Finite Group Databasebeta

← #8466944

Subgroups — #8466944

Order 512.

5324 conjugacy classes of subgroups.

The subgroup lattice has 1858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59234C211yesmaximal, characteristic, complemented
3#59230C211yesmaximal, characteristic, complemented
4#56018C214yesmaximal, complemented
5#54894C214yesmaximal, complemented
6#54862C214yesmaximal, complemented
7#53106C212yesmaximal, complemented
8#53046C212yesmaximal, complemented
9#50003C214yesmaximal, complemented
10#46345C212yesmaximal, complemented
11#45601C212yesmaximal, complemented
12#45208C212yesmaximal, complemented
13#44946C212yesmaximal, complemented
14#42977C212yesmaximal, complemented
15#42648C212yesmaximal, complemented
16#42643C212yesmaximal, complemented
17#42592C212yesmaximal, complemented
18#39887C212yesmaximal, complemented
19#39725C211yesmaximal, characteristic, complemented
20#39725C211yesmaximal, characteristic, complemented
21#39506C211yesmaximal, characteristic, complemented
22#39341C211yesmaximal, characteristic, complemented
23#39201C212yesmaximal, complemented
24#38216C212yesmaximal, complemented
25#37656C212yesmaximal, complemented
26#37640C211yesmaximal, characteristic, complemented
27#37334C212yesmaximal, complemented
28#37271C212yesmaximal, complemented
29#36270C211yesmaximal, characteristic, complemented
30#36211C211yesmaximal, characteristic, complemented
31#36101C211yesmaximal, characteristic, complemented
32#35198C211yesmaximal, characteristic, complemented
33#35172C211yesmaximal, characteristic, complemented
34#34929C211yesmaximal, characteristic, complemented
35#34681C211yesmaximal, characteristic, complemented
36C2×#552C2212yescomplemented
37C2×#550C2211yescharacteristic
38C2×#550C2211yescharacteristic, complemented
39C2×#547C2212yescomplemented
40C2×#542C2212yescomplemented
41C2×#537C2212yescomplemented
42C2×#533C2211yescharacteristic
43C2×#533C2211yescharacteristic, complemented
44C2×#532C2211yescharacteristic
45C2×#525C2212yes—
46C2×#525C2212yes—
47C22×C4×D4C2211yescharacteristic
48#2860C2212yes—
49#2860C2212yescomplemented
50#2859C2211yescharacteristic, complemented
51#2858C2212yes—
52#2856C2211yescharacteristic
53#2856C2211yescharacteristic, complemented
54#2848C2212yes—
55#2848C2212yes—
56#2847C2212yes—
57#2832C2214yescomplemented
58#2828C2214yes—
59#2824C2214yescomplemented
60#2824C2214yescomplemented
61#2820C2214yescomplemented
62#2819C2214yescomplemented
63#2816C2214yescomplemented
64#2813C2214yescomplemented
65#2804C2214yes—
66#2803C2214yes—
67#2784C2214yes—
68#2783C2214yescomplemented
69#2783C2214yescomplemented
70#2782C2214yescomplemented
71#2775C2214yescomplemented
72#2763C2214yescomplemented
73#2753C2214yes—
74#2753C2214yescomplemented
75#2737C2214yescomplemented
76#2733C2214yes—
77#2731C2214yescomplemented
78#2723C2214yescomplemented
79#2723C2214yescomplemented
80#2720C2214yescomplemented
81#2718C2214yescomplemented
82#2718C2214yescomplemented
83#2718C2214yescomplemented
84#2714C2214yes—
85#2714C2214yes—
86#2712C2214yescomplemented
87#2712C2214yescomplemented
88#2711C2214yescomplemented
89#2711C2214yescomplemented
90#2711C2214yescomplemented
91#2710C2214yes—
92#2710C2214yescomplemented
93#2710C2214yescomplemented
94#2706C2214yescomplemented
95#2706C2214yescomplemented
96#2692C2214yes—
97#2686C2214yescomplemented
98#2685C2214yes—
99#2684C2214yes—
100#2682C2214yescomplemented
101#2680C2214yescomplemented
102#2678C2214yes—
103#2678C2214yes—
104#2678C2214yes—
105#2676C2214yes—
106#2676C2214yescomplemented
107#2676C2214yescomplemented
108#2676C2214yescomplemented
109#2675C2214yescomplemented
110#2671C2214yescomplemented
111#2670C2214yes—
112#2670C2214yes—
113#2668C2214yes—
114#2662C2214yescomplemented
115#2661C2214yes—
116#2661C2214yes—
117#2633C2214yescomplemented
118#2626C2214yes—
119#2624C2212yes—
120#2624C2212yescomplemented
121#2624C2214yescomplemented
122#2623C2214yescomplemented
123#2621C2212yescomplemented
124#2620C2214yescomplemented
125#2619C2212yes—
126#2619C2212yes—
127#2616C2212yescomplemented
128#2616C2212yescomplemented
129#2615C2212yescomplemented
130#2601C2214yescomplemented
131#2598C2214yes—
132#2580C2212yes—
133#2580C2212yes—
134#2580C2212yescomplemented
135#2580C2212yescomplemented
136#2574C2214yescomplemented
137#2574C2214yescomplemented
138#2567C2212yescomplemented
139#2566C2214yes—
140#2566C2214yes—
141#2563C2212yes—
142#2563C2212yes—
143#2563C2212yescomplemented
144#2562C2212yescomplemented
145#2558C2214yescomplemented
146#2556C2212yes—
147#2556C2212yescomplemented
148#2555C2214yes—
149#2551C2211yescharacteristic, complemented
150#2551C2211yescharacteristic, complemented
151#2548C2212yes—
152#2548C2212yes—
153#2548C2212yescomplemented
154#2548C2211yescharacteristic, complemented
