Finite Group Databasebeta

← #7647561

Subgroups — #7647561

Order 512.

5168 conjugacy classes of subgroups.

The subgroup lattice has 1769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42904C212yesmaximal, complemented
2#42871C212yesmaximal, complemented
3#42556C212yesmaximal, complemented
4#42540C212yesmaximal, complemented
5#40812C214yesmaximal, complemented
6#40791C214yesmaximal, complemented
7#40149C212yesmaximal, complemented
8#40119C212yesmaximal, complemented
9#39409C212yesmaximal, complemented
10#39245C212yesmaximal, complemented
11#38504C214yesmaximal, complemented
12#37724C214yesmaximal, complemented
13#37524C212yesmaximal, complemented
14#37520C212yesmaximal, complemented
15#37326C212yesmaximal, complemented
16#37315C212yesmaximal, complemented
17#37288C212yesmaximal, complemented
18#37286C212yesmaximal, complemented
19#35585C211yesmaximal, characteristic, complemented
20#35557C211yesmaximal, characteristic, complemented
21#35541C211yesmaximal, characteristic, complemented
22#35515C211yesmaximal, characteristic, complemented
23#35280C211yesmaximal, characteristic, complemented
24#35256C211yesmaximal, characteristic
25#35255C211yesmaximal, characteristic, complemented
26#35254C211yesmaximal, characteristic, complemented
27#35254C211yesmaximal, characteristic, complemented
28#35159C211yesmaximal, characteristic, complemented
29#35083C212yesmaximal, complemented
30#35006C212yesmaximal, complemented
31C2×#2512C211yesmaximal, characteristic, complemented
32#34745C211yesmaximal, characteristic, complemented
33#34269C211yesmaximal, characteristic, complemented
34C4⋊C4×#41C211yesmaximal, characteristic, complemented
35C4×#537C211yesmaximal, characteristic, complemented
36C2×#539C2214yescomplemented
37C2×#537C2211yescharacteristic
38C2×#535C2211yescharacteristic
39C2×#535C2211yescharacteristic
40C2×#533C2211yescharacteristic
41C22×#126C2212yes—
42C2×#518C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47#2857C2212yescomplemented
48#2857C2212yescomplemented
49#2856C2212yes—
50#2855C2212yescomplemented
51#2854C2212yes—
52#2854C2212yes—
53#2854C2212yes—
54#2854C2212yes—
55#2854C2212yescomplemented
56#2851C2214yes—
57#2850C2212yes—
58#2837C2214yescomplemented
59#2837C2214yescomplemented
60#2827C2214yescomplemented
61#2827C2214yescomplemented
62#2808C2214yescomplemented
63#2807C2214yescomplemented
64#2798C2214yescomplemented
65#2790C2214yescomplemented
66#2786C2214yescomplemented
67#2783C2214yescomplemented
68#2783C2214yescomplemented
69#2781C2214yescomplemented
70#2781C2214yescomplemented
71#2750C2214yescomplemented
72#2744C2214yescomplemented
73#2743C2214yescomplemented
74#2740C2214yescomplemented
75#2732C2214yescomplemented
76#2728C2214yescomplemented
77#2727C2214yescomplemented
78#2724C2214yescomplemented
79#2723C2214yescomplemented
80#2721C2214yescomplemented
81#2718C2214yescomplemented
82#2718C2214yescomplemented
83#2707C2214yescomplemented
84#2705C2214yescomplemented
85#2705C2214yescomplemented
86#2695C2214yescomplemented
87#2693C2214yescomplemented
88#2693C2214yescomplemented
89#2691C2214yescomplemented
90#2691C2214yescomplemented
91#2689C2214yescomplemented
92#2681C2214yescomplemented
93#2681C2214yescomplemented
94#2667C2214yescomplemented
95#2664C2214yescomplemented
96#2654C2214yescomplemented
97#2654C2214yescomplemented
98#2652C2214yescomplemented
99#2650C2214yescomplemented
100#2646C2214yes—
101#2639C2214yescomplemented
102#2636C2214yescomplemented
103#2636C2214yescomplemented
104#2630C2214yescomplemented
105#2630C2214yescomplemented
106#2629C2212yescomplemented
107#2629C2212yescomplemented
108#2625C2212yescomplemented
109#2624C2212yes—
110#2624C2212yes—
111#2624C2212yes—
