Finite Group Databasebeta

← #7674996

Subgroups — #7674996

Order 512.

8038 conjugacy classes of subgroups.

The subgroup lattice has 1831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3519C212yesmaximal, complemented
2#59119C212yesmaximal, complemented
3#59117C212yesmaximal, complemented
4#59103C212yesmaximal, complemented
5#59097C212yesmaximal, complemented
6#59026C212yesmaximal, complemented
7#59020C212yesmaximal, complemented
8#59004C212yesmaximal, complemented
9#58999C212yesmaximal, complemented
10#43927C214yesmaximal, complemented
11#43923C214yesmaximal, complemented
12#43043C214yesmaximal, complemented
13#43039C214yesmaximal, complemented
14#39742C211yesmaximal, characteristic, complemented
15#39614C211yesmaximal, characteristic, complemented
16#38949C214yesmaximal, complemented
17#38949C212yesmaximal, complemented
18#37860C212yesmaximal, complemented
19#37672C212yesmaximal, complemented
20#36518C212yesmaximal, complemented
21#36153C211yesmaximal, characteristic, complemented
22D4×#121C211yesmaximal, characteristic, complemented
23#35365C214yesmaximal, complemented
24#35032C211yesmaximal, characteristic, complemented
25#35003C212yesmaximal, complemented
26#34737C212yesmaximal, complemented
27#34205C212yesmaximal, complemented
28C2×#2363C211yesmaximal, characteristic, complemented
29C4×#534C211yesmaximal, characteristic, complemented
30#3519—232no—
31C2×#555C2212yes—
32C2×#554C2212yescomplemented
33C2×#553C2214yescomplemented
34C2×#553C2212yescomplemented
35C2×#553C2212yescomplemented
36C2×#550C2212yescomplemented
37C2×#547C2211yescharacteristic, complemented
38C2×#546C2212yes—
39C2×#546C2214yescomplemented
40C2×#546C2212yescomplemented
41C2×#546C2214yescomplemented
42C2×D42C2214yescomplemented
43C2×D42C2212yescomplemented
44C2×D42C2211yescharacteristic, complemented
45C2×#540C2214yescomplemented
46C2×#538C2214yescomplemented
47C2×#538C2214yescomplemented
48C2×#534C2211yescharacteristic
49C2×#532C2212yescomplemented
50C2×#529C2212yescomplemented
51C2×#525C2212yescomplemented
52C2×#525C2212yescomplemented
53C2×#525C2212yescomplemented
54C22×#121C2212yes—
55C22×#121C2211yescharacteristic
56C22×#121C2212yescomplemented
57C2×#518C2214yescomplemented
58C22×C4×D4C2212yescomplemented
59C22×C4×D4C2211yescharacteristic, complemented
60C22×#117C2211yescharacteristic, complemented
61#2857C2211yescharacteristic, complemented
62#2856C2211yescharacteristic, complemented
63#2850C2214yescomplemented
64#2850C2212yescomplemented
65#2847C2212yescomplemented
66#2847C2212yescomplemented
67#2727C2212yescomplemented
68#2726C2212yescomplemented
69#2717C2214yescomplemented
70#2708C2214yescomplemented
71#2705C2214yescomplemented
72#2704C2214yescomplemented
73#2701C2214yescomplemented
74#2701C2214yescomplemented
75#2701C2214yescomplemented
76#2699C2214yescomplemented
77#2699C2214yescomplemented
78#2699C2214yescomplemented
79#2697C2214yescomplemented
80#2697C2214yescomplemented
81#2697C2214yescomplemented
82#2686C2214yescomplemented
83#2683C2212yescomplemented
84#2682C2212yescomplemented
85#2678C2214yescomplemented
86#2678C2214yescomplemented
87#2678C2214yescomplemented
88#2673C2214yescomplemented
89#2671C2214yescomplemented
90#2671C2214yescomplemented
91#2669C2214yescomplemented
92#2668C2214yescomplemented
93#2659C2212yescomplemented
94#2656C2212yescomplemented
95#2617C2214yescomplemented
96#2617C2212yescomplemented
97#2617C2212yescomplemented
98#2602C2214yescomplemented
99#2602C2214yescomplemented
100#2564C2214yescomplemented
101#2560C2214yescomplemented
102#2558C2214yescomplemented
103#2555C2214yescomplemented
104#2555C2214yescomplemented
105#2553C2214yescomplemented
106#2553C2214yescomplemented
107#2550C2212yescomplemented
108#2547C2211yescharacteristic, complemented
109#2543C2214yescomplemented
110#2541C2211yescharacteristic, complemented
111#2540C2212yescomplemented
112#2537C2211yescharacteristic, complemented
113#2537C2211yescharacteristic, complemented
114#2521C2214yescomplemented
115#2521C2214yescomplemented
116#2519C2214yescomplemented
117#2500C2212yescomplemented
118#2499C2212yescomplemented
119#2491C2212yescomplemented
120#2489C2212yescomplemented
121#2486C2212yescomplemented
122#2480C2214yescomplemented
123#2478C2214yescomplemented
124#2476C2214yescomplemented
125#2474C2214yescomplemented
126#2472C2214yescomplemented
127#2470C2214yescomplemented
128#2468C2214yescomplemented
129#2466C2214yescomplemented
130#2464C2214yescomplemented
131#2464C2214yescomplemented
132#2464C2214yescomplemented
133#2461C2214yescomplemented
134#2461C2214yescomplemented
135#2459C2214yescomplemented
