Finite Group Databasebeta

← #8429551

Subgroups — #8429551

Order 512.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59476C212yesmaximal, complemented
3#59375C212yesmaximal, complemented
4#59143C211yesmaximal, characteristic, complemented
5#59084C211yesmaximal, characteristic, complemented
6#56922C214yesmaximal, complemented
7#53909C214yesmaximal, complemented
8#53129C212yesmaximal, complemented
9#53116C212yesmaximal, complemented
10#53088C212yesmaximal, complemented
11#53071C212yesmaximal, complemented
12#52409C214yesmaximal, complemented
13#42629C212yesmaximal, complemented
14#42627C212yesmaximal, complemented
15#42624C212yesmaximal, complemented
16#42619C212yesmaximal, complemented
17#40596C214yesmaximal, complemented
18#39821C212yesmaximal, complemented
19#39808C212yesmaximal, complemented
20#39201C211yesmaximal, characteristic, complemented
21#39168C211yesmaximal, characteristic, complemented
22#39157C211yesmaximal, characteristic, complemented
23#39125C211yesmaximal, characteristic, complemented
24#39034C212yesmaximal, complemented
25#39020C212yesmaximal, complemented
26#37625C211yesmaximal, characteristic, complemented
27#37614C211yesmaximal, characteristic, complemented
28#37572C212yesmaximal, complemented
29#37523C212yesmaximal, complemented
30#36493C211yesmaximal, characteristic, complemented
31#36302C211yesmaximal, characteristic, complemented
32#36121C211yesmaximal, characteristic, complemented
33#34977C211yesmaximal, characteristic, complemented
34#34803C211yesmaximal, characteristic, complemented
35#34724C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic
37C2×Q82C2211yescharacteristic, complemented
38C2×#551C2214yes—
39C2×#546C2212yes—
40C2×#532C2211yescharacteristic
41C22×#127C2211yescharacteristic
42C2×#529C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic, complemented
44#2861C2212yescomplemented
45#2858C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2850C2212yescomplemented
49#2837C2214yescomplemented
50#2832C2214yescomplemented
51#2829C2214yescomplemented
52#2829C2214yescomplemented
53#2828C2214yescomplemented
54#2828C2214yescomplemented
55#2826C2214yescomplemented
56#2825C2214yescomplemented
57#2824C2214yescomplemented
58#2824C2214yescomplemented
59#2819C2214yescomplemented
60#2818C2214yes—
61#2813C2214yescomplemented
62#2812C2214yes—
63#2808C2214yescomplemented
64#2803C2214yescomplemented
65#2803C2214yescomplemented
66#2801C2214yescomplemented
67#2797C2214yescomplemented
68#2797C2214yescomplemented
69#2781C2214yescomplemented
70#2779C2214yescomplemented
71#2778C2214yescomplemented
72#2778C2214yescomplemented
73#2762C2214yescomplemented
74#2753C2214yescomplemented
75#2741C2214yescomplemented
76#2741C2214yescomplemented
77#2736C2214yes—
78#2735C2214yes—
79#2735C2214yes—
80#2731C2214yescomplemented
81#2730C2214yescomplemented
82#2716C2214yescomplemented
83#2712C2214yescomplemented
84#2710C2214yescomplemented
85#2710C2214yescomplemented
86#2709C2214yes—
87#2703C2214yescomplemented
88#2696C2214yescomplemented
89#2693C2214yescomplemented
90#2689C2214yes—
91#2685C2214yes—
92#2685C2214yes—
93#2684C2214yes—
94#2684C2214yes—
95#2674C2214yes—
96#2674C2214yescomplemented
97#2674C2214yescomplemented
98#2672C2214yescomplemented
99#2670C2214yes—
100#2663C2214yescomplemented
101#2663C2214yescomplemented
102#2657C2212yes—
103#2653C2214yescomplemented
104#2653C2214yescomplemented
105#2649C2214yescomplemented
106#2649C2214yescomplemented
107#2649C2214yescomplemented
108#2645C2212yescomplemented
109#2644C2212yescomplemented
110#2641C2212yes—
111#2641C2212yescomplemented
112#2640C2212yescomplemented
113#2630C2214yescomplemented
114#2628C2212yescomplemented
115#2624C2212yescomplemented
116#2624C2212yescomplemented
117#2624C2214yescomplemented
118#2622C2214yes—
119#2620C2212yescomplemented
120#2619C2212yes—
121#2619C2212yes—
122#2613C2214yes—
123#2610C2214yescomplemented
124#2602C2214yescomplemented
