Finite Group Databasebeta

← #8094811

Subgroups — #8094811

Order 512.

5044 conjugacy classes of subgroups.

The subgroup lattice has 1805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53130C212yesmaximal, complemented
2#53122C212yesmaximal, complemented
3#53110C212yesmaximal, complemented
4#53094C212yesmaximal, complemented
5#53062C212yesmaximal, complemented
6#53021C212yesmaximal, complemented
7#52982C212yesmaximal, complemented
8#52979C212yesmaximal, complemented
9#52451C214yesmaximal, complemented
10#52427C214yesmaximal, complemented
11#46032C214yesmaximal, complemented
12#45978C214yesmaximal, complemented
13#45717C212yesmaximal, complemented
14#45675C212yesmaximal, complemented
15#45656C212yesmaximal, complemented
16#45634C212yesmaximal, complemented
17#45592C212yesmaximal, complemented
18#45516C212yesmaximal, complemented
19#45484C212yesmaximal, complemented
20#45482C212yesmaximal, complemented
21#35564C211yesmaximal, characteristic, complemented
22#35564C211yesmaximal, characteristic, complemented
23#35532C211yesmaximal, characteristic, complemented
24#35519C211yesmaximal, characteristic, complemented
25#35517C211yesmaximal, characteristic, complemented
26#35517C211yesmaximal, characteristic, complemented
27#35273C211yesmaximal, characteristic, complemented
28#35257C211yesmaximal, characteristic, complemented
29#35255C211yesmaximal, characteristic, complemented
30#35255C211yesmaximal, characteristic, complemented
31#35180C211yesmaximal, characteristic, complemented
32#35158C211yesmaximal, characteristic, complemented
33#34937C211yesmaximal, characteristic, complemented
34C2×#2506C211yesmaximal, characteristic, complemented
35#34745C211yesmaximal, characteristic, complemented
36C2×#562C2214yes—
37C2×#544C2211yescharacteristic
38C2×#537C2211yescharacteristic
39C2×#537C2211yescharacteristic
40C2×#537C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C2×#532C2211yescharacteristic
45C22×#125C2212yes—
46C2×#520C2211yescharacteristic
47C2×#520C2211yescharacteristic
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2211yescharacteristic
50#2857C2212yes—
51#2857C2212yes—
52#2856C2212yes—
53#2855C2212yes—
54#2855C2212yes—
55#2854C2212yes—
56#2854C2212yes—
57#2851C2212yes—
58#2850C2214yes—
59#2850C2214yes—
60#2841C2214yes—
61#2839C2214yes—
62#2837C2214yes—
63#2836C2214yes—
64#2836C2214yes—
65#2832C2214yes—
66#2831C2214yes—
67#2831C2214yes—
68#2830C2214yes—
69#2829C2214yes—
70#2829C2214yes—
71#2827C2214yes—
72#2827C2214yes—
73#2826C2214yes—
74#2824C2214yes—
75#2820C2214yes—
76#2820C2214yes—
77#2816C2214yes—
78#2814C2214yes—
79#2813C2214yes—
80#2802C2214yes—
81#2800C2214yes—
82#2798C2214yes—
83#2788C2214yes—
84#2786C2214yes—
85#2783C2214yes—
86#2779C2214yes—
87#2761C2214yes—
88#2755C2214yes—
89#2751C2214yes—
90#2750C2214yes—
91#2747C2214yes—
92#2744C2214yes—
93#2743C2214yes—
94#2741C2214yes—
95#2740C2214yes—
96#2739C2214yes—
97#2730C2214yes—
98#2711C2214yes—
99#2711C2214yes—
100#2711C2214yes—
101#2711C2214yes—
102#2708C2214yes—
103#2704C2214yes—
104#2704C2214yes—
105#2704C2214yes—
106#2704C2214yes—
107#2701C2214yes—
108#2700C2214yes—
109#2696C2214yes—
110#2694C2214yes—
111#2694C2214yes—
112#2694C2214yes—
113#2694C2214yes—
114#2692C2214yes—
115#2687C2214yes—
116#2686C2214yes—
117#2681C2214yes—
118#2676C2214yes—
119#2671C2214yes—
120#2639C2214yes—
121#2639C2214yes—
122#2629C2212yes—
123#2628C2212yes—
124#2625C2212yes—
125#2625C2212yes—
126#2624C2212yes—
127#2624C2212yes—
128#2620C2212yes—
129#2620C2212yes—
130#2592C2212yes—
131#2592C2212yes—
132#2582C2212yes—
133#2581C2212yes—
134#2580C2212yes—
135#2568C2212yes—
136#2567C2212yes—
137#2566C2212yes—
138#2565C2212yes—
139#2563C2212yes—
