Finite Group Databasebeta

← #8467122

Subgroups — #8467122

Order 512.

5052 conjugacy classes of subgroups.

The subgroup lattice has 1814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59412C211yesmaximal, characteristic, complemented
2#59244C211yesmaximal, characteristic, complemented
3#59233C211yesmaximal, characteristic, complemented
4#58154C214yesmaximal, complemented
5#57367C214yesmaximal, complemented
6#55305C214yesmaximal, complemented
7#53116C212yesmaximal, complemented
8#53103C212yesmaximal, complemented
9#49751C214yesmaximal, complemented
10#45641C212yesmaximal, complemented
11#45518C212yesmaximal, complemented
12#45404C212yesmaximal, complemented
13#44961C212yesmaximal, complemented
14#42887C212yesmaximal, complemented
15#42783C212yesmaximal, complemented
16#42778C212yesmaximal, complemented
17#42607C212yesmaximal, complemented
18#40173C212yesmaximal, complemented
19#39960C212yesmaximal, complemented
20#39763C211yesmaximal, characteristic, complemented
21#39273C212yesmaximal, complemented
22#38978C211yesmaximal, characteristic, complemented
23#38910C211yesmaximal, characteristic, complemented
24#38910C211yesmaximal, characteristic, complemented
25#38119C212yesmaximal, complemented
26#37629C211yesmaximal, characteristic, complemented
27#37371C212yesmaximal, complemented
28#37331C212yesmaximal, complemented
29#36576C211yesmaximal, characteristic, complemented
30#36410C211yesmaximal, characteristic, complemented
31#36211C211yesmaximal, characteristic, complemented
32#35247C211yesmaximal, characteristic, complemented
33#35189C211yesmaximal, characteristic, complemented
34#34727C211yesmaximal, characteristic, complemented
35#34708C211yesmaximal, characteristic, complemented
36C2×#556C2212yescomplemented
37C2×#550C2211yescharacteristic
38C2×#548C2212yescomplemented
39C2×#546C2212yes—
40C2×D42C2211yescharacteristic
41C2×#529C2211yescharacteristic
42C2×#529C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic, complemented
44C22×C4×Q8C2211yescharacteristic, complemented
45#2859C2211yescharacteristic, complemented
46#2856C2211yescharacteristic
47#2856C2211yescharacteristic
48#2856C2212yescomplemented
49#2855C2212yescomplemented
50#2854C2212yes—
51#2854C2212yescomplemented
52#2851C2212yescomplemented
53#2850C2212yes—
54#2830C2214yescomplemented
55#2829C2214yescomplemented
56#2829C2214yescomplemented
57#2828C2214yescomplemented
58#2824C2214yescomplemented
59#2819C2214yescomplemented
60#2815C2214yescomplemented
61#2812C2214yescomplemented
62#2808C2214yescomplemented
63#2803C2214yescomplemented
64#2800C2214yescomplemented
65#2800C2214yescomplemented
66#2800C2214yescomplemented
67#2797C2214yescomplemented
68#2797C2214yescomplemented
69#2796C2214yescomplemented
70#2785C2214yescomplemented
71#2777C2214yescomplemented
72#2773C2214yescomplemented
73#2772C2214yescomplemented
74#2772C2214yescomplemented
75#2761C2214yescomplemented
76#2757C2214yescomplemented
77#2753C2214yescomplemented
78#2753C2214yescomplemented
79#2752C2214yescomplemented
80#2752C2214yescomplemented
81#2751C2214yescomplemented
82#2736C2214yescomplemented
83#2735C2214yescomplemented
84#2735C2214yescomplemented
85#2723C2214yescomplemented
86#2723C2214yescomplemented
87#2715C2214yescomplemented
88#2714C2214yescomplemented
89#2714C2214yescomplemented
90#2714C2214yescomplemented
91#2710C2214yescomplemented
92#2705C2214yescomplemented
93#2697C2214yescomplemented
94#2696C2214yescomplemented
95#2688C2214yescomplemented
96#2687C2214yescomplemented
97#2686C2214yescomplemented
98#2685C2214yes—
99#2685C2214yes—
100#2685C2214yescomplemented
101#2684C2214yescomplemented
102#2684C2214yescomplemented
103#2682C2214yescomplemented
104#2678C2214yes—
105#2678C2214yes—
106#2678C2214yes—
107#2678C2214yescomplemented
108#2678C2214yescomplemented
109#2670C2214yescomplemented
110#2668C2214yescomplemented
111#2663C2214yescomplemented
112#2649C2214yescomplemented
113#2644C2212yes—
114#2644C2214yescomplemented
115#2644C2212yescomplemented
116#2644C2212yescomplemented
117#2641C2212yes—
118#2640C2212yescomplemented
119#2640C2212yescomplemented
120#2638C2214yescomplemented
121#2637C2214yescomplemented
122#2632C2214yescomplemented
123#2631C2214yescomplemented
124#2630C2214yescomplemented
125#2624C2212yes—