136#2457C2214yescomplemented
137#2456C2214yescomplemented
138#2455C2214yescomplemented
139#2454C2212yescomplemented
140#2451C2212yescomplemented
141#2447C2214yescomplemented
142#2447C2212yescomplemented
143#2445C2214yescomplemented
144#2445C2212yescomplemented
145#2443C2214yescomplemented
146#2443C2214yescomplemented
147#2441C2212yescomplemented
148#2440C2212yescomplemented
149#2435C2214yescomplemented
150#2435C2212yescomplemented
151#2432C2212yescomplemented
152#2431C2212yescomplemented
153#2431C2214yescomplemented
154#2431C2212yescomplemented
155#2430C2214yescomplemented
156#2429C2212yescomplemented
157#2428C2212yescomplemented
158#2428C2212yescomplemented
159#2427C2212yescomplemented
160#2425C2214yescomplemented
161#2424C2214yescomplemented
162#2424C2214yescomplemented
163#2420C2214yescomplemented
164#2420C2212yescomplemented
165#2420C2212yescomplemented
166#2420C2214yescomplemented
167#2419C2214yescomplemented
168#2418C2214yescomplemented
169#2418C2214yescomplemented
170#2417C2214yescomplemented
171#2417C2212yescomplemented
172#2417C2212yescomplemented
173#2417C2212yescomplemented
174#2416C2214yescomplemented
175#2416C2212yescomplemented
176#2416C2212yescomplemented
177#2416C2212yescomplemented
178#2416C2212yescomplemented
179#2415C2212yescomplemented
180#2415C2212yescomplemented
181#2414C2212yescomplemented
182#2414C2212yescomplemented
183#2414C2212yescomplemented
184#2413C2214yescomplemented
185#2412C2214yescomplemented
186#2412C2214yescomplemented
187#2412C2214yescomplemented
188#2411C2214yescomplemented
189#2410C2214yescomplemented
190#2410C2214yescomplemented
191#2410C2214yescomplemented
192#2410C2214yescomplemented
193#2408C2212yescomplemented
194#2408C2212yescomplemented
195#2408C2214yescomplemented
196#2407C2214yescomplemented
197#2407C2212yescomplemented
198#2406C2214yescomplemented
199#2403C2214yescomplemented
200#2392C2214yescomplemented
201#2392C2214yescomplemented
202#2367C2212yescomplemented
203#2364C2214yescomplemented
204#2364C2214yescomplemented
205#2363C2214yescomplemented
206#2363C2214yescomplemented
207#2363C2212yescomplemented
208#2363C2212yescomplemented
209#2363C2212yescomplemented
210#2363C2212yescomplemented
211#2362C2212yescomplemented
212#2361C2214yescomplemented
213#2361C2212yescomplemented
214#2361C2214yescomplemented
215#2352C2212yescomplemented
216D4×C4⋊C4C2211yescharacteristic, complemented
217D4×C4⋊C4C2211yescharacteristic, complemented
218#2344C2214yescomplemented
219#2342C2214yescomplemented
220#2342C2214yescomplemented
221#2339C2212yescomplemented
222D4×C22⋊C4C2214yescomplemented
223D4×C22⋊C4C2212yescomplemented
224#2325C2211yescharacteristic
225#2325C2212yes—
226#2325C2212yescomplemented
227#2325C2212yescomplemented
228#2325C2211yescharacteristic, complemented
229#2325C2212yescomplemented
230#2325C2212yescomplemented
231#2322C2212yescomplemented
232#2322C2212yescomplemented
233#2321C2212yescomplemented
234#2321C2212yescomplemented
235#2315C2211yescharacteristic, complemented
236#2308C2212yescomplemented
237#2308C2214yescomplemented
238C4×#123C2212yescomplemented
239C4×#123C2212yescomplemented
240C4×#121C2211yescharacteristic
241C4×#121C2214yescomplemented
242C4×#121C2214yescomplemented
243C4×#121C2212yescomplemented
244C4×#121C2214yescomplemented
245C4×#121C2211yescharacteristic, complemented
246C4×#120C2212yescomplemented
247C4×#120C2212yescomplemented
248#2297C2212yescomplemented
249#2296C2212yescomplemented
250C2×#390C2212yescomplemented
251C2×#390C2211yescharacteristic, complemented
252C2×#389C2211yescharacteristic, complemented
253C2×#388C2212yescomplemented
254C2×#386C2212yescomplemented
255#2280C2212yescomplemented
256C2×#380C2212yescomplemented
257C2×C4×C4⋊C4C2211yescharacteristic, complemented
258C2×C4×C22⋊C4C2211yescharacteristic, complemented
259C2×C4×C22⋊C4C2212yescomplemented
260C22×#41C2312yes—
261C22×#41C2312yes—
262C22×#41C2314yes—
263C23×D4C2312yes—
264C23×D4C2314yes—
265C23×D4C2312yes—
266C23×D4C2312yes—
267C23×D4C2314yes—
268C23×D4C2311yescharacteristic
269C23×D4C2312yes—
270C24×C4C2312yes—
271C24×C4C2312yes—
272C24×C4C2311yescharacteristic
273#555—216no—
274#554—216no—
275#553—232no—
276#553—216no—
277#553—216no—
278#550—216no—
279#547—44no—
280#546—216no—
281#546—232no—
282#546—216no—
283#546—232no—
284D42—216no—
285D42—232no—
286D42—44no—
287#540—232no—
288#538—232no—
289#538—232no—
290#534—28no—
291#532—216no—
292C2×C4⋊Q8C2312yes—
293C2×C4⋊Q8C2311yescharacteristic
294C2×#127C2314yes—
295C2×#127C2312yes—
296C2×#127C2311yescharacteristic
297#529—216no—
298C2×#126C2314yes—
299C2×#126C2314yes—
300C2×#126C2314yes—
