—
747C2×#41C2×D418yes—
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×D4—28no—
753C22×D4—28no—
754C22×D4—28no—
755C22×D4—44no—
756C22×D4—84no—
757C22×D4C2414yes—
758C22×D4C2414yes—
759C22×D4C2412yes—
760C22×D4C2412yes—
761C22×D4C2412yes—
762C22×D4C2412yes—
763C22×D4C2414yes—
764C22×D4C2414yes—
765C22×D4C2412yes—
766C22×D4C2412yes—
767C22×D4C2411yescharacteristic
768C22×D4C2411yescharacteristic
769C22×D4C2412yes—
770C22×D4C2414yes—
771C22×D4C2414yes—
772C22×D4C2412yes—
773C22×D4C2411yescharacteristic
774C23×C4C2414yes—
775C23×C4C2412yes—
776C23×C4C2412yes—
777C23×C4C2412yes—
778C23×C4C2411yescharacteristic
779C23×C4C2414yes—
780C23×C4C2412yes—
781C23×C4C2414yes—
782C23×C4C2414yes—
783C23×C4C2414yes—
784C23×C4C2414yes—
785C23×C4C2412yes—
786C23×C4C2414yes—
787C23×C4C2412yes—
788C23×C4C2412yes—
789C23×C4C2414yes—
790C23×C4C2412yes—
791C4⋊Q8—28no—
792C4⋊Q8—28no—
793C4⋊Q8—42no—
794#127—42no—
795#126—216no—
796#126—216no—
797#126—216no—
798#126—28no—
799#126—216no—
800#126—216no—
801#126—216no—
802#126—216no—
803#126—216no—
804#126—216no—
805#126—216no—
806#126—28no—
807#125—216no—
808#125—216no—
809#125—28no—
810#125—216no—
811#125—28no—
812#125—28no—
813#124—28no—
814#124—216no—
815#124—216no—
816#124—28no—
817#124—28no—
818#124—44no—
819#123—216no—
820#123—216no—
821#123—216no—
822#123—216no—
823#123—28no—
824#123—28no—
825#123—216no—
826#123—216no—
827#123—216no—
828#123—216no—
829#123—48no—
830#123—48no—
831C22⋊Q8—28no—
832C22⋊Q8—28no—
833C22⋊Q8—28no—
834C22⋊Q8—28no—
835C22⋊Q8—216no—
836C22⋊Q8—216no—
837C22⋊Q8—28no—
838C22⋊Q8—216no—
839C22⋊Q8—216no—
840C22⋊Q8—216no—
841C22⋊Q8—44no—
842C22⋊Q8—44no—
843C22⋊Q8—84no—
844C22⋊Q8—84no—
845C22⋊Q8—84no—
846#121—216no—
847#121—216no—
848#121—28no—
849#121—28no—
850#121—216no—
851#121—28no—
852#121—216no—
853#121—44no—
854#121—44no—
855#121—44no—
856#121—48no—
857#121—44no—
858#121—84no—
859#121—84no—
860#121—84no—
861#121—84no—
862#121—84no—
863#120—216no—
864#120—216no—
865#120—48no—
866#120—48no—
867C4×Q8—28no—
868C4×Q8—28no—
869C4×Q8—216no—
870C4×Q8—28no—
871C4×Q8—44no—
872C4×Q8—42no—
873C4×Q8—42no—
874C4×Q8C2×D4116yescomplemented
875C4×D4—28no—
876C4×D4—28no—
877C4×D4—24no—
878C4×D4—28no—
879C4×D4—24no—
880C4×D4—216no—
881C4×D4—216no—
882C4×D4—28no—
883C4×D4—28no—
884C4×D4—216no—
885C4×D4—28no—
886C4×D4—216no—
887C4×D4—216no—
888C4×D4—28no—
889C4×D4—28no—
890C4×D4—216no—
891C4×D4—42no—
892C4×D4—44no—
893C4×D4—42no—
894C4×D4—44no—
895C4×D4—48no—
896C4×D4—44no—
897C4×D4C2×D4116yes—
898C4×D4C2×D4132yescomplemented
899#117—28no—
900#117—216no—
901#117—28no—
902#117—28no—
903#117—216no—