126#2624C2212yes—
127#2610C2214yescomplemented
128#2602C2214yescomplemented
129#2601C2214yescomplemented
130#2592C2212yes—
131#2584C2212yescomplemented
132#2582C2211yescharacteristic, complemented
133#2582C2211yescharacteristic, complemented
134#2580C2214yescomplemented
135#2563C2212yescomplemented
136#2563C2212yescomplemented
137#2561C2214yescomplemented
138#2551C2211yescharacteristic, complemented
139#2548C2211yescharacteristic
140#2548C2211yescharacteristic
141#2548C2212yescomplemented
142#2540C2212yes—
143#2540C2212yes—
144#2538C2211yescharacteristic
145#2538C2211yescharacteristic
146#2538C2211yescharacteristic
147#2538C2212yescomplemented
148#2538C2211yescharacteristic, complemented
149#2537C2211yescharacteristic
150#2535C2212yes—
151#2535C2212yescomplemented
152#2531C2214yescomplemented
153#2530C2214yescomplemented
154#2526C2214yescomplemented
155#2518C2214yescomplemented
156#2517C2214yescomplemented
157#2513C2212yes—
158#2513C2212yescomplemented
159#2513C2212yescomplemented
160#2513C2212yescomplemented
161#2512C2212yes—
162#2509C2212yescomplemented
163#2499C2212yescomplemented
164#2496C2212yescomplemented
165#2495C2212yescomplemented
166#2491C2212yes—
167#2491C2212yes—
168#2491C2212yescomplemented
169#2490C2212yes—
170#2490C2212yes—
171#2490C2212yescomplemented
172#2490C2212yescomplemented
173#2489C2212yescomplemented
174#2486C2212yescomplemented
175#2485C2212yescomplemented
176#2485C2212yescomplemented
177#2485C2212yescomplemented
178#2485C2212yescomplemented
179#2481C2212yescomplemented
180#2480C2214yescomplemented
181#2479C2212yescomplemented
182#2476C2214yescomplemented
183#2472C2214yescomplemented
184#2471C2212yescomplemented
185#2469C2212yescomplemented
186#2469C2214yescomplemented
187#2467C2212yescomplemented
188#2464C2214yescomplemented
189#2458C2212yescomplemented
190#2458C2214yescomplemented
191#2456C2212yescomplemented
192#2454C2211yescharacteristic, complemented
193#2453C2211yescharacteristic, complemented
194#2452C2212yescomplemented
195#2452C2212yescomplemented
196#2448C2212yes—
197#2448C2211yescharacteristic
198#2448C2211yescharacteristic
199#2447C2212yescomplemented
200#2447C2212yescomplemented
201#2445C2212yescomplemented
202#2443C2212yescomplemented
203#2442C2211yescharacteristic, complemented
204#2441C2211yescharacteristic, complemented
205#2441C2212yescomplemented
206#2439C2212yescomplemented
207#2436C2211yescharacteristic
208#2435C2212yes—
209#2435C2212yes—
210#2433C2212yes—
211#2431C2211yescharacteristic
212#2431C2212yescomplemented
213#2428C2212yes—
214#2428C2211yescharacteristic
215#2426C2211yescharacteristic
216#2426C2214yescomplemented
217#2426C2212yescomplemented
218#2426C2214yescomplemented
219#2424C2214yes—
220#2423C2211yescharacteristic, complemented
221#2422C2212yes—
222#2421C2212yescomplemented
223#2421C2211yescharacteristic, complemented
224#2420C2212yescomplemented
225#2420C2212yescomplemented
226#2416C2211yescharacteristic
227#2416C2214yescomplemented
228#2416C2212yescomplemented
229#2415C2212yescomplemented
230#2415C2212yescomplemented
231#2415C2212yescomplemented
232#2414C2212yes—
233#2414C2212yes—
234#2414C2212yes—
235#2414C2212yes—
236#2414C2211yescharacteristic
237#2414C2212yescomplemented
238#2414C2212yescomplemented
239#2414C2212yescomplemented
240#2414C2212yescomplemented
241#2413C2214yescomplemented
242#2409C2212yescomplemented
243#2409C2211yescharacteristic, complemented
244#2408C2212yes—
245#2408C2212yes—
246#2408C2212yes—
247#2408C2212yes—
248#2408C2212yes—
249#2407C2212yes—
250#2407C2212yescomplemented
251#2407C2212yescomplemented
252#2407C2211yescharacteristic, complemented
253#2398C2212yescomplemented
254#2397C2212yescomplemented
255#2396C2212yescomplemented
256#2392C2212yescomplemented
257#2377C2214yescomplemented
258#2367C2212yescomplemented
259#2365C2212yescomplemented
260#2363C2212yescomplemented
261#2363C2212yescomplemented
262#2363C2212yescomplemented
263#2357C2212yescomplemented
264#2354C2211yescharacteristic
265#2354C2211yescharacteristic
266#2354C2211yescharacteristic, complemented
267Q8×C4⋊C4C2211yescharacteristic, complemented
268#2346C2212yescomplemented
269#2346C2212yescomplemented
270#2341C2212yescomplemented
271D4×C22⋊C4C2212yes—
272#2330C2212yescomplemented
273#2324C2212yescomplemented
