Finite Group Databasebeta

← #7708759

Subgroups — #7708759

Order 512.

6270 conjugacy classes of subgroups.

The subgroup lattice has 1964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59321C211yesmaximal, characteristic, complemented
2#59304C211yesmaximal, characteristic, complemented
3#59124C211yesmaximal, characteristic, complemented
4#59124C211yesmaximal, characteristic, complemented
5#59028C212yesmaximal, complemented
6#59003C212yesmaximal, complemented
7#46028C214yesmaximal, complemented
8#45649C212yesmaximal, complemented
9#45604C212yesmaximal, complemented
10#39786C212yesmaximal, complemented
11#39402C212yesmaximal, complemented
12#39147C211yesmaximal, characteristic, complemented
13#39138C211yesmaximal, characteristic, complemented
14#39132C212yesmaximal, complemented
15#38942C211yesmaximal, characteristic, complemented
16#38916C212yesmaximal, complemented
17#38909C211yesmaximal, characteristic, complemented
18#38208C214yesmaximal, complemented
19#38129C212yesmaximal, complemented
20#38089C212yesmaximal, complemented
21#37722C214yesmaximal, complemented
22#37493C212yesmaximal, complemented
23#36923C214yesmaximal, complemented
24C2×#2856C211yesmaximal, characteristic, complemented
25#36621C211yesmaximal, characteristic, complemented
26#36472C211yesmaximal, characteristic, complemented
27#36455C211yesmaximal, characteristic, complemented
28#36410C211yesmaximal, characteristic, complemented
29#36362C212yesmaximal, complemented
30#36302C211yesmaximal, characteristic, complemented
31#36291C212yesmaximal, complemented
32#35171C212yesmaximal, complemented
33#35038C212yesmaximal, complemented
34#34476C212yesmaximal, complemented
35C4×#525C211yesmaximal, characteristic, complemented
36C2×#553C2212yes—
37C2×#553C2212yescomplemented
38C2×#550C2211yescharacteristic, complemented
39C2×#550C2212yescomplemented
40C2×#550C2211yescharacteristic, complemented
41C2×#546C2212yes—
42C2×#546C2212yes—
43C2×#540C2214yescomplemented
44C22×#127C2211yescharacteristic
45C2×#529C2211yescharacteristic, complemented
46C2×#525C2211yescharacteristic
47C22×#121C2212yes—
48C22×#121C2212yes—
49C22×#121C2212yes—
50C2×C4×#41C2211yescharacteristic, complemented
51C23×C42C2211yescharacteristic
52#2861C2212yescomplemented
53#2860C2212yescomplemented
54#2856C2211yescharacteristic
55#2856C2212yes—
56#2856C2211yescharacteristic
57#2856C2212yes—
58#2856C2212yes—
59#2856C2211yescharacteristic
60#2856C2212yes—
61#2856C2212yes—
62#2856C2212yes—
63#2856C2211yescharacteristic
64#2856C2212yescomplemented
65#2855C2211yescharacteristic, complemented
66#2854C2211yescharacteristic, complemented
67#2854C2212yescomplemented
68#2853C2212yescomplemented
69#2852C2212yes—
70#2852C2212yescomplemented
71#2851C2211yescharacteristic
72#2851C2211yescharacteristic, complemented
73#2850C2211yescharacteristic
74#2850C2211yescharacteristic, complemented
75#2849C2212yes—
76#2848C2211yescharacteristic
77#2847C2211yescharacteristic
78#2829C2214yescomplemented
79#2828C2214yescomplemented
80#2797C2214yescomplemented
81#2791C2214yescomplemented
82#2786C2214yescomplemented
83#2757C2214yescomplemented
84#2756C2214yescomplemented
85#2718C2214yescomplemented
86#2714C2214yescomplemented
87#2714C2214yescomplemented
88#2714C2214yescomplemented
89#2711C2214yescomplemented
90#2711C2214yescomplemented
91#2708C2214yescomplemented
92#2708C2214yescomplemented
93#2703C2214yescomplemented
94#2701C2214yescomplemented
95#2701C2214yescomplemented
96#2699C2214yescomplemented
97#2691C2214yescomplemented
98#2688C2214yescomplemented
99#2688C2214yescomplemented
100#2682C2214yescomplemented
101#2673C2214yescomplemented
102#2673C2214yescomplemented
103#2673C2214yescomplemented
104#2673C2214yescomplemented
105#2673C2214yescomplemented
106#2673C2214yescomplemented
107#2673C2214yescomplemented
108#2671C2214yescomplemented
109#2671C2214yescomplemented
110#2671C2214yescomplemented
111#2671C2214yescomplemented
112#2661C2214yescomplemented
113#2661C2214yescomplemented
114#2648C2214yescomplemented
115#2644C2212yescomplemented
116#2641C2212yescomplemented
117#2635C2214yescomplemented
118#2624C2212yescomplemented
119#2622C2214yes—
120#2619C2212yescomplemented
121#2617C2214yes—
122#2603C2214yescomplemented
123#2595C2214yescomplemented
124#2595C2214yescomplemented
125#2582C2211yescharacteristic, complemented
126#2566C2212yescomplemented
127#2565C2212yescomplemented
128#2559C2214yescomplemented
129#2554C2214yescomplemented
130#2554C2214yescomplemented
131#2552C2211yescharacteristic, complemented
132#2552C2212yescomplemented
133#2552C2211yescharacteristic, complemented
134#2548C2211yescharacteristic, complemented
135#2548C2211yescharacteristic, complemented
136#2544C2212yescomplemented
137#2541C2211yescharacteristic, complemented
138#2541C2212yescomplemented
139#2541C2212yescomplemented
140#2541C2212yescomplemented
141#2541C2211yescharacteristic, complemented
142#2541C2212yescomplemented
143#2541C2212yescomplemented
144#2537C2212yescomplemented
145#2537C2212yescomplemented
146#2537C2211yescharacteristic, complemented
147#2535C2212yescomplemented
148#2531C2214yescomplemented
149#2516C2214yescomplemented
150#2513C2212yescomplemented
151#2513C2212yescomplemented
152#2511C2212yescomplemented
153#2506C2212yescomplemented
154#2502C2212yes—
155#2501C2212yescomplemented
156#2500C2212yescomplemented
157#2500C2212yescomplemented
158#2496C2212yescomplemented