140#2562C2212yes—
141#2562C2212yes—
142#2548C2212yes—
143#2548C2211yescharacteristic
144#2547C2212yes—
145#2547C2211yescharacteristic
146#2546C2211yescharacteristic
147#2545C2211yescharacteristic
148#2545C2211yescharacteristic
149#2544C2211yescharacteristic
150#2544C2211yescharacteristic
151#2543C2212yes—
152#2543C2212yes—
153#2543C2214yes—
154#2543C2214yes—
155#2542C2212yes—
156#2541C2211yescharacteristic
157#2538C2212yes—
158#2538C2212yes—
159#2538C2212yes—
160#2537C2212yes—
161#2537C2212yes—
162#2506C2212yes—
163#2506C2212yes—
164#2506C2212yes—
165#2506C2212yes—
166#2506C2212yes—
167#2506C2212yes—
168#2506C2212yes—
169#2506C2212yes—
170#2492C2212yes—
171#2492C2212yes—
172#2491C2212yes—
173#2491C2212yes—
174#2490C2212yes—
175#2490C2212yes—
176#2489C2212yes—
177#2489C2212yes—
178#2487C2212yes—
179#2487C2212yes—
180#2486C2212yes—
181#2486C2212yes—
182#2485C2212yes—
183#2485C2212yes—
184#2485C2212yes—
185#2485C2212yes—
186#2454C2211yescharacteristic
187#2454C2211yescharacteristic
188#2454C2212yes—
189#2453C2212yes—
190#2453C2211yescharacteristic
191#2453C2211yescharacteristic
192#2452C2211yescharacteristic
193#2452C2212yes—
194#2452C2211yescharacteristic
195#2451C2212yes—
196#2451C2211yescharacteristic
197#2451C2211yescharacteristic
198#2450C2212yes—
199#2450C2212yes—
200#2450C2214yes—
201#2450C2214yes—
202#2449C2212yes—
203#2449C2214yes—
204#2449C2214yes—
205#2449C2214yes—
206#2449C2212yes—
207#2449C2214yes—
208#2448C2212yes—
209#2448C2212yes—
210#2447C2212yes—
211#2447C2212yes—
212#2446C2212yes—
213#2446C2212yes—
214#2445C2212yes—
215#2445C2212yes—
216#2444C2214yes—
217#2444C2214yes—
218#2444C2214yes—
219#2444C2214yes—
220#2443C2214yes—
221#2443C2214yes—
222#2443C2214yes—
223#2443C2214yes—
224#2442C2212yes—
225#2441C2212yes—
226#2441C2212yes—
227#2441C2212yes—
228#2440C2212yes—
229#2440C2212yes—
230#2440C2212yes—
231#2439C2212yes—
232#2429C2212yes—
233#2429C2212yes—
234#2428C2212yes—
235#2428C2212yes—
236#2427C2212yes—
237#2427C2212yes—
238#2426C2212yes—
239#2426C2212yes—
240#2423C2212yes—
241#2423C2212yes—
242#2422C2212yes—
243#2422C2212yes—
244#2421C2212yes—
245#2421C2212yes—
246#2420C2212yes—
247#2420C2212yes—
248#2417C2212yes—
249#2417C2212yes—
250#2416C2212yes—
251#2416C2212yes—
252#2416C2212yes—
253#2416C2212yes—
254#2416C2214yes—
255#2416C2214yes—
256#2416C2214yes—
257#2416C2214yes—
258#2415C2212yes—
259#2415C2212yes—
260#2414C2212yes—
261#2414C2212yes—
262#2396C2212yes—
263#2396C2212yes—
264C2×#400C2212yes—
265#2392C2212yes—
266#2392C2212yes—
267C2×#398C2212yes—
268#2382C2214yes—
269#2378C2214yes—
270#2377C2214yes—
271#2317C2211yescharacteristic
272#2317C2211yescharacteristic
273#2311C2211yescharacteristic
274#2311C2211yescharacteristic
275#2311C2211yescharacteristic
276#2311C2211yescharacteristic
277#2311C2211yescharacteristic
278#2311C2211yescharacteristic
279#2311C2211yescharacteristic
280#2311C2211yescharacteristic
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2212yes—
283C4×#121C2212yes—
284C4×#121C2212yes—
285#2297C2211yescharacteristic
286#2297C2211yescharacteristic
287#2297C2211yescharacteristic
288#2297C2211yescharacteristic
289#2296C2211yescharacteristic
290#2296C2211yescharacteristic
291C2×#389C2211yescharacteristic
292C2×#389C2211yescharacteristic
293C2×#389C2211yescharacteristic
294C2×#389C2211yescharacteristic
295C2×#387C2212yes—
296C2×#384C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C22×#41C2311yescharacteristic
302C22×#41C2311yescharacteristic
303#562—416no—
304#544—44no—
305#537—44no—
306#537—44no—
307#537—44no—
308#533—44no—
309#532—44no—
310#532—44no—
311#532—44no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2311yescharacteristic
