Finite Group Databasebeta

← #7746757

Subgroups — #7746757

Order 512.

5125 conjugacy classes of subgroups.

The subgroup lattice has 1854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45360C212yesmaximal, complemented
2#45311C212yesmaximal, complemented
3#45307C212yesmaximal, complemented
4#45289C212yesmaximal, complemented
5#45156C212yesmaximal, complemented
6#45095C212yesmaximal, complemented
7#45040C212yesmaximal, complemented
8#45037C212yesmaximal, complemented
9#45032C212yesmaximal, complemented
10#45027C212yesmaximal, complemented
11#44975C212yesmaximal, complemented
12#44925C212yesmaximal, complemented
13#42857C212yesmaximal, complemented
14#42847C212yesmaximal, complemented
15#42618C212yesmaximal, complemented
16#42614C212yesmaximal, complemented
17#42583C212yesmaximal, complemented
18#42579C212yesmaximal, complemented
19#36594C211yesmaximal, characteristic, complemented
20#36563C211yesmaximal, characteristic, complemented
21#36211C211yesmaximal, characteristic, complemented
22#36210C211yesmaximal, characteristic, complemented
23#36194C211yesmaximal, characteristic, complemented
24#36122C211yesmaximal, characteristic, complemented
25#36122C211yesmaximal, characteristic, complemented
26D4×C4⋊Q8C211yesmaximal, characteristic, complemented
27#36000C212yesmaximal, complemented
28#35905C212yesmaximal, complemented
29#35871C212yesmaximal, complemented
30#35817C212yesmaximal, complemented
31#35771C212yesmaximal, complemented
32#35722C212yesmaximal, complemented
33#35288C211yesmaximal, characteristic, complemented
34#35284C211yesmaximal, characteristic, complemented
35#35277C211yesmaximal, characteristic, complemented
36#34551C211yesmaximal, characteristic, complemented
37#34226C211yesmaximal, characteristic, complemented
38#34216C211yesmaximal, characteristic, complemented
39#34209C211yesmaximal, characteristic, complemented
40C2×#556C2212yes—
41C2×D4×Q8C2212yes—
42C2×#548C2212yes—
43C2×#548C2212yes—
44C2×#542C2212yes—
45C2×#532C2211yescharacteristic
46C22×C4⋊Q8C2211yescharacteristic
47C22×C4⋊Q8C2211yescharacteristic
48C2×#519C2212yes—
49#2868C2211yescharacteristic
50#2868C2211yescharacteristic
51#2859C2211yescharacteristic
52#2859C2211yescharacteristic
53#2858C2211yescharacteristic
54#2858C2211yescharacteristic
55#2857C2211yescharacteristic
56#2857C2211yescharacteristic
57#2857C2211yescharacteristic
58#2857C2211yescharacteristic
59#2856C2211yescharacteristic
60#2856C2211yescharacteristic
61#2831C2214yes—
62#2830C2214yes—
63#2808C2214yes—
64#2800C2214yes—
65#2793C2214yes—
66#2790C2214yes—
67#2788C2214yes—
68#2787C2214yes—
69#2786C2214yes—
70#2784C2214yes—
71#2783C2214yes—
72#2765C2214yes—
73#2759C2214yes—
74#2745C2214yes—
75#2716C2214yes—
76#2715C2214yes—
77#2701C2214yes—
78#2700C2214yes—
79#2700C2214yes—
80#2700C2214yes—
81#2692C2214yes—
82#2691C2214yes—
83#2689C2214yes—
84#2689C2214yes—
85#2687C2214yes—
86#2686C2214yes—
87#2665C2214yes—
88#2653C2214yes—
89#2652C2214yes—
90#2651C2214yes—
91#2647C2212yes—
92#2644C2212yes—
93#2640C2212yes—
94#2637C2214yes—
95#2629C2212yes—
96#2624C2212yes—
97#2620C2214yes—
98#2620C2212yes—
99#2609C2214yes—
100#2601C2214yes—
101#2594C2214yes—
102#2589C2214yes—
103#2587C2214yes—
104#2582C2212yes—
105#2578C2214yes—
106#2573C2214yes—
107#2571C2212yes—
108#2567C2212yes—
109#2563C2212yes—
110#2562C2212yes—
111#2560C2214yes—
112#2552C2212yes—
113#2551C2212yes—
114#2551C2212yes—
115#2550C2212yes—
116#2550C2212yes—
117#2549C2214yes—
118#2547C2212yes—
119#2546C2212yes—
120#2545C2212yes—
121#2545C2212yes—
122#2545C2212yes—
123#2545C2212yes—
124#2545C2214yes—
125#2538C2212yes—
126#2538C2214yes—
127#2538C2212yes—
128#2538C2212yes—
129#2535C2212yes—