159#2490C2212yescomplemented
160#2490C2214yescomplemented
161#2490C2212yescomplemented
162#2490C2212yescomplemented
163#2490C2212yescomplemented
164#2490C2212yescomplemented
165#2487C2212yes—
166#2480C2214yes—
167#2476C2214yescomplemented
168#2476C2214yescomplemented
169#2473C2214yes—
170#2471C2214yescomplemented
171#2467C2214yescomplemented
172#2467C2214yescomplemented
173#2464C2214yescomplemented
174#2464C2214yescomplemented
175#2464C2214yescomplemented
176#2464C2214yescomplemented
177#2464C2214yescomplemented
178#2464C2214yescomplemented
179#2456C2214yescomplemented
180#2454C2212yescomplemented
181#2445C2212yescomplemented
182#2445C2212yescomplemented
183#2445C2212yescomplemented
184#2443C2214yes—
185#2442C2212yes—
186#2441C2212yescomplemented
187#2433C2212yes—
188#2433C2214yes—
189#2433C2212yes—
190#2431C2212yescomplemented
191#2431C2212yescomplemented
192#2431C2212yescomplemented
193#2431C2212yescomplemented
194#2428C2212yescomplemented
195#2428C2212yescomplemented
196#2428C2214yescomplemented
197#2428C2212yescomplemented
198#2428C2214yescomplemented
199#2428C2212yescomplemented
200#2428C2212yescomplemented
201#2428C2212yescomplemented
202#2427C2212yescomplemented
203#2427C2212yescomplemented
204#2426C2212yescomplemented
205#2424C2214yes—
206#2424C2214yes—
207#2422C2212yescomplemented
208#2422C2212yescomplemented
209#2422C2212yescomplemented
210#2422C2212yescomplemented
211#2420C2212yescomplemented
212#2418C2214yes—
213#2416C2212yes—
214#2416C2212yescomplemented
215#2414C2212yescomplemented
216#2414C2212yescomplemented
217#2414C2214yescomplemented
218#2414C2212yescomplemented
219#2414C2212yescomplemented
220#2410C2214yes—
221#2410C2214yes—
222#2410C2214yes—
223#2408C2214yes—
224#2408C2212yes—
225#2408C2212yes—
226#2407C2212yescomplemented
227#2407C2212yescomplemented
228#2407C2212yescomplemented
229#2405C2214yes—
230#2377C2214yescomplemented
231#2376C2214yescomplemented
232#2367C2212yescomplemented
233#2366C2211yescharacteristic, complemented
234#2366C2211yescharacteristic, complemented
235#2363C2212yescomplemented
236#2363C2212yescomplemented
237#2361C2212yescomplemented
238#2360C2212yes—
239#2358C2214yes—
240#2358C2214yes—
241#2358C2214yes—
242#2355C2211yescharacteristic, complemented
243#2354C2211yescharacteristic, complemented
244#2354C2212yescomplemented
245Q8×C4⋊C4C2211yescharacteristic, complemented
246D4×C4⋊C4C2212yes—
247D4×C4⋊C4C2211yescharacteristic, complemented
248#2345C2212yes—
249#2342C2214yes—
250#2341C2212yescomplemented
251D4×C22⋊C4C2212yes—
252D4×C22⋊C4C2212yes—
253#2335C2214yescomplemented
254#2333C2214yescomplemented
255#2326C2212yescomplemented
256#2324C2214yescomplemented
257#2324C2212yescomplemented
258#2321C2214yes—
259#2319C2212yescomplemented
260#2315C2214yes—
261#2311C2212yescomplemented
262C4×#127C2212yescomplemented
263C4×C22⋊Q8C2211yescharacteristic
264C4×C22⋊Q8C2211yescharacteristic
265C4×C22⋊Q8C2211yescharacteristic
266C4×C22⋊Q8C2211yescharacteristic, complemented
267C4×C22⋊Q8C2211yescharacteristic, complemented
268C4×C22⋊Q8C2211yescharacteristic, complemented
269C4×#123C2212yescomplemented
270C4×#123C2212yescomplemented
271C4×#123C2212yescomplemented
272C4×#121C2211yescharacteristic
273C4×#121C2211yescharacteristic
274C4×#121C2211yescharacteristic
275C4×#121C2211yescharacteristic, complemented
276C4×#121C2211yescharacteristic, complemented
277C4×#121C2212yescomplemented
278C4×#121C2211yescharacteristic, complemented
279C4×#120C2212yes—
280C4×#120C2212yes—
281C4×#120C2212yes—
282#2297C2212yescomplemented
283#2297C2211yescharacteristic, complemented
284#2296C2211yescharacteristic, complemented
285#2293C2212yescomplemented
286C2×#390C2212yes—
287C2×#390C2212yes—
288C2×#390C2212yes—
289#2290C2212yes—
290#2290C2212yes—
291#2290C2212yescomplemented
292#2290C2212yescomplemented
293C2×#384C2211yescharacteristic
294#2283C2211yescharacteristic, complemented
295#2280C2211yescharacteristic
296C42×D4C2212yes—
297C42×D4C2212yescomplemented
298C4×#117C2211yescharacteristic, complemented
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×D4C2312yes—
303C23×D4C2312yes—
304C23×D4C2314yes—
305C23×D4C2312yes—
306C24×C4C2311yescharacteristic
307C24×C4C2311yescharacteristic
308C24×C4C2311yescharacteristic
309#553—48no—
310#553—48no—
311#550—44no—
312#550—44no—
313#550—48no—
314#546—216no—
315#546—48no—
316#540—416no—
317C2×#127—44no—
318C2×#127C2311yescharacteristic
319C2×#127C2311yescharacteristic
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2312yes—
326C2×#127C2312yes—
327C2×#127C2314yes—
328C2×#127C2314yes—
329#529—44no—
330C2×#126C2312yes—
331C2×#126C2314yes—
332C2×#126C2314yes—
333C2×#125C2312yes—
334C2×#125C2312yes—
335C2×#125C2311yescharacteristic
336C2×#125C2314yes—
337C2×#124C2312yes—
338C2×#124C2311yescharacteristic
339C2×#124C2312yes—
340#525—28no—
341C2×#123C2314yes—
342C2×#123C2312yes—
343C2×#123C2312yes—
344C2×#123C2312yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2311yescharacteristic
355C2×C22⋊Q8C2311yescharacteristic
356C2×#121—48no—
357C2×#121—48no—
358C2×#121—48no—
359C2×#121C2312yes—
360C2×#121C2314yes—
361C2×#121C2314yes—
362C2×#121C2311yescharacteristic
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2311yescharacteristic
366C2×#121C2311yescharacteristic
367C2×#121C2311yescharacteristic
368C2×#121C2311yescharacteristic
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2312yes—
374C2×#121C2312yes—
375C2×#121C2314yes—