301C2×#125C2312yes—
302C2×#125C2314yes—
303C2×#124C2312yes—
304C2×#124C2314yes—
305C2×#124C2314yes—
306C2×#124C2314yes—
307C2×#124C2312yes—
308C2×#124C2314yes—
309#525—216no—
310#525—216no—
311#525—48no—
312C2×#123C2312yes—
313C2×#123C2312yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2314yes—
332C2×#121—216no—
333C2×#121—216no—
334C2×#121D4116yescomplemented
335C2×#121C2312yes—
336C2×#121C2311yescharacteristic
337C2×#121C2312yes—
338C2×#121C2312yes—
339C2×#121C2314yes—
340C2×#121C2314yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2314yes—
346C2×#121C2312yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2314yes—
352C2×#121C2314yes—
353C2×#121C2314yes—
354C2×#121C2314yes—
355C2×#121C2314yes—
356C2×#121C2314yes—
357C2×#121C2314yes—
358C2×#121C2314yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2314yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2311yescharacteristic
371C2×#120C2312yes—
372C2×#120C2312yes—
373C2×#120C2314yes—
374C2×#120C2314yes—
375C2×#120C2314yes—
376C2×#120C2314yes—
377C2×#120C2314yes—
378C2×#120C2314yes—
379C2×#120C2314yes—
380C2×#120C2314yes—
381C2×#120C2314yes—
382#518—232no—
383C2×C4×Q8C2312yes—
384C2×C4×D4—216no—
385C2×C4×D4—44no—
386C2×C4×D4C2314yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2314yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2314yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2314yes—
399C2×C4×D4C2314yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2314yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2314yes—
408C2×C4×D4C2314yes—
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2314yes—
411C2×C4×D4C2311yescharacteristic
412C2×C4×D4C2312yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2314yes—
416C2×C4×D4C2311yescharacteristic
417C2×C4×D4C2311yescharacteristic
418C2×C4×D4C2314yes—
419C2×#117—44no—
420C2×#117C2314yes—
421C2×#117C2314yes—
422C2×#117C2312yes—
423C2×#117C2312yes—
424C2×#117C2312yes—
425C2×#117C2314yes—
426C2×#117C2312yes—
427C22×C4⋊C4C2312yes—
428C22×C4⋊C4C2312yes—
429C22×C4⋊C4C2312yes—
430C22×C4⋊C4C2311yescharacteristic
431C22×C4⋊C4C2312yes—
432C22×C4⋊C4C2311yescharacteristic
433C22×C4⋊C4C2312yes—
434C22×C4⋊C4C2312yes—
435C22×C4⋊C4C2311yescharacteristic
436C22×C22⋊C4C2312yes—
437C22×C22⋊C4C2314yes—
438C22×C22⋊C4C2311yescharacteristic
439C22×C22⋊C4C2312yes—
440C22×C22⋊C4C2314yes—
441C22×C22⋊C4C2314yes—
442C22×C22⋊C4C2314yes—
443C22×C22⋊C4C2312yes—
444C22×C22⋊C4C2311yescharacteristic
445C22×C22⋊C4C2312yes—
446C22×C22⋊C4C2312yes—
447C22×C22⋊C4C2312yes—
448C22×C22⋊C4C2312yes—
449C22×C42C2312yes—
450C22×C42C2311yescharacteristic
451C22×C42C2311yescharacteristic
452C22×C42C2312yes—
453C22×C42C2312yes—
454#400C2314yes—
455#399C2314yes—
456#399C2314yes—
457#399C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#395C2314yes—
485#395C2314yes—
486#395C2314yes—
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#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#393C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#392C2314yes—
524#392C2314yes—
525#392C2314yes—
526#391C2314yes—
527#391C2312yes—
528#391C2312yes—
529#391C2312yes—
530#391C2312yes—
531#391C2314yes—
532#390C2314yes—
533#390C2311yescharacteristic
534#390C2311yescharacteristic
535#390C2312yes—
536#390C2312yes—
537#390C2314yes—
538#390C2312yes—
539#390C2312yes—
540#390C2314yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2312yes—
546#390C2314yes—
547#390C2314yes—
548#390C2314yes—
549#390C2314yes—
550#390C2314yes—
551#390C2312yes—
552#390C2314yes—
553#389C2311yescharacteristic
554#389C2312yes—
555#389C2311yescharacteristic
556#389C2314yes—
557#389C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2314yes—
570#389C2314yes—
571#388C2312yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#388C2312yes—
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2312yes—
614#386C2312yes—
615#386C2312yes—
616#386C2312yes—
617#386C2314yes—
618#386C2312yes—
619#386C2314yes—
620#386C2312yes—
621#386C2314yes—
622#386C2312yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#386C2312yes—
631#386C2312yes—
632#386C2312yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2312yes—
656#385C2312yes—
657#385C2312yes—
658#385C2312yes—
659#385C2312yes—
660#385C2312yes—
661#385C2312yes—
662#385C2312yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#384C2311yescharacteristic
674#384C2311yescharacteristic
675#382C2312yes—
676#382C2314yes—
677#381C2312yes—
678#381C2312yes—
679#381C2314yes—
680#381C2314yes—
681#381C2314yes—
682#381C2314yes—
683#381C2314yes—
684#380C2312yes—
685#380C2314yes—
686#380C2311yescharacteristic