904#117—216no—
905#117—216no—
906#117—42no—
907#117—42no—
908#117—44no—
909#117—44no—
910#117C2×D4116yescomplemented
911#117C2×D418yescomplemented
912C2×C4⋊C4—216no—
913C2×C4⋊C4—216no—
914C2×C4⋊C4—216no—
915C2×C4⋊C4—28no—
916C2×C4⋊C4—42no—
917C2×C4⋊C4—42no—
918C2×C4⋊C4—44no—
919C2×C4⋊C4—44no—
920C2×C4⋊C4—44no—
921C2×C4⋊C4—84no—
922C2×C4⋊C4—84no—
923C2×C4⋊C4—84no—
924C2×C4⋊C4—84no—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2411yescharacteristic
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C22⋊C4—216no—
995C2×C22⋊C4—216no—
996C2×C22⋊C4—216no—
997C2×C22⋊C4—216no—
998C2×C22⋊C4—48no—
999C2×C22⋊C4—84no—
1000C2×C22⋊C4—84no—
1001C2×C22⋊C4C2412yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2412yes—
1004C2×C22⋊C4C2412yes—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2414yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2414yes—
1009C2×C22⋊C4C2414yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C42C2×D4116yescomplemented
1065C2×C42C2×D418yescomplemented
1066C2×C42C2414yes—
1067C2×C42C2414yes—
1068C2×C42C2414yes—
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2411yescharacteristic
1073C2×C42C2411yescharacteristic
1074C2×C42C2412yes—
1075C2×C42C2414yes—
1076C2×C42C2412yes—
1077C2×C42C2411yescharacteristic
1078C2×C42C2412yes—
1079C2×C42C2412yes—
1080C2×C42C2414yes—
1081C2×C42C2411yescharacteristic
1082#95C2412yes—
1083#95C2412yes—
1084#95C2411yescharacteristic
1085#95C2411yescharacteristic
1086#95C2414yes—
1087#95C2412yes—
1088#95C2414yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2412yes—
1100#95C2412yes—
1101#95C2412yes—
1102#95C2411yescharacteristic
1103#95C2411yescharacteristic
1104#95C2412yes—
1105#95C2412yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2412yes—
1124C24—28no—
1125C24—28no—
1126C24—28no—
1127C24—44no—
1128C24—44no—
1129C24—44no—
1130C24—44no—
1131C24C2512yes—
1132C24C2514yes—
1133C24C2512yes—
1134C24C2511yescharacteristic
1135C24C2512yes—
1136#41—232no—
1137#41—432no—
1138C2×Q8—24no—
1139C2×Q8—24no—
1140C2×Q8—28no—
1141C2×Q8—22no—
1142C2×Q8—24no—
1143C2×Q8—22no—
1144C2×Q8—24no—
1145C2×Q8—42no—
1146C2×Q8—44no—
1147C2×Q8—42no—
1148C2×Q8—44no—
1149C2×Q8C22×D414yes—
1150C2×D4—24no—
1151C2×D4—24no—
1152C2×D4—28no—
1153C2×D4—28no—
1154C2×D4—28no—
1155C2×D4—28no—
1156C2×D4—28no—
1157C2×D4—28no—
1158C2×D4—24no—
1159C2×D4—28no—
1160C2×D4—24no—
1161C2×D4—24no—
1162C2×D4—24no—
1163C2×D4—28no—
1164C2×D4—24no—
1165C2×D4—24no—
1166C2×D4—41no—
1167C2×D4—42no—
1168C2×D4—42no—
1169C2×D4—41no—
1170C2×D4—44no—
1171C2×D4—42no—
1172C2×D4—42no—
1173C2×D4—44no—
1174C2×D4—44no—
1175C2×D4—42no—