130#2525C2214yes—
131#2521C2214yes—
132#2514C2212yes—
133#2513C2212yes—
134#2513C2212yes—
135#2513C2212yes—
136#2512C2212yes—
137#2512C2212yes—
138#2512C2212yes—
139#2512C2212yes—
140#2512C2212yes—
141#2512C2212yes—
142#2509C2212yes—
143#2507C2212yes—
144#2507C2212yes—
145#2507C2212yes—
146#2507C2212yes—
147#2497C2212yes—
148#2497C2212yes—
149#2497C2212yes—
150#2497C2212yes—
151#2495C2212yes—
152#2494C2212yes—
153#2494C2212yes—
154#2492C2214yes—
155#2492C2212yes—
156#2492C2212yes—
157#2491C2212yes—
158#2491C2212yes—
159#2491C2212yes—
160#2491C2212yes—
161#2491C2212yes—
162#2491C2212yes—
163#2490C2212yes—
164#2490C2212yes—
165#2490C2212yes—
166#2485C2212yes—
167#2479C2214yes—
168#2477C2214yes—
169#2476C2214yes—
170#2469C2214yes—
171#2466C2214yes—
172#2465C2214yes—
173#2459C2214yes—
174#2457C2214yes—
175#2454C2212yes—
176#2452C2212yes—
177#2452C2212yes—
178#2452C2212yes—
179#2452C2212yes—
180#2452C2212yes—
181#2452C2212yes—
182#2451C2212yes—
183#2451C2212yes—
184#2450C2214yes—
185#2448C2212yes—
186#2447C2212yes—
187#2447C2214yes—
188#2446C2212yes—
189#2446C2212yes—
190#2440C2212yes—
191#2440C2212yes—
192#2440C2212yes—
193#2440C2212yes—
194#2439C2212yes—
195#2439C2212yes—
196#2438C2214yes—
197#2436C2212yes—
198#2436C2212yes—
199#2434C2212yes—
200#2434C2212yes—
201#2432C2212yes—
202#2432C2212yes—
203#2429C2214yes—
204#2429C2212yes—
205#2429C2212yes—
206#2427C2212yes—
207#2426C2212yes—
208#2426C2214yes—
209#2422C2212yes—
210#2422C2212yes—
211#2421C2212yes—
212#2420C2212yes—
213#2420C2212yes—
214#2420C2212yes—
215#2419C2214yes—
216#2416C2212yes—
217#2416C2212yes—
218#2416C2212yes—
219#2416C2212yes—
220#2415C2212yes—
221#2415C2214yes—
222#2414C2212yes—
223#2414C2212yes—
224#2414C2214yes—
225#2402C2211yescharacteristic
226#2402C2211yescharacteristic
227#2402C2211yescharacteristic
228#2401C2211yescharacteristic
229#2401C2211yescharacteristic
230#2401C2211yescharacteristic
231#2401C2211yescharacteristic
232#2401C2211yescharacteristic
233#2401C2211yescharacteristic
234#2398C2211yescharacteristic
235#2398C2211yescharacteristic
236#2398C2211yescharacteristic
237#2396C2214yes—
238#2396C2211yescharacteristic
239#2396C2211yescharacteristic
240#2396C2211yescharacteristic
241#2395C2211yescharacteristic
242#2395C2211yescharacteristic
243#2395C2211yescharacteristic
244#2395C2211yescharacteristic
245#2395C2211yescharacteristic
246#2395C2211yescharacteristic
247#2392C2214yes—
248#2392C2211yescharacteristic
249#2392C2211yescharacteristic
250#2392C2211yescharacteristic
251#2370C2212yes—
252#2369C2212yes—
253#2369C2212yes—
254#2369C2212yes—
255#2369C2212yes—
256#2367C2212yes—
257#2367C2212yes—
258#2365C2212yes—
259#2365C2212yes—
260#2365C2212yes—
261#2365C2212yes—
262#2365C2212yes—
263#2365C2212yes—
264#2363C2212yes—
265#2363C2212yes—
266#2363C2212yes—
267#2363C2212yes—
268#2362C2212yes—
269#2361C2212yes—
270#2361C2212yes—
271#2361C2212yes—
272#2361C2212yes—
273#2357C2212yes—
274#2357C2212yes—
275#2355C2212yes—
276#2355C2212yes—
277#2354C2212yes—
278#2354C2212yes—
279#2354C2212yes—
280Q8×C4⋊C4C2212yes—
281#2349C2212yes—
282D4×C4⋊C4C2212yes—
283D4×C4⋊C4C2212yes—
284#2347C2212yes—
285#2345C2212yes—
286#2345C2212yes—
287#2344C2212yes—
288#2344C2212yes—
289#2344C2212yes—
290#2344C2212yes—
291#2341C2212yes—
292Q8×C22⋊C4C2212yes—
293Q8×C22⋊C4C2212yes—
294#2339C2212yes—
295#2331C2212yes—
296#2331C2212yes—
297#2330C2212yes—
298#2327C2212yes—
299#2327C2212yes—
300#2326C2212yes—
301#2324C2212yes—
302#2324C2212yes—
303#2324C2212yes—
304#2319C2212yes—
305#2319C2212yes—
306#2316C2212yes—
307#2314C2212yes—
308#2310C2212yes—
309C4×C4⋊Q8C2211yescharacteristic
310C4×C4⋊Q8C2211yescharacteristic
311C4×C4⋊Q8C2211yescharacteristic