687#380C2311yescharacteristic
688#380C2312yes—
689#380C2312yes—
690#380C2312yes—
691#380C2312yes—
692#380C2312yes—
693#380C2312yes—
694#380C2314yes—
695#380C2312yes—
696#380C2312yes—
697#380C2312yes—
698#380C2312yes—
699#380C2314yes—
700#380C2312yes—
701#380C2314yes—
702#380C2312yes—
703#380C2314yes—
704#379C2312yes—
705#379C2312yes—
706#379C2314yes—
707#379C2314yes—
708#379C2314yes—
709#379C2314yes—
710#379C2314yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2314yes—
714C4×C4⋊C4C2311yescharacteristic
715C4×C4⋊C4C2311yescharacteristic
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2314yes—
730C4×C22⋊C4C2314yes—
731C4×C22⋊C4C2312yes—
732C4×C22⋊C4C2312yes—
733C4×C22⋊C4C2314yes—
734C4×C22⋊C4C2312yes—
735C4×C22⋊C4C2312yes—
736C4×C22⋊C4C2314yes—
737C4×C22⋊C4C2314yes—
738C2×#95C2312yes—
739C2×#95C2311yescharacteristic
740C2×#95C2312yes—
741C2×#95C2311yescharacteristic
742C2×#95C2314yes—
743C25C2414yes—
744C25C2412yes—
745C25C2411yescharacteristic
746C25C2412yes—
747C2×#41—28no—
748C2×#41—216no—
749C2×#41—28no—
750C2×#41—44no—
751C2×#41—44no—
752C2×#41—44no—
753C2×#41—44no—
754C2×#41—84no—
755C2×#41—84no—
756C22×Q8C2412yes—
757C22×Q8C2414yes—
758C22×D4—28no—
759C22×D4—216no—
760C22×D4—216no—
761C22×D4—28no—
762C22×D4—28no—
763C22×D4—216no—
764C22×D4—28no—
765C22×D4—42no—
766C22×D4—42no—
767C22×D4—44no—
768C22×D4—44no—
769C22×D4—44no—
770C22×D4—44no—
771C22×D4—48no—
772C22×D4—82no—
773C22×D4—82no—
774C22×D4—82no—
775C22×D4—84no—
776C22×D4—84no—
777C22×D4C2×D418yes—
778C22×D4C2×D4116yescomplemented
779C22×D4C2414yes—
780C22×D4C2412yes—
781C22×D4C2412yes—
782C22×D4C2412yes—
783C22×D4C2414yes—
784C22×D4C2414yes—
785C22×D4C2412yes—
786C22×D4C2414yes—
787C22×D4C2411yescharacteristic
788C22×D4C2411yescharacteristic
789C22×D4C2412yes—
790C22×D4C2412yes—
791C22×D4C2411yescharacteristic
792C22×D4C2414yes—
793C22×D4C2414yes—
794C22×D4C2414yes—
795C22×D4C2414yes—
796C22×D4C2414yes—
797C22×D4C2414yes—
798C22×D4C2414yes—
799C22×D4C2412yes—
800C22×D4C2414yes—
801C22×D4C2412yes—
802C22×D4C2412yes—
803C22×D4C2414yes—
804C22×D4C2414yes—
805C22×D4C2411yescharacteristic
806C23×C4—28no—
807C23×C4—28no—
808C23×C4—42no—
809C23×C4—42no—
810C23×C4—44no—
811C23×C4—44no—
812C23×C4—44no—
813C23×C4—82no—
814C23×C4C2×D418yescomplemented
815C23×C4C2412yes—
816C23×C4C2412yes—
817C23×C4C2412yes—
818C23×C4C2414yes—
819C23×C4C2412yes—
820C23×C4C2412yes—
821C23×C4C2412yes—
822C23×C4C2411yescharacteristic
823C23×C4C2412yes—
824C23×C4C2411yescharacteristic
825C23×C4C2412yes—
826C23×C4C2411yescharacteristic
827C23×C4C2411yescharacteristic
828C23×C4C2412yes—
829C23×C4C2412yes—
830C23×C4C2412yes—
831C23×C4C2414yes—
832C23×C4C2414yes—
833C23×C4C2414yes—
834C23×C4C2412yes—
835C23×C4C2414yes—
836C23×C4C2414yes—
837C23×C4C2412yes—
838C23×C4C2412yes—
839C23×C4C2411yescharacteristic
840C23×C4C2412yes—
841C23×C4C2412yes—
842C23×C4C2411yescharacteristic
843C4⋊Q8—28no—
844C4⋊Q8—42no—
845#127—28no—
846#127—216no—
847#127—42no—
848#126—216no—
849#126—216no—
850#126—216no—
851#125—28no—
852#125—216no—
853#124—28no—
854#124—216no—
855#124—216no—
856#124—216no—
857#124—44no—
858#124—84no—
859#123—216no—
860#123—216no—
861#123—216no—
862#123—216no—
863#123—216no—
864#123—28no—
865#123—216no—
866#123—216no—
867#123—28no—
868#123—48no—
869#123—48no—
870#123—84no—
871C22⋊Q8—28no—
872C22⋊Q8—28no—
873C22⋊Q8—216no—
874C22⋊Q8—28no—
875C22⋊Q8—216no—
876C22⋊Q8—28no—
877C22⋊Q8—44no—
878C22⋊Q8—84no—
879#121—216no—
880#121—28no—
881#121—28no—
882#121—216no—
883#121—216no—
884#121—216no—
885#121—216no—
886#121—216no—
887#121—216no—
888#121—216no—
889#121—28no—
890#121—216no—
891#121—28no—
892#121—28no—
893#121—28no—
894#121—216no—
895#121—28no—
896#121—24no—
897#121—28no—
898#121—28no—
899#121—28no—
900#121—216no—
901#121—216no—
902#121—216no—
903#121—44no—
904#121—44no—
905#121—44no—
906#121—48no—
907#121—44no—
908#121—84no—
909#121—82no—
910#121—82no—
911#121C2×D4116yes—
912#121C2×D4116yescomplemented
913#121C2×D4132yescomplemented
914#121#4118yescomplemented
915#120—216no—
916#120—216no—
917#120—216no—
918#120—216no—
919#120—216no—
920#120—216no—
921#120—28no—
922#120—28no—
923#120—48no—
924#120—48no—
925#120—84no—
926C4×Q8—28no—
927C4×D4—216no—
928C4×D4—216no—
929C4×D4—28no—
930C4×D4—28no—
931C4×D4—28no—
932C4×D4—28no—
933C4×D4—28no—
934C4×D4—28no—
935C4×D4—28no—
936C4×D4—28no—
937C4×D4—28no—
938C4×D4—28no—
939C4×D4—216no—
940C4×D4—216no—
941C4×D4—216no—
942C4×D4—216no—
943C4×D4—28no—
944C4×D4—24no—
945C4×D4—24no—
946C4×D4—216no—
947C4×D4—216no—
948C4×D4—216no—
949C4×D4—216no—
950C4×D4—48no—
951C4×D4—42no—
952C4×D4—42no—
953C4×D4—48no—