1176C2×D4—42no—
1177C2×D4—42no—
1178C2×D4—44no—
1179C2×D4—44no—
1180C2×D4—44no—
1181C2×D4—42no—
1182C2×D4—44no—
1183C2×D4—42no—
1184C2×D4—42no—
1185C2×D4—44no—
1186C2×D4—42no—
1187C2×D4—42no—
1188C2×D4—42no—
1189C2×D4—44no—
1190C2×D4—44no—
1191C2×D4—44no—
1192C2×D4—44no—
1193C2×D4—432no—
1194C2×D4—816no—
1195C2×D4C22×D418yes—
1196C2×D4C22×D414yes—
1197C2×D4H(5,𝔽2)14yes—
1198C2×D42−1+414yes—
1199C22×C4—24no—
1200C22×C4—24no—
1201C22×C4—22no—
1202C22×C4—22no—
1203C22×C4—28no—
1204C22×C4—28no—
1205C22×C4—28no—
1206C22×C4—28no—
1207C22×C4—28no—
1208C22×C4—28no—
1209C22×C4—24no—
1210C22×C4—24no—
1211C22×C4—24no—
1212C22×C4—24no—
1213C22×C4—24no—
1214C22×C4—24no—
1215C22×C4—24no—
1216C22×C4—24no—
1217C22×C4—28no—
1218C22×C4—28no—
1219C22×C4—28no—
1220C22×C4—44no—
1221C22×C4—42no—
1222C22×C4—44no—
1223C22×C4—42no—
1224C22×C4—44no—
1225C22×C4—44no—
1226C22×C4—44no—
1227C22×C4—44no—
1228C22×C4—44no—
1229C22×C4—44no—
1230C22×C4—44no—
1231C22×C4—44no—
1232C22×C4—44no—
1233C22×C4—44no—
1234C22×C4—44no—
1235C22×C4—44no—
1236C22×C4—44no—
1237C22×C4—44no—
1238C22×C4—42no—
1239C22×C4—42no—
1240C22×C4—44no—
1241C22×C4—44no—
1242C22×C4C22×D418yes—
1243C22×C4C22×D414yes—
1244C22×C4C22×D4116yes—
1245C22×C4C22×D418yes—
1246C22×C4C2511yescharacteristic
1247C22×C4C2512yes—
1248C22×C4C2511yescharacteristic
1249C22×C4C2511yescharacteristic
1250C22×C4C2512yes—
1251C22×C4C2512yes—
1252C22×C4C2514yes—
1253C22×C4C2512yes—
1254C22×C4C2512yes—
1255C22×C4C2514yes—
1256C22×C4C2512yes—
1257C22×C4C2512yes—
1258C22×C4C2514yes—
1259C22×C4C2511yescharacteristic
1260C22×C4C2514yes—
1261C22×C4C2512yes—
1262C22×C4C2512yes—
1263C22×C4C2512yes—
1264C22×C4C2512yes—
1265C22×C4C2514yes—
1266C22×C4C2512yes—
1267C22×C4C2511yescharacteristic
1268C22×C4C2512yes—
1269C22×C4C2511yescharacteristic
1270C4⋊C4—24no—
1271C4⋊C4—28no—
1272C4⋊C4—24no—
1273C4⋊C4—24no—
1274C4⋊C4—28no—
1275C4⋊C4—28no—
1276C4⋊C4—24no—
1277C4⋊C4—28no—
1278C4⋊C4—28no—
1279C4⋊C4—28no—
1280C4⋊C4—28no—
1281C4⋊C4—28no—
1282C4⋊C4—28no—
1283C4⋊C4—24no—
1284C4⋊C4—24no—
1285C4⋊C4—24no—
1286C4⋊C4—24no—
1287C4⋊C4—24no—
1288C4⋊C4—28no—
1289C4⋊C4—28no—
1290C4⋊C4—28no—
1291C4⋊C4—24no—
1292C4⋊C4—28no—
1293C4⋊C4—24no—
1294C4⋊C4—24no—
1295C4⋊C4—28no—
1296C4⋊C4—22no—
1297C4⋊C4—24no—
1298C4⋊C4—22no—
1299C4⋊C4—41no—
1300C4⋊C4—41no—
1301C4⋊C4—42no—
1302C4⋊C4—42no—
1303C4⋊C4—41no—
1304C4⋊C4—44no—
1305C4⋊C4—42no—
1306C4⋊C4—42no—
1307C4⋊C4—42no—
1308C4⋊C4—44no—
1309C4⋊C4—42no—
1310C4⋊C4—44no—
1311C4⋊C4—42no—
1312C4⋊C4—44no—
1313C4⋊C4—42no—
1314C4⋊C4—44no—
1315C4⋊C4—44no—
1316C4⋊C4—44no—
1317C4⋊C4—44no—
1318C4⋊C4—44no—
1319C4⋊C4—44no—
1320C4⋊C4—44no—