125#2600C2214yescomplemented
126#2598C2214yescomplemented
127#2592C2212yescomplemented
128#2592C2212yescomplemented
129#2580C2212yescomplemented
130#2571C2212yescomplemented
131#2567C2211yescharacteristic, complemented
132#2563C2211yescharacteristic, complemented
133#2563C2212yescomplemented
134#2552C2211yescharacteristic, complemented
135#2550C2212yescomplemented
136#2548C2211yescharacteristic
137#2548C2211yescharacteristic
138#2548C2211yescharacteristic
139#2548C2211yescharacteristic
140#2548C2212yescomplemented
141#2547C2212yes—
142#2547C2212yescomplemented
143#2545C2212yescomplemented
144#2544C2212yes—
145#2544C2212yes—
146#2544C2212yes—
147#2542C2212yescomplemented
148#2541C2211yescharacteristic
149#2541C2211yescharacteristic
150#2540C2212yescomplemented
151#2538C2211yescharacteristic, complemented
152#2536C2212yes—
153#2535C2212yescomplemented
154#2533C2212yescomplemented
155#2531C2214yescomplemented
156#2527C2212yes—
157#2523C2212yescomplemented
158#2518C2214yescomplemented
159#2514C2211yescharacteristic, complemented
160#2513C2212yescomplemented
161#2513C2212yescomplemented
162#2513C2212yescomplemented
163#2513C2212yescomplemented
164#2509C2212yescomplemented
165#2509C2211yescharacteristic, complemented
166#2500C2212yescomplemented
167#2500C2212yescomplemented
168#2499C2211yescharacteristic, complemented
169#2496C2212yes—
170#2496C2212yes—
171#2496C2211yescharacteristic
172#2494C2212yes—
173#2492C2211yescharacteristic
174#2491C2212yes—
175#2491C2212yescomplemented
176#2491C2212yescomplemented
177#2491C2212yescomplemented
178#2490C2212yescomplemented
179#2489C2212yes—
180#2485C2211yescharacteristic
181#2485C2214yescomplemented
182#2480C2214yes—
183#2480C2214yes—
184#2478C2212yescomplemented
185#2477C2214yescomplemented
186#2477C2214yescomplemented
187#2476C2214yescomplemented
188#2472C2214yes—
189#2471C2214yescomplemented
190#2471C2214yescomplemented
191#2470C2212yes—
192#2470C2214yescomplemented
193#2466C2212yes—
194#2466C2212yescomplemented
195#2463C2214yescomplemented
196#2459C2214yescomplemented
197#2456C2214yescomplemented
198#2455C2212yes—
199#2455C2214yescomplemented
200#2454C2212yescomplemented
201#2453C2211yescharacteristic, complemented
202#2452C2212yescomplemented
203#2452C2212yescomplemented
204#2452C2212yescomplemented
205#2452C2212yescomplemented
206#2448C2212yescomplemented
207#2448C2212yescomplemented
208#2448C2212yescomplemented
209#2448C2212yescomplemented
210#2447C2211yescharacteristic, complemented
211#2445C2212yes—
212#2445C2212yes—
213#2445C2212yes—
214#2445C2212yes—
215#2445C2212yescomplemented
216#2445C2212yescomplemented
217#2441C2211yescharacteristic, complemented
218#2439C2211yescharacteristic, complemented
219#2435C2212yes—
220#2435C2212yes—
221#2435C2212yes—
222#2435C2212yes—
223#2433C2212yes—
224#2432C2211yescharacteristic, complemented
225#2432C2214yescomplemented
226#2431C2212yes—
227#2431C2212yescomplemented
228#2431C2212yescomplemented
229#2429C2211yescharacteristic
230#2428C2212yes—
231#2428C2212yes—
232#2427C2212yescomplemented
233#2427C2212yescomplemented
234#2426C2212yescomplemented
235#2426C2212yescomplemented
236#2422C2211yescharacteristic
237#2422C2212yescomplemented
238#2422C2212yescomplemented
239#2421C2212yes—
240#2418C2214yes—
241#2415C2211yescharacteristic
242#2415C2211yescharacteristic
243#2414C2212yescomplemented
244#2414C2212yescomplemented
245#2408C2212yes—
246#2408C2212yes—
247#2408C2212yes—
248#2408C2212yes—
249#2407C2211yescharacteristic
250#2405C2214yes—
251#2401C2212yescomplemented
252#2398C2212yes—
253#2395C2212yescomplemented
254#2392C2212yes—
255#2388C2214yescomplemented
256#2369C2211yescharacteristic, complemented
257#2367C2212yescomplemented
258#2367C2212yescomplemented
259#2366C2211yescharacteristic
260#2366C2212yescomplemented
261#2363C2212yescomplemented
262#2363C2212yescomplemented
263#2355C2211yescharacteristic, complemented