954C4×D4—44no—
955C4×D4—42no—
956C4×D4—42no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—84no—
960#117—28no—
961#117—28no—
962#117—28no—
963#117—216no—
964#117—216no—
965#117—48no—
966#117—44no—
967C2×C4⋊C4—28no—
968C2×C4⋊C4—28no—
969C2×C4⋊C4—28no—
970C2×C4⋊C4—24no—
971C2×C4⋊C4—42no—
972C2×C4⋊C4—44no—
973C2×C4⋊C4—82no—
974C2×C4⋊C4—82no—
975C2×C4⋊C4C2×D418yescomplemented
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C22⋊C4—28no—
1021C2×C22⋊C4—216no—
1022C2×C22⋊C4—28no—
1023C2×C22⋊C4—24no—
1024C2×C22⋊C4—216no—
1025C2×C22⋊C4—216no—
1026C2×C22⋊C4—216no—
1027C2×C22⋊C4—44no—
1028C2×C22⋊C4—44no—
1029C2×C22⋊C4—42no—
1030C2×C22⋊C4—44no—
1031C2×C22⋊C4—82no—
1032C2×C22⋊C4C2×D4116yescomplemented
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C42—28no—
1103C2×C42—44no—
1104C2×C42—42no—
1105C2×C42—42no—
1106C2×C42—82no—
1107C2×C42C2412yes—
1108C2×C42C2414yes—
1109C2×C42C2414yes—
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2414yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2412yes—
1130#95C2414yes—
1131#95C2412yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162C24—22no—
1163C24—24no—
1164C24—24no—
1165C24—22no—
1166C24—24no—
1167C24—28no—
1168C24—28no—
1169C24—24no—
1170C24—41no—
1171C24—42no—
1172C24—42no—
1173C24—41no—
1174C24—42no—
1175C24—42no—
1176C24—42no—
1177C24—41no—
1178C24—41no—
1179C24—42no—
1180C24—42no—
1181C24—44no—
1182C24—42no—
1183C24—42no—
1184C24—44no—
1185C24—44no—
1186C24—44no—
1187C24—44no—
1188C24C22×D418yes—
1189C24C22×D414yes—
1190C24C2512yes—
1191C24C2514yes—
1192C24C2512yes—
1193C24C2512yes—
1194C24C2512yes—
1195C24C2512yes—
1196C24C2511yescharacteristic
1197#41—816no—
1198#41—816no—
1199#41—832no—
1200C2×Q8—24no—
1201C2×Q8—28no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—44no—
1205C2×Q8—44no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—24no—
1209C2×D4—28no—
1210C2×D4—24no—
1211C2×D4—28no—
1212C2×D4—24no—
1213C2×D4—28no—
1214C2×D4—28no—
1215C2×D4—24no—
1216C2×D4—28no—
1217C2×D4—28no—
1218C2×D4—28no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—28no—
1222C2×D4—28no—
1223C2×D4—28no—
1224C2×D4—28no—
1225C2×D4—28no—
1226C2×D4—28no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—28no—
1230C2×D4—24no—
1231C2×D4—28no—
1232C2×D4—22no—
1233C2×D4—24no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—28no—
1237C2×D4—24no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—24no—
1241C2×D4—416no—
1242C2×D4—42no—
1243C2×D4—41no—
1244C2×D4—44no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—44no—
1248C2×D4—42no—
1249C2×D4—44no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—41no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C2×D4—41no—
1259C2×D4—42no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C2×D4—42no—
1263C2×D4—44no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C2×D4—42no—
1267C2×D4—44no—
1268C2×D4—41no—
1269C2×D4—44no—
1270C2×D4—42no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—432no—
1282C2×D4—464no—
1283C2×D4—816no—
1284C2×D4—816no—
1285C2×D4—816no—
1286C2×D4—832no—
1287C2×D4C22×D414yes—
1288C2×D4C22×D414yes—
1289C2×D4C22×D4116yes—
1290C2×D4C22×D4116yes—
1291C2×D4C22×D418yes—
1292C2×D4C2×#4118yes—
1293C2×D4C2×#4114yes—
1294C22×C4—22no—
1295C22×C4—24no—
1296C22×C4—22no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—24no—
1300C22×C4—28no—
1301C22×C4—24no—
1302C22×C4—22no—
1303C22×C4—24no—
1304C22×C4—28no—
1305C22×C4—28no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—24no—
1311C22×C4—28no—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—24no—
1317C22×C4—24no—
1318C22×C4—24no—
1319C22×C4—24no—
1320C22×C4—24no—
1321C22×C4—24no—
1322C22×C4—24no—
1323C22×C4—28no—
1324C22×C4—28no—
1325C22×C4—28no—
1326C22×C4—24no—
1327C22×C4—24no—
1328C22×C4—24no—
1329C22×C4—416no—
1330C22×C4—41no—
1331C22×C4—41no—
1332C22×C4—41no—
1333C22×C4—41no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—42no—
1339C22×C4—42no—
1340C22×C4—41no—
1341C22×C4—41no—
1342C22×C4—42no—
1343C22×C4—44no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—42no—
1347C22×C4—41no—
1348C22×C4—42no—
1349C22×C4—41no—
1350C22×C4—41no—
1351C22×C4—42no—
1352C22×C4—44no—
1353C22×C4—41no—
1354C22×C4—44no—
1355C22×C4—42no—
1356C22×C4—42no—
1357C22×C4—42no—
1358C22×C4—42no—
1359C22×C4—44no—
1360C22×C4—44no—
1361C22×C4—44no—
1362C22×C4—42no—
1363C22×C4—42no—
1364C22×C4—44no—
1365C22×C4—44no—
1366C22×C4—42no—
1367C22×C4—44no—
1368C22×C4—42no—
1369C22×C4—42no—
1370C22×C4—42no—
1371C22×C4—44no—
1372C22×C4—44no—
1373C22×C4—816no—
1374C22×C4—816no—
1375C22×C4C22×D418yes—
1376C22×C4C22×D414yes—
