Finite Group Databasebeta

← #7688163

Subgroups — #7688163

Order 512.

6027 conjugacy classes of subgroups.

The subgroup lattice has 1880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59691C212yesmaximal, complemented
2#59647C211yesmaximal, characteristic, complemented
3#59592C212yesmaximal, complemented
4#59129C212yesmaximal, complemented
5#59099C212yesmaximal, complemented
6#59057C212yesmaximal, complemented
7#59051C211yesmaximal, characteristic, complemented
8#59049C211yesmaximal, characteristic, complemented
9#59024C212yesmaximal, complemented
10#44178C214yesmaximal, complemented
11#44161C214yesmaximal, complemented
12#44128C214yesmaximal, complemented
13#40103C212yesmaximal, complemented
14#40092C212yesmaximal, complemented
15#40007C212yesmaximal, complemented
16#39862C212yesmaximal, complemented
17#39532C212yesmaximal, complemented
18#39212C212yesmaximal, complemented
19#36561C211yesmaximal, characteristic, complemented
20#36504C211yesmaximal, characteristic, complemented
21#36454C211yesmaximal, characteristic, complemented
22#36406C211yesmaximal, characteristic, complemented
23#36288C211yesmaximal, characteristic, complemented
24#36153C211yesmaximal, characteristic, complemented
25#36149C212yesmaximal, complemented
26#36149C211yesmaximal, characteristic, complemented
27#36147C212yesmaximal, complemented
28#35698C214yesmaximal, complemented
29#34937C211yesmaximal, characteristic, complemented
30#34936C211yesmaximal, characteristic, complemented
31#34925C211yesmaximal, characteristic, complemented
32#34330C212yesmaximal, complemented
33#34233C212yesmaximal, complemented
34C4×#553C211yesmaximal, characteristic, complemented
35C4×#546C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic, complemented
37C2×#554C2212yescomplemented
38C2×#553C2211yescharacteristic
39C2×#550C2212yes—
40C2×#547C2211yescharacteristic
41C2×#546C2211yescharacteristic
42C2×#546C2212yes—
43C2×#532C2212yes—
44C2×#532C2211yescharacteristic
45C2×#532C2212yes—
46C2×#532C2212yescomplemented
47C2×#532C2211yescharacteristic, complemented
48C2×#525C2212yes—
49C2×#525C2212yes—
50C2×C4×#41C2211yescharacteristic
51C22×C4×D4C2211yescharacteristic
52#2862C2211yescharacteristic, complemented
53#2862C2212yescomplemented
54#2857C2211yescharacteristic
55#2857C2212yescomplemented
56#2857C2212yescomplemented
57#2857C2211yescharacteristic, complemented
58#2855C2212yescomplemented
59#2850C2212yescomplemented
60#2847C2212yes—
61#2797C2214yescomplemented
62#2797C2214yescomplemented
63#2786C2214yescomplemented
64#2773C2214yescomplemented
65#2761C2214yescomplemented
66#2753C2214yescomplemented
67#2751C2214yescomplemented
68#2741C2214yescomplemented
69#2740C2214yescomplemented
70#2730C2214yescomplemented
71#2730C2214yescomplemented
72#2714C2214yes—
73#2707C2214yes—
74#2706C2214yes—
75#2703C2214yes—
76#2696C2214yes—
77#2688C2214yes—
78#2678C2214yes—
79#2673C2214yescomplemented
80#2671C2214yes—
81#2669C2214yes—
82#2667C2214yescomplemented
83#2649C2214yescomplemented
84#2636C2214yescomplemented
85#2612C2214yescomplemented
86#2603C2214yescomplemented
87#2600C2214yescomplemented
88#2595C2214yescomplemented
89#2589C2214yescomplemented
90#2575C2214yescomplemented
91#2574C2214yes—
92#2564C2214yescomplemented
93#2557C2214yes—
94#2557C2214yes—
95#2556C2214yescomplemented
96#2555C2214yescomplemented
97#2553C2214yescomplemented
98#2553C2214yescomplemented
99#2551C2211yescharacteristic, complemented
100#2548C2212yescomplemented
101#2548C2211yescharacteristic, complemented
102#2547C2211yescharacteristic
103#2546C2211yescharacteristic, complemented
104#2545C2212yescomplemented
105#2544C2212yes—
106#2544C2212yes—
107#2543C2214yescomplemented
108#2542C2211yescharacteristic
109#2542C2211yescharacteristic
110#2541C2211yescharacteristic
111#2541C2211yescharacteristic
112#2541C2211yescharacteristic, complemented
113#2541C2212yescomplemented
114#2540C2212yes—
115#2540C2212yes—
116#2540C2212yes—
117#2540C2212yescomplemented
118#2539C2214yes—
119#2537C2211yescharacteristic
120#2536C2212yescomplemented
121#2535C2212yes—
122#2535C2214yescomplemented
123#2517C2214yescomplemented
124#2513C2212yescomplemented
125#2511C2212yescomplemented
126#2508C2212yescomplemented
127#2506C2212yescomplemented
128#2504C2212yescomplemented
129#2501C2212yes—
130#2499C2212yescomplemented
131#2492C2212yes—
132#2492C2212yescomplemented
133#2491C2212yescomplemented
134#2491C2212yescomplemented
135#2490C2214yescomplemented
136#2490C2212yescomplemented
137#2489C2212yescomplemented
138#2486C2212yes—
139#2479C2214yescomplemented
140#2472C2214yes—
141#2467C2214yescomplemented
142#2467C2214yescomplemented
143#2464C2214yes—
144#2460C2214yescomplemented
145#2459C2214yescomplemented
146#2457C2214yes—
