Finite Group Databasebeta

← #7654487

Subgroups — #7654487

Order 512.

4786 conjugacy classes of subgroups.

The subgroup lattice has 1648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42728C212yesmaximal, complemented
2#42723C212yesmaximal, complemented
3#41493C214yesmaximal, complemented
4#40788C214yesmaximal, complemented
5#40130C212yesmaximal, complemented
6#39514C211yesmaximal, characteristic, complemented
7#39250C212yesmaximal, complemented
8#39192C211yesmaximal, characteristic, complemented
9#39157C211yesmaximal, characteristic, complemented
10#38931C211yesmaximal, characteristic, complemented
11#38515C214yesmaximal, complemented
12#38122C212yesmaximal, complemented
13#37882C212yesmaximal, complemented
14#37850C212yesmaximal, complemented
15#37850C212yesmaximal, complemented
16#37727C214yesmaximal, complemented
17#37637C211yesmaximal, characteristic, complemented
18#37504C212yesmaximal, complemented
19#36290C211yesmaximal, characteristic, complemented
20#36239C212yesmaximal, complemented
21#36180C211yesmaximal, characteristic, complemented
22#36154C211yesmaximal, characteristic
23#36154C211yesmaximal, characteristic
24D4×#126C212yesmaximal
25#35961C212yesmaximal, complemented
26#35873C212yesmaximal
27#35319C211yesmaximal, characteristic, complemented
28#35231C212yesmaximal, complemented
29#35185C211yesmaximal, characteristic, complemented
30#35086C212yesmaximal, complemented
31#34975C211yesmaximal, characteristic, complemented
32C2×#2496C212yesmaximal, complemented
33#34332C211yesmaximal, characteristic, complemented
34C4×#554C211yesmaximal, characteristic, complemented
35#34126C211yesmaximal, characteristic
36C2×#554C2211yescharacteristic
37C2×#554C2211yescharacteristic
38C2×#541C2212yes—
39C22×#126C2214yes—
40C22×C4×D4C2211yescharacteristic
41#2868C2211yescharacteristic, complemented
42#2864C2212yescomplemented
43#2860C2212yes—
44#2859C2211yescharacteristic, complemented
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2857C2212yescomplemented
48#2852C2214yes—
49#2851C2212yescomplemented
50#2851C2214yescomplemented
51#2848C2212yes—
52#2848C2212yes—
53#2839C2214yescomplemented
54#2836C2214yescomplemented
55#2831C2214yescomplemented
56#2802C2214yescomplemented
57#2794C2214yescomplemented
58#2794C2214yescomplemented
59#2783C2214yescomplemented
60#2776C2214yescomplemented
61#2772C2214yescomplemented
62#2762C2214yescomplemented
63#2758C2214yescomplemented
64#2747C2214yes—
65#2747C2214yes—
66#2744C2214yescomplemented
67#2744C2214yescomplemented
68#2739C2214yescomplemented
69#2739C2214yescomplemented
70#2725C2214yescomplemented
71#2725C2214yescomplemented
72#2722C2214yes—
73#2722C2214yes—
74#2721C2214yescomplemented
75#2721C2214yescomplemented
76#2716C2214yescomplemented
77#2716C2214yescomplemented
78#2698C2214yes—
79#2689C2214yes—
80#2664C2214yescomplemented
81#2655C2214yescomplemented
82#2655C2214yescomplemented
83#2654C2214yescomplemented
84#2652C2214yes—
85#2652C2214yescomplemented
86#2650C2214yescomplemented
87#2647C2212yescomplemented
88#2647C2212yescomplemented
89#2646C2214yescomplemented
90#2645C2212yescomplemented
91#2644C2212yes—
92#2643C2214yes—
93#2642C2212yescomplemented
94#2637C2214yescomplemented
95#2629C2212yescomplemented
96#2629C2212yescomplemented
97#2625C2212yescomplemented
98#2625C2212yescomplemented
99#2621C2212yes—
100#2571C2211yescharacteristic, complemented
101#2571C2212yescomplemented
102#2570C2212yescomplemented
103#2570C2212yescomplemented
104#2570C2212yescomplemented
105#2569C2214yescomplemented
106#2569C2214yescomplemented
107#2569C2214yescomplemented
108#2567C2211yescharacteristic, complemented
109#2567C2211yescharacteristic, complemented
110#2563C2211yescharacteristic
111#2563C2211yescharacteristic
112#2552C2211yescharacteristic, complemented
113#2552C2212yescomplemented
114#2552C2212yescomplemented