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379C2×#121C2314yes—
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×#121C2312yes—
383C2×#121C2314yes—
384C2×#121C2312yes—
385C2×#121C2314yes—
386C2×#121C2314yes—
387C2×#121C2312yes—
388C2×#121C2312yes—
389C2×#121C2314yes—
390C2×#121C2312yes—
391C2×#121C2312yes—
392C2×#121C2312yes—
393C2×#121C2312yes—
394C2×#121C2314yes—
395C2×#121C2314yes—
396C2×#121C2314yes—
397C2×#121C2314yes—
398C2×#121C2314yes—
399C2×#121C2314yes—
400C2×#121C2314yes—
401C2×#121C2314yes—
402C2×#121C2314yes—
403C2×#120C2314yes—
404C2×#120C2312yes—
405C2×#120C2312yes—
406C2×#120C2314yes—
407C2×#120C2314yes—
408C2×#120C2314yes—
409C4×#41—44no—
410C2×C4×Q8C2311yescharacteristic
411C2×C4×Q8C2311yescharacteristic
412C2×C4×Q8C2312yes—
413C2×C4×Q8C2311yescharacteristic
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2311yescharacteristic
417C2×C4×D4C2311yescharacteristic
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2312yes—
421C2×C4×D4C2312yes—
422C2×C4×D4C2312yes—
423C2×C4×D4C2312yes—
424C2×C4×D4C2314yes—
425C2×C4×D4C2314yes—
426C2×C4×D4C2312yes—
427C2×C4×D4C2314yes—
428C2×C4×D4C2312yes—
429C2×C4×D4C2312yes—
430C2×C4×D4C2312yes—
431C2×C4×D4C2312yes—
432C2×C4×D4C2314yes—
433C2×C4×D4C2312yes—
434C2×C4×D4C2311yescharacteristic
435C2×C4×D4C2312yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2312yes—
438C2×C4×D4C2312yes—
439C2×#117C2311yescharacteristic
440C2×#117C2311yescharacteristic
441C2×#117C2312yes—
442C2×#117C2314yes—
443C2×#117C2312yes—
444C2×#117C2311yescharacteristic
445C2×#117C2312yes—
446C22×C4⋊C4C2312yes—
447C22×C4⋊C4C2312yes—
448C22×C4⋊C4C2312yes—
449C22×C4⋊C4C2312yes—
450C22×C22⋊C4C2314yes—
451C22×C22⋊C4C2314yes—
452C22×C22⋊C4C2314yes—
453C22×C22⋊C4C2314yes—
454C22×C22⋊C4C2314yes—
455C22×C42—44no—
456C22×C42C2311yescharacteristic
457C22×C42C2311yescharacteristic
458C22×C42C2311yescharacteristic
459C22×C42C2311yescharacteristic
460C22×C42C2311yescharacteristic
461C22×C42C2311yescharacteristic
462C22×C42C2311yescharacteristic
463C22×C42C2311yescharacteristic
464C22×C42C2311yescharacteristic
465C22×C42C2312yes—
466C22×C42C2311yescharacteristic
467C22×C42C2311yescharacteristic
468C22×C42C2311yescharacteristic
469#400C2314yes—
470#400C2314yes—
471#400C2314yes—
472#399C2314yes—
473#399C2314yes—
474#399C2314yes—
475#398C2314yes—
476#398C2314yes—
477#398C2314yes—
478#398C2314yes—
479#398C2314yes—
480#398C2314yes—
481#398C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#397C2314yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2314yes—
490#397C2314yes—
491#397C2314yes—
492#397C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#392C2314yes—
531#392C2314yes—
532#392C2314yes—
533#392C2314yes—
534#392C2314yes—
535#392C2314yes—
536#392C2314yes—
537#392C2314yes—
538#392C2314yes—
539#392C2314yes—
540#392C2314yes—
541#392C2314yes—
542#392C2314yes—
543#392C2314yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2314yes—
549#391C2311yescharacteristic
550#391C2312yes—
551#391C2311yescharacteristic
552#391C2312yes—
553#391C2311yescharacteristic
554#391C2311yescharacteristic
555#391C2312yes—
556#390C2311yescharacteristic
557#390C2312yes—
558#390C2314yes—
559#390C2314yes—
560#390C2312yes—
561#390C2312yes—
562#390C2312yes—
563#390C2312yes—
564#390C2314yes—
565#390C2312yes—
566#390C2314yes—
567#390C2314yes—
568#390C2312yes—
569#390C2314yes—
570#390C2314yes—
571#390C2314yes—
572#390C2314yes—
573#390C2312yes—
574#390C2312yes—
575#390C2311yescharacteristic
576#390C2314yes—
577#390C2314yes—
578#390C2312yes—
579#390C2312yes—
580#390C2312yes—
581#390C2312yes—
582#390C2312yes—
583#390C2312yes—
584#390C2312yes—
585#390C2314yes—
586#390C2312yes—
587#390C2314yes—
588#390C2314yes—
589#390C2312yes—
590#390C2312yes—
591#390C2312yes—
592#390C2314yes—
593#390C2312yes—
594#390C2312yes—
595#390C2314yes—
596#390C2314yes—
597#390C2311yescharacteristic
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2311yescharacteristic
602#389C2311yescharacteristic
603#389C2312yes—
604#389C2314yes—
605#389C2312yes—
606#389C2312yes—
607#389C2314yes—
608#389C2311yescharacteristic
609#389C2311yescharacteristic
610#389C2311yescharacteristic
611#389C2311yescharacteristic
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2314yes—
616#389C2312yes—
617#389C2311yescharacteristic
618#389C2312yes—
619#389C2311yescharacteristic
620#389C2311yescharacteristic
621#388C2312yes—
622#388C2312yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2312yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2312yes—
645#388C2312yes—
646#388C2312yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2312yes—
652#388C2312yes—
653#388C2312yes—
654#388C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2312yes—
658#387C2314yes—
659#387C2312yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2314yes—
668#387C2314yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#386C2314yes—
674#386C2314yes—
675#386C2312yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2312yes—
685#386C2312yes—
686#386C2312yes—
687#386C2312yes—
688#386C2312yes—
689#386C2312yes—
690#386C2314yes—
691#386C2314yes—
692#386C2312yes—
693#386C2312yes—
694#386C2312yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2312yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2312yes—
708#386C2312yes—
709#386C2312yes—
710#386C2312yes—
711#386C2312yes—
712#386C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2312yes—