274#2323C2212yescomplemented
275#2323C2212yescomplemented
276#2323C2212yescomplemented
277#2321C2214yescomplemented
278#2320C2212yescomplemented
279#2309C2212yes—
280#2309C2212yes—
281C4×#127C2211yescharacteristic
282C4×#127C2211yescharacteristic
283C4×#124C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic, complemented
285C4×#121C2211yescharacteristic
286C4×#121C2211yescharacteristic
287C4×#121C2212yescomplemented
288C4×#121C2211yescharacteristic, complemented
289C4×#121C2212yescomplemented
290C4×#121C2212yescomplemented
291#2297C2212yescomplemented
292#2295C2211yescharacteristic, complemented
293#2295C2211yescharacteristic, complemented
294#2290C2212yescomplemented
295#2290C2212yescomplemented
296#2285C2211yescharacteristic, complemented
297#2285C2211yescharacteristic, complemented
298C42×D4C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C23×Q8C2311yescharacteristic
302C23×D4C2312yes—
303C23×D4C2312yes—
304#556—48no—
305#550—44no—
306#548—48no—
307#546—48no—
308D42—44no—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×#127C2311yescharacteristic
312C2×#127C2311yescharacteristic
313C2×#127C2312yes—
314#529—44no—
315#529—44no—
316C2×#126C2312yes—
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#125C2311yescharacteristic
321C2×#125C2312yes—
322C2×#125C2311yescharacteristic
323C2×#124C2311yescharacteristic
324C2×#124C2314yes—
325C2×#124C2314yes—
326C2×#124C2311yescharacteristic
327C2×#124C2311yescharacteristic
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2314yes—
331C2×#123C2314yes—
332C2×#123C2312yes—
333C2×#123C2312yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2314yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2311yescharacteristic
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2312yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2311yescharacteristic
355C2×#121C2314yes—
356C2×#121C2314yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2311yescharacteristic
360C2×#121C2311yescharacteristic
361C2×#121C2311yescharacteristic
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365C2×#121C2314yes—
366C2×#121C2312yes—
367C2×#120C2314yes—
368C2×#120C2314yes—
369C2×#120C2314yes—
370C2×#120C2314yes—
371C2×#120C2314yes—
372C4×#41—44no—
373C2×C4×Q8—44no—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2314yes—
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2314yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×#117C2312yes—
406C2×#117C2312yes—
407C2×#117C2312yes—
408C2×#117C2312yes—
409C2×#117C2312yes—
410C2×#117C2312yes—
411C2×#117C2311yescharacteristic
412C2×#117C2312yes—
413C2×#117C2312yes—
414C22×C4⋊C4C2312yes—
415C22×C4⋊C4C2311yescharacteristic
416C22×C22⋊C4C2314yes—
417C22×C42C2311yescharacteristic
418C22×C42C2311yescharacteristic
419C22×C42C2312yes—
420C22×C42C2312yes—
421#400C2312yes—
422#400C2314yes—
423#400C2312yes—
424#400C2314yes—
425#400C2312yes—
426#400C2314yes—
427#399C2312yes—
428#399C2312yes—
429#399C2312yes—
430#399C2314yes—
431#399C2314yes—
432#399C2312yes—
433#399C2312yes—
434#399C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2312yes—
439#398C2312yes—
440#398C2312yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2312yes—
446#397C2314yes—
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#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2312yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#396C2312yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2312yes—
479#396C2314yes—
480#396C2312yes—
481#396C2312yes—
482#396C2314yes—
483#395C2314yes—
484#395C2314yes—
485#395C2312yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2312yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2312yes—
514#394C2312yes—
515#394C2312yes—
516#394C2312yes—
517#394C2314yes—
518#394C2314yes—
519#393C2312yes—
520#393C2314yes—
521#393C2314yes—
522#393C2314yes—
523#393C2314yes—
524#393C2312yes—
525#393C2314yes—
526#393C2314yes—
527#393C2314yes—
528#393C2314yes—
529#393C2312yes—
530#392C2312yes—
531#392C2314yes—
532#392C2314yes—
533#392C2314yes—
534#392C2314yes—
535#392C2312yes—
536#392C2314yes—
537#392C2314yes—
538#392C2314yes—
539#392C2314yes—
540#392C2314yes—
541#392C2314yes—
542#392C2312yes—
543#392C2314yes—
544#392C2314yes—
545#392C2312yes—
546#392C2312yes—