1377C22×C4C22×D418yes—
1378C22×C4C22×D414yes—
1379C22×C4C22×D418yes—
1380C22×C4C2×#4114yes—
1381C22×C4C2512yes—
1382C22×C4C2512yes—
1383C22×C4C2512yes—
1384C22×C4C2511yescharacteristic
1385C22×C4C2514yes—
1386C22×C4C2514yes—
1387C22×C4C2512yes—
1388C22×C4C2512yes—
1389C22×C4C2512yes—
1390C22×C4C2512yes—
1391C22×C4C2514yes—
1392C22×C4C2514yes—
1393C22×C4C2512yes—
1394C22×C4C2511yescharacteristic
1395C22×C4C2512yes—
1396C22×C4C2514yes—
1397C22×C4C2511yescharacteristic
1398C22×C4C2511yescharacteristic
1399C22×C4C2512yes—
1400C22×C4C2511yescharacteristic
1401C22×C4C2512yes—
1402C22×C4C2511yescharacteristic
1403C4⋊C4—24no—
1404C4⋊C4—24no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—24no—
1408C4⋊C4—28no—
1409C4⋊C4—24no—
1410C4⋊C4—28no—
1411C4⋊C4—28no—
1412C4⋊C4—28no—
1413C4⋊C4—28no—
1414C4⋊C4—28no—
1415C4⋊C4—28no—
1416C4⋊C4—28no—
1417C4⋊C4—28no—
1418C4⋊C4—24no—
1419C4⋊C4—24no—
1420C4⋊C4—22no—
1421C4⋊C4—24no—
1422C4⋊C4—22no—
1423C4⋊C4—24no—
1424C4⋊C4—28no—
1425C4⋊C4—41no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—41no—
1429C4⋊C4—44no—
1430C4⋊C4—42no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—42no—
1434C4⋊C4—41no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—42no—
1438C4⋊C4—41no—
1439C4⋊C4—42no—
1440C4⋊C4—44no—
1441C4⋊C4—42no—
1442C4⋊C4—42no—
1443C4⋊C4C22×D418yes—
1444C4⋊C4C22×D418yes—
1445C4⋊C4C2×#4114yes—
1446C4⋊C4H(5,𝔽2)14yes—
1447C22⋊C4—24no—
1448C22⋊C4—28no—
1449C22⋊C4—28no—
1450C22⋊C4—24no—
1451C22⋊C4—28no—
1452C22⋊C4—24no—
1453C22⋊C4—24no—
1454C22⋊C4—28no—
1455C22⋊C4—28no—
1456C22⋊C4—28no—
1457C22⋊C4—28no—
1458C22⋊C4—28no—
1459C22⋊C4—28no—
1460C22⋊C4—28no—
1461C22⋊C4—24no—
1462C22⋊C4—24no—
1463C22⋊C4—24no—
1464C22⋊C4—28no—
1465C22⋊C4—28no—
1466C22⋊C4—24no—
1467C22⋊C4—28no—
1468C22⋊C4—24no—
1469C22⋊C4—28no—
1470C22⋊C4—28no—
1471C22⋊C4—28no—
1472C22⋊C4—24no—
1473C22⋊C4—24no—
1474C22⋊C4—28no—
1475C22⋊C4—28no—
1476C22⋊C4—24no—
1477C22⋊C4—24no—
1478C22⋊C4—28no—
1479C22⋊C4—24no—
1480C22⋊C4—24no—
1481C22⋊C4—28no—
1482C22⋊C4—28no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4—42no—
1489C22⋊C4—42no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—42no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—42no—
1498C22⋊C4—42no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—42no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—42no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C22⋊C4—42no—
1513C22⋊C4C22×D4116yes—
1514C22⋊C4C22×D4116yes—
1515C22⋊C4C2×#4118yes—
1516C42—24no—
1517C42—24no—
1518C42—24no—
1519C42—24no—
1520C42—28no—
1521C42—28no—
1522C42—28no—
1523C42—28no—
1524C42—22no—
1525C42—22no—
1526C42—24no—
1527C42—42no—
1528C42—44no—
1529C42—41no—
1530C42—41no—
1531C42—44no—
1532C42—44no—
1533C23—21no—
1534C23—21no—
1535C23—21no—
1536C23—21no—
1537C23—22no—
1538C23—22no—
1539C23—22no—
1540C23—22no—
1541C23—22no—
1542C23—22no—
1543C23—22no—
1544C23—22no—
1545C23—22no—
1546C23—22no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—22no—
1553C23—22no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—216no—
1562C23—28no—
1563C23—22no—
1564C23—24no—
1565C23—24no—
1566C23—22no—
1567C23—22no—
1568C23—24no—
1569C23—24no—
1570C23—22no—
1571C23—24no—
1572C23—22no—
1573C23—22no—
1574C23—24no—
1575C23—24no—
1576C23—22no—
1577C23—44no—
1578C23—48no—
1579C23—44no—
1580C23—48no—
1581C23—48no—
1582C23—416no—
1583C23—48no—
1584C23—84no—
1585C23—84no—
1586C23—82no—
1587C23—84no—
1588C23—82no—
1589C23—84no—
1590C23—82no—
1591C23—84no—
1592C23—82no—
1593C23—84no—
1594C23—84no—
1595C23—88no—
1596C23—88no—
1597C23—88no—
1598C23—88no—
1599C23—84no—
1600C23—84no—
1601C23—164no—
1602C23—164no—
1603C23C23×D414yes—
1604C23C23×D414yes—
1605C23C23×D414yes—
1606C23C23×D412yes—
1607C23C22×#4114yes—
1608C23C22×#4112yes—
1609C23#58512yes—
1610C23C2611yescharacteristic
1611Q8—48no—
1612Q8—88no—
1613D4—216no—
1614D4—28no—
1615D4—28no—
1616D4—48no—
1617D4—416no—
1618D4—44no—
1619D4—416no—
1620D4—48no—
1621D4—416no—
1622D4—416no—
1623D4—48no—
1624D4—416no—
1625D4—416no—
1626D4—48no—
1627D4—416no—
1628D4—48no—
1629D4—82no—
1630D4—84no—
1631D4—88no—
1632D4—84no—
1633D4—88no—
1634D4—88no—
1635D4—88no—
1636D4—88no—
1637D4—88no—
1638D4—88no—
1639D4—162no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—24no—
1651C2×C4—21no—
1652C2×C4—24no—
1653C2×C4—21no—
1654C2×C4—216no—
1655C2×C4—28no—
1656C2×C4—22no—
1657C2×C4—24no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—24no—
1662C2×C4—24no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—24no—
1667C2×C4—22no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—24no—
1671C2×C4—22no—
1672C2×C4—22no—
1673C2×C4—24no—
