Finite Group Databasebeta

← #8425005

Subgroups — #8425005

Order 512.

5477 conjugacy classes of subgroups.

The subgroup lattice has 1852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59679C211yesmaximal, characteristic, complemented
2#59378C212yesmaximal, complemented
3#59129C212yesmaximal, complemented
4#59124C211yesmaximal, characteristic, complemented
5#59080C211yesmaximal, characteristic, complemented
6#53514C214yesmaximal, complemented
7#53392C214yesmaximal, complemented
8#53004C212yesmaximal, complemented
9#52977C212yesmaximal, complemented
10#52971C212yesmaximal, complemented
11#52970C212yesmaximal, complemented
12#52488C214yesmaximal, complemented
13#42943C212yesmaximal, complemented
14#42903C212yesmaximal, complemented
15#42617C212yesmaximal, complemented
16#42606C212yesmaximal, complemented
17#41033C214yesmaximal, complemented
18#40053C212yesmaximal, complemented
19#39960C212yesmaximal, complemented
20#39818C212yesmaximal, complemented
21#39363C211yesmaximal, characteristic, complemented
22#39202C211yesmaximal, characteristic, complemented
23#39149C211yesmaximal, characteristic, complemented
24#39124C211yesmaximal, characteristic, complemented
25#37683C212yesmaximal, complemented
26#37626C211yesmaximal, characteristic, complemented
27#37614C211yesmaximal, characteristic, complemented
28#37523C212yesmaximal, complemented
29#37498C212yesmaximal, complemented
30#36587C211yesmaximal, characteristic, complemented
31#36455C211yesmaximal, characteristic, complemented
32#36121C211yesmaximal, characteristic, complemented
33#34937C211yesmaximal, characteristic, complemented
34#34788C211yesmaximal, characteristic, complemented
35#34724C211yesmaximal, characteristic, complemented
36C2×#550C2211yescharacteristic
37C2×#550C2212yescomplemented
38C2×D4×Q8C2211yescharacteristic, complemented
39C2×#548C2212yescomplemented
40C2×#546C2212yes—
41C2×#546C2212yes—
42C2×#536C2212yescomplemented
43C2×#532C2211yescharacteristic
44C2×#532C2212yescomplemented
45C22×#127C2211yescharacteristic
46C2×#529C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic, complemented
48#2858C2211yescharacteristic
49#2857C2211yescharacteristic
50#2856C2211yescharacteristic
51#2856C2212yescomplemented
52#2850C2212yescomplemented
53#2829C2214yescomplemented
54#2829C2214yescomplemented
55#2828C2214yescomplemented
56#2828C2214yescomplemented
57#2826C2214yescomplemented
58#2826C2214yescomplemented
59#2825C2214yescomplemented
60#2825C2214yescomplemented
61#2824C2214yescomplemented
62#2824C2214yescomplemented
63#2824C2214yescomplemented
64#2818C2214yes—
65#2814C2214yescomplemented
66#2812C2214yes—
67#2803C2214yescomplemented
68#2800C2214yescomplemented
69#2797C2214yescomplemented
70#2797C2214yescomplemented
71#2781C2214yescomplemented
72#2776C2214yescomplemented
73#2760C2214yescomplemented
74#2752C2214yescomplemented
75#2750C2214yescomplemented
76#2739C2214yes—
77#2723C2214yescomplemented
78#2714C2214yescomplemented
79#2701C2214yescomplemented
80#2701C2214yescomplemented
81#2697C2214yes—
82#2697C2214yes—
83#2697C2214yes—
84#2696C2214yes—
85#2688C2214yescomplemented
86#2688C2214yescomplemented
87#2688C2214yescomplemented
88#2688C2214yescomplemented
89#2686C2214yescomplemented
90#2685C2214yes—
91#2684C2214yes—
92#2681C2214yescomplemented
93#2681C2214yescomplemented
94#2678C2214yes—
95#2676C2214yescomplemented
96#2676C2214yescomplemented
97#2676C2214yescomplemented
98#2673C2214yes—
99#2673C2214yescomplemented
100#2673C2214yescomplemented
101#2671C2214yescomplemented
102#2669C2214yes—
103#2668C2214yes—
104#2663C2214yescomplemented
105#2663C2214yescomplemented
106#2657C2212yes—
107#2649C2214yescomplemented
108#2649C2214yescomplemented
109#2648C2214yescomplemented
110#2648C2214yescomplemented
111#2645C2212yescomplemented
112#2641C2212yes—
113#2636C2214yescomplemented
114#2635C2214yescomplemented
115#2635C2214yescomplemented
116#2628C2212yescomplemented
117#2626C2214yes—
118#2624C2212yescomplemented
119#2624C2212yescomplemented
120#2624C2212yescomplemented
121#2620C2212yescomplemented
122#2619C2212yes—
123#2619C2212yes—
124#2619C2212yescomplemented
125#2619C2212yescomplemented
126#2613C2214yes—
127#2602C2214yescomplemented
128#2597C2214yescomplemented
129#2576C2214yescomplemented
130#2576C2214yescomplemented
131#2571C2211yescharacteristic, complemented
132#2570C2212yescomplemented
133#2566C2212yescomplemented
134#2563C2212yes—
135#2561C2214yes—
136#2561C2214yes—
137#2559C2214yescomplemented
138#2548C2211yescharacteristic
139#2548C2211yescharacteristic
140#2548C2211yescharacteristic
141#2548C2212yescomplemented
142#2547C2211yescharacteristic, complemented
143#2546C2211yescharacteristic, complemented