312C4×C4⋊Q8C2211yescharacteristic
313C4×C4⋊Q8C2211yescharacteristic
314C4×C4⋊Q8C2211yescharacteristic
315C4×C4⋊Q8C2211yescharacteristic
316C4×C4⋊Q8C2211yescharacteristic
317C4×#127C2211yescharacteristic
318C4×#127C2211yescharacteristic
319#2285C2211yescharacteristic
320#2285C2211yescharacteristic
321#2285C2211yescharacteristic
322#2275C2212yes—
323#2274C2212yes—
324C42×Q8C2211yescharacteristic
325C42×D4C2211yescharacteristic
326C42×D4C2211yescharacteristic
327C42×D4C2211yescharacteristic
328C4×#117C2211yescharacteristic
329C4×#117C2211yescharacteristic
330C4×#117C2211yescharacteristic
331C22×#41C2312yes—
332C23×Q8C2312yes—
333C23×Q8C2312yes—
334#556—48no—
335D4×Q8—48no—
336#548—48no—
337#548—48no—
338#542—48no—
339#532—28no—
340C2×C4⋊Q8—28no—
341C2×C4⋊Q8—28no—
342C2×C4⋊Q8C2311yescharacteristic
343C2×C4⋊Q8C2311yescharacteristic
344C2×C4⋊Q8C2312yes—
345C2×C4⋊Q8C2312yes—
346C2×C4⋊Q8C2312yes—
347C2×C4⋊Q8C2312yes—
348C2×C4⋊Q8C2312yes—
349C2×C4⋊Q8C2312yes—
350C2×C4⋊Q8C2312yes—
351C2×C4⋊Q8C2312yes—
352C2×C4⋊Q8C2312yes—
353C2×C4⋊Q8C2312yes—
354C2×C4⋊Q8C2312yes—
355C2×C4⋊Q8C2314yes—
356C2×C4⋊Q8C2311yescharacteristic
357C2×#127C2311yescharacteristic
358C2×#126C2314yes—
359C2×#126C2314yes—
360C2×#126C2314yes—
361C2×#125C2312yes—
362C2×#125C2312yes—
363C2×#124C2312yes—
364C2×#124C2312yes—
365C2×#124C2312yes—
366C2×#124C2312yes—
367C2×#124C2312yes—
368C2×#124C2314yes—
369C2×#124C2314yes—
370C2×#124C2314yes—
371C2×#123C2314yes—
372C2×C22⋊Q8C2312yes—
373C2×C22⋊Q8C2314yes—
374C2×C22⋊Q8C2312yes—
375C2×C22⋊Q8C2312yes—
376C2×C22⋊Q8C2312yes—
377C2×C22⋊Q8C2314yes—
378C2×C22⋊Q8C2314yes—
379C2×C22⋊Q8C2314yes—
380C2×C22⋊Q8C2314yes—
381C2×C22⋊Q8C2314yes—
382C2×#121C2312yes—
383C2×#121C2312yes—
384C2×#121C2312yes—
385C2×#121C2312yes—
386C2×#121C2312yes—
387C2×#121C2312yes—
388C2×#121C2312yes—
389C2×#121C2312yes—
390C2×#121C2314yes—
391C2×#121C2314yes—
392#519—48no—
393C2×C4×Q8C2312yes—
394C2×C4×Q8C2312yes—
395C2×C4×Q8C2311yescharacteristic
396C2×C4×Q8C2311yescharacteristic
397C2×C4×Q8C2312yes—
398C2×C4×Q8C2312yes—
399C2×C4×Q8C2312yes—
400C2×C4×Q8C2312yes—
401C2×C4×Q8C2312yes—
402C2×C4×Q8C2312yes—
403C2×C4×Q8C2311yescharacteristic
404C2×C4×Q8C2314yes—
405C2×C4×Q8C2314yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2311yescharacteristic
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2312yes—
411C2×C4×D4C2311yescharacteristic
412C2×C4×D4C2311yescharacteristic
413C2×C4×D4C2311yescharacteristic
414C2×C4×D4C2311yescharacteristic
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2311yescharacteristic
421C2×C4×D4C2311yescharacteristic
422C2×C4×D4C2314yes—
423C2×C4×D4C2314yes—
424C2×C4×D4C2314yes—
425C2×C4×D4C2311yescharacteristic
426C2×#117C2311yescharacteristic
427C2×#117C2311yescharacteristic
428C2×#117C2311yescharacteristic
429C2×#117C2311yescharacteristic
430C2×#117C2312yes—
431C2×#117C2311yescharacteristic
432C2×#117C2312yes—
433C2×#117C2311yescharacteristic
434C2×#117C2314yes—
435C2×#117C2314yes—
436C2×#117C2312yes—
437C2×#117C2314yes—
438C22×C4⋊C4C2312yes—
439C22×C4⋊C4C2312yes—
440C22×C4⋊C4C2312yes—
441C22×C4⋊C4C2312yes—
442C22×C42C2311yescharacteristic
443C22×C42C2311yescharacteristic
444C22×C42C2311yescharacteristic
445#401C2314yes—
446#401C2311yescharacteristic
447#401C2311yescharacteristic
448#400C2314yes—
449#400C2314yes—
450#400C2314yes—
451#400C2311yescharacteristic
452#400C2314yes—
453#400C2311yescharacteristic
454#400C2314yes—
455#400C2311yescharacteristic
456#400C2311yescharacteristic
457#400C2311yescharacteristic
458#400C2311yescharacteristic
459#400C2311yescharacteristic
460#400C2311yescharacteristic
461#400C2311yescharacteristic
462#400C2311yescharacteristic