147#2457C2214yes—
148#2456C2214yescomplemented
149#2455C2214yes—
150#2454C2214yescomplemented
151#2452C2212yes—
152#2450C2214yescomplemented
153#2448C2212yescomplemented
154#2447C2212yes—
155#2447C2212yescomplemented
156#2447C2212yescomplemented
157#2447C2214yescomplemented
158#2447C2212yescomplemented
159#2444C2214yescomplemented
160#2439C2212yes—
161#2433C2212yes—
162#2432C2212yes—
163#2431C2212yes—
164#2431C2212yes—
165#2429C2212yes—
166#2428C2212yes—
167#2428C2214yes—
168#2428C2212yescomplemented
169#2428C2212yescomplemented
170#2427C2212yes—
171#2427C2212yes—
172#2427C2212yescomplemented
173#2427C2212yescomplemented
174#2427C2212yescomplemented
175#2427C2214yescomplemented
176#2427C2212yescomplemented
177#2426C2212yescomplemented
178#2425C2214yes—
179#2424C2214yes—
180#2424C2214yes—
181#2423C2212yescomplemented
182#2421C2212yescomplemented
183#2420C2212yes—
184#2420C2214yescomplemented
185#2420C2212yescomplemented
186#2420C2212yescomplemented
187#2420C2214yescomplemented
188#2417C2212yes—
189#2417C2212yescomplemented
190#2416C2212yes—
191#2416C2212yescomplemented
192#2416C2212yescomplemented
193#2416C2212yescomplemented
194#2414C2212yes—
195#2412C2214yes—
196#2407C2212yes—
197#2407C2212yes—
198#2407C2212yes—
199#2407C2214yes—
200#2407C2212yescomplemented
201#2407C2214yescomplemented
202#2404C2214yes—
203#2397C2214yes—
204#2392C2214yescomplemented
205#2388C2214yescomplemented
206#2374C2212yes—
207#2373C2212yescomplemented
208#2370C2211yescharacteristic, complemented
209#2369C2212yescomplemented
210#2367C2212yes—
211#2367C2211yescharacteristic
212#2366C2212yes—
213#2366C2214yescomplemented
214#2365C2211yescharacteristic, complemented
215#2365C2211yescharacteristic, complemented
216#2364C2212yes—
217#2364C2212yes—
218#2364C2214yescomplemented
219#2364C2214yescomplemented
220#2363C2211yescharacteristic
221#2363C2212yes—
222#2363C2211yescharacteristic
223#2363C2212yescomplemented
224#2361C2211yescharacteristic, complemented
225#2361C2212yescomplemented
226#2361C2212yescomplemented
227#2360C2211yescharacteristic
228#2360C2212yescomplemented
229#2360C2212yescomplemented
230#2360C2212yescomplemented
231#2359C2212yes—
232#2358C2214yes—
233#2358C2212yes—
234#2358C2214yes—
235#2357C2214yescomplemented
236#2357C2211yescharacteristic, complemented
237#2355C2212yescomplemented
238#2355C2211yescharacteristic, complemented
239#2354C2212yescomplemented
240#2353C2214yescomplemented
241#2353C2212yescomplemented
242#2352C2211yescharacteristic
243#2352C2211yescharacteristic
244#2349C2211yescharacteristic
245#2349C2212yescomplemented
246#2349C2214yescomplemented
247D4×C4⋊C4C2211yescharacteristic
248#2347C2211yescharacteristic
249#2346C2212yes—
250#2345C2211yescharacteristic, complemented
251#2342C2212yes—
252#2341C2212yes—
253#2339C2212yes—
254#2339C2212yes—
255#2339C2211yescharacteristic
256#2339C2212yescomplemented
257#2339C2214yescomplemented
258D4×C22⋊C4C2211yescharacteristic
259#2335C2214yes—
260#2335C2214yes—
261#2333C2214yescomplemented
262#2333C2214yescomplemented
263#2328C2214yescomplemented
264#2318C2214yescomplemented
265C4×#127C2212yes—
266C4×#127C2212yes—
267C4×#127C2211yescharacteristic, complemented
268C4×#125C2211yescharacteristic, complemented
269C4×#126C2212yescomplemented
270C4×#124C2211yescharacteristic
271C4×C22⋊Q8C2211yescharacteristic
272C4×C22⋊Q8C2212yescomplemented
273C4×C22⋊Q8C2212yescomplemented
274C4×#123C2212yes—
275C4×#123C2212yes—
276C4×#121C2212yes—
277C4×#121C2211yescharacteristic
278C4×#121C2212yes—
279C4×#121C2212yes—
280C4×#121C2211yescharacteristic
281C4×#121C2212yescomplemented
282C4×#121C2212yescomplemented
283C4×#121C2212yescomplemented
284C4×#121C2212yescomplemented
285C4×#121C2211yescharacteristic, complemented
286C4×#120C2212yes—
287#2297C2212yes—
288#2297C2212yescomplemented
289#2295C2212yescomplemented
290C2×#380C2212yes—
291#2275C2214yescomplemented
292C42×D4C2211yescharacteristic
293C42×D4C2211yescharacteristic
294C42×D4C2212yescomplemented
295C42×D4C2211yescharacteristic, complemented
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic, complemented
298C2×C4×C22⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C22×#41C2312yes—
303C22×#41C2314yes—
304C23×D4C2311yescharacteristic
305C24×C4C2312yes—
306#556—44no—
307#554—48no—
308#553—28no—
309#550—216no—
310#547—44no—
311#546—28no—
312#546—48no—
313#532—44no—
314#532—44no—
315#532—48no—
316#532—48no—
317#532—48no—
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2311yescharacteristic
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2311yescharacteristic
326C2×#127C2314yes—
327C2×#127C2312yes—
328C2×#126C2312yes—
329C2×#126C2314yes—
330C2×#125C2311yescharacteristic
331C2×#125C2314yes—
332C2×#124C2312yes—