144#2545C2212yescomplemented
145#2545C2212yescomplemented
146#2544C2212yes—
147#2544C2212yescomplemented
148#2544C2212yescomplemented
149#2543C2214yescomplemented
150#2541C2211yescharacteristic
151#2541C2211yescharacteristic
152#2541C2212yes—
153#2541C2211yescharacteristic
154#2541C2212yescomplemented
155#2540C2212yes—
156#2537C2212yescomplemented
157#2537C2211yescharacteristic, complemented
158#2535C2212yes—
159#2525C2212yescomplemented
160#2516C2212yes—
161#2513C2212yescomplemented
162#2513C2212yescomplemented
163#2513C2211yescharacteristic, complemented
164#2513C2212yescomplemented
165#2512C2212yescomplemented
166#2512C2212yescomplemented
167#2510C2212yescomplemented
168#2509C2212yescomplemented
169#2509C2211yescharacteristic, complemented
170#2504C2211yescharacteristic, complemented
171#2504C2212yescomplemented
172#2497C2212yes—
173#2494C2211yescharacteristic
174#2494C2212yes—
175#2491C2212yescomplemented
176#2490C2211yescharacteristic
177#2490C2212yescomplemented
178#2489C2212yescomplemented
179#2487C2211yescharacteristic
180#2478C2212yescomplemented
181#2470C2212yes—
182#2466C2212yescomplemented
183#2466C2214yescomplemented
184#2464C2214yescomplemented
185#2463C2214yescomplemented
186#2463C2214yescomplemented
187#2463C2214yescomplemented
188#2456C2214yescomplemented
189#2456C2214yescomplemented
190#2455C2212yes—
191#2455C2214yescomplemented
192#2453C2211yescharacteristic, complemented
193#2452C2212yescomplemented
194#2452C2212yescomplemented
195#2452C2212yescomplemented
196#2448C2212yescomplemented
197#2447C2211yescharacteristic, complemented
198#2447C2212yescomplemented
199#2447C2212yescomplemented
200#2447C2212yescomplemented
201#2445C2212yes—
202#2445C2212yes—
203#2445C2212yes—
204#2445C2212yescomplemented
205#2445C2212yescomplemented
206#2444C2212yes—
207#2444C2214yescomplemented
208#2442C2211yescharacteristic, complemented
209#2441C2211yescharacteristic, complemented
210#2436C2212yescomplemented
211#2436C2212yescomplemented
212#2436C2212yescomplemented
213#2435C2212yes—
214#2435C2212yes—
215#2433C2212yes—
216#2433C2212yes—
217#2432C2211yescharacteristic, complemented
218#2432C2212yescomplemented
219#2431C2212yes—
220#2431C2212yes—
221#2429C2211yescharacteristic
222#2429C2212yes—
223#2428C2212yes—
224#2428C2212yes—
225#2428C2212yes—
226#2428C2214yescomplemented
227#2428C2214yescomplemented
228#2428C2212yescomplemented
229#2428C2212yescomplemented
230#2428C2212yescomplemented
231#2428C2212yescomplemented
232#2426C2212yescomplemented
233#2424C2214yes—
234#2424C2214yes—
235#2422C2211yescharacteristic
236#2421C2212yes—
237#2420C2212yescomplemented
238#2420C2212yescomplemented
239#2420C2212yescomplemented
240#2416C2211yescharacteristic
241#2416C2212yescomplemented
242#2416C2212yescomplemented
243#2415C2211yescharacteristic
244#2414C2214yescomplemented
245#2414C2212yescomplemented
246#2410C2214yes—
247#2409C2212yes—
248#2408C2212yes—
249#2408C2212yes—
250#2408C2212yes—
251#2408C2212yes—
252#2408C2212yes—
253#2407C2211yescharacteristic
254#2407C2212yescomplemented
255#2401C2212yescomplemented
256#2395C2212yes—
257#2395C2212yescomplemented
258#2392C2212yes—
259#2392C2214yescomplemented
260#2367C2212yescomplemented
261#2366C2211yescharacteristic
262#2366C2212yescomplemented
263#2365C2211yescharacteristic, complemented
264#2361C2212yescomplemented
265#2358C2214yes—
266#2357C2212yescomplemented
267#2357C2212yescomplemented
268#2355C2211yescharacteristic, complemented
269Q8×C4⋊C4C2211yescharacteristic, complemented
270#2341C2212yescomplemented
271D4×C22⋊C4C2212yes—
272D4×C22⋊C4C2212yes—
273D4×C22⋊C4C2212yes—
274#2327C2212yescomplemented
275#2324C2212yescomplemented
276#2324C2212yescomplemented
277#2321C2214yes—
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×#127C2211yescharacteristic
280C4×#125C2211yescharacteristic, complemented
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2211yescharacteristic, complemented
283C4×#123C2212yes—
284C4×#121C2212yes—
285C4×#121C2211yescharacteristic
286C4×#121C2212yescomplemented
287C4×#121C2211yescharacteristic, complemented
288C4×#121C2212yescomplemented
289C4×#121C2212yescomplemented
290C4×#121C2212yescomplemented
291#2297C2212yescomplemented
292#2296C2212yescomplemented
293#2293C2211yescharacteristic, complemented
294#2293C2211yescharacteristic, complemented
295#2290C2212yescomplemented
296#2283C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic, complemented
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×Q8C2312yes—
303C23×D4C2312yes—
304C23×D4C2312yes—
305C23×D4C2312yes—
306#550—44no—
307#550—48no—
308D4×Q8—44no—
309#548—48no—
310#546—48no—
311#546—48no—
312#536—48no—
313#532—44no—