112#2624C2212yes—
113#2624C2212yescomplemented
114#2620C2212yes—
115#2619C2212yes—
116#2618C2214yescomplemented
117#2582C2212yescomplemented
118#2582C2212yescomplemented
119#2580C2212yes—
120#2580C2212yes—
121#2569C2214yes—
122#2560C2214yescomplemented
123#2560C2214yescomplemented
124#2558C2214yescomplemented
125#2558C2214yescomplemented
126#2553C2214yescomplemented
127#2553C2214yescomplemented
128#2538C2212yes—
129#2538C2212yes—
130#2538C2212yescomplemented
131#2538C2212yescomplemented
132#2512C2212yes—
133#2512C2212yes—
134#2512C2212yes—
135#2512C2212yes—
136#2512C2212yes—
137#2512C2212yes—
138#2512C2212yes—
139#2512C2212yes—
140#2512C2212yescomplemented
141#2512C2212yescomplemented
142#2511C2212yescomplemented
143#2511C2212yescomplemented
144#2509C2212yescomplemented
145#2509C2212yescomplemented
146#2509C2212yescomplemented
147#2509C2212yescomplemented
148#2508C2212yescomplemented
149#2508C2212yescomplemented
150#2508C2212yescomplemented
151#2508C2212yescomplemented
152#2507C2212yescomplemented
153#2507C2212yescomplemented
154#2507C2212yescomplemented
155#2507C2212yescomplemented
156#2506C2212yescomplemented
157#2506C2212yescomplemented
158#2506C2212yescomplemented
159#2506C2212yescomplemented
160#2497C2212yescomplemented
161#2497C2212yescomplemented
162#2496C2212yescomplemented
163#2496C2212yescomplemented
164#2488C2214yescomplemented
165#2481C2214yes—
166#2481C2214yes—
167#2481C2214yescomplemented
168#2466C2214yescomplemented
169#2460C2214yescomplemented
170#2454C2212yes—
171#2454C2212yes—
172#2454C2211yescharacteristic, complemented
173#2454C2211yescharacteristic, complemented
174#2453C2211yescharacteristic, complemented
175#2453C2211yescharacteristic, complemented
176#2452C2212yes—
177#2452C2212yes—
178#2452C2211yescharacteristic, complemented
179#2452C2211yescharacteristic, complemented
180#2451C2211yescharacteristic, complemented
181#2451C2211yescharacteristic, complemented
182#2450C2212yes—
183#2450C2212yes—
184#2449C2212yes—
185#2449C2212yes—
186#2449C2214yescomplemented
187#2448C2212yes—
188#2448C2212yes—
189#2448C2212yes—
190#2448C2212yes—
191#2447C2212yes—
192#2447C2212yes—
193#2445C2212yes—
194#2445C2212yes—
195#2445C2212yes—
196#2445C2212yes—
197#2445C2212yes—
198#2445C2212yes—
199#2444C2214yes—
200#2443C2214yes—
201#2442C2214yes—
202#2437C2214yes—
203#2437C2214yes—
204#2428C2212yes—
205#2428C2212yes—
206#2426C2212yes—
207#2426C2212yes—
208#2424C2214yes—
209#2424C2214yes—
210#2423C2212yescomplemented
211#2422C2212yes—
212#2422C2212yes—
213#2422C2212yescomplemented
214#2421C2212yescomplemented
215#2420C2212yes—
216#2420C2212yes—
217#2420C2212yescomplemented
218#2419C2214yescomplemented
219#2418C2214yes—
220#2418C2214yes—
221#2418C2214yes—
222#2418C2214yes—
223#2417C2214yes—
224#2417C2214yes—
225#2412C2214yes—
226#2412C2214yes—
227#2396C2212yescomplemented
228#2396C2212yescomplemented
229C2×#397C2212yes—
230C2×#396C2212yes—
231#2367C2212yes—
232#2367C2212yes—
233#2366C2212yes—
234#2366C2212yes—
235#2358C2214yes—
236#2358C2214yes—
237#2351C2211yescharacteristic, complemented
238#2351C2211yescharacteristic, complemented
239Q8×C4⋊C4C2211yescharacteristic, complemented
240Q8×C4⋊C4C2211yescharacteristic, complemented
241#2349C2212yes—
242#2349C2212yes—
243#2349C2211yescharacteristic, complemented
244#2349C2211yescharacteristic, complemented
245D4×C4⋊C4C2212yes—
246D4×C4⋊C4C2212yes—
247D4×C4⋊C4C2211yescharacteristic, complemented
248D4×C4⋊C4C2211yescharacteristic, complemented
249#2334C2214yescomplemented
250#2332C2214yescomplemented
251#2325C2214yes—
252#2325C2214yescomplemented
253#2324C2212yes—
254#2324C2212yes—
255#2324C2212yescomplemented
256#2324C2212yescomplemented
