Finite Group Databasebeta

← #8458720

Subgroups — #8458720

Order 512.

5383 conjugacy classes of subgroups.

The subgroup lattice has 1846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C211yesmaximal, characteristic, complemented
2#59136C211yesmaximal, characteristic, complemented
3#59039C211yesmaximal, characteristic, complemented
4#57866C214yesmaximal, complemented
5#56379C214yesmaximal, complemented
6#53876C214yesmaximal, complemented
7#52985C212yesmaximal, complemented
8#52963C212yesmaximal, complemented
9#50642C214yesmaximal, complemented
10#46049C212yesmaximal, complemented
11#45601C212yesmaximal, complemented
12#45104C212yesmaximal, complemented
13#45038C212yesmaximal, complemented
14#42609C212yesmaximal, complemented
15#42566C212yesmaximal, complemented
16#42555C212yesmaximal, complemented
17#42447C212yesmaximal, complemented
18#39628C212yesmaximal, complemented
19#39405C212yesmaximal, complemented
20#39349C212yesmaximal, complemented
21#39341C211yesmaximal, characteristic, complemented
22#39201C211yesmaximal, characteristic, complemented
23#39169C211yesmaximal, characteristic, complemented
24#38932C211yesmaximal, characteristic, complemented
25#37836C212yesmaximal, complemented
26#37637C211yesmaximal, characteristic, complemented
27#37336C212yesmaximal, complemented
28#37268C212yesmaximal, complemented
29#36472C211yesmaximal, characteristic, complemented
30#36154C211yesmaximal, characteristic, complemented
31#36122C211yesmaximal, characteristic, complemented
32#35289C211yesmaximal, characteristic, complemented
33#35237C211yesmaximal, characteristic, complemented
34#34803C211yesmaximal, characteristic, complemented
35#34681C211yesmaximal, characteristic, complemented
36C2×#554C2211yescharacteristic
37C2×#553C2212yescomplemented
38C2×#550C2211yescharacteristic, complemented
39C2×#548C2212yes—
40C2×#538C2214yes—
41C2×#537C2212yescomplemented
42C2×#532C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C22×C4⋊Q8C2211yescharacteristic, complemented
45C2×#525C2212yes—
46C22×C4×D4C2211yescharacteristic
47#2862C2212yescomplemented
48#2860C2212yescomplemented
49#2858C2212yes—
50#2858C2211yescharacteristic, complemented
51#2857C2211yescharacteristic
52#2856C2211yescharacteristic, complemented
53#2848C2212yes—
54#2847C2212yes—
55#2847C2212yes—
56#2831C2214yescomplemented
57#2831C2214yescomplemented
58#2827C2214yescomplemented
59#2827C2214yescomplemented
60#2827C2214yescomplemented
61#2826C2214yes—
62#2824C2214yes—
63#2824C2214yescomplemented
64#2804C2214yescomplemented
65#2804C2214yescomplemented
66#2804C2214yescomplemented
67#2782C2214yescomplemented
68#2778C2214yescomplemented
69#2775C2214yescomplemented
70#2764C2214yescomplemented
71#2764C2214yescomplemented
72#2753C2214yescomplemented
73#2749C2214yes—
74#2732C2214yescomplemented
75#2732C2214yescomplemented
76#2730C2214yescomplemented
77#2729C2214yescomplemented
78#2728C2214yes—
79#2715C2214yes—
80#2714C2214yes—
81#2712C2214yescomplemented
82#2712C2214yescomplemented
83#2710C2214yescomplemented
84#2710C2214yescomplemented
85#2708C2214yes—
86#2708C2214yescomplemented
87#2708C2214yescomplemented
88#2708C2214yescomplemented
89#2705C2214yescomplemented
90#2702C2214yes—
91#2701C2214yescomplemented
92#2698C2214yescomplemented
93#2695C2214yescomplemented
94#2693C2214yescomplemented
95#2691C2214yescomplemented
96#2688C2214yes—
97#2688C2214yescomplemented
98#2687C2214yes—
99#2686C2214yescomplemented
100#2686C2214yescomplemented
101#2684C2214yes—
102#2678C2214yes—
103#2676C2214yes—
104#2676C2214yescomplemented
105#2676C2214yescomplemented
106#2676C2214yescomplemented
107#2675C2214yescomplemented
108#2672C2214yescomplemented
109#2671C2214yes—
110#2671C2214yes—
111#2670C2214yes—
112#2668C2214yes—
113#2647C2212yescomplemented
114#2647C2212yescomplemented
115#2644C2212yes—
116#2643C2214yescomplemented
117#2641C2212yescomplemented
118#2640C2214yescomplemented
119#2637C2214yescomplemented
120#2636C2214yescomplemented
121#2631C2214yes—
122#2631C2214yes—
123#2631C2214yes—
124#2629C2212yescomplemented
125#2625C2212yescomplemented
126#2624C2212yescomplemented
127#2622C2214yes—
128#2615C2212yescomplemented
129#2603C2214yescomplemented
130#2580C2212yes—
131#2580C2214yescomplemented
132#2580C2212yescomplemented
133#2580C2212yescomplemented
134#2571C2212yescomplemented
135#2567C2211yescharacteristic, complemented