1674C2×C4—22no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—24no—
1680C2×C4—21no—
1681C2×C4—24no—
1682C2×C4—22no—
1683C2×C4—24no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—24no—
1690C2×C4—22no—
1691C2×C4—22no—
1692C2×C4—21no—
1693C2×C4—21no—
1694C2×C4—24no—
1695C2×C4—24no—
1696C2×C4—22no—
1697C2×C4—22no—
1698C2×C4—44no—
1699C2×C4—48no—
1700C2×C4—44no—
1701C2×C4—48no—
1702C2×C4—48no—
1703C2×C4—48no—
1704C2×C4—48no—
1705C2×C4—416no—
1706C2×C4—48no—
1707C2×C4—44no—
1708C2×C4—48no—
1709C2×C4—48no—
1710C2×C4—48no—
1711C2×C4—84no—
1712C2×C4—84no—
1713C2×C4—84no—
1714C2×C4—84no—
1715C2×C4—88no—
1716C2×C4—88no—
1717C2×C4—88no—
1718C2×C4—82no—
1719C2×C4—82no—
1720C2×C4—84no—
1721C2×C4—84no—
1722C2×C4—88no—
1723C2×C4—88no—
1724C2×C4C23×D414yes—
1725C2×C4C23×D418yes—
1726C2×C4C23×D412yes—
1727C2×C4C23×D412yes—
1728C2×C4C22×#4112yes—
1729C2×C4C22×#4112yes—
1730C2×C4C22×#4114yes—
1731C2×C4C2×H(5,𝔽2)14yes—
1732C2×C4C2×H(5,𝔽2)12yes—
1733C2×C4#58512yes—
1734C22—22no—
1735C22—22no—
1736C22—22no—
1737C22—22no—
1738C22—22no—
1739C22—22no—
1740C22—24no—
1741C22—24no—
1742C22—24no—
1743C22—24no—
1744C22—24no—
1745C22—24no—
1746C22—24no—
1747C22—24no—
1748C22—24no—
1749C22—24no—
1750C22—24no—
1751C22—24no—
1752C22—42no—
1753C22—42no—
1754C22—42no—
1755C22—42no—
1756C22—42no—
1757C22—42no—
1758C22—42no—
1759C22—42no—
1760C22—42no—
1761C22—42no—
1762C22—42no—
1763C22—42no—
1764C22—42no—
1765C22—42no—
1766C22—42no—
1767C22—42no—
1768C22—44no—
1769C22—42no—
1770C22—42no—
1771C22—44no—
1772C22—42no—
1773C22—44no—
1774C22—44no—
1775C22—42no—
1776C22—42no—
1777C22—44no—
1778C22—42no—
1779C22—44no—
1780C22—42no—
1781C22—44no—
1782C22—816no—
1783C22—88no—
1784C22—816no—
1785C22—1616no—
1786C22D4×#4114yes—
1787C22C24×D411yescharacteristic
1788C22C23×#4111yescharacteristic
1789C22C22×H(5,𝔽2)11yescharacteristic
1790C22C2×#58511yescharacteristic
1791C22C2×#58511yescharacteristic
1792C22H(7,𝔽2)11yescharacteristic
1793C22H(7,𝔽2)11yescharacteristic
1794C4—22no—
1795C4—22no—
1796C4—24no—
1797C4—24no—
1798C4—22no—
1799C4—28no—
1800C4—24no—
1801C4—42no—
1802C4—42no—
1803C4—42no—
1804C4—42no—
1805C4—44no—
1806C4—42no—
1807C4—42no—
1808C4—44no—
1809C4—41no—
1810C4—44no—
1811C4—41no—
1812C4—42no—
1813C4—42no—
1814C4—44no—
1815C4#349614yes—
1816C2—24no—
1817C2—44no—
1818C2—44no—
1819C2—44no—
1820C2—44no—
1821C2—82no—
1822C2—84no—
1823C2C2×D4×#4111yescharacteristic
1824C2C2×#349611yescharacteristic
1825C2#6284211yescharacteristic
1826C2#6289911yescharacteristic
1827C2#6290811yescharacteristic
1828C2#6298311yescharacteristic
1829C2#6299411yescharacteristic
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. C2×#3519C2semidirect
2. #59119C2semidirect
3. #59117C2semidirect
4. #59103C2semidirect
5. #59097C2semidirect
6. #59026C2semidirect
7. #59020C2semidirect
8. #59004C2semidirect
9. #58999C2semidirect
10. #43927C2semidirect
11. #43923C2semidirect
12. #43043C2semidirect
13. #43039C2semidirect
14. #39742C2semidirect
15. #39614C2semidirect
16. #38949C2semidirect
17. #38949C2semidirect
18. #37860C2semidirect
19. #37672C2semidirect
20. #36518C2semidirect
21. #36153C2semidirect
22. D4×#121C2semidirect
23. #35365C2semidirect
24. #35032C2semidirect
25. #35003C2semidirect
26. #34737C2semidirect
27. #34205C2semidirect
28. C2×#2363C2semidirect
29. C4×#534C2semidirect
32. C2×#554C22semidirect
33. C2×#553C22semidirect
34. C2×#553C22semidirect
35. C2×#553C22semidirect
36. C2×#550C22semidirect
37. C2×#547C22semidirect
39. C2×#546C22semidirect
40. C2×#546C22semidirect
41. C2×#546C22semidirect
42. C2×D42C22semidirect
43. C2×D42C22semidirect
44. C2×D42C22semidirect
45. C2×#540C22semidirect
46. C2×#538C22semidirect
47. C2×#538C22semidirect
49. C2×#532C22semidirect
50. C2×#529C22semidirect
51. C2×#525C22semidirect
52. C2×#525C22semidirect
53. C2×#525C22semidirect
56. C22×#121C22semidirect
57. C2×#518C22semidirect
58. C22×C4×D4C22semidirect
59. C22×C4×D4C22semidirect
60. C22×#117C22semidirect
61. #2857C22semidirect
62. #2856C22semidirect
63. #2850C22semidirect
64. #2850C22semidirect
65. #2847C22semidirect
66. #2847C22semidirect
67. #2727C22semidirect
68. #2726C22semidirect
69. #2717C22semidirect
70. #2708C22semidirect
71. #2705C22semidirect
72. #2704C22semidirect
73. #2701C22semidirect
74. #2701C22semidirect
75. #2701C22semidirect
76. #2699C22semidirect
77. #2699C22semidirect
78. #2699C22semidirect
79. #2697C22semidirect
80. #2697C22semidirect
81. #2697C22semidirect
82. #2686C22semidirect
83. #2683C22semidirect
84. #2682C22semidirect
85. #2678C22semidirect
86. #2678C22semidirect
87. #2678C22semidirect
88. #2673C22semidirect