257#2323C2212yescomplemented
258#2323C2212yescomplemented
259#2317C2211yescharacteristic
260#2317C2211yescharacteristic
261#2316C2211yescharacteristic
262#2316C2211yescharacteristic
263#2316C2211yescharacteristic
264#2316C2211yescharacteristic
265#2311C2211yescharacteristic
266#2311C2211yescharacteristic
267#2311C2211yescharacteristic
268#2311C2211yescharacteristic
269#2309C2211yescharacteristic
270C4×C22⋊Q8C2212yescomplemented
271C4×C22⋊Q8C2212yescomplemented
272C4×C22⋊Q8C2212yescomplemented
273C4×C22⋊Q8C2212yescomplemented
274C4×#121C2212yes—
275C4×#121C2214yes—
276C4×#121C2212yes—
277C4×#121C2212yescomplemented
278C4×#121C2212yescomplemented
279#2297C2211yescharacteristic
280#2297C2211yescharacteristic
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283#2296C2211yescharacteristic
284#2296C2211yescharacteristic
285#2296C2212yescomplemented
286#2296C2212yescomplemented
287C2×#390C2211yescharacteristic
288C2×#390C2211yescharacteristic
289C2×#390C2211yescharacteristic
290C2×#389C2211yescharacteristic
291C2×#388C2212yes—
292#2285C2211yescharacteristic
293#2285C2212yescomplemented
294C2×#384C2211yescharacteristic
295#2274C2211yescharacteristic
296C2×C4×C4⋊C4C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2212yescomplemented
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C23×D4C2311yescharacteristic
302#539—416no—
303#537—28no—
304#535—28no—
305#535—44no—
306#533—44no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×#127C2312yes—
310C2×#127C2312yes—
311C2×#126—48no—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#126C2314yes—
318C2×#125C2314yes—
319C2×#125C2311yescharacteristic
320C2×#125C2311yescharacteristic
321C2×#125C2314yes—
322C2×#124C2312yes—
323C2×#124C2312yes—
324C2×#123C2314yes—
325C2×#123C2314yes—
326C2×#123C2314yes—
327C2×#123C2314yes—
328C2×#123C2314yes—
329C2×#123C2314yes—
330C2×#123C2314yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2314yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2314yes—
346C2×#121C2314yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2314yes—
350C2×#120C2314yes—
351C2×#120C2314yes—
352#518—44no—
353C4×#41—28no—
354C4×#41—44no—
355C4×#41—44no—
356C4×#41—44no—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2314yes—
380C2×C4×D4C2314yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2312yes—
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2314yes—
390C2×#117C2311yescharacteristic
391C2×#117C2311yescharacteristic
392C2×#117C2311yescharacteristic
393C2×#117C2311yescharacteristic
394C2×#117C2311yescharacteristic
395C2×#117C2311yescharacteristic
396C2×#117C2312yes—
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2312yes—
400C22×C4⋊C4C2311yescharacteristic
401C22×C4⋊C4C2311yescharacteristic
402C22×C4⋊C4C2311yescharacteristic
403C22×C4⋊C4C2311yescharacteristic
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2311yescharacteristic
406C22×C4⋊C4C2312yes—
407C22×C4⋊C4C2312yes—
408C22×C4⋊C4C2312yes—
409C22×C4⋊C4C2312yes—
410C22×C22⋊C4C2314yes—
411C22×C22⋊C4C2312yes—
412C22×C22⋊C4C2312yes—
413C22×C22⋊C4C2312yes—
414C22×C22⋊C4C2312yes—
415C22×C22⋊C4C2312yes—
416C22×C22⋊C4C2312yes—
417C22×C42C2312yes—
418C22×C42C2311yescharacteristic
419C22×C42C2311yescharacteristic
420C22×C42C2311yescharacteristic
421C22×C42C2312yes—
422C22×C42C2312yes—
423C22×C42C2312yes—
424C22×C42C2312yes—
425#400C2314yes—
426#400C2314yes—
427#400C2312yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2314yes—
438#400C2312yes—
439#400C2314yes—
440#399C2314yes—
441#399C2314yes—
442#399C2314yes—
443#399C2312yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#399C2314yes—