136#2566C2212yescomplemented
137#2563C2211yescharacteristic
138#2563C2211yescharacteristic
139#2563C2211yescharacteristic
140#2563C2211yescharacteristic, complemented
141#2563C2212yescomplemented
142#2563C2211yescharacteristic, complemented
143#2562C2212yes—
144#2552C2211yescharacteristic, complemented
145#2550C2212yescomplemented
146#2548C2212yes—
147#2547C2212yescomplemented
148#2547C2212yescomplemented
149#2545C2212yescomplemented
150#2543C2214yescomplemented
151#2541C2211yescharacteristic
152#2541C2212yes—
153#2541C2211yescharacteristic
154#2541C2212yes—
155#2538C2211yescharacteristic
156#2537C2212yes—
157#2535C2212yes—
158#2535C2212yes—
159#2535C2214yescomplemented
160#2533C2212yescomplemented
161#2527C2212yes—
162#2523C2212yescomplemented
163#2514C2211yescharacteristic, complemented
164#2513C2212yescomplemented
165#2512C2212yes—
166#2509C2211yescharacteristic, complemented
167#2508C2212yescomplemented
168#2504C2212yes—
169#2504C2212yes—
170#2504C2212yescomplemented
171#2499C2211yescharacteristic, complemented
172#2496C2211yescharacteristic
173#2496C2212yescomplemented
174#2495C2212yes—
175#2495C2212yescomplemented
176#2492C2211yescharacteristic
177#2492C2212yescomplemented
178#2491C2212yes—
179#2491C2212yes—
180#2491C2212yescomplemented
181#2490C2212yescomplemented
182#2489C2212yescomplemented
183#2487C2212yes—
184#2487C2212yescomplemented
185#2487C2212yescomplemented
186#2486C2212yes—
187#2485C2211yescharacteristic
188#2472C2212yes—
189#2466C2212yes—
190#2464C2212yes—
191#2464C2214yescomplemented
192#2461C2212yes—
193#2456C2214yes—
194#2456C2214yescomplemented
195#2454C2212yes—
196#2452C2212yes—
197#2452C2211yescharacteristic
198#2452C2212yescomplemented
199#2452C2212yescomplemented
200#2452C2212yescomplemented
201#2450C2214yes—
202#2450C2214yescomplemented
203#2450C2214yescomplemented
204#2450C2214yescomplemented
205#2450C2214yescomplemented
206#2445C2212yes—
207#2445C2211yescharacteristic
208#2445C2212yescomplemented
209#2444C2214yescomplemented
210#2442C2212yes—
211#2442C2212yescomplemented
212#2442C2212yescomplemented
213#2440C2211yescharacteristic
214#2440C2212yescomplemented
215#2439C2211yescharacteristic, complemented
216#2437C2214yes—
217#2436C2212yescomplemented
218#2436C2214yescomplemented
219#2433C2212yes—
220#2433C2211yescharacteristic
221#2432C2212yes—
222#2430C2214yes—
223#2428C2212yes—
224#2428C2212yes—
225#2428C2211yescharacteristic
226#2428C2212yes—
227#2428C2212yescomplemented
228#2425C2214yescomplemented
229#2424C2214yes—
230#2424C2214yes—
231#2424C2212yes—
232#2422C2212yes—
233#2422C2211yescharacteristic
234#2422C2212yescomplemented
235#2422C2212yescomplemented
236#2422C2212yescomplemented
237#2420C2212yes—
238#2417C2212yes—
239#2417C2212yescomplemented
240#2416C2212yes—
241#2416C2212yes—
242#2416C2211yescharacteristic
243#2416C2212yescomplemented
244#2416C2212yescomplemented
245#2416C2212yescomplemented
246#2415C2211yescharacteristic
247#2414C2212yescomplemented
248#2409C2214yescomplemented
249#2408C2211yescharacteristic
250#2407C2212yes—
251#2407C2212yescomplemented
252#2407C2212yescomplemented
253#2407C2212yescomplemented
254#2404C2214yes—
255#2401C2212yescomplemented
256#2398C2212yes—
257#2392C2212yes—
258#2388C2212yes—
259#2379C2214yes—
260#2369C2211yescharacteristic, complemented
261#2366C2212yes—
262#2366C2211yescharacteristic, complemented
263#2361C2212yes—
264#2361C2212yescomplemented
265#2361C2212yescomplemented
266#2361C2212yescomplemented
267#2349C2212yes—
268#2349C2212yescomplemented
269D4×C4⋊C4C2211yescharacteristic
270D4×C4⋊C4C2212yescomplemented
271D4×C4⋊C4C2211yescharacteristic, complemented
272D4×C4⋊C4C2212yescomplemented
273#2339C2212yescomplemented
274D4×C22⋊C4C2212yes—
275#2328C2212yes—
276#2328C2212yes—
277#2328C2212yes—
278#2324C2212yescomplemented
279#2319C2212yescomplemented
280#2311C2212yescomplemented
281#2311C2212yescomplemented
282C4×C4⋊Q8C2211yescharacteristic, complemented
283C4×C4⋊Q8C2211yescharacteristic, complemented
284C4×#127C2211yescharacteristic
285C4×#127C2212yes—
286C4×#126C2212yes—
287C4×C22⋊Q8C2211yescharacteristic
288C4×C22⋊Q8C2211yescharacteristic, complemented
289C4×#121C2211yescharacteristic
290C4×#121C2211yescharacteristic
291C4×#120C2212yes—
292#2295C2211yescharacteristic, complemented
293#2295C2212yescomplemented
294#2293C2211yescharacteristic