115#2538C2211yescharacteristic
116#2538C2211yescharacteristic
117#2533C2212yescomplemented
118#2528C2212yescomplemented
119#2524C2214yescomplemented
120#2519C2214yescomplemented
121#2514C2211yescharacteristic, complemented
122#2513C2212yes—
123#2513C2212yes—
124#2512C2212yes—
125#2512C2212yes—
126#2512C2212yes—
127#2512C2212yes—
128#2510C2214yes—
129#2510C2214yes—
130#2509C2212yescomplemented
131#2509C2212yescomplemented
132#2509C2212yescomplemented
133#2509C2212yescomplemented
134#2508C2212yescomplemented
135#2508C2212yescomplemented
136#2507C2212yescomplemented
137#2507C2212yescomplemented
138#2506C2212yescomplemented
139#2506C2212yescomplemented
140#2506C2212yescomplemented
141#2506C2211yescharacteristic, complemented
142#2506C2212yescomplemented
143#2505C2214yescomplemented
144#2505C2214yescomplemented
145#2505C2214yescomplemented
146#2505C2214yescomplemented
147#2505C2214yescomplemented
148#2505C2214yescomplemented
149#2502C2212yescomplemented
150#2502C2212yescomplemented
151#2496C2212yes—
152#2496C2212yes—
153#2496C2212yes—
154#2496C2212yes—
155#2496C2212yes—
156#2496C2212yes—
157#2496C2214yes—
158#2496C2214yes—
159#2496C2211yescharacteristic
160#2496C2212yes—
161#2496C2212yes—
162#2496C2212yescomplemented
163#2496C2212yescomplemented
164#2496C2214yescomplemented
165#2496C2212yescomplemented
166#2496C2212yescomplemented
167#2496C2212yescomplemented
168#2496C2214yescomplemented
169#2495C2212yes—
170#2494C2212yes—
171#2489C2212yes—
172#2489C2211yescharacteristic
173#2489C2212yescomplemented
174#2487C2212yes—
175#2487C2212yes—
176#2481C2214yes—
177#2481C2214yes—
178#2481C2214yes—
179#2481C2214yes—
180#2480C2214yes—
181#2480C2214yes—
182#2480C2214yes—
183#2480C2214yes—
184#2480C2214yes—
185#2480C2214yes—
186#2478C2212yes—
187#2475C2212yes—
188#2473C2214yescomplemented
189#2473C2214yescomplemented
190#2473C2214yescomplemented
191#2473C2214yescomplemented
192#2469C2214yescomplemented
193#2454C2212yes—
194#2454C2212yes—
195#2453C2211yescharacteristic, complemented
196#2450C2214yes—
197#2450C2214yes—
198#2446C2211yescharacteristic, complemented
199#2442C2212yes—
200#2442C2212yes—
201#2442C2214yescomplemented
202#2442C2212yescomplemented
203#2442C2212yescomplemented
204#2440C2214yescomplemented
205#2440C2214yescomplemented
206#2437C2214yes—
207#2437C2214yes—
208#2429C2211yescharacteristic
209#2429C2212yescomplemented
210#2421C2212yes—
211#2421C2211yescharacteristic
212#2421C2212yescomplemented
213#2417C2212yes—
214#2417C2212yes—
215#2402C2212yescomplemented
216#2401C2212yes—
217C2×#400C2214yescomplemented
218C2×#397C2214yes—
219#2370C2212yescomplemented
220#2370C2212yescomplemented
221#2369C2211yescharacteristic, complemented
222#2369C2211yescharacteristic, complemented
223#2368C2214yescomplemented
224#2360C2214yescomplemented
225#2360C2212yescomplemented
226#2360C2212yescomplemented
227#2357C2211yescharacteristic
228#2357C2211yescharacteristic
229#2355C2211yescharacteristic, complemented
230#2353C2212yes—
231#2353C2212yes—
232Q8×C4⋊C4C2211yescharacteristic, complemented
233#2349C2212yes—
234#2349C2212yes—
235#2349C2212yes—
236#2349C2212yes—
237#2349C2211yescharacteristic
238#2349C2211yescharacteristic
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2212yes—
241D4×C4⋊C4C2212yes—
242D4×C4⋊C4C2211yescharacteristic
243D4×C4⋊C4C2212yes—
244D4×C4⋊C4C2211yescharacteristic
245#2345C2211yescharacteristic
246#2345C2211yescharacteristic
247#2345C2212yescomplemented
248#2345C2212yescomplemented
249#2342C2212yes—
250#2342C2212yes—
251D4×C22⋊C4C2211yescharacteristic
252D4×C22⋊C4C2212yes—
253D4×C22⋊C4C2212yes—
254D4×C22⋊C4C2211yescharacteristic
255#2334C2214yes—
256#2334C2214yescomplemented
257#2330C2212yescomplemented
258#2330C2212yescomplemented
259#2329C2214yescomplemented
260#2327C2212yescomplemented
261#2323C2212yescomplemented