448#399C2312yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2312yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2312yes—
464#398C2312yes—
465#398C2312yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2312yes—
488#396C2314yes—
489#396C2314yes—
490#396C2312yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2312yes—
501#396C2312yes—
502#396C2314yes—
503#395C2312yes—
504#395C2312yes—
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#393C2312yes—
524#393C2314yes—
525#393C2314yes—
526#393C2312yes—
527#392C2314yes—
528#392C2314yes—
529#391C2314yes—
530#391C2312yes—
531#391C2312yes—
532#391C2312yes—
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2311yescharacteristic
537#391C2311yescharacteristic
538#391C2311yescharacteristic
539#391C2311yescharacteristic
540#391C2312yes—
541#390C2314yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2314yes—
552#390C2314yes—
553#390C2314yes—
554#390C2312yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2311yescharacteristic
560#390C2311yescharacteristic
561#390C2314yes—
562#390C2311yescharacteristic
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2311yescharacteristic
567#390C2312yes—
568#390C2312yes—
569#390C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2314yes—
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2312yes—
596#389C2312yes—
597#389C2314yes—
598#389C2314yes—
599#389C2314yes—
600#389C2314yes—
601#389C2314yes—
602#389C2311yescharacteristic
603#389C2311yescharacteristic
604#389C2311yescharacteristic
605#389C2311yescharacteristic
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2311yescharacteristic
611#389C2311yescharacteristic
612#389C2311yescharacteristic
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2311yescharacteristic
617#389C2311yescharacteristic
618#389C2311yescharacteristic
619#389C2312yes—
620#389C2312yes—
621#389C2314yes—
622#389C2312yes—
623#389C2312yes—
624#389C2312yes—
625#389C2311yescharacteristic
626#389C2311yescharacteristic
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2312yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2312yes—
670#387C2314yes—
671#387C2312yes—
672#387C2312yes—
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#386C2312yes—
693#386C2312yes—
694#386C2312yes—
695#386C2312yes—
696#385C2312yes—
697#385C2314yes—
698#385C2314yes—
699#385C2312yes—
700#385C2312yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2312yes—
710#385C2314yes—
711#385C2312yes—
712#385C2312yes—
713#385C2314yes—
714#385C2312yes—
715#385C2312yes—
716#385C2312yes—
717#385C2312yes—
718#385C2312yes—
719#385C2312yes—
720#385C2312yes—
721#385C2312yes—
722#385C2312yes—
723#385C2312yes—
724#385C2312yes—
725#385C2314yes—
726#385C2312yes—
727#385C2312yes—
728#385C2312yes—
729#384C2312yes—
730#384C2312yes—
731#384C2312yes—
732#384C2312yes—
733#384C2312yes—
734#384C2312yes—
735#384C2312yes—
736#384C2311yescharacteristic
737#384C2311yescharacteristic
738#384C2312yes—
739#382C2312yes—
740#382C2312yes—
741#382C2314yes—
742#382C2312yes—
743#382C2312yes—
744#382C2311yescharacteristic
745#382C2311yescharacteristic
746#382C2314yes—
747#381C2314yes—
748#381C2314yes—
749#381C2314yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2314yes—
760#380C2314yes—
761#380C2314yes—
762#380C2314yes—
763#380C2314yes—
764#380C2314yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2314yes—
772#380C2314yes—
773#380C2312yes—
774#379C2314yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2311yescharacteristic
803C4×C4⋊C4C2312yes—
804C4×C4⋊C4C2312yes—
805C4×C4⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2314yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2314yes—
815C2×#95C2312yes—
816C2×#95C2312yes—
817C2×#95C2312yes—
818C2×#95C2311yescharacteristic