295#2283C2211yescharacteristic
296C2×#380C2212yes—
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×Q8C2312yes—
303C23×D4C2311yescharacteristic
304C24×C4C2312yes—
305#554—44no—
306#553—48no—
307#550—44no—
308#548—48no—
309#538—416no—
310#537—48no—
311#532—44no—
312#532—44no—
313C2×C4⋊Q8—44no—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×#127C2312yes—
322C2×#127C2311yescharacteristic
323C2×#127C2311yescharacteristic
324C2×#127C2312yes—
325C2×#127C2311yescharacteristic
326C2×#127C2312yes—
327C2×#126C2312yes—
328C2×#126C2314yes—
329C2×#126C2314yes—
330C2×#125C2312yes—
331C2×#125C2312yes—
332C2×#124C2314yes—
333C2×#124C2314yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#124C2312yes—
339C2×#124C2314yes—
340#525—48no—
341C2×#123C2312yes—
342C2×#123C2312yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2314yes—
358C2×#121C2312yes—
359C2×#121C2311yescharacteristic
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2311yescharacteristic
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2314yes—
372C2×#121C2314yes—
373C2×#121C2314yes—
374C2×#121C2314yes—
375C2×#121C2312yes—
376C2×#121C2311yescharacteristic
377C2×#121C2311yescharacteristic
378C2×#121C2314yes—
379C2×#121C2314yes—
380C2×#121C2312yes—
381C2×#121C2314yes—
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C2×#120C2312yes—
386C2×#120C2314yes—
387C2×#120C2312yes—
388C2×#120C2312yes—
389C2×#120C2314yes—
390C2×C4×Q8C2311yescharacteristic
391C2×C4×Q8C2312yes—
392C2×C4×Q8C2312yes—
393C2×C4×D4—44no—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2314yes—
404C2×C4×D4C2314yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2314yes—
411C2×C4×D4C2311yescharacteristic
412C2×C4×D4C2312yes—
413C2×C4×D4C2311yescharacteristic
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2314yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2311yescharacteristic
421C2×C4×D4C2314yes—
422C2×#117C2311yescharacteristic
423C2×#117C2311yescharacteristic
424C2×#117C2312yes—
425C22×C4⋊C4C2312yes—
426C22×C4⋊C4C2312yes—
427C22×C4⋊C4C2312yes—
428C22×C4⋊C4C2312yes—
429C22×C4⋊C4C2312yes—
430C22×C4⋊C4C2311yescharacteristic
431C22×C22⋊C4C2314yes—
432C22×C22⋊C4C2312yes—
433C22×C42C2311yescharacteristic
434C22×C42C2311yescharacteristic
435#401C2312yes—
436#400C2314yes—
437#400C2314yes—
438#400C2314yes—
439#400C2314yes—
440#400C2314yes—
441#400C2312yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2312yes—
446#400C2312yes—
447#400C2314yes—
448#400C2314yes—
449#400C2312yes—
450#400C2312yes—
451#399C2314yes—
452#399C2314yes—
453#399C2314yes—
454#399C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2312yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2312yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2312yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2312yes—
483#397C2312yes—
484#397C2312yes—
485#397C2312yes—
486#397C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2312yes—
492#396C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2312yes—
496#396C2314yes—
497#396C2312yes—
498#396C2314yes—
499#396C2314yes—
500#395C2314yes—
501#395C2314yes—
502#395C2312yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2312yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2312yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2312yes—
521#394C2314yes—
522#394C2312yes—
523#394C2312yes—
524#394C2312yes—
525#394C2312yes—
526#394C2312yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2314yes—
536#393C2314yes—
537#393C2312yes—
538#393C2314yes—
539#393C2312yes—
540#393C2314yes—
541#393C2314yes—
542#393C2314yes—
543#393C2312yes—
544#393C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2314yes—
549#392C2314yes—
550#392C2314yes—
551#392C2314yes—
552#392C2312yes—
553#392C2312yes—
554#392C2314yes—
555#392C2314yes—
556#392C2314yes—
557#392C2314yes—
558#392C2312yes—
559#392C2312yes—
560#392C2314yes—
561#391C2312yes—
562#391C2312yes—
563#391C2314yes—
564#391C2314yes—
565#391C2312yes—
566#391C2314yes—
567#391C2311yescharacteristic
568#391C2312yes—
569#391C2314yes—
570#391C2314yes—
571#391C2311yescharacteristic
572#391C2314yes—
573#391C2311yescharacteristic
574#391C2311yescharacteristic
575#391C2312yes—
576#391C2312yes—
577#390C2311yescharacteristic
578#390C2311yescharacteristic
579#390C2311yescharacteristic
580#390C2312yes—
581#390C2312yes—
582#390C2314yes—
583#390C2314yes—
584#390C2312yes—