463#400C2311yescharacteristic
464#400C2314yes—
465#400C2311yescharacteristic
466#400C2311yescharacteristic
467#400C2311yescharacteristic
468#400C2311yescharacteristic
469#399C2314yes—
470#399C2311yescharacteristic
471#399C2311yescharacteristic
472#399C2311yescharacteristic
473#398C2314yes—
474#398C2314yes—
475#398C2314yes—
476#398C2314yes—
477#398C2314yes—
478#398C2314yes—
479#398C2311yescharacteristic
480#398C2314yes—
481#398C2311yescharacteristic
482#398C2314yes—
483#398C2311yescharacteristic
484#398C2314yes—
485#398C2311yescharacteristic
486#398C2311yescharacteristic
487#398C2311yescharacteristic
488#398C2311yescharacteristic
489#398C2311yescharacteristic
490#398C2311yescharacteristic
491#398C2314yes—
492#397C2311yescharacteristic
493#397C2314yes—
494#397C2311yescharacteristic
495#397C2314yes—
496#397C2314yes—
497#397C2314yes—
498#397C2314yes—
499#397C2314yes—
500#397C2314yes—
501#397C2311yescharacteristic
502#397C2314yes—
503#397C2314yes—
504#397C2314yes—
505#397C2314yes—
506#397C2311yescharacteristic
507#397C2311yescharacteristic
508#397C2311yescharacteristic
509#397C2314yes—
510#397C2311yescharacteristic
511#397C2311yescharacteristic
512#397C2311yescharacteristic
513#397C2311yescharacteristic
514#397C2311yescharacteristic
515#397C2311yescharacteristic
516#397C2311yescharacteristic
517#397C2311yescharacteristic
518#397C2311yescharacteristic
519#397C2314yes—
520#396C2314yes—
521#396C2314yes—
522#396C2314yes—
523#396C2314yes—
524#396C2314yes—
525#396C2314yes—
526#396C2314yes—
527#396C2311yescharacteristic
528#396C2311yescharacteristic
529#396C2314yes—
530#396C2314yes—
531#396C2314yes—
532#396C2314yes—
533#396C2314yes—
534#396C2314yes—
535#396C2311yescharacteristic
536#396C2311yescharacteristic
537#396C2311yescharacteristic
538#396C2311yescharacteristic
539#396C2314yes—
540#396C2314yes—
541#395C2314yes—
542#395C2314yes—
543#395C2314yes—
544#395C2314yes—
545#395C2311yescharacteristic
546#395C2314yes—
547#395C2314yes—
548#394C2314yes—
549#394C2314yes—
550#394C2314yes—
551#394C2314yes—
552#394C2314yes—
553#394C2314yes—
554#394C2311yescharacteristic
555#394C2314yes—
556#394C2314yes—
557#394C2311yescharacteristic
558#394C2311yescharacteristic
559#394C2311yescharacteristic
560#394C2311yescharacteristic
561#394C2311yescharacteristic
562#394C2311yescharacteristic
563#394C2311yescharacteristic
564#394C2311yescharacteristic
565#394C2314yes—
566#394C2314yes—
567#394C2314yes—
568#393C2314yes—
569#393C2314yes—
570#393C2314yes—
571#393C2314yes—
572#393C2314yes—
573#393C2314yes—
574#393C2314yes—
575#393C2311yescharacteristic
576#393C2311yescharacteristic
577#393C2311yescharacteristic
578#393C2314yes—
579#392C2311yescharacteristic
580#392C2314yes—
581#391C2314yes—
582#391C2312yes—
583#391C2312yes—
584#391C2312yes—
585#391C2312yes—
586#391C2312yes—
587#391C2312yes—
588#391C2312yes—
589#391C2312yes—
590#391C2314yes—
591#391C2314yes—
592#391C2314yes—
593#391C2312yes—
594#391C2314yes—
595#391C2314yes—
596#391C2314yes—
597#391C2314yes—
598#391C2314yes—
599#391C2312yes—
600#391C2312yes—
601#391C2312yes—
602#391C2314yes—
603#391C2314yes—
604#390C2314yes—
605#390C2312yes—
606#390C2312yes—
607#390C2312yes—
608#390C2312yes—
609#390C2312yes—
610#390C2312yes—
611#390C2314yes—
612#390C2314yes—
613#390C2312yes—
614#390C2312yes—
615#390C2314yes—
616#390C2312yes—
617#390C2314yes—
618#390C2312yes—
619#390C2312yes—
620#390C2312yes—
621#390C2312yes—
622#390C2312yes—
623#390C2314yes—
624#390C2312yes—
625#390C2312yes—
626#390C2312yes—
627#390C2312yes—
628#390C2312yes—
629#390C2312yes—
630#389C2312yes—
631#389C2312yes—
632#389C2312yes—
633#389C2312yes—
634#389C2312yes—
635#389C2312yes—
636#389C2312yes—
637#389C2312yes—