716#385C2312yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2312yes—
725#385C2312yes—
726#385C2312yes—
727#385C2312yes—
728#385C2312yes—
729#385C2312yes—
730#385C2314yes—
731#385C2312yes—
732#385C2312yes—
733#385C2312yes—
734#385C2314yes—
735#385C2314yes—
736#385C2312yes—
737#385C2312yes—
738#385C2312yes—
739#385C2312yes—
740#385C2312yes—
741#384C2312yes—
742#384C2312yes—
743#384C2312yes—
744#384C2312yes—
745#384C2311yescharacteristic
746#384C2311yescharacteristic
747#384C2312yes—
748#384C2312yes—
749#383C2312yes—
750#382C2312yes—
751#382C2311yescharacteristic
752#382C2311yescharacteristic
753#381C2314yes—
754#381C2312yes—
755#381C2312yes—
756#381C2312yes—
757#380C2314yes—
758#380C2314yes—
759#380C2314yes—
760#380C2314yes—
761#380C2314yes—
762#380C2312yes—
763#380C2311yescharacteristic
764#380C2311yescharacteristic
765#380C2311yescharacteristic
766#380C2311yescharacteristic
767#380C2311yescharacteristic
768#380C2311yescharacteristic
769#380C2311yescharacteristic
770#380C2312yes—
771#380C2314yes—
772#380C2312yes—
773#380C2312yes—
774#380C2311yescharacteristic
775#380C2311yescharacteristic
776#380C2311yescharacteristic
777#379C2314yes—
778#379C2312yes—
779#379C2314yes—
780#379C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2312yes—
818C4×C22⋊C4C2312yes—
819C4×C22⋊C4C2312yes—
820C4×C22⋊C4C2312yes—
821C4×C22⋊C4C2312yes—
822C4×C22⋊C4C2312yes—
823#376C2312yes—
824#376C2312yes—
825C43C2312yes—
826C25C2411yescharacteristic
827C25C2414yes—
828C2×#41—24no—
829C2×#41—28no—
830C2×#41—24no—
831C2×#41—42no—
832C2×#41—44no—
833C2×#41—44no—
834C2×#41—44no—
835C2×#41—44no—
836C2×#41—44no—
837C22×Q8C2411yescharacteristic
838C22×Q8C2411yescharacteristic
839C22×D4—28no—
840C22×D4—28no—
841C22×D4—44no—
842C22×D4—44no—
843C22×D4—44no—
844C22×D4—44no—
845C22×D4—44no—
846C22×D4—44no—
847C22×D4—48no—
848C22×D4—44no—
849C22×D4—48no—
850C22×D4—48no—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2411yescharacteristic
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2411yescharacteristic
857C22×D4C2412yes—
858C22×D4C2412yes—
859C22×D4C2412yes—
860C22×D4C2412yes—
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2414yes—
865C22×D4C2414yes—
866C22×D4C2414yes—
867C22×D4C2414yes—
868C22×D4C2414yes—
869C22×D4C2414yes—
870C22×D4C2412yes—
871C22×D4C2412yes—
872C22×D4C2414yes—
873C22×D4C2414yes—
874C22×D4C2414yes—
875C22×D4C2414yes—
876C22×D4C2414yes—
877C22×D4C2414yes—
878C22×D4C2414yes—
879C22×D4C2414yes—
880C22×D4C2414yes—
881C23×C4—24no—
882C23×C4—24no—
883C23×C4—24no—
884C23×C4—24no—
885C23×C4—42no—
886C23×C4—42no—
887C23×C4—42no—
888C23×C4—42no—
889C23×C4—42no—
890C23×C4C2411yescharacteristic
891C23×C4C2412yes—
892C23×C4C2412yes—
893C23×C4C2411yescharacteristic
894C23×C4C2411yescharacteristic
895C23×C4C2411yescharacteristic
896C23×C4C2411yescharacteristic
897C23×C4C2411yescharacteristic
898C23×C4C2412yes—
899C23×C4C2411yescharacteristic
900C23×C4C2411yescharacteristic
901C23×C4C2411yescharacteristic
902C23×C4C2411yescharacteristic
903C23×C4C2411yescharacteristic
904C23×C4C2411yescharacteristic
905C23×C4C2411yescharacteristic
906C23×C4C2411yescharacteristic
907C23×C4C2414yes—
908C23×C4C2414yes—
909C23×C4C2414yes—
910C23×C4C2412yes—
911C23×C4C2411yescharacteristic
912C23×C4C2411yescharacteristic
913C23×C4C2411yescharacteristic
914C23×C4C2414yes—
915C23×C4C2414yes—
916C23×C4C2414yes—
917C23×C4C2411yescharacteristic
918#127—24no—
919#127—24no—
920#127—44no—
921#127—44no—
922#127—44no—
923#127—44no—
924#127—44no—
925#127—44no—
926#127—44no—
927#127—48no—
928#127—48no—
929#126—44no—
930#126—48no—
931#126—48no—
932#125—42no—
933#125—44no—
934#125—44no—
935#125—48no—
936#124—28no—
937#124—42no—
938#124—44no—
939#123—28no—
940#123—28no—
941#123—216no—
942#123—48no—
943#123—48no—
944#123—48no—
945#123—48no—
946#123—44no—
947#123—48no—
948#123—48no—
949C22⋊Q8—24no—
950C22⋊Q8—24no—
951C22⋊Q8—42no—
952C22⋊Q8—42no—
953C22⋊Q8#4118yescomplemented
954#121—24no—
955#121—216no—
956#121—28no—
957#121—28no—
958#121—24no—
959#121—24no—
960#121—28no—
961#121—216no—
962#121—44no—
963#121—48no—
964#121—44no—
965#121—48no—
966#121—48no—
967#121—48no—
968#121—48no—
969#121—48no—
970#121—48no—
971#121—48no—
972#121—48no—
973#121—48no—
974#121—48no—
975#121—48no—
976#121—44no—
977#121—44no—
978#121—44no—
979#121—44no—
980#121—48no—
981#121—48no—
982#121—44no—
983#121—44no—
984#121—48no—
985#121—44no—
986#121—42no—
987#121—42no—
988#121—44no—
989#121—44no—
990#121—44no—
991#121—44no—
992#121—44no—
993#121—44no—
994#121—44no—
995#121—48no—
996#121—44no—
997#121—48no—
998#120—28no—
999#120—216no—
1000#120—48no—
1001#120—48no—
1002#120—44no—
1003#120—48no—
1004C4×Q8—24no—
1005C4×Q8—24no—
1006C4×Q8—42no—
1007C4×Q8—44no—
1008C4×D4—28no—
1009C4×D4—28no—
1010C4×D4—28no—
1011C4×D4—28no—
1012C4×D4—28no—
1013C4×D4—28no—
1014C4×D4—28no—
1015C4×D4—24no—
1016C4×D4—24no—
1017C4×D4—48no—
1018C4×D4—48no—
1019C4×D4—44no—
1020C4×D4—42no—
1021C4×D4—44no—
1022C4×D4—44no—
1023C4×D4—44no—
1024C4×D4—44no—
1025C4×D4—44no—
1026C4×D4—44no—
1027C4×D4—44no—
1028C4×D4—44no—
1029C4×D4—44no—
1030C4×D4—48no—
1031C4×D4—44no—
1032C4×D4—48no—
1033#117—24no—
1034#117—24no—
1035#117—44no—
1036#117—44no—
1037#117—48no—
1038#117—42no—
1039#117—44no—
1040C2×C4⋊C4—28no—
1041C2×C4⋊C4—44no—
1042C2×C4⋊C4—44no—
1043C2×C4⋊C4—44no—
1044C2×C4⋊C4C2411yescharacteristic
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2411yescharacteristic