319C2×#127C2311yescharacteristic
320C2×#127C2311yescharacteristic
321C2×#127C2311yescharacteristic
322C2×#125—48no—
323C2×#125C2314yes—
324C2×#125C2311yescharacteristic
325C2×#125C2311yescharacteristic
326C2×#125C2314yes—
327C2×#125C2312yes—
328C2×#125C2312yes—
329C2×#125C2314yes—
330C2×#125C2314yes—
331C2×#124C2314yes—
332C2×#124C2314yes—
333C2×#124C2311yescharacteristic
334C2×#124C2311yescharacteristic
335C2×#124C2311yescharacteristic
336C2×#124C2311yescharacteristic
337C2×#124C2311yescharacteristic
338C2×#124C2311yescharacteristic
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2314yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2312yes—
361C2×#121C2314yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2314yes—
372C2×#121C2312yes—
373C2×#121C2312yes—
374C2×#121C2312yes—
375C2×#121C2314yes—
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379#520—44no—
380#520—44no—
381C4×#41—44no—
382C4×#41—44no—
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2311yescharacteristic
388C2×C4×Q8C2311yescharacteristic
389C2×C4×Q8C2311yescharacteristic
390C2×C4×Q8C2311yescharacteristic
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2311yescharacteristic
405C2×C4×D4C2312yes—
406C2×C4×D4C2314yes—
407C2×C4×D4C2314yes—
408C2×C4×D4C2312yes—
409C2×#117C2311yescharacteristic
410C2×#117C2311yescharacteristic
411C2×#117C2311yescharacteristic
412C2×#117C2311yescharacteristic
413C2×#117C2312yes—
414C2×#117C2312yes—
415C2×#117C2312yes—
416C2×#117C2312yes—
417C22×C4⋊C4C2311yescharacteristic
418C22×C4⋊C4C2311yescharacteristic
419C22×C4⋊C4C2311yescharacteristic
420C22×C4⋊C4C2311yescharacteristic
421C22×C4⋊C4C2311yescharacteristic
422C22×C4⋊C4C2311yescharacteristic
423C22×C4⋊C4C2312yes—
424C22×C4⋊C4C2312yes—
425C22×C4⋊C4C2312yes—
426C22×C4⋊C4C2312yes—
427C22×C4⋊C4C2312yes—
428C22×C4⋊C4C2312yes—
429C22×C4⋊C4C2312yes—
430C22×C4⋊C4C2312yes—
431C22×C42C2311yescharacteristic
432C22×C42C2311yescharacteristic
433C22×C42C2311yescharacteristic
434C22×C42C2312yes—
435C22×C42C2312yes—
436C22×C42C2312yes—
437#400C2314yes—
438#400C2314yes—
439#400C2314yes—
440#400C2314yes—
441#400C2314yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2312yes—
446#400C2312yes—
447#400C2314yes—
448#400C2314yes—
449#400C2314yes—
450#400C2314yes—
451#400C2314yes—
452#400C2314yes—
453#399C2314yes—
454#399C2314yes—
455#399C2314yes—
456#399C2314yes—
457#399C2314yes—
458#399C2312yes—
459#399C2314yes—
460#399C2314yes—
461#399C2312yes—
462#399C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2312yes—
467#398C2312yes—
468#398C2314yes—
469#398C2314yes—
470#398C2314yes—
471#398C2314yes—
472#398C2314yes—
473#398C2314yes—
474#398C2314yes—
475#398C2314yes—
476#398C2314yes—
477#398C2314yes—
478#398C2312yes—
479#398C2314yes—
480#398C2314yes—
481#398C2312yes—
482#398C2312yes—
483#398C2312yes—
484#398C2314yes—
485#397C2314yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2314yes—
490#397C2314yes—
491#397C2314yes—
492#397C2314yes—
493#397C2314yes—
494#397C2314yes—
495#397C2314yes—
496#397C2314yes—
497#397C2314yes—
498#397C2312yes—
499#397C2314yes—
500#397C2314yes—
501#397C2314yes—
502#397C2312yes—
503#397C2314yes—
504#397C2314yes—
505#396C2312yes—
506#396C2312yes—
507#396C2314yes—
508#396C2314yes—
509#396C2314yes—
510#396C2314yes—
511#396C2314yes—
512#396C2314yes—
513#396C2314yes—
514#396C2312yes—
515#396C2314yes—
516#396C2314yes—
517#396C2312yes—
518#396C2314yes—
519#396C2314yes—
520#396C2314yes—
521#396C2312yes—
522#396C2314yes—
523#396C2312yes—
524#396C2312yes—
525#396C2312yes—
526#396C2314yes—
527#395C2312yes—
528#395C2314yes—
529#395C2314yes—
530#395C2314yes—
531#395C2314yes—
532#395C2312yes—
533#394C2312yes—
