Finite Group Databasebeta

← #7653653

Subgroups — #7653653

Order 512.

5856 conjugacy classes of subgroups.

The subgroup lattice has 1816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42575C212yesmaximal, complemented
2#42566C212yesmaximal, complemented
3#41218C214yesmaximal, complemented
4#41212C214yesmaximal, complemented
5#40358C214yesmaximal, complemented
6#40117C212yesmaximal, complemented
7#39361C211yesmaximal, characteristic, complemented
8#39212C212yesmaximal, complemented
9#39064C212yesmaximal, complemented
10#39052C212yesmaximal, complemented
11#38964C211yesmaximal, characteristic, complemented
12#38910C211yesmaximal, characteristic, complemented
13#38909C211yesmaximal, characteristic, complemented
14#38250C212yesmaximal, complemented
15#37802C214yesmaximal, complemented
16#37748C212yesmaximal, complemented
17#37629C211yesmaximal, characteristic, complemented
18#37523C212yesmaximal, complemented
19#36595C211yesmaximal, characteristic, complemented
20#36587C211yesmaximal, characteristic, complemented
21#36441C212yesmaximal, complemented
22#36299C211yesmaximal, characteristic, complemented
23#36126C211yesmaximal, characteristic, complemented
24#36102C212yesmaximal, complemented
25#35912C212yesmaximal, complemented
26#35882C212yesmaximal, complemented
27#35278C211yesmaximal, characteristic, complemented
28#35197C211yesmaximal, characteristic, complemented
29#35152C212yesmaximal, complemented
30#35044C212yesmaximal, complemented
31#34969C211yesmaximal, characteristic, complemented
32#34681C212yesmaximal, complemented
33#34330C211yesmaximal, characteristic, complemented
34C4×D42C211yesmaximal, characteristic, complemented
35#34153C211yesmaximal, characteristic, complemented
36C2×#559C2212yescomplemented
37C2×#550C2211yescharacteristic
38C2×#547C2212yescomplemented
39C2×D42C2211yescharacteristic
40C2×#540C2212yescomplemented
41C2×#535C2212yes—
42C2×#532C2212yes—
43C2×#529C2211yescharacteristic
44C2×#525C2214yescomplemented
45C22×C4×D4C2212yes—
46C22×C4×D4C2212yes—
47#2867C2211yescharacteristic
48#2863C2212yescomplemented
49#2859C2211yescharacteristic, complemented
50#2858C2212yescomplemented
51#2856C2211yescharacteristic
52#2856C2211yescharacteristic, complemented
53#2854C2212yescomplemented
54#2854C2212yescomplemented
55#2850C2212yescomplemented
56#2850C2212yescomplemented
57#2849C2214yescomplemented
58#2849C2214yescomplemented
59#2830C2214yescomplemented
60#2826C2214yescomplemented
61#2824C2214yescomplemented
62#2797C2214yescomplemented
63#2795C2214yescomplemented
64#2778C2214yescomplemented
65#2763C2214yescomplemented
66#2753C2214yescomplemented
67#2749C2214yescomplemented
68#2740C2214yescomplemented
69#2737C2214yescomplemented
70#2730C2214yescomplemented
71#2720C2214yescomplemented
72#2697C2214yescomplemented
73#2696C2214yescomplemented
74#2691C2214yescomplemented
75#2688C2214yescomplemented
76#2688C2214yescomplemented
77#2686C2214yescomplemented
78#2685C2214yes—
79#2684C2214yescomplemented
80#2684C2214yescomplemented
81#2678C2214yes—
82#2671C2214yescomplemented
83#2669C2214yes—
84#2669C2214yes—
85#2668C2214yescomplemented
86#2663C2214yescomplemented
87#2663C2214yescomplemented
88#2649C2214yescomplemented
89#2649C2214yescomplemented
90#2648C2214yescomplemented
91#2648C2214yescomplemented
92#2644C2212yescomplemented
93#2644C2212yescomplemented
94#2641C2212yescomplemented
95#2640C2212yescomplemented
96#2640C2212yescomplemented
97#2638C2214yescomplemented
98#2631C2214yescomplemented
99#2628C2212yescomplemented
100#2624C2212yes—
101#2624C2212yescomplemented
102#2622C2214yescomplemented
103#2622C2214yescomplemented
104#2619C2212yes—
105#2619C2212yescomplemented
106#2602C2214yescomplemented
107#2600C2214yescomplemented
108#2597C2214yescomplemented
109#2597C2214yescomplemented
110#2582C2211yescharacteristic, complemented
111#2580C2212yes—
112#2576C2214yescomplemented
113#2571C2211yescharacteristic, complemented
114#2567C2212yescomplemented
115#2564C2214yescomplemented
116#2557C2214yescomplemented
117#2557C2214yescomplemented
118#2551C2211yescharacteristic, complemented
119#2548C2211yescharacteristic
120#2548C2211yescharacteristic
121#2548C2212yescomplemented
122#2548C2212yescomplemented
123#2548C2211yescharacteristic, complemented
124#2544C2212yes—
125#2544C2214yescomplemented
126#2541C2211yescharacteristic
127#2540C2212yes—