333C2×#124C2311yescharacteristic
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2314yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2314yes—
340#525—216no—
341#525—48no—
342C2×#123C2314yes—
343C2×#123C2312yes—
344C2×#123C2312yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2314yes—
359C2×#121C2314yes—
360C2×#121C2314yes—
361C2×#121C2311yescharacteristic
362C2×#121C2312yes—
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2314yes—
374C2×#121C2312yes—
375C2×#121C2312yes—
376C2×#121C2314yes—
377C2×#121C2312yes—
378C2×#121C2314yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2314yes—
382C2×#121C2314yes—
383C2×#121C2311yescharacteristic
384C2×#120C2314yes—
385C2×#120C2312yes—
386C2×#120C2314yes—
387C2×#120C2314yes—
388C4×#41—44no—
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2311yescharacteristic
391C2×C4×Q8C2312yes—
392C2×C4×Q8C2312yes—
393C2×C4×Q8C2311yescharacteristic
394C2×C4×D4—44no—
395C2×C4×D4C2314yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2312yes—
404C2×C4×D4C2314yes—
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2311yescharacteristic
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2311yescharacteristic
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2311yescharacteristic
411C2×C4×D4C2312yes—
412C2×C4×D4C2314yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2314yes—
418C2×C4×D4C2311yescharacteristic
419C2×C4×D4C2312yes—
420C2×C4×D4C2312yes—
421C2×C4×D4C2314yes—
422C2×C4×D4C2314yes—
423C2×C4×D4C2314yes—
424C2×C4×D4C2314yes—
425C2×C4×D4C2312yes—
426C2×C4×D4C2312yes—
427C2×C4×D4C2311yescharacteristic
428C2×C4×D4C2312yes—
429C2×C4×D4C2312yes—
430C2×C4×D4C2312yes—
431C2×C4×D4C2314yes—
432C2×C4×D4C2312yes—
433C2×C4×D4C2312yes—
434C2×C4×D4C2312yes—
435C2×C4×D4C2312yes—
436C2×#117C2311yescharacteristic
437C2×#117C2312yes—
438C2×#117C2311yescharacteristic
439C2×#117C2312yes—
440C2×#117C2311yescharacteristic
441C22×C4⋊C4C2311yescharacteristic
442C22×C4⋊C4C2311yescharacteristic
443C22×C4⋊C4C2312yes—
444C22×C4⋊C4C2311yescharacteristic
445C22×C4⋊C4C2312yes—
446C22×C22⋊C4C2312yes—
447C22×C22⋊C4C2312yes—
448C22×C22⋊C4C2312yes—
449C22×C22⋊C4C2314yes—
450C22×C42C2311yescharacteristic
451C22×C42C2311yescharacteristic
452C22×C42C2312yes—
453C22×C42C2312yes—
454C22×C42C2312yes—
455C22×C42C2312yes—
456#400C2314yes—
457#400C2314yes—
458#400C2314yes—
459#400C2314yes—
460#399C2314yes—
461#399C2314yes—
462#399C2314yes—
463#399C2314yes—
464#399C2314yes—
465#399C2314yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2314yes—
470#398C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#395C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
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#393C2314yes—
511#393C2314yes—
512#393C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#392C2314yes—
524#392C2314yes—
525#392C2314yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2312yes—
530#391C2312yes—
531#391C2312yes—
532#391C2311yescharacteristic
533#391C2311yescharacteristic
534#391C2312yes—
535#391C2312yes—
536#391C2314yes—
537#391C2312yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2312yes—
542#391C2312yes—
543#390C2314yes—
544#390C2314yes—
545#390C2314yes—
546#390C2312yes—
547#390C2312yes—
548#390C2314yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2312yes—
553#390C2312yes—
554#390C2314yes—
555#390C2314yes—
556#390C2312yes—
557#390C2314yes—
558#390C2314yes—
559#390C2314yes—
560#390C2311yescharacteristic
561#390C2311yescharacteristic
562#390C2311yescharacteristic
563#390C2312yes—
564#390C2312yes—
565#390C2314yes—
566#390C2314yes—
567#390C2311yescharacteristic
568#390C2312yes—
569#390C2312yes—
570#390C2312yes—
571#390C2314yes—
572#389C2311yescharacteristic
573#389C2311yescharacteristic
574#389C2312yes—
575#389C2314yes—
576#389C2314yes—
577#389C2312yes—
578#389C2311yescharacteristic
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2314yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2311yescharacteristic
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2314yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2312yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2312yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2312yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#388C2314yes—
623#388C2314yes—
624#388C2312yes—
625#388C2312yes—
626#388C2314yes—
627#388C2312yes—
628#388C2314yes—
629#387C2312yes—
630#387C2312yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#387C2314yes—
651#387C2312yes—
652#386C2312yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2312yes—
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#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#386C2314yes—
674#386C2314yes—
675#386C2312yes—