638#389C2312yes—
639#389C2312yes—
640#389C2312yes—
641#389C2312yes—
642#389C2312yes—
643#389C2312yes—
644#389C2312yes—
645#389C2312yes—
646#389C2312yes—
647#389C2312yes—
648#389C2312yes—
649#389C2312yes—
650#389C2314yes—
651#389C2314yes—
652#389C2314yes—
653#389C2314yes—
654#389C2312yes—
655#389C2312yes—
656#389C2312yes—
657#389C2314yes—
658#389C2312yes—
659#389C2312yes—
660#389C2314yes—
661#389C2314yes—
662#389C2314yes—
663#389C2314yes—
664#389C2312yes—
665#389C2312yes—
666#389C2312yes—
667#389C2312yes—
668#389C2312yes—
669#389C2312yes—
670#389C2312yes—
671#389C2314yes—
672#389C2314yes—
673#388C2314yes—
674#388C2314yes—
675#388C2314yes—
676#388C2314yes—
677#388C2314yes—
678#388C2314yes—
679#388C2314yes—
680#388C2314yes—
681#388C2314yes—
682#388C2314yes—
683#388C2314yes—
684#388C2314yes—
685#388C2314yes—
686#388C2314yes—
687#388C2314yes—
688#388C2314yes—
689#388C2314yes—
690#388C2314yes—
691#388C2314yes—
692#388C2314yes—
693#388C2314yes—
694#388C2314yes—
695#388C2314yes—
696#388C2314yes—
697#388C2314yes—
698#388C2314yes—
699#388C2314yes—
700#388C2314yes—
701#388C2314yes—
702#387C2314yes—
703#387C2314yes—
704#387C2314yes—
705#387C2314yes—
706#387C2314yes—
707#387C2314yes—
708#387C2314yes—
709#387C2314yes—
710#387C2314yes—
711#387C2314yes—
712#387C2314yes—
713#387C2314yes—
714#387C2314yes—
715#387C2314yes—
716#387C2314yes—
717#387C2314yes—
718#387C2314yes—
719#387C2314yes—
720#387C2314yes—
721#387C2314yes—
722#387C2314yes—
723#387C2314yes—
724#387C2314yes—
725#386C2314yes—
726#386C2314yes—
727#386C2314yes—
728#386C2314yes—
729#386C2314yes—
730#386C2314yes—
731#386C2314yes—
732#386C2314yes—
733#386C2314yes—
734#385C2314yes—
735#385C2314yes—
736#385C2314yes—
737#385C2314yes—
738#385C2314yes—
739#385C2314yes—
740#385C2314yes—
741#385C2314yes—
742#385C2314yes—
743#385C2314yes—
744#385C2314yes—
745#385C2314yes—
746#385C2314yes—
747#384C2311yescharacteristic
748#384C2311yescharacteristic
749#384C2311yescharacteristic
750#384C2311yescharacteristic
751#384C2314yes—
752#384C2312yes—
753#384C2312yes—
754#384C2312yes—
755#384C2312yes—
756#384C2312yes—
757#384C2312yes—
758#384C2312yes—
759#383C2314yes—
760#382C2314yes—
761#382C2312yes—
762#382C2312yes—
763#382C2312yes—
764#382C2312yes—
765#382C2312yes—
766#381C2314yes—
767#381C2314yes—
768#381C2314yes—
769#381C2314yes—
770#381C2314yes—
771#380C2312yes—
772#380C2312yes—
773#380C2312yes—
774#380C2312yes—
775#380C2312yes—
776#380C2312yes—
777#380C2312yes—
778#380C2314yes—
779#380C2314yes—
780#380C2314yes—
781#380C2314yes—
782#380C2314yes—
783#380C2312yes—
784#380C2312yes—
785#380C2312yes—
786#380C2312yes—
787#380C2312yes—
788#380C2312yes—
789#380C2312yes—
790#380C2314yes—
791C4×C4⋊C4C2314yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2312yes—
802C4×C4⋊C4C2312yes—
803C4×C4⋊C4C2312yes—
804C4×C4⋊C4C2312yes—
805C4×C4⋊C4C2312yes—
806C4×C4⋊C4C2312yes—
807C4×C4⋊C4C2312yes—
808C4×C4⋊C4C2311yescharacteristic
809C4×C4⋊C4C2314yes—
810C4×C4⋊C4C2312yes—
811C4×C4⋊C4C2314yes—
812C4×C4⋊C4C2314yes—
813C4×C4⋊C4C2314yes—
814C4×C4⋊C4C2312yes—
815C4×C4⋊C4C2311yescharacteristic
816C4×C4⋊C4C2311yescharacteristic
817C4×C4⋊C4C2311yescharacteristic
818C4×C4⋊C4C2311yescharacteristic
819C4×C4⋊C4C2311yescharacteristic
820C4×C4⋊C4C2312yes—
821C4×C4⋊C4C2312yes—
822C4×C4⋊C4C2311yescharacteristic
823C4×C4⋊C4C2311yescharacteristic
824C4×C4⋊C4C2312yes—
825C4×C4⋊C4C2312yes—
826C4×C4⋊C4C2311yescharacteristic
827C4×C4⋊C4C2311yescharacteristic
828C4×C4⋊C4C2311yescharacteristic
829C4×C4⋊C4C2311yescharacteristic
830C4×C4⋊C4C2311yescharacteristic
831C4×C4⋊C4C2311yescharacteristic
832C4×C4⋊C4C2311yescharacteristic
833C4×C4⋊C4C2311yescharacteristic
834C4×C4⋊C4C2311yescharacteristic