155#2547C2212yescomplemented
156#2547C2212yescomplemented
157#2546C2211yescharacteristic, complemented
158#2542C2211yescharacteristic
159#2542C2212yes—
160#2542C2212yescomplemented
161#2541C2211yescharacteristic
162#2541C2212yes—
163#2541C2212yes—
164#2540C2212yes—
165#2540C2212yescomplemented
166#2538C2211yescharacteristic
167#2538C2211yescharacteristic
168#2538C2211yescharacteristic
169#2538C2211yescharacteristic
170#2538C2211yescharacteristic
171#2538C2211yescharacteristic
172#2538C2211yescharacteristic, complemented
173#2538C2211yescharacteristic, complemented
174#2537C2212yescomplemented
175#2536C2212yescomplemented
176#2535C2212yes—
177#2518C2214yescomplemented
178#2513C2212yes—
179#2513C2212yes—
180#2513C2212yes—
181#2513C2212yescomplemented
182#2513C2212yescomplemented
183#2508C2212yescomplemented
184#2508C2212yescomplemented
185#2508C2212yescomplemented
186#2506C2212yescomplemented
187#2506C2212yescomplemented
188#2502C2214yescomplemented
189#2500C2214yescomplemented
190#2495C2212yescomplemented
191#2492C2211yescharacteristic
192#2492C2212yescomplemented
193#2492C2211yescharacteristic, complemented
194#2492C2212yescomplemented
195#2491C2212yes—
196#2491C2214yescomplemented
197#2491C2212yescomplemented
198#2491C2212yescomplemented
199#2491C2212yescomplemented
200#2490C2212yes—
201#2490C2212yescomplemented
202#2489C2212yescomplemented
203#2489C2212yescomplemented
204#2474C2214yescomplemented
205#2472C2212yes—
206#2464C2214yes—
207#2464C2212yes—
208#2461C2212yes—
209#2461C2214yescomplemented
210#2456C2214yes—
211#2452C2211yescharacteristic
212#2452C2212yes—
213#2452C2212yescomplemented
214#2452C2212yescomplemented
215#2449C2214yes—
216#2445C2212yes—
217#2445C2212yes—
218#2445C2211yescharacteristic
219#2445C2212yes—
220#2445C2212yes—
221#2445C2212yescomplemented
222#2443C2214yescomplemented
223#2440C2211yescharacteristic
224#2439C2212yes—
225#2433C2212yes—
226#2433C2211yescharacteristic
227#2432C2212yescomplemented
228#2432C2212yescomplemented
229#2429C2211yescharacteristic
230#2429C2211yescharacteristic, complemented
231#2428C2212yes—
232#2428C2211yescharacteristic
233#2428C2212yescomplemented
234#2426C2212yescomplemented
235#2424C2214yes—
236#2424C2212yes—
237#2422C2211yescharacteristic
238#2422C2214yescomplemented
239#2420C2212yes—
240#2420C2212yescomplemented
241#2417C2212yes—
242#2416C2211yescharacteristic
243#2416C2214yescomplemented
244#2416C2212yescomplemented
245#2415C2212yescomplemented
246#2414C2212yes—
247#2414C2212yes—
248#2414C2212yes—
249#2408C2211yescharacteristic
250#2407C2212yes—
251#2407C2212yes—
252#2407C2212yescomplemented
253#2407C2212yescomplemented
254#2407C2212yescomplemented
255#2407C2212yescomplemented
256#2396C2212yes—
257#2396C2212yescomplemented
258#2392C2212yes—
259#2388C2212yes—
260#2379C2214yescomplemented
261#2369C2212yescomplemented
262#2366C2212yes—
263#2363C2212yes—
264#2363C2212yes—
265#2363C2212yescomplemented
266#2361C2212yes—
267#2357C2212yescomplemented
268#2355C2211yescharacteristic, complemented
269#2355C2211yescharacteristic, complemented
270#2354C2211yescharacteristic
271#2352C2212yescomplemented
272D4×C4⋊C4C2211yescharacteristic, complemented
273D4×C4⋊C4C2212yescomplemented
274#2347C2212yescomplemented
275#2345C2212yescomplemented
276#2324C2212yes—
277#2324C2212yescomplemented
278#2324C2214yescomplemented
279#2324C2212yescomplemented
280#2317C2212yes—
281#2314C2212yescomplemented
282#2309C2212yes—
283C4×C4⋊Q8C2212yescomplemented
284C4×C4⋊Q8C2211yescharacteristic, complemented
285C4×#127C2211yescharacteristic
286C4×#127C2211yescharacteristic, complemented
287C4×C22⋊Q8C2211yescharacteristic
288C4×C22⋊Q8C2211yescharacteristic, complemented
289C4×#121C2211yescharacteristic
290C4×#121C2211yescharacteristic
291C4×#120C2212yes—
292#2293C2212yes—
293#2293C2211yescharacteristic
294#2293C2212yescomplemented
295#2285C2211yescharacteristic
296#2285C2211yescharacteristic, complemented
297C42×Q8C2211yescharacteristic, complemented
298C42×D4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×D4C2311yescharacteristic
303C24×C4C2312yes—
304#552—48no—
305#550—44no—
306#550—44no—
307#547—48no—
308#542—48no—
309#537—48no—
310#533—44no—
311#533—44no—
312#532—44no—
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2311yescharacteristic
320C2×C4⋊Q8C2311yescharacteristic
321C2×C4⋊Q8C2311yescharacteristic
322C2×#127C2311yescharacteristic
323C2×#127C2311yescharacteristic
324C2×#127C2312yes—
325C2×#127C2312yes—
326C2×#127C2312yes—
327C2×#127C2311yescharacteristic
328C2×#126C2314yes—
329C2×#126C2314yes—
330C2×#125C2312yes—
331C2×#125C2312yes—
332C2×#125C2312yes—
333C2×#125C2314yes—
334C2×#124C2312yes—
335C2×#124C2314yes—
336C2×#124C2314yes—
337C2×#124C2312yes—
338C2×#124C2314yes—
339C2×#124C2314yes—