585#390C2312yes—
586#390C2312yes—
587#390C2312yes—
588#390C2312yes—
589#390C2312yes—
590#390C2314yes—
591#390C2312yes—
592#390C2312yes—
593#390C2314yes—
594#390C2314yes—
595#390C2311yescharacteristic
596#390C2312yes—
597#390C2314yes—
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2312yes—
603#390C2312yes—
604#390C2312yes—
605#390C2312yes—
606#390C2311yescharacteristic
607#390C2311yescharacteristic
608#389C2311yescharacteristic
609#389C2312yes—
610#389C2312yes—
611#389C2311yescharacteristic
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2312yes—
617#389C2314yes—
618#389C2312yes—
619#389C2312yes—
620#389C2311yescharacteristic
621#389C2312yes—
622#389C2312yes—
623#389C2314yes—
624#389C2311yescharacteristic
625#389C2312yes—
626#389C2311yescharacteristic
627#389C2312yes—
628#389C2312yes—
629#389C2311yescharacteristic
630#389C2312yes—
631#389C2311yescharacteristic
632#389C2311yescharacteristic
633#389C2312yes—
634#389C2311yescharacteristic
635#389C2311yescharacteristic
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2312yes—
643#388C2314yes—
644#388C2314yes—
645#388C2312yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2312yes—
653#388C2314yes—
654#388C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2312yes—
702#386C2312yes—
703#386C2312yes—
704#386C2312yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2312yes—
729#385C2314yes—
730#385C2312yes—
731#385C2312yes—
732#385C2312yes—
733#385C2312yes—
734#384C2311yescharacteristic
735#384C2312yes—
736#384C2311yescharacteristic
737#384C2311yescharacteristic
738#384C2312yes—
739#383C2312yes—
740#383C2312yes—
741#383C2314yes—
742#382C2312yes—
743#382C2312yes—
744#382C2312yes—
745#382C2312yes—
746#382C2312yes—
747#382C2314yes—
748#382C2314yes—
749#382C2311yescharacteristic
750#382C2311yescharacteristic
751#381C2314yes—
752#381C2314yes—
753#381C2312yes—
754#380C2311yescharacteristic
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2314yes—
769#380C2311yescharacteristic
770#380C2312yes—
771#380C2311yescharacteristic
772#380C2314yes—
773#380C2314yes—
774#380C2312yes—
775#380C2311yescharacteristic
776#380C2314yes—
777#380C2314yes—
778#380C2311yescharacteristic
779#380C2314yes—
780#380C2311yescharacteristic
781#379C2314yes—
782#379C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2311yescharacteristic
814#376C2312yes—
815#376C2312yes—
816#376C2312yes—
817C2×#95C2314yes—
818C2×#95C2314yes—
819C43C2312yes—
820C43C2311yescharacteristic
821C25C2412yes—
822C2×#41—28no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—82no—
831C22×Q8—44no—
832C22×Q8—44no—
833C22×Q8—82no—
834C22×Q8C2411yescharacteristic
835C22×Q8C2412yes—
836C22×Q8C2412yes—
837C22×Q8C2412yes—
838C22×Q8C2414yes—
839C22×Q8C2412yes—
840C22×D4—24no—
841C22×D4—42no—
842C22×D4—42no—
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2411yescharacteristic
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2411yescharacteristic
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2412yes—
860C22×D4C2412yes—
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2414yes—
865C22×D4C2414yes—
866C22×D4C2414yes—
867C23×C4—44no—
868C23×C4—44no—
869C23×C4—44no—
870C23×C4C2412yes—
871C23×C4C2411yescharacteristic
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2412yes—
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2411yescharacteristic
878C23×C4C2411yescharacteristic
879C23×C4C2414yes—
880C23×C4C2414yes—
881C23×C4C2412yes—
882C23×C4C2414yes—
883C23×C4C2414yes—
884C23×C4C2414yes—
885C23×C4C2414yes—
886C23×C4C2412yes—
887C23×C4C2412yes—
888C23×C4C2414yes—
889C4⋊Q8—24no—
890C4⋊Q8—24no—
891C4⋊Q8—44no—
892C4⋊Q8—44no—
893C4⋊Q8—42no—
894C4⋊Q8—42no—
895C4⋊Q8—44no—
896#127—24no—
897#127—28no—
898#127—24no—
899#127—44no—
900#127—42no—
901#127—44no—
902#126—28no—
903#126—48no—
904#126—48no—
905#125—44no—
906#125—44no—
907#124—216no—
908#124—44no—
909#124—44no—
910#124—44no—
911#124—48no—
912#124—84no—
913#124—84no—
914#124—82no—
915#123—48no—
916#123—44no—
917#123—48no—
918#123—48no—
919#123—44no—
920#123—84no—
921C22⋊Q8—24no—
922C22⋊Q8—44no—
923C22⋊Q8—44no—
924C22⋊Q8—44no—
925C22⋊Q8—48no—
926C22⋊Q8—48no—
927C22⋊Q8—48no—
928C22⋊Q8—48no—
929C22⋊Q8—42no—
930C22⋊Q8—44no—
931C22⋊Q8—44no—
932#121—24no—
933#121—28no—
934#121—44no—
935#121—44no—
936#121—48no—
937#121—48no—
938#121—48no—
939#121—48no—
940#121—44no—
941#121—44no—
942#121—48no—