128#2538C2211yescharacteristic
129#2530C2212yescomplemented
130#2527C2212yescomplemented
131#2515C2214yescomplemented
132#2513C2212yescomplemented
133#2513C2212yescomplemented
134#2513C2212yescomplemented
135#2511C2211yescharacteristic, complemented
136#2509C2212yescomplemented
137#2509C2211yescharacteristic, complemented
138#2508C2212yescomplemented
139#2504C2212yescomplemented
140#2495C2212yescomplemented
141#2494C2211yescharacteristic, complemented
142#2492C2211yescharacteristic, complemented
143#2491C2212yescomplemented
144#2490C2212yes—
145#2477C2212yescomplemented
146#2475C2214yescomplemented
147#2472C2214yescomplemented
148#2472C2214yescomplemented
149#2471C2214yescomplemented
150#2470C2212yescomplemented
151#2464C2214yescomplemented
152#2463C2214yescomplemented
153#2463C2214yescomplemented
154#2461C2214yescomplemented
155#2461C2214yescomplemented
156#2459C2214yescomplemented
157#2457C2214yescomplemented
158#2456C2214yescomplemented
159#2456C2214yescomplemented
160#2455C2214yescomplemented
161#2454C2212yescomplemented
162#2452C2212yes—
163#2452C2211yescharacteristic
164#2452C2212yescomplemented
165#2452C2212yescomplemented
166#2452C2212yescomplemented
167#2447C2211yescharacteristic
168#2447C2212yes—
169#2447C2212yescomplemented
170#2447C2212yescomplemented
171#2447C2212yescomplemented
172#2445C2212yes—
173#2445C2212yes—
174#2445C2214yescomplemented
175#2445C2212yescomplemented
176#2445C2212yescomplemented
177#2445C2212yescomplemented
178#2445C2212yescomplemented
179#2445C2212yescomplemented
180#2445C2212yescomplemented
181#2444C2214yescomplemented
182#2444C2214yescomplemented
183#2440C2212yescomplemented
184#2439C2212yescomplemented
185#2435C2212yes—
186#2433C2212yes—
187#2433C2212yes—
188#2433C2212yes—
189#2431C2212yes—
190#2430C2214yescomplemented
191#2430C2214yescomplemented
192#2428C2212yes—
193#2428C2212yes—
194#2428C2212yes—
195#2428C2212yescomplemented
196#2428C2212yescomplemented
197#2428C2212yescomplemented
198#2428C2212yescomplemented
199#2427C2211yescharacteristic
200#2427C2212yescomplemented
201#2427C2212yescomplemented
202#2424C2214yescomplemented
203#2422C2211yescharacteristic
204#2422C2214yescomplemented
205#2422C2214yescomplemented
206#2422C2214yescomplemented
207#2421C2212yescomplemented
208#2420C2212yescomplemented
209#2420C2214yescomplemented
210#2420C2214yescomplemented
211#2419C2214yescomplemented
212#2418C2214yescomplemented
213#2416C2212yescomplemented
214#2416C2212yescomplemented
215#2414C2212yes—
216#2411C2214yescomplemented
217#2408C2212yes—
218#2408C2212yes—
219#2407C2212yescomplemented
220#2404C2214yescomplemented
221#2401C2212yescomplemented
222#2398C2212yescomplemented
223#2392C2214yescomplemented
224#2388C2214yescomplemented
225#2373C2212yescomplemented
226#2373C2212yescomplemented
227#2370C2211yescharacteristic, complemented
228#2370C2211yescharacteristic, complemented
229#2367C2211yescharacteristic
230#2367C2211yescharacteristic
231#2366C2212yes—
232#2366C2211yescharacteristic
233#2366C2212yescomplemented
234#2366C2211yescharacteristic, complemented
235#2364C2214yescomplemented
236#2363C2212yescomplemented
237#2361C2211yescharacteristic
238#2361C2212yes—
239#2361C2211yescharacteristic
240#2361C2212yes—
241#2361C2212yescomplemented
242#2361C2212yescomplemented
243#2360C2211yescharacteristic, complemented
244#2360C2211yescharacteristic, complemented
245#2360C2212yescomplemented
246#2359C2212yescomplemented
247#2359C2212yescomplemented
248#2358C2214yes—
249#2357C2212yescomplemented
250#2357C2212yescomplemented
251#2355C2211yescharacteristic, complemented
252#2354C2211yescharacteristic
253D4×C4⋊C4C2211yescharacteristic
254D4×C4⋊C4C2211yescharacteristic
255#2344C2212yescomplemented
256#2339C2212yescomplemented
257D4×C22⋊C4C2212yes—
258D4×C22⋊C4C2212yes—
259#2337C2214yescomplemented
260#2333C2214yescomplemented
261#2333C2214yescomplemented
262#2328C2212yes—
263#2328C2212yes—
264#2328C2212yescomplemented
265#2319C2212yescomplemented
266#2317C2212yescomplemented
267#2311C2212yescomplemented
268#2309C2212yes—
269C4×C4⋊Q8C2211yescharacteristic, complemented
270C4×#127C2211yescharacteristic
271C4×#127C2211yescharacteristic, complemented
272C4×#127C2212yescomplemented
273C4×#124C2211yescharacteristic
274C4×C22⋊Q8C2212yescomplemented
275C4×C22⋊Q8C2211yescharacteristic, complemented