676#386C2312yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2312yes—
682#386C2312yes—
683#386C2314yes—
684#386C2314yes—
685#386C2312yes—
686#386C2312yes—
687#386C2312yes—
688#386C2312yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2312yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2312yes—
701#385C2312yes—
702#385C2314yes—
703#385C2312yes—
704#385C2314yes—
705#385C2314yes—
706#385C2312yes—
707#385C2314yes—
708#385C2312yes—
709#384C2312yes—
710#384C2312yes—
711#384C2311yescharacteristic
712#383C2312yes—
713#382C2311yescharacteristic
714#382C2314yes—
715#382C2314yes—
716#382C2312yes—
717#382C2314yes—
718#382C2312yes—
719#382C2311yescharacteristic
720#382C2312yes—
721#381C2314yes—
722#381C2314yes—
723#381C2314yes—
724#381C2314yes—
725#381C2312yes—
726#381C2314yes—
727#381C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2314yes—
731#380C2312yes—
732#380C2314yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2311yescharacteristic
737#380C2311yescharacteristic
738#380C2312yes—
739#380C2312yes—
740#380C2314yes—
741#380C2311yescharacteristic
742#380C2312yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2314yes—
746#380C2314yes—
747#380C2314yes—
748#380C2312yes—
749#380C2312yes—
750#379C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2314yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2314yes—
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—
817#376C2314yes—
818#376C2312yes—
819C2×#95C2312yes—
820C2×#95C2314yes—
821C2×#95C2312yes—
822C2×#95C2314yes—
823C2×#95C2312yes—
824C43C2312yes—
825C43C2311yescharacteristic
826C25C2412yes—
827C2×#41—28no—
828C2×#41—24no—
829C2×#41—24no—
830C2×#41—28no—
831C2×#41—28no—
832C2×#41—48no—
833C2×#41—48no—
834C2×#41—42no—
835C2×#41—44no—
836C2×#41—44no—
837C2×#41—44no—
838C2×#41—44no—
839C2×#41—48no—
840C2×#41—44no—
841C2×#41—44no—
842C22×Q8C2412yes—
843C22×Q8C2411yescharacteristic
844C22×Q8C2412yes—
845C22×Q8C2414yes—
846C22×D4—24no—
847C22×D4—24no—
848C22×D4—42no—
849C22×D4C2411yescharacteristic
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2411yescharacteristic
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2412yes—
856C22×D4C2412yes—
857C22×D4C2414yes—
858C22×D4C2412yes—
859C22×D4C2411yescharacteristic
860C22×D4C2411yescharacteristic
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2414yes—
865C22×D4C2414yes—
866C22×D4C2414yes—
867C22×D4C2414yes—
868C22×D4C2414yes—
869C22×D4C2414yes—
870C22×D4C2412yes—
871C23×C4—28no—
872C23×C4—44no—
873C23×C4—44no—
874C23×C4C2411yescharacteristic
875C23×C4C2412yes—
876C23×C4C2411yescharacteristic
877C23×C4C2412yes—
878C23×C4C2412yes—
879C23×C4C2412yes—
880C23×C4C2412yes—
881C23×C4C2412yes—
882C23×C4C2411yescharacteristic
883C23×C4C2411yescharacteristic
884C23×C4C2411yescharacteristic
885C23×C4C2414yes—
886C23×C4C2412yes—
887C23×C4C2412yes—
888C23×C4C2412yes—
889C23×C4C2412yes—
890C23×C4C2412yes—
891C23×C4C2412yes—
892C23×C4C2414yes—
893C23×C4C2414yes—
894C23×C4C2414yes—
895C23×C4C2411yescharacteristic
896C23×C4C2412yes—
897C23×C4C2414yes—
898C23×C4C2412yes—
899C4⋊Q8—28no—
900C4⋊Q8—24no—
901C4⋊Q8—24no—
902C4⋊Q8—44no—
903C4⋊Q8—44no—
904#127—28no—
905#127—216no—
906#127—28no—
907#127—24no—
908#127—44no—
909#126—28no—
910#126—48no—
911#125—24no—
912#125—48no—
913#124—24no—
914#124—28no—
915#124—44no—
916#124—44no—
917#124—44no—
918#124—44no—
919#124—48no—
920#124—48no—
921#123—216no—
922#123—28no—
923#123—28no—
924#123—48no—
925#123—48no—
926#123—48no—
927C22⋊Q8—28no—
928C22⋊Q8—28no—
929C22⋊Q8—24no—
930C22⋊Q8—28no—
931C22⋊Q8—48no—
932C22⋊Q8—44no—
933C22⋊Q8—44no—
934C22⋊Q8—44no—
935C22⋊Q8—44no—
936C22⋊Q8—48no—
937C22⋊Q8—44no—
938#121—28no—
939#121—216no—
940#121—28no—
941#121—24no—
942#121—28no—
943#121—28no—
944#121—28no—
945#121—24no—
946#121—28no—
947#121—216no—
948#121—28no—
949#121—48no—
950#121—48no—
951#121—48no—
952#121—48no—
953#121—48no—
954#121—44no—
955#121—44no—
956#121—44no—
957#121—44no—
958#121—44no—
959#121—44no—
960#121—44no—
961#121—44no—
962#121#4118yescomplemented
963#120—28no—
964#120—216no—
965#120—48no—
966#120—48no—
967C4×Q8—28no—
968C4×Q8—24no—
969C4×Q8—42no—
970C4×Q8—44no—
971C4×Q8—44no—
972C4×D4—24no—
973C4×D4—24no—
974C4×D4—28no—
975C4×D4—24no—
976C4×D4—24no—
977C4×D4—24no—
978C4×D4—24no—
979C4×D4—216no—
980C4×D4—216no—
981C4×D4—216no—
982C4×D4—28no—
983C4×D4—24no—
984C4×D4—24no—
985C4×D4—24no—
986C4×D4—44no—
987C4×D4—42no—
988C4×D4—48no—
989C4×D4—42no—
990C4×D4—42no—
991C4×D4—42no—
992C4×D4—48no—
993C4×D4—44no—
994C4×D4—44no—
995C4×D4—44no—
996C4×D4—44no—
997C4×D4—44no—
998C4×D4—44no—
999C4×D4—44no—
1000C4×D4—44no—
1001C4×D4—44no—
1002C4×D4—44no—
1003C4×D4—44no—
1004C4×D4—44no—
1005C4×D4—48no—
1006C4×D4—44no—
1007C4×D4—44no—
1008C4×D4—48no—
1009C4×D4—48no—
1010C4×D4—48no—