819C2×#95C2311yescharacteristic
820C2×#95C2312yes—
821C25C2412yes—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C2×#41—24no—
827C2×#41#4118yes—
828C22×Q8C2411yescharacteristic
829C22×Q8C2411yescharacteristic
830C22×Q8C2412yes—
831C22×Q8C2412yes—
832C22×D4—24no—
833C22×D4—24no—
834C22×D4—24no—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2412yes—
838C22×D4C2411yescharacteristic
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2414yes—
842C22×D4C2414yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2411yescharacteristic
868C4⋊Q8—42no—
869C4⋊Q8—42no—
870#127—28no—
871#127—44no—
872#126—216no—
873#126—48no—
874#126—48no—
875#126—48no—
876#126—48no—
877#126—84no—
878#125—42no—
879#125—42no—
880#125—48no—
881#125—48no—
882#124—28no—
883#124—44no—
884#123—48no—
885#123—48no—
886#123—48no—
887#123—48no—
888#123—84no—
889#123—84no—
890#123—84no—
891C22⋊Q8—28no—
892C22⋊Q8—28no—
893C22⋊Q8—28no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—48no—
897C22⋊Q8—44no—
898C22⋊Q8—48no—
899C22⋊Q8—48no—
900C22⋊Q8—84no—
901#121—28no—
902#121—216no—
903#121—28no—
904#121—28no—
905#121—28no—
906#121—48no—
907#121—48no—
908#121—44no—
909#121—44no—
910#120—216no—
911#120—48no—
912C4×Q8—24no—
913C4×Q8—24no—
914C4×Q8—44no—
915C4×Q8—44no—
916C4×Q8—42no—
917C4×Q8—42no—
918C4×Q8—42no—
919C4×Q8—42no—
920C4×Q8—42no—
921C4×Q8—42no—
922C4×D4—28no—
923C4×D4—24no—
924C4×D4—28no—
925C4×D4—24no—
926C4×D4—42no—
927C4×D4—42no—
928C4×D4—42no—
929C4×D4—42no—
930C4×D4—42no—
931C4×D4—42no—
932C4×D4—44no—
933C4×D4—44no—
934C4×D4—44no—
935C4×D4—44no—
936C4×D4—48no—
937C4×D4—48no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—44no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—84no—
945#117—28no—
946#117—24no—
947#117—24no—
948#117—24no—
949#117—24no—
950#117—24no—
951#117—24no—
952#117—44no—
953#117—44no—
954#117—44no—
955C2×C4⋊C4—24no—
956C2×C4⋊C4—24no—
957C2×C4⋊C4—24no—
958C2×C4⋊C4—24no—
959C2×C4⋊C4—28no—
960C2×C4⋊C4—42no—
961C2×C4⋊C4—44no—
962C2×C4⋊C4—44no—
963C2×C4⋊C4—44no—
964C2×C4⋊C4—82no—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2411yescharacteristic
1044C2×C22⋊C4—44no—
1045C2×C22⋊C4—44no—
1046C2×C22⋊C4—44no—
1047C2×C22⋊C4—44no—
1048C2×C22⋊C4—48no—
1049C2×C22⋊C4—82no—
1050C2×C22⋊C4—82no—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2414yes—
1105C2×C42—28no—
1106C2×C42—24no—
1107C2×C42—24no—
1108C2×C42—24no—
1109C2×C42—44no—
1110C2×C42—44no—
1111C2×C42—44no—
1112C2×C42—44no—
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2411yescharacteristic
1129C2×C42C2412yes—
1130C2×C42C2412yes—
1131C2×C42C2414yes—
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2412yes—
1135C2×C42C2412yes—
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2414yes—
1141C2×C42C2414yes—
1142C2×C42C2414yes—
1143#95C2411yescharacteristic
1144#95C2411yescharacteristic
1145#95C2411yescharacteristic
1146#95C2412yes—
1147#95C2412yes—
1148#95C2411yescharacteristic
1149#95C2411yescharacteristic
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2411yescharacteristic
1154#95C2411yescharacteristic
1155#95C2412yes—
1156#95C2411yescharacteristic
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205C24—24no—
1206C24—24no—
1207C24—24no—
1208C24—42no—
1209C24—42no—
1210C24—42no—
1211C24—42no—
1212C24C2514yes—
1213C24C2512yes—
1214C24C2512yes—
1215C24C2511yescharacteristic
1216#41—232no—
1217#41—416no—
1218C2×Q8—22no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—24no—
1222C2×Q8—22no—
1223C2×Q8—22no—
1224C2×Q8—24no—
1225C2×Q8—42no—
1226C2×Q8—42no—
1227C2×Q8—42no—
1228C2×Q8—42no—
1229C2×Q8C2×#4114yes—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—28no—
1236C2×D4—28no—
1237C2×D4—28no—