276C4×#123C2212yescomplemented
277C4×#121C2211yescharacteristic
278C4×#121C2212yes—
279C4×#121C2212yes—
280C4×#121C2212yescomplemented
281C4×#121C2212yescomplemented
282C4×#120C2214yes—
283C4×#120C2214yescomplemented
284#2298C2212yescomplemented
285#2297C2212yescomplemented
286#2296C2212yescomplemented
287#2295C2211yescharacteristic, complemented
288#2295C2211yescharacteristic, complemented
289#2293C2211yescharacteristic
290#2293C2212yes—
291#2290C2212yescomplemented
292#2275C2212yescomplemented
293C42×Q8C2211yescharacteristic, complemented
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2212yescomplemented
297C4×#117C2211yescharacteristic, complemented
298C2×C4×C4⋊C4C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C22×#41C2314yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303C24×C4C2314yes—
304#559—48no—
305#550—28no—
306#547—48no—
307D42—28no—
308#540—48no—
309#535—48no—
310#532—48no—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×#127C2311yescharacteristic
315C2×#127C2311yescharacteristic
316C2×#127C2312yes—
317C2×#127C2312yes—
318C2×#127C2312yes—
319C2×#127C2312yes—
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2312yes—
324#529—28no—
325C2×#126C2312yes—
326C2×#125C2311yescharacteristic
327C2×#125C2312yes—
328C2×#124C2311yescharacteristic
329C2×#124C2311yescharacteristic
330C2×#124C2314yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2314yes—
334C2×#124C2312yes—
335C2×#124C2314yes—
336#525—416no—
337C2×#123C2312yes—
338C2×#123C2312yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×#121C2314yes—
354C2×#121C2314yes—
355C2×#121C2311yescharacteristic
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2311yescharacteristic
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2314yes—
369C2×#121C2314yes—
370C2×#121C2314yes—
371C2×#121C2314yes—
372C2×#121C2314yes—
373C2×#120C2314yes—
374C2×#120C2314yes—
375C2×#120C2314yes—
376C2×#120C2314yes—
377C2×#120C2314yes—
378C2×#120C2314yes—
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2311yescharacteristic
384C2×C4×D4—48no—
385C2×C4×D4—48no—
386C2×C4×D4C2312yes—
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2314yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2314yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2311yescharacteristic
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2314yes—
409C2×C4×D4C2314yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2314yes—
412C2×C4×D4C2314yes—
413C2×C4×D4C2314yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2314yes—
416C2×C4×D4C2314yes—
417C2×C4×D4C2311yescharacteristic
418C2×#117C2312yes—
419C2×#117C2311yescharacteristic
420C2×#117C2312yes—
421C2×#117C2312yes—
422C2×#117C2314yes—
423C2×#117C2311yescharacteristic
424C22×C4⋊C4C2312yes—
425C22×C4⋊C4C2311yescharacteristic
426C22×C4⋊C4C2312yes—
427C22×C4⋊C4C2311yescharacteristic
428C22×C22⋊C4C2314yes—
429C22×C22⋊C4C2314yes—
430C22×C42C2311yescharacteristic
431C22×C42C2312yes—
432C22×C42C2312yes—
433C22×C42C2312yes—
434#401C2312yes—
435#400C2312yes—
436#400C2312yes—
437#400C2314yes—
438#400C2312yes—
439#400C2314yes—
440#400C2314yes—
441#400C2312yes—
442#400C2314yes—
443#400C2312yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#398C2314yes—
448#398C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2312yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2312yes—
469#397C2312yes—
470#397C2312yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2312yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2312yes—
510#393C2314yes—
511#393C2314yes—
512#393C2314yes—
513#393C2314yes—
514#393C2314yes—
515#393C2314yes—
516#393C2312yes—
517#393C2312yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#392C2314yes—
524#392C2314yes—
525#392C2314yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#391C2312yes—
531#391C2311yescharacteristic
532#391C2312yes—
533#391C2314yes—
534#391C2312yes—
535#391C2312yes—
536#391C2311yescharacteristic
537#391C2312yes—
538#391C2311yescharacteristic
539#391C2311yescharacteristic
540#391C2311yescharacteristic
541#391C2311yescharacteristic
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2314yes—
550#390C2312yes—
551#390C2314yes—
552#390C2311yescharacteristic
553#390C2312yes—
554#390C2312yes—
555#390C2312yes—
556#390C2314yes—
557#390C2314yes—
558#390C2312yes—
559#390C2312yes—
560#390C2311yescharacteristic