547#391C2311yescharacteristic
548#391C2312yes—
549#391C2312yes—
550#391C2312yes—
551#391C2312yes—
552#391C2314yes—
553#391C2311yescharacteristic
554#391C2311yescharacteristic
555#391C2311yescharacteristic
556#391C2311yescharacteristic
557#391C2311yescharacteristic
558#390C2312yes—
559#390C2311yescharacteristic
560#390C2312yes—
561#390C2312yes—
562#390C2311yescharacteristic
563#390C2312yes—
564#390C2312yes—
565#390C2314yes—
566#390C2314yes—
567#390C2311yescharacteristic
568#390C2311yescharacteristic
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2312yes—
574#390C2312yes—
575#390C2314yes—
576#390C2314yes—
577#390C2314yes—
578#390C2314yes—
579#390C2314yes—
580#390C2314yes—
581#390C2314yes—
582#390C2312yes—
583#390C2312yes—
584#390C2314yes—
585#390C2314yes—
586#390C2312yes—
587#390C2314yes—
588#390C2312yes—
589#390C2314yes—
590#390C2312yes—
591#390C2312yes—
592#390C2312yes—
593#390C2312yes—
594#390C2314yes—
595#390C2312yes—
596#390C2312yes—
597#390C2312yes—
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2311yescharacteristic
602#390C2314yes—
603#390C2312yes—
604#390C2311yescharacteristic
605#389C2312yes—
606#389C2312yes—
607#389C2314yes—
608#389C2312yes—
609#389C2312yes—
610#389C2314yes—
611#389C2314yes—
612#389C2312yes—
613#389C2312yes—
614#389C2314yes—
615#389C2312yes—
616#389C2312yes—
617#389C2312yes—
618#389C2314yes—
619#389C2311yescharacteristic
620#389C2311yescharacteristic
621#389C2311yescharacteristic
622#389C2312yes—
623#389C2312yes—
624#389C2312yes—
625#389C2312yes—
626#389C2312yes—
627#389C2312yes—
628#389C2314yes—
629#389C2311yescharacteristic
630#389C2311yescharacteristic
631#389C2311yescharacteristic
632#389C2314yes—
633#389C2312yes—
634#389C2311yescharacteristic
635#389C2311yescharacteristic
636#389C2312yes—
637#388C2312yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2312yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#388C2314yes—
668#388C2314yes—
669#388C2312yes—
670#388C2312yes—
671#388C2312yes—
672#388C2314yes—
673#388C2314yes—
674#388C2312yes—
675#388C2312yes—
676#388C2312yes—
677#388C2314yes—
678#388C2312yes—
679#388C2312yes—
680#388C2312yes—
681#388C2312yes—
682#388C2312yes—
683#387C2314yes—
684#387C2314yes—
685#387C2312yes—
686#387C2312yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2314yes—
692#387C2314yes—
693#387C2314yes—
694#387C2314yes—
695#387C2314yes—
696#387C2314yes—
697#387C2312yes—
698#387C2312yes—
699#387C2312yes—
700#387C2312yes—
701#387C2312yes—
702#387C2312yes—
703#387C2312yes—
704#386C2312yes—
705#386C2314yes—
706#386C2312yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2312yes—
714#386C2312yes—
715#386C2312yes—
716#386C2314yes—
717#386C2314yes—
718#386C2312yes—
719#386C2312yes—
720#386C2314yes—
721#386C2314yes—
722#386C2312yes—
723#386C2314yes—
724#386C2312yes—
725#386C2312yes—
726#386C2312yes—
727#386C2314yes—
728#385C2314yes—
729#385C2314yes—
730#385C2314yes—
731#385C2312yes—
732#385C2314yes—
733#385C2314yes—
734#385C2314yes—
735#385C2314yes—
736#385C2312yes—
737#385C2312yes—
738#385C2312yes—
739#385C2312yes—
740#384C2311yescharacteristic
741#384C2311yescharacteristic
742#384C2311yescharacteristic
743#384C2311yescharacteristic
744#384C2312yes—
745#383C2314yes—
746#382C2314yes—
747#382C2314yes—
748#382C2314yes—
749#382C2312yes—
750#382C2312yes—
751#382C2312yes—
752#382C2311yescharacteristic
753#381C2314yes—
754#381C2314yes—
755#381C2314yes—
756#380C2311yescharacteristic
757#380C2311yescharacteristic
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2314yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2311yescharacteristic
773#380C2312yes—
774#380C2311yescharacteristic
775#380C2312yes—
776#379C2314yes—
777#379C2314yes—
778#379C2314yes—
779#379C2314yes—
780#379C2314yes—
781#379C2314yes—
782#379C2314yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815#376C2312yes—
816#376C2312yes—
817#376C2314yes—
818C43C2311yescharacteristic
819C25C2414yes—
820C2×#41—28no—
821C2×#41—42no—
822C2×#41—42no—
823C2×#41—42no—
824C2×#41—44no—
825C2×#41—44no—
826C22×Q8—24no—
827C22×Q8—42no—
828C22×Q8—42no—
829C22×Q8C2411yescharacteristic
830C22×Q8C2411yescharacteristic
831C22×Q8C2411yescharacteristic
832C22×Q8C2412yes—
833C22×Q8C2414yes—
834C22×D4—44no—
835C22×D4—44no—
836C22×D4—44no—