943#121—48no—
944#121—48no—
945#121—48no—
946#121—48no—
947#121—44no—
948#121—44no—
949#121—42no—
950#121—44no—
951#121—42no—
952#121—44no—
953#121—44no—
954#121—42no—
955#121—44no—
956#121—44no—
957#121—44no—
958#121—84no—
959#120—28no—
960#120—44no—
961#120—48no—
962#120—44no—
963#120—84no—
964C4×Q8—24no—
965C4×Q8—44no—
966C4×Q8—44no—
967C4×D4—24no—
968C4×D4—28no—
969C4×D4—24no—
970C4×D4—24no—
971C4×D4—24no—
972C4×D4—24no—
973C4×D4—44no—
974C4×D4—48no—
975C4×D4—48no—
976C4×D4—48no—
977C4×D4—42no—
978C4×D4—42no—
979C4×D4—44no—
980C4×D4—44no—
981C4×D4—44no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—48no—
985C4×D4—44no—
986C4×D4—44no—
987C4×D4—44no—
988C4×D4—44no—
989C4×D4—44no—
990C4×D4—42no—
991C4×D4—44no—
992C4×D4—44no—
993C4×D4—44no—
994C4×D4—84no—
995#117—24no—
996#117—44no—
997#117—42no—
998C2×C4⋊C4—42no—
999C2×C4⋊C4—44no—
1000C2×C4⋊C4—44no—
1001C2×C4⋊C4—44no—
1002C2×C4⋊C4—44no—
1003C2×C4⋊C4—44no—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2411yescharacteristic
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2412yes—
1060C2×C4⋊C4C2412yes—
1061C2×C22⋊C4—44no—
1062C2×C22⋊C4—48no—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2411yescharacteristic
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2411yescharacteristic
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2411yescharacteristic
1105C2×C22⋊C4C2411yescharacteristic
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2412yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2412yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2411yescharacteristic
1133C2×C42—24no—
1134C2×C42—24no—
1135C2×C42C2411yescharacteristic
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2411yescharacteristic
1139C2×C42C2411yescharacteristic
1140C2×C42C2414yes—
1141C2×C42C2412yes—
1142C2×C42C2412yes—
1143C2×C42C2412yes—
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2411yescharacteristic
1147C2×C42C2411yescharacteristic
1148C2×C42C2411yescharacteristic
1149C2×C42C2412yes—
1150C2×C42C2411yescharacteristic
1151C2×C42C2411yescharacteristic
1152C2×C42C2412yes—
1153C2×C42C2411yescharacteristic
1154C2×C42C2412yes—
1155C2×C42C2414yes—
1156C2×C42C2411yescharacteristic
1157C2×C42C2412yes—
1158C2×C42C2411yescharacteristic
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2411yescharacteristic
1180#95C2411yescharacteristic
1181#95C2411yescharacteristic
1182#95C2411yescharacteristic
1183#95C2411yescharacteristic
1184#95C2411yescharacteristic
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2414yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221C24—24no—
1222C24—24no—
1223C24—42no—
1224C24—42no—
1225C24—42no—
1226C24—42no—
1227C24—42no—
1228C24C2512yes—
1229C24C2514yes—
1230C24C2512yes—
1231C24C2511yescharacteristic
1232C24C2511yescharacteristic
1233C24C2512yes—
1234#41—816no—
1235#41—816no—
1236#41—816no—
1237C2×Q8—22no—
1238C2×Q8—22no—
1239C2×Q8—24no—
1240C2×Q8—24no—
1241C2×Q8—28no—
1242C2×Q8—24no—
1243C2×Q8—22no—
1244C2×Q8—42no—
1245C2×Q8—42no—
1246C2×Q8—42no—
1247C2×Q8—42no—
1248C2×Q8—42no—
1249C2×Q8—42no—
1250C2×Q8—44no—
1251C2×Q8—42no—
1252C2×Q8—44no—
1253C2×Q8—42no—
1254C2×Q8—42no—
1255C2×Q8—816no—
1256C2×D4—22no—
1257C2×D4—24no—
1258C2×D4—22no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—28no—
1265C2×D4—28no—
1266C2×D4—24no—
1267C2×D4—24no—
1268C2×D4—28no—
1269C2×D4—28no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—24no—
1274C2×D4—24no—
1275C2×D4—24no—
1276C2×D4—24no—
1277C2×D4—24no—
1278C2×D4—24no—
1279C2×D4—24no—
1280C2×D4—22no—
1281C2×D4—24no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—22no—
1285C2×D4—24no—
1286C2×D4—24no—
1287C2×D4—22no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—41no—
1291C2×D4—42no—
1292C2×D4—42no—
1293C2×D4—42no—
1294C2×D4—42no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—42no—
1299C2×D4—44no—
1300C2×D4—44no—
1301C2×D4—42no—
1302C2×D4—42no—
1303C2×D4—44no—
1304C2×D4—44no—
1305C2×D4—42no—
1306C2×D4—44no—
1307C2×D4—44no—
1308C2×D4—44no—
1309C2×D4—42no—
1310C2×D4—42no—
1311C2×D4—42no—
1312C2×D4—42no—
1313C2×D4—42no—
1314C2×D4—42no—
1315C2×D4—42no—
1316C2×D4—42no—
1317C2×D4—44no—
1318C2×D4—44no—
1319C2×D4—44no—
1320C2×D4—44no—
1321C2×D4—44no—
1322C2×D4—44no—
1323C2×D4—44no—
1324C2×D4—44no—
1325C2×D4—44no—
1326C2×D4—44no—
1327C2×D4—416no—
1328C2×D42−1+414yes—
1329C22×C4—22no—
