Finite Group Databasebeta

← #8425171

Subgroups — #8425171

Order 512.

5037 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#59451C211yesmaximal, characteristic, complemented
2#59272C212yesmaximal, complemented
3#59079C211yesmaximal, characteristic, complemented
4#59044C212yesmaximal, complemented
5#59035C211yesmaximal, characteristic, complemented
6#55006C214yesmaximal, complemented
7#54948C214yesmaximal, complemented
8#53129C212yesmaximal, complemented
9#53068C212yesmaximal, complemented
10#53065C212yesmaximal, complemented
11#53003C212yesmaximal, complemented
12#52533C214yesmaximal, complemented
13#42563C212yesmaximal, complemented
14#42544C212yesmaximal, complemented
15#42471C212yesmaximal, complemented
16#42432C212yesmaximal, complemented
17#40774C214yesmaximal, complemented
18#39795C212yesmaximal, complemented
19#39479C211yesmaximal, characteristic, complemented
20#39342C211yesmaximal, characteristic, complemented
21#39237C212yesmaximal, complemented
22#39147C211yesmaximal, characteristic, complemented
23#39126C211yesmaximal, characteristic, complemented
24#37952C212yesmaximal, complemented
25#37786C212yesmaximal, complemented
26#37634C211yesmaximal, characteristic, complemented
27#37616C211yesmaximal, characteristic, complemented
28#37512C212yesmaximal, complemented
29#37493C212yesmaximal, complemented
30#36463C211yesmaximal, characteristic, complemented
31#36289C211yesmaximal, characteristic, complemented
32#36150C211yesmaximal, characteristic, complemented
33#34932C211yesmaximal, characteristic, complemented
34#34917C211yesmaximal, characteristic, complemented
35#34889C211yesmaximal, characteristic, complemented
36C2×#554C2211yescharacteristic
37C2×#546C2212yes—
38C2×D42C2211yescharacteristic
39C2×#535C2212yes—
40C2×#533C2211yescharacteristic, complemented
41C2×#532C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#529C2212yes—
44C2×#529C2211yescharacteristic, complemented
45#2858C2211yescharacteristic
46#2857C2211yescharacteristic, complemented
47#2856C2211yescharacteristic
48#2854C2212yescomplemented
49#2850C2212yes—
50#2837C2214yescomplemented
51#2836C2214yescomplemented
52#2835C2214yescomplemented
53#2831C2214yescomplemented
54#2829C2214yescomplemented
55#2829C2214yescomplemented
56#2828C2214yescomplemented
57#2828C2214yescomplemented
58#2828C2214yescomplemented
59#2827C2214yescomplemented
60#2826C2214yescomplemented
61#2816C2214yescomplemented
62#2813C2214yescomplemented
63#2812C2214yescomplemented
64#2803C2214yescomplemented
65#2800C2214yescomplemented
66#2797C2214yescomplemented
67#2787C2214yescomplemented
68#2786C2214yescomplemented
69#2785C2214yescomplemented
70#2781C2214yescomplemented
71#2778C2214yescomplemented
72#2773C2214yescomplemented
73#2761C2214yescomplemented
74#2757C2214yescomplemented
75#2754C2214yescomplemented
76#2753C2214yescomplemented
77#2753C2214yescomplemented
78#2753C2214yescomplemented
79#2753C2214yescomplemented
80#2744C2214yescomplemented
81#2735C2214yescomplemented
82#2728C2214yescomplemented
83#2717C2214yescomplemented
84#2715C2214yescomplemented
85#2709C2214yescomplemented
86#2709C2214yescomplemented
87#2702C2214yescomplemented
88#2702C2214yescomplemented
89#2701C2214yescomplemented
90#2697C2214yescomplemented
91#2695C2214yescomplemented
92#2686C2214yescomplemented
93#2685C2214yescomplemented
94#2685C2214yescomplemented
95#2685C2214yescomplemented
96#2681C2214yescomplemented
97#2673C2214yescomplemented
98#2670C2214yes—
99#2669C2214yes—
100#2668C2214yes—
101#2661C2214yescomplemented
102#2660C2212yescomplemented
103#2648C2214yescomplemented
104#2648C2214yescomplemented
105#2648C2214yescomplemented
106#2644C2212yescomplemented
107#2641C2212yes—
108#2636C2214yescomplemented
109#2636C2214yescomplemented
110#2632C2214yescomplemented
111#2630C2214yescomplemented
112#2629C2212yescomplemented
113#2624C2212yes—
114#2622C2214yescomplemented
115#2622C2214yescomplemented
116#2620C2212yescomplemented
117#2620C2212yescomplemented
118#2620C2212yescomplemented
119#2619C2212yescomplemented
120#2617C2214yescomplemented
121#2616C2212yescomplemented
122#2616C2212yescomplemented
123#2615C2212yes—
124#2597C2214yescomplemented