835C4×C4⋊C4C2311yescharacteristic
836C4×C4⋊C4C2311yescharacteristic
837C4×C4⋊C4C2311yescharacteristic
838C4×C4⋊C4C2311yescharacteristic
839C4×C4⋊C4C2311yescharacteristic
840C4×C4⋊C4C2311yescharacteristic
841C4×C4⋊C4C2311yescharacteristic
842C4×C4⋊C4C2311yescharacteristic
843C4×C4⋊C4C2311yescharacteristic
844C4×C4⋊C4C2311yescharacteristic
845C4×C4⋊C4C2311yescharacteristic
846C4×C4⋊C4C2311yescharacteristic
847C4×C4⋊C4C2311yescharacteristic
848C4×C22⋊C4C2314yes—
849C4×C22⋊C4C2314yes—
850C4×C22⋊C4C2314yes—
851C4×C22⋊C4C2314yes—
852C4×C22⋊C4C2314yes—
853C4×C22⋊C4C2311yescharacteristic
854C4×C22⋊C4C2311yescharacteristic
855C4×C22⋊C4C2311yescharacteristic
856C4×C22⋊C4C2311yescharacteristic
857C4×C22⋊C4C2311yescharacteristic
858C4×C22⋊C4C2311yescharacteristic
859C4×C22⋊C4C2311yescharacteristic
860C4×C22⋊C4C2311yescharacteristic
861C4×C22⋊C4C2311yescharacteristic
862C4×C22⋊C4C2311yescharacteristic
863C4×C22⋊C4C2311yescharacteristic
864C4×C22⋊C4C2314yes—
865C4×C22⋊C4C2311yescharacteristic
866C4×C22⋊C4C2311yescharacteristic
867C4×C22⋊C4C2311yescharacteristic
868C4×C22⋊C4C2311yescharacteristic
869C4×C22⋊C4C2311yescharacteristic
870C4×C22⋊C4C2311yescharacteristic
871C4×C22⋊C4C2311yescharacteristic
872C4×C22⋊C4C2311yescharacteristic
873C4×C22⋊C4C2311yescharacteristic
874C4×C22⋊C4C2311yescharacteristic
875C4×C22⋊C4C2311yescharacteristic
876C4×C22⋊C4C2311yescharacteristic
877C4×C22⋊C4C2311yescharacteristic
878C4×C22⋊C4C2311yescharacteristic
879C4×C22⋊C4C2311yescharacteristic
880C4×C22⋊C4C2311yescharacteristic
881C4×C22⋊C4C2311yescharacteristic
882C4×C22⋊C4C2311yescharacteristic
883C4×C22⋊C4C2311yescharacteristic
884#376C2311yescharacteristic
885#376C2311yescharacteristic
886#376C2311yescharacteristic
887#376C2311yescharacteristic
888#376C2311yescharacteristic
889#376C2311yescharacteristic
890C2×#95C2314yes—
891C43C2311yescharacteristic
892C43C2311yescharacteristic
893C43C2311yescharacteristic
894C43C2311yescharacteristic
895C2×#41—28no—
896C2×#41—44no—
897C2×#41—44no—
898C22×Q8—28no—
899C22×Q8—28no—
900C22×Q8—28no—
901C22×Q8—44no—
902C22×Q8—44no—
903C22×Q8—44no—
904C22×Q8C2412yes—
905C22×Q8C2412yes—
906C22×Q8C2411yescharacteristic
907C22×Q8C2414yes—
908C22×Q8C2412yes—
909C22×Q8C2414yes—
910C22×Q8C2414yes—
911C22×D4C2411yescharacteristic
912C22×D4C2412yes—
913C22×D4C2412yes—
914C22×D4C2412yes—
915C22×D4C2411yescharacteristic
916C22×D4C2411yescharacteristic
917C22×D4C2414yes—
918C22×D4C2414yes—
919C22×D4C2414yes—
920C23×C4C2411yescharacteristic
921C23×C4C2411yescharacteristic
922C23×C4C2411yescharacteristic
923C23×C4C2411yescharacteristic
924C23×C4C2411yescharacteristic
925C23×C4C2411yescharacteristic
926C23×C4C2411yescharacteristic
927C23×C4C2414yes—
928C23×C4C2411yescharacteristic
929C23×C4C2411yescharacteristic
930C23×C4C2414yes—
931C23×C4C2414yes—
932C23×C4C2414yes—
933C23×C4C2414yes—
934C4⋊Q8—28no—
935C4⋊Q8—28no—
936C4⋊Q8—28no—
937C4⋊Q8—28no—
938C4⋊Q8—28no—
939C4⋊Q8—28no—
940C4⋊Q8—24no—
941C4⋊Q8—24no—
942C4⋊Q8—44no—
943C4⋊Q8—44no—
944C4⋊Q8—44no—
945C4⋊Q8—44no—
946C4⋊Q8—44no—
947C4⋊Q8—48no—
948C4⋊Q8#4118yes—
949#127—24no—
950#126—48no—
951#126—48no—
952#126—48no—
953#125—44no—
954#125—44no—
955#124—28no—
956#124—28no—
957#124—48no—
958#124—44no—
959#124—44no—
960#124—44no—
961#124—48no—
962#124—48no—
963#123—48no—
964C22⋊Q8—28no—
965C22⋊Q8—48no—
966C22⋊Q8—48no—
967C22⋊Q8—48no—
968C22⋊Q8—48no—
969C22⋊Q8—48no—
970C22⋊Q8—48no—
971C22⋊Q8—44no—
972C22⋊Q8—44no—
973C22⋊Q8—44no—
974#121—28no—
975#121—28no—
976#121—28no—
977#121—28no—
978#121—48no—
979#121—44no—
980#121—44no—
981#121—44no—
982#121—44no—
983#121—48no—
984C4×Q8—28no—
985C4×Q8—28no—
986C4×Q8—24no—
987C4×Q8—24no—
988C4×Q8—42no—