1330C22×C4—22no—
1331C22×C4—22no—
1332C22×C4—22no—
1333C22×C4—22no—
1334C22×C4—22no—
1335C22×C4—22no—
1336C22×C4—22no—
1337C22×C4—24no—
1338C22×C4—24no—
1339C22×C4—24no—
1340C22×C4—24no—
1341C22×C4—22no—
1342C22×C4—24no—
1343C22×C4—24no—
1344C22×C4—22no—
1345C22×C4—22no—
1346C22×C4—22no—
1347C22×C4—22no—
1348C22×C4—24no—
1349C22×C4—22no—
1350C22×C4—24no—
1351C22×C4—24no—
1352C22×C4—22no—
1353C22×C4—41no—
1354C22×C4—41no—
1355C22×C4—42no—
1356C22×C4—44no—
1357C22×C4—42no—
1358C22×C4—42no—
1359C22×C4—44no—
1360C22×C4—44no—
1361C22×C4—44no—
1362C22×C4—44no—
1363C22×C4—44no—
1364C22×C4—42no—
1365C22×C4—42no—
1366C22×C4—44no—
1367C22×C4—42no—
1368C22×C4—44no—
1369C22×C4—42no—
1370C22×C4—42no—
1371C22×C4—42no—
1372C22×C4—44no—
1373C22×C4—44no—
1374C22×C4—44no—
1375C22×C4—44no—
1376C22×C4—44no—
1377C22×C4—44no—
1378C22×C4—44no—
1379C22×C4—44no—
1380C22×C4—44no—
1381C22×C4—44no—
1382C22×C4—44no—
1383C22×C4—44no—
1384C22×C4—44no—
1385C22×C4—816no—
1386C22×C4H(5,𝔽2)14yes—
1387C22×C4C2511yescharacteristic
1388C22×C4C2512yes—
1389C22×C4C2512yes—
1390C22×C4C2511yescharacteristic
1391C22×C4C2511yescharacteristic
1392C22×C4C2512yes—
1393C22×C4C2511yescharacteristic
1394C22×C4C2511yescharacteristic
1395C22×C4C2512yes—
1396C22×C4C2512yes—
1397C22×C4C2512yes—
1398C22×C4C2512yes—
1399C22×C4C2512yes—
1400C22×C4C2512yes—
1401C22×C4C2511yescharacteristic
1402C22×C4C2514yes—
1403C22×C4C2512yes—
1404C22×C4C2514yes—
1405C22×C4C2512yes—
1406C22×C4C2514yes—
1407C22×C4C2512yes—
1408C22×C4C2512yes—
1409C22×C4C2511yescharacteristic
1410C22×C4C2511yescharacteristic
1411C22×C4C2511yescharacteristic
1412C22×C4C2511yescharacteristic
1413C22×C4C2511yescharacteristic
1414C22×C4C2511yescharacteristic
1415C22×C4C2511yescharacteristic
1416C4⋊C4—22no—
1417C4⋊C4—22no—
1418C4⋊C4—24no—
1419C4⋊C4—22no—
1420C4⋊C4—24no—
1421C4⋊C4—22no—
1422C4⋊C4—22no—
1423C4⋊C4—24no—
1424C4⋊C4—24no—
1425C4⋊C4—24no—
1426C4⋊C4—22no—
1427C4⋊C4—22no—
1428C4⋊C4—22no—
1429C4⋊C4—22no—
1430C4⋊C4—24no—
1431C4⋊C4—24no—
1432C4⋊C4—24no—
1433C4⋊C4—24no—
1434C4⋊C4—24no—
1435C4⋊C4—24no—
1436C4⋊C4—22no—
1437C4⋊C4—22no—
1438C4⋊C4—22no—
1439C4⋊C4—24no—
1440C4⋊C4—22no—
1441C4⋊C4—22no—
1442C4⋊C4—42no—
1443C4⋊C4—44no—
1444C4⋊C4—44no—
1445C4⋊C4—44no—
1446C4⋊C4—44no—
1447C4⋊C4—44no—
1448C4⋊C4—42no—
1449C4⋊C4—42no—
1450C4⋊C4—42no—
1451C4⋊C4—41no—
1452C4⋊C4—42no—
1453C4⋊C4—44no—
1454C4⋊C4—42no—
1455C4⋊C4—42no—
1456C4⋊C4—44no—
1457C4⋊C4—44no—
1458C4⋊C4—44no—
1459C4⋊C4—42no—
1460C4⋊C4—42no—
1461C4⋊C4—42no—
1462C4⋊C4—42no—
1463C4⋊C4—44no—
1464C4⋊C4—44no—
1465C4⋊C4—44no—
1466C4⋊C4—44no—
1467C4⋊C4—42no—
1468C4⋊C4—42no—
1469C4⋊C4—44no—
1470C4⋊C4—44no—
1471C4⋊C4—42no—
1472C4⋊C4—42no—
1473C22⋊C4—24no—
1474C22⋊C4—28no—
1475C22⋊C4—24no—
1476C22⋊C4—22no—
1477C22⋊C4—24no—
1478C22⋊C4—24no—
1479C22⋊C4—24no—
1480C22⋊C4—24no—
1481C22⋊C4—24no—
1482C22⋊C4—24no—
1483C22⋊C4—22no—
1484C22⋊C4—24no—
1485C22⋊C4—22no—
1486C22⋊C4—24no—
1487C22⋊C4—24no—
1488C22⋊C4—28no—
1489C22⋊C4—28no—
1490C22⋊C4—28no—
1491C22⋊C4—24no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—42no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C22⋊C4—41no—
1504C22⋊C4—41no—
1505C22⋊C4—44no—
1506C22⋊C4—42no—
1507C22⋊C4—42no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C22⋊C4—42no—
1513C22⋊C4—42no—
1514C22⋊C4—44no—
1515C22⋊C4—44no—
1516C22⋊C4—44no—
1517C22⋊C4—44no—
1518C22⋊C4—44no—
1519C22⋊C4—42no—
1520C22⋊C4—44no—
1521C22⋊C4—44no—
1522C22⋊C4—42no—
1523C22⋊C4—44no—
1524C22⋊C4—44no—
1525C22⋊C4—44no—
1526C22⋊C4—42no—
1527C22⋊C4—44no—
1528C22⋊C4—44no—
1529C22⋊C4—44no—
1530C22⋊C4—44no—
1531C22⋊C4—44no—
1532C22⋊C4—44no—
1533C22⋊C4—44no—
1534C22⋊C4—44no—
1535C22⋊C4—42no—
1536C22⋊C4—42no—
1537C22⋊C4—44no—
1538C22⋊C4—44no—
1539C22⋊C4—42no—
1540C22⋊C4—44no—
1541C22⋊C4—44no—
1542C22⋊C4H(5,𝔽2)14yes—
1543C42—22no—
1544C42—22no—
1545C42—22no—
1546C42—22no—
1547C42—22no—
1548C42—22no—
1549C42—24no—
1550C42—22no—
1551C42—24no—
1552C42—22no—
1553C42—24no—
1554C42—28no—
1555C42—24no—
1556C42—22no—
1557C42—24no—
1558C42—24no—
1559C42—22no—
1560C42—22no—
1561C42—24no—
1562C42—42no—
1563C42—44no—
1564C42—42no—
1565C42—41no—
1566C42H(5,𝔽2)14yes—
1567C23—22no—
1568C23—21no—
1569C23—22no—
1570C23—22no—
1571C23—21no—
1572C23—21no—
1573C23—21no—
1574C23—21no—
1575C23—21no—
1576C23—21no—
1577C23—21no—
1578C23—22no—
1579C23—22no—
1580C23—21no—
1581C23—21no—
1582C23—21no—
1583C23—22no—
1584C23—21no—