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2411yescharacteristic
1054C2×C4⋊C4C2411yescharacteristic
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2411yescharacteristic
1057C2×C4⋊C4C2411yescharacteristic
1058C2×C4⋊C4C2411yescharacteristic
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2411yescharacteristic
1061C2×C4⋊C4C2411yescharacteristic
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2412yes—
1065C2×C4⋊C4C2412yes—
1066C2×C4⋊C4C2411yescharacteristic
1067C2×C4⋊C4C2412yes—
1068C2×C4⋊C4C2411yescharacteristic
1069C2×C4⋊C4C2412yes—
1070C2×C4⋊C4C2412yes—
1071C2×C4⋊C4C2412yes—
1072C2×C4⋊C4C2414yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2414yes—
1075C2×C4⋊C4C2412yes—
1076C2×C4⋊C4C2412yes—
1077C2×C4⋊C4C2414yes—
1078C2×C4⋊C4C2412yes—
1079C2×C4⋊C4C2414yes—
1080C2×C4⋊C4C2414yes—
1081C2×C4⋊C4C2414yes—
1082C2×C4⋊C4C2412yes—
1083C2×C4⋊C4C2412yes—
1084C2×C4⋊C4C2412yes—
1085C2×C4⋊C4C2414yes—
1086C2×C4⋊C4C2414yes—
1087C2×C4⋊C4C2414yes—
1088C2×C4⋊C4C2414yes—
1089C2×C4⋊C4C2414yes—
1090C2×C4⋊C4C2412yes—
1091C2×C4⋊C4C2411yescharacteristic
1092C2×C4⋊C4C2412yes—
1093C2×C22⋊C4—216no—
1094C2×C22⋊C4—48no—
1095C2×C22⋊C4—48no—
1096C2×C22⋊C4—48no—
1097C2×C22⋊C4—48no—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2412yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2412yes—
1123C2×C22⋊C4C2412yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2412yes—
1127C2×C22⋊C4C2412yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2412yes—
1139C2×C22⋊C4C2412yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2414yes—
1142C2×C22⋊C4C2412yes—
1143C2×C22⋊C4C2412yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2414yes—
1146C2×C22⋊C4C2414yes—
1147C2×C22⋊C4C2414yes—
1148C2×C22⋊C4C2414yes—
1149C2×C22⋊C4C2414yes—
1150C2×C22⋊C4C2414yes—
1151C2×C22⋊C4C2412yes—
1152C2×C22⋊C4C2412yes—
1153C2×C22⋊C4C2412yes—
1154C2×C22⋊C4C2412yes—
1155C2×C22⋊C4C2412yes—
1156C2×C22⋊C4C2414yes—
1157C2×C22⋊C4C2414yes—
1158C2×C22⋊C4C2412yes—
1159C2×C22⋊C4C2412yes—
1160C2×C22⋊C4C2414yes—
1161C2×C22⋊C4C2414yes—
1162C2×C22⋊C4C2414yes—
1163C2×C22⋊C4C2414yes—
1164C2×C22⋊C4C2414yes—
1165C2×C22⋊C4C2414yes—
1166C2×C22⋊C4C2414yes—
1167C2×C22⋊C4C2414yes—
1168C2×C22⋊C4C2412yes—
1169C2×C22⋊C4C2412yes—
1170C2×C22⋊C4C2412yes—
1171C2×C42—24no—
1172C2×C42—24no—
1173C2×C42—24no—
1174C2×C42—44no—
1175C2×C42—42no—
1176C2×C42—42no—
1177C2×C42—42no—
1178C2×C42—42no—
1179C2×C42—42no—
1180C2×C42—42no—
1181C2×C42—42no—
1182C2×C42—42no—
1183C2×C42—42no—
1184C2×C42C2412yes—
1185C2×C42C2411yescharacteristic
1186C2×C42C2411yescharacteristic
1187C2×C42C2412yes—
1188C2×C42C2412yes—
1189C2×C42C2412yes—
1190C2×C42C2412yes—
1191C2×C42C2412yes—
1192C2×C42C2412yes—
1193C2×C42C2412yes—
1194C2×C42C2412yes—
1195C2×C42C2411yescharacteristic
1196C2×C42C2411yescharacteristic
1197C2×C42C2411yescharacteristic
1198C2×C42C2411yescharacteristic
1199C2×C42C2411yescharacteristic
1200C2×C42C2411yescharacteristic
1201C2×C42C2411yescharacteristic
1202C2×C42C2412yes—
1203C2×C42C2414yes—
1204C2×C42C2414yes—
1205C2×C42C2414yes—
1206C2×C42C2412yes—
1207C2×C42C2412yes—
1208C2×C42C2411yescharacteristic
1209C2×C42C2411yescharacteristic
1210C2×C42C2411yescharacteristic
1211C2×C42C2411yescharacteristic
1212C2×C42C2411yescharacteristic
1213C2×C42C2411yescharacteristic
1214C2×C42C2411yescharacteristic
1215#95C2412yes—
1216#95C2412yes—
1217#95C2412yes—
1218#95C2412yes—
1219#95C2412yes—
1220#95C2412yes—
1221#95C2412yes—
1222#95C2412yes—
1223#95C2412yes—
1224#95C2412yes—
1225#95C2412yes—
1226#95C2412yes—
1227#95C2412yes—
1228#95C2412yes—
1229#95C2412yes—
1230#95C2412yes—
1231#95C2412yes—
1232#95C2412yes—
1233#95C2412yes—
1234#95C2412yes—
1235#95C2412yes—
1236#95C2412yes—
1237#95C2412yes—
1238#95C2412yes—
1239#95C2412yes—
1240#95C2414yes—
1241#95C2412yes—
1242#95C2414yes—
1243#95C2414yes—
1244#95C2412yes—
1245#95C2414yes—
1246#95C2412yes—
1247#95C2412yes—
1248#95C2412yes—
1249#95C2412yes—
1250#95C2414yes—
1251#95C2414yes—
1252#95C2414yes—
1253#95C2414yes—
1254#95C2414yes—
1255#95C2412yes—
1256#95C2412yes—
1257#95C2414yes—
1258#95C2412yes—
1259#95C2412yes—
1260#95C2412yes—
1261#95C2414yes—
1262#95C2414yes—
1263C24—22no—
1264C24—22no—
1265C24—22no—
1266C24—22no—
1267C24—22no—
1268C24—28no—
1269C24—28no—
1270C24—28no—
1271C24—41no—
1272C24—41no—
1273C24—44no—
1274C24—44no—
1275C24—44no—
1276C24—44no—
1277C24C2514yes—
1278C24C2514yes—
1279C24C2512yes—
1280C24C2512yes—
1281C24C2511yescharacteristic
1282C24C2511yescharacteristic
1283C24C2511yescharacteristic
1284#41—416no—
1285#41—816no—
1286#41—816no—
1287C2×Q8—22no—
1288C2×Q8—22no—
1289C2×Q8—22no—
1290C2×Q8—22no—
1291C2×Q8—22no—
1292C2×Q8C2×#4114yes—
1293C2×D4—24no—
1294C2×D4—24no—
1295C2×D4—24no—
1296C2×D4—24no—
1297C2×D4—24no—
1298C2×D4—24no—
1299C2×D4—24no—
1300C2×D4—24no—
1301C2×D4—24no—
1302C2×D4—28no—
1303C2×D4—28no—
1304C2×D4—28no—
1305C2×D4—28no—
1306C2×D4—24no—
1307C2×D4—24no—
1308C2×D4—24no—
1309C2×D4—24no—
1310C2×D4—22no—
1311C2×D4—24no—
1312C2×D4—28no—
1313C2×D4—28no—
1314C2×D4—28no—
1315C2×D4—22no—
1316C2×D4—22no—
1317C2×D4—22no—
1318C2×D4—24no—
1319C2×D4—24no—
1320C2×D4—24no—
1321C2×D4—24no—
1322C2×D4—24no—
1323C2×D4—24no—
1324C2×D4—22no—
1325C2×D4—24no—
1326C2×D4—24no—
1327C2×D4—28no—
1328C2×D4—28no—
1329C2×D4—24no—
1330C2×D4—24no—
1331C2×D4—24no—
1332C2×D4—22no—
1333C2×D4—24no—
1334C2×D4—42no—
1335C2×D4—42no—
1336C2×D4—44no—
1337C2×D4—42no—
1338C2×D4—44no—
1339C2×D4—44no—