1321C4⋊C4—44no—
1322C4⋊C4—44no—
1323C4⋊C4—42no—
1324C4⋊C4—42no—
1325C4⋊C4—42no—
1326C4⋊C4—44no—
1327C4⋊C4—42no—
1328C4⋊C4—41no—
1329C4⋊C4—41no—
1330C4⋊C4—41no—
1331C4⋊C4—42no—
1332C4⋊C4—44no—
1333C4⋊C4—44no—
1334C4⋊C4—44no—
1335C4⋊C4—42no—
1336C4⋊C4—42no—
1337C4⋊C4C22×D418yes—
1338C4⋊C4C22×D4116yes—
1339C22⋊C4—28no—
1340C22⋊C4—28no—
1341C22⋊C4—24no—
1342C22⋊C4—28no—
1343C22⋊C4—24no—
1344C22⋊C4—24no—
1345C22⋊C4—28no—
1346C22⋊C4—24no—
1347C22⋊C4—24no—
1348C22⋊C4—28no—
1349C22⋊C4—24no—
1350C22⋊C4—24no—
1351C22⋊C4—24no—
1352C22⋊C4—28no—
1353C22⋊C4—28no—
1354C22⋊C4—28no—
1355C22⋊C4—28no—
1356C22⋊C4—28no—
1357C22⋊C4—28no—
1358C22⋊C4—28no—
1359C22⋊C4—28no—
1360C22⋊C4—24no—
1361C22⋊C4—24no—
1362C22⋊C4—24no—
1363C22⋊C4—28no—
1364C22⋊C4—28no—
1365C22⋊C4—28no—
1366C22⋊C4—24no—
1367C22⋊C4—42no—
1368C22⋊C4—44no—
1369C22⋊C4—44no—
1370C22⋊C4—44no—
1371C22⋊C4—42no—
1372C22⋊C4—42no—
1373C22⋊C4—44no—
1374C22⋊C4—44no—
1375C22⋊C4—44no—
1376C22⋊C4—44no—
1377C22⋊C4—44no—
1378C22⋊C4—44no—
1379C22⋊C4—44no—
1380C22⋊C4—42no—
1381C22⋊C4—44no—
1382C22⋊C4—42no—
1383C22⋊C4—42no—
1384C22⋊C4—42no—
1385C22⋊C4—41no—
1386C22⋊C4—42no—
1387C22⋊C4—41no—
1388C22⋊C4—42no—
1389C22⋊C4—42no—
1390C22⋊C4—42no—
1391C22⋊C4—44no—
1392C22⋊C4—44no—
1393C22⋊C4—44no—
1394C22⋊C4—44no—
1395C22⋊C4—42no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—42no—
1400C22⋊C4C22×D4116yes—
1401C22⋊C4C22×D418yes—
1402C42—28no—
1403C42—28no—
1404C42—28no—
1405C42—24no—
1406C42—24no—
1407C42—24no—
1408C42—22no—
1409C42—22no—
1410C42—42no—
1411C42—44no—
1412C42—42no—
1413C42C22×D414yes—
1414C42C22×D414yes—
1415C42C22×D418yes—
1416C42C22×D4116yes—
1417C42C22×D418yes—
1418C23—24no—
1419C23—24no—
1420C23—21no—
1421C23—21no—
1422C23—22no—
1423C23—22no—
1424C23—22no—
1425C23—24no—
1426C23—22no—
1427C23—22no—
1428C23—22no—
1429C23—24no—
1430C23—22no—
1431C23—22no—
1432C23—24no—
1433C23—22no—
1434C23—24no—
1435C23—24no—
1436C23—22no—
1437C23—22no—
1438C23—22no—
1439C23—22no—
1440C23—24no—
1441C23—24no—
1442C23—22no—
1443C23—22no—
1444C23—22no—
1445C23—416no—
1446C23—88no—
1447C23—88no—
1448C23—88no—
1449C23—88no—
1450C23—88no—
1451C23—88no—
1452C23C23×D412yes—
1453C23C23×D414yes—
1454C23C2×H(5,𝔽2)14yes—
1455C23C2×2−1+414yes—
1456C23C2611yescharacteristic
1457Q8—28no—
1458Q8—48no—
1459Q8—84no—
1460Q8—88no—
1461D4—216no—
1462D4—44no—
1463D4—416no—
1464D4—416no—
1465D4—48no—
1466D4—84no—
1467D4—88no—
1468D4—88no—
1469D4—84no—
1470D4—84no—
1471D4—82no—
1472D4—84no—
1473D4—84no—
1474D4—88no—
1475D4—164no—
1476D4—162no—
1477D4#537116yes—
1478C2×C4—22no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—22no—