262#2323C2212yescomplemented
263#2320C2212yescomplemented
264#2314C2212yescomplemented
265#2314C2212yescomplemented
266C4×C4⋊Q8C2211yescharacteristic, complemented
267C4×C4⋊Q8C2211yescharacteristic, complemented
268C4×C4⋊Q8C2211yescharacteristic, complemented
269C4×#125C2212yescomplemented
270C4×#125C2211yescharacteristic, complemented
271C4×#125C2212yescomplemented
272C4×#126C2212yes—
273C4×C22⋊Q8C2211yescharacteristic
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2212yescomplemented
276C4×C22⋊Q8C2212yescomplemented
277C4×C22⋊Q8C2214yescomplemented
278#2295C2211yescharacteristic, complemented
279#2293C2211yescharacteristic
280#2293C2211yescharacteristic
281C2×#389C2212yescomplemented
282C2×#389C2212yescomplemented
283#2290C2212yes—
284#2290C2212yes—
285C2×#387C2214yescomplemented
286C2×#384C2212yescomplemented
287#2283C2211yescharacteristic
288#2280C2212yes—
289C2×#380C2212yes—
290C2×#380C2212yes—
291#2275C2212yes—
292C42×Q8C2211yescharacteristic, complemented
293C42×D4C2212yes—
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2212yescomplemented
298C2×C4×C22⋊C4C2212yes—
299C23×D4C2311yescharacteristic
300C24×C4C2312yes—
301#554—28no—
302#554—28no—
303#541—48no—
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×#126—416no—
310C2×#126C2312yes—
311C2×#126C2314yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2311yescharacteristic
323C2×#125C2312yes—
324C2×#125C2312yes—
325C2×#125C2314yes—
326C2×#125C2312yes—
327C2×#125C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2311yescharacteristic
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2312yes—
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×D4—28no—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2312yes—
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×#117C2311yescharacteristic
361C2×#117C2312yes—
362C2×#117C2312yes—
363C2×#117C2311yescharacteristic
364C22×C4⋊C4C2311yescharacteristic
365C22×C4⋊C4C2312yes—
366C22×C4⋊C4C2312yes—
367C22×C4⋊C4C2314yes—
368C22×C4⋊C4C2312yes—
369C22×C4⋊C4C2312yes—
370C22×C4⋊C4C2314yes—
371C22×C4⋊C4C2314yes—
372C22×C4⋊C4C2314yes—
373C22×C22⋊C4C2312yes—
374C22×C22⋊C4C2312yes—
375C22×C22⋊C4C2312yes—
376C22×C22⋊C4C2314yes—
377C22×C22⋊C4C2314yes—
378C22×C42C2311yescharacteristic
379C22×C42C2314yes—
380C22×C42C2312yes—
381C22×C42C2312yes—
382#401C2314yes—
383#401C2312yes—
384#400C2312yes—
385#400C2314yes—
386#400C2314yes—
387#400C2314yes—
388#400C2314yes—
389#400C2314yes—
390#400C2314yes—
391#400C2314yes—
392#400C2314yes—
393#400C2314yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2312yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2312yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2312yes—
413#400C2314yes—
414#400C2314yes—
415#400C2312yes—
416#400C2312yes—
417#400C2312yes—
418#399C2314yes—
419#399C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2312yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2312yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2312yes—
443#398C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2312yes—
463#397C2312yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2312yes—
472#396C2314yes—
473#396C2314yes—
474#395C2314yes—
475#395C2314yes—
476#393C2314yes—
477#393C2314yes—
478#391C2312yes—
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2311yescharacteristic
482#391C2312yes—
483#391C2312yes—
484#391C2311yescharacteristic
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2311yescharacteristic
490#391C2314yes—
491#391C2311yescharacteristic
492#391C2311yescharacteristic
493#390C2312yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#390C2312yes—
497#390C2311yescharacteristic
498#390C2311yescharacteristic
499#390C2311yescharacteristic
500#390C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2312yes—
506#389C2311yescharacteristic