314#532—48no—
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2312yes—
319C2×#127—44no—
320C2×#127C2311yescharacteristic
321C2×#127C2311yescharacteristic
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2312yes—
326C2×#127C2312yes—
327C2×#127C2312yes—
328C2×#127C2312yes—
329C2×#127C2314yes—
330#529—44no—
331C2×#126C2312yes—
332C2×#126C2314yes—
333C2×#125C2311yescharacteristic
334C2×#125C2311yescharacteristic
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2311yescharacteristic
340C2×#124C2312yes—
341C2×#124C2312yes—
342C2×#124C2312yes—
343C2×#124C2314yes—
344C2×#123C2314yes—
345C2×#123C2312yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×#123C2312yes—
350C2×C22⋊Q8C2311yescharacteristic
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2311yescharacteristic
358C2×C22⋊Q8C2314yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2314yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2311yescharacteristic
372C2×#121C2312yes—
373C2×#121C2312yes—
374C2×#121C2314yes—
375C2×#121C2312yes—
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2314yes—
379C2×#121C2314yes—
380C2×#121C2311yescharacteristic
381C2×#121C2311yescharacteristic
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2312yes—
385C2×#121C2314yes—
386C2×#121C2314yes—
387C2×#121C2314yes—
388C2×#120C2314yes—
389C2×#120C2314yes—
390C2×#120C2314yes—
391C2×#120C2314yes—
392C2×#120C2314yes—
393C4×#41—44no—
394C2×C4×Q8C2311yescharacteristic
395C2×C4×Q8C2311yescharacteristic
396C2×C4×Q8C2312yes—
397C2×C4×Q8C2312yes—
398C2×C4×Q8C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2312yes—
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2314yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2314yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2311yescharacteristic
416C2×C4×D4C2312yes—
417C2×C4×D4C2314yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2311yescharacteristic
420C2×C4×D4C2312yes—
421C2×C4×D4C2311yescharacteristic
422C2×C4×D4C2312yes—
423C2×C4×D4C2314yes—
424C2×#117C2312yes—
425C2×#117C2312yes—
426C2×#117C2312yes—
427C2×#117C2312yes—
428C2×#117C2311yescharacteristic
429C22×C4⋊C4C2311yescharacteristic
430C22×C4⋊C4C2311yescharacteristic
431C22×C22⋊C4C2314yes—
432C22×C22⋊C4C2314yes—
433C22×C42C2311yescharacteristic
434C22×C42C2311yescharacteristic
435C22×C42C2312yes—
436C22×C42C2312yes—
437#401C2314yes—
438#401C2312yes—
439#400C2312yes—
440#400C2312yes—
441#400C2312yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2312yes—
446#400C2314yes—
447#400C2314yes—
448#400C2314yes—
449#400C2312yes—
450#399C2312yes—
451#399C2314yes—
452#399C2314yes—
453#399C2314yes—
454#399C2312yes—
455#398C2314yes—
456#398C2312yes—
457#398C2312yes—
458#398C2314yes—
459#398C2312yes—
460#397C2312yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2312yes—
465#397C2312yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2312yes—
476#397C2312yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2312yes—
481#397C2312yes—
482#397C2312yes—
483#397C2312yes—
484#397C2312yes—
485#396C2314yes—
486#396C2314yes—
487#396C2312yes—
488#396C2312yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2312yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#395C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#394C2312yes—
533#394C2312yes—
534#394C2312yes—
535#394C2314yes—
536#394C2314yes—
537#394C2312yes—
538#394C2312yes—
539#394C2312yes—
540#394C2312yes—
541#393C2314yes—
542#393C2314yes—
543#393C2314yes—
544#393C2314yes—
545#393C2314yes—
546#393C2314yes—
547#393C2314yes—
548#392C2314yes—
549#392C2314yes—
550#392C2314yes—
551#392C2314yes—
552#392C2314yes—
553#392C2314yes—
554#392C2314yes—
555#392C2314yes—
556#392C2314yes—
557#392C2314yes—
558#392C2314yes—
559#392C2314yes—
560#392C2314yes—
561#392C2314yes—
562#392C2314yes—
563#392C2314yes—
564#392C2314yes—
565#392C2314yes—
566#392C2314yes—
567#392C2314yes—
568#392C2312yes—
569#392C2314yes—
570#392C2314yes—
571#391C2311yescharacteristic
572#391C2311yescharacteristic
573#391C2311yescharacteristic
574#391C2312yes—
575#391C2312yes—
576#391C2312yes—
577#391C2312yes—
578#391C2312yes—
579#391C2311yescharacteristic
580#390C2312yes—
581#390C2312yes—
582#390C2312yes—
583#390C2314yes—
584#390C2312yes—
585#390C2312yes—
586#390C2314yes—
587#390C2314yes—
588#390C2314yes—
589#390C2312yes—
590#390C2314yes—
591#390C2311yescharacteristic
592#390C2312yes—
593#390C2314yes—
594#390C2312yes—
595#390C2312yes—
596#390C2312yes—
597#390C2312yes—
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2314yes—
603#390C2312yes—
604#390C2311yescharacteristic
605#390C2312yes—
606#390C2312yes—
607#390C2312yes—
608#390C2312yes—
609#390C2311yescharacteristic
610#390C2311yescharacteristic