561#390C2312yes—
562#390C2312yes—
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2314yes—
567#390C2314yes—
568#390C2314yes—
569#390C2312yes—
570#390C2312yes—
571#390C2314yes—
572#390C2312yes—
573#390C2312yes—
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#390C2311yescharacteristic
578#390C2312yes—
579#390C2312yes—
580#390C2312yes—
581#390C2311yescharacteristic
582#389C2311yescharacteristic
583#389C2311yescharacteristic
584#389C2312yes—
585#389C2311yescharacteristic
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2311yescharacteristic
597#389C2312yes—
598#389C2312yes—
599#389C2314yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2311yescharacteristic
604#389C2312yes—
605#389C2312yes—
606#389C2311yescharacteristic
607#389C2311yescharacteristic
608#389C2311yescharacteristic
609#389C2311yescharacteristic
610#389C2312yes—
611#389C2311yescharacteristic
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2312yes—
628#388C2312yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2312yes—
633#388C2312yes—
634#388C2312yes—
635#388C2312yes—
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#388C2312yes—
640#388C2314yes—
641#388C2314yes—
642#388C2312yes—
643#388C2312yes—
644#387C2312yes—
645#387C2314yes—
646#387C2312yes—
647#387C2312yes—
648#387C2312yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2312yes—
654#387C2314yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2312yes—
698#386C2312yes—
699#386C2314yes—
700#386C2312yes—
701#386C2312yes—
702#386C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2312yes—
706#385C2312yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2312yes—
713#385C2312yes—
714#385C2312yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2312yes—
720#385C2312yes—
721#385C2314yes—
722#385C2312yes—
723#385C2312yes—
724#385C2312yes—
725#384C2311yescharacteristic
726#384C2311yescharacteristic
727#384C2311yescharacteristic
728#384C2314yes—
729#383C2314yes—
730#382C2312yes—
731#382C2312yes—
732#382C2314yes—
733#382C2312yes—
734#382C2312yes—
735#382C2311yescharacteristic
736#381C2314yes—
737#381C2314yes—
738#381C2314yes—
739#381C2312yes—
740#381C2314yes—
741#381C2314yes—
742#380C2314yes—
743#380C2314yes—
744#380C2314yes—
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2311yescharacteristic
749#380C2312yes—
750#380C2311yescharacteristic
751#380C2312yes—
752#379C2314yes—
753#379C2314yes—
754#379C2314yes—
755#379C2314yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812#376C2312yes—
813#376C2312yes—
814#376C2311yescharacteristic
815#376C2311yescharacteristic
816C2×#95C2314yes—
817C2×#95C2312yes—
818C43C2311yescharacteristic
819C43C2312yes—
820C43C2311yescharacteristic
821C25C2414yes—
822C2×#41—28no—
823C2×#41—48no—
824C2×#41—48no—
825C2×#41—48no—
826C2×#41—44no—
827C2×#41—44no—
828C22×Q8C2411yescharacteristic
829C22×Q8C2411yescharacteristic
830C22×Q8C2412yes—
831C22×Q8C2414yes—
832C22×D4—28no—
833C22×D4—28no—
834C22×D4—28no—
835C22×D4—44no—
836C22×D4—44no—
837C22×D4—44no—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2411yescharacteristic
846C22×D4C2411yescharacteristic
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C22×D4C2412yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2412yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C23×C4—48no—
861C23×C4—48no—
862C23×C4—48no—
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2411yescharacteristic
866C23×C4C2414yes—
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2414yes—
874C23×C4C2414yes—
875C23×C4C2414yes—
876C23×C4C2412yes—
877C23×C4C2412yes—
878C23×C4C2414yes—
879C23×C4C2412yes—
880C23×C4C2414yes—
881C4⋊Q8—42no—
882C4⋊Q8—44no—
883C4⋊Q8—44no—
884#127—28no—
885#127—28no—
886#127—24no—
887#127—24no—
888#127—44no—
889#127—44no—
890#127—44no—
891#127—44no—
892#127—44no—
893#127—44no—
894#126—28no—
895#125—24no—
896#125—44no—
897#124—24no—
898#124—24no—
899#124—48no—
900#124—48no—
901#124—44no—
902#124—44no—
903#124—44no—
904#124—48no—
905#123—28no—
906#123—28no—
907#123—48no—
908#123—48no—
909#123—48no—
910#123—48no—
911#123—48no—
912#123—48no—
913#123—48no—
914C22⋊Q8—24no—
915C22⋊Q8—48no—
916C22⋊Q8—44no—
917C22⋊Q8—48no—
918C22⋊Q8—48no—
919C22⋊Q8—44no—
920C22⋊Q8—42no—
921#121—24no—
922#121—24no—
923#121—28no—
924#121—28no—
925#121—28no—
926#121—216no—
927#121—216no—
928#121—48no—
929#121—48no—
930#121—48no—