125#2596C2214yescomplemented
126#2593C2214yescomplemented
127#2578C2212yescomplemented
128#2576C2212yescomplemented
129#2574C2214yescomplemented
130#2570C2212yescomplemented
131#2570C2211yescharacteristic, complemented
132#2568C2211yescharacteristic, complemented
133#2566C2211yescharacteristic
134#2566C2212yescomplemented
135#2566C2212yescomplemented
136#2563C2211yescharacteristic
137#2563C2211yescharacteristic, complemented
138#2562C2212yescomplemented
139#2562C2211yescharacteristic, complemented
140#2562C2212yescomplemented
141#2559C2212yescomplemented
142#2557C2214yescomplemented
143#2557C2212yescomplemented
144#2554C2214yescomplemented
145#2553C2214yescomplemented
146#2552C2211yescharacteristic, complemented
147#2550C2211yescharacteristic, complemented
148#2548C2211yescharacteristic
149#2547C2211yescharacteristic
150#2544C2211yescharacteristic
151#2544C2212yescomplemented
152#2542C2211yescharacteristic
153#2542C2211yescharacteristic, complemented
154#2541C2212yes—
155#2541C2211yescharacteristic
156#2540C2211yescharacteristic
157#2540C2212yescomplemented
158#2537C2212yes—
159#2537C2211yescharacteristic
160#2537C2212yes—
161#2536C2212yescomplemented
162#2536C2212yescomplemented
163#2536C2212yescomplemented
164#2535C2211yescharacteristic
165#2535C2211yescharacteristic, complemented
166#2521C2212yescomplemented
167#2515C2212yescomplemented
168#2513C2212yes—
169#2513C2212yescomplemented
170#2513C2212yescomplemented
171#2512C2212yes—
172#2509C2212yescomplemented
173#2504C2212yes—
174#2500C2212yes—
175#2500C2212yescomplemented
176#2499C2212yescomplemented
177#2497C2211yescharacteristic, complemented
178#2496C2212yescomplemented
179#2496C2212yescomplemented
180#2494C2211yescharacteristic, complemented
181#2492C2211yescharacteristic, complemented
182#2491C2212yes—
183#2490C2211yescharacteristic
184#2490C2212yes—
185#2490C2212yes—
186#2490C2212yescomplemented
187#2490C2212yescomplemented
188#2490C2212yescomplemented
189#2489C2212yescomplemented
190#2489C2212yescomplemented
191#2489C2212yescomplemented
192#2489C2212yescomplemented
193#2485C2212yescomplemented
194#2480C2214yescomplemented
195#2476C2214yescomplemented
196#2474C2214yescomplemented
197#2472C2214yes—
198#2472C2214yes—
199#2464C2212yescomplemented
200#2464C2214yescomplemented
201#2459C2214yescomplemented
202#2457C2212yescomplemented
203#2457C2214yescomplemented
204#2454C2212yescomplemented
205#2453C2212yescomplemented
206#2448C2212yes—
207#2448C2212yescomplemented
208#2445C2214yescomplemented
209#2445C2212yescomplemented
210#2442C2212yescomplemented
211#2442C2212yescomplemented
212#2441C2212yescomplemented
213#2435C2212yes—
214#2435C2212yes—
215#2433C2212yes—
216#2428C2211yescharacteristic
217#2427C2212yes—
218#2427C2212yes—
219#2427C2212yes—
220#2427C2212yescomplemented
221#2427C2211yescharacteristic, complemented
222#2426C2212yescomplemented
223#2426C2212yescomplemented
224#2426C2212yescomplemented
225#2426C2212yescomplemented
226#2424C2214yescomplemented
227#2423C2212yescomplemented
228#2422C2212yes—
229#2422C2211yescharacteristic
230#2422C2212yescomplemented
231#2422C2212yescomplemented
232#2422C2212yescomplemented
233#2421C2214yescomplemented
234#2420C2211yescharacteristic
235#2420C2212yescomplemented
236#2418C2214yes—
237#2418C2214yescomplemented
238#2418C2214yescomplemented
239#2416C2212yescomplemented
240#2415C2212yescomplemented
241#2414C2212yes—
242#2414C2212yescomplemented
243#2412C2214yescomplemented
244#2411C2214yescomplemented
245#2408C2212yes—
246#2408C2212yes—
247#2408C2212yes—
248#2407C2212yes—
249#2407C2212yescomplemented
250#2407C2212yescomplemented
251#2407C2212yescomplemented
252#2401C2212yescomplemented
253#2395C2214yescomplemented
254#2395C2212yescomplemented
255#2392C2212yescomplemented
256#2388C2212yescomplemented
257#2369C2211yescharacteristic, complemented
258#2367C2212yes—
259#2367C2212yescomplemented
260#2366C2211yescharacteristic
261#2366C2212yescomplemented
262#2363C2212yescomplemented
263#2362C2212yescomplemented
264#2357C2212yescomplemented
265#2355C2212yescomplemented
266#2354C2211yescharacteristic
267#2352C2212yescomplemented
268Q8×C4⋊C4C2211yescharacteristic, complemented