1482C2×C4—22no—
1483C2×C4—24no—
1484C2×C4—22no—
1485C2×C4—22no—
1486C2×C4—24no—
1487C2×C4—22no—
1488C2×C4—216no—
1489C2×C4—28no—
1490C2×C4—22no—
1491C2×C4—24no—
1492C2×C4—22no—
1493C2×C4—24no—
1494C2×C4—22no—
1495C2×C4—22no—
1496C2×C4—24no—
1497C2×C4—22no—
1498C2×C4—22no—
1499C2×C4—21no—
1500C2×C4—22no—
1501C2×C4—21no—
1502C2×C4—22no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—22no—
1506C2×C4—24no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—22no—
1510C2×C4—24no—
1511C2×C4—22no—
1512C2×C4—22no—
1513C2×C4—24no—
1514C2×C4—22no—
1515C2×C4—24no—
1516C2×C4—22no—
1517C2×C4—24no—
1518C2×C4—22no—
1519C2×C4—24no—
1520C2×C4—22no—
1521C2×C4—24no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—24no—
1526C2×C4—24no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—24no—
1533C2×C4—22no—
1534C2×C4—22no—
1535C2×C4—24no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—416no—
1539C2×C4—48no—
1540C2×C4—416no—
1541C2×C4—48no—
1542C2×C4—48no—
1543C2×C4—88no—
1544C2×C4—88no—
1545C2×C4—88no—
1546C2×C4—88no—
1547C2×C4—84no—
1548C2×C4—88no—
1549C2×C4—88no—
1550C2×C4—84no—
1551C2×C4—162no—
1552C2×C4—162no—
1553C2×C4C23×D414yes—
1554C2×C4C23×D418yes—
1555C2×C4C23×D414yes—
1556C2×C4C23×D412yes—
1557C2×C4C23×D414yes—
1558C2×C4C23×D412yes—
1559C2×C4C2×H(5,𝔽2)12yes—
1560C2×C4C2×2−1+412yes—
1561C22—24no—
1562C22—28no—
1563C22—24no—
1564C22—28no—
1565C22—24no—
1566C22—22no—
1567C22—41no—
1568C22—42no—
1569C22—41no—
1570C22—42no—
1571C22—44no—
1572C22—42no—
1573C22—42no—
1574C22—42no—
1575C22—44no—
1576C22—44no—
1577C22—42no—
1578C22—42no—
1579C22—42no—
1580C22—42no—
1581C22—44no—
1582C22—42no—
1583C22—44no—
1584C22—44no—
1585C22—42no—
1586C22—42no—
1587C22—42no—
1588C22—42no—
1589C22—42no—
1590C22—44no—
1591C22—1616no—
1592C22C2×#53718yes—
1593C22C24×D411yescharacteristic
1594C22C22×H(5,𝔽2)11yescharacteristic
1595C22C22×2−1+411yescharacteristic
1596C22H(7,𝔽2)12yes—
1597C222−1+612yes—
1598C4—24no—
1599C4—28no—
1600C4—24no—
1601C4—22no—
1602C4—24no—
1603C4—42no—
1604C4—41no—
1605C4—41no—
1606C4—42no—
1607C4—42no—
1608C4—44no—
1609C4—41no—
1610C4—42no—
1611C4—41no—
1612C4—44no—
1613C4—42no—
1614C4—42no—
1615C4—44no—
1616C4—42no—
1617C4—42no—
1618C4—42no—
1619C4—42no—
1620C4—44no—
1621C4C2×#53714yes—
1622C2—28no—
1623C2—42no—
1624C2—82no—
1625C2—84no—
1626C2—82no—
1627C2C22×#53711yescharacteristic
1628C2#6285312yes—
1629C2#6304111yescharacteristic
1630C2#6305812yes—
1631C2#6306311yescharacteristic
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×#3521C2semidirect
2. #42952C2semidirect
3. #42929C2semidirect
4. #42928C2semidirect