534#394C2314yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2312yes—
542#394C2314yes—
543#394C2314yes—
544#394C2312yes—
545#394C2314yes—
546#394C2314yes—
547#394C2314yes—
548#394C2312yes—
549#394C2314yes—
550#394C2314yes—
551#394C2312yes—
552#394C2314yes—
553#394C2314yes—
554#394C2314yes—
555#394C2314yes—
556#394C2314yes—
557#394C2314yes—
558#394C2314yes—
559#394C2312yes—
560#394C2314yes—
561#393C2314yes—
562#393C2314yes—
563#393C2314yes—
564#393C2312yes—
565#393C2314yes—
566#393C2314yes—
567#393C2314yes—
568#393C2312yes—
569#392C2314yes—
570#392C2314yes—
571#392C2312yes—
572#392C2312yes—
573#391C2311yescharacteristic
574#391C2312yes—
575#391C2312yes—
576#391C2312yes—
577#391C2312yes—
578#391C2312yes—
579#391C2312yes—
580#391C2312yes—
581#391C2312yes—
582#391C2311yescharacteristic
583#391C2314yes—
584#391C2314yes—
585#391C2314yes—
586#391C2314yes—
587#391C2311yescharacteristic
588#391C2311yescharacteristic
589#391C2311yescharacteristic
590#391C2311yescharacteristic
591#391C2311yescharacteristic
592#391C2311yescharacteristic
593#391C2312yes—
594#391C2312yes—
595#390C2314yes—
596#390C2311yescharacteristic
597#390C2312yes—
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2312yes—
603#390C2312yes—
604#390C2312yes—
605#390C2314yes—
606#390C2314yes—
607#390C2312yes—
608#390C2311yescharacteristic
609#390C2311yescharacteristic
610#390C2311yescharacteristic
611#390C2314yes—
612#390C2314yes—
613#390C2311yescharacteristic
614#390C2314yes—
615#390C2311yescharacteristic
616#390C2311yescharacteristic
617#390C2312yes—
618#390C2311yescharacteristic
619#389C2314yes—
620#389C2314yes—
621#389C2312yes—
622#389C2312yes—
623#389C2312yes—
624#389C2312yes—
625#389C2312yes—
626#389C2314yes—
627#389C2312yes—
628#389C2314yes—
629#389C2314yes—
630#389C2311yescharacteristic
631#389C2312yes—
632#389C2312yes—
633#389C2312yes—
634#389C2311yescharacteristic
635#389C2314yes—
636#389C2312yes—
637#389C2312yes—
638#389C2311yescharacteristic
639#389C2312yes—
640#389C2311yescharacteristic
641#389C2312yes—
642#389C2314yes—
643#389C2314yes—
644#389C2312yes—
645#389C2312yes—
646#389C2312yes—
647#389C2312yes—
648#389C2312yes—
649#389C2312yes—
650#389C2312yes—
651#389C2312yes—
652#389C2312yes—
653#389C2312yes—
654#389C2312yes—
655#389C2311yescharacteristic
656#389C2311yescharacteristic
657#389C2311yescharacteristic
658#389C2311yescharacteristic
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2314yes—
664#388C2312yes—
665#388C2314yes—
666#388C2314yes—
667#388C2314yes—
668#388C2314yes—
669#388C2314yes—
670#388C2314yes—
671#388C2314yes—
672#388C2314yes—
673#388C2314yes—
674#388C2314yes—
675#388C2314yes—
676#388C2314yes—
677#388C2314yes—
678#388C2314yes—
679#388C2312yes—
680#388C2314yes—
681#388C2312yes—
682#388C2312yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2312yes—
691#387C2314yes—
692#387C2314yes—
693#387C2312yes—
694#387C2314yes—
695#387C2314yes—
696#387C2314yes—
697#387C2314yes—
698#387C2312yes—
699#387C2314yes—
700#387C2312yes—
701#387C2314yes—
702#387C2314yes—
703#387C2314yes—
704#387C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#386C2314yes—
715#386C2312yes—
716#386C2314yes—
717#386C2314yes—
718#386C2314yes—
719#386C2312yes—
720#386C2312yes—
721#386C2314yes—
722#386C2312yes—
723#386C2314yes—
724#386C2314yes—
725#386C2312yes—
726#386C2312yes—
727#386C2312yes—
728#386C2312yes—
729#386C2312yes—
730#386C2312yes—
731#386C2312yes—
732#386C2312yes—
733#385C2314yes—
734#385C2314yes—
735#385C2314yes—
736#385C2314yes—
737#385C2314yes—
738#385C2314yes—
739#385C2314yes—
740#385C2314yes—
741#385C2314yes—
742#385C2314yes—
743#385C2314yes—
744#385C2314yes—
745#385C2312yes—
746#385C2312yes—
747#385C2312yes—
748#385C2312yes—
749#385C2312yes—
750#385C2312yes—