340C2×#124C2314yes—
341C2×#124C2314yes—
342#525—48no—
343#525—48no—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2312yes—
348C2×#123C2312yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2311yescharacteristic
355C2×C22⋊Q8C2311yescharacteristic
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2311yescharacteristic
361C2×C22⋊Q8C2311yescharacteristic
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2312yes—
364C2×C22⋊Q8C2312yes—
365C2×C22⋊Q8C2312yes—
366C2×C22⋊Q8C2312yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2312yes—
369C2×C22⋊Q8C2314yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2311yescharacteristic
373C2×#121C2314yes—
374C2×#121C2312yes—
375C2×#121C2314yes—
376C2×#121C2312yes—
377C2×#121C2312yes—
378C2×#121C2312yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×#121C2311yescharacteristic
383C2×#121C2312yes—
384C2×#121C2311yescharacteristic
385C2×#121C2311yescharacteristic
386C2×#121C2314yes—
387C2×#121C2312yes—
388C2×#121C2312yes—
389C2×#121C2314yes—
390C2×#121C2314yes—
391C2×#121C2314yes—
392C2×#121C2314yes—
393C2×#121C2312yes—
394C2×#121C2314yes—
395C2×#120C2312yes—
396C2×#120C2312yes—
397C2×#120C2314yes—
398C2×#120C2312yes—
399C2×#120C2314yes—
400C2×C4×Q8C2311yescharacteristic
401C2×C4×Q8C2311yescharacteristic
402C2×C4×Q8C2311yescharacteristic
403C2×C4×Q8C2311yescharacteristic
404C2×C4×Q8C2311yescharacteristic
405C2×C4×Q8C2312yes—
406C2×C4×Q8C2312yes—
407C2×C4×D4—44no—
408C2×C4×D4C2311yescharacteristic
409C2×C4×D4C2312yes—
410C2×C4×D4C2311yescharacteristic
411C2×C4×D4C2312yes—
412C2×C4×D4C2311yescharacteristic
413C2×C4×D4C2311yescharacteristic
414C2×C4×D4C2311yescharacteristic
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2312yes—
421C2×C4×D4C2314yes—
422C2×C4×D4C2312yes—
423C2×C4×D4C2312yes—
424C2×C4×D4C2314yes—
425C2×C4×D4C2311yescharacteristic
426C2×C4×D4C2311yescharacteristic
427C2×C4×D4C2312yes—
428C2×C4×D4C2312yes—
429C2×C4×D4C2311yescharacteristic
430C2×C4×D4C2312yes—
431C2×#117C2312yes—
432C2×#117C2312yes—
433C2×#117C2312yes—
434C2×#117C2312yes—
435C2×#117C2314yes—
436C2×#117C2312yes—
437C2×#117C2312yes—
438C22×C4⋊C4C2312yes—
439C22×C4⋊C4C2311yescharacteristic
440C22×C4⋊C4C2314yes—
441C22×C22⋊C4C2312yes—
442C22×C42C2311yescharacteristic
443C22×C42C2311yescharacteristic
444#400C2314yes—
445#400C2312yes—
446#400C2314yes—
447#400C2314yes—
448#400C2312yes—
449#400C2314yes—
450#400C2314yes—
451#399C2314yes—
452#399C2314yes—
453#399C2314yes—
454#399C2314yes—
455#399C2314yes—
456#399C2314yes—
457#399C2312yes—
458#399C2312yes—
459#398C2312yes—
460#398C2314yes—
461#398C2312yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2312yes—
466#398C2312yes—
467#398C2312yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2312yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2312yes—
493#396C2312yes—
494#396C2312yes—
495#396C2312yes—
496#396C2312yes—
497#395C2314yes—
498#395C2314yes—
499#395C2312yes—
500#395C2314yes—
501#395C2312yes—
502#395C2312yes—
503#394C2312yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2312yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2312yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2312yes—
531#394C2312yes—
532#394C2312yes—
533#394C2314yes—
534#394C2314yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#393C2314yes—
540#393C2314yes—
541#393C2314yes—
542#393C2314yes—
543#393C2314yes—
544#393C2314yes—
545#393C2312yes—
546#393C2314yes—
547#393C2314yes—
548#393C2314yes—
549#393C2312yes—
550#393C2314yes—
551#393C2312yes—
552#392C2312yes—
553#392C2314yes—
554#392C2314yes—
555#392C2314yes—
556#392C2314yes—
557#392C2314yes—
558#392C2312yes—
559#392C2314yes—
560#392C2314yes—
561#392C2314yes—
562#392C2314yes—
563#392C2314yes—
564#392C2312yes—
565#392C2312yes—
566#392C2314yes—
567#392C2314yes—
568#392C2314yes—
569#392C2314yes—
570#391C2312yes—
571#391C2312yes—
572#391C2311yescharacteristic
573#391C2311yescharacteristic
574#391C2314yes—
575#391C2314yes—
576#391C2312yes—
577#391C2312yes—
578#391C2314yes—
579#391C2314yes—
580#391C2311yescharacteristic
581#391C2311yescharacteristic
582#390C2312yes—
583#390C2311yescharacteristic
584#390C2311yescharacteristic
585#390C2312yes—
586#390C2312yes—
587#390C2312yes—
588#390C2312yes—
589#390C2314yes—
590#390C2314yes—
591#390C2311yescharacteristic
592#390C2312yes—
593#390C2314yes—
594#390C2312yes—
595#390C2312yes—
596#390C2312yes—
597#390C2312yes—
598#390C2314yes—
599#390C2314yes—
600#390C2312yes—
601#390C2312yes—
602#390C2314yes—
603#390C2314yes—
604#390C2314yes—
605#390C2312yes—
606#390C2314yes—
607#390C2314yes—
608#390C2312yes—
609#390C2312yes—
610#390C2312yes—
611#390C2312yes—
612#390C2312yes—
613#390C2312yes—
614#390C2311yescharacteristic
615#390C2312yes—
616#390C2312yes—
617#390C2314yes—
618#390C2312yes—
619#390C2312yes—