264#2355C2211yescharacteristic, complemented
265#2354C2212yescomplemented
266#2354C2212yescomplemented
267#2354C2212yescomplemented
268D4×C22⋊C4C2212yes—
269D4×C22⋊C4C2212yes—
270D4×C22⋊C4C2212yes—
271D4×C22⋊C4C2212yes—
272#2330C2212yescomplemented
273#2326C2212yescomplemented
274#2324C2212yescomplemented
275#2323C2212yescomplemented
276#2312C2214yes—
277C4×C4⋊Q8C2211yescharacteristic, complemented
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×#127C2211yescharacteristic
280C4×#127C2212yescomplemented
281C4×#126C2212yes—
282C4×#124C2212yescomplemented
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic, complemented
286C4×C22⋊Q8C2211yescharacteristic, complemented
287C4×#123C2212yes—
288C4×#121C2212yescomplemented
289C4×#121C2212yescomplemented
290C4×#121C2212yescomplemented
291#2296C2212yescomplemented
292#2295C2211yescharacteristic, complemented
293#2295C2212yescomplemented
294#2293C2211yescharacteristic, complemented
295#2293C2212yescomplemented
296#2283C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic, complemented
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303C23×D4C2312yes—
304#559—44no—
305Q82—44no—
306#551—416no—
307#546—48no—
308#532—44no—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2314yes—
315C2×#127—44no—
316C2×#127C2311yescharacteristic
317C2×#127C2311yescharacteristic
318C2×#127C2312yes—
319C2×#127C2312yes—
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323#529—44no—
324C2×#126C2312yes—
325C2×#126C2312yes—
326C2×#126C2314yes—
327C2×#125C2312yes—
328C2×#125C2311yescharacteristic
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2311yescharacteristic
338C2×#124C2314yes—
339C2×#124C2314yes—
340C2×#124C2314yes—
341C2×#124C2312yes—
342C2×#123C2312yes—
343C2×#123C2314yes—
344C2×#123C2312yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2311yescharacteristic
355C2×C22⋊Q8C2311yescharacteristic
356C2×C22⋊Q8C2311yescharacteristic
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2314yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2314yes—
367C2×#121C2311yescharacteristic
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#120C2314yes—
371C2×#120C2314yes—
372C2×#120C2314yes—
373C4×#41—44no—
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2312yes—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2312yes—
388C2×C4×D4C2314yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2314yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2314yes—
401C2×#117C2312yes—
402C2×#117C2312yes—
403C2×#117C2314yes—
404C2×#117C2314yes—
405C2×#117C2312yes—
406C2×#117C2311yescharacteristic
407C2×#117C2311yescharacteristic
408C2×#117C2311yescharacteristic
409C22×C22⋊C4C2314yes—
410C22×C22⋊C4C2314yes—
411C22×C42C2311yescharacteristic
412C22×C42C2311yescharacteristic
413C22×C42C2312yes—
414#401C2314yes—
415#401C2312yes—
416#400C2312yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2312yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2312yes—
425#400C2312yes—
426#400C2312yes—
427#400C2312yes—
428#399C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#399C2312yes—
434#399C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2312yes—
438#398C2312yes—
439#397C2312yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2312yes—
449#397C2312yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2314yes—
461#397C2312yes—
462#397C2312yes—
463#397C2312yes—
464#397C2312yes—
465#397C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2312yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2312yes—
474#396C2312yes—
475#396C2314yes—
476#395C2314yes—
477#395C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2312yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2312yes—
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#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2312yes—
515#394C2312yes—
516#394C2314yes—
517#394C2312yes—
518#394C2312yes—
519#394C2312yes—