751#385C2312yes—
752#385C2312yes—
753#384C2312yes—
754#384C2312yes—
755#384C2312yes—
756#384C2312yes—
757#384C2312yes—
758#384C2312yes—
759#382C2314yes—
760#382C2314yes—
761#382C2312yes—
762#382C2312yes—
763#381C2314yes—
764#381C2314yes—
765#381C2314yes—
766#381C2314yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2312yes—
773#380C2312yes—
774#380C2312yes—
775#380C2312yes—
776#380C2312yes—
777#380C2312yes—
778#380C2312yes—
779#380C2312yes—
780#380C2312yes—
781#380C2312yes—
782#380C2312yes—
783#380C2314yes—
784#380C2314yes—
785#380C2314yes—
786#380C2314yes—
787#380C2314yes—
788#380C2312yes—
789#380C2314yes—
790#380C2312yes—
791#380C2312yes—
792#380C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2311yescharacteristic
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2311yescharacteristic
803C4×C4⋊C4C2312yes—
804C4×C4⋊C4C2312yes—
805C4×C4⋊C4C2311yescharacteristic
806C4×C4⋊C4C2311yescharacteristic
807C4×C4⋊C4C2311yescharacteristic
808C4×C4⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2312yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C2×#95C2312yes—
820C2×#95C2311yescharacteristic
821C2×#95C2312yes—
822C2×#95C2312yes—
823C2×#95C2311yescharacteristic
824C2×#41—24no—
825C2×#41—24no—
826C2×#41—24no—
827C2×#41—24no—
828C2×#41—24no—
829C2×#41—24no—
830C2×#41—24no—
831C2×#41—24no—
832C2×#41—24no—
833C2×#41—24no—
834C2×#41—24no—
835C2×#41—24no—
836C22×Q8C2411yescharacteristic
837C22×Q8C2411yescharacteristic
838C22×Q8C2411yescharacteristic
839C22×Q8C2411yescharacteristic
840C22×Q8C2412yes—
841C22×Q8C2412yes—
842C22×Q8C2414yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2411yescharacteristic
848C22×D4C2411yescharacteristic
849C22×D4C2411yescharacteristic
850C22×D4C2411yescharacteristic
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2412yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2411yescharacteristic
868C23×C4C2412yes—
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2411yescharacteristic
873C23×C4C2412yes—
874C23×C4C2412yes—
875C23×C4C2412yes—
876C23×C4C2411yescharacteristic
877C23×C4C2414yes—
878C23×C4C2414yes—
879C23×C4C2412yes—
880C23×C4C2411yescharacteristic
881C4⋊Q8—42no—
882C4⋊Q8—42no—
883C4⋊Q8—44no—
884C4⋊Q8—44no—
885C4⋊Q8—42no—
886C4⋊Q8—42no—
887C4⋊Q8—42no—
888#127—42no—
889#127—42no—
890#127—42no—
891#125—216no—
892#125—48no—
893#125—42no—
894#125—42no—
895#125—44no—
896#125—44no—
897#125—48no—
898#125—48no—
899#124—48no—
900#124—42no—
901#124—42no—
902#124—42no—
903#124—42no—
904#124—42no—
905#124—42no—
906#124—48no—
907#123—48no—
908#123—48no—
909#123—48no—
910#123—48no—
911C22⋊Q8—28no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—48no—
915C22⋊Q8—48no—
916C22⋊Q8—48no—
917C22⋊Q8—48no—
918C22⋊Q8—44no—
919C22⋊Q8—48no—
920C22⋊Q8—44no—
921C22⋊Q8—44no—
922C22⋊Q8—44no—
923C22⋊Q8—44no—
924C22⋊Q8—44no—
925C22⋊Q8—44no—
926#121—28no—
927#121—44no—
928#121—48no—
929#121—48no—
930#121—48no—
931#121—44no—
932#121—44no—
933#121—44no—
934#121—44no—
935#121—44no—
936#121—44no—
937#121—48no—
938#121—44no—
939#121—44no—
940#121—44no—
941#121—44no—
942#121—44no—
943#121—44no—
944#121—48no—
945#121—48no—
946#121—48no—
947C4×Q8—44no—
948C4×Q8—44no—
949C4×Q8—42no—
950C4×Q8—42no—
951C4×Q8—42no—
952C4×Q8—42no—
953C4×Q8—44no—
954C4×Q8—44no—
955C4×D4—42no—
956C4×D4—42no—
957C4×D4—42no—
958C4×D4—42no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—44no—
971C4×D4—48no—
972C4×D4—48no—
973#117—24no—
974#117—24no—
975#117—24no—
976#117—24no—
977#117—44no—
978#117—44no—
979#117—44no—
980#117—44no—
981C2×C4⋊C4—24no—
982C2×C4⋊C4—24no—
983C2×C4⋊C4—24no—
984C2×C4⋊C4—24no—
985C2×C4⋊C4—24no—
986C2×C4⋊C4—42no—
987C2×C4⋊C4—44no—
988C2×C4⋊C4—44no—
989C2×C4⋊C4—44no—