611#390C2312yes—
612#390C2312yes—
613#390C2314yes—
614#390C2312yes—
615#390C2312yes—
616#390C2311yescharacteristic
617#390C2312yes—
618#390C2311yescharacteristic
619#389C2311yescharacteristic
620#389C2311yescharacteristic
621#389C2312yes—
622#389C2312yes—
623#389C2312yes—
624#389C2312yes—
625#389C2312yes—
626#389C2312yes—
627#389C2312yes—
628#389C2312yes—
629#389C2312yes—
630#389C2314yes—
631#389C2312yes—
632#389C2311yescharacteristic
633#389C2311yescharacteristic
634#389C2311yescharacteristic
635#389C2311yescharacteristic
636#389C2312yes—
637#389C2312yes—
638#389C2312yes—
639#389C2312yes—
640#389C2314yes—
641#389C2311yescharacteristic
642#389C2312yes—
643#389C2311yescharacteristic
644#389C2311yescharacteristic
645#389C2311yescharacteristic
646#388C2312yes—
647#388C2312yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2312yes—
655#388C2312yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#388C2312yes—
668#388C2314yes—
669#388C2312yes—
670#388C2312yes—
671#388C2312yes—
672#388C2314yes—
673#388C2314yes—
674#388C2312yes—
675#388C2312yes—
676#388C2312yes—
677#387C2312yes—
678#387C2312yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2312yes—
683#387C2312yes—
684#387C2312yes—
685#387C2314yes—
686#387C2314yes—
687#387C2312yes—
688#387C2314yes—
689#387C2314yes—
690#387C2312yes—
691#387C2312yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2312yes—
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#386C2312yes—
716#386C2314yes—
717#386C2314yes—
718#386C2314yes—
719#386C2312yes—
720#386C2314yes—
721#386C2314yes—
722#386C2312yes—
723#386C2312yes—
724#386C2312yes—
725#386C2312yes—
726#386C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2312yes—
730#385C2314yes—
731#385C2312yes—
732#385C2312yes—
733#385C2314yes—
734#385C2314yes—
735#385C2314yes—
736#385C2314yes—
737#385C2312yes—
738#385C2314yes—
739#385C2312yes—
740#385C2312yes—
741#385C2312yes—
742#385C2312yes—
743#385C2312yes—
744#384C2311yescharacteristic
745#384C2311yescharacteristic
746#384C2312yes—
747#383C2312yes—
748#382C2311yescharacteristic
749#382C2314yes—
750#382C2312yes—
751#382C2311yescharacteristic
752#382C2312yes—
753#382C2312yes—
754#382C2311yescharacteristic
755#381C2314yes—
756#381C2314yes—
757#381C2314yes—
758#381C2314yes—
759#381C2312yes—
760#381C2312yes—
761#380C2311yescharacteristic
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2314yes—
768#380C2312yes—
769#380C2311yescharacteristic
770#380C2311yescharacteristic
771#380C2311yescharacteristic
772#380C2311yescharacteristic
773#380C2312yes—
774#380C2311yescharacteristic
775#379C2314yes—
776#379C2314yes—
777#379C2314yes—
778#379C2314yes—
779#379C2314yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2311yescharacteristic
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2311yescharacteristic
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2311yescharacteristic
818C4×C22⋊C4C2311yescharacteristic
819#376C2312yes—
820C2×#95C2312yes—
821C43C2311yescharacteristic
822C25C2414yes—
823C2×#41—24no—
824C2×#41—28no—
825C2×#41—24no—
826C2×#41—28no—
827C2×#41—42no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—44no—
832C22×Q8—44no—
833C22×Q8—44no—
834C22×Q8—44no—
835C22×Q8C2411yescharacteristic
836C22×Q8C2412yes—
837C22×Q8C2411yescharacteristic
838C22×Q8C2414yes—
839C22×D4—44no—
840C22×D4—44no—
841C22×D4—44no—
842C22×D4—44no—
843C22×D4—44no—
844C22×D4—44no—
845C22×D4—44no—
846C22×D4—44no—
847C22×D4—82no—
848C22×D4C2411yescharacteristic
849C22×D4C2411yescharacteristic
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2411yescharacteristic
855C22×D4C2412yes—
856C22×D4C2412yes—
857C22×D4C2412yes—
858C22×D4C2412yes—
859C22×D4C2414yes—
860C22×D4C2412yes—
861C22×D4C2414yes—
862C22×D4C2414yes—
863C22×D4C2412yes—
864C22×D4C2414yes—
865C22×D4C2414yes—
866C22×D4C2414yes—
867C22×D4C2414yes—
868C22×D4C2414yes—
869C22×D4C2414yes—
870C22×D4C2414yes—
871C22×D4C2414yes—
872C22×D4C2414yes—
873C22×D4C2414yes—
874C22×D4C2414yes—
875C23×C4C2411yescharacteristic
876C23×C4C2412yes—
877C23×C4C2412yes—
878C23×C4C2411yescharacteristic
879C23×C4C2411yescharacteristic
880C23×C4C2412yes—
881C23×C4C2411yescharacteristic
882C23×C4C2411yescharacteristic
883C23×C4C2414yes—
884C23×C4C2414yes—
885C23×C4C2411yescharacteristic
886C23×C4C2414yes—
887C23×C4C2414yes—
888C23×C4C2412yes—
889C23×C4C2412yes—
890C23×C4C2412yes—
891C23×C4C2414yes—
892C4⋊Q8—28no—
893C4⋊Q8—24no—
894C4⋊Q8—24no—
895C4⋊Q8—44no—
896#127—24no—
897#127—24no—
898#127—44no—
899#127—44no—
900#127—44no—
901#127—44no—
902#127—44no—
903#127—44no—
904#127—44no—
905#127—48no—
906#126—44no—
907#126—84no—
908#125—42no—
909#125—42no—
910#124—28no—
911#124—42no—
912#124—44no—
913#124—44no—