620#390C2314yes—
621#390C2314yes—
622#390C2312yes—
623#390C2311yescharacteristic
624#390C2312yes—
625#390C2311yescharacteristic
626#389C2312yes—
627#389C2312yes—
628#389C2312yes—
629#389C2312yes—
630#389C2312yes—
631#389C2312yes—
632#389C2312yes—
633#389C2312yes—
634#389C2312yes—
635#389C2312yes—
636#389C2312yes—
637#389C2312yes—
638#389C2312yes—
639#389C2312yes—
640#389C2311yescharacteristic
641#389C2311yescharacteristic
642#389C2311yescharacteristic
643#389C2312yes—
644#389C2311yescharacteristic
645#389C2312yes—
646#389C2312yes—
647#389C2312yes—
648#389C2312yes—
649#389C2311yescharacteristic
650#389C2312yes—
651#389C2314yes—
652#389C2311yescharacteristic
653#389C2312yes—
654#389C2312yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2312yes—
662#388C2314yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#388C2314yes—
668#388C2314yes—
669#388C2312yes—
670#388C2314yes—
671#388C2314yes—
672#388C2314yes—
673#388C2314yes—
674#388C2314yes—
675#388C2314yes—
676#388C2314yes—
677#388C2314yes—
678#388C2314yes—
679#388C2314yes—
680#388C2312yes—
681#388C2314yes—
682#388C2312yes—
683#388C2312yes—
684#388C2314yes—
685#388C2312yes—
686#388C2312yes—
687#388C2312yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2312yes—
692#387C2314yes—
693#387C2314yes—
694#387C2314yes—
695#387C2314yes—
696#387C2312yes—
697#386C2312yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2312yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2312yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#386C2314yes—
715#386C2312yes—
716#386C2312yes—
717#385C2312yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2314yes—
730#385C2314yes—
731#385C2314yes—
732#385C2314yes—
733#385C2314yes—
734#385C2314yes—
735#385C2312yes—
736#385C2312yes—
737#385C2314yes—
738#385C2312yes—
739#385C2312yes—
740#384C2311yescharacteristic
741#384C2311yescharacteristic
742#384C2311yescharacteristic
743#384C2312yes—
744#384C2314yes—
745#384C2314yes—
746#384C2311yescharacteristic
747#384C2311yescharacteristic
748#383C2314yes—
749#382C2314yes—
750#382C2314yes—
751#382C2312yes—
752#382C2312yes—
753#382C2314yes—
754#382C2312yes—
755#382C2312yes—
756#382C2312yes—
757#382C2314yes—
758#381C2314yes—
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2311yescharacteristic
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#380C2314yes—
770#380C2314yes—
771#380C2312yes—
772#380C2314yes—
773#380C2311yescharacteristic
774#380C2311yescharacteristic
775#380C2311yescharacteristic
776#380C2312yes—
777#380C2312yes—
778#380C2312yes—
779#379C2314yes—
780#379C2314yes—
781#379C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2314yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2311yescharacteristic
803C4×C4⋊C4C2312yes—
804C4×C4⋊C4C2312yes—
805C4×C4⋊C4C2311yescharacteristic
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2314yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2311yescharacteristic
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2311yescharacteristic
817C4×C22⋊C4C2312yes—
818C4×C22⋊C4C2311yescharacteristic
819C4×C22⋊C4C2311yescharacteristic
820C43C2311yescharacteristic
821C43C2312yes—
822C25C2412yes—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—44no—
832C22×Q8C2411yescharacteristic
833C22×Q8C2411yescharacteristic
834C22×Q8C2411yescharacteristic
835C22×Q8C2412yes—
836C22×Q8C2412yes—
837C22×Q8C2412yes—
838C22×Q8C2414yes—
839C22×D4—24no—
840C22×D4—42no—
841C22×D4—42no—
842C22×D4C2411yescharacteristic
843C22×D4C2412yes—
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2414yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2412yes—
857C22×D4C2412yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C22×D4C2412yes—
861C22×D4C2414yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2414yes—
865C22×D4C2414yes—
866C23×C4—44no—
867C23×C4—44no—
868C23×C4—44no—
869C23×C4C2412yes—
870C23×C4C2411yescharacteristic
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2411yescharacteristic
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2411yescharacteristic
878C23×C4C2414yes—
879C23×C4C2414yes—
880C23×C4C2412yes—
881C23×C4C2414yes—
882C23×C4C2414yes—
883C23×C4C2412yes—
884C23×C4C2412yes—
885C4⋊Q8—24no—
886C4⋊Q8—44no—
887C4⋊Q8—42no—
888C4⋊Q8—42no—
889C4⋊Q8—42no—
890C4⋊Q8—44no—
891C4⋊Q8—42no—
892C4⋊Q8—42no—
893C4⋊Q8—44no—
894#127—24no—
895#127—42no—
896#127—44no—
897#127—42no—
898#127—44no—
899#127—44no—
900#126—48no—
901#126—48no—
902#125—44no—
903#125—44no—
904#125—48no—
905#125—44no—
906#124—44no—
907#124—48no—
908#124—44no—
909#124—48no—
910#124—84no—
911#124—84no—
912#124—84no—
913#124—84no—
914#123—44no—
915#123—48no—
916#123—44no—
917#123—48no—
918#123—48no—
919#123—48no—
920#123—48no—
921C22⋊Q8—24no—
922C22⋊Q8—24no—
923C22⋊Q8—44no—
924C22⋊Q8—44no—