520#394C2314yes—
521#394C2314yes—
522#393C2314yes—
523#393C2314yes—
524#393C2314yes—
525#393C2312yes—
526#393C2314yes—
527#393C2314yes—
528#393C2314yes—
529#393C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2312yes—
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#392C2312yes—
548#391C2311yescharacteristic
549#391C2311yescharacteristic
550#391C2312yes—
551#391C2312yes—
552#391C2312yes—
553#391C2311yescharacteristic
554#391C2312yes—
555#391C2312yes—
556#391C2311yescharacteristic
557#391C2312yes—
558#391C2311yescharacteristic
559#391C2311yescharacteristic
560#391C2314yes—
561#391C2311yescharacteristic
562#391C2312yes—
563#391C2314yes—
564#391C2311yescharacteristic
565#390C2312yes—
566#390C2312yes—
567#390C2312yes—
568#390C2312yes—
569#390C2312yes—
570#390C2314yes—
571#390C2314yes—
572#390C2312yes—
573#390C2312yes—
574#390C2314yes—
575#390C2314yes—
576#390C2314yes—
577#390C2314yes—
578#390C2312yes—
579#390C2312yes—
580#390C2312yes—
581#390C2312yes—
582#390C2312yes—
583#390C2312yes—
584#390C2312yes—
585#390C2312yes—
586#390C2312yes—
587#390C2312yes—
588#390C2312yes—
589#390C2312yes—
590#390C2312yes—
591#390C2312yes—
592#390C2312yes—
593#390C2312yes—
594#390C2312yes—
595#390C2312yes—
596#390C2314yes—
597#390C2312yes—
598#390C2312yes—
599#390C2312yes—
600#390C2311yescharacteristic
601#390C2311yescharacteristic
602#389C2311yescharacteristic
603#389C2311yescharacteristic
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2314yes—
611#389C2314yes—
612#389C2311yescharacteristic
613#389C2312yes—
614#389C2312yes—
615#389C2311yescharacteristic
616#389C2312yes—
617#389C2314yes—
618#389C2312yes—
619#389C2312yes—
620#389C2311yescharacteristic
621#389C2312yes—
622#389C2311yescharacteristic
623#389C2312yes—
624#389C2312yes—
625#389C2312yes—
626#389C2312yes—
627#389C2312yes—
628#389C2312yes—
629#389C2311yescharacteristic
630#389C2311yescharacteristic
631#389C2311yescharacteristic
632#389C2311yescharacteristic
633#388C2312yes—
634#388C2312yes—
635#388C2312yes—
636#388C2312yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2312yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#388C2314yes—
668#388C2314yes—
669#388C2314yes—
670#388C2314yes—
671#388C2312yes—
672#388C2314yes—
673#388C2314yes—
674#388C2312yes—
675#387C2312yes—
676#387C2312yes—
677#387C2312yes—
678#387C2312yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2312yes—
683#387C2312yes—
684#387C2314yes—
685#387C2314yes—
686#387C2312yes—
687#387C2312yes—
688#387C2314yes—
689#387C2312yes—
690#387C2312yes—
691#387C2312yes—
692#387C2312yes—
693#387C2312yes—
694#387C2312yes—
695#387C2312yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#386C2314yes—
715#386C2314yes—
716#386C2312yes—
717#385C2312yes—
718#385C2314yes—
719#385C2312yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2312yes—
724#385C2314yes—
725#385C2314yes—
726#385C2312yes—
727#385C2314yes—
728#385C2312yes—
729#385C2312yes—
730#385C2312yes—
731#385C2312yes—
732#385C2312yes—
733#384C2311yescharacteristic
734#384C2312yes—
735#384C2311yescharacteristic
736#384C2311yescharacteristic
737#384C2312yes—
738#383C2312yes—
739#383C2312yes—
740#382C2312yes—
741#382C2312yes—
742#382C2312yes—
743#382C2314yes—
744#382C2311yescharacteristic
745#382C2311yescharacteristic
746#381C2312yes—
747#381C2312yes—
748#380C2314yes—
749#380C2312yes—
750#380C2314yes—
751#380C2312yes—
752#380C2314yes—
753#380C2311yescharacteristic
754#380C2311yescharacteristic
755#380C2312yes—
756#380C2312yes—
757#380C2314yes—
758#380C2314yes—
759#380C2312yes—
760#380C2311yescharacteristic
761#380C2311yescharacteristic
762#380C2311yescharacteristic
763#380C2311yescharacteristic
764#379C2314yes—
765#379C2314yes—
766#379C2314yes—
767#379C2314yes—
768#379C2314yes—
769#379C2314yes—
770#379C2314yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813#376C2312yes—
814#376C2312yes—
815#376C2312yes—
816C43C2312yes—
817C43C2311yescharacteristic