931#121—48no—
932#121—48no—
933#121—44no—
934#121—44no—
935#121—44no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—44no—
940#121—44no—
941#120—216no—
942#120—48no—
943#120—48no—
944#120—48no—
945#120—48no—
946#120—48no—
947C4×Q8—24no—
948C4×Q8—24no—
949C4×Q8—24no—
950C4×Q8—44no—
951C4×Q8—42no—
952C4×D4—24no—
953C4×D4—28no—
954C4×D4—28no—
955C4×D4—28no—
956C4×D4—24no—
957C4×D4—28no—
958C4×D4—28no—
959C4×D4—28no—
960C4×D4—24no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—42no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—42no—
971C4×D4—48no—
972C4×D4—44no—
973C4×D4—44no—
974C4×D4—44no—
975C4×D4—48no—
976C4×D4—48no—
977C4×D4—48no—
978C4×D4—48no—
979C4×D4—48no—
980C4×D4—48no—
981C4×D4—48no—
982C4×D4—48no—
983C4×D4#4118yescomplemented
984#117—28no—
985#117—24no—
986#117—44no—
987#117—42no—
988#117—48no—
989#117—44no—
990C2×C4⋊C4—28no—
991C2×C4⋊C4—24no—
992C2×C4⋊C4—42no—
993C2×C4⋊C4—44no—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2411yescharacteristic
1047C2×C4⋊C4C2411yescharacteristic
1048C2×C22⋊C4—48no—
1049C2×C22⋊C4—48no—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2411yescharacteristic
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2411yescharacteristic
1118C2×C42—24no—
1119C2×C42—44no—
1120C2×C42—44no—
1121C2×C42—44no—
1122C2×C42C2412yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2412yes—
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2412yes—
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2411yescharacteristic
1141C2×C42C2411yescharacteristic
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2414yes—
1146C2×C42C2411yescharacteristic
1147C2×C42C2414yes—
1148C2×C42C2412yes—
1149C2×C42C2412yes—
1150C2×C42C2412yes—
1151C2×C42C2412yes—
1152C2×C42C2412yes—
1153C2×C42C2412yes—
1154C2×C42C2412yes—
1155C2×C42C2411yescharacteristic
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2411yescharacteristic
1165#95C2411yescharacteristic
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2411yescharacteristic
1170#95C2411yescharacteristic
1171#95C2411yescharacteristic
1172#95C2411yescharacteristic
1173#95C2411yescharacteristic
1174#95C2411yescharacteristic
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2414yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2412yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2414yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218C24—28no—
1219C24—28no—
1220C24—44no—
1221C24—44no—
1222C24—44no—
1223C24—44no—
1224C24—44no—
1225C24C2514yes—
1226C24C2514yes—
1227C24C2512yes—
1228C24C2512yes—
1229C24C2511yescharacteristic
1230#41—816no—
1231#41—832no—
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—22no—
1235C2×Q8—22no—
1236C2×Q8—22no—
1237C2×Q8—22no—
1238C2×Q8—24no—
1239C2×Q8—42no—
1240C2×Q8—44no—
1241C2×Q8—44no—
1242C2×Q8—44no—
1243C2×Q8—42no—
1244C2×D4—24no—
1245C2×D4—28no—
1246C2×D4—24no—
1247C2×D4—28no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—28no—
1251C2×D4—28no—
1252C2×D4—28no—
1253C2×D4—28no—
1254C2×D4—28no—
1255C2×D4—28no—
1256C2×D4—22no—
1257C2×D4—24no—
1258C2×D4—28no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—22no—
1265C2×D4—24no—
1266C2×D4—24no—
1267C2×D4—24no—
1268C2×D4—24no—
1269C2×D4—28no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—24no—
1273C2×D4—24no—
1274C2×D4—24no—
1275C2×D4—24no—
1276C2×D4—28no—
1277C2×D4—432no—
1278C2×D4—44no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—42no—
1285C2×D4—42no—
1286C2×D4—44no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—44no—
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—42no—
1300C2×D4—44no—
1301C2×D4—44no—
1302C2×D4—44no—
1303C2×D4—44no—
1304C2×D4—44no—
1305C2×D4—44no—
1306C2×D4—44no—
1307C2×D4—44no—
1308C2×D4—44no—
1309C2×D4—432no—
1310C2×D4C2×#4114yes—
1311C2×D4H(5,𝔽2)14yes—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—22no—
1315C22×C4—24no—
1316C22×C4—28no—
1317C22×C4—24no—
1318C22×C4—22no—
1319C22×C4—22no—
1320C22×C4—22no—
1321C22×C4—24no—
1322C22×C4—22no—
1323C22×C4—24no—
1324C22×C4—28no—
1325C22×C4—22no—
1326C22×C4—24no—
1327C22×C4—24no—
1328C22×C4—24no—
1329C22×C4—24no—
1330C22×C4—22no—
1331C22×C4—22no—
1332C22×C4—24no—
1333C22×C4—28no—
1334C22×C4—28no—
1335C22×C4—28no—
1336C22×C4—28no—
1337C22×C4—42no—
1338C22×C4—42no—
1339C22×C4—42no—
1340C22×C4—44no—
1341C22×C4—41no—