1011C4×D4—48no—
1012C4×D4—48no—
1013#117—24no—
1014#117—44no—
1015#117—42no—
1016#117—44no—
1017#117#4118yescomplemented
1018C2×C4⋊C4—24no—
1019C2×C4⋊C4—24no—
1020C2×C4⋊C4—42no—
1021C2×C4⋊C4—44no—
1022C2×C4⋊C4—44no—
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2411yescharacteristic
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2411yescharacteristic
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2411yescharacteristic
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2411yescharacteristic
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2411yescharacteristic
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2414yes—
1066C2×C4⋊C4C2414yes—
1067C2×C4⋊C4C2414yes—
1068C2×C4⋊C4C2412yes—
1069C2×C4⋊C4C2412yes—
1070C2×C4⋊C4C2411yescharacteristic
1071C2×C4⋊C4C2411yescharacteristic
1072C2×C4⋊C4C2411yescharacteristic
1073C2×C4⋊C4C2411yescharacteristic
1074C2×C22⋊C4—28no—
1075C2×C22⋊C4—44no—
1076C2×C22⋊C4—44no—
1077C2×C22⋊C4—48no—
1078C2×C22⋊C4C2411yescharacteristic
1079C2×C22⋊C4C2411yescharacteristic
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2411yescharacteristic
1089C2×C22⋊C4C2411yescharacteristic
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2411yescharacteristic
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2411yescharacteristic
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2412yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2412yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2414yes—
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2412yes—
1142C2×C22⋊C4C2412yes—
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2412yes—
1145C2×C22⋊C4C2412yes—
1146C2×C42—24no—
1147C2×C42—24no—
1148C2×C42—44no—
1149C2×C42—44no—
1150C2×C42—44no—
1151C2×C42—44no—
1152C2×C42C2411yescharacteristic
1153C2×C42C2412yes—
1154C2×C42C2411yescharacteristic
1155C2×C42C2411yescharacteristic
1156C2×C42C2411yescharacteristic
1157C2×C42C2411yescharacteristic
1158C2×C42C2411yescharacteristic
1159C2×C42C2411yescharacteristic
1160C2×C42C2412yes—
1161C2×C42C2411yescharacteristic
1162C2×C42C2411yescharacteristic
1163C2×C42C2411yescharacteristic
1164C2×C42C2412yes—
1165C2×C42C2411yescharacteristic
1166C2×C42C2412yes—
1167C2×C42C2412yes—
1168C2×C42C2414yes—
1169C2×C42C2412yes—
1170C2×C42C2412yes—
1171C2×C42C2414yes—
1172C2×C42C2412yes—
1173C2×C42C2412yes—
1174C2×C42C2412yes—
1175C2×C42C2412yes—
1176C2×C42C2414yes—
1177C2×C42C2412yes—
1178C2×C42C2412yes—
1179C2×C42C2414yes—
1180C2×C42C2412yes—
1181C2×C42C2412yes—
1182C2×C42C2411yescharacteristic
1183C2×C42C2412yes—
1184C2×C42C2412yes—
1185C2×C42C2411yescharacteristic
1186#95C2411yescharacteristic
1187#95C2414yes—
1188#95C2412yes—
1189#95C2411yescharacteristic
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2411yescharacteristic
1210#95C2412yes—
1211#95C2411yescharacteristic
1212#95C2411yescharacteristic
1213#95C2412yes—
1214#95C2412yes—
1215#95C2411yescharacteristic
1216#95C2412yes—
1217#95C2412yes—
1218#95C2412yes—
1219#95C2412yes—
1220#95C2412yes—
1221#95C2412yes—
1222#95C2412yes—
1223#95C2414yes—
1224#95C2412yes—
1225#95C2414yes—
1226#95C2414yes—
1227#95C2414yes—
1228#95C2412yes—
1229#95C2414yes—
1230#95C2412yes—
1231#95C2414yes—
1232#95C2412yes—
1233#95C2412yes—
1234#95C2414yes—
1235#95C2414yes—
1236#95C2414yes—
1237#95C2414yes—
1238#95C2412yes—
1239#95C2414yes—
1240#95C2414yes—
1241#95C2414yes—
1242#95C2414yes—
1243#95C2414yes—
1244C24—24no—
1245C24—24no—
1246C24—24no—
1247C24—42no—
1248C24—42no—
1249C24—42no—
1250C24—42no—
1251C24C2512yes—
1252C24C2514yes—
1253C24C2511yescharacteristic
1254C24C2512yes—
1255C24C2511yescharacteristic
1256C24C2512yes—
1257#41—416no—
1258#41—816no—
1259#41—816no—
1260#41—832no—
1261#41—816no—
1262C2×Q8—24no—
1263C2×Q8—24no—
1264C2×Q8—22no—
1265C2×Q8—22no—
1266C2×Q8—24no—
1267C2×Q8—24no—
1268C2×Q8—24no—
1269C2×Q8—24no—
1270C2×Q8—22no—
1271C2×Q8—28no—
1272C2×Q8—44no—
1273C2×Q8—44no—
1274C2×D4—22no—
1275C2×D4—22no—
1276C2×D4—24no—
1277C2×D4—28no—
1278C2×D4—24no—
1279C2×D4—24no—
1280C2×D4—28no—
1281C2×D4—28no—
1282C2×D4—24no—
1283C2×D4—24no—
1284C2×D4—28no—
1285C2×D4—24no—
1286C2×D4—28no—
1287C2×D4—28no—
1288C2×D4—28no—
1289C2×D4—28no—
1290C2×D4—22no—
1291C2×D4—28no—
1292C2×D4—28no—
1293C2×D4—24no—
1294C2×D4—22no—
1295C2×D4—24no—
1296C2×D4—24no—
1297C2×D4—28no—
1298C2×D4—22no—
1299C2×D4—22no—
1300C2×D4—22no—
1301C2×D4—22no—
1302C2×D4—22no—
1303C2×D4—24no—
1304C2×D4—28no—
1305C2×D4—24no—
1306C2×D4—24no—
1307C2×D4—24no—
1308C2×D4—24no—
1309C2×D4—42no—
1310C2×D4—42no—
1311C2×D4—42no—
1312C2×D4—42no—
1313C2×D4—44no—
1314C2×D4—42no—
1315C2×D4—41no—
1316C2×D4—44no—
1317C2×D4—42no—
1318C2×D4—42no—
1319C2×D4—44no—
1320C2×D4—42no—
1321C2×D4—44no—
1322C2×D4—44no—
1323C2×D4—44no—
1324C2×D4—44no—
1325C2×D4—44no—