269#2342C2214yescomplemented
270#2341C2212yescomplemented
271D4×C22⋊C4C2212yes—
272D4×C22⋊C4C2212yes—
273D4×C22⋊C4C2212yes—
274#2335C2214yescomplemented
275#2326C2212yescomplemented
276#2324C2212yes—
277#2314C2212yescomplemented
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×#125C2211yescharacteristic, complemented
280C4×#124C2211yescharacteristic
281C4×C22⋊Q8C2211yescharacteristic, complemented
282C4×C22⋊Q8C2212yescomplemented
283C4×#123C2212yescomplemented
284C4×#121C2211yescharacteristic
285C4×#121C2211yescharacteristic
286C4×#121C2211yescharacteristic
287C4×#121C2212yescomplemented
288C4×#121C2212yescomplemented
289C4×#121C2212yescomplemented
290#2297C2212yescomplemented
291C2×#390C2212yes—
292#2290C2212yescomplemented
293#2285C2211yescharacteristic, complemented
294#2285C2212yescomplemented
295#2283C2211yescharacteristic, complemented
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic, complemented
298C42×D4C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C22×#41C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303#554—44no—
304#546—48no—
305D42—44no—
306#535—48no—
307#533—44no—
308#532—44no—
309#532—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×#127C2311yescharacteristic
314C2×#127C2312yes—
315C2×#127C2311yescharacteristic
316C2×#127C2314yes—
317#529—44no—
318#529—48no—
319C2×#126C2312yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#125C2311yescharacteristic
323C2×#125C2312yes—
324C2×#125C2312yes—
325C2×#125C2311yescharacteristic
326C2×#125C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2314yes—
333C2×#124C2311yescharacteristic
334C2×#124C2311yescharacteristic
335C2×#124C2312yes—
336C2×#123C2314yes—
337C2×#123C2312yes—
338C2×#123C2314yes—
339C2×#123C2312yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2311yescharacteristic
350C2×C22⋊Q8C2311yescharacteristic
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×#121C2312yes—
354C2×#121C2311yescharacteristic
355C2×#121C2311yescharacteristic
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2311yescharacteristic
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2312yes—
371C2×#121C2311yescharacteristic
372C2×#121C2312yes—
373C2×#121C2314yes—
374C2×#120C2314yes—
375C2×#120C2314yes—
376C2×#120C2314yes—
377C2×#120C2314yes—
378C2×#120C2314yes—
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2312yes—
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2312yes—
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2314yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2311yescharacteristic
405C2×C4×D4C2314yes—
406C2×#117C2312yes—
407C2×#117C2312yes—
408C2×#117C2314yes—
409C2×#117C2312yes—
410C2×#117C2312yes—
411C22×C4⋊C4C2312yes—
412C22×C22⋊C4C2314yes—
413C22×C22⋊C4C2314yes—
414C22×C22⋊C4C2314yes—
415C22×C42C2311yescharacteristic
416C22×C42C2311yescharacteristic
417C22×C42C2312yes—
418C22×C42C2312yes—
419#401C2312yes—
420#400C2312yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2312yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2312yes—
431#400C2312yes—
432#399C2314yes—
433#399C2314yes—
434#399C2314yes—
435#399C2314yes—
436#399C2314yes—
437#399C2312yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2312yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2312yes—
463#397C2312yes—
464#397C2312yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2312yes—
469#397C2314yes—
470#397C2312yes—
471#397C2314yes—
472#397C2312yes—
473#397C2312yes—
474#396C2312yes—
475#396C2312yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#395C2314yes—
488#395C2312yes—
489#395C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2312yes—
497#394C2314yes—
498#394C2314yes—
499#394C2312yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2312yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2312yes—
518#394C2312yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2312yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2312yes—
530#394C2312yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2314yes—
535#393C2314yes—
536#393C2314yes—
537#393C2314yes—
538#393C2312yes—
539#392C2314yes—
540#392C2312yes—
541#392C2314yes—
542#392C2312yes—
543#392C2312yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2314yes—