837C22×D4—44no—
838C22×D4—44no—
839C22×D4—44no—
840C22×D4C2412yes—
841C22×D4C2411yescharacteristic
842C22×D4C2411yescharacteristic
843C22×D4C2412yes—
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2412yes—
851C22×D4C2414yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2412yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C22×D4C2414yes—
861C22×D4C2414yes—
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2411yescharacteristic
870C23×C4C2414yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2414yes—
875C23×C4C2412yes—
876C23×C4C2412yes—
877C4⋊Q8—44no—
878C4⋊Q8—44no—
879#127—24no—
880#127—42no—
881#127—44no—
882#126—44no—
883#126—44no—
884#126—48no—
885#126—48no—
886#125—44no—
887#125—42no—
888#125—42no—
889#124—24no—
890#124—48no—
891#124—44no—
892#124—42no—
893#124—42no—
894#124—44no—
895#124—48no—
896#124—84no—
897#123—44no—
898#123—44no—
899#123—48no—
900#123—84no—
901#123—84no—
902C22⋊Q8—28no—
903C22⋊Q8—24no—
904C22⋊Q8—44no—
905C22⋊Q8—44no—
906C22⋊Q8—42no—
907C22⋊Q8—42no—
908C22⋊Q8—44no—
909C22⋊Q8—48no—
910C22⋊Q8—84no—
911#121—48no—
912#121—48no—
913#121—44no—
914#121—42no—
915#121—42no—
916#121—44no—
917#121—44no—
918#121—44no—
919#121—44no—
920#121—42no—
921#121—42no—
922#121—42no—
923#121—44no—
924#121—44no—
925#121—44no—
926#121—44no—
927#121—48no—
928#121—44no—
929#121—44no—
930#121—44no—
931#121—48no—
932#121—82no—
933#120—48no—
934#120—48no—
935#120—48no—
936#120—84no—
937#120—84no—
938C4×Q8—28no—
939C4×Q8—24no—
940C4×Q8—24no—
941C4×Q8—24no—
942C4×Q8—44no—
943C4×Q8—44no—
944C4×Q8—48no—
945C4×Q8—42no—
946C4×Q8—42no—
947C4×Q8—42no—
948C4×D4—24no—
949C4×D4—24no—
950C4×D4—24no—
951C4×D4—44no—
952C4×D4—42no—
953C4×D4—44no—
954C4×D4—44no—
955C4×D4—44no—
956C4×D4—42no—
957C4×D4—42no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—48no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—42no—
968C4×D4—82no—
969#117—44no—
970#117—44no—
971#117—44no—
972#117—44no—
973#117—44no—
974#117—42no—
975#117—44no—
976#117—44no—
977#117—82no—
978C2×C4⋊C4—42no—
979C2×C4⋊C4—44no—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C22⋊C4—48no—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2411yescharacteristic
1074C2×C22⋊C4C2411yescharacteristic
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2411yescharacteristic
1077C2×C22⋊C4C2411yescharacteristic
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C42—24no—
1118C2×C42—24no—
1119C2×C42—44no—
1120C2×C42—44no—
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2411yescharacteristic
1129C2×C42C2412yes—
1130C2×C42C2414yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2414yes—
1139C2×C42C2414yes—
1140C2×C42C2414yes—
1141C2×C42C2414yes—
1142C2×C42C2414yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2412yes—
1145C2×C42C2411yescharacteristic
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2411yescharacteristic
1149#95C2412yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2411yescharacteristic
1162#95C2412yes—
1163#95C2412yes—
1164#95C2411yescharacteristic
1165#95C2412yes—
1166#95C2411yescharacteristic
1167#95C2411yescharacteristic
1168#95C2411yescharacteristic
1169#95C2411yescharacteristic
1170#95C2414yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205C24—44no—
1206C24—44no—
1207C24—44no—
1208C24—44no—
1209C24—44no—
1210C24—44no—
1211C24—44no—
1212C24C2512yes—
1213C24C2512yes—
1214C24C2514yes—
1215C24C2511yescharacteristic
1216C24C2512yes—
1217C24C2511yescharacteristic
1218#41—416no—
1219#41—816no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—24no—
1224C2×Q8—22no—
1225C2×Q8—22no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—42no—
1230C2×Q8—42no—
1231C2×Q8—44no—
1232C2×Q8—44no—
1233C2×Q8—44no—
1234C2×Q8—416no—
1235C2×Q8H(5,𝔽2)14yes—
1236C2×D4—22no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—28no—
1240C2×D4—24no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—24no—
1245C2×D4—24no—
1246C2×D4—22no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—28no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—24no—
1257C2×D4—22no—
1258C2×D4—42no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—42no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—42no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—44no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—44no—