1326C2×D4—44no—
1327C2×D4—44no—
1328C2×D4—44no—
1329C2×D4—44no—
1330C2×D4—44no—
1331C2×D4—44no—
1332C2×D4—44no—
1333C2×D4—44no—
1334C2×D4—42no—
1335C2×D4—44no—
1336C2×D4—44no—
1337C2×D4—416no—
1338C2×D4C2×#4114yes—
1339C2×D4C2×#4118yes—
1340C2×D4H(5,𝔽2)14yes—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—22no—
1345C22×C4—24no—
1346C22×C4—24no—
1347C22×C4—28no—
1348C22×C4—24no—
1349C22×C4—24no—
1350C22×C4—22no—
1351C22×C4—24no—
1352C22×C4—22no—
1353C22×C4—24no—
1354C22×C4—24no—
1355C22×C4—22no—
1356C22×C4—22no—
1357C22×C4—24no—
1358C22×C4—24no—
1359C22×C4—24no—
1360C22×C4—22no—
1361C22×C4—24no—
1362C22×C4—24no—
1363C22×C4—24no—
1364C22×C4—24no—
1365C22×C4—22no—
1366C22×C4—24no—
1367C22×C4—24no—
1368C22×C4—24no—
1369C22×C4—24no—
1370C22×C4—24no—
1371C22×C4—24no—
1372C22×C4—24no—
1373C22×C4—28no—
1374C22×C4—28no—
1375C22×C4—22no—
1376C22×C4—22no—
1377C22×C4—24no—
1378C22×C4—28no—
1379C22×C4—42no—
1380C22×C4—42no—
1381C22×C4—42no—
1382C22×C4—42no—
1383C22×C4—42no—
1384C22×C4—42no—
1385C22×C4—42no—
1386C22×C4—42no—
1387C22×C4—42no—
1388C22×C4—44no—
1389C22×C4—42no—
1390C22×C4—44no—
1391C22×C4—42no—
1392C22×C4—42no—
1393C22×C4—42no—
1394C22×C4—42no—
1395C22×C4—44no—
1396C22×C4—44no—
1397C22×C4—44no—
1398C22×C4—44no—
1399C22×C4—44no—
1400C22×C4—44no—
1401C22×C4—41no—
1402C22×C4—41no—
1403C22×C4—42no—
1404C22×C4—42no—
1405C22×C4—41no—
1406C22×C4—42no—
1407C22×C4—42no—
1408C22×C4—41no—
1409C22×C4—42no—
1410C22×C4—42no—
1411C22×C4—44no—
1412C22×C4—44no—
1413C22×C4—44no—
1414C22×C4—816no—
1415C22×C4C2×#4114yes—
1416C22×C4C2×#4114yes—
1417C22×C4C2511yescharacteristic
1418C22×C4C2511yescharacteristic
1419C22×C4C2511yescharacteristic
1420C22×C4C2511yescharacteristic
1421C22×C4C2512yes—
1422C22×C4C2512yes—
1423C22×C4C2512yes—
1424C22×C4C2514yes—
1425C22×C4C2511yescharacteristic
1426C22×C4C2512yes—
1427C22×C4C2514yes—
1428C22×C4C2512yes—
1429C22×C4C2512yes—
1430C22×C4C2512yes—
1431C22×C4C2512yes—
1432C22×C4C2514yes—
1433C22×C4C2511yescharacteristic
1434C22×C4C2512yes—
1435C22×C4C2511yescharacteristic
1436C22×C4C2511yescharacteristic
1437C22×C4C2511yescharacteristic
1438C22×C4C2512yes—
1439C22×C4C2512yes—
1440C22×C4C2512yes—
1441C22×C4C2511yescharacteristic
1442C22×C4C2512yes—
1443C22×C4C2511yescharacteristic
1444C22×C4C2511yescharacteristic
1445C22×C4C2511yescharacteristic
1446C4⋊C4—22no—
1447C4⋊C4—24no—
1448C4⋊C4—24no—
1449C4⋊C4—28no—
1450C4⋊C4—28no—
1451C4⋊C4—22no—
1452C4⋊C4—24no—
1453C4⋊C4—22no—
1454C4⋊C4—28no—
1455C4⋊C4—24no—
1456C4⋊C4—24no—
1457C4⋊C4—22no—
1458C4⋊C4—24no—
1459C4⋊C4—22no—
1460C4⋊C4—22no—
1461C4⋊C4—22no—
1462C4⋊C4—24no—
1463C4⋊C4—24no—
1464C4⋊C4—22no—
1465C4⋊C4—22no—
1466C4⋊C4—24no—
1467C4⋊C4—24no—
1468C4⋊C4—22no—
1469C4⋊C4—24no—
1470C4⋊C4—28no—
1471C4⋊C4—24no—
1472C4⋊C4—24no—
1473C4⋊C4—28no—
1474C4⋊C4—24no—
1475C4⋊C4—42no—
1476C4⋊C4—44no—
1477C4⋊C4—44no—
1478C4⋊C4—42no—
1479C4⋊C4—42no—
1480C4⋊C4—42no—
1481C4⋊C4—42no—
1482C4⋊C4—41no—
1483C4⋊C4—44no—
1484C4⋊C4—44no—
1485C4⋊C4—44no—
1486C4⋊C4—44no—
1487C4⋊C4—42no—
1488C4⋊C4—42no—
1489C4⋊C4—44no—
1490C4⋊C4—44no—
1491C4⋊C4—44no—
1492C4⋊C4—44no—
1493C4⋊C4C2×#4114yes—
1494C4⋊C4C2×#4114yes—
1495C4⋊C4C2×#4114yes—
1496C4⋊C4H(5,𝔽2)14yes—
1497C22⋊C4—24no—
1498C22⋊C4—22no—
1499C22⋊C4—24no—
1500C22⋊C4—22no—
1501C22⋊C4—24no—
1502C22⋊C4—28no—
1503C22⋊C4—28no—
1504C22⋊C4—24no—
1505C22⋊C4—28no—
1506C22⋊C4—22no—
1507C22⋊C4—24no—
1508C22⋊C4—22no—
1509C22⋊C4—28no—
1510C22⋊C4—28no—
1511C22⋊C4—24no—
1512C22⋊C4—24no—
1513C22⋊C4—28no—
1514C22⋊C4—28no—
1515C22⋊C4—28no—
1516C22⋊C4—24no—
1517C22⋊C4—24no—
1518C22⋊C4—24no—
1519C22⋊C4—24no—
1520C22⋊C4—24no—
1521C22⋊C4—24no—
1522C22⋊C4—24no—
1523C22⋊C4—24no—
1524C22⋊C4—28no—
1525C22⋊C4—28no—
1526C22⋊C4—22no—
1527C22⋊C4—24no—
1528C22⋊C4—22no—
1529C22⋊C4—42no—
1530C22⋊C4—42no—
1531C22⋊C4—42no—
1532C22⋊C4—42no—
1533C22⋊C4—42no—
1534C22⋊C4—44no—
1535C22⋊C4—42no—
1536C22⋊C4—42no—
1537C22⋊C4—44no—
1538C22⋊C4—42no—
1539C22⋊C4—42no—
1540C22⋊C4—44no—
1541C22⋊C4—44no—
1542C22⋊C4—44no—
1543C22⋊C4—42no—
1544C22⋊C4—44no—
1545C22⋊C4—44no—
1546C22⋊C4—42no—
1547C22⋊C4—44no—
1548C22⋊C4—44no—
1549C22⋊C4—44no—
1550C22⋊C4—44no—
1551C22⋊C4—44no—
1552C22⋊C4—44no—
1553C22⋊C4—44no—
1554C22⋊C4—44no—
1555C22⋊C4—44no—
1556C22⋊C4—44no—
1557C22⋊C4—44no—
1558C22⋊C4—42no—
1559C22⋊C4—42no—
1560C22⋊C4—44no—
1561C22⋊C4—44no—
1562C22⋊C4—44no—
1563C22⋊C4C2×#4118yes—
1564C22⋊C4C2×#4118yes—
1565C42—22no—
1566C42—22no—
1567C42—24no—
1568C42—28no—
1569C42—22no—
1570C42—22no—
1571C42—22no—
1572C42—22no—
1573C42—22no—
1574C42—22no—
1575C42—22no—
1576C42—22no—
1577C42—24no—
1578C42—24no—
1579C42—24no—
1580C42—24no—
1581C42—24no—
1582C42—22no—
1583C42—42no—
1584C42—42no—
1585C42—42no—
1586C42—42no—
1587C42—42no—
1588C42—42no—
1589C42—42no—
1590C42—42no—
1591C42—42no—