1342C22×C4—42no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—44no—
1346C22×C4—42no—
1347C22×C4—44no—
1348C22×C4—44no—
1349C22×C4—44no—
1350C22×C4—44no—
1351C22×C4—44no—
1352C22×C4—44no—
1353C22×C4—44no—
1354C22×C4—42no—
1355C22×C4—42no—
1356C22×C4—42no—
1357C22×C4—42no—
1358C22×C4—44no—
1359C22×C4—44no—
1360C22×C4—42no—
1361C22×C4—44no—
1362C22×C4—44no—
1363C22×C4—44no—
1364C22×C4—44no—
1365C22×C4—832no—
1366C22×C4C2×#4118yes—
1367C22×C4C2512yes—
1368C22×C4C2511yescharacteristic
1369C22×C4C2511yescharacteristic
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2512yes—
1374C22×C4C2511yescharacteristic
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2514yes—
1378C22×C4C2511yescharacteristic
1379C22×C4C2512yes—
1380C22×C4C2512yes—
1381C22×C4C2512yes—
1382C22×C4C2511yescharacteristic
1383C22×C4C2511yescharacteristic
1384C22×C4C2512yes—
1385C22×C4C2512yes—
1386C22×C4C2512yes—
1387C22×C4C2514yes—
1388C22×C4C2511yescharacteristic
1389C22×C4C2511yescharacteristic
1390C22×C4C2512yes—
1391C22×C4C2511yescharacteristic
1392C22×C4C2512yes—
1393C22×C4C2511yescharacteristic
1394C22×C4C2511yescharacteristic
1395C22×C4C2511yescharacteristic
1396C22×C4C2511yescharacteristic
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—22no—
1400C4⋊C4—24no—
1401C4⋊C4—22no—
1402C4⋊C4—24no—
1403C4⋊C4—22no—
1404C4⋊C4—24no—
1405C4⋊C4—24no—
1406C4⋊C4—28no—
1407C4⋊C4—22no—
1408C4⋊C4—24no—
1409C4⋊C4—22no—
1410C4⋊C4—24no—
1411C4⋊C4—22no—
1412C4⋊C4—22no—
1413C4⋊C4—28no—
1414C4⋊C4—24no—
1415C4⋊C4—22no—
1416C4⋊C4—24no—
1417C4⋊C4—24no—
1418C4⋊C4—24no—
1419C4⋊C4—22no—
1420C4⋊C4—22no—
1421C4⋊C4—22no—
1422C4⋊C4—24no—
1423C4⋊C4—22no—
1424C4⋊C4—24no—
1425C4⋊C4—22no—
1426C4⋊C4—42no—
1427C4⋊C4—44no—
1428C4⋊C4—41no—
1429C4⋊C4—42no—
1430C4⋊C4—42no—
1431C4⋊C4—44no—
1432C4⋊C4—42no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—44no—
1437C4⋊C4—42no—
1438C4⋊C4—44no—
1439C4⋊C4—42no—
1440C4⋊C4—42no—
1441C4⋊C4—42no—
1442C4⋊C4—44no—
1443C4⋊C4—44no—
1444C4⋊C4—42no—
1445C4⋊C4—42no—
1446C4⋊C4—42no—
1447C4⋊C4—44no—
1448C4⋊C4—42no—
1449C4⋊C4C2×#4114yes—
1450C4⋊C4H(5,𝔽2)14yes—
1451C22⋊C4—24no—
1452C22⋊C4—24no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—28no—
1456C22⋊C4—22no—
1457C22⋊C4—24no—
1458C22⋊C4—24no—
1459C22⋊C4—24no—
1460C22⋊C4—24no—
1461C22⋊C4—24no—
1462C22⋊C4—28no—
1463C22⋊C4—24no—
1464C22⋊C4—28no—
1465C22⋊C4—24no—
1466C22⋊C4—28no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—28no—
1470C22⋊C4—28no—
1471C22⋊C4—22no—
1472C22⋊C4—24no—
1473C22⋊C4—24no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—41no—
1479C22⋊C4—44no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—42no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—42no—
1495C22⋊C4—42no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—42no—
1510C22⋊C4—42no—
1511C22⋊C4—44no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C22⋊C4—44no—
1516C22⋊C4—44no—
1517C22⋊C4C2×#4118yes—
1518C22⋊C4H(5,𝔽2)14yes—
1519C42—22no—
1520C42—22no—
1521C42—22no—
1522C42—24no—
1523C42—24no—
1524C42—22no—
1525C42—22no—
1526C42—24no—
1527C42—24no—
1528C42—24no—
1529C42—22no—
1530C42—22no—
1531C42—24no—
1532C42—22no—
1533C42—24no—
1534C42—24no—
1535C42—22no—
1536C42—22no—
1537C42—22no—
1538C42—22no—
1539C42—24no—
1540C42—22no—
1541C42—22no—
1542C42—42no—
1543C42—42no—
1544C42—42no—
1545C42—42no—
1546C42—42no—
1547C42—42no—
1548C42—41no—
1549C42—44no—
1550C42—44no—
1551C42—42no—
1552C42C2×#4114yes—
1553C23—21no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—21no—
1559C23—22no—
1560C23—22no—
1561C23—21no—
1562C23—21no—
1563C23—22no—
1564C23—22no—
1565C23—21no—
1566C23—22no—
1567C23—22no—
1568C23—22no—
1569C23—22no—
1570C23—21no—
1571C23—24no—
1572C23—24no—
1573C23—24no—
1574C23—24no—
1575C23—24no—
1576C23—24no—
1577C23—24no—
1578C23—24no—
1579C23—24no—
1580C23—24no—
1581C23—24no—
1582C23—24no—
1583C23—24no—
1584C23—24no—
1585C23—416no—
1586C23—416no—
1587C23—88no—
1588C23—88no—
1589C23—88no—
1590C23—88no—
1591C23—88no—
1592C23C22×#4114yes—
1593C23C2×H(5,𝔽2)14yes—
1594C23C2×H(5,𝔽2)12yes—
1595C23C2611yescharacteristic
1596Q8—44no—
1597Q8—44no—
1598Q8—84no—
1599Q8—88no—
1600D4—28no—
1601D4—28no—
1602D4—416no—
1603D4—48no—
1604D4—48no—
1605D4—416no—
1606D4—48no—
1607D4—48no—
1608D4—48no—
1609D4—48no—
1610D4—88no—
1611D4—88no—
1612D4—84no—
1613D4—84no—
1614D4—88no—
1615D4—88no—
1616D4—88no—
1617D4—88no—
1618D4—88no—
1619D4—88no—