1290C2×D4—44no—
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—
1300C2×D4—44no—
1301C2×D4—44no—
1302C2×D4—816no—
1303C2×D4—816no—
1304C22×C4—22no—
1305C22×C4—24no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—24no—
1312C22×C4—22no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—24no—
1317C22×C4—22no—
1318C22×C4—24no—
1319C22×C4—24no—
1320C22×C4—24no—
1321C22×C4—22no—
1322C22×C4—22no—
1323C22×C4—24no—
1324C22×C4—22no—
1325C22×C4—22no—
1326C22×C4—24no—
1327C22×C4—22no—
1328C22×C4—22no—
1329C22×C4—22no—
1330C22×C4—28no—
1331C22×C4—42no—
1332C22×C4—42no—
1333C22×C4—41no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—42no—
1339C22×C4—44no—
1340C22×C4—41no—
1341C22×C4—42no—
1342C22×C4—41no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—44no—
1346C22×C4—44no—
1347C22×C4—44no—
1348C22×C4—44no—
1349C22×C4C2511yescharacteristic
1350C22×C4C2511yescharacteristic
1351C22×C4C2512yes—
1352C22×C4C2511yescharacteristic
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2514yes—
1358C22×C4C2512yes—
1359C22×C4C2511yescharacteristic
1360C22×C4C2514yes—
1361C22×C4C2512yes—
1362C22×C4C2511yescharacteristic
1363C22×C4C2512yes—
1364C22×C4C2512yes—
1365C22×C4C2514yes—
1366C22×C4C2512yes—
1367C22×C4C2511yescharacteristic
1368C22×C4C2512yes—
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2511yescharacteristic
1374C22×C4C2512yes—
1375C22×C4C2511yescharacteristic
1376C22×C4C2511yescharacteristic
1377C22×C4C2511yescharacteristic
1378C4⋊C4—24no—
1379C4⋊C4—22no—
1380C4⋊C4—22no—
1381C4⋊C4—24no—
1382C4⋊C4—24no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—28no—
1391C4⋊C4—24no—
1392C4⋊C4—28no—
1393C4⋊C4—22no—
1394C4⋊C4—22no—
1395C4⋊C4—24no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—22no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—41no—
1411C4⋊C4—41no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—41no—
1415C4⋊C4—42no—
1416C4⋊C4—44no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—42no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—42no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C22⋊C4—22no—
1437C22⋊C4—24no—
1438C22⋊C4—28no—
1439C22⋊C4—24no—
1440C22⋊C4—24no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—24no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—42no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—42no—
1458C22⋊C4—44no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—41no—
1463C22⋊C4—41no—
1464C22⋊C4—41no—
1465C22⋊C4—41no—
1466C22⋊C4—41no—
1467C22⋊C4—42no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—42no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—42no—
1494C22⋊C4—42no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—42no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—42no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C22⋊C4—42no—
1513C22⋊C4—42no—
1514C42—22no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—22no—
1519C42—22no—
1520C42—24no—
1521C42—24no—
1522C42—24no—
1523C42—22no—
1524C42—24no—
1525C42—28no—
1526C42—22no—
1527C42—22no—
1528C42—24no—
1529C42—22no—
1530C42—42no—
1531C42—42no—
1532C42—42no—
1533C42—42no—
1534C42—44no—
1535C42—44no—
1536C42—44no—
1537C42—44no—
1538C42—44no—
1539C42—41no—
1540C42—41no—
1541C42H(5,𝔽2)14yes—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—22no—
1553C23—22no—
1554C23—21no—
1555C23—24no—
1556C23—22no—
1557C23—24no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—21no—
1562C23—24no—
1563C23—24no—
1564C23—22no—
1565C23—22no—
1566C23—22no—
1567C23—22no—
1568C23—24no—
1569C23—21no—
1570C23—21no—
1571C23—22no—
1572C23—22no—
1573C23—24no—
1574C23—22no—
1575C23—22no—
1576C23—21no—
1577C23—22no—
1578C23—24no—
1579C23—22no—
1580C23—22no—
1581C23—22no—
1582C23—21no—
1583C23—88no—
1584C23—88no—
1585C23—88no—
1586C23—164no—
1587C23—164no—
1588C23—164no—
1589C23—164no—
1590C23#58512yes—
1591C23C2611yescharacteristic
1592Q8—28no—
1593Q8—48no—
1594Q8—44no—
1595Q8—44no—
1596Q8—88no—
1597D4—44no—
1598D4—48no—
1599D4—48no—
1600D4—44no—
1601D4—44no—
1602D4—44no—
1603D4—48no—
1604D4—84no—
1605D4—88no—
1606D4—84no—
1607D4—88no—
1608D4—84no—
1609D4—84no—
1610D4—84no—
1611D4—84no—
1612D4—84no—
1613D4—84no—
1614D4—88no—
1615D4—88no—
1616D4—164no—