1585C23—24no—
1586C23—22no—
1587C23—24no—
1588C23—22no—
1589C23—22no—
1590C23—22no—
1591C23—22no—
1592C23—24no—
1593C23—22no—
1594C23—22no—
1595C23—24no—
1596C23—22no—
1597C23—22no—
1598C23—24no—
1599C23—24no—
1600C23—22no—
1601C23—22no—
1602C23—22no—
1603C23—22no—
1604C23—22no—
1605C23—24no—
1606C23—48no—
1607C23—48no—
1608C23—84no—
1609C23—84no—
1610C23—84no—
1611C23—84no—
1612C23—84no—
1613C23C2×H(5,𝔽2)12yes—
1614C23C2×H(5,𝔽2)12yes—
1615C23C2×2−1+414yes—
1616C23C2611yescharacteristic
1617Q8—48no—
1618Q8—44no—
1619Q8—84no—
1620Q8—88no—
1621Q8—84no—
1622Q8—84no—
1623D4—28no—
1624D4—48no—
1625D4—44no—
1626D4—48no—
1627D4—48no—
1628D4—44no—
1629D4—48no—
1630D4—44no—
1631D4—48no—
1632D4—84no—
1633D4—84no—
1634D4—84no—
1635D4—88no—
1636D4—88no—
1637D4—84no—
1638D4—84no—
1639D4—88no—
1640D4—84no—
1641D4—84no—
1642D4—88no—
1643D4—88no—
1644D4—164no—
1645D4—164no—
1646D4—164no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—28no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—21no—
1661C2×C4—22no—
1662C2×C4—24no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—21no—
1668C2×C4—22no—
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—22no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—21no—
1681C2×C4—22no—
1682C2×C4—22no—
1683C2×C4—22no—
1684C2×C4—24no—
1685C2×C4—21no—
1686C2×C4—24no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—24no—
1690C2×C4—22no—
1691C2×C4—21no—
1692C2×C4—22no—
1693C2×C4—21no—
1694C2×C4—22no—
1695C2×C4—21no—
1696C2×C4—22no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—22no—
1700C2×C4—21no—
1701C2×C4—22no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—22no—
1705C2×C4—21no—
1706C2×C4—22no—
1707C2×C4—24no—
1708C2×C4—22no—
1709C2×C4—21no—
1710C2×C4—22no—
1711C2×C4—22no—
1712C2×C4—22no—
1713C2×C4—22no—
1714C2×C4—21no—
1715C2×C4—22no—
1716C2×C4—22no—
1717C2×C4—22no—
1718C2×C4—21no—
1719C2×C4—22no—
1720C2×C4—21no—
1721C2×C4—24no—
1722C2×C4—24no—
1723C2×C4—21no—
1724C2×C4—22no—
1725C2×C4—44no—
1726C2×C4—44no—
1727C2×C4—44no—
1728C2×C4—44no—
1729C2×C4—48no—
1730C2×C4—44no—
1731C2×C4—48no—
1732C2×C4—48no—
1733C2×C4—84no—
1734C2×C4—84no—
1735C2×C4—84no—
1736C2×C4—88no—
1737C2×C4—88no—
1738C2×C4—88no—
1739C2×C4—164no—
1740C2×C4—164no—
1741C2×C4—164no—
1742C2×C4—164no—
1743C2×C4C2×H(5,𝔽2)12yes—
1744C2×C4C2×H(5,𝔽2)12yes—
1745C2×C4C2×H(5,𝔽2)12yes—
1746C2×C4C2×H(5,𝔽2)12yes—
1747C2×C4C2×H(5,𝔽2)12yes—
1748C2×C4C2×H(5,𝔽2)12yes—
1749C2×C4C2×H(5,𝔽2)12yes—
1750C2×C4C2×2−1+412yes—
1751C2×C4#58512yes—
1752C2×C4#58512yes—
1753C22—24no—
1754C22—22no—
1755C22—24no—
1756C22—22no—
1757C22—22no—
1758C22—22no—
1759C22—22no—
1760C22—22no—
1761C22—24no—
1762C22—41no—
1763C22—41no—
1764C22—41no—
1765C22—42no—
1766C22—41no—
1767C22—42no—
1768C22—41no—
1769C22—42no—
1770C22—41no—
1771C22—42no—
1772C22—41no—
1773C22—41no—
1774C22—42no—
1775C22—42no—
1776C22—44no—
1777C22—42no—
1778C22—42no—
1779C22—44no—
1780C22—42no—
1781C22—44no—
1782C22—42no—
1783C22—42no—
1784C22—44no—
1785C22—42no—
1786C22—44no—
1787C22—42no—
1788C22—42no—
1789C22—42no—
1790C22—44no—
1791C22—42no—
1792C22—44no—
1793C22—42no—
1794C22—42no—
1795C22—816no—
1796C22C22×H(5,𝔽2)11yescharacteristic
1797C22C22×H(5,𝔽2)11yescharacteristic
1798C22C22×H(5,𝔽2)11yescharacteristic
1799C22C22×2−1+411yescharacteristic
1800C22C2×#58511yescharacteristic
1801C22C2×#58511yescharacteristic
1802C22H(7,𝔽2)11yescharacteristic
1803C4—22no—
1804C4—22no—
1805C4—22no—
1806C4—22no—
1807C4—41no—
1808C4—41no—
1809C4—42no—
1810C4—41no—
1811C4—42no—
1812C4—42no—
1813C4—42no—
1814C4—42no—
1815C4—42no—
1816C4—42no—
1817C4—44no—
1818C4—42no—
1819C4—41no—
1820C4—41no—
1821C4—44no—
1822C4—44no—
1823C4—42no—
1824C4—42no—
1825C4—42no—
1826C4—41no—
1827C4—42no—
1828C4—41no—
1829C4—42no—
1830C4#354114yes—
1831C4#355814yes—
1832C2—42no—
1833C2—44no—
1834C2—42no—
1835C2—82no—
1836C2—84no—
1837C2—82no—
1838C2C2×#354111yescharacteristic
1839C2C2×#355811yescharacteristic
1840C2#6283411yescharacteristic
1841C2#6291211yescharacteristic
1842C2#6293711yescharacteristic
1843C2#6294411yescharacteristic
1844C2#6301311yescharacteristic
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. #59864C2semidirect
2. #59136C2semidirect
3. #59039C2semidirect
4. #57866C2semidirect
5. #56379C2semidirect
6. #53876C2semidirect
7. #52985C2semidirect
8. #52963C2semidirect
9. #50642C2semidirect
10. #46049C2semidirect