914#124—44no—
915#124—44no—
916#124—44no—
917#124—44no—
918#124—48no—
919#123—44no—
920#123—44no—
921#123—48no—
922#123—48no—
923#123—48no—
924#123—48no—
925C22⋊Q8—24no—
926C22⋊Q8—24no—
927C22⋊Q8—48no—
928C22⋊Q8—48no—
929C22⋊Q8—48no—
930C22⋊Q8—48no—
931C22⋊Q8—42no—
932C22⋊Q8—44no—
933C22⋊Q8—44no—
934#121—28no—
935#121—48no—
936#121—48no—
937#121—48no—
938#121—48no—
939#121—48no—
940#121—44no—
941#121—48no—
942#121—48no—
943#121—48no—
944#121—44no—
945#121—44no—
946#121—42no—
947#121—44no—
948#121—44no—
949#121—42no—
950#121—44no—
951#121—44no—
952#121—42no—
953#121—44no—
954#121—44no—
955#121—44no—
956#121—44no—
957#121—44no—
958#121—44no—
959#121—82no—
960#121—84no—
961#121—84no—
962#121—84no—
963#120—48no—
964#120—48no—
965#120—48no—
966#120—48no—
967#120—84no—
968C4×Q8—24no—
969C4×Q8—24no—
970C4×Q8—42no—
971C4×Q8—44no—
972C4×Q8—44no—
973C4×D4—24no—
974C4×D4—28no—
975C4×D4—24no—
976C4×D4—24no—
977C4×D4—44no—
978C4×D4—44no—
979C4×D4—42no—
980C4×D4—44no—
981C4×D4—44no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—44no—
985C4×D4—44no—
986C4×D4—42no—
987C4×D4—44no—
988C4×D4—44no—
989C4×D4—44no—
990C4×D4—44no—
991C4×D4—48no—
992C4×D4—48no—
993C4×D4—48no—
994C4×D4—48no—
995C4×D4—42no—
996C4×D4—82no—
997C4×D4—84no—
998#117—44no—
999#117—44no—
1000#117—44no—
1001#117—44no—
1002#117—42no—
1003C2×C4⋊C4—42no—
1004C2×C4⋊C4—42no—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2411yescharacteristic
1045C2×C4⋊C4C2411yescharacteristic
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2412yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2412yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2412yes—
1059C2×C22⋊C4—48no—
1060C2×C22⋊C4—48no—
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2411yescharacteristic
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2411yescharacteristic
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2411yescharacteristic
1104C2×C22⋊C4C2411yescharacteristic
1105C2×C22⋊C4C2411yescharacteristic
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2412yes—
1127C2×C22⋊C4C2412yes—
1128C2×C22⋊C4C2412yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2412yes—
1137C2×C42—24no—
1138C2×C42—24no—
1139C2×C42—44no—
1140C2×C42—44no—
1141C2×C42C2411yescharacteristic
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2412yes—
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2412yes—
1150C2×C42C2412yes—
1151C2×C42C2411yescharacteristic
1152C2×C42C2411yescharacteristic
1153C2×C42C2412yes—
1154C2×C42C2411yescharacteristic
1155C2×C42C2411yescharacteristic
1156C2×C42C2411yescharacteristic
1157C2×C42C2412yes—
1158C2×C42C2411yescharacteristic
1159C2×C42C2412yes—
1160C2×C42C2412yes—
1161C2×C42C2414yes—
1162C2×C42C2414yes—
1163C2×C42C2412yes—
1164C2×C42C2414yes—
1165C2×C42C2411yescharacteristic
1166C2×C42C2411yescharacteristic
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2411yescharacteristic
1179#95C2412yes—
1180#95C2411yescharacteristic
1181#95C2411yescharacteristic
1182#95C2411yescharacteristic
1183#95C2411yescharacteristic
1184#95C2411yescharacteristic
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2414yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2414yes—
1209#95C2412yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2412yes—
1213#95C2412yes—
1214#95C2412yes—
1215#95C2414yes—
1216#95C2412yes—
1217#95C2412yes—
1218#95C2412yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225C24—28no—
1226C24—44no—
1227C24—44no—
1228C24—44no—
1229C24—44no—
1230C24—44no—
1231C24—44no—
1232C24C2514yes—
1233C24C2514yes—
1234C24C2512yes—
1235C24C2512yes—
1236C24C2511yescharacteristic
1237C24C2511yescharacteristic
1238#41—416no—
1239#41—816no—
1240#41—816no—
1241C2×Q8—22no—
1242C2×Q8—22no—
1243C2×Q8—22no—
1244C2×Q8—24no—
1245C2×Q8—22no—
1246C2×Q8—24no—
1247C2×Q8—22no—
1248C2×Q8—24no—
1249C2×Q8—44no—
1250C2×Q8—44no—
1251C2×Q8—44no—
1252C2×Q8—816no—
1253C2×Q8H(5,𝔽2)14yes—
1254C2×D4—22no—
1255C2×D4—24no—
1256C2×D4—22no—
1257C2×D4—24no—
1258C2×D4—28no—
1259C2×D4—28no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—22no—
1263C2×D4—22no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—24no—
1267C2×D4—24no—
1268C2×D4—24no—
1269C2×D4—24no—
1270C2×D4—24no—
1271C2×D4—22no—
1272C2×D4—24no—
1273C2×D4—24no—
1274C2×D4—22no—
1275C2×D4—24no—
1276C2×D4—28no—
1277C2×D4—24no—
1278C2×D4—24no—
1279C2×D4—24no—
1280C2×D4—22no—
1281C2×D4—24no—
1282C2×D4—22no—
1283C2×D4—24no—
1284C2×D4—42no—
1285C2×D4—41no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—44no—
1290C2×D4—42no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—42no—
1299C2×D4—44no—
1300C2×D4—44no—
1301C2×D4—44no—
1302C2×D4—44no—
1303C2×D4—44no—
1304C2×D4—44no—