1617D4—164no—
1618D4—164no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—22no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—24no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—21no—
1662C2×C4—24no—
1663C2×C4—24no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—22no—
1670C2×C4—24no—
1671C2×C4—22no—
1672C2×C4—22no—
1673C2×C4—21no—
1674C2×C4—22no—
1675C2×C4—21no—
1676C2×C4—22no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—21no—
1680C2×C4—24no—
1681C2×C4—24no—
1682C2×C4—22no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—21no—
1689C2×C4—24no—
1690C2×C4—24no—
1691C2×C4—21no—
1692C2×C4—22no—
1693C2×C4—22no—
1694C2×C4—22no—
1695C2×C4—21no—
1696C2×C4—22no—
1697C2×C4—22no—
1698C2×C4—44no—
1699C2×C4—48no—
1700C2×C4—48no—
1701C2×C4—44no—
1702C2×C4—48no—
1703C2×C4—44no—
1704C2×C4—44no—
1705C2×C4—48no—
1706C2×C4—44no—
1707C2×C4—48no—
1708C2×C4—82no—
1709C2×C4—88no—
1710C2×C4—84no—
1711C2×C4—84no—
1712C2×C4—164no—
1713C2×C4C2×H(5,𝔽2)12yes—
1714C2×C4C2×H(5,𝔽2)14yes—
1715C2×C4C2×H(5,𝔽2)12yes—
1716C2×C4C2×H(5,𝔽2)12yes—
1717C2×C4C2×H(5,𝔽2)12yes—
1718C2×C4#58512yes—
1719C2×C4#58512yes—
1720C2×C4#58512yes—
1721C22—22no—
1722C22—22no—
1723C22—22no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—42no—
1729C22—41no—
1730C22—42no—
1731C22—42no—
1732C22—44no—
1733C22—42no—
1734C22—44no—
1735C22—42no—
1736C22—41no—
1737C22—42no—
1738C22—41no—
1739C22—42no—
1740C22—42no—
1741C22—44no—
1742C22—42no—
1743C22—44no—
1744C22—41no—
1745C22—42no—
1746C22—42no—
1747C22—42no—
1748C22—41no—
1749C22—42no—
1750C22—44no—
1751C22—42no—
1752C22—42no—
1753C22—42no—
1754C22—42no—
1755C22—41no—
1756C22—44no—
1757C22—42no—
1758C22—42no—
1759C22—41no—
1760C22—42no—
1761C22—44no—
1762C22—42no—
1763C22—1616no—
1764C22C22×H(5,𝔽2)11yescharacteristic
1765C22C22×H(5,𝔽2)11yescharacteristic
1766C22C2×#58511yescharacteristic
1767C22C2×#58511yescharacteristic
1768C22C2×#58511yescharacteristic
1769C22C2×#58511yescharacteristic
1770C22H(7,𝔽2)11yescharacteristic
1771C4—22no—
1772C4—24no—
1773C4—41no—
1774C4—41no—
1775C4—42no—
1776C4—42no—
1777C4—44no—
1778C4—42no—
1779C4—41no—
1780C4—41no—
1781C4—42no—
1782C4—41no—
1783C4—44no—
1784C4—42no—
1785C4—42no—
1786C4—41no—
1787C4—41no—
1788C4—42no—
1789C4—42no—
1790C4—42no—
1791C4—41no—
1792C4—44no—
1793C4—41no—
1794C4—42no—
1795C4—42no—
1796C4—41no—
1797C4—42no—
1798C4#354014yes—
1799C4#354214yes—
1800C2—42no—
1801C2—82no—
1802C2—81no—
1803C2—84no—
1804C2—82no—
1805C2—82no—
1806C2C2×#354211yescharacteristic
1807C2C2×#354011yescharacteristic
1808C2#6282711yescharacteristic
1809C2#6292311yescharacteristic
1810C2#6295711yescharacteristic
1811C2#6296611yescharacteristic
1812C2#6301911yescharacteristic
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. #59412C2semidirect
2. #59244C2semidirect
3. #59233C2semidirect
4. #58154C2semidirect
5. #57367C2semidirect
6. #55305C2semidirect
7. #53116C2semidirect
8. #53103C2semidirect
9. #49751C2semidirect
10. #45641C2semidirect
11. #45518C2semidirect
12. #45404C2semidirect
13. #44961C2semidirect
14. #42887C2semidirect
15. #42783C2semidirect
16. #42778C2semidirect
17. #42607C2semidirect
18. #40173C2semidirect
19. #39960C2semidirect
20. #39763C2semidirect
21. #39273C2semidirect
22. #38978C2semidirect
23. #38910C2semidirect
24. #38910C2semidirect
25. #38119C2semidirect
26. #37629C2semidirect
27. #37371C2semidirect
28. #37331C2semidirect
29. #36576C2semidirect
30. #36410C2semidirect
31. #36211C2semidirect
32. #35247C2semidirect
33. #35189C2semidirect
34. #34727C2semidirect
35. #34708C2semidirect
36. C2×#556C22semidirect
38. C2×#548C22semidirect
43. C2×C4×#41C22semidirect
44. C22×C4×Q8C22semidirect
45. #2859C22semidirect
48. #2856C22semidirect
49. #2855C22semidirect
51. #2854C22semidirect
52. #2851C22semidirect
54. #2830C22semidirect
55. #2829C22semidirect
56. #2829C22semidirect
57. #2828C22semidirect
58. #2824C22semidirect
59. #2819C22semidirect
60. #2815C22semidirect
61. #2812C22semidirect
62. #2808C22semidirect
63. #2803C22semidirect
64. #2800C22semidirect
65. #2800C22semidirect
66. #2800C22semidirect
67. #2797C22semidirect
68. #2797C22semidirect
69. #2796C22semidirect
70. #2785C22semidirect
71. #2777C22semidirect
72. #2773C22semidirect
73. #2772C22semidirect
74. #2772C22semidirect