5. #42803C2semidirect
6. #42802C2semidirect
7. #42799C2semidirect
8. #42798C2semidirect
9. #42167C2semidirect
10. #41984C2semidirect
11. #41983C2semidirect
12. #40519C2semidirect
13. #40518C2semidirect
14. #40515C2semidirect
15. #40514C2semidirect
16. #37620C2semidirect
17. #37620C2semidirect
18. #37542C2semidirect
19. #37538C2semidirect
20. #36684C2semidirect
21. C2×#2823C2semidirect
22. #36020C2semidirect
23. #35821C2semidirect
24. #35821C2semidirect
25. #35806C2semidirect
26. #35776C2semidirect
27. #35761C2semidirect
28. #35728C2semidirect
29. #34183C2semidirect
31. C2×#556C22semidirect
32. C2×#556C22semidirect
34. C2×#553C22semidirect
35. C2×#553C22semidirect
36. C2×#552C22semidirect
37. C2×#552C22semidirect
38. C2×#551C22semidirect
39. C2×#551C22semidirect
46. C2×#542C22semidirect
47. C2×#541C22semidirect
48. C2×#539C22semidirect
49. C2×#538C22semidirect
50. C2×#529C22semidirect
51. C2×#529C22semidirect
52. C2×#529C22semidirect
53. C22×#126C22semidirect
62. #2823C22semidirect
63. #2823C22semidirect
64. #2823C22semidirect
65. #2823C22semidirect
66. #2823C22semidirect
67. #2823C22semidirect
68. #2823C22semidirect
69. #2823C22semidirect
70. #2823C22semidirect
71. #2823C22semidirect
72. #2823C22semidirect
73. #2822C22semidirect
74. #2820C22semidirect
76. #2814C22semidirect
77. #2814C22semidirect
79. #2813C22semidirect
80. #2727C22semidirect
81. #2726C22semidirect
82. #2725C22semidirect
83. #2725C22semidirect
84. #2722C22semidirect
85. #2715C22semidirect
87. #2707C22semidirect
88. #2707C22semidirect
90. #2705C22semidirect
91. #2704C22semidirect
92. #2704C22semidirect
93. #2702C22semidirect
94. #2702C22semidirect
95. #2695C22semidirect
96. #2693C22semidirect
97. #2691C22semidirect
98. #2683C22semidirect
99. #2682C22semidirect
100. #2681C22semidirect
101. #2681C22semidirect
102. #2676C22semidirect
103. #2675C22semidirect
104. #2672C22semidirect
105. #2671C22semidirect
106. #2664C22semidirect
107. #2664C22semidirect
108. #2662C22semidirect
109. #2662C22semidirect
110. #2637C22semidirect
111. #2637C22semidirect
112. #2636C22semidirect
113. #2636C22semidirect
114. #2630C22semidirect
115. #2630C22semidirect
116. #2629C22semidirect
117. #2629C22semidirect
118. #2629C22semidirect
119. #2629C22semidirect
120. #2629C22semidirect
121. #2627C22semidirect
122. #2626C22semidirect
123. #2621C22semidirect
125. #2620C22semidirect
126. #2620C22semidirect
127. #2620C22semidirect
128. #2620C22semidirect
129. #2620C22semidirect
132. #2618C22semidirect
133. #2618C22semidirect
134. #2618C22semidirect
135. #2618C22semidirect
136. #2618C22semidirect
138. #2609C22semidirect