1305C2×D4—44no—
1306C2×D4—42no—
1307C2×D4—44no—
1308C2×D4—42no—
1309C2×D4—44no—
1310C2×D4—44no—
1311C2×D4—44no—
1312C2×D4—42no—
1313C2×D4—42no—
1314C2×D4—44no—
1315C2×D4—44no—
1316C2×D4—44no—
1317C2×D4—44no—
1318C2×D4—44no—
1319C2×D4—42no—
1320C2×D4—44no—
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—44no—
1335C2×D4—816no—
1336C2×D4—816no—
1337C2×D4—816no—
1338C22×C4—22no—
1339C22×C4—22no—
1340C22×C4—22no—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—22no—
1345C22×C4—24no—
1346C22×C4—24no—
1347C22×C4—24no—
1348C22×C4—24no—
1349C22×C4—22no—
1350C22×C4—24no—
1351C22×C4—24no—
1352C22×C4—22no—
1353C22×C4—22no—
1354C22×C4—22no—
1355C22×C4—24no—
1356C22×C4—22no—
1357C22×C4—24no—
1358C22×C4—22no—
1359C22×C4—22no—
1360C22×C4—28no—
1361C22×C4—28no—
1362C22×C4—42no—
1363C22×C4—41no—
1364C22×C4—42no—
1365C22×C4—42no—
1366C22×C4—42no—
1367C22×C4—42no—
1368C22×C4—42no—
1369C22×C4—44no—
1370C22×C4—44no—
1371C22×C4—44no—
1372C22×C4—44no—
1373C22×C4—44no—
1374C22×C4—44no—
1375C22×C4—41no—
1376C22×C4—42no—
1377C22×C4—42no—
1378C22×C4—41no—
1379C22×C4—42no—
1380C22×C4—44no—
1381C22×C4—42no—
1382C22×C4—44no—
1383C22×C4—44no—
1384C22×C4—44no—
1385C22×C4—44no—
1386C22×C4—44no—
1387C22×C4—44no—
1388C22×C4H(5,𝔽2)14yes—
1389C22×C4C2511yescharacteristic
1390C22×C4C2511yescharacteristic
1391C22×C4C2511yescharacteristic
1392C22×C4C2512yes—
1393C22×C4C2512yes—
1394C22×C4C2512yes—
1395C22×C4C2511yescharacteristic
1396C22×C4C2512yes—
1397C22×C4C2512yes—
1398C22×C4C2512yes—
1399C22×C4C2512yes—
1400C22×C4C2512yes—
1401C22×C4C2514yes—
1402C22×C4C2511yescharacteristic
1403C22×C4C2512yes—
1404C22×C4C2511yescharacteristic
1405C22×C4C2512yes—
1406C22×C4C2511yescharacteristic
1407C22×C4C2512yes—
1408C22×C4C2514yes—
1409C22×C4C2512yes—
1410C22×C4C2511yescharacteristic
1411C22×C4C2512yes—
1412C22×C4C2511yescharacteristic
1413C22×C4C2511yescharacteristic
1414C22×C4C2511yescharacteristic
1415C22×C4C2512yes—
1416C22×C4C2511yescharacteristic
1417C22×C4C2511yescharacteristic
1418C4⋊C4—22no—
1419C4⋊C4—24no—
1420C4⋊C4—22no—
1421C4⋊C4—24no—
1422C4⋊C4—22no—
1423C4⋊C4—22no—
1424C4⋊C4—22no—
1425C4⋊C4—24no—
1426C4⋊C4—24no—
1427C4⋊C4—24no—
1428C4⋊C4—24no—
1429C4⋊C4—28no—
1430C4⋊C4—28no—
1431C4⋊C4—22no—
1432C4⋊C4—24no—
1433C4⋊C4—22no—
1434C4⋊C4—24no—
1435C4⋊C4—24no—
1436C4⋊C4—24no—
1437C4⋊C4—22no—
1438C4⋊C4—22no—
1439C4⋊C4—22no—
1440C4⋊C4—22no—
1441C4⋊C4—24no—
1442C4⋊C4—22no—
1443C4⋊C4—22no—
1444C4⋊C4—42no—
1445C4⋊C4—42no—
1446C4⋊C4—42no—
1447C4⋊C4—42no—
1448C4⋊C4—42no—
1449C4⋊C4—42no—
1450C4⋊C4—42no—
1451C4⋊C4—42no—
1452C4⋊C4—42no—
1453C4⋊C4—41no—
1454C4⋊C4—41no—
1455C4⋊C4—42no—
1456C4⋊C4—42no—
1457C4⋊C4—42no—
1458C4⋊C4—44no—
1459C4⋊C4—44no—
1460C4⋊C4—44no—
1461C4⋊C4—42no—
1462C4⋊C4—44no—
1463C4⋊C4—42no—
1464C4⋊C4—44no—
1465C4⋊C4—44no—
1466C4⋊C4—42no—
1467C4⋊C4—42no—
1468C4⋊C4—42no—
1469C4⋊C4—42no—
1470C4⋊C4—42no—
1471C4⋊C4—42no—
1472C22⋊C4—22no—
1473C22⋊C4—24no—
1474C22⋊C4—24no—
1475C22⋊C4—22no—
1476C22⋊C4—24no—
1477C22⋊C4—24no—
1478C22⋊C4—22no—
1479C22⋊C4—24no—
1480C22⋊C4—28no—
1481C22⋊C4—28no—
1482C22⋊C4—24no—
1483C22⋊C4—24no—
1484C22⋊C4—24no—
1485C22⋊C4—28no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—42no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—42no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—44no—
1499C22⋊C4—41no—
1500C22⋊C4—41no—
1501C22⋊C4—44no—
1502C22⋊C4—41no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—42no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C22⋊C4—44no—
1513C22⋊C4—42no—
1514C22⋊C4—44no—
1515C22⋊C4—42no—
1516C22⋊C4—42no—
1517C22⋊C4—44no—
1518C22⋊C4—44no—
1519C22⋊C4—44no—
1520C22⋊C4—44no—
1521C22⋊C4—44no—
1522C22⋊C4—44no—
1523C22⋊C4—44no—
1524C22⋊C4—42no—
1525C22⋊C4—44no—
1526C22⋊C4—42no—
1527C22⋊C4—44no—
1528C22⋊C4—44no—
1529C22⋊C4—44no—
1530C22⋊C4—44no—
1531C22⋊C4—44no—
1532C22⋊C4—44no—
1533C22⋊C4—42no—
1534C22⋊C4—42no—
1535C22⋊C4—44no—
1536C22⋊C4—44no—
1537C22⋊C4—42no—
1538C22⋊C4—42no—
1539C22⋊C4—42no—
1540C22⋊C4—44no—
1541C22⋊C4—42no—
1542C22⋊C4—44no—
1543C22⋊C4—44no—
1544C22⋊C4—44no—
1545C22⋊C4—44no—
1546C22⋊C4—44no—
1547C22⋊C4—42no—
1548C42—22no—
1549C42—22no—
1550C42—22no—
1551C42—22no—
1552C42—22no—
1553C42—22no—
1554C42—24no—
1555C42—24no—
1556C42—24no—
1557C42—22no—
1558C42—24no—
1559C42—22no—
1560C42—24no—
1561C42—22no—
1562C42—24no—
1563C42—22no—
1564C42—42no—
1565C42—42no—
1566C42—42no—
1567C42—42no—
1568C42—41no—
1569C42—44no—
1570C42—44no—
1571C42—41no—
1572C42—44no—
1573C42H(5,𝔽2)14yes—
1574C23—21no—
1575C23—21no—
1576C23—21no—
1577C23—21no—
1578C23—21no—
1579C23—21no—
1580C23—21no—
1581C23—21no—
1582C23—21no—
1583C23—21no—
1584C23—21no—
1585C23—21no—
1586C23—24no—
1587C23—22no—
1588C23—22no—
1589C23—24no—