989C4×Q8—48no—
990C4×Q8—48no—
991C4×Q8—44no—
992C4×Q8—44no—
993C4×Q8—44no—
994C4×Q8—44no—
995C4×Q8—44no—
996C4×Q8—44no—
997C4×D4—24no—
998C4×D4—24no—
999C4×D4—24no—
1000C4×D4—24no—
1001C4×D4—28no—
1002C4×D4—28no—
1003C4×D4—24no—
1004C4×D4—24no—
1005C4×D4—28no—
1006C4×D4—48no—
1007C4×D4—44no—
1008C4×D4—44no—
1009C4×D4—44no—
1010C4×D4—44no—
1011C4×D4—44no—
1012C4×D4—42no—
1013C4×D4—42no—
1014C4×D4—42no—
1015C4×D4—48no—
1016C4×D4—48no—
1017#117—24no—
1018#117—24no—
1019#117—24no—
1020#117—24no—
1021#117—42no—
1022#117—42no—
1023#117—48no—
1024#117—48no—
1025#117—48no—
1026#117—44no—
1027#117—44no—
1028#117—44no—
1029C2×C4⋊C4—28no—
1030C2×C4⋊C4—28no—
1031C2×C4⋊C4—28no—
1032C2×C4⋊C4—28no—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2411yescharacteristic
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2411yescharacteristic
1046C2×C4⋊C4C2411yescharacteristic
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2414yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2411yescharacteristic
1052C2×C4⋊C4C2411yescharacteristic
1053C2×C4⋊C4C2411yescharacteristic
1054C2×C4⋊C4C2411yescharacteristic
1055C2×C4⋊C4C2411yescharacteristic
1056C2×C4⋊C4C2411yescharacteristic
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2411yescharacteristic
1059C2×C4⋊C4C2411yescharacteristic
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2411yescharacteristic
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2411yescharacteristic
1064C2×C4⋊C4C2411yescharacteristic
1065C2×C4⋊C4C2411yescharacteristic
1066C2×C4⋊C4C2412yes—
1067C2×C4⋊C4C2411yescharacteristic
1068C2×C4⋊C4C2411yescharacteristic
1069C2×C4⋊C4C2411yescharacteristic
1070C2×C4⋊C4C2411yescharacteristic
1071C2×C4⋊C4C2411yescharacteristic
1072C2×C4⋊C4C2412yes—
1073C2×C4⋊C4C2412yes—
1074C2×C4⋊C4C2412yes—
1075C2×C4⋊C4C2414yes—
1076C2×C4⋊C4C2414yes—
1077C2×C4⋊C4C2414yes—
1078C2×C4⋊C4C2414yes—
1079C2×C4⋊C4C2411yescharacteristic
1080C2×C4⋊C4C2411yescharacteristic
1081C2×C4⋊C4C2411yescharacteristic
1082C2×C4⋊C4C2411yescharacteristic
1083C2×C4⋊C4C2414yes—
1084C2×C4⋊C4C2414yes—
1085C2×C4⋊C4C2414yes—
1086C2×C4⋊C4C2411yescharacteristic
1087C2×C4⋊C4C2411yescharacteristic
1088C2×C4⋊C4C2411yescharacteristic
1089C2×C4⋊C4C2414yes—
1090C2×C4⋊C4C2414yes—
1091C2×C4⋊C4C2414yes—
1092C2×C4⋊C4C2414yes—
1093C2×C4⋊C4C2411yescharacteristic
1094C2×C4⋊C4C2411yescharacteristic
1095C2×C4⋊C4C2411yescharacteristic
1096C2×C4⋊C4C2414yes—
1097C2×C4⋊C4C2414yes—
1098C2×C4⋊C4C2414yes—
1099C2×C4⋊C4C2414yes—
1100C2×C4⋊C4C2414yes—
1101C2×C4⋊C4C2414yes—
1102C2×C4⋊C4C2414yes—
1103C2×C4⋊C4C2414yes—
1104C2×C4⋊C4C2414yes—
1105C2×C4⋊C4C2414yes—
1106C2×C4⋊C4C2412yes—
1107C2×C4⋊C4C2412yes—
1108C2×C22⋊C4C2411yescharacteristic
1109C2×C22⋊C4C2411yescharacteristic
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2411yescharacteristic
1112C2×C22⋊C4C2411yescharacteristic
1113C2×C22⋊C4C2411yescharacteristic
1114C2×C22⋊C4C2411yescharacteristic
1115C2×C22⋊C4C2411yescharacteristic
1116C2×C22⋊C4C2411yescharacteristic
1117C2×C22⋊C4C2411yescharacteristic
1118C2×C22⋊C4C2411yescharacteristic
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2411yescharacteristic
1122C2×C22⋊C4C2411yescharacteristic
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2411yescharacteristic
1126C2×C22⋊C4C2411yescharacteristic
1127C2×C22⋊C4C2411yescharacteristic
1128C2×C22⋊C4C2411yescharacteristic
1129C2×C22⋊C4C2411yescharacteristic
1130C2×C22⋊C4C2411yescharacteristic
1131C2×C22⋊C4C2411yescharacteristic
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2411yescharacteristic
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2414yes—
1138C2×C22⋊C4C2411yescharacteristic
1139C2×C22⋊C4C2414yes—