549#392C2314yes—
550#392C2314yes—
551#392C2312yes—
552#392C2314yes—
553#391C2312yes—
554#391C2312yes—
555#391C2312yes—
556#391C2312yes—
557#391C2312yes—
558#391C2312yes—
559#391C2311yescharacteristic
560#391C2311yescharacteristic
561#391C2312yes—
562#391C2314yes—
563#391C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2311yescharacteristic
567#390C2311yescharacteristic
568#390C2312yes—
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2314yes—
573#390C2314yes—
574#390C2314yes—
575#390C2312yes—
576#390C2314yes—
577#390C2312yes—
578#390C2314yes—
579#390C2314yes—
580#390C2311yescharacteristic
581#390C2312yes—
582#390C2312yes—
583#390C2312yes—
584#390C2312yes—
585#390C2312yes—
586#390C2314yes—
587#390C2314yes—
588#390C2312yes—
589#390C2312yes—
590#390C2312yes—
591#390C2312yes—
592#390C2314yes—
593#390C2312yes—
594#390C2312yes—
595#390C2312yes—
596#390C2311yescharacteristic
597#390C2312yes—
598#389C2311yescharacteristic
599#389C2311yescharacteristic
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2311yescharacteristic
604#389C2311yescharacteristic
605#389C2312yes—
606#389C2314yes—
607#389C2314yes—
608#389C2314yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2312yes—
613#389C2311yescharacteristic
614#389C2311yescharacteristic
615#389C2312yes—
616#389C2312yes—
617#388C2314yes—
618#388C2312yes—
619#388C2314yes—
620#388C2312yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2312yes—
631#388C2312yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2312yes—
641#388C2312yes—
642#388C2314yes—
643#388C2314yes—
644#388C2312yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2314yes—
657#388C2312yes—
658#388C2312yes—
659#388C2312yes—
660#387C2312yes—
661#387C2312yes—
662#387C2314yes—
663#387C2314yes—
664#387C2312yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2312yes—
670#387C2314yes—
671#387C2312yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2312yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#386C2312yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2312yes—
695#386C2312yes—
696#386C2314yes—
697#386C2312yes—
698#386C2314yes—
699#386C2312yes—
700#386C2312yes—
701#386C2312yes—
702#386C2312yes—
703#386C2312yes—
704#385C2312yes—
705#385C2312yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2312yes—
717#385C2312yes—
718#384C2311yescharacteristic
719#384C2311yescharacteristic
720#384C2312yes—
721#384C2312yes—
722#384C2312yes—
723#384C2312yes—
724#384C2311yescharacteristic
725#383C2312yes—
726#382C2311yescharacteristic
727#382C2312yes—
728#382C2312yes—
729#382C2311yescharacteristic
730#382C2311yescharacteristic
731#382C2312yes—
732#382C2311yescharacteristic
733#382C2314yes—
734#382C2312yes—
735#382C2314yes—
736#382C2314yes—
737#381C2312yes—
738#381C2312yes—
739#381C2314yes—
740#380C2311yescharacteristic
741#380C2311yescharacteristic
742#380C2312yes—
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2311yescharacteristic
747#380C2312yes—
748#380C2311yescharacteristic
749#380C2312yes—
750#380C2312yes—
751#380C2311yescharacteristic
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2314yes—
758#380C2314yes—
759#380C2311yescharacteristic
760#380C2311yescharacteristic
761#380C2314yes—
762#380C2311yescharacteristic
763#380C2312yes—
764#380C2312yes—
765#380C2314yes—
766#379C2314yes—
767#379C2314yes—
768#379C2314yes—
769#379C2314yes—
770#379C2314yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2312yes—
817#376C2312yes—
818C43C2311yescharacteristic
819C25C2414yes—
820C2×#41—44no—
821C2×#41—44no—
822C2×#41—44no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—44no—
826C22×Q8C2411yescharacteristic
827C22×Q8C2412yes—
828C22×Q8C2412yes—
829C22×Q8C2412yes—
830C22×D4—28no—
831C22×D4—44no—
832C22×D4—44no—
833C22×D4—44no—
834C22×D4—44no—
835C22×D4—44no—
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2414yes—
846C22×D4C2411yescharacteristic
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2412yes—
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2414yes—
870C23×C4C2412yes—
871C23×C4C2414yes—
872C23×C4C2414yes—
873C23×C4C2412yes—
874C4⋊Q8—24no—
875C4⋊Q8—24no—
876C4⋊Q8—42no—
877#127—24no—