1340C2×D4—44no—
1341C2×D4—44no—
1342C2×D4—42no—
1343C2×D4—42no—
1344C2×D4—44no—
1345C2×D4—44no—
1346C2×D4—42no—
1347C2×D4—42no—
1348C2×D4—44no—
1349C2×D4—44no—
1350C2×D4—44no—
1351C2×D4—44no—
1352C2×D4—44no—
1353C2×D4—44no—
1354C2×D4—44no—
1355C2×D4—44no—
1356C2×D4—44no—
1357C2×D4—44no—
1358C2×D4—44no—
1359C2×D4—42no—
1360C2×D4—44no—
1361C2×D4—44no—
1362C2×D4—44no—
1363C2×D4—44no—
1364C2×D4—44no—
1365C2×D4—44no—
1366C2×D4—44no—
1367C2×D4—44no—
1368C2×D4—42no—
1369C2×D4—42no—
1370C2×D4—44no—
1371C2×D4—44no—
1372C2×D4—44no—
1373C2×D4—44no—
1374C2×D4—44no—
1375C2×D4—44no—
1376C2×D4—44no—
1377C2×D4—44no—
1378C2×D4—44no—
1379C2×D4—44no—
1380C2×D4—44no—
1381C2×D4—44no—
1382C2×D4—44no—
1383C2×D4—816no—
1384C2×D4—816no—
1385C2×D4—816no—
1386C2×D4—832no—
1387C22×C4—22no—
1388C22×C4—22no—
1389C22×C4—22no—
1390C22×C4—22no—
1391C22×C4—22no—
1392C22×C4—22no—
1393C22×C4—22no—
1394C22×C4—22no—
1395C22×C4—22no—
1396C22×C4—22no—
1397C22×C4—22no—
1398C22×C4—22no—
1399C22×C4—22no—
1400C22×C4—22no—
1401C22×C4—28no—
1402C22×C4—22no—
1403C22×C4—24no—
1404C22×C4—24no—
1405C22×C4—22no—
1406C22×C4—22no—
1407C22×C4—22no—
1408C22×C4—22no—
1409C22×C4—22no—
1410C22×C4—22no—
1411C22×C4—22no—
1412C22×C4—24no—
1413C22×C4—22no—
1414C22×C4—22no—
1415C22×C4—24no—
1416C22×C4—24no—
1417C22×C4—24no—
1418C22×C4—24no—
1419C22×C4—22no—
1420C22×C4—22no—
1421C22×C4—22no—
1422C22×C4—22no—
1423C22×C4—22no—
1424C22×C4—22no—
1425C22×C4—22no—
1426C22×C4—22no—
1427C22×C4—22no—
1428C22×C4—24no—
1429C22×C4—22no—
1430C22×C4—28no—
1431C22×C4—28no—
1432C22×C4—24no—
1433C22×C4—41no—
1434C22×C4—41no—
1435C22×C4—41no—
1436C22×C4—41no—
1437C22×C4—41no—
1438C22×C4—41no—
1439C22×C4—41no—
1440C22×C4—41no—
1441C22×C4—41no—
1442C22×C4—42no—
1443C22×C4—41no—
1444C22×C4—41no—
1445C22×C4—41no—
1446C22×C4—41no—
1447C22×C4—41no—
1448C22×C4—41no—
1449C22×C4—41no—
1450C22×C4—416no—
1451C22×C4—42no—
1452C22×C4—44no—
1453C22×C4—44no—
1454C22×C4—44no—
1455C22×C4—44no—
1456C22×C4—44no—
1457C22×C4—44no—
1458C22×C4—44no—
1459C22×C4—44no—
1460C22×C4—42no—
1461C22×C4—44no—
1462C22×C4—44no—
1463C22×C4—44no—
1464C22×C4—44no—
1465C22×C4—44no—
1466C22×C4—44no—
1467C22×C4—44no—
1468C22×C4—416no—
1469C22×C4—416no—
1470C22×C4C2×#4114yes—
1471C22×C4H(5,𝔽2)14yes—
1472C22×C4H(5,𝔽2)14yes—
1473C22×C4H(5,𝔽2)14yes—
1474C22×C4C2512yes—
1475C22×C4C2512yes—
1476C22×C4C2512yes—
1477C22×C4C2512yes—
1478C22×C4C2511yescharacteristic
1479C22×C4C2511yescharacteristic
1480C22×C4C2511yescharacteristic
1481C22×C4C2511yescharacteristic
1482C22×C4C2512yes—
1483C22×C4C2512yes—
1484C22×C4C2512yes—
1485C22×C4C2512yes—
1486C22×C4C2512yes—
1487C22×C4C2512yes—
1488C22×C4C2512yes—
1489C22×C4C2514yes—
1490C22×C4C2512yes—
1491C22×C4C2514yes—
1492C22×C4C2512yes—
1493C22×C4C2512yes—
1494C22×C4C2511yescharacteristic
1495C22×C4C2511yescharacteristic
1496C22×C4C2511yescharacteristic
1497C22×C4C2511yescharacteristic
1498C22×C4C2511yescharacteristic
1499C22×C4C2511yescharacteristic
1500C22×C4C2511yescharacteristic
1501C22×C4C2511yescharacteristic
1502C4⋊C4—22no—
1503C4⋊C4—24no—
1504C4⋊C4—24no—
1505C4⋊C4—24no—
1506C4⋊C4—24no—
1507C4⋊C4—28no—
1508C4⋊C4—22no—
1509C4⋊C4—24no—
1510C4⋊C4—24no—
1511C4⋊C4—28no—
1512C4⋊C4—22no—
1513C4⋊C4—22no—
1514C4⋊C4—24no—
1515C4⋊C4—22no—
1516C4⋊C4—24no—
1517C4⋊C4—22no—
1518C4⋊C4—22no—
1519C4⋊C4—24no—
1520C4⋊C4—24no—
1521C4⋊C4—24no—
1522C4⋊C4—22no—
1523C4⋊C4—22no—
1524C4⋊C4—24no—
1525C4⋊C4—24no—
1526C4⋊C4—24no—
1527C4⋊C4—22no—
1528C4⋊C4—22no—
1529C4⋊C4—44no—
1530C4⋊C4—42no—
1531C4⋊C4—42no—
1532C4⋊C4—44no—
1533C4⋊C4—42no—
1534C4⋊C4—42no—
1535C4⋊C4—44no—
1536C4⋊C4—42no—
1537C4⋊C4—42no—
1538C4⋊C4—42no—
1539C4⋊C4—44no—
1540C4⋊C4—44no—
1541C4⋊C4—44no—
1542C4⋊C4—42no—
1543C4⋊C4—44no—
1544C4⋊C4—44no—
1545C4⋊C4—44no—
1546C4⋊C4—44no—
1547C4⋊C4—44no—
1548C4⋊C4—42no—
1549C4⋊C4C2×#4114yes—
1550C4⋊C4C2×#4118yes—
1551C22⋊C4—24no—
1552C22⋊C4—24no—
1553C22⋊C4—24no—
1554C22⋊C4—24no—
1555C22⋊C4—24no—
1556C22⋊C4—24no—
1557C22⋊C4—24no—
1558C22⋊C4—24no—
1559C22⋊C4—24no—
1560C22⋊C4—28no—
1561C22⋊C4—28no—
1562C22⋊C4—24no—
1563C22⋊C4—24no—
1564C22⋊C4—28no—
1565C22⋊C4—24no—
1566C22⋊C4—24no—
1567C22⋊C4—24no—
1568C22⋊C4—28no—
1569C22⋊C4—28no—
1570C22⋊C4—28no—
1571C22⋊C4—28no—
1572C22⋊C4—28no—
1573C22⋊C4—24no—
1574C22⋊C4—24no—
1575C22⋊C4—24no—
1576C22⋊C4—24no—
1577C22⋊C4—24no—
1578C22⋊C4—24no—
1579C22⋊C4—24no—
1580C22⋊C4—24no—
1581C22⋊C4—44no—
1582C22⋊C4—44no—
1583C22⋊C4—44no—
1584C22⋊C4—44no—
1585C22⋊C4—44no—
1586C22⋊C4—44no—
1587C22⋊C4—44no—
1588C22⋊C4—44no—
1589C22⋊C4—44no—
1590C22⋊C4—44no—
1591C22⋊C4—42no—
1592C22⋊C4—42no—
1593C22⋊C4—44no—
1594C22⋊C4—44no—
1595C22⋊C4—42no—
1596C22⋊C4—42no—
1597C22⋊C4—44no—
1598C22⋊C4—42no—
1599C22⋊C4—42no—
1600C22⋊C4—42no—
1601C22⋊C4—44no—
1602C22⋊C4—44no—
1603C22⋊C4—44no—
1604C22⋊C4—44no—
1605C22⋊C4—44no—
1606C22⋊C4—44no—
1607C22⋊C4—44no—
1608C22⋊C4—42no—
1609C22⋊C4—42no—
1610C22⋊C4—44no—
1611C22⋊C4—44no—
1612C22⋊C4—44no—
1613C22⋊C4—42no—
1614C22⋊C4—42no—
1615C22⋊C4—44no—
1616C22⋊C4—44no—
1617C22⋊C4—44no—
1618C22⋊C4—42no—
1619C22⋊C4—44no—
1620C22⋊C4—44no—
1621C22⋊C4—44no—
1622C22⋊C4—42no—
1623C22⋊C4C2×#4118yes—
1624C42—24no—
1625C42—24no—
1626C42—22no—
1627C42—22no—
1628C42—22no—
1629C42—22no—
1630C42—22no—
1631C42—22no—
1632C42—22no—
1633C42—22no—
1634C42—22no—
1635C42—24no—
1636C42—24no—
1637C42—24no—
1638C42—24no—
1639C42—24no—
1640C42—24no—
1641C42—24no—
1642C42—41no—
1643C42—41no—
1644C42—41no—
1645C42—41no—
1646C42—41no—
1647C42—41no—
1648C42—42no—