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2311yescharacteristic
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2311yescharacteristic
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2314yes—
552#389C2314yes—
553#389C2312yes—
554#389C2311yescharacteristic
555#389C2311yescharacteristic
556#389C2314yes—
557#389C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
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#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
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#387C2312yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2312yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2312yes—
628#387C2314yes—
629#387C2312yes—
630#387C2312yes—
631#387C2314yes—
632#387C2314yes—
633#386C2312yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#386C2314yes—
640#386C2314yes—
641#385C2312yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2312yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2312yes—
660#385C2312yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2312yes—
668#385C2312yes—
669#384C2311yescharacteristic
670#384C2311yescharacteristic
671#384C2311yescharacteristic
672#384C2312yes—
673#384C2312yes—
674#384C2312yes—
675#384C2312yes—
676#384C2312yes—
677#384C2312yes—
678#384C2312yes—
679#384C2312yes—
680#384C2314yes—
681#384C2314yes—
682#383C2312yes—
683#383C2314yes—
684#383C2312yes—
685#382C2311yescharacteristic
686#382C2312yes—
687#382C2312yes—
688#382C2312yes—
689#382C2312yes—
690#382C2312yes—
691#382C2311yescharacteristic
692#382C2312yes—
693#382C2311yescharacteristic
694#382C2314yes—
695#382C2314yes—
696#382C2312yes—
697#382C2314yes—
698#381C2312yes—
699#381C2312yes—
700#381C2312yes—
701#380C2312yes—
702#380C2312yes—
703#380C2312yes—
704#380C2312yes—
705#380C2312yes—
706#380C2312yes—
707#380C2314yes—
708#380C2314yes—
709#380C2314yes—
710#380C2314yes—
711#380C2314yes—
712#380C2314yes—
713#380C2314yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2311yescharacteristic
720#380C2311yescharacteristic
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2314yes—
726#380C2312yes—
727#380C2311yescharacteristic
728#380C2314yes—
729#380C2314yes—
730#380C2314yes—
731#380C2314yes—
732#380C2311yescharacteristic
733#379C2314yes—
734#379C2314yes—
735#379C2312yes—
736#379C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C22⋊C4C2311yescharacteristic
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801#376C2312yes—
802#376C2311yescharacteristic
803#376C2312yes—
804#376C2311yescharacteristic
805C2×#95C2314yes—
806C2×#95C2314yes—
807C2×#95C2314yes—
808C2×#95C2314yes—
809C2×#95C2312yes—
810C2×#95C2312yes—
811C2×#95C2314yes—
812C43C2312yes—
813C43C2311yescharacteristic
814C43C2311yescharacteristic
815C25C2412yes—
816C22×Q8C2411yescharacteristic
817C22×Q8C2411yescharacteristic
818C22×Q8C2412yes—
819C22×Q8C2412yes—
820C22×D4—24no—
821C22×D4—24no—
822C22×D4—24no—
823C22×D4C2412yes—
824C22×D4C2411yescharacteristic
825C22×D4C2411yescharacteristic
826C23×C4—28no—
827C23×C4—44no—
828C23×C4—44no—
829C23×C4C2411yescharacteristic
830C23×C4C2412yes—
831C23×C4C2411yescharacteristic
832C23×C4C2411yescharacteristic
833C23×C4C2412yes—
834C23×C4C2412yes—
835C23×C4C2412yes—
836C23×C4C2412yes—
837C23×C4C2414yes—
838C23×C4C2414yes—
839C23×C4C2414yes—
840C23×C4C2414yes—
841C23×C4C2412yes—
842C23×C4C2412yes—
843C23×C4C2412yes—
844C23×C4C2412yes—
845C4⋊Q8—24no—
846C4⋊Q8—24no—
847C4⋊Q8—44no—
848C4⋊Q8—44no—
849C4⋊Q8—42no—
850#126—28no—
851#126—216no—
852#126—48no—
853#126—48no—
854#126—48no—
855#126—48no—
856#126—48no—
857#126—48no—
858#126—48no—
859#126—48no—
860#125—28no—
861#125—28no—
862#125—44no—
863#125—42no—
864#125—48no—
865#125—44no—
866#125—44no—
867#125—48no—
868C22⋊Q8—28no—
869C22⋊Q8—28no—
870C22⋊Q8—216no—
871C22⋊Q8—216no—
872C22⋊Q8—44no—
873C22⋊Q8—44no—
874C22⋊Q8—44no—
875C22⋊Q8—44no—