925C22⋊Q8—48no—
926C22⋊Q8—44no—
927C22⋊Q8—44no—
928C22⋊Q8—48no—
929C22⋊Q8—44no—
930C22⋊Q8—42no—
931C22⋊Q8—42no—
932C22⋊Q8—42no—
933C22⋊Q8—42no—
934C22⋊Q8—44no—
935C22⋊Q8—44no—
936C22⋊Q8—44no—
937C22⋊Q8—44no—
938C22⋊Q8—44no—
939C22⋊Q8—44no—
940#121—28no—
941#121—24no—
942#121—28no—
943#121—44no—
944#121—44no—
945#121—48no—
946#121—48no—
947#121—44no—
948#121—44no—
949#121—48no—
950#121—48no—
951#121—48no—
952#121—44no—
953#121—42no—
954#121—44no—
955#121—42no—
956#121—42no—
957#121—44no—
958#121—48no—
959#121—44no—
960#121—48no—
961#121—44no—
962#121—44no—
963#121—82no—
964#121—84no—
965#120—44no—
966#120—44no—
967#120—48no—
968#120—44no—
969#120—84no—
970C4×Q8—24no—
971C4×Q8—24no—
972C4×Q8—24no—
973C4×Q8—24no—
974C4×Q8—24no—
975C4×Q8—44no—
976C4×Q8—44no—
977C4×D4—24no—
978C4×D4—24no—
979C4×D4—24no—
980C4×D4—24no—
981C4×D4—28no—
982C4×D4—24no—
983C4×D4—28no—
984C4×D4—44no—
985C4×D4—48no—
986C4×D4—42no—
987C4×D4—42no—
988C4×D4—44no—
989C4×D4—44no—
990C4×D4—48no—
991C4×D4—44no—
992C4×D4—44no—
993C4×D4—44no—
994C4×D4—44no—
995C4×D4—44no—
996C4×D4—44no—
997C4×D4—44no—
998C4×D4—42no—
999C4×D4—82no—
1000#117—28no—
1001#117—28no—
1002#117—44no—
1003#117—44no—
1004#117—48no—
1005#117—44no—
1006#117—82no—
1007C2×C4⋊C4—28no—
1008C2×C4⋊C4—42no—
1009C2×C4⋊C4—48no—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2411yescharacteristic
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2411yescharacteristic
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2411yescharacteristic
1039C2×C4⋊C4C2411yescharacteristic
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2412yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2412yes—
1065C2×C4⋊C4C2414yes—
1066C2×C4⋊C4C2412yes—
1067C2×C4⋊C4C2414yes—
1068C2×C4⋊C4C2414yes—
1069C2×C4⋊C4C2414yes—
1070C2×C4⋊C4C2414yes—
1071C2×C4⋊C4C2412yes—
1072C2×C4⋊C4C2414yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2411yescharacteristic
1075C2×C22⋊C4—44no—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2411yescharacteristic
1083C2×C22⋊C4C2411yescharacteristic
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2411yescharacteristic
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2411yescharacteristic
1091C2×C22⋊C4C2411yescharacteristic
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2411yescharacteristic
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2412yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2414yes—
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2414yes—
1141C2×C22⋊C4C2412yes—
1142C2×C22⋊C4C2412yes—
1143C2×C22⋊C4C2412yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2414yes—
1146C2×C22⋊C4C2414yes—
1147C2×C22⋊C4C2414yes—
1148C2×C22⋊C4C2414yes—
1149C2×C42—24no—
1150C2×C42—24no—
1151C2×C42C2414yes—
1152C2×C42C2412yes—
1153C2×C42C2412yes—
1154C2×C42C2412yes—
1155C2×C42C2412yes—
1156C2×C42C2412yes—
1157C2×C42C2411yescharacteristic
1158C2×C42C2411yescharacteristic
1159C2×C42C2411yescharacteristic
1160C2×C42C2411yescharacteristic
1161C2×C42C2411yescharacteristic
1162C2×C42C2411yescharacteristic
1163C2×C42C2412yes—
1164C2×C42C2411yescharacteristic
1165C2×C42C2411yescharacteristic
1166C2×C42C2412yes—
1167C2×C42C2411yescharacteristic
1168C2×C42C2414yes—
1169C2×C42C2414yes—
1170C2×C42C2411yescharacteristic
1171C2×C42C2411yescharacteristic
1172C2×C42C2412yes—
1173C2×C42C2414yes—
1174C2×C42C2414yes—
1175C2×C42C2412yes—
1176C2×C42C2411yescharacteristic
1177C2×C42C2411yescharacteristic
1178#95C2411yescharacteristic
1179#95C2412yes—
1180#95C2411yescharacteristic
1181#95C2411yescharacteristic
1182#95C2411yescharacteristic
1183#95C2411yescharacteristic
1184#95C2411yescharacteristic
1185#95C2412yes—
1186#95C2414yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2412yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2412yes—
1212#95C2414yes—
1213#95C2412yes—
1214#95C2412yes—
1215#95C2414yes—
1216#95C2412yes—
1217#95C2414yes—
1218#95C2412yes—
1219#95C2412yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226#95C2414yes—
1227#95C2414yes—
1228C24—24no—
1229C24—42no—
1230C24—42no—
1231C24—42no—
1232C24—42no—
1233C24—42no—
1234C24—42no—
1235C24C2512yes—
1236C24C2512yes—
1237C24C2511yescharacteristic
1238C24C2514yes—
1239C24C2512yes—
1240C24C2511yescharacteristic
1241#41—816no—
1242#41—816no—
1243#41—816no—
1244C2×Q8—22no—
1245C2×Q8—22no—
1246C2×Q8—22no—
1247C2×Q8—22no—
1248C2×Q8—22no—
1249C2×Q8—22no—
1250C2×Q8—22no—
1251C2×Q8—22no—
1252C2×Q8—22no—
1253C2×Q8—24no—
1254C2×Q8—42no—
1255C2×Q8—42no—
1256C2×Q8—42no—
1257C2×Q8—42no—
1258C2×Q8—42no—
1259C2×Q8—42no—
1260C2×Q8—42no—
1261C2×Q8—42no—
1262C2×Q8—44no—
1263C2×Q8—44no—
1264C2×Q8—44no—
1265C2×D4—22no—
1266C2×D4—28no—
1267C2×D4—24no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—24no—
1272C2×D4—22no—
1273C2×D4—24no—