1238C2×D4—24no—
1239C2×D4—22no—
1240C2×D4—24no—
1241C2×D4—22no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—22no—
1249C2×D4—44no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—416no—
1262C2×D4C2×#4118yes—
1263C2×D4C2×#4114yes—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—24no—
1272C22×C4—22no—
1273C22×C4—24no—
1274C22×C4—22no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—24no—
1278C22×C4—22no—
1279C22×C4—24no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—24no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—41no—
1290C22×C4—42no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—41no—
1305C22×C4—41no—
1306C22×C4—42no—
1307C22×C4—42no—
1308C22×C4—41no—
1309C22×C4—42no—
1310C22×C4—42no—
1311C22×C4—42no—
1312C22×C4—42no—
1313C22×C4—42no—
1314C22×C4—42no—
1315C22×C4—42no—
1316C22×C4—42no—
1317C22×C4—42no—
1318C22×C4—42no—
1319C22×C4—41no—
1320C22×C4—44no—
1321C22×C4—44no—
1322C22×C4—44no—
1323C22×C4—44no—
1324C22×C4—44no—
1325C22×C4—44no—
1326C22×C4C2×#4118yes—
1327C22×C4C2×#4114yes—
1328C22×C4H(5,𝔽2)14yes—
1329C22×C42−1+414yes—
1330C22×C4C2511yescharacteristic
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2511yescharacteristic
1334C22×C4C2512yes—
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2514yes—
1341C22×C4C2514yes—
1342C22×C4C2514yes—
1343C22×C4C2512yes—
1344C22×C4C2512yes—
1345C22×C4C2512yes—
1346C22×C4C2512yes—
1347C22×C4C2511yescharacteristic
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2511yescharacteristic
1352C22×C4C2511yescharacteristic
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2511yescharacteristic
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2511yescharacteristic
1360C22×C4C2511yescharacteristic
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—24no—
1364C4⋊C4—24no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—28no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—28no—
1377C4⋊C4—28no—
1378C4⋊C4—22no—
1379C4⋊C4—22no—
1380C4⋊C4—22no—
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—24no—
1390C4⋊C4—24no—
1391C4⋊C4—24no—
1392C4⋊C4—22no—
1393C4⋊C4—22no—
1394C4⋊C4—24no—
1395C4⋊C4—41no—
1396C4⋊C4—42no—
1397C4⋊C4—41no—
1398C4⋊C4—42no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—44no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—44no—
1438C4⋊C4—42no—
1439C4⋊C4H(5,𝔽2)14yes—
1440C22⋊C4—24no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—24no—
1444C22⋊C4—28no—
1445C22⋊C4—24no—
1446C22⋊C4—24no—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—28no—
1450C22⋊C4—28no—
1451C22⋊C4—28no—
1452C22⋊C4—28no—
1453C22⋊C4—28no—
1454C22⋊C4—28no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—28no—
1458C22⋊C4—24no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—42no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—42no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—42no—
1494C42—22no—
1495C42—24no—
1496C42—22no—
1497C42—24no—
1498C42—22no—
1499C42—24no—
1500C42—22no—
1501C42—24no—
1502C42—22no—
1503C42—22no—
1504C42—22no—
1505C42—22no—
1506C42—22no—
1507C42—22no—
1508C42—22no—
1509C42—22no—
1510C42—24no—
1511C42—24no—
1512C42—24no—
1513C42—28no—
1514C42—24no—
1515C42—42no—
1516C42—42no—
1517C42—42no—
1518C42—42no—
1519C42—42no—
1520C42—42no—
1521C42—44no—
1522C42—44no—
1523C42—44no—
1524C23—21no—
1525C23—21no—
1526C23—21no—
1527C23—21no—
1528C23—22no—
1529C23—22no—
1530C23—22no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—22no—
1535C23—24no—
1536C23—24no—
1537C23—22no—
1538C23—24no—
1539C23—22no—
1540C23—22no—
1541C23—24no—
1542C23—24no—
1543C23—22no—
1544C23—22no—
1545C23—24no—
1546C23—22no—
1547C23—24no—
1548C23—48no—
1549C23—84no—
1550C23—84no—