11. #45601C2semidirect
12. #45104C2semidirect
13. #45038C2semidirect
14. #42609C2semidirect
15. #42566C2semidirect
16. #42555C2semidirect
17. #42447C2semidirect
18. #39628C2semidirect
19. #39405C2semidirect
20. #39349C2semidirect
21. #39341C2semidirect
22. #39201C2semidirect
23. #39169C2semidirect
24. #38932C2semidirect
25. #37836C2semidirect
26. #37637C2semidirect
27. #37336C2semidirect
28. #37268C2semidirect
29. #36472C2semidirect
30. #36154C2semidirect
31. #36122C2semidirect
32. #35289C2semidirect
33. #35237C2semidirect
34. #34803C2semidirect
35. #34681C2semidirect
37. C2×#553C22semidirect
38. C2×#550C22semidirect
41. C2×#537C22semidirect
44. C22×C4⋊Q8C22semidirect
47. #2862C22semidirect
48. #2860C22semidirect
50. #2858C22semidirect
52. #2856C22semidirect
56. #2831C22semidirect
57. #2831C22semidirect
58. #2827C22semidirect
59. #2827C22semidirect
60. #2827C22semidirect
63. #2824C22semidirect
64. #2804C22semidirect
65. #2804C22semidirect
66. #2804C22semidirect
67. #2782C22semidirect
68. #2778C22semidirect
69. #2775C22semidirect
70. #2764C22semidirect
71. #2764C22semidirect
72. #2753C22semidirect
74. #2732C22semidirect
75. #2732C22semidirect
76. #2730C22semidirect
77. #2729C22semidirect
81. #2712C22semidirect
82. #2712C22semidirect
83. #2710C22semidirect
84. #2710C22semidirect
86. #2708C22semidirect
87. #2708C22semidirect
88. #2708C22semidirect
89. #2705C22semidirect
91. #2701C22semidirect
92. #2698C22semidirect
93. #2695C22semidirect
94. #2693C22semidirect
95. #2691C22semidirect
97. #2688C22semidirect
99. #2686C22semidirect
100. #2686C22semidirect
104. #2676C22semidirect
105. #2676C22semidirect
106. #2676C22semidirect
107. #2675C22semidirect
108. #2672C22semidirect
113. #2647C22semidirect
114. #2647C22semidirect
116. #2643C22semidirect
117. #2641C22semidirect
118. #2640C22semidirect
119. #2637C22semidirect
120. #2636C22semidirect
124. #2629C22semidirect
125. #2625C22semidirect
126. #2624C22semidirect
128. #2615C22semidirect
129. #2603C22semidirect
131. #2580C22semidirect
132. #2580C22semidirect
133. #2580C22semidirect
134. #2571C22semidirect
135. #2567C22semidirect
136. #2566C22semidirect
140. #2563C22semidirect
141. #2563C22semidirect
142. #2563C22semidirect
144. #2552C22semidirect
145. #2550C22semidirect
147. #2547C22semidirect
148. #2547C22semidirect
149. #2545C22semidirect
150. #2543C22semidirect
159. #2535C22semidirect
160. #2533C22semidirect
162. #2523C22semidirect
163. #2514C22semidirect
164. #2513C22semidirect
166. #2509C22semidirect
167. #2508C22semidirect
170. #2504C22semidirect
171. #2499C22semidirect
173. #2496C22semidirect
175. #2495C22semidirect
177. #2492C22semidirect
180. #2491C22semidirect
181. #2490C22semidirect
182. #2489C22semidirect
184. #2487C22semidirect
185. #2487C22semidirect
191. #2464C22semidirect
194. #2456C22semidirect
198. #2452C22semidirect
199. #2452C22semidirect
200. #2452C22semidirect
202. #2450C22semidirect
203. #2450C22semidirect
204. #2450C22semidirect
205. #2450C22semidirect
208. #2445C22semidirect
209. #2444C22semidirect
211. #2442C22semidirect
212. #2442C22semidirect
214. #2440C22semidirect
215. #2439C22semidirect
217. #2436C22semidirect
218. #2436C22semidirect
227. #2428C22semidirect
228. #2425C22semidirect
234. #2422C22semidirect
235. #2422C22semidirect
236. #2422C22semidirect
239. #2417C22semidirect
243. #2416C22semidirect
244. #2416C22semidirect
245. #2416C22semidirect
247. #2414C22semidirect
248. #2409C22semidirect
251. #2407C22semidirect
252. #2407C22semidirect
253. #2407C22semidirect
255. #2401C22semidirect
260. #2369C22semidirect
262. #2366C22semidirect
264. #2361C22semidirect
265. #2361C22semidirect
266. #2361C22semidirect
268. #2349C22semidirect
270. D4×C4⋊C4C22semidirect
271. D4×C4⋊C4C22semidirect
272. D4×C4⋊C4C22semidirect
273. #2339C22semidirect
278. #2324C22semidirect
279. #2319C22semidirect
280. #2311C22semidirect
281. #2311C22semidirect
282. C4×C4⋊Q8C22semidirect
283. C4×C4⋊Q8C22semidirect
288. C4×C22⋊Q8C22semidirect
292. #2295C22semidirect
293. #2295C22semidirect
298. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#598642
#591362
#590392
#578662
#563792
#538762
#529852
#529632
#506422
#460492
#456012
#451042
#450382
#426092
#425662
#425552
#424472
#396282
#394052
#393492
#393412
#392012
#391692
#389322
#378362
#376372
#373362
#372682
#364722
#361542
#361222
#352892
#352372
#348032
#346812