878#127—44no—
879#127—42no—
880#127—48no—
881#126—44no—
882#126—48no—
883#126—84no—
884#125—42no—
885#125—42no—
886#125—44no—
887#125—44no—
888#125—44no—
889#124—28no—
890#124—44no—
891#124—44no—
892#124—44no—
893#124—42no—
894#124—42no—
895#124—44no—
896#124—48no—
897#124—82no—
898#123—48no—
899#123—48no—
900#123—48no—
901#123—44no—
902#123—44no—
903#123—84no—
904C22⋊Q8—48no—
905C22⋊Q8—42no—
906C22⋊Q8—44no—
907C22⋊Q8—44no—
908C22⋊Q8—42no—
909C22⋊Q8—44no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—82no—
915#121—28no—
916#121—24no—
917#121—24no—
918#121—44no—
919#121—44no—
920#121—48no—
921#121—42no—
922#121—44no—
923#121—44no—
924#121—44no—
925#121—42no—
926#121—44no—
927#121—42no—
928#121—42no—
929#121—44no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—44no—
934#121—84no—
935#121—82no—
936#120—48no—
937#120—48no—
938#120—48no—
939#120—48no—
940#120—84no—
941C4×Q8—24no—
942C4×Q8—44no—
943C4×Q8—44no—
944C4×Q8—44no—
945C4×Q8—44no—
946C4×D4—24no—
947C4×D4—24no—
948C4×D4—24no—
949C4×D4—24no—
950C4×D4—42no—
951C4×D4—42no—
952C4×D4—44no—
953C4×D4—42no—
954C4×D4—42no—
955C4×D4—44no—
956C4×D4—44no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—42no—
962C4×D4—42no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—48no—
967C4×D4—84no—
968#117—44no—
969#117—44no—
970#117—48no—
971#117—44no—
972#117—44no—
973C2×C4⋊C4—44no—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C22⋊C4—48no—
1031C2×C22⋊C4—48no—
1032C2×C22⋊C4—84no—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2411yescharacteristic
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2411yescharacteristic
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2411yescharacteristic
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C42—24no—
1111C2×C42—24no—
1112C2×C42—44no—
1113C2×C42—44no—
1114C2×C42C2411yescharacteristic
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130C2×C42C2412yes—
1131C2×C42C2414yes—
1132C2×C42C2414yes—
1133C2×C42C2414yes—
1134C2×C42C2414yes—
1135C2×C42C2414yes—
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2411yescharacteristic
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2411yescharacteristic
1146#95C2411yescharacteristic
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2411yescharacteristic
1152#95C2411yescharacteristic
1153#95C2412yes—
1154#95C2411yescharacteristic
1155#95C2412yes—
1156#95C2411yescharacteristic
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201C24—28no—
1202C24—44no—
1203C24—44no—
1204C24—44no—
1205C24—44no—
1206C24—44no—
1207C24—44no—
1208C24C2512yes—
1209C24C2514yes—
1210C24C2512yes—
1211C24C2511yescharacteristic
1212C24C2511yescharacteristic
1213C24C2512yes—
1214#41—816no—
1215#41—816no—
1216C2×Q8—22no—
1217C2×Q8—24no—
1218C2×Q8—24no—
1219C2×Q8—24no—
1220C2×Q8—22no—
1221C2×Q8—24no—
1222C2×Q8—22no—
1223C2×Q8—42no—
1224C2×Q8—42no—
1225C2×Q8—42no—
1226C2×Q8—42no—
1227C2×Q8—42no—
1228C2×D4—28no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—28no—
1232C2×D4—22no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—24no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—24no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—24no—
1245C2×D4—24no—
1246C2×D4—22no—
1247C2×D4—41no—
1248C2×D4—41no—
1249C2×D4—41no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C2×D4—44no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—42no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—44no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—44no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—42no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—42no—
1284C2×D4—44no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—816no—
1294C2×D4—816no—
1295C2×D4H(5,𝔽2)14yes—
1296C22×C4—24no—
1297C22×C4—22no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—24no—
1302C22×C4—24no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—24no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—24no—
1318C22×C4—24no—
1319C22×C4—22no—
1320C22×C4—22no—
1321C22×C4—24no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—44no—
1327C22×C4—42no—
1328C22×C4—44no—
1329C22×C4—42no—
1330C22×C4—41no—
1331C22×C4—41no—
1332C22×C4—42no—