818C25C2414yes—
819C2×#41—44no—
820C2×#41—42no—
821C2×#41—42no—
822C2×#41—42no—
823C2×#41—44no—
824C2×#41—82no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2411yescharacteristic
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2412yes—
830C22×Q8C2414yes—
831C22×D4—44no—
832C22×D4—44no—
833C22×D4—44no—
834C22×D4—44no—
835C22×D4—44no—
836C22×D4—44no—
837C22×D4—44no—
838C22×D4—44no—
839C22×D4—82no—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2411yescharacteristic
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2411yescharacteristic
866C23×C4C2414yes—
867C23×C4C2414yes—
868C23×C4C2412yes—
869C23×C4C2414yes—
870C23×C4C2414yes—
871C23×C4C2412yes—
872C4⋊Q8—24no—
873C4⋊Q8—42no—
874C4⋊Q8—44no—
875C4⋊Q8—44no—
876C4⋊Q8—42no—
877C4⋊Q8—48no—
878#127—24no—
879#127—24no—
880#127—44no—
881#127—44no—
882#127—44no—
883#127—44no—
884#127—44no—
885#126—28no—
886#126—44no—
887#126—48no—
888#125—44no—
889#125—42no—
890#124—44no—
891#124—44no—
892#124—44no—
893#124—44no—
894#124—44no—
895#124—42no—
896#124—44no—
897#124—44no—
898#124—44no—
899#124—48no—
900#124—84no—
901#124—84no—
902#124—82no—
903#123—28no—
904#123—48no—
905#123—44no—
906#123—48no—
907#123—48no—
908#123—48no—
909#123—84no—
910C22⋊Q8—44no—
911C22⋊Q8—48no—
912C22⋊Q8—48no—
913C22⋊Q8—42no—
914C22⋊Q8—42no—
915C22⋊Q8—44no—
916C22⋊Q8—42no—
917C22⋊Q8—42no—
918C22⋊Q8—42no—
919C22⋊Q8—84no—
920#121—44no—
921#121—48no—
922#121—44no—
923#121—44no—
924#121—44no—
925#121—44no—
926#121—44no—
927#121—44no—
928#121—42no—
929#121—44no—
930#121—44no—
931#120—48no—
932#120—48no—
933#120—84no—
934C4×Q8—24no—
935C4×Q8—24no—
936C4×Q8—24no—
937C4×Q8—44no—
938C4×Q8—42no—
939C4×Q8—44no—
940C4×Q8—44no—
941C4×D4—24no—
942C4×D4—24no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—44no—
947C4×D4—42no—
948C4×D4—44no—
949C4×D4—44no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—42no—
953C4×D4—42no—
954C4×D4—44no—
955C4×D4—44no—
956C4×D4—44no—
957C4×D4—48no—
958C4×D4—44no—
959C4×D4—48no—
960C4×D4—84no—
961#117—44no—
962#117—44no—
963#117—44no—
964#117—48no—
965#117—42no—
966#117—42no—
967#117—42no—
968#117—48no—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C22⋊C4—216no—
1028C2×C22⋊C4—48no—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C22⋊C4C2411yescharacteristic
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2411yescharacteristic
1101C2×C42—24no—
1102C2×C42—24no—
1103C2×C42—44no—
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2412yes—
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2411yescharacteristic
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2411yescharacteristic
1123C2×C42C2414yes—
1124C2×C42C2412yes—
1125C2×C42C2414yes—
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2414yes—
1131C2×C42C2411yescharacteristic
1132C2×C42C2414yes—
1133C2×C42C2411yescharacteristic
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2411yescharacteristic
1149#95C2412yes—
1150#95C2411yescharacteristic
1151#95C2412yes—
1152#95C2411yescharacteristic
1153#95C2411yescharacteristic
1154#95C2411yescharacteristic
1155#95C2411yescharacteristic
1156#95C2412yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2412yes—
1190#95C2414yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198C24—28no—
1199C24—44no—
1200C24—44no—
1201C24—44no—
1202C24—44no—
1203C24—44no—
1204C24—44no—
1205C24C2514yes—
1206C24C2514yes—
1207C24C2512yes—
1208C24C2511yescharacteristic
1209C24C2511yescharacteristic
1210#41—416no—
1211#41—816no—
1212C2×Q8—22no—
1213C2×Q8—22no—
1214C2×Q8—22no—
1215C2×Q8—24no—
1216C2×Q8—22no—
1217C2×Q8—22no—
1218C2×Q8—22no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—42no—
1223C2×Q8—42no—
1224C2×Q8—42no—
1225C2×Q8—42no—
1226C2×Q8—42no—
1227C2×Q8—44no—
1228C2×Q8—44no—
1229C2×Q8—44no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—22no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—24no—
1245C2×D4—24no—