1620D4—164no—
1621D4—164no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—216no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—22no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—24no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—24no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—22no—
1672C2×C4—24no—
1673C2×C4—22no—
1674C2×C4—24no—
1675C2×C4—22no—
1676C2×C4—21no—
1677C2×C4—22no—
1678C2×C4—21no—
1679C2×C4—21no—
1680C2×C4—21no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—22no—
1684C2×C4—21no—
1685C2×C4—24no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—22no—
1689C2×C4—22no—
1690C2×C4—22no—
1691C2×C4—22no—
1692C2×C4—21no—
1693C2×C4—21no—
1694C2×C4—22no—
1695C2×C4—24no—
1696C2×C4—21no—
1697C2×C4—22no—
1698C2×C4—22no—
1699C2×C4—22no—
1700C2×C4—22no—
1701C2×C4—48no—
1702C2×C4—44no—
1703C2×C4—48no—
1704C2×C4—416no—
1705C2×C4—48no—
1706C2×C4—44no—
1707C2×C4—48no—
1708C2×C4—44no—
1709C2×C4—88no—
1710C2×C4—88no—
1711C2×C4—88no—
1712C2×C4—88no—
1713C2×C4—84no—
1714C2×C4—84no—
1715C2×C4—84no—
1716C2×C4—88no—
1717C2×C4—164no—
1718C2×C4C22×#4112yes—
1719C2×C4C22×#4114yes—
1720C2×C4C22×#4112yes—
1721C2×C4C22×#4112yes—
1722C2×C4C2×H(5,𝔽2)12yes—
1723C2×C4C2×H(5,𝔽2)14yes—
1724C2×C4C2×H(5,𝔽2)12yes—
1725C2×C4C2×H(5,𝔽2)12yes—
1726C2×C4C2×H(5,𝔽2)12yes—
1727C2×C4#58512yes—
1728C2×C4#58512yes—
1729C2×C4#58512yes—
1730C22—24no—
1731C22—22no—
1732C22—22no—
1733C22—24no—
1734C22—24no—
1735C22—24no—
1736C22—22no—
1737C22—24no—
1738C22—24no—
1739C22—42no—
1740C22—42no—
1741C22—41no—
1742C22—42no—
1743C22—41no—
1744C22—42no—
1745C22—42no—
1746C22—42no—
1747C22—41no—
1748C22—42no—
1749C22—41no—
1750C22—42no—
1751C22—44no—
1752C22—44no—
1753C22—44no—
1754C22—44no—
1755C22—44no—
1756C22—44no—
1757C22—44no—
1758C22—44no—
1759C22—44no—
1760C22—44no—
1761C22—44no—
1762C22—44no—
1763C22—44no—
1764C22—44no—
1765C22—832no—
1766C22C23×#4111yescharacteristic
1767C22C22×H(5,𝔽2)11yescharacteristic
1768C22C22×H(5,𝔽2)11yescharacteristic
1769C22C22×H(5,𝔽2)11yescharacteristic
1770C22C2×#58511yescharacteristic
1771C22C2×#58511yescharacteristic
1772C22C2×#58511yescharacteristic
1773C4—22no—
1774C4—24no—
1775C4—22no—
1776C4—22no—
1777C4—24no—
1778C4—22no—
1779C4—42no—
1780C4—44no—
1781C4—42no—
1782C4—42no—
1783C4—41no—
1784C4—41no—
1785C4—42no—
1786C4—42no—
1787C4—41no—
1788C4—42no—
1789C4—42no—
1790C4—41no—
1791C4—44no—
1792C4—41no—
1793C4—41no—
1794C4—42no—
1795C4—41no—
1796C4—42no—
1797C4—42no—
1798C4—41no—
1799C4—42no—
1800C4—42no—
1801C4#346014yes—
1802C4#351314yes—
1803C2—42no—
1804C2—44no—
1805C2—44no—
1806C2—84no—
1807C2—84no—
1808C2C2×#346011yescharacteristic
1809C2C2×#351311yescharacteristic
1810C2#6280011yescharacteristic
1811C2#6301111yescharacteristic
1812C2#6301911yescharacteristic
1813C2#6302111yescharacteristic
1814C2#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. #42575C2semidirect
2. #42566C2semidirect
3. #41218C2semidirect
4. #41212C2semidirect
5. #40358C2semidirect
6. #40117C2semidirect
7. #39361C2semidirect
8. #39212C2semidirect
9. #39064C2semidirect
10. #39052C2semidirect
11. #38964C2semidirect
12. #38910C2semidirect
13. #38909C2semidirect
14. #38250C2semidirect
15. #37802C2semidirect
16. #37748C2semidirect
17. #37629C2semidirect
18. #37523C2semidirect
19. #36595C2semidirect
20. #36587C2semidirect
21. #36441C2semidirect
22. #36299C2semidirect
23. #36126C2semidirect
24. #36102C2semidirect
25. #35912C2semidirect
26. #35882C2semidirect
27. #35278C2semidirect
28. #35197C2semidirect
29. #35152C2semidirect
30. #35044C2semidirect
31. #34969C2semidirect
32. #34681C2semidirect
33. #34330C2semidirect
34. C4×D42C2semidirect
35. #34153C2semidirect
36. C2×#559C22semidirect
38. C2×#547C22semidirect
40. C2×#540C22semidirect
44. C2×#525C22semidirect
48. #2863C22semidirect
49. #2859C22semidirect
50. #2858C22semidirect
52. #2856C22semidirect
53. #2854C22semidirect
54. #2854C22semidirect
55. #2850C22semidirect
56. #2850C22semidirect
57. #2849C22semidirect
58. #2849C22semidirect
59. #2830C22semidirect
60. #2826C22semidirect
61. #2824C22semidirect
62. #2797C22semidirect
63. #2795C22semidirect
64. #2778C22semidirect
65. #2763C22semidirect
66. #2753C22semidirect
67. #2749C22semidirect
68. #2740C22semidirect
69. #2737C22semidirect
70. #2730C22semidirect
71. #2720C22semidirect
72. #2697C22semidirect
73. #2696C22semidirect