1333C22×C4—42no—
1334C22×C4—42no—
1335C22×C4—41no—
1336C22×C4—41no—
1337C22×C4—44no—
1338C22×C4—44no—
1339C22×C4—44no—
1340C22×C4—44no—
1341C22×C4—44no—
1342C22×C4—44no—
1343C22×C4—44no—
1344C22×C4C2511yescharacteristic
1345C22×C4C2511yescharacteristic
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2512yes—
1349C22×C4C2511yescharacteristic
1350C22×C4C2511yescharacteristic
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2512yes—
1358C22×C4C2512yes—
1359C22×C4C2511yescharacteristic
1360C22×C4C2511yescharacteristic
1361C22×C4C2512yes—
1362C22×C4C2514yes—
1363C22×C4C2511yescharacteristic
1364C22×C4C2512yes—
1365C22×C4C2514yes—
1366C22×C4C2512yes—
1367C22×C4C2514yes—
1368C22×C4C2511yescharacteristic
1369C22×C4C2511yescharacteristic
1370C22×C4C2511yescharacteristic
1371C22×C4C2511yescharacteristic
1372C22×C4C2511yescharacteristic
1373C4⋊C4—22no—
1374C4⋊C4—24no—
1375C4⋊C4—22no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—22no—
1379C4⋊C4—22no—
1380C4⋊C4—22no—
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—24no—
1384C4⋊C4—24no—
1385C4⋊C4—24no—
1386C4⋊C4—22no—
1387C4⋊C4—22no—
1388C4⋊C4—22no—
1389C4⋊C4—24no—
1390C4⋊C4—22no—
1391C4⋊C4—22no—
1392C4⋊C4—24no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—44no—
1398C4⋊C4—42no—
1399C4⋊C4—44no—
1400C4⋊C4—41no—
1401C4⋊C4—41no—
1402C4⋊C4—41no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—44no—
1409C4⋊C4—42no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—42no—
1415C4⋊C4—44no—
1416C4⋊C4—42no—
1417C4⋊C4—44no—
1418C4⋊C4—42no—
1419C4⋊C4—44no—
1420C4⋊C4—44no—
1421C4⋊C4—44no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—42no—
1425C4⋊C4—44no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C22⋊C4—24no—
1430C22⋊C4—28no—
1431C22⋊C4—28no—
1432C22⋊C4—24no—
1433C22⋊C4—28no—
1434C22⋊C4—24no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—24no—
1439C22⋊C4—28no—
1440C22⋊C4—22no—
1441C22⋊C4—22no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—42no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—44no—
1453C22⋊C4—42no—
1454C22⋊C4—44no—
1455C22⋊C4—42no—
1456C22⋊C4—44no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—41no—
1462C22⋊C4—41no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—42no—
1466C22⋊C4—41no—
1467C22⋊C4—41no—
1468C22⋊C4—44no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—44no—
1474C22⋊C4—44no—
1475C22⋊C4—42no—
1476C22⋊C4—44no—
1477C22⋊C4—42no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—42no—
1489C22⋊C4—44no—
1490C22⋊C4—44no—
1491C22⋊C4—42no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—44no—
1498C22⋊C4—42no—
1499C22⋊C4—42no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—42no—
1503C22⋊C4—44no—
1504C22⋊C4—42no—
1505C22⋊C4—42no—
1506C42—22no—
1507C42—22no—
1508C42—22no—
1509C42—22no—
1510C42—22no—
1511C42—22no—
1512C42—22no—
1513C42—24no—
1514C42—24no—
1515C42—22no—
1516C42—24no—
1517C42—24no—
1518C42—24no—
1519C42—22no—
1520C42—22no—
1521C42—22no—
1522C42—42no—
1523C42—42no—
1524C42—42no—
1525C42—42no—
1526C42—44no—
1527C42—44no—
1528C42—44no—
1529C42—44no—
1530C42—44no—
1531C42—41no—
1532C42H(5,𝔽2)14yes—
1533C23—22no—
1534C23—22no—
1535C23—22no—
1536C23—22no—
1537C23—22no—
1538C23—22no—
1539C23—22no—
1540C23—22no—
1541C23—22no—
1542C23—21no—
1543C23—24no—
1544C23—24no—
1545C23—21no—
1546C23—22no—
1547C23—21no—
1548C23—21no—
1549C23—24no—
1550C23—21no—
1551C23—22no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—24no—
1561C23—24no—
1562C23—22no—
1563C23—21no—
1564C23—21no—
1565C23—21no—
1566C23—22no—
1567C23—24no—
1568C23—22no—
1569C23—22no—
1570C23—21no—
1571C23—21no—
1572C23—24no—
1573C23—22no—
1574C23—88no—
1575C23—88no—
1576C23—88no—
1577C23—88no—
1578C23—88no—
1579C23—164no—
1580C23—164no—
1581C23C2×H(5,𝔽2)14yes—
1582C23C2611yescharacteristic
1583Q8—44no—
1584Q8—48no—
1585Q8—84no—
1586Q8—84no—
1587D4—28no—
1588D4—44no—
1589D4—44no—
1590D4—48no—
1591D4—44no—
1592D4—48no—
1593D4—84no—
1594D4—84no—
1595D4—84no—
1596D4—88no—
1597D4—88no—
1598D4—84no—
1599D4—88no—
1600D4—84no—
1601D4—84no—
1602D4—88no—
1603D4—84no—
1604D4—84no—
1605D4—84no—
1606D4—88no—
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—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—24no—