990C2×C4⋊C4—44no—
991C2×C4⋊C4—44no—
992C2×C4⋊C4—44no—
993C2×C4⋊C4—44no—
994C2×C4⋊C4—44no—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C4⋊C4C2411yescharacteristic
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2412yes—
1065C2×C4⋊C4C2414yes—
1066C2×C4⋊C4C2411yescharacteristic
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2412yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C42—24no—
1128C2×C42—24no—
1129C2×C42—24no—
1130C2×C42—44no—
1131C2×C42—44no—
1132C2×C42—44no—
1133C2×C42C2411yescharacteristic
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2411yescharacteristic
1140C2×C42C2411yescharacteristic
1141C2×C42C2411yescharacteristic
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2411yescharacteristic
1147C2×C42C2411yescharacteristic
1148C2×C42C2414yes—
1149C2×C42C2411yescharacteristic
1150C2×C42C2414yes—
1151C2×C42C2414yes—
1152C2×C42C2412yes—
1153C2×C42C2412yes—
1154C2×C42C2412yes—
1155C2×C42C2412yes—
1156C2×C42C2414yes—
1157#95C2411yescharacteristic
1158#95C2411yescharacteristic
1159#95C2411yescharacteristic
1160#95C2411yescharacteristic
1161#95C2411yescharacteristic
1162#95C2411yescharacteristic
1163#95C2411yescharacteristic
1164#95C2414yes—
1165#95C2411yescharacteristic
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
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#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219C24C2512yes—
1220C24C2512yes—
1221C24C2512yes—
1222C24C2512yes—
1223C24C2511yescharacteristic
1224#41—416no—
1225#41—416no—
1226#41—416no—
1227#41—416no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—22no—
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—22no—
1235C2×Q8—22no—
1236C2×Q8—24no—
1237C2×Q8—22no—
1238C2×Q8—22no—
1239C2×Q8—22no—
1240C2×Q8—22no—
1241C2×Q8—42no—
1242C2×Q8—42no—
1243C2×Q8—42no—
1244C2×Q8—42no—
1245C2×Q8—42no—
1246C2×Q8—44no—
1247C2×Q8—44no—
1248C2×Q8—44no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—24no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—22no—
1264C2×D4—22no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
1269C2×D4—24no—
1270C2×D4—24no—
1271C2×D4—24no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—22no—
1275C2×D4—22no—
1276C2×D4—24no—
1277C2×D4—42no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—42no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—42no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—44no—
1299C2×D4—44no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—24no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—22no—
1311C22×C4—24no—
1312C22×C4—24no—
1313C22×C4—22no—
1314C22×C4—22no—
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—24no—
1324C22×C4—24no—
1325C22×C4—22no—
1326C22×C4—24no—
1327C22×C4—24no—
1328C22×C4—24no—
1329C22×C4—42no—
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—42no—
1341C22×C4—42no—
1342C22×C4—41no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—42no—
1347C22×C4—42no—
1348C22×C4—42no—
1349C22×C4—42no—
1350C22×C4—41no—
1351C22×C4—41no—
1352C22×C4—41no—
1353C22×C4—42no—
1354C22×C4—44no—
1355C22×C4—44no—
1356C22×C4—44no—
1357C22×C4—44no—
1358C22×C4—44no—
1359C22×C4—44no—
1360C22×C4H(5,𝔽2)14yes—
1361C22×C4H(5,𝔽2)14yes—
1362C22×C42−1+414yes—
1363C22×C4C2511yescharacteristic
1364C22×C4C2511yescharacteristic
1365C22×C4C2514yes—
1366C22×C4C2511yescharacteristic
1367C22×C4C2511yescharacteristic
1368C22×C4C2512yes—
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2512yes—
1373C22×C4C2512yes—
1374C22×C4C2512yes—
1375C22×C4C2512yes—
1376C22×C4C2511yescharacteristic
1377C22×C4C2512yes—
1378C22×C4C2512yes—
1379C22×C4C2514yes—
1380C22×C4C2512yes—
1381C22×C4C2512yes—
1382C22×C4C2514yes—