1274C2×D4—24no—
1275C2×D4—24no—
1276C2×D4—24no—
1277C2×D4—28no—
1278C2×D4—24no—
1279C2×D4—22no—
1280C2×D4—24no—
1281C2×D4—24no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—22no—
1285C2×D4—24no—
1286C2×D4—22no—
1287C2×D4—22no—
1288C2×D4—24no—
1289C2×D4—42no—
1290C2×D4—41no—
1291C2×D4—42no—
1292C2×D4—416no—
1293C2×D4—42no—
1294C2×D4—42no—
1295C2×D4—44no—
1296C2×D4—42no—
1297C2×D4—42no—
1298C2×D4—42no—
1299C2×D4—42no—
1300C2×D4—44no—
1301C2×D4—42no—
1302C2×D4—42no—
1303C2×D4—42no—
1304C2×D4—44no—
1305C2×D4—42no—
1306C2×D4—42no—
1307C2×D4—42no—
1308C2×D4—44no—
1309C2×D4—42no—
1310C2×D4—42no—
1311C2×D4—42no—
1312C2×D4—44no—
1313C2×D4—44no—
1314C2×D4—44no—
1315C2×D4—44no—
1316C2×D4—44no—
1317C2×D4—42no—
1318C2×D4—42no—
1319C2×D4—42no—
1320C2×D4—42no—
1321C2×D4—42no—
1322C2×D4—42no—
1323C2×D4—44no—
1324C2×D4—42no—
1325C2×D4—42no—
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—44no—
1335C2×D4—44no—
1336C2×D4—44no—
1337C2×D4—44no—
1338C22×C4—22no—
1339C22×C4—22no—
1340C22×C4—22no—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—24no—
1345C22×C4—24no—
1346C22×C4—24no—
1347C22×C4—22no—
1348C22×C4—24no—
1349C22×C4—22no—
1350C22×C4—24no—
1351C22×C4—24no—
1352C22×C4—24no—
1353C22×C4—24no—
1354C22×C4—24no—
1355C22×C4—22no—
1356C22×C4—22no—
1357C22×C4—22no—
1358C22×C4—22no—
1359C22×C4—22no—
1360C22×C4—22no—
1361C22×C4—28no—
1362C22×C4—28no—
1363C22×C4—41no—
1364C22×C4—42no—
1365C22×C4—44no—
1366C22×C4—44no—
1367C22×C4—42no—
1368C22×C4—42no—
1369C22×C4—42no—
1370C22×C4—42no—
1371C22×C4—44no—
1372C22×C4—44no—
1373C22×C4—44no—
1374C22×C4—44no—
1375C22×C4—44no—
1376C22×C4—41no—
1377C22×C4—44no—
1378C22×C4—42no—
1379C22×C4—42no—
1380C22×C4—44no—
1381C22×C4—44no—
1382C22×C4—41no—
1383C22×C4—42no—
1384C22×C4—42no—
1385C22×C4—816no—
1386C22×C42−1+414yes—
1387C22×C4C2512yes—
1388C22×C4C2512yes—
1389C22×C4C2511yescharacteristic
1390C22×C4C2514yes—
1391C22×C4C2512yes—
1392C22×C4C2511yescharacteristic
1393C22×C4C2512yes—
1394C22×C4C2512yes—
1395C22×C4C2511yescharacteristic
1396C22×C4C2514yes—
1397C22×C4C2511yescharacteristic
1398C22×C4C2512yes—
1399C22×C4C2514yes—
1400C22×C4C2512yes—
1401C22×C4C2511yescharacteristic
1402C22×C4C2511yescharacteristic
1403C22×C4C2512yes—
1404C22×C4C2512yes—
1405C22×C4C2512yes—
1406C22×C4C2512yes—
1407C22×C4C2512yes—
1408C22×C4C2511yescharacteristic
1409C22×C4C2512yes—
1410C22×C4C2511yescharacteristic
1411C22×C4C2511yescharacteristic
1412C22×C4C2511yescharacteristic
1413C22×C4C2511yescharacteristic
1414C22×C4C2511yescharacteristic
1415C22×C4C2511yescharacteristic
1416C4⋊C4—24no—
1417C4⋊C4—28no—
1418C4⋊C4—24no—
1419C4⋊C4—24no—
1420C4⋊C4—22no—
1421C4⋊C4—22no—
1422C4⋊C4—24no—
1423C4⋊C4—24no—
1424C4⋊C4—24no—
1425C4⋊C4—22no—
1426C4⋊C4—24no—
1427C4⋊C4—22no—
1428C4⋊C4—24no—
1429C4⋊C4—24no—
1430C4⋊C4—24no—
1431C4⋊C4—22no—
1432C4⋊C4—22no—
1433C4⋊C4—22no—
1434C4⋊C4—24no—
1435C4⋊C4—24no—
1436C4⋊C4—22no—
1437C4⋊C4—24no—
1438C4⋊C4—24no—
1439C4⋊C4—24no—
1440C4⋊C4—22no—
1441C4⋊C4—22no—
1442C4⋊C4—24no—
1443C4⋊C4—24no—
1444C4⋊C4—24no—
1445C4⋊C4—22no—
1446C4⋊C4—24no—
1447C4⋊C4—22no—
1448C4⋊C4—42no—
1449C4⋊C4—44no—
1450C4⋊C4—44no—
1451C4⋊C4—44no—
1452C4⋊C4—44no—
1453C4⋊C4—42no—
1454C4⋊C4—42no—
1455C4⋊C4—42no—
1456C4⋊C4—42no—
1457C4⋊C4—42no—
1458C4⋊C4—42no—
1459C4⋊C4—42no—
1460C4⋊C4—42no—
1461C4⋊C4—42no—
1462C4⋊C4—44no—
1463C4⋊C4—42no—
1464C4⋊C4—42no—
1465C4⋊C4—42no—
1466C4⋊C4—42no—
1467C4⋊C4—42no—
1468C4⋊C4—42no—
1469C4⋊C4—42no—
1470C4⋊C4—42no—
1471C4⋊C4—44no—
1472C4⋊C4—42no—
1473C4⋊C4—44no—
1474C4⋊C4—44no—
1475C4⋊C4—44no—
1476C4⋊C4—44no—
1477C4⋊C4—44no—
1478C4⋊C4—42no—
1479C4⋊C4—42no—
1480C4⋊C4H(5,𝔽2)14yes—
1481C22⋊C4—22no—
1482C22⋊C4—24no—
1483C22⋊C4—24no—
1484C22⋊C4—24no—
1485C22⋊C4—28no—
1486C22⋊C4—24no—
1487C22⋊C4—22no—
1488C22⋊C4—24no—
1489C22⋊C4—24no—
1490C22⋊C4—22no—
1491C22⋊C4—24no—
1492C22⋊C4—28no—
1493C22⋊C4—24no—
1494C22⋊C4—28no—
1495C22⋊C4—24no—
1496C22⋊C4—22no—
1497C22⋊C4—24no—
1498C22⋊C4—28no—
1499C22⋊C4—22no—
1500C22⋊C4—24no—
1501C22⋊C4—28no—
1502C22⋊C4—42no—
1503C22⋊C4—42no—
1504C22⋊C4—44no—
1505C22⋊C4—42no—
1506C22⋊C4—42no—
1507C22⋊C4—42no—
1508C22⋊C4—42no—
1509C22⋊C4—42no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—41no—
1515C22⋊C4—42no—
1516C22⋊C4—42no—
1517C22⋊C4—44no—
1518C22⋊C4—44no—
1519C22⋊C4—44no—
1520C22⋊C4—42no—
1521C22⋊C4—42no—
1522C22⋊C4—44no—
1523C22⋊C4—42no—
1524C22⋊C4—42no—
1525C22⋊C4—42no—
1526C22⋊C4—44no—
1527C22⋊C4—42no—
1528C22⋊C4—42no—
1529C22⋊C4—44no—
1530C22⋊C4—44no—
1531C22⋊C4—44no—
1532C22⋊C4—44no—
1533C22⋊C4—42no—
1534C22⋊C4—44no—
1535C22⋊C4—44no—
1536C22⋊C4—44no—
1537C22⋊C4—44no—
1538C22⋊C4—44no—
1539C22⋊C4—44no—
1540C22⋊C4—44no—
1541C22⋊C4—44no—
1542C22⋊C4—44no—
1543C22⋊C4—44no—
1544C22⋊C4—44no—
1545C22⋊C4—44no—
1546C22⋊C4—44no—
1547C22⋊C4—44no—
1548C22⋊C4—42no—
1549C22⋊C4—44no—