1653C2×C4—24no—
1654C2×C4—21no—
1655C2×C4—22no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—21no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—21no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—22no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—24no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—22no—
1679C2×C4—21no—
1680C2×C4—24no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—24no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—48no—
1689C2×C4—44no—
1690C2×C4—44no—
1691C2×C4—48no—
1692C2×C4—48no—
1693C2×C4—48no—
1694C2×C4—44no—
1695C2×C4—44no—
1696C2×C4—84no—
1697C2×C4—82no—
1698C2×C4—82no—
1699C2×C4—84no—
1700C2×C4—84no—
1701C2×C4—88no—
1702C2×C4—164no—
1703C2×C4—164no—
1704C2×C4C2×H(5,𝔽2)12yes—
1705C2×C4C2×H(5,𝔽2)12yes—
1706C2×C4C2×H(5,𝔽2)12yes—
1707C2×C4C2×H(5,𝔽2)12yes—
1708C2×C4#58512yes—
1709C2×C4#58512yes—
1710C2×C4#58512yes—
1711C2×C4#58512yes—
1712C22—24no—
1713C22—24no—
1714C22—24no—
1715C22—42no—
1716C22—42no—
1717C22—42no—
1718C22—42no—
1719C22—41no—
1720C22—41no—
1721C22—42no—
1722C22—42no—
1723C22—44no—
1724C22—41no—
1725C22—41no—
1726C22—42no—
1727C22—44no—
1728C22—42no—
1729C22—41no—
1730C22—41no—
1731C22—42no—
1732C22—44no—
1733C22—42no—
1734C22—42no—
1735C22—41no—
1736C22—41no—
1737C22—42no—
1738C22—44no—
1739C22—42no—
1740C22—44no—
1741C22—41no—
1742C22—41no—
1743C22—42no—
1744C22—42no—
1745C22—44no—
1746C22—41no—
1747C22—41no—
1748C22—42no—
1749C22—41no—
1750C22—41no—
1751C22—42no—
1752C22—44no—
1753C22—42no—
1754C22—1616no—
1755C22C22×H(5,𝔽2)11yescharacteristic
1756C22C22×H(5,𝔽2)11yescharacteristic
1757C22C2×#58511yescharacteristic
1758C22C2×#58511yescharacteristic
1759C22C2×#58511yescharacteristic
1760C22C2×#58511yescharacteristic
1761C22H(7,𝔽2)11yescharacteristic
1762C4—22no—
1763C4—22no—
1764C4—41no—
1765C4—42no—
1766C4—41no—
1767C4—42no—
1768C4—44no—
1769C4—41no—
1770C4—41no—
1771C4—42no—
1772C4—42no—
1773C4—42no—
1774C4—41no—
1775C4—42no—
1776C4—42no—
1777C4—42no—
1778C4—41no—
1779C4—42no—
1780C4—42no—
1781C4—44no—
1782C4—42no—
1783C4—41no—
1784C4—42no—
1785C4—41no—
1786C4—41no—
1787C4—42no—
1788C4—44no—
1789C4#355114yes—
1790C4#355814yes—
1791C2—44no—
1792C2—81no—
1793C2—81no—
1794C2—82no—
1795C2—84no—
1796C2—82no—
1797C2C2×#355811yescharacteristic
1798C2C2×#355111yescharacteristic
1799C2#6276211yescharacteristic
1800C2#6292011yescharacteristic
1801C2#6293811yescharacteristic
1802C2#6295511yescharacteristic
1803C2#6301811yescharacteristic
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. #59451C2semidirect
2. #59272C2semidirect
3. #59079C2semidirect
4. #59044C2semidirect
5. #59035C2semidirect
6. #55006C2semidirect
7. #54948C2semidirect
8. #53129C2semidirect
9. #53068C2semidirect
10. #53065C2semidirect
11. #53003C2semidirect
12. #52533C2semidirect
13. #42563C2semidirect
14. #42544C2semidirect
15. #42471C2semidirect
16. #42432C2semidirect
17. #40774C2semidirect
18. #39795C2semidirect
19. #39479C2semidirect
20. #39342C2semidirect
21. #39237C2semidirect
22. #39147C2semidirect
23. #39126C2semidirect
24. #37952C2semidirect
25. #37786C2semidirect
26. #37634C2semidirect
27. #37616C2semidirect
28. #37512C2semidirect
29. #37493C2semidirect
30. #36463C2semidirect
31. #36289C2semidirect
32. #36150C2semidirect
33. #34932C2semidirect
34. #34917C2semidirect
35. #34889C2semidirect
40. C2×#533C22semidirect
44. C2×#529C22semidirect
46. #2857C22semidirect
48. #2854C22semidirect
50. #2837C22semidirect
51. #2836C22semidirect
52. #2835C22semidirect
53. #2831C22semidirect
54. #2829C22semidirect
55. #2829C22semidirect
56. #2828C22semidirect
57. #2828C22semidirect
58. #2828C22semidirect
59. #2827C22semidirect
60. #2826C22semidirect
61. #2816C22semidirect
62. #2813C22semidirect
63. #2812C22semidirect
64. #2803C22semidirect
65. #2800C22semidirect
66. #2797C22semidirect
67. #2787C22semidirect
68. #2786C22semidirect
69. #2785C22semidirect
70. #2781C22semidirect
71. #2778C22semidirect
72. #2773C22semidirect
73. #2761C22semidirect
74. #2757C22semidirect
75. #2754C22semidirect
76. #2753C22semidirect
77. #2753C22semidirect
78. #2753C22semidirect
79. #2753C22semidirect
80. #2744C22semidirect