876C22⋊Q8—42no—
877C22⋊Q8—42no—
878C4×Q8—24no—
879C4×Q8—24no—
880C4×Q8—44no—
881C4×Q8—44no—
882C4×Q8—42no—
883C4×Q8—44no—
884C4×Q8—42no—
885C4×D4—24no—
886C4×D4—28no—
887C4×D4—28no—
888C4×D4—24no—
889C4×D4—24no—
890C4×D4—24no—
891C4×D4—28no—
892C4×D4—28no—
893C4×D4—24no—
894C4×D4—28no—
895C4×D4—24no—
896C4×D4—28no—
897C4×D4—24no—
898C4×D4#4118yes—
899#117—24no—
900#117—44no—
901#117—44no—
902#117—42no—
903C2×C4⋊C4—28no—
904C2×C4⋊C4—28no—
905C2×C4⋊C4—24no—
906C2×C4⋊C4—44no—
907C2×C4⋊C4—44no—
908C2×C4⋊C4—48no—
909C2×C4⋊C4—48no—
910C2×C4⋊C4—48no—
911C2×C4⋊C4—48no—
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2411yescharacteristic
933C2×C4⋊C4C2411yescharacteristic
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2411yescharacteristic
938C2×C4⋊C4C2411yescharacteristic
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C22⋊C4—28no—
992C2×C22⋊C4—28no—
993C2×C22⋊C4—44no—
994C2×C22⋊C4—48no—
995C2×C22⋊C4—48no—
996C2×C22⋊C4C2411yescharacteristic
997C2×C22⋊C4C2412yes—
998C2×C22⋊C4C2412yes—
999C2×C22⋊C4C2412yes—
1000C2×C22⋊C4C2412yes—
1001C2×C22⋊C4C2412yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2414yes—
1004C2×C22⋊C4C2412yes—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2412yes—
1008C2×C22⋊C4C2411yescharacteristic
1009C2×C22⋊C4C2414yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2411yescharacteristic
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C42—24no—
1037C2×C42—48no—
1038C2×C42—44no—
1039C2×C42—44no—
1040C2×C42C2411yescharacteristic
1041C2×C42C2411yescharacteristic
1042C2×C42C2411yescharacteristic
1043C2×C42C2412yes—
1044C2×C42C2411yescharacteristic
1045C2×C42C2412yes—
1046C2×C42C2411yescharacteristic
1047C2×C42C2411yescharacteristic
1048C2×C42C2411yescharacteristic
1049C2×C42C2411yescharacteristic
1050C2×C42C2412yes—
1051C2×C42C2412yes—
1052C2×C42C2411yescharacteristic
1053C2×C42C2411yescharacteristic
1054C2×C42C2412yes—
1055C2×C42C2411yescharacteristic
1056C2×C42C2411yescharacteristic
1057C2×C42C2412yes—
1058C2×C42C2414yes—
1059C2×C42C2411yescharacteristic
1060C2×C42C2412yes—
1061C2×C42C2411yescharacteristic
1062C2×C42C2411yescharacteristic
1063C2×C42C2414yes—
1064C2×C42C2412yes—
1065C2×C42C2412yes—
1066C2×C42C2414yes—
1067C2×C42C2412yes—
1068C2×C42C2414yes—
1069C2×C42C2414yes—
1070C2×C42C2414yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2411yescharacteristic
1076#95C2411yescharacteristic
1077#95C2411yescharacteristic
1078#95C2412yes—
1079#95C2412yes—
1080#95C2412yes—
1081#95C2412yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2411yescharacteristic
1108#95C2411yescharacteristic
1109#95C2411yescharacteristic
1110#95C2411yescharacteristic
1111#95C2411yescharacteristic
1112#95C2411yescharacteristic
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160C24—24no—
1161C24—24no—
1162C24—24no—
1163C24—24no—
1164C24—42no—
1165C24—42no—
1166C24—42no—
1167C24C2512yes—
1168C24C2511yescharacteristic
1169C24C2512yes—
1170C2×Q8—22no—
1171C2×Q8—22no—
1172C2×Q8—24no—
1173C2×Q8—24no—
1174C2×Q8—22no—
1175C2×Q8—22no—
1176C2×Q8—22no—
1177C2×Q8—22no—
1178C2×Q8—42no—
1179C2×Q8—42no—
1180C2×Q8—42no—
1181C2×Q8—42no—
1182C2×D4—24no—
1183C2×D4—24no—
1184C2×D4—24no—
1185C2×D4—22no—
1186C2×D4—22no—
1187C2×D4—22no—
1188C2×D4—416no—
1189C2×D4C2×#4114yes—
1190C2×D42−1+414yes—
1191C2×D42−1+414yes—
1192C22×C4—24no—
1193C22×C4—24no—
1194C22×C4—22no—
1195C22×C4—24no—
1196C22×C4—24no—
1197C22×C4—24no—
1198C22×C4—28no—
1199C22×C4—28no—
1200C22×C4—24no—
1201C22×C4—28no—
1202C22×C4—28no—
1203C22×C4—24no—
1204C22×C4—22no—
1205C22×C4—22no—
1206C22×C4—22no—
1207C22×C4—24no—
1208C22×C4—24no—
1209C22×C4—24no—
1210C22×C4—22no—
1211C22×C4—22no—
1212C22×C4—24no—
1213C22×C4—24no—
1214C22×C4—24no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—24no—
1218C22×C4—24no—
1219C22×C4—42no—
1220C22×C4—42no—
1221C22×C4—42no—
1222C22×C4—41no—