1550C22⋊C4—44no—
1551C22⋊C4—42no—
1552C22⋊C4—42no—
1553C22⋊C4—44no—
1554C42—22no—
1555C42—22no—
1556C42—22no—
1557C42—22no—
1558C42—22no—
1559C42—22no—
1560C42—28no—
1561C42—24no—
1562C42—24no—
1563C42—24no—
1564C42—24no—
1565C42—24no—
1566C42—22no—
1567C42—24no—
1568C42—22no—
1569C42—22no—
1570C42—24no—
1571C42—44no—
1572C42—44no—
1573C42—41no—
1574C42—41no—
1575C42—44no—
1576C42—42no—
1577C42—44no—
1578C42—42no—
1579C42H(5,𝔽2)14yes—
1580C42H(5,𝔽2)14yes—
1581C23—21no—
1582C23—21no—
1583C23—21no—
1584C23—21no—
1585C23—21no—
1586C23—21no—
1587C23—22no—
1588C23—22no—
1589C23—21no—
1590C23—24no—
1591C23—22no—
1592C23—22no—
1593C23—22no—
1594C23—21no—
1595C23—24no—
1596C23—22no—
1597C23—22no—
1598C23—21no—
1599C23—22no—
1600C23—22no—
1601C23—24no—
1602C23—21no—
1603C23—22no—
1604C23—24no—
1605C23—22no—
1606C23—22no—
1607C23—22no—
1608C23—24no—
1609C23—22no—
1610C23—22no—
1611C23—24no—
1612C23—21no—
1613C23—22no—
1614C23—21no—
1615C23—22no—
1616C23—22no—
1617C23—21no—
1618C23—22no—
1619C23—22no—
1620C23—22no—
1621C23—24no—
1622C23—48no—
1623C23—84no—
1624C23—84no—
1625C23—84no—
1626C23—84no—
1627C23—84no—
1628C23—84no—
1629C23C2×2−1+412yes—
1630C23C2611yescharacteristic
1631Q8—44no—
1632Q8—44no—
1633Q8—44no—
1634Q8—84no—
1635Q8—84no—
1636Q8—84no—
1637Q8—164no—
1638D4—44no—
1639D4—48no—
1640D4—44no—
1641D4—48no—
1642D4—44no—
1643D4—44no—
1644D4—48no—
1645D4—88no—
1646D4—84no—
1647D4—84no—
1648D4—84no—
1649D4—84no—
1650D4—88no—
1651D4—84no—
1652D4—84no—
1653D4—84no—
1654D4—84no—
1655D4—84no—
1656D4—88no—
1657D4—88no—
1658D4—164no—
1659D4—164no—
1660D4—164no—
1661D4—164no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—22no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—22no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—21no—
1673C2×C4—21no—
1674C2×C4—28no—
1675C2×C4—21no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—21no—
1680C2×C4—21no—
1681C2×C4—22no—
1682C2×C4—22no—
1683C2×C4—24no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—22no—
1690C2×C4—22no—
1691C2×C4—22no—
1692C2×C4—22no—
1693C2×C4—21no—
1694C2×C4—22no—
1695C2×C4—24no—
1696C2×C4—22no—
1697C2×C4—22no—
1698C2×C4—21no—
1699C2×C4—22no—
1700C2×C4—21no—
1701C2×C4—22no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—22no—
1705C2×C4—21no—
1706C2×C4—21no—
1707C2×C4—24no—
1708C2×C4—22no—
1709C2×C4—22no—
1710C2×C4—22no—
1711C2×C4—22no—
1712C2×C4—21no—
1713C2×C4—21no—
1714C2×C4—22no—
1715C2×C4—24no—
1716C2×C4—21no—
1717C2×C4—22no—
1718C2×C4—22no—
1719C2×C4—22no—
1720C2×C4—21no—
1721C2×C4—24no—
1722C2×C4—22no—
1723C2×C4—24no—
1724C2×C4—24no—
1725C2×C4—21no—
1726C2×C4—22no—
1727C2×C4—21no—
1728C2×C4—22no—
1729C2×C4—21no—
1730C2×C4—24no—
1731C2×C4—22no—
1732C2×C4—22no—
1733C2×C4—22no—
1734C2×C4—24no—
1735C2×C4—22no—
1736C2×C4—21no—
1737C2×C4—22no—
1738C2×C4—44no—
1739C2×C4—44no—
1740C2×C4—44no—
1741C2×C4—48no—
1742C2×C4—48no—
1743C2×C4—48no—
1744C2×C4—44no—
1745C2×C4—88no—
1746C2×C4—88no—
1747C2×C4—82no—
1748C2×C4—84no—
1749C2×C4—84no—
1750C2×C4—84no—
1751C2×C4—88no—
1752C2×C4—88no—
1753C2×C4C2×H(5,𝔽2)14yes—
1754C2×C4C2×H(5,𝔽2)12yes—
1755C2×C4C2×H(5,𝔽2)12yes—
1756C2×C4C2×H(5,𝔽2)12yes—
1757C2×C4C2×H(5,𝔽2)12yes—
1758C2×C4C2×H(5,𝔽2)12yes—
1759C2×C4C2×H(5,𝔽2)12yes—
1760C2×C4C2×H(5,𝔽2)12yes—
1761C2×C4C2×2−1+412yes—
1762C2×C4C2×2−1+412yes—
1763C2×C4#58512yes—
1764C2×C4#58512yes—
1765C22—22no—
1766C22—22no—
1767C22—22no—
1768C22—41no—
1769C22—41no—
1770C22—41no—
1771C22—41no—
1772C22—41no—
1773C22—42no—
1774C22—42no—
1775C22—42no—
1776C22—44no—
1777C22—42no—
1778C22—42no—
1779C22—41no—
1780C22—42no—
1781C22—44no—
1782C22—42no—
1783C22—42no—
1784C22—44no—
1785C22—42no—
1786C22—41no—
1787C22—41no—
1788C22—42no—
1789C22—44no—
1790C22—42no—
1791C22—42no—
1792C22—44no—
1793C22—41no—
1794C22—42no—
1795C22—42no—
1796C22—42no—
1797C22—44no—
1798C22—41no—
1799C22—42no—
1800C22—42no—
1801C22—42no—
1802C22—41no—
1803C22—42no—
1804C22—44no—
1805C22—42no—
1806C22—42no—
1807C22—816no—
1808C22C22×H(5,𝔽2)11yescharacteristic
1809C22C22×H(5,𝔽2)11yescharacteristic
1810C22C22×H(5,𝔽2)11yescharacteristic
1811C22C22×2−1+411yescharacteristic
1812C22C2×#58511yescharacteristic
1813C22C2×#58511yescharacteristic
1814C22H(7,𝔽2)11yescharacteristic
1815C4—22no—
1816C4—24no—
1817C4—22no—
1818C4—22no—
1819C4—22no—
1820C4—22no—
1821C4—41no—
1822C4—42no—
1823C4—41no—
1824C4—42no—
1825C4—42no—
1826C4—41no—
1827C4—42no—
1828C4—42no—
1829C4—42no—
1830C4—44no—
1831C4—41no—
1832C4—42no—
1833C4—41no—
1834C4—44no—
1835C4—44no—
1836C4—42no—
1837C4—42no—
1838C4—41no—
1839C4—42no—
1840C4—42no—
1841C4—42no—
1842C4#354114yes—
1843C4#354914yes—
1844C2—42no—
1845C2—81no—
1846C2—82no—
1847C2—84no—
1848C2—82no—
1849C2—82no—
1850C2C2×#354111yescharacteristic
1851C2C2×#354911yescharacteristic
1852C2#6283511yescharacteristic