81. #2735C22semidirect
82. #2728C22semidirect
83. #2717C22semidirect
84. #2715C22semidirect
85. #2709C22semidirect
86. #2709C22semidirect
87. #2702C22semidirect
88. #2702C22semidirect
89. #2701C22semidirect
90. #2697C22semidirect
91. #2695C22semidirect
92. #2686C22semidirect
93. #2685C22semidirect
94. #2685C22semidirect
95. #2685C22semidirect
96. #2681C22semidirect
97. #2673C22semidirect
101. #2661C22semidirect
102. #2660C22semidirect
103. #2648C22semidirect
104. #2648C22semidirect
105. #2648C22semidirect
106. #2644C22semidirect
108. #2636C22semidirect
109. #2636C22semidirect
110. #2632C22semidirect
111. #2630C22semidirect
112. #2629C22semidirect
114. #2622C22semidirect
115. #2622C22semidirect
116. #2620C22semidirect
117. #2620C22semidirect
118. #2620C22semidirect
119. #2619C22semidirect
120. #2617C22semidirect
121. #2616C22semidirect
122. #2616C22semidirect
124. #2597C22semidirect
125. #2596C22semidirect
126. #2593C22semidirect
127. #2578C22semidirect
128. #2576C22semidirect
129. #2574C22semidirect
130. #2570C22semidirect
131. #2570C22semidirect
132. #2568C22semidirect
134. #2566C22semidirect
135. #2566C22semidirect
137. #2563C22semidirect
138. #2562C22semidirect
139. #2562C22semidirect
140. #2562C22semidirect
141. #2559C22semidirect
142. #2557C22semidirect
143. #2557C22semidirect
144. #2554C22semidirect
145. #2553C22semidirect
146. #2552C22semidirect
147. #2550C22semidirect
151. #2544C22semidirect
153. #2542C22semidirect
157. #2540C22semidirect
161. #2536C22semidirect
162. #2536C22semidirect
163. #2536C22semidirect
165. #2535C22semidirect
166. #2521C22semidirect
167. #2515C22semidirect
169. #2513C22semidirect
170. #2513C22semidirect
172. #2509C22semidirect
175. #2500C22semidirect
176. #2499C22semidirect
177. #2497C22semidirect
178. #2496C22semidirect
179. #2496C22semidirect
180. #2494C22semidirect
181. #2492C22semidirect
186. #2490C22semidirect
187. #2490C22semidirect
188. #2490C22semidirect
189. #2489C22semidirect
190. #2489C22semidirect
191. #2489C22semidirect
192. #2489C22semidirect
193. #2485C22semidirect
194. #2480C22semidirect
195. #2476C22semidirect
196. #2474C22semidirect
199. #2464C22semidirect
200. #2464C22semidirect
201. #2459C22semidirect
202. #2457C22semidirect
203. #2457C22semidirect
204. #2454C22semidirect
205. #2453C22semidirect
207. #2448C22semidirect
208. #2445C22semidirect
209. #2445C22semidirect
210. #2442C22semidirect
211. #2442C22semidirect
212. #2441C22semidirect
220. #2427C22semidirect
221. #2427C22semidirect
222. #2426C22semidirect
223. #2426C22semidirect
224. #2426C22semidirect
225. #2426C22semidirect
226. #2424C22semidirect
227. #2423C22semidirect
230. #2422C22semidirect
231. #2422C22semidirect
232. #2422C22semidirect
233. #2421C22semidirect
235. #2420C22semidirect
237. #2418C22semidirect
238. #2418C22semidirect
239. #2416C22semidirect
240. #2415C22semidirect
242. #2414C22semidirect
243. #2412C22semidirect
244. #2411C22semidirect
249. #2407C22semidirect
250. #2407C22semidirect
251. #2407C22semidirect
252. #2401C22semidirect
253. #2395C22semidirect
254. #2395C22semidirect
255. #2392C22semidirect
256. #2388C22semidirect
257. #2369C22semidirect
259. #2367C22semidirect
261. #2366C22semidirect
262. #2363C22semidirect
263. #2362C22semidirect
264. #2357C22semidirect
265. #2355C22semidirect
267. #2352C22semidirect
268. Q8×C4⋊C4C22semidirect
269. #2342C22semidirect
270. #2341C22semidirect
274. #2335C22semidirect
275. #2326C22semidirect
277. #2314C22semidirect
278. C4×C4⋊Q8C22semidirect
279. C4×#125C22semidirect
281. C4×C22⋊Q8C22semidirect
282. C4×C22⋊Q8C22semidirect
283. C4×#123C22semidirect
287. C4×#121C22semidirect
288. C4×#121C22semidirect
289. C4×#121C22semidirect
290. #2297C22semidirect
292. #2290C22semidirect
293. #2285C22semidirect
294. #2285C22semidirect
295. #2283C22semidirect
297. C42×D4C22semidirect
298. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#594512
#592722
#590792
#590442
#590352
#550062
#549482
#531292
#530682
#530652
#530032
#525332
#425632
#425442
#424712
#424322
#407742
#397952
#394792
#393422
#392372
#391472
#391262
#379522
#377862
#376342
#376162
#375122
#374932
#364632
#362892
#361502
#349322
#349172
#348892