1592C42—41no—
1593C42—44no—
1594C42—42no—
1595C42—44no—
1596C42—44no—
1597C42C2×#4118yes—
1598C42H(5,𝔽2)14yes—
1599C23—21no—
1600C23—22no—
1601C23—22no—
1602C23—21no—
1603C23—22no—
1604C23—22no—
1605C23—21no—
1606C23—22no—
1607C23—22no—
1608C23—21no—
1609C23—21no—
1610C23—21no—
1611C23—22no—
1612C23—22no—
1613C23—21no—
1614C23—21no—
1615C23—21no—
1616C23—22no—
1617C23—21no—
1618C23—22no—
1619C23—22no—
1620C23—21no—
1621C23—22no—
1622C23—21no—
1623C23—22no—
1624C23—24no—
1625C23—22no—
1626C23—24no—
1627C23—22no—
1628C23—22no—
1629C23—24no—
1630C23—24no—
1631C23—24no—
1632C23—22no—
1633C23—24no—
1634C23—22no—
1635C23—22no—
1636C23—24no—
1637C23—48no—
1638C23—48no—
1639C23—48no—
1640C23—84no—
1641C23—84no—
1642C23—84no—
1643C23—84no—
1644C23C22×#4112yes—
1645C23C22×#4114yes—
1646C23C22×#4112yes—
1647C23C2×H(5,𝔽2)14yes—
1648C23C2611yescharacteristic
1649Q8—48no—
1650Q8—44no—
1651Q8—48no—
1652Q8—88no—
1653D4—28no—
1654D4—28no—
1655D4—48no—
1656D4—416no—
1657D4—48no—
1658D4—416no—
1659D4—416no—
1660D4—48no—
1661D4—44no—
1662D4—48no—
1663D4—48no—
1664D4—44no—
1665D4—48no—
1666D4—48no—
1667D4—88no—
1668D4—88no—
1669D4—84no—
1670D4—88no—
1671D4—88no—
1672D4—88no—
1673D4—88no—
1674D4—88no—
1675C2×C4—22no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—21no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—22no—
1682C2×C4—21no—
1683C2×C4—21no—
1684C2×C4—21no—
1685C2×C4—21no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—21no—
1690C2×C4—22no—
1691C2×C4—28no—
1692C2×C4—28no—
1693C2×C4—21no—
1694C2×C4—21no—
1695C2×C4—21no—
1696C2×C4—21no—
1697C2×C4—22no—
1698C2×C4—24no—
1699C2×C4—21no—
1700C2×C4—22no—
1701C2×C4—22no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—24no—
1705C2×C4—22no—
1706C2×C4—21no—
1707C2×C4—21no—
1708C2×C4—21no—
1709C2×C4—21no—
1710C2×C4—21no—
1711C2×C4—22no—
1712C2×C4—21no—
1713C2×C4—21no—
1714C2×C4—22no—
1715C2×C4—22no—
1716C2×C4—22no—
1717C2×C4—22no—
1718C2×C4—22no—
1719C2×C4—22no—
1720C2×C4—22no—
1721C2×C4—22no—
1722C2×C4—22no—
1723C2×C4—22no—
1724C2×C4—24no—
1725C2×C4—24no—
1726C2×C4—24no—
1727C2×C4—22no—
1728C2×C4—24no—
1729C2×C4—22no—
1730C2×C4—22no—
1731C2×C4—22no—
1732C2×C4—24no—
1733C2×C4—24no—
1734C2×C4—21no—
1735C2×C4—21no—
1736C2×C4—21no—
1737C2×C4—22no—
1738C2×C4—21no—
1739C2×C4—24no—
1740C2×C4—21no—
1741C2×C4—22no—
1742C2×C4—22no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—22no—
1746C2×C4—21no—
1747C2×C4—22no—
1748C2×C4—22no—
1749C2×C4—21no—
1750C2×C4—48no—
1751C2×C4—48no—
1752C2×C4—48no—
1753C2×C4—44no—
1754C2×C4—48no—
1755C2×C4—48no—
1756C2×C4—44no—
1757C2×C4—48no—
1758C2×C4—84no—
1759C2×C4—84no—
1760C2×C4—84no—
1761C2×C4—84no—
1762C2×C4—82no—
1763C2×C4—82no—
1764C2×C4—84no—
1765C2×C4—84no—
1766C2×C4—88no—
1767C2×C4—88no—
1768C2×C4—88no—
1769C2×C4—84no—
1770C2×C4—88no—
1771C2×C4—84no—
1772C2×C4—164no—
1773C2×C4C22×#4114yes—
1774C2×C4C22×#4112yes—
1775C2×C4C22×#4114yes—
1776C2×C4C22×#4114yes—
1777C2×C4C22×#4112yes—
1778C2×C4C22×#4112yes—
1779C2×C4C22×#4112yes—
1780C2×C4C2×H(5,𝔽2)12yes—
1781C2×C4C2×H(5,𝔽2)14yes—
1782C2×C4C2×H(5,𝔽2)12yes—
1783C2×C4C2×H(5,𝔽2)12yes—
1784C2×C4C2×H(5,𝔽2)12yes—
1785C2×C4C2×H(5,𝔽2)12yes—
1786C2×C4#58512yes—
1787C22—22no—
1788C22—24no—
1789C22—24no—
1790C22—22no—
1791C22—24no—
1792C22—22no—
1793C22—24no—
1794C22—24no—
1795C22—22no—
1796C22—22no—
1797C22—24no—
1798C22—22no—
1799C22—42no—
1800C22—41no—
1801C22—41no—
1802C22—42no—
1803C22—41no—
1804C22—42no—
1805C22—41no—
1806C22—41no—
1807C22—42no—
1808C22—42no—
1809C22—41no—
1810C22—41no—
1811C22—42no—
1812C22—41no—
1813C22—42no—
1814C22—42no—
1815C22—42no—
1816C22—44no—
1817C22—42no—
1818C22—44no—
1819C22—42no—
1820C22—44no—
1821C22—42no—
1822C22—44no—
1823C22—44no—
1824C22—42no—
1825C22—44no—
1826C22—42no—
1827C22—42no—
1828C22—44no—
1829C22—816no—
1830C22C23×#4111yescharacteristic
1831C22C23×#4111yescharacteristic
1832C22C22×H(5,𝔽2)11yescharacteristic
1833C22C22×H(5,𝔽2)11yescharacteristic
1834C22C22×H(5,𝔽2)11yescharacteristic
1835C22C2×#58511yescharacteristic
1836C222−1+611yescharacteristic
1837C4—24no—
1838C4—24no—
1839C4—22no—
1840C4—24no—
1841C4—22no—
1842C4—22no—
1843C4—22no—
1844C4—24no—
1845C4—41no—
1846C4—42no—
1847C4—41no—
1848C4—42no—
1849C4—42no—
1850C4—42no—
1851C4—44no—
1852C4—42no—
1853C4—41no—
1854C4—42no—
1855C4—44no—
1856C4—41no—
1857C4—42no—
1858C4—42no—
1859C4—44no—
1860C4—41no—
1861C4—42no—
1862C4—41no—
1863C4—41no—
1864C4#350814yes—
1865C4#351914yes—
1866C2—42no—
1867C2—44no—
1868C2—44no—
1869C2—42no—
1870C2—82no—
1871C2—84no—
1872C2#41211yescharacteristic
1873C2C2×#351911yescharacteristic
1874C2C2×#350811yescharacteristic
1875C2#6292511yescharacteristic
1876C2#6298411yescharacteristic
1877C2#6298511yescharacteristic
1878C2#6301211yescharacteristic