1246C2×D4—24no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—42no—
1250C2×D4—42no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C2×D4—42no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C2×D4—42no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—42no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—42no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—42no—
1270C2×D4—44no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C2×D4—44no—
1287C2×D4—816no—
1288C2×D4—816no—
1289C2×D4—816no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—24no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—24no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—24no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—28no—
1310C22×C4—28no—
1311C22×C4—24no—
1312C22×C4—42no—
1313C22×C4—41no—
1314C22×C4—42no—
1315C22×C4—42no—
1316C22×C4—41no—
1317C22×C4—42no—
1318C22×C4—44no—
1319C22×C4—44no—
1320C22×C4—44no—
1321C22×C4—44no—
1322C22×C4—44no—
1323C22×C4—44no—
1324C22×C4—42no—
1325C22×C4—44no—
1326C22×C4—44no—
1327C22×C4—44no—
1328C22×C4—44no—
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2512yes—
1332C22×C4C2511yescharacteristic
1333C22×C4C2511yescharacteristic
1334C22×C4C2512yes—
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2514yes—
1341C22×C4C2511yescharacteristic
1342C22×C4C2512yes—
1343C22×C4C2511yescharacteristic
1344C22×C4C2512yes—
1345C22×C4C2511yescharacteristic
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2511yescharacteristic
1349C22×C4C2512yes—
1350C22×C4C2514yes—
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2511yescharacteristic
1355C22×C4C2511yescharacteristic
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—24no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—24no—
1370C4⋊C4—22no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—22no—
1377C4⋊C4—22no—
1378C4⋊C4—22no—
1379C4⋊C4—24no—
1380C4⋊C4—24no—
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—22no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—44no—
1390C4⋊C4—41no—
1391C4⋊C4—41no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—44no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—44no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—44no—
1406C4⋊C4—42no—
1407C4⋊C4—44no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C22⋊C4—28no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—28no—
1422C22⋊C4—28no—
1423C22⋊C4—24no—
1424C22⋊C4—22no—
1425C22⋊C4—24no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—44no—
1439C22⋊C4—41no—
1440C22⋊C4—44no—
1441C22⋊C4—41no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—41no—
1445C22⋊C4—41no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—42no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—42no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—44no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4H(5,𝔽2)14yes—
1489C42—22no—
1490C42—22no—
1491C42—22no—
1492C42—22no—
1493C42—22no—
1494C42—22no—
1495C42—24no—
1496C42—24no—
1497C42—24no—
1498C42—22no—
1499C42—24no—
1500C42—22no—
1501C42—24no—
1502C42—22no—
1503C42—22no—
1504C42—22no—
1505C42—24no—
1506C42—24no—
1507C42—24no—
1508C42—42no—
1509C42—42no—
1510C42—42no—
1511C42—42no—
1512C42—44no—
1513C42—44no—
1514C42—42no—
1515C42—44no—
1516C42—41no—
1517C42—44no—
1518C42H(5,𝔽2)14yes—
1519C23—21no—
1520C23—21no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—21no—
1525C23—24no—
1526C23—22no—
1527C23—22no—
1528C23—21no—
1529C23—24no—
1530C23—24no—
1531C23—21no—
1532C23—24no—
1533C23—21no—
1534C23—24no—
1535C23—21no—
1536C23—24no—
1537C23—24no—
1538C23—22no—
1539C23—22no—
1540C23—21no—
1541C23—24no—
1542C23—24no—
1543C23—24no—
1544C23—24no—
1545C23—24no—
1546C23—21no—
1547C23—22no—
1548C23—22no—
1549C23—21no—
1550C23—24no—
1551C23—22no—
1552C23—24no—
1553C23—88no—
1554C23—88no—
1555C23—88no—
1556C23—88no—
1557C23—88no—
1558C23—164no—
1559C23—164no—
1560C23C2×H(5,𝔽2)12yes—