1551C23—84no—
1552C23—84no—
1553C23—84no—
1554C23—84no—
1555C23C22×#4114yes—
1556C23C22×#4112yes—
1557C23C2×H(5,𝔽2)12yes—
1558C23C2×2−1+412yes—
1559C23C2611yescharacteristic
1560Q8—28no—
1561Q8—44no—
1562Q8—84no—
1563Q8—84no—
1564D4—216no—
1565D4—28no—
1566D4—48no—
1567D4—48no—
1568D4—48no—
1569D4—44no—
1570D4—88no—
1571D4—88no—
1572D4—88no—
1573D4—164no—
1574D4—164no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—216no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—24no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—24no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—24no—
1622C2×C4—24no—
1623C2×C4—22no—
1624C2×C4—24no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—24no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—24no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—44no—
1659C2×C4—48no—
1660C2×C4—44no—
1661C2×C4—44no—
1662C2×C4—44no—
1663C2×C4—48no—
1664C2×C4—84no—
1665C2×C4—84no—
1666C2×C4—84no—
1667C2×C4—84no—
1668C2×C4—84no—
1669C2×C4—82no—
1670C2×C4—84no—
1671C2×C4—84no—
1672C2×C4—84no—
1673C2×C4—82no—
1674C2×C4—84no—
1675C2×C4—84no—
1676C2×C4—164no—
1677C2×C4—164no—
1678C2×C4#539116yescomplemented
1679C2×C4C22×#4114yes—
1680C2×C4C22×#4112yes—
1681C2×C4C22×#4112yes—
1682C2×C4C2×H(5,𝔽2)12yes—
1683C2×C4C2×H(5,𝔽2)12yes—
1684C2×C4C2×H(5,𝔽2)12yes—
1685C2×C4C2×H(5,𝔽2)12yes—
1686C2×C4C2×H(5,𝔽2)12yes—
1687C2×C4C2×2−1+412yes—
1688C2×C4C2×2−1+412yes—
1689C2×C4#58512yes—
1690C22—22no—
1691C22—22no—
1692C22—22no—
1693C22—22no—
1694C22—22no—
1695C22—22no—
1696C22—24no—
1697C22—24no—
1698C22—24no—
1699C22—42no—
1700C22—42no—
1701C22—42no—
1702C22—42no—
1703C22—42no—
1704C22—44no—
1705C22—44no—
1706C22—42no—
1707C22—42no—
1708C22—44no—
1709C22—42no—
1710C22—44no—
1711C22—42no—
1712C22—44no—
1713C22—42no—
1714C22—44no—
1715C22—42no—
1716C22—44no—
1717C22—168no—
1718C22C2×#53914yes—
1719C22C23×#4111yescharacteristic
1720C22C22×H(5,𝔽2)11yescharacteristic
1721C22C22×H(5,𝔽2)11yescharacteristic
1722C22C22×2−1+411yescharacteristic
1723C22C2×#58511yescharacteristic
1724C22H(7,𝔽2)11yescharacteristic
1725C222−1+611yescharacteristic
1726C4—22no—
1727C4—22no—
1728C4—22no—
1729C4—24no—
1730C4—22no—
1731C4—41no—
1732C4—42no—
1733C4—44no—
1734C4—42no—
1735C4—41no—
1736C4—42no—
1737C4—41no—
1738C4—42no—
1739C4—41no—
1740C4—41no—
1741C4—42no—
1742C4—42no—
1743C4—42no—
1744C4—42no—
1745C4—44no—
1746C4—44no—
1747C4—42no—
1748C4—41no—
1749C4—41no—
1750C4—41no—
1751C4—42no—
1752C4—42no—
1753C4—42no—
1754C4—42no—
1755C4C2×#53914yes—
1756C4C2×#53914yes—
1757C2—24no—
1758C2—44no—
1759C2—82no—
1760C2—84no—
1761C2C22×#53911yescharacteristic
1762C2#6280011yescharacteristic
1763C2#6285711yescharacteristic
1764C2#6291411yescharacteristic
1765C2#6291711yescharacteristic
1766C2#6293211yescharacteristic
1767C2#6295711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35256C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42904C2semidirect
2. #42871C2semidirect
3. #42556C2semidirect
4. #42540C2semidirect
5. #40812C2semidirect
6. #40791C2semidirect
7. #40149C2semidirect
8. #40119C2semidirect
9. #39409C2semidirect
10. #39245C2semidirect
11. #38504C2semidirect
12. #37724C2semidirect
13. #37524C2semidirect
14. #37520C2semidirect
15. #37326C2semidirect
16. #37315C2semidirect
17. #37288C2semidirect
18. #37286C2semidirect
19. #35585C2semidirect
20. #35557C2semidirect
21. #35541C2semidirect
22. #35515C2semidirect
23. #35280C2semidirect
25. #35255C2semidirect
26. #35254C2semidirect
27. #35254C2semidirect
28. #35159C2semidirect
29. #35083C2semidirect
30. #35006C2semidirect
31. C2×#2512C2semidirect
32. #34745C2semidirect
33. #34269C2semidirect
34. C4⋊C4×#41C2semidirect
35. C4×#537C2semidirect