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. #59691C2semidirect
2. #59647C2semidirect
3. #59592C2semidirect
4. #59129C2semidirect
5. #59099C2semidirect
6. #59057C2semidirect
7. #59051C2semidirect
8. #59049C2semidirect
9. #59024C2semidirect
10. #44178C2semidirect
11. #44161C2semidirect
12. #44128C2semidirect
13. #40103C2semidirect
14. #40092C2semidirect
15. #40007C2semidirect
16. #39862C2semidirect
17. #39532C2semidirect
18. #39212C2semidirect
19. #36561C2semidirect
20. #36504C2semidirect
21. #36454C2semidirect
22. #36406C2semidirect
23. #36288C2semidirect
24. #36153C2semidirect
25. #36149C2semidirect
26. #36149C2semidirect
27. #36147C2semidirect
28. #35698C2semidirect
29. #34937C2semidirect
30. #34936C2semidirect
31. #34925C2semidirect
32. #34330C2semidirect
33. #34233C2semidirect
34. C4×#553C2semidirect
35. C4×#546C2semidirect
36. C2×#556C22semidirect
37. C2×#554C22semidirect
46. C2×#532C22semidirect
47. C2×#532C22semidirect
52. #2862C22semidirect
53. #2862C22semidirect
55. #2857C22semidirect
56. #2857C22semidirect
57. #2857C22semidirect
58. #2855C22semidirect
59. #2850C22semidirect
61. #2797C22semidirect
62. #2797C22semidirect
63. #2786C22semidirect
64. #2773C22semidirect
65. #2761C22semidirect
66. #2753C22semidirect
67. #2751C22semidirect
68. #2741C22semidirect
69. #2740C22semidirect
70. #2730C22semidirect
71. #2730C22semidirect
79. #2673C22semidirect
82. #2667C22semidirect
83. #2649C22semidirect
84. #2636C22semidirect
85. #2612C22semidirect
86. #2603C22semidirect
87. #2600C22semidirect
88. #2595C22semidirect
89. #2589C22semidirect
90. #2575C22semidirect
92. #2564C22semidirect
95. #2556C22semidirect
96. #2555C22semidirect
97. #2553C22semidirect
98. #2553C22semidirect
99. #2551C22semidirect
100. #2548C22semidirect
101. #2548C22semidirect
103. #2546C22semidirect
104. #2545C22semidirect
107. #2543C22semidirect
112. #2541C22semidirect
113. #2541C22semidirect
117. #2540C22semidirect
120. #2536C22semidirect
122. #2535C22semidirect
123. #2517C22semidirect
124. #2513C22semidirect
125. #2511C22semidirect
126. #2508C22semidirect
127. #2506C22semidirect
128. #2504C22semidirect
130. #2499C22semidirect
132. #2492C22semidirect
133. #2491C22semidirect
134. #2491C22semidirect
135. #2490C22semidirect
136. #2490C22semidirect
137. #2489C22semidirect
139. #2479C22semidirect
141. #2467C22semidirect
142. #2467C22semidirect
144. #2460C22semidirect
145. #2459C22semidirect
148. #2456C22semidirect
150. #2454C22semidirect
152. #2450C22semidirect
153. #2448C22semidirect
155. #2447C22semidirect
156. #2447C22semidirect
157. #2447C22semidirect
158. #2447C22semidirect
159. #2444C22semidirect
168. #2428C22semidirect
169. #2428C22semidirect
172. #2427C22semidirect
173. #2427C22semidirect
174. #2427C22semidirect
175. #2427C22semidirect
176. #2427C22semidirect
177. #2426C22semidirect
181. #2423C22semidirect
182. #2421C22semidirect
184. #2420C22semidirect
185. #2420C22semidirect
186. #2420C22semidirect
187. #2420C22semidirect
189. #2417C22semidirect
191. #2416C22semidirect
192. #2416C22semidirect
193. #2416C22semidirect
200. #2407C22semidirect
201. #2407C22semidirect
204. #2392C22semidirect
205. #2388C22semidirect
207. #2373C22semidirect
208. #2370C22semidirect
209. #2369C22semidirect
213. #2366C22semidirect
214. #2365C22semidirect
215. #2365C22semidirect
218. #2364C22semidirect
219. #2364C22semidirect
223. #2363C22semidirect
224. #2361C22semidirect
225. #2361C22semidirect
226. #2361C22semidirect
228. #2360C22semidirect
229. #2360C22semidirect
230. #2360C22semidirect
235. #2357C22semidirect
236. #2357C22semidirect
237. #2355C22semidirect
238. #2355C22semidirect
239. #2354C22semidirect
240. #2353C22semidirect
241. #2353C22semidirect
245. #2349C22semidirect
246. #2349C22semidirect
250. #2345C22semidirect
256. #2339C22semidirect
257. #2339C22semidirect
261. #2333C22semidirect
262. #2333C22semidirect
263. #2328C22semidirect
264. #2318C22semidirect
267. C4×#127C22semidirect
268. C4×#125C22semidirect
269. C4×#126C22semidirect
272. C4×C22⋊Q8C22semidirect
273. C4×C22⋊Q8C22semidirect
281. C4×#121C22semidirect
282. C4×#121C22semidirect
283. C4×#121C22semidirect
284. C4×#121C22semidirect
285. C4×#121C22semidirect
288. #2297C22semidirect
289. #2295C22semidirect
291. #2275C22semidirect
294. C42×D4C22semidirect
295. C42×D4C22semidirect
297. C2×C4×C4⋊C4C22semidirect
962. #121#41semidirect
1017. #117#41semidirect

Maximal subgroups

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

subgroupindex
#596912
#596472
#595922
#591292
#590992
#590572
#590512
#590492
#590242
#441782
#441612
#441282
#401032
#400922
#400072
#398622
#395322
#392122
#365612
#365042
#364542
#364062
#362882
#361532
#361492
#361472
#356982
#349372
#349362
#349252
#343302
#342332
C4×#5532
C4×#5462