1853C2#6291711yescharacteristic
1854C2#6295511yescharacteristic
1855C2#6295711yescharacteristic
1856C2#6302111yescharacteristic
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. #59815C2semidirect
2. #59234C2semidirect
3. #59230C2semidirect
4. #56018C2semidirect
5. #54894C2semidirect
6. #54862C2semidirect
7. #53106C2semidirect
8. #53046C2semidirect
9. #50003C2semidirect
10. #46345C2semidirect
11. #45601C2semidirect
12. #45208C2semidirect
13. #44946C2semidirect
14. #42977C2semidirect
15. #42648C2semidirect
16. #42643C2semidirect
17. #42592C2semidirect
18. #39887C2semidirect
19. #39725C2semidirect
20. #39725C2semidirect
21. #39506C2semidirect
22. #39341C2semidirect
23. #39201C2semidirect
24. #38216C2semidirect
25. #37656C2semidirect
26. #37640C2semidirect
27. #37334C2semidirect
28. #37271C2semidirect
29. #36270C2semidirect
30. #36211C2semidirect
31. #36101C2semidirect
32. #35198C2semidirect
33. #35172C2semidirect
34. #34929C2semidirect
35. #34681C2semidirect
36. C2×#552C22semidirect
38. C2×#550C22semidirect
39. C2×#547C22semidirect
40. C2×#542C22semidirect
41. C2×#537C22semidirect
43. C2×#533C22semidirect
49. #2860C22semidirect
50. #2859C22semidirect
53. #2856C22semidirect
57. #2832C22semidirect
59. #2824C22semidirect
60. #2824C22semidirect
61. #2820C22semidirect
62. #2819C22semidirect
63. #2816C22semidirect
64. #2813C22semidirect
68. #2783C22semidirect
69. #2783C22semidirect
70. #2782C22semidirect
71. #2775C22semidirect
72. #2763C22semidirect
74. #2753C22semidirect
75. #2737C22semidirect
77. #2731C22semidirect
78. #2723C22semidirect
79. #2723C22semidirect
80. #2720C22semidirect
81. #2718C22semidirect
82. #2718C22semidirect
83. #2718C22semidirect
86. #2712C22semidirect
87. #2712C22semidirect
88. #2711C22semidirect
89. #2711C22semidirect
90. #2711C22semidirect
92. #2710C22semidirect
93. #2710C22semidirect
94. #2706C22semidirect
95. #2706C22semidirect
97. #2686C22semidirect
100. #2682C22semidirect
101. #2680C22semidirect
106. #2676C22semidirect
107. #2676C22semidirect
108. #2676C22semidirect
109. #2675C22semidirect
110. #2671C22semidirect
114. #2662C22semidirect
117. #2633C22semidirect
120. #2624C22semidirect
121. #2624C22semidirect
122. #2623C22semidirect
123. #2621C22semidirect
124. #2620C22semidirect
127. #2616C22semidirect
128. #2616C22semidirect
129. #2615C22semidirect
130. #2601C22semidirect
134. #2580C22semidirect
135. #2580C22semidirect
136. #2574C22semidirect
137. #2574C22semidirect
138. #2567C22semidirect
143. #2563C22semidirect
144. #2562C22semidirect
145. #2558C22semidirect
147. #2556C22semidirect
149. #2551C22semidirect
150. #2551C22semidirect
153. #2548C22semidirect
154. #2548C22semidirect
155. #2547C22semidirect
156. #2547C22semidirect
157. #2546C22semidirect
160. #2542C22semidirect
165. #2540C22semidirect
172. #2538C22semidirect
173. #2538C22semidirect
174. #2537C22semidirect
175. #2536C22semidirect
177. #2518C22semidirect
181. #2513C22semidirect
182. #2513C22semidirect
183. #2508C22semidirect
184. #2508C22semidirect
185. #2508C22semidirect
186. #2506C22semidirect
187. #2506C22semidirect
188. #2502C22semidirect
189. #2500C22semidirect
190. #2495C22semidirect
192. #2492C22semidirect
193. #2492C22semidirect
194. #2492C22semidirect
196. #2491C22semidirect
197. #2491C22semidirect
198. #2491C22semidirect
199. #2491C22semidirect
201. #2490C22semidirect
202. #2489C22semidirect
203. #2489C22semidirect
204. #2474C22semidirect
209. #2461C22semidirect
213. #2452C22semidirect
214. #2452C22semidirect
221. #2445C22semidirect
222. #2443C22semidirect
227. #2432C22semidirect
228. #2432C22semidirect
230. #2429C22semidirect
233. #2428C22semidirect
234. #2426C22semidirect
238. #2422C22semidirect
240. #2420C22semidirect
243. #2416C22semidirect
244. #2416C22semidirect
245. #2415C22semidirect
252. #2407C22semidirect
253. #2407C22semidirect
254. #2407C22semidirect
255. #2407C22semidirect
257. #2396C22semidirect
260. #2379C22semidirect
261. #2369C22semidirect
265. #2363C22semidirect
267. #2357C22semidirect
268. #2355C22semidirect
269. #2355C22semidirect
271. #2352C22semidirect
272. D4×C4⋊C4C22semidirect
273. D4×C4⋊C4C22semidirect
274. #2347C22semidirect
275. #2345C22semidirect
277. #2324C22semidirect
278. #2324C22semidirect
279. #2324C22semidirect
281. #2314C22semidirect
283. C4×C4⋊Q8C22semidirect
284. C4×C4⋊Q8C22semidirect
286. C4×#127C22semidirect
288. C4×C22⋊Q8C22semidirect
294. #2293C22semidirect
296. #2285C22semidirect
297. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598152
#592342
#592302
#560182
#548942
#548622
#531062
#530462
#500032
#463452
#456012
#452082
#449462
#429772
#426482
#426432
#425922
#398872
#397252
#395062
#393412
#392012
#382162
#376562
#376402
#373342
#372712
#362702
#362112
#361012
#351982
#351722
#349292
#346812