1561C23C2611yescharacteristic
1562Q8—44no—
1563Q8—44no—
1564Q8—44no—
1565Q8—84no—
1566Q8—84no—
1567Q8—164no—
1568D4—48no—
1569D4—44no—
1570D4—48no—
1571D4—48no—
1572D4—48no—
1573D4—44no—
1574D4—48no—
1575D4—48no—
1576D4—84no—
1577D4—84no—
1578D4—88no—
1579D4—88no—
1580D4—88no—
1581D4—88no—
1582D4—88no—
1583D4—88no—
1584D4—88no—
1585D4—164no—
1586D4—164no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—24no—
1613C2×C4—22no—
1614C2×C4—24no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—24no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—22no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—22no—
1663C2×C4—24no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—21no—
1668C2×C4—44no—
1669C2×C4—44no—
1670C2×C4—48no—
1671C2×C4—44no—
1672C2×C4—44no—
1673C2×C4—44no—
1674C2×C4—48no—
1675C2×C4—44no—
1676C2×C4—88no—
1677C2×C4—84no—
1678C2×C4—88no—
1679C2×C4—88no—
1680C2×C4—164no—
1681C2×C4C2×H(5,𝔽2)12yes—
1682C2×C4C2×H(5,𝔽2)12yes—
1683C2×C4C2×H(5,𝔽2)12yes—
1684C2×C4C2×H(5,𝔽2)12yes—
1685C2×C4C2×H(5,𝔽2)12yes—
1686C2×C4#58512yes—
1687C2×C4#58512yes—
1688C2×C4#58512yes—
1689C2×C4#58512yes—
1690C22—22no—
1691C22—22no—
1692C22—22no—
1693C22—41no—
1694C22—41no—
1695C22—41no—
1696C22—41no—
1697C22—42no—
1698C22—41no—
1699C22—44no—
1700C22—44no—
1701C22—42no—
1702C22—41no—
1703C22—44no—
1704C22—44no—
1705C22—44no—
1706C22—41no—
1707C22—42no—
1708C22—44no—
1709C22—44no—
1710C22—42no—
1711C22—41no—
1712C22—44no—
1713C22—41no—
1714C22—44no—
1715C22—42no—
1716C22—44no—
1717C22—42no—
1718C22—44no—
1719C22—41no—
1720C22—44no—
1721C22—42no—
1722C22—44no—
1723C22—41no—
1724C22—44no—
1725C22—1616no—
1726C22C22×H(5,𝔽2)11yescharacteristic
1727C22C22×H(5,𝔽2)11yescharacteristic
1728C22C2×#58511yescharacteristic
1729C22C2×#58511yescharacteristic
1730C22C2×#58511yescharacteristic
1731C22C2×#58511yescharacteristic
1732C22H(7,𝔽2)11yescharacteristic
1733C4—22no—
1734C4—22no—
1735C4—22no—
1736C4—41no—
1737C4—42no—
1738C4—41no—
1739C4—42no—
1740C4—41no—
1741C4—42no—
1742C4—41no—
1743C4—42no—
1744C4—42no—
1745C4—42no—
1746C4—41no—
1747C4—42no—
1748C4—44no—
1749C4—42no—
1750C4—41no—
1751C4—42no—
1752C4—44no—
1753C4—42no—
1754C4—42no—
1755C4—42no—
1756C4—42no—
1757C4—41no—
1758C4—42no—
1759C4—41no—
1760C4—42no—
1761C4#354014yes—
1762C4#356214yes—
1763C2—42no—
1764C2—81no—
1765C2—82no—
1766C2—84no—
1767C2—84no—
1768C2C2×#354011yescharacteristic
1769C2C2×#356211yescharacteristic
1770C2#6275911yescharacteristic
1771C2#6291211yescharacteristic
1772C2#6296611yescharacteristic
1773C2#6296911yescharacteristic
1774C2#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. #59863C2semidirect
2. #59476C2semidirect
3. #59375C2semidirect
4. #59143C2semidirect
5. #59084C2semidirect
6. #56922C2semidirect
7. #53909C2semidirect
8. #53129C2semidirect
9. #53116C2semidirect
10. #53088C2semidirect
11. #53071C2semidirect
12. #52409C2semidirect
13. #42629C2semidirect
14. #42627C2semidirect
15. #42624C2semidirect
16. #42619C2semidirect
17. #40596C2semidirect
18. #39821C2semidirect
19. #39808C2semidirect
20. #39201C2semidirect
21. #39168C2semidirect
22. #39157C2semidirect
23. #39125C2semidirect
24. #39034C2semidirect
25. #39020C2semidirect
26. #37625C2semidirect
27. #37614C2semidirect
28. #37572C2semidirect
29. #37523C2semidirect
30. #36493C2semidirect
31. #36302C2semidirect
32. #36121C2semidirect
33. #34977C2semidirect
34. #34803C2semidirect
35. #34724C2semidirect
37. C2×Q82C22semidirect
43. C2×C4×#41C22semidirect
44. #2861C22semidirect
48. #2850C22semidirect
49. #2837C22semidirect
50. #2832C22semidirect
51. #2829C22semidirect
52. #2829C22semidirect
53. #2828C22semidirect
54. #2828C22semidirect
55. #2826C22semidirect
56. #2825C22semidirect
57. #2824C22semidirect
58. #2824C22semidirect
59. #2819C22semidirect
61. #2813C22semidirect
63. #2808C22semidirect
64. #2803C22semidirect
65. #2803C22semidirect
66. #2801C22semidirect
67. #2797C22semidirect