1590C23—22no—
1591C23—24no—
1592C23—24no—
1593C23—22no—
1594C23—22no—
1595C23—22no—
1596C23—24no—
1597C23—24no—
1598C23—22no—
1599C23—22no—
1600C23—24no—
1601C23—24no—
1602C23—24no—
1603C23—24no—
1604C23—24no—
1605C23—22no—
1606C23—22no—
1607C23—22no—
1608C23—24no—
1609C23—22no—
1610C23—24no—
1611C23—22no—
1612C23—24no—
1613C23—22no—
1614C23—88no—
1615C23—88no—
1616C23—88no—
1617C23—88no—
1618C23—88no—
1619C23—164no—
1620C23—164no—
1621C23C2×H(5,𝔽2)12yes—
1622C23#58512yes—
1623C23C2611yescharacteristic
1624Q8—28no—
1625Q8—44no—
1626Q8—48no—
1627Q8—88no—
1628D4—48no—
1629D4—48no—
1630D4—44no—
1631D4—48no—
1632D4—48no—
1633D4—44no—
1634D4—44no—
1635D4—48no—
1636D4—48no—
1637D4—84no—
1638D4—88no—
1639D4—84no—
1640D4—84no—
1641D4—84no—
1642D4—88no—
1643D4—88no—
1644D4—88no—
1645D4—88no—
1646D4—88no—
1647D4—88no—
1648D4—88no—
1649D4—88no—
1650D4—88no—
1651D4—164no—
1652D4—164no—
1653D4—164no—
1654D4—164no—
1655C2×C4—21no—
1656C2×C4—22no—
1657C2×C4—21no—
1658C2×C4—22no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—28no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—22no—
1673C2×C4—22no—
1674C2×C4—21no—
1675C2×C4—21no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—22no—
1682C2×C4—24no—
1683C2×C4—24no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—21no—
1689C2×C4—24no—
1690C2×C4—22no—
1691C2×C4—24no—
1692C2×C4—22no—
1693C2×C4—21no—
1694C2×C4—21no—
1695C2×C4—21no—
1696C2×C4—22no—
1697C2×C4—21no—
1698C2×C4—22no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—21no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—22no—
1705C2×C4—22no—
1706C2×C4—21no—
1707C2×C4—22no—
1708C2×C4—22no—
1709C2×C4—21no—
1710C2×C4—22no—
1711C2×C4—22no—
1712C2×C4—24no—
1713C2×C4—22no—
1714C2×C4—21no—
1715C2×C4—22no—
1716C2×C4—22no—
1717C2×C4—22no—
1718C2×C4—22no—
1719C2×C4—21no—
1720C2×C4—22no—
1721C2×C4—21no—
1722C2×C4—21no—
1723C2×C4—22no—
1724C2×C4—22no—
1725C2×C4—21no—
1726C2×C4—21no—
1727C2×C4—24no—
1728C2×C4—21no—
1729C2×C4—22no—
1730C2×C4—22no—
1731C2×C4—22no—
1732C2×C4—22no—
1733C2×C4—21no—
1734C2×C4—48no—
1735C2×C4—44no—
1736C2×C4—44no—
1737C2×C4—48no—
1738C2×C4—44no—
1739C2×C4—48no—
1740C2×C4—44no—
1741C2×C4—82no—
1742C2×C4—88no—
1743C2×C4—88no—
1744C2×C4—84no—
1745C2×C4—84no—
1746C2×C4—84no—
1747C2×C4—88no—
1748C2×C4—164no—
1749C2×C4—164no—
1750C2×C4C2×H(5,𝔽2)12yes—
1751C2×C4C2×H(5,𝔽2)12yes—
1752C2×C4C2×H(5,𝔽2)14yes—
1753C2×C4C2×H(5,𝔽2)12yes—
1754C2×C4C2×H(5,𝔽2)12yes—
1755C2×C4C2×H(5,𝔽2)12yes—
1756C2×C4C2×H(5,𝔽2)12yes—
1757C2×C4#58512yes—
1758C2×C4#58512yes—
1759C22—22no—
1760C22—22no—
1761C22—22no—
1762C22—22no—
1763C22—22no—
1764C22—22no—
1765C22—41no—
1766C22—41no—
1767C22—41no—
1768C22—41no—
1769C22—41no—
1770C22—41no—
1771C22—41no—
1772C22—41no—
1773C22—42no—
1774C22—42no—
1775C22—44no—
1776C22—44no—
1777C22—42no—
1778C22—44no—
1779C22—44no—
1780C22—42no—
1781C22—42no—
1782C22—42no—
1783C22—44no—
1784C22—44no—
1785C22—42no—
1786C22—42no—
1787C22—44no—
1788C22—44no—
1789C22—44no—
1790C22—42no—
1791C22—44no—
1792C22—42no—
1793C22—42no—
1794C22—44no—
1795C22—44no—
1796C22—42no—
1797C22—44no—
1798C22—44no—
1799C22—42no—
1800C22—42no—
1801C22—1616no—
1802C22C22×H(5,𝔽2)11yescharacteristic
1803C22C22×H(5,𝔽2)11yescharacteristic
1804C22C22×H(5,𝔽2)11yescharacteristic
1805C22C2×#58511yescharacteristic
1806C22C2×#58511yescharacteristic
1807C22C2×#58511yescharacteristic
1808C22H(7,𝔽2)11yescharacteristic
1809C4—22no—
1810C4—24no—
1811C4—22no—
1812C4—42no—
1813C4—41no—
1814C4—44no—
1815C4—42no—
1816C4—41no—
1817C4—42no—
1818C4—41no—
1819C4—41no—
1820C4—42no—
1821C4—42no—
1822C4—41no—
1823C4—42no—
1824C4—42no—
1825C4—41no—
1826C4—42no—
1827C4—42no—
1828C4—42no—
1829C4—41no—
1830C4—41no—
1831C4—42no—
1832C4—42no—
1833C4—41no—
1834C4—44no—
1835C4—42no—
1836C4#353714yes—
1837C4#356214yes—
1838C2—42no—
1839C2—42no—
1840C2—82no—
1841C2—82no—
1842C2—84no—
1843C2—84no—
1844C2C2×#353711yescharacteristic
1845C2C2×#356211yescharacteristic
1846C2#6274811yescharacteristic
1847C2#6292311yescharacteristic
1848C2#6292411yescharacteristic
1849C2#6296111yescharacteristic
1850C2#6301911yescharacteristic
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. #59679C2semidirect
2. #59378C2semidirect
3. #59129C2semidirect
4. #59124C2semidirect
5. #59080C2semidirect
6. #53514C2semidirect
7. #53392C2semidirect
8. #53004C2semidirect
9. #52977C2semidirect
10. #52971C2semidirect
11. #52970C2semidirect
12. #52488C2semidirect
13. #42943C2semidirect
14. #42903C2semidirect
15. #42617C2semidirect
16. #42606C2semidirect
17. #41033C2semidirect
18. #40053C2semidirect
19. #39960C2semidirect
20. #39818C2semidirect
21. #39363C2semidirect
22. #39202C2semidirect
23. #39149C2semidirect
24. #39124C2semidirect