1649C42—42no—
1650C42—44no—
1651C42—44no—
1652C42—42no—
1653C42—44no—
1654C42H(5,𝔽2)14yes—
1655C23—21no—
1656C23—21no—
1657C23—21no—
1658C23—21no—
1659C23—28no—
1660C23—21no—
1661C23—21no—
1662C23—21no—
1663C23—21no—
1664C23—21no—
1665C23—21no—
1666C23—21no—
1667C23—21no—
1668C23—21no—
1669C23—21no—
1670C23—21no—
1671C23—21no—
1672C23—24no—
1673C23—22no—
1674C23—24no—
1675C23—22no—
1676C23—22no—
1677C23—22no—
1678C23—22no—
1679C23—24no—
1680C23—22no—
1681C23—22no—
1682C23—24no—
1683C23—24no—
1684C23—22no—
1685C23—24no—
1686C23—22no—
1687C23—24no—
1688C23—24no—
1689C23—22no—
1690C23—24no—
1691C23—24no—
1692C23—24no—
1693C23—24no—
1694C23—24no—
1695C23—22no—
1696C23—22no—
1697C23—22no—
1698C23—24no—
1699C23—22no—
1700C23—44no—
1701C23—44no—
1702C23—44no—
1703C23—44no—
1704C23—44no—
1705C23—44no—
1706C23—416no—
1707C23—88no—
1708C23—88no—
1709C23—88no—
1710C23—88no—
1711C23—88no—
1712C23—88no—
1713C23C22×#4112yes—
1714C23C2×H(5,𝔽2)12yes—
1715C23C2×H(5,𝔽2)12yes—
1716C23C2×H(5,𝔽2)12yes—
1717C23#58512yes—
1718C23C2611yescharacteristic
1719Q8—28no—
1720Q8—44no—
1721D4—48no—
1722D4—48no—
1723D4—48no—
1724D4—48no—
1725D4—48no—
1726D4—48no—
1727D4—44no—
1728D4—44no—
1729D4—48no—
1730D4—48no—
1731D4—88no—
1732D4—88no—
1733D4—88no—
1734D4—84no—
1735D4—84no—
1736D4—88no—
1737D4—88no—
1738D4—84no—
1739D4—84no—
1740D4—88no—
1741D4—88no—
1742D4—88no—
1743D4—88no—
1744D4—88no—
1745D4—88no—
1746D4—88no—
1747D4—164no—
1748D4—164no—
1749D4—164no—
1750D4—164no—
1751C2×C4—28no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—21no—
1756C2×C4—21no—
1757C2×C4—21no—
1758C2×C4—22no—
1759C2×C4—22no—
1760C2×C4—22no—
1761C2×C4—21no—
1762C2×C4—21no—
1763C2×C4—22no—
1764C2×C4—21no—
1765C2×C4—21no—
1766C2×C4—21no—
1767C2×C4—21no—
1768C2×C4—28no—
1769C2×C4—28no—
1770C2×C4—28no—
1771C2×C4—22no—
1772C2×C4—22no—
1773C2×C4—22no—
1774C2×C4—22no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—22no—
1781C2×C4—22no—
1782C2×C4—22no—
1783C2×C4—22no—
1784C2×C4—22no—
1785C2×C4—22no—
1786C2×C4—22no—
1787C2×C4—22no—
1788C2×C4—22no—
1789C2×C4—22no—
1790C2×C4—22no—
1791C2×C4—22no—
1792C2×C4—22no—
1793C2×C4—22no—
1794C2×C4—24no—
1795C2×C4—24no—
1796C2×C4—24no—
1797C2×C4—22no—
1798C2×C4—22no—
1799C2×C4—22no—
1800C2×C4—22no—
1801C2×C4—22no—
1802C2×C4—22no—
1803C2×C4—22no—
1804C2×C4—24no—
1805C2×C4—24no—
1806C2×C4—21no—
1807C2×C4—21no—
1808C2×C4—21no—
1809C2×C4—21no—
1810C2×C4—24no—
1811C2×C4—22no—
1812C2×C4—22no—
1813C2×C4—22no—
1814C2×C4—22no—
1815C2×C4—22no—
1816C2×C4—22no—
1817C2×C4—22no—
1818C2×C4—22no—
1819C2×C4—22no—
1820C2×C4—22no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—21no—
1824C2×C4—22no—
1825C2×C4—44no—
1826C2×C4—44no—
1827C2×C4—44no—
1828C2×C4—48no—
1829C2×C4—44no—
1830C2×C4—44no—
1831C2×C4—44no—
1832C2×C4—44no—
1833C2×C4—44no—
1834C2×C4—44no—
1835C2×C4—44no—
1836C2×C4—44no—
1837C2×C4—44no—
1838C2×C4—48no—
1839C2×C4—44no—
1840C2×C4—44no—
1841C2×C4—48no—
1842C2×C4—88no—
1843C2×C4—84no—
1844C2×C4—88no—
1845C2×C4—88no—
1846C2×C4—88no—
1847C2×C4—164no—
1848C2×C4—164no—
1849C2×C4C22×#4114yes—
1850C2×C4C22×#4114yes—
1851C2×C4C22×#4112yes—
1852C2×C4C22×#4112yes—
1853C2×C4C2×H(5,𝔽2)12yes—
1854C2×C4C2×H(5,𝔽2)12yes—
1855C2×C4C2×H(5,𝔽2)12yes—
1856C2×C4C2×H(5,𝔽2)12yes—
1857C2×C4C2×H(5,𝔽2)12yes—
1858C2×C4C2×H(5,𝔽2)12yes—
1859C2×C4C2×H(5,𝔽2)12yes—
1860C2×C4C2×H(5,𝔽2)12yes—
1861C2×C4C2×H(5,𝔽2)12yes—
1862C2×C4#58512yes—
1863C22—22no—
1864C22—22no—
1865C22—22no—
1866C22—22no—
1867C22—22no—
1868C22—22no—
1869C22—22no—
1870C22—22no—
1871C22—22no—
1872C22—22no—
1873C22—22no—
1874C22—22no—
1875C22—416no—
1876C22—41no—
1877C22—41no—
1878C22—41no—
1879C22—41no—
1880C22—41no—
1881C22—41no—
1882C22—41no—
1883C22—41no—
1884C22—42no—
1885C22—42no—
1886C22—44no—
1887C22—44no—
1888C22—42no—
1889C22—42no—
1890C22—44no—
1891C22—44no—
1892C22—42no—
1893C22—42no—
1894C22—44no—
1895C22—44no—
1896C22—44no—
1897C22—42no—
1898C22—42no—
1899C22—44no—
1900C22—42no—
1901C22—44no—
1902C22—44no—
1903C22—42no—
1904C22—42no—
1905C22—44no—
1906C22—44no—
1907C22—42no—
1908C22—42no—
1909C22—44no—
1910C22—44no—
1911C22—42no—
1912C22—1616no—
1913C22#351714yes—
1914C22C23×#4111yescharacteristic
1915C22C22×H(5,𝔽2)11yescharacteristic
1916C22C22×H(5,𝔽2)11yescharacteristic
1917C22C22×H(5,𝔽2)11yescharacteristic
1918C22C22×H(5,𝔽2)11yescharacteristic
1919C22C2×#58511yescharacteristic
1920C22C2×#58511yescharacteristic
1921C4—22no—
1922C4—22no—
1923C4—24no—
1924C4—24no—
1925C4—22no—
1926C4—22no—
1927C4—22no—
1928C4—22no—
1929C4—42no—
1930C4—42no—
1931C4—41no—
1932C4—42no—
1933C4—42no—
1934C4—42no—
1935C4—42no—
1936C4—41no—
1937C4—42no—
1938C4—42no—
1939C4—44no—
1940C4—44no—
1941C4—42no—
1942C4—42no—
1943C4—41no—
1944C4—41no—
1945C4—42no—
1946C4—42no—
1947C4#351914yes—
1948C4#354214yes—
1949C2—24no—
1950C2—42no—
1951C2—42no—
1952C2—82no—
1953C2—82no—
1954C2—84no—
1955C2—84no—
1956C2C2×#354211yescharacteristic
1957C2#6274811yescharacteristic
1958C2C2×#351911yescharacteristic
1959C2C2×#351711yescharacteristic
1960C2#6280011yescharacteristic
1961C2#6281811yescharacteristic
1962C2#6283211yescharacteristic
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. #59321C2semidirect
2. #59304C2semidirect
3. #59124C2semidirect
4. #59124C2semidirect
5. #59028C2semidirect
6. #59003C2semidirect
7. #46028C2semidirect
8. #45649C2semidirect
9. #45604C2semidirect
10. #39786C2semidirect
11. #39402C2semidirect
12. #39147C2semidirect
13. #39138C2semidirect