1223C22×C4—44no—
1224C22×C4—44no—
1225C22×C4—42no—
1226C22×C4—44no—
1227C22×C4—44no—
1228C22×C4—42no—
1229C22×C4—44no—
1230C22×C4—44no—
1231C22×C4—44no—
1232C22×C4—44no—
1233C22×C4—42no—
1234C22×C4—42no—
1235C22×C4—42no—
1236C22×C4—42no—
1237C22×C4—42no—
1238C22×C4—42no—
1239C22×C4—816no—
1240C22×C4C2×#4118yes—
1241C22×C4C2511yescharacteristic
1242C22×C4C2511yescharacteristic
1243C22×C4C2511yescharacteristic
1244C22×C4C2512yes—
1245C22×C4C2512yes—
1246C22×C4C2512yes—
1247C22×C4C2511yescharacteristic
1248C22×C4C2512yes—
1249C22×C4C2511yescharacteristic
1250C22×C4C2512yes—
1251C22×C4C2512yes—
1252C22×C4C2512yes—
1253C22×C4C2512yes—
1254C22×C4C2512yes—
1255C22×C4C2512yes—
1256C22×C4C2514yes—
1257C22×C4C2514yes—
1258C22×C4C2512yes—
1259C22×C4C2511yescharacteristic
1260C22×C4C2512yes—
1261C22×C4C2511yescharacteristic
1262C22×C4C2514yes—
1263C22×C4C2514yes—
1264C22×C4C2512yes—
1265C22×C4C2511yescharacteristic
1266C22×C4C2511yescharacteristic
1267C22×C4C2512yes—
1268C22×C4C2511yescharacteristic
1269C22×C4C2511yescharacteristic
1270C22×C4C2511yescharacteristic
1271C22×C4C2511yescharacteristic
1272C22×C4C2511yescharacteristic
1273C4⋊C4—22no—
1274C4⋊C4—22no—
1275C4⋊C4—24no—
1276C4⋊C4—22no—
1277C4⋊C4—28no—
1278C4⋊C4—28no—
1279C4⋊C4—24no—
1280C4⋊C4—24no—
1281C4⋊C4—24no—
1282C4⋊C4—24no—
1283C4⋊C4—24no—
1284C4⋊C4—24no—
1285C4⋊C4—28no—
1286C4⋊C4—28no—
1287C4⋊C4—24no—
1288C4⋊C4—24no—
1289C4⋊C4—24no—
1290C4⋊C4—28no—
1291C4⋊C4—28no—
1292C4⋊C4—28no—
1293C4⋊C4—22no—
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—22no—
1297C4⋊C4—22no—
1298C4⋊C4—22no—
1299C4⋊C4—24no—
1300C4⋊C4—24no—
1301C4⋊C4—22no—
1302C4⋊C4—24no—
1303C4⋊C4—22no—
1304C4⋊C4—24no—
1305C4⋊C4—24no—
1306C4⋊C4—28no—
1307C4⋊C4—22no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—24no—
1311C4⋊C4—44no—
1312C4⋊C4—44no—
1313C4⋊C4—44no—
1314C4⋊C4—44no—
1315C4⋊C4—44no—
1316C4⋊C4—44no—
1317C4⋊C4—44no—
1318C4⋊C4—44no—
1319C4⋊C4—44no—
1320C4⋊C4—44no—
1321C4⋊C4—42no—
1322C4⋊C4—42no—
1323C4⋊C4—42no—
1324C4⋊C4—42no—
1325C4⋊C4—41no—
1326C4⋊C4—42no—
1327C4⋊C4—44no—
1328C4⋊C4—42no—
1329C4⋊C4—42no—
1330C4⋊C4—42no—
1331C4⋊C4—44no—
1332C4⋊C4—42no—
1333C4⋊C4—44no—
1334C4⋊C4—42no—
1335C4⋊C4—44no—
1336C4⋊C4—44no—
1337C4⋊C4—44no—
1338C4⋊C4—44no—
1339C4⋊C4—44no—
1340C4⋊C4—42no—
1341C4⋊C4—42no—
1342C4⋊C4—42no—
1343C4⋊C4—42no—
1344C4⋊C4—42no—
1345C4⋊C4—44no—
1346C4⋊C4—44no—
1347C4⋊C4—44no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—44no—
1351C4⋊C4C2×#4114yes—
1352C22⋊C4—24no—
1353C22⋊C4—28no—
1354C22⋊C4—28no—
1355C22⋊C4—24no—
1356C22⋊C4—24no—
1357C22⋊C4—24no—
1358C22⋊C4—28no—
1359C22⋊C4—28no—
1360C22⋊C4—22no—
1361C22⋊C4—24no—
1362C22⋊C4—24no—
1363C22⋊C4—24no—
1364C22⋊C4—28no—
1365C22⋊C4—24no—
1366C22⋊C4—28no—
1367C22⋊C4—24no—
1368C22⋊C4—24no—
1369C22⋊C4—24no—
1370C22⋊C4—24no—
1371C22⋊C4—22no—
1372C22⋊C4—24no—
1373C22⋊C4—42no—
1374C22⋊C4—42no—
1375C22⋊C4—44no—
1376C22⋊C4—44no—
1377C22⋊C4—44no—
1378C22⋊C4—44no—
1379C22⋊C4—42no—
1380C22⋊C4—42no—
1381C22⋊C4—42no—
1382C22⋊C4—42no—
1383C22⋊C4—41no—
1384C22⋊C4—42no—
1385C22⋊C4—44no—
1386C22⋊C4—42no—
1387C22⋊C4—44no—
1388C22⋊C4—44no—
1389C22⋊C4—44no—
1390C22⋊C4C2×#4118yes—
1391C22⋊C4H(5,𝔽2)14yes—
1392C42—22no—
1393C42—22no—
1394C42—22no—
1395C42—24no—
1396C42—24no—
1397C42—24no—
1398C42—28no—
1399C42—22no—
1400C42—22no—
1401C42—22no—
1402C42—22no—
1403C42—22no—
1404C42—22no—
1405C42—24no—
1406C42—24no—
1407C42—22no—
1408C42—22no—
1409C42—24no—
1410C42—24no—
1411C42—22no—
1412C42—22no—
1413C42—22no—
1414C42—42no—
1415C42—42no—
1416C42—42no—
1417C42—42no—
1418C42—44no—
1419C42—44no—
1420C42—41no—
1421C42—42no—
1422C42—44no—
1423C42—42no—
1424C42—44no—
1425C42—42no—
1426C42—44no—
1427C42C2×#4114yes—
1428C23—22no—
1429C23—22no—
1430C23—22no—
1431C23—22no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—22no—
1439C23—22no—
1440C23—22no—
1441C23—22no—