36. C2×#539C22semidirect
47. #2857C22semidirect
48. #2857C22semidirect
50. #2855C22semidirect
55. #2854C22semidirect
58. #2837C22semidirect
59. #2837C22semidirect
60. #2827C22semidirect
61. #2827C22semidirect
62. #2808C22semidirect
63. #2807C22semidirect
64. #2798C22semidirect
65. #2790C22semidirect
66. #2786C22semidirect
67. #2783C22semidirect
68. #2783C22semidirect
69. #2781C22semidirect
70. #2781C22semidirect
71. #2750C22semidirect
72. #2744C22semidirect
73. #2743C22semidirect
74. #2740C22semidirect
75. #2732C22semidirect
76. #2728C22semidirect
77. #2727C22semidirect
78. #2724C22semidirect
79. #2723C22semidirect
80. #2721C22semidirect
81. #2718C22semidirect
82. #2718C22semidirect
83. #2707C22semidirect
84. #2705C22semidirect
85. #2705C22semidirect
86. #2695C22semidirect
87. #2693C22semidirect
88. #2693C22semidirect
89. #2691C22semidirect
90. #2691C22semidirect
91. #2689C22semidirect
92. #2681C22semidirect
93. #2681C22semidirect
94. #2667C22semidirect
95. #2664C22semidirect
96. #2654C22semidirect
97. #2654C22semidirect
98. #2652C22semidirect
99. #2650C22semidirect
101. #2639C22semidirect
102. #2636C22semidirect
103. #2636C22semidirect
104. #2630C22semidirect
105. #2630C22semidirect
106. #2629C22semidirect
107. #2629C22semidirect
108. #2625C22semidirect
113. #2624C22semidirect
116. #2618C22semidirect
117. #2582C22semidirect
118. #2582C22semidirect
122. #2560C22semidirect
123. #2560C22semidirect
124. #2558C22semidirect
125. #2558C22semidirect
126. #2553C22semidirect
127. #2553C22semidirect
130. #2538C22semidirect
131. #2538C22semidirect
140. #2512C22semidirect
141. #2512C22semidirect
142. #2511C22semidirect
143. #2511C22semidirect
144. #2509C22semidirect
145. #2509C22semidirect
146. #2509C22semidirect
147. #2509C22semidirect
148. #2508C22semidirect
149. #2508C22semidirect
150. #2508C22semidirect
151. #2508C22semidirect
152. #2507C22semidirect
153. #2507C22semidirect
154. #2507C22semidirect
155. #2507C22semidirect
156. #2506C22semidirect
157. #2506C22semidirect
158. #2506C22semidirect
159. #2506C22semidirect
160. #2497C22semidirect
161. #2497C22semidirect
162. #2496C22semidirect
163. #2496C22semidirect
164. #2488C22semidirect
167. #2481C22semidirect
168. #2466C22semidirect
169. #2460C22semidirect
172. #2454C22semidirect
173. #2454C22semidirect
174. #2453C22semidirect
175. #2453C22semidirect
178. #2452C22semidirect
179. #2452C22semidirect
180. #2451C22semidirect
181. #2451C22semidirect
186. #2449C22semidirect
210. #2423C22semidirect
213. #2422C22semidirect
214. #2421C22semidirect
217. #2420C22semidirect
218. #2419C22semidirect
227. #2396C22semidirect
228. #2396C22semidirect
237. #2351C22semidirect
238. #2351C22semidirect
239. Q8×C4⋊C4C22semidirect
240. Q8×C4⋊C4C22semidirect
243. #2349C22semidirect
244. #2349C22semidirect
247. D4×C4⋊C4C22semidirect
248. D4×C4⋊C4C22semidirect
249. #2334C22semidirect
250. #2332C22semidirect
252. #2325C22semidirect
255. #2324C22semidirect
256. #2324C22semidirect
257. #2323C22semidirect
258. #2323C22semidirect
270. C4×C22⋊Q8C22semidirect
271. C4×C22⋊Q8C22semidirect
272. C4×C22⋊Q8C22semidirect
273. C4×C22⋊Q8C22semidirect
277. C4×#121C22semidirect
278. C4×#121C22semidirect
285. #2296C22semidirect
286. #2296C22semidirect
293. #2285C22semidirect
298. C2×C4×C4⋊C4C22semidirect
1678. C2×C4#539semidirect

Maximal subgroups

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

subgroupindex
#429042
#428712
#425562
#425402
#408122
#407912
#401492
#401192
#394092
#392452
#385042
#377242
#375242
#375202
#373262
#373152
#372882
#372862
#355852
#355572
#355412
#355152
#352802
#352562
#352552
#352542
#351592
#350832
#350062
C2×#25122
#347452
#342692
C4⋊C4×#412
C4×#5372