139. #2609C22semidirect
140. #2601C22semidirect
141. #2601C22semidirect
142. #2601C22semidirect
143. #2601C22semidirect
144. #2582C22semidirect
145. #2582C22semidirect
146. #2579C22semidirect
147. #2579C22semidirect
148. #2566C22semidirect
149. #2565C22semidirect
151. #2546C22semidirect
152. #2545C22semidirect
153. #2545C22semidirect
156. #2543C22semidirect
157. #2538C22semidirect
158. #2538C22semidirect
159. #2538C22semidirect
160. #2538C22semidirect
162. #2537C22semidirect
164. #2536C22semidirect
166. #2534C22semidirect
167. #2534C22semidirect
168. #2486C22semidirect
169. #2454C22semidirect
170. #2453C22semidirect
171. #2452C22semidirect
172. #2451C22semidirect
173. #2450C22semidirect
174. #2450C22semidirect
175. #2449C22semidirect
176. #2449C22semidirect
177. #2442C22semidirect
178. #2441C22semidirect
179. #2440C22semidirect
180. #2439C22semidirect
181. #2438C22semidirect
182. #2438C22semidirect
183. #2437C22semidirect
184. #2437C22semidirect
185. #2429C22semidirect
186. #2429C22semidirect
187. #2429C22semidirect
191. #2426C22semidirect
192. #2426C22semidirect
194. #2425C22semidirect
195. #2425C22semidirect
196. #2425C22semidirect
199. #2424C22semidirect
200. #2424C22semidirect
201. #2417C22semidirect
202. #2417C22semidirect
203. #2417C22semidirect
204. #2417C22semidirect
205. #2417C22semidirect
206. #2417C22semidirect
209. #2416C22semidirect
210. #2416C22semidirect
211. #2416C22semidirect
212. #2416C22semidirect
213. #2416C22semidirect
216. #2413C22semidirect
217. #2413C22semidirect
218. #2413C22semidirect
221. #2411C22semidirect
222. #2411C22semidirect
225. #2396C22semidirect
226. #2396C22semidirect
229. #2392C22semidirect
230. #2392C22semidirect
231. #2392C22semidirect
232. C2×#398C22semidirect
233. C2×#398C22semidirect
234. C2×#396C22semidirect
235. C2×#396C22semidirect
236. C2×#396C22semidirect
239. Q8×C4⋊C4C22semidirect
240. Q8×C4⋊C4C22semidirect
246. D4×C4⋊C4C22semidirect
247. D4×C4⋊C4C22semidirect
252. #2317C22semidirect
253. #2317C22semidirect
254. #2317C22semidirect
255. #2317C22semidirect
256. #2285C22semidirect
257. #2285C22semidirect
258. C2×#384C22semidirect
259. C2×#384C22semidirect
367. C4×#41D4semidirect
874. C4×Q8C2×D4semidirect
898. C4×D4C2×D4semidirect
910. #117C2×D4semidirect
911. #117C2×D4semidirect
1064. C2×C42C2×D4semidirect
1065. C2×C42C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35212
#429522
#429292
#429282
#428032
#428022
#427992
#427982
#421672
#419842
#419832
#405192
#405182
#405152
#405142
#376202
#375422
#375382
#366842
C2×#28232
#360202
#358212
#358062
#357762
#357612
#357282
#341832