1442C23—22no—
1443C23—22no—
1444C23—22no—
1445C23—48no—
1446C23—48no—
1447C23—48no—
1448C23—48no—
1449C23—84no—
1450C23—84no—
1451C23—84no—
1452C23C22×#4114yes—
1453C23C2×H(5,𝔽2)12yes—
1454C23C2×2−1+414yes—
1455C23C2×2−1+414yes—
1456C23C2611yescharacteristic
1457Q8—44no—
1458Q8—44no—
1459Q8—84no—
1460Q8—84no—
1461D4—48no—
1462D4—44no—
1463D4#541116yescomplemented
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—22no—
1473C2×C4—22no—
1474C2×C4—216no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—22no—
1479C2×C4—22no—
1480C2×C4—22no—
1481C2×C4—22no—
1482C2×C4—22no—
1483C2×C4—24no—
1484C2×C4—24no—
1485C2×C4—21no—
1486C2×C4—22no—
1487C2×C4—22no—
1488C2×C4—24no—
1489C2×C4—24no—
1490C2×C4—21no—
1491C2×C4—22no—
1492C2×C4—24no—
1493C2×C4—24no—
1494C2×C4—22no—
1495C2×C4—22no—
1496C2×C4—22no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—22no—
1502C2×C4—21no—
1503C2×C4—22no—
1504C2×C4—22no—
1505C2×C4—22no—
1506C2×C4—21no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—24no—
1510C2×C4—24no—
1511C2×C4—22no—
1512C2×C4—22no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—22no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—21no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—24no—
1534C2×C4—24no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—24no—
1542C2×C4—24no—
1543C2×C4—21no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—48no—
1551C2×C4—48no—
1552C2×C4—48no—
1553C2×C4—44no—
1554C2×C4—44no—
1555C2×C4—48no—
1556C2×C4—44no—
1557C2×C4—84no—
1558C2×C4—84no—
1559C2×C4—88no—
1560C2×C4—88no—
1561C2×C4—84no—
1562C2×C4—88no—
1563C2×C4—88no—
1564C2×C4—84no—
1565C2×C4C22×#4112yes—
1566C2×C4C22×#4114yes—
1567C2×C4C22×#4112yes—
1568C2×C4C22×#4112yes—
1569C2×C4C2×H(5,𝔽2)12yes—
1570C2×C4C2×H(5,𝔽2)12yes—
1571C2×C4C2×2−1+412yes—
1572C2×C4C2×2−1+412yes—
1573C2×C4#58512yes—
1574C2×C4#58512yes—
1575C2×C4#58512yes—
1576C22—24no—
1577C22—24no—
1578C22—24no—
1579C22—24no—
1580C22—24no—
1581C22—24no—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—42no—
1590C22—42no—
1591C22—42no—
1592C22—42no—
1593C22—42no—
1594C22—42no—
1595C22—42no—
1596C22—816no—
1597C22C2×#54118yes—
1598C22C23×#4111yescharacteristic
1599C22C22×H(5,𝔽2)11yescharacteristic
1600C22C22×2−1+411yescharacteristic
1601C22C22×2−1+411yescharacteristic
1602C22C2×#58511yescharacteristic
1603C22C2×#58511yescharacteristic
1604C22C2×#58511yescharacteristic
1605C4—22no—
1606C4—22no—
1607C4—22no—
1608C4—24no—
1609C4—22no—
1610C4—41no—
1611C4—41no—
1612C4—42no—
1613C4—42no—
1614C4—44no—
1615C4—44no—
1616C4—42no—
1617C4—42no—
1618C4—41no—
1619C4—42no—
1620C4—42no—
1621C4—41no—
1622C4—42no—
1623C4—42no—
1624C4—41no—
1625C4—42no—
1626C4—41no—
1627C4—42no—
1628C4—42no—
1629C4—41no—
1630C4—42no—
1631C4—42no—
1632C4—44no—
1633C4—44no—
1634C4—41no—
1635C4C2×#54114yes—
1636C4#352114yes—
1637C2—28no—
1638C2—42no—
1639C2—82no—
1640C2C22×#54111yescharacteristic
1641C2C2×#352111yescharacteristic
1642C2#6280011yescharacteristic
1643C2#6301311yescharacteristic
1644C2#6301311yescharacteristic
1645C2#6302311yescharacteristic
1646C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42728C2semidirect
2. #42723C2semidirect
3. #41493C2semidirect
4. #40788C2semidirect
5. #40130C2semidirect
6. #39514C2semidirect
7. #39250C2semidirect
8. #39192C2semidirect
9. #39157C2semidirect
10. #38931C2semidirect
11. #38515C2semidirect
12. #38122C2semidirect
13. #37882C2semidirect
14. #37850C2semidirect
15. #37850C2semidirect
16. #37727C2semidirect
17. #37637C2semidirect
18. #37504C2semidirect
19. #36290C2semidirect
20. #36239C2semidirect
21. #36180C2semidirect
25. #35961C2semidirect
27. #35319C2semidirect
28. #35231C2semidirect
29. #35185C2semidirect
30. #35086C2semidirect
31. #34975C2semidirect
32. C2×#2496C2semidirect
33. #34332C2semidirect
34. C4×#554C2semidirect
41. #2868C22semidirect