25. #37683C2semidirect
26. #37626C2semidirect
27. #37614C2semidirect
28. #37523C2semidirect
29. #37498C2semidirect
30. #36587C2semidirect
31. #36455C2semidirect
32. #36121C2semidirect
33. #34937C2semidirect
34. #34788C2semidirect
35. #34724C2semidirect
37. C2×#550C22semidirect
38. C2×D4×Q8C22semidirect
39. C2×#548C22semidirect
42. C2×#536C22semidirect
44. C2×#532C22semidirect
47. C2×C4×#41C22semidirect
51. #2856C22semidirect
52. #2850C22semidirect
53. #2829C22semidirect
54. #2829C22semidirect
55. #2828C22semidirect
56. #2828C22semidirect
57. #2826C22semidirect
58. #2826C22semidirect
59. #2825C22semidirect
60. #2825C22semidirect
61. #2824C22semidirect
62. #2824C22semidirect
63. #2824C22semidirect
65. #2814C22semidirect
67. #2803C22semidirect
68. #2800C22semidirect
69. #2797C22semidirect
70. #2797C22semidirect
71. #2781C22semidirect
72. #2776C22semidirect
73. #2760C22semidirect
74. #2752C22semidirect
75. #2750C22semidirect
77. #2723C22semidirect
78. #2714C22semidirect
79. #2701C22semidirect
80. #2701C22semidirect
85. #2688C22semidirect
86. #2688C22semidirect
87. #2688C22semidirect
88. #2688C22semidirect
89. #2686C22semidirect
92. #2681C22semidirect
93. #2681C22semidirect
95. #2676C22semidirect
96. #2676C22semidirect
97. #2676C22semidirect
99. #2673C22semidirect
100. #2673C22semidirect
101. #2671C22semidirect
104. #2663C22semidirect
105. #2663C22semidirect
107. #2649C22semidirect
108. #2649C22semidirect
109. #2648C22semidirect
110. #2648C22semidirect
111. #2645C22semidirect
113. #2636C22semidirect
114. #2635C22semidirect
115. #2635C22semidirect
116. #2628C22semidirect
118. #2624C22semidirect
119. #2624C22semidirect
120. #2624C22semidirect
121. #2620C22semidirect
124. #2619C22semidirect
125. #2619C22semidirect
127. #2602C22semidirect
128. #2597C22semidirect
129. #2576C22semidirect
130. #2576C22semidirect
131. #2571C22semidirect
132. #2570C22semidirect
133. #2566C22semidirect
137. #2559C22semidirect
141. #2548C22semidirect
142. #2547C22semidirect
143. #2546C22semidirect
144. #2545C22semidirect
145. #2545C22semidirect
147. #2544C22semidirect
148. #2544C22semidirect
149. #2543C22semidirect
154. #2541C22semidirect
156. #2537C22semidirect
157. #2537C22semidirect
159. #2525C22semidirect
161. #2513C22semidirect
162. #2513C22semidirect
163. #2513C22semidirect
164. #2513C22semidirect
165. #2512C22semidirect
166. #2512C22semidirect
167. #2510C22semidirect
168. #2509C22semidirect
169. #2509C22semidirect
170. #2504C22semidirect
171. #2504C22semidirect
175. #2491C22semidirect
177. #2490C22semidirect
178. #2489C22semidirect
180. #2478C22semidirect
182. #2466C22semidirect
183. #2466C22semidirect
184. #2464C22semidirect
185. #2463C22semidirect
186. #2463C22semidirect
187. #2463C22semidirect
188. #2456C22semidirect
189. #2456C22semidirect
191. #2455C22semidirect
192. #2453C22semidirect
193. #2452C22semidirect
194. #2452C22semidirect
195. #2452C22semidirect
196. #2448C22semidirect
197. #2447C22semidirect
198. #2447C22semidirect
199. #2447C22semidirect
200. #2447C22semidirect
204. #2445C22semidirect
205. #2445C22semidirect
207. #2444C22semidirect
208. #2442C22semidirect
209. #2441C22semidirect
210. #2436C22semidirect
211. #2436C22semidirect
212. #2436C22semidirect
217. #2432C22semidirect
218. #2432C22semidirect
226. #2428C22semidirect
227. #2428C22semidirect
228. #2428C22semidirect
229. #2428C22semidirect
230. #2428C22semidirect
231. #2428C22semidirect
232. #2426C22semidirect
237. #2420C22semidirect
238. #2420C22semidirect
239. #2420C22semidirect
241. #2416C22semidirect
242. #2416C22semidirect
244. #2414C22semidirect
245. #2414C22semidirect
254. #2407C22semidirect
255. #2401C22semidirect
257. #2395C22semidirect
259. #2392C22semidirect
260. #2367C22semidirect
262. #2366C22semidirect
263. #2365C22semidirect
264. #2361C22semidirect
266. #2357C22semidirect
267. #2357C22semidirect
268. #2355C22semidirect
269. Q8×C4⋊C4C22semidirect
270. #2341C22semidirect
274. #2327C22semidirect
275. #2324C22semidirect
276. #2324C22semidirect
278. C4×C4⋊Q8C22semidirect
280. C4×#125C22semidirect
282. C4×C22⋊Q8C22semidirect
286. C4×#121C22semidirect
287. C4×#121C22semidirect
288. C4×#121C22semidirect
289. C4×#121C22semidirect
290. C4×#121C22semidirect
291. #2297C22semidirect
292. #2296C22semidirect
293. #2293C22semidirect
294. #2293C22semidirect
295. #2290C22semidirect
298. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#596792
#593782
#591292
#591242
#590802
#535142
#533922
#530042
#529772
#529712
#529702
#524882
#429432
#429032
#426172
#426062
#410332
#400532
#399602
#398182
#393632
#392022
#391492
#391242
#376832
#376262
#376142
#375232
#374982
#365872
#364552
#361212
#349372
#347882
#347242