89. #2671C22semidirect
90. #2671C22semidirect
91. #2669C22semidirect
92. #2668C22semidirect
93. #2659C22semidirect
94. #2656C22semidirect
95. #2617C22semidirect
96. #2617C22semidirect
97. #2617C22semidirect
98. #2602C22semidirect
99. #2602C22semidirect
100. #2564C22semidirect
101. #2560C22semidirect
102. #2558C22semidirect
103. #2555C22semidirect
104. #2555C22semidirect
105. #2553C22semidirect
106. #2553C22semidirect
107. #2550C22semidirect
108. #2547C22semidirect
109. #2543C22semidirect
110. #2541C22semidirect
111. #2540C22semidirect
112. #2537C22semidirect
113. #2537C22semidirect
114. #2521C22semidirect
115. #2521C22semidirect
116. #2519C22semidirect
117. #2500C22semidirect
118. #2499C22semidirect
119. #2491C22semidirect
120. #2489C22semidirect
121. #2486C22semidirect
122. #2480C22semidirect
123. #2478C22semidirect
124. #2476C22semidirect
125. #2474C22semidirect
126. #2472C22semidirect
127. #2470C22semidirect
128. #2468C22semidirect
129. #2466C22semidirect
130. #2464C22semidirect
131. #2464C22semidirect
132. #2464C22semidirect
133. #2461C22semidirect
134. #2461C22semidirect
135. #2459C22semidirect
136. #2457C22semidirect
137. #2456C22semidirect
138. #2455C22semidirect
139. #2454C22semidirect
140. #2451C22semidirect
141. #2447C22semidirect
142. #2447C22semidirect
143. #2445C22semidirect
144. #2445C22semidirect
145. #2443C22semidirect
146. #2443C22semidirect
147. #2441C22semidirect
148. #2440C22semidirect
149. #2435C22semidirect
150. #2435C22semidirect
151. #2432C22semidirect
152. #2431C22semidirect
153. #2431C22semidirect
154. #2431C22semidirect
155. #2430C22semidirect
156. #2429C22semidirect
157. #2428C22semidirect
158. #2428C22semidirect
159. #2427C22semidirect
160. #2425C22semidirect
161. #2424C22semidirect
162. #2424C22semidirect
163. #2420C22semidirect
164. #2420C22semidirect
165. #2420C22semidirect
166. #2420C22semidirect
167. #2419C22semidirect
168. #2418C22semidirect
169. #2418C22semidirect
170. #2417C22semidirect
171. #2417C22semidirect
172. #2417C22semidirect
173. #2417C22semidirect
174. #2416C22semidirect
175. #2416C22semidirect
176. #2416C22semidirect
177. #2416C22semidirect
178. #2416C22semidirect
179. #2415C22semidirect
180. #2415C22semidirect
181. #2414C22semidirect
182. #2414C22semidirect
183. #2414C22semidirect
184. #2413C22semidirect
185. #2412C22semidirect
186. #2412C22semidirect
187. #2412C22semidirect
188. #2411C22semidirect
189. #2410C22semidirect
190. #2410C22semidirect
191. #2410C22semidirect
192. #2410C22semidirect
193. #2408C22semidirect
194. #2408C22semidirect
195. #2408C22semidirect
196. #2407C22semidirect
197. #2407C22semidirect
198. #2406C22semidirect
199. #2403C22semidirect
200. #2392C22semidirect
201. #2392C22semidirect
202. #2367C22semidirect
203. #2364C22semidirect
204. #2364C22semidirect
205. #2363C22semidirect
206. #2363C22semidirect
207. #2363C22semidirect
208. #2363C22semidirect
209. #2363C22semidirect
210. #2363C22semidirect
211. #2362C22semidirect
212. #2361C22semidirect
213. #2361C22semidirect
214. #2361C22semidirect
215. #2352C22semidirect
216. D4×C4⋊C4C22semidirect
217. D4×C4⋊C4C22semidirect
218. #2344C22semidirect
219. #2342C22semidirect
220. #2342C22semidirect
221. #2339C22semidirect
222. D4×C22⋊C4C22semidirect
223. D4×C22⋊C4C22semidirect
226. #2325C22semidirect
227. #2325C22semidirect
228. #2325C22semidirect
229. #2325C22semidirect
230. #2325C22semidirect
231. #2322C22semidirect
232. #2322C22semidirect
233. #2321C22semidirect
234. #2321C22semidirect
235. #2315C22semidirect
236. #2308C22semidirect
237. #2308C22semidirect
238. C4×#123C22semidirect
239. C4×#123C22semidirect
241. C4×#121C22semidirect
242. C4×#121C22semidirect
243. C4×#121C22semidirect
244. C4×#121C22semidirect
245. C4×#121C22semidirect
246. C4×#120C22semidirect
247. C4×#120C22semidirect
248. #2297C22semidirect
249. #2296C22semidirect
250. C2×#390C22semidirect
251. C2×#390C22semidirect
252. C2×#389C22semidirect
253. C2×#388C22semidirect
254. C2×#386C22semidirect
255. #2280C22semidirect
256. C2×#380C22semidirect
257. C2×C4×C4⋊C4C22semidirect
258. C2×C4×C22⋊C4C22semidirect
259. C2×C4×C22⋊C4C22semidirect
334. C2×#121D4semidirect
778. C22×D4C2×D4semidirect
814. C23×C4C2×D4semidirect
912. #121C2×D4semidirect
913. #121C2×D4semidirect
914. #121#41semidirect
975. C2×C4⋊C4C2×D4semidirect
1032. C2×C22⋊C4C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35192
#591192
#591172
#591032
#590972
#590262
#590202
#590042
#589992
#439272
#439232
#430432
#430392
#397422
#396142
#389492
#378602
#376722
#365182
#361532
D4×#1212
#353652
#350322
#350032
#347372
#342052
C2×#23632
C4×#5342