1383C22×C4C2514yes—
1384C22×C4C2511yescharacteristic
1385C22×C4C2511yescharacteristic
1386C22×C4C2511yescharacteristic
1387C22×C4C2511yescharacteristic
1388C22×C4C2511yescharacteristic
1389C22×C4C2511yescharacteristic
1390C22×C4C2511yescharacteristic
1391C22×C4C2511yescharacteristic
1392C22×C4C2511yescharacteristic
1393C4⋊C4—24no—
1394C4⋊C4—24no—
1395C4⋊C4—24no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—22no—
1400C4⋊C4—22no—
1401C4⋊C4—22no—
1402C4⋊C4—22no—
1403C4⋊C4—22no—
1404C4⋊C4—28no—
1405C4⋊C4—28no—
1406C4⋊C4—28no—
1407C4⋊C4—28no—
1408C4⋊C4—28no—
1409C4⋊C4—22no—
1410C4⋊C4—22no—
1411C4⋊C4—22no—
1412C4⋊C4—22no—
1413C4⋊C4—22no—
1414C4⋊C4—22no—
1415C4⋊C4—24no—
1416C4⋊C4—24no—
1417C4⋊C4—24no—
1418C4⋊C4—24no—
1419C4⋊C4—22no—
1420C4⋊C4—28no—
1421C4⋊C4—22no—
1422C4⋊C4—24no—
1423C4⋊C4—41no—
1424C4⋊C4—41no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—44no—
1438C4⋊C4—42no—
1439C4⋊C4—42no—
1440C4⋊C4—42no—
1441C4⋊C4—42no—
1442C4⋊C4—42no—
1443C4⋊C4—42no—
1444C4⋊C4—42no—
1445C4⋊C4—42no—
1446C4⋊C4—42no—
1447C4⋊C4—42no—
1448C4⋊C4—42no—
1449C4⋊C4—42no—
1450C4⋊C4—42no—
1451C4⋊C4—42no—
1452C4⋊C4—42no—
1453C4⋊C4—42no—
1454C4⋊C4—44no—
1455C4⋊C4—44no—
1456C4⋊C4—44no—
1457C4⋊C4—44no—
1458C4⋊C4—42no—
1459C4⋊C4—44no—
1460C4⋊C4—44no—
1461C4⋊C4—44no—
1462C4⋊C4—44no—
1463C4⋊C4—44no—
1464C4⋊C4H(5,𝔽2)14yes—
1465C22⋊C4—24no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—24no—
1470C22⋊C4—24no—
1471C22⋊C4—24no—
1472C22⋊C4—24no—
1473C22⋊C4—24no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—44no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—44no—
1481C22⋊C4—42no—
1482C22⋊C4—42no—
1483C22⋊C4—44no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—42no—
1487C22⋊C4—42no—
1488C22⋊C4—42no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—42no—
1494C22⋊C4—42no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—42no—
1499C22⋊C4—42no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C22⋊C4—42no—
1504C22⋊C4—42no—
1505C22⋊C4—42no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C22⋊C4—44no—
1516C22⋊C4—44no—
1517C22⋊C4—44no—
1518C22⋊C4—42no—
1519C22⋊C4—44no—
1520C22⋊C4—42no—
1521C22⋊C4—44no—
1522C22⋊C4—44no—
1523C22⋊C4—44no—
1524C22⋊C4—44no—
1525C42—22no—
1526C42—22no—
1527C42—22no—
1528C42—22no—
1529C42—22no—
1530C42—22no—
1531C42—22no—
1532C42—22no—
1533C42—22no—
1534C42—22no—
1535C42—22no—
1536C42—22no—
1537C42—24no—
1538C42—24no—
1539C42—28no—
1540C42—24no—
1541C42—24no—
1542C42—42no—
1543C42—42no—
1544C42—42no—
1545C42—42no—
1546C42—44no—
1547C42—44no—
1548C42—44no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—22no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—22no—
1562C23—22no—
1563C23—22no—
1564C23—22no—
1565C23—22no—
1566C23—22no—
1567C23—22no—
1568C23—22no—
1569C23—22no—
1570C23—22no—
1571C23—22no—
1572C23—22no—
1573C23—22no—
1574C23—22no—
1575C23—22no—
1576C23—22no—
1577C23—22no—
1578C23—22no—
1579C23—22no—
1580C23—22no—
1581C23C2×H(5,𝔽2)12yes—
1582C23C2×H(5,𝔽2)12yes—
1583C23C2×2−1+412yes—
1584C23C2611yescharacteristic
1585Q8—44no—
1586Q8—44no—
1587Q8—44no—
1588Q8—44no—
1589Q8—84no—
1590Q8—84no—
1591Q8—164no—
1592D4—48no—
1593D4—48no—
1594D4—48no—
1595D4—48no—
1596D4—44no—
1597D4—44no—
1598D4—44no—
1599D4—44no—
1600D4—84no—
1601D4—84no—
1602D4—84no—
1603D4—84no—
1604D4—84no—
1605D4—84no—
1606D4—164no—
1607D4—164no—
1608D4—164no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—24no—
1632C2×C4—24no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—24no—
1641C2×C4—24no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—24no—
1651C2×C4—24no—
1652C2×C4—24no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—24no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—24no—