42. #2864C22semidirect
44. #2859C22semidirect
47. #2857C22semidirect
49. #2851C22semidirect
50. #2851C22semidirect
53. #2839C22semidirect
54. #2836C22semidirect
55. #2831C22semidirect
56. #2802C22semidirect
57. #2794C22semidirect
58. #2794C22semidirect
59. #2783C22semidirect
60. #2776C22semidirect
61. #2772C22semidirect
62. #2762C22semidirect
63. #2758C22semidirect
66. #2744C22semidirect
67. #2744C22semidirect
68. #2739C22semidirect
69. #2739C22semidirect
70. #2725C22semidirect
71. #2725C22semidirect
74. #2721C22semidirect
75. #2721C22semidirect
76. #2716C22semidirect
77. #2716C22semidirect
80. #2664C22semidirect
81. #2655C22semidirect
82. #2655C22semidirect
83. #2654C22semidirect
85. #2652C22semidirect
86. #2650C22semidirect
87. #2647C22semidirect
88. #2647C22semidirect
89. #2646C22semidirect
90. #2645C22semidirect
93. #2642C22semidirect
94. #2637C22semidirect
95. #2629C22semidirect
96. #2629C22semidirect
97. #2625C22semidirect
98. #2625C22semidirect
100. #2571C22semidirect
101. #2571C22semidirect
102. #2570C22semidirect
103. #2570C22semidirect
104. #2570C22semidirect
105. #2569C22semidirect
106. #2569C22semidirect
107. #2569C22semidirect
108. #2567C22semidirect
109. #2567C22semidirect
112. #2552C22semidirect
113. #2552C22semidirect
114. #2552C22semidirect
117. #2533C22semidirect
118. #2528C22semidirect
119. #2524C22semidirect
120. #2519C22semidirect
121. #2514C22semidirect
130. #2509C22semidirect
131. #2509C22semidirect
132. #2509C22semidirect
133. #2509C22semidirect
134. #2508C22semidirect
135. #2508C22semidirect
136. #2507C22semidirect
137. #2507C22semidirect
138. #2506C22semidirect
139. #2506C22semidirect
140. #2506C22semidirect
141. #2506C22semidirect
142. #2506C22semidirect
143. #2505C22semidirect
144. #2505C22semidirect
145. #2505C22semidirect
146. #2505C22semidirect
147. #2505C22semidirect
148. #2505C22semidirect
149. #2502C22semidirect
150. #2502C22semidirect
162. #2496C22semidirect
163. #2496C22semidirect
164. #2496C22semidirect
165. #2496C22semidirect
166. #2496C22semidirect
167. #2496C22semidirect
168. #2496C22semidirect
173. #2489C22semidirect
188. #2473C22semidirect
189. #2473C22semidirect
190. #2473C22semidirect
191. #2473C22semidirect
192. #2469C22semidirect
195. #2453C22semidirect
198. #2446C22semidirect
201. #2442C22semidirect
202. #2442C22semidirect
203. #2442C22semidirect
204. #2440C22semidirect
205. #2440C22semidirect
209. #2429C22semidirect
212. #2421C22semidirect
215. #2402C22semidirect
217. C2×#400C22semidirect
219. #2370C22semidirect
220. #2370C22semidirect
221. #2369C22semidirect
222. #2369C22semidirect
223. #2368C22semidirect
224. #2360C22semidirect
225. #2360C22semidirect
226. #2360C22semidirect
229. #2355C22semidirect
232. Q8×C4⋊C4C22semidirect
247. #2345C22semidirect
248. #2345C22semidirect
256. #2334C22semidirect
257. #2330C22semidirect
258. #2330C22semidirect
259. #2329C22semidirect
260. #2327C22semidirect
261. #2323C22semidirect
262. #2323C22semidirect
263. #2320C22semidirect
264. #2314C22semidirect
265. #2314C22semidirect
266. C4×C4⋊Q8C22semidirect
267. C4×C4⋊Q8C22semidirect
268. C4×C4⋊Q8C22semidirect
269. C4×#125C22semidirect
270. C4×#125C22semidirect
271. C4×#125C22semidirect
275. C4×C22⋊Q8C22semidirect
276. C4×C22⋊Q8C22semidirect
277. C4×C22⋊Q8C22semidirect
278. #2295C22semidirect
281. C2×#389C22semidirect
282. C2×#389C22semidirect
285. C2×#387C22semidirect
286. C2×#384C22semidirect
292. C42×Q8C22semidirect
297. C2×C4×C4⋊C4C22semidirect
1463. D4#541semidirect

Maximal subgroups

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

subgroupindex
#427282
#427232
#414932
#407882
#401302
#395142
#392502
#391922
#391572
#389312
#385152
#381222
#378822
#378502
#377272
#376372
#375042
#362902
#362392
#361802
#361542
D4×#1262
#359612
#358732
#353192
#352312
#351852
#350862
#349752
C2×#24962
#343322
C4×#5542
#341262