75. #2761C22semidirect
76. #2757C22semidirect
77. #2753C22semidirect
78. #2753C22semidirect
79. #2752C22semidirect
80. #2752C22semidirect
81. #2751C22semidirect
82. #2736C22semidirect
83. #2735C22semidirect
84. #2735C22semidirect
85. #2723C22semidirect
86. #2723C22semidirect
87. #2715C22semidirect
88. #2714C22semidirect
89. #2714C22semidirect
90. #2714C22semidirect
91. #2710C22semidirect
92. #2705C22semidirect
93. #2697C22semidirect
94. #2696C22semidirect
95. #2688C22semidirect
96. #2687C22semidirect
97. #2686C22semidirect
100. #2685C22semidirect
101. #2684C22semidirect
102. #2684C22semidirect
103. #2682C22semidirect
107. #2678C22semidirect
108. #2678C22semidirect
109. #2670C22semidirect
110. #2668C22semidirect
111. #2663C22semidirect
112. #2649C22semidirect
114. #2644C22semidirect
115. #2644C22semidirect
116. #2644C22semidirect
118. #2640C22semidirect
119. #2640C22semidirect
120. #2638C22semidirect
121. #2637C22semidirect
122. #2632C22semidirect
123. #2631C22semidirect
124. #2630C22semidirect
127. #2610C22semidirect
128. #2602C22semidirect
129. #2601C22semidirect
131. #2584C22semidirect
132. #2582C22semidirect
133. #2582C22semidirect
134. #2580C22semidirect
135. #2563C22semidirect
136. #2563C22semidirect
137. #2561C22semidirect
138. #2551C22semidirect
141. #2548C22semidirect
147. #2538C22semidirect
148. #2538C22semidirect
151. #2535C22semidirect
152. #2531C22semidirect
153. #2530C22semidirect
154. #2526C22semidirect
155. #2518C22semidirect
156. #2517C22semidirect
158. #2513C22semidirect
159. #2513C22semidirect
160. #2513C22semidirect
162. #2509C22semidirect
163. #2499C22semidirect
164. #2496C22semidirect
165. #2495C22semidirect
168. #2491C22semidirect
171. #2490C22semidirect
172. #2490C22semidirect
173. #2489C22semidirect
174. #2486C22semidirect
175. #2485C22semidirect
176. #2485C22semidirect
177. #2485C22semidirect
178. #2485C22semidirect
179. #2481C22semidirect
180. #2480C22semidirect
181. #2479C22semidirect
182. #2476C22semidirect
183. #2472C22semidirect
184. #2471C22semidirect
185. #2469C22semidirect
186. #2469C22semidirect
187. #2467C22semidirect
188. #2464C22semidirect
189. #2458C22semidirect
190. #2458C22semidirect
191. #2456C22semidirect
192. #2454C22semidirect
193. #2453C22semidirect
194. #2452C22semidirect
195. #2452C22semidirect
199. #2447C22semidirect
200. #2447C22semidirect
201. #2445C22semidirect
202. #2443C22semidirect
203. #2442C22semidirect
204. #2441C22semidirect
205. #2441C22semidirect
206. #2439C22semidirect
212. #2431C22semidirect
216. #2426C22semidirect
217. #2426C22semidirect
218. #2426C22semidirect
220. #2423C22semidirect
222. #2421C22semidirect
223. #2421C22semidirect
224. #2420C22semidirect
225. #2420C22semidirect
227. #2416C22semidirect
228. #2416C22semidirect
229. #2415C22semidirect
230. #2415C22semidirect
231. #2415C22semidirect
237. #2414C22semidirect
238. #2414C22semidirect
239. #2414C22semidirect
240. #2414C22semidirect
241. #2413C22semidirect
242. #2409C22semidirect
243. #2409C22semidirect
250. #2407C22semidirect
251. #2407C22semidirect
252. #2407C22semidirect
253. #2398C22semidirect
254. #2397C22semidirect
255. #2396C22semidirect
256. #2392C22semidirect
257. #2377C22semidirect
258. #2367C22semidirect
259. #2365C22semidirect
260. #2363C22semidirect
261. #2363C22semidirect
262. #2363C22semidirect
263. #2357C22semidirect
266. #2354C22semidirect
267. Q8×C4⋊C4C22semidirect
268. #2346C22semidirect
269. #2346C22semidirect
270. #2341C22semidirect
272. #2330C22semidirect
273. #2324C22semidirect
274. #2323C22semidirect
275. #2323C22semidirect
276. #2323C22semidirect
277. #2321C22semidirect
278. #2320C22semidirect
284. C4×C22⋊Q8C22semidirect
287. C4×#121C22semidirect
288. C4×#121C22semidirect
289. C4×#121C22semidirect
290. C4×#121C22semidirect
291. #2297C22semidirect
292. #2295C22semidirect
293. #2295C22semidirect
294. #2290C22semidirect
295. #2290C22semidirect
296. #2285C22semidirect
297. #2285C22semidirect
298. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#594122
#592442
#592332
#581542
#573672
#553052
#531162
#531032
#497512
#456412
#455182
#454042
#449612
#428872
#427832
#427782
#426072
#401732
#399602
#397632
#392732
#389782
#389102
#381192
#376292
#373712
#373312
#365762
#364102
#362112
#352472
#351892
#347272
#347082