1666C2×C4—21no—
1667C2×C4—24no—
1668C2×C4—22no—
1669C2×C4—21no—
1670C2×C4—22no—
1671C2×C4—24no—
1672C2×C4—21no—
1673C2×C4—22no—
1674C2×C4—22no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—21no—
1678C2×C4—21no—
1679C2×C4—22no—
1680C2×C4—21no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—21no—
1684C2×C4—24no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—21no—
1689C2×C4—44no—
1690C2×C4—44no—
1691C2×C4—44no—
1692C2×C4—44no—
1693C2×C4—48no—
1694C2×C4—48no—
1695C2×C4—48no—
1696C2×C4—48no—
1697C2×C4—48no—
1698C2×C4—84no—
1699C2×C4—84no—
1700C2×C4—84no—
1701C2×C4—84no—
1702C2×C4—84no—
1703C2×C4—82no—
1704C2×C4—84no—
1705C2×C4—82no—
1706C2×C4—84no—
1707C2×C4—164no—
1708C2×C4—164no—
1709C2×C4#562116yescomplemented
1710C2×C4C2×H(5,𝔽2)12yes—
1711C2×C4C2×H(5,𝔽2)12yes—
1712C2×C4C2×H(5,𝔽2)12yes—
1713C2×C4C2×H(5,𝔽2)12yes—
1714C2×C4C2×H(5,𝔽2)12yes—
1715C2×C4C2×H(5,𝔽2)12yes—
1716C2×C4C2×H(5,𝔽2)12yes—
1717C2×C4C2×2−1+412yes—
1718C2×C4C2×2−1+412yes—
1719C2×C4#58512yes—
1720C22—22no—
1721C22—22no—
1722C22—22no—
1723C22—22no—
1724C22—22no—
1725C22—22no—
1726C22—42no—
1727C22—42no—
1728C22—42no—
1729C22—42no—
1730C22—42no—
1731C22—42no—
1732C22—42no—
1733C22—42no—
1734C22—42no—
1735C22—42no—
1736C22—42no—
1737C22—42no—
1738C22—42no—
1739C22—42no—
1740C22—42no—
1741C22—42no—
1742C22—42no—
1743C22—42no—
1744C22—42no—
1745C22—42no—
1746C22—42no—
1747C22—42no—
1748C22—42no—
1749C22—42no—
1750C22—42no—
1751C22—42no—
1752C22—42no—
1753C22—42no—
1754C22C2×#56214yes—
1755C22C22×H(5,𝔽2)11yescharacteristic
1756C22C22×H(5,𝔽2)11yescharacteristic
1757C22C22×H(5,𝔽2)11yescharacteristic
1758C22C22×2−1+411yescharacteristic
1759C22C2×#58511yescharacteristic
1760C222−1+611yescharacteristic
1761C222−1+611yescharacteristic
1762C4—22no—
1763C4—22no—
1764C4—22no—
1765C4—22no—
1766C4—41no—
1767C4—44no—
1768C4—44no—
1769C4—42no—
1770C4—42no—
1771C4—42no—
1772C4—42no—
1773C4—41no—
1774C4—41no—
1775C4—44no—
1776C4—41no—
1777C4—41no—
1778C4—44no—
1779C4—42no—
1780C4—42no—
1781C4—41no—
1782C4—41no—
1783C4—42no—
1784C4—41no—
1785C4—42no—
1786C4—42no—
1787C4—42no—
1788C4—42no—
1789C4—42no—
1790C4C2×#56214yes—
1791C4C2×#56214yes—
1792C2—24no—
1793C2—82no—
1794C2—82no—
1795C2—82no—
1796C2—82no—
1797C2C22×#56211yescharacteristic
1798C2#6283411yescharacteristic
1799C2#6288811yescharacteristic
1800C2#6291311yescharacteristic
1801C2#6291411yescharacteristic
1802C2#6292711yescharacteristic
1803C2#6295611yescharacteristic
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. #53130C2semidirect
2. #53122C2semidirect
3. #53110C2semidirect
4. #53094C2semidirect
5. #53062C2semidirect
6. #53021C2semidirect
7. #52982C2semidirect
8. #52979C2semidirect
9. #52451C2semidirect
10. #52427C2semidirect
11. #46032C2semidirect
12. #45978C2semidirect
13. #45717C2semidirect
14. #45675C2semidirect
15. #45656C2semidirect
16. #45634C2semidirect
17. #45592C2semidirect
18. #45516C2semidirect
19. #45484C2semidirect
20. #45482C2semidirect
21. #35564C2semidirect
22. #35564C2semidirect
23. #35532C2semidirect
24. #35519C2semidirect
25. #35517C2semidirect
26. #35517C2semidirect
27. #35273C2semidirect
28. #35257C2semidirect
29. #35255C2semidirect
30. #35255C2semidirect
31. #35180C2semidirect
32. #35158C2semidirect
33. #34937C2semidirect
34. C2×#2506C2semidirect
35. #34745C2semidirect
1709. C2×C4#562semidirect

Maximal subgroups

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

subgroupindex
#531302
#531222
#531102
#530942
#530622
#530212
#529822
#529792
#524512
#524272
#460322
#459782
#457172
#456752
#456562
#456342
#455922
#455162
#454842
#454822
#355642
#355322
#355192
#355172
#352732
#352572
#352552
#351802
#351582
#349372
C2×#25062
#347452