74. #2691C22semidirect
75. #2688C22semidirect
76. #2688C22semidirect
77. #2686C22semidirect
79. #2684C22semidirect
80. #2684C22semidirect
82. #2671C22semidirect
85. #2668C22semidirect
86. #2663C22semidirect
87. #2663C22semidirect
88. #2649C22semidirect
89. #2649C22semidirect
90. #2648C22semidirect
91. #2648C22semidirect
92. #2644C22semidirect
93. #2644C22semidirect
94. #2641C22semidirect
95. #2640C22semidirect
96. #2640C22semidirect
97. #2638C22semidirect
98. #2631C22semidirect
99. #2628C22semidirect
101. #2624C22semidirect
102. #2622C22semidirect
103. #2622C22semidirect
105. #2619C22semidirect
106. #2602C22semidirect
107. #2600C22semidirect
108. #2597C22semidirect
109. #2597C22semidirect
110. #2582C22semidirect
112. #2576C22semidirect
113. #2571C22semidirect
114. #2567C22semidirect
115. #2564C22semidirect
116. #2557C22semidirect
117. #2557C22semidirect
118. #2551C22semidirect
121. #2548C22semidirect
122. #2548C22semidirect
123. #2548C22semidirect
125. #2544C22semidirect
129. #2530C22semidirect
130. #2527C22semidirect
131. #2515C22semidirect
132. #2513C22semidirect
133. #2513C22semidirect
134. #2513C22semidirect
135. #2511C22semidirect
136. #2509C22semidirect
137. #2509C22semidirect
138. #2508C22semidirect
139. #2504C22semidirect
140. #2495C22semidirect
141. #2494C22semidirect
142. #2492C22semidirect
143. #2491C22semidirect
145. #2477C22semidirect
146. #2475C22semidirect
147. #2472C22semidirect
148. #2472C22semidirect
149. #2471C22semidirect
150. #2470C22semidirect
151. #2464C22semidirect
152. #2463C22semidirect
153. #2463C22semidirect
154. #2461C22semidirect
155. #2461C22semidirect
156. #2459C22semidirect
157. #2457C22semidirect
158. #2456C22semidirect
159. #2456C22semidirect
160. #2455C22semidirect
161. #2454C22semidirect
164. #2452C22semidirect
165. #2452C22semidirect
166. #2452C22semidirect
169. #2447C22semidirect
170. #2447C22semidirect
171. #2447C22semidirect
174. #2445C22semidirect
175. #2445C22semidirect
176. #2445C22semidirect
177. #2445C22semidirect
178. #2445C22semidirect
179. #2445C22semidirect
180. #2445C22semidirect
181. #2444C22semidirect
182. #2444C22semidirect
183. #2440C22semidirect
184. #2439C22semidirect
190. #2430C22semidirect
191. #2430C22semidirect
195. #2428C22semidirect
196. #2428C22semidirect
197. #2428C22semidirect
198. #2428C22semidirect
200. #2427C22semidirect
201. #2427C22semidirect
202. #2424C22semidirect
204. #2422C22semidirect
205. #2422C22semidirect
206. #2422C22semidirect
207. #2421C22semidirect
208. #2420C22semidirect
209. #2420C22semidirect
210. #2420C22semidirect
211. #2419C22semidirect
212. #2418C22semidirect
213. #2416C22semidirect
214. #2416C22semidirect
216. #2411C22semidirect
219. #2407C22semidirect
220. #2404C22semidirect
221. #2401C22semidirect
222. #2398C22semidirect
223. #2392C22semidirect
224. #2388C22semidirect
225. #2373C22semidirect
226. #2373C22semidirect
227. #2370C22semidirect
228. #2370C22semidirect
233. #2366C22semidirect
234. #2366C22semidirect
235. #2364C22semidirect
236. #2363C22semidirect
241. #2361C22semidirect
242. #2361C22semidirect
243. #2360C22semidirect
244. #2360C22semidirect
245. #2360C22semidirect
246. #2359C22semidirect
247. #2359C22semidirect
249. #2357C22semidirect
250. #2357C22semidirect
251. #2355C22semidirect
255. #2344C22semidirect
256. #2339C22semidirect
259. #2337C22semidirect
260. #2333C22semidirect
261. #2333C22semidirect
264. #2328C22semidirect
265. #2319C22semidirect
266. #2317C22semidirect
267. #2311C22semidirect
269. C4×C4⋊Q8C22semidirect
271. C4×#127C22semidirect
272. C4×#127C22semidirect
274. C4×C22⋊Q8C22semidirect
275. C4×C22⋊Q8C22semidirect
276. C4×#123C22semidirect
280. C4×#121C22semidirect
281. C4×#121C22semidirect
283. C4×#120C22semidirect
284. #2298C22semidirect
285. #2297C22semidirect
286. #2296C22semidirect
287. #2295C22semidirect
288. #2295C22semidirect
291. #2290C22semidirect
292. #2275C22semidirect
293. C42×Q8C22semidirect
296. C42×D4C22semidirect
297. C4×#117C22semidirect
298. C2×C4×C4⋊C4C22semidirect
983. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#425752
#425662
#412182
#412122
#403582
#401172
#393612
#392122
#390642
#390522
#389642
#389102
#389092
#382502
#378022
#377482
#376292
#375232
#365952
#365872
#364412
#362992
#361262
#361022
#359122
#358822
#352782
#351972
#351522
#350442
#349692
#346812
#343302
C4×D422
#341532