68. #2797C22semidirect
69. #2781C22semidirect
70. #2779C22semidirect
71. #2778C22semidirect
72. #2778C22semidirect
73. #2762C22semidirect
74. #2753C22semidirect
75. #2741C22semidirect
76. #2741C22semidirect
80. #2731C22semidirect
81. #2730C22semidirect
82. #2716C22semidirect
83. #2712C22semidirect
84. #2710C22semidirect
85. #2710C22semidirect
87. #2703C22semidirect
88. #2696C22semidirect
89. #2693C22semidirect
96. #2674C22semidirect
97. #2674C22semidirect
98. #2672C22semidirect
100. #2663C22semidirect
101. #2663C22semidirect
103. #2653C22semidirect
104. #2653C22semidirect
105. #2649C22semidirect
106. #2649C22semidirect
107. #2649C22semidirect
108. #2645C22semidirect
109. #2644C22semidirect
111. #2641C22semidirect
112. #2640C22semidirect
113. #2630C22semidirect
114. #2628C22semidirect
115. #2624C22semidirect
116. #2624C22semidirect
117. #2624C22semidirect
119. #2620C22semidirect
123. #2610C22semidirect
124. #2602C22semidirect
125. #2600C22semidirect
126. #2598C22semidirect
127. #2592C22semidirect
128. #2592C22semidirect
129. #2580C22semidirect
130. #2571C22semidirect
131. #2567C22semidirect
132. #2563C22semidirect
133. #2563C22semidirect
134. #2552C22semidirect
135. #2550C22semidirect
140. #2548C22semidirect
142. #2547C22semidirect
143. #2545C22semidirect
147. #2542C22semidirect
150. #2540C22semidirect
151. #2538C22semidirect
153. #2535C22semidirect
154. #2533C22semidirect
155. #2531C22semidirect
157. #2523C22semidirect
158. #2518C22semidirect
159. #2514C22semidirect
160. #2513C22semidirect
161. #2513C22semidirect
162. #2513C22semidirect
163. #2513C22semidirect
164. #2509C22semidirect
165. #2509C22semidirect
166. #2500C22semidirect
167. #2500C22semidirect
168. #2499C22semidirect
175. #2491C22semidirect
176. #2491C22semidirect
177. #2491C22semidirect
178. #2490C22semidirect
181. #2485C22semidirect
184. #2478C22semidirect
185. #2477C22semidirect
186. #2477C22semidirect
187. #2476C22semidirect
189. #2471C22semidirect
190. #2471C22semidirect
192. #2470C22semidirect
194. #2466C22semidirect
195. #2463C22semidirect
196. #2459C22semidirect
197. #2456C22semidirect
199. #2455C22semidirect
200. #2454C22semidirect
201. #2453C22semidirect
202. #2452C22semidirect
203. #2452C22semidirect
204. #2452C22semidirect
205. #2452C22semidirect
206. #2448C22semidirect
207. #2448C22semidirect
208. #2448C22semidirect
209. #2448C22semidirect
210. #2447C22semidirect
215. #2445C22semidirect
216. #2445C22semidirect
217. #2441C22semidirect
218. #2439C22semidirect
224. #2432C22semidirect
225. #2432C22semidirect
227. #2431C22semidirect
228. #2431C22semidirect
232. #2427C22semidirect
233. #2427C22semidirect
234. #2426C22semidirect
235. #2426C22semidirect
237. #2422C22semidirect
238. #2422C22semidirect
243. #2414C22semidirect
244. #2414C22semidirect
251. #2401C22semidirect
253. #2395C22semidirect
255. #2388C22semidirect
256. #2369C22semidirect
257. #2367C22semidirect
258. #2367C22semidirect
260. #2366C22semidirect
261. #2363C22semidirect
262. #2363C22semidirect
263. #2355C22semidirect
264. #2355C22semidirect
265. #2354C22semidirect
266. #2354C22semidirect
267. #2354C22semidirect
272. #2330C22semidirect
273. #2326C22semidirect
274. #2324C22semidirect
275. #2323C22semidirect
277. C4×C4⋊Q8C22semidirect
278. C4×C4⋊Q8C22semidirect
280. C4×#127C22semidirect
282. C4×#124C22semidirect
285. C4×C22⋊Q8C22semidirect
286. C4×C22⋊Q8C22semidirect
288. C4×#121C22semidirect
289. C4×#121C22semidirect
290. C4×#121C22semidirect
291. #2296C22semidirect
292. #2295C22semidirect
293. #2295C22semidirect
294. #2293C22semidirect
295. #2293C22semidirect
298. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#598632
#594762
#593752
#591432
#590842
#569222
#539092
#531292
#531162
#530882
#530712
#524092
#426292
#426272
#426242
#426192
#405962
#398212
#398082
#392012
#391682
#391572
#391252
#390342
#390202
#376252
#376142
#375722
#375232
#364932
#363022
#361212
#349772
#348032
#347242