14. #39132C2semidirect
15. #38942C2semidirect
16. #38916C2semidirect
17. #38909C2semidirect
18. #38208C2semidirect
19. #38129C2semidirect
20. #38089C2semidirect
21. #37722C2semidirect
22. #37493C2semidirect
23. #36923C2semidirect
24. C2×#2856C2semidirect
25. #36621C2semidirect
26. #36472C2semidirect
27. #36455C2semidirect
28. #36410C2semidirect
29. #36362C2semidirect
30. #36302C2semidirect
31. #36291C2semidirect
32. #35171C2semidirect
33. #35038C2semidirect
34. #34476C2semidirect
35. C4×#525C2semidirect
37. C2×#553C22semidirect
38. C2×#550C22semidirect
39. C2×#550C22semidirect
40. C2×#550C22semidirect
43. C2×#540C22semidirect
45. C2×#529C22semidirect
50. C2×C4×#41C22semidirect
52. #2861C22semidirect
53. #2860C22semidirect
64. #2856C22semidirect
65. #2855C22semidirect
66. #2854C22semidirect
67. #2854C22semidirect
68. #2853C22semidirect
70. #2852C22semidirect
72. #2851C22semidirect
74. #2850C22semidirect
78. #2829C22semidirect
79. #2828C22semidirect
80. #2797C22semidirect
81. #2791C22semidirect
82. #2786C22semidirect
83. #2757C22semidirect
84. #2756C22semidirect
85. #2718C22semidirect
86. #2714C22semidirect
87. #2714C22semidirect
88. #2714C22semidirect
89. #2711C22semidirect
90. #2711C22semidirect
91. #2708C22semidirect
92. #2708C22semidirect
93. #2703C22semidirect
94. #2701C22semidirect
95. #2701C22semidirect
96. #2699C22semidirect
97. #2691C22semidirect
98. #2688C22semidirect
99. #2688C22semidirect
100. #2682C22semidirect
101. #2673C22semidirect
102. #2673C22semidirect
103. #2673C22semidirect
104. #2673C22semidirect
105. #2673C22semidirect
106. #2673C22semidirect
107. #2673C22semidirect
108. #2671C22semidirect
109. #2671C22semidirect
110. #2671C22semidirect
111. #2671C22semidirect
112. #2661C22semidirect
113. #2661C22semidirect
114. #2648C22semidirect
115. #2644C22semidirect
116. #2641C22semidirect
117. #2635C22semidirect
118. #2624C22semidirect
120. #2619C22semidirect
122. #2603C22semidirect
123. #2595C22semidirect
124. #2595C22semidirect
125. #2582C22semidirect
126. #2566C22semidirect
127. #2565C22semidirect
128. #2559C22semidirect
129. #2554C22semidirect
130. #2554C22semidirect
131. #2552C22semidirect
132. #2552C22semidirect
133. #2552C22semidirect
134. #2548C22semidirect
135. #2548C22semidirect
136. #2544C22semidirect
137. #2541C22semidirect
138. #2541C22semidirect
139. #2541C22semidirect
140. #2541C22semidirect
141. #2541C22semidirect
142. #2541C22semidirect
143. #2541C22semidirect
144. #2537C22semidirect
145. #2537C22semidirect
146. #2537C22semidirect
147. #2535C22semidirect
148. #2531C22semidirect
149. #2516C22semidirect
150. #2513C22semidirect
151. #2513C22semidirect
152. #2511C22semidirect
153. #2506C22semidirect
155. #2501C22semidirect
156. #2500C22semidirect
157. #2500C22semidirect
158. #2496C22semidirect
159. #2490C22semidirect
160. #2490C22semidirect
161. #2490C22semidirect
162. #2490C22semidirect
163. #2490C22semidirect
164. #2490C22semidirect
167. #2476C22semidirect
168. #2476C22semidirect
170. #2471C22semidirect
171. #2467C22semidirect
172. #2467C22semidirect
173. #2464C22semidirect
174. #2464C22semidirect
175. #2464C22semidirect
176. #2464C22semidirect
177. #2464C22semidirect
178. #2464C22semidirect
179. #2456C22semidirect
180. #2454C22semidirect
181. #2445C22semidirect
182. #2445C22semidirect
183. #2445C22semidirect
186. #2441C22semidirect
190. #2431C22semidirect
191. #2431C22semidirect
192. #2431C22semidirect
193. #2431C22semidirect
194. #2428C22semidirect
195. #2428C22semidirect
196. #2428C22semidirect
197. #2428C22semidirect
198. #2428C22semidirect
199. #2428C22semidirect
200. #2428C22semidirect
201. #2428C22semidirect
202. #2427C22semidirect
203. #2427C22semidirect
204. #2426C22semidirect
207. #2422C22semidirect
208. #2422C22semidirect
209. #2422C22semidirect
210. #2422C22semidirect
211. #2420C22semidirect
214. #2416C22semidirect
215. #2414C22semidirect
216. #2414C22semidirect
217. #2414C22semidirect
218. #2414C22semidirect
219. #2414C22semidirect
226. #2407C22semidirect
227. #2407C22semidirect
228. #2407C22semidirect
230. #2377C22semidirect
231. #2376C22semidirect
232. #2367C22semidirect
233. #2366C22semidirect
234. #2366C22semidirect
235. #2363C22semidirect
236. #2363C22semidirect
237. #2361C22semidirect
242. #2355C22semidirect
243. #2354C22semidirect
244. #2354C22semidirect
245. Q8×C4⋊C4C22semidirect
247. D4×C4⋊C4C22semidirect
250. #2341C22semidirect
253. #2335C22semidirect
254. #2333C22semidirect
255. #2326C22semidirect
256. #2324C22semidirect
257. #2324C22semidirect
259. #2319C22semidirect
261. #2311C22semidirect
262. C4×#127C22semidirect
266. C4×C22⋊Q8C22semidirect
267. C4×C22⋊Q8C22semidirect
268. C4×C22⋊Q8C22semidirect
269. C4×#123C22semidirect
270. C4×#123C22semidirect
271. C4×#123C22semidirect
275. C4×#121C22semidirect
276. C4×#121C22semidirect
277. C4×#121C22semidirect
278. C4×#121C22semidirect
282. #2297C22semidirect
283. #2297C22semidirect
284. #2296C22semidirect
285. #2293C22semidirect
291. #2290C22semidirect
292. #2290C22semidirect
294. #2283C22semidirect
297. C42×D4C22semidirect
298. C4×#117C22semidirect
953. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#593212
#593042
#591242
#590282
#590032
#460282
#456492
#456042
#397862
#394022
#391472
#391382
#391322
#389422
#389162
#389092
#382082
#381292
#380892
#377222
#374932
#369232
C2×#28562
#366212
#364722
#364552
#364102
#363622
#363022
#362912
#351712
#350382
#344762
C4×#5252