1140C2×C22⋊C4C2411yescharacteristic
1141C2×C22⋊C4C2411yescharacteristic
1142C2×C22⋊C4C2411yescharacteristic
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2414yes—
1145C2×C22⋊C4C2414yes—
1146C2×C22⋊C4C2414yes—
1147C2×C22⋊C4C2414yes—
1148C2×C22⋊C4C2411yescharacteristic
1149C2×C22⋊C4C2411yescharacteristic
1150C2×C22⋊C4C2411yescharacteristic
1151C2×C22⋊C4C2411yescharacteristic
1152C2×C22⋊C4C2414yes—
1153C2×C22⋊C4C2411yescharacteristic
1154C2×C22⋊C4C2411yescharacteristic
1155C2×C22⋊C4C2414yes—
1156C2×C22⋊C4C2414yes—
1157C2×C22⋊C4C2414yes—
1158C2×C22⋊C4C2414yes—
1159C2×C22⋊C4C2414yes—
1160C2×C22⋊C4C2414yes—
1161C2×C22⋊C4C2414yes—
1162C2×C22⋊C4C2414yes—
1163C2×C22⋊C4C2414yes—
1164C2×C22⋊C4C2414yes—
1165C2×C22⋊C4C2414yes—
1166C2×C22⋊C4C2414yes—
1167C2×C42—24no—
1168C2×C42—24no—
1169C2×C42—24no—
1170C2×C42C2414yes—
1171C2×C42C2411yescharacteristic
1172C2×C42C2411yescharacteristic
1173C2×C42C2411yescharacteristic
1174C2×C42C2414yes—
1175C2×C42C2411yescharacteristic
1176C2×C42C2411yescharacteristic
1177C2×C42C2411yescharacteristic
1178C2×C42C2411yescharacteristic
1179C2×C42C2411yescharacteristic
1180C2×C42C2411yescharacteristic
1181C2×C42C2411yescharacteristic
1182C2×C42C2411yescharacteristic
1183C2×C42C2411yescharacteristic
1184C2×C42C2411yescharacteristic
1185C2×C42C2411yescharacteristic
1186C2×C42C2411yescharacteristic
1187C2×C42C2411yescharacteristic
1188C2×C42C2411yescharacteristic
1189C2×C42C2411yescharacteristic
1190C2×C42C2411yescharacteristic
1191C2×C42C2411yescharacteristic
1192C2×C42C2411yescharacteristic
1193C2×C42C2411yescharacteristic
1194C2×C42C2411yescharacteristic
1195C2×C42C2411yescharacteristic
1196C2×C42C2411yescharacteristic
1197C2×C42C2411yescharacteristic
1198C2×C42C2411yescharacteristic
1199C2×C42C2411yescharacteristic
1200C2×C42C2411yescharacteristic
1201C2×C42C2411yescharacteristic
1202C2×C42C2411yescharacteristic
1203C2×C42C2414yes—
1204C2×C42C2414yes—
1205C2×C42C2414yes—
1206C2×C42C2414yes—
1207C2×C42C2414yes—
1208C2×C42C2414yes—
1209C2×C42C2414yes—
1210C2×C42C2414yes—
1211C2×C42C2414yes—
1212C2×C42C2411yescharacteristic
1213C2×C42C2411yescharacteristic
1214C2×C42C2411yescharacteristic
1215#95C2411yescharacteristic
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2411yescharacteristic
1220#95C2411yescharacteristic
1221#95C2411yescharacteristic
1222#95C2411yescharacteristic
1223#95C2411yescharacteristic
1224#95C2411yescharacteristic
1225#95C2411yescharacteristic
1226#95C2411yescharacteristic
1227#95C2411yescharacteristic
1228#95C2411yescharacteristic
1229#95C2411yescharacteristic
1230#95C2411yescharacteristic
1231#95C2411yescharacteristic
1232#95C2411yescharacteristic
1233#95C2411yescharacteristic
1234#95C2411yescharacteristic
1235#95C2411yescharacteristic
1236#95C2411yescharacteristic
1237#95C2411yescharacteristic
1238#95C2411yescharacteristic
1239#95C2411yescharacteristic
1240#95C2411yescharacteristic
1241#95C2411yescharacteristic
1242#95C2411yescharacteristic
1243#95C2411yescharacteristic
1244#95C2411yescharacteristic
1245#95C2411yescharacteristic
1246#95C2411yescharacteristic
1247#95C2411yescharacteristic
1248#95C2411yescharacteristic
1249#95C2411yescharacteristic
1250#95C2411yescharacteristic
1251#95C2411yescharacteristic
1252#95C2411yescharacteristic
1253#95C2411yescharacteristic
1254#95C2411yescharacteristic
1255#95C2411yescharacteristic
1256#95C2411yescharacteristic
1257#95C2411yescharacteristic
1258#95C2411yescharacteristic
1259#95C2411yescharacteristic
1260#95C2414yes—
1261#95C2414yes—
1262#95C2414yes—
1263#95C2414yes—
1264#95C2414yes—
1265#95C2411yescharacteristic
1266#95C2411yescharacteristic
1267#95C2411yescharacteristic
1268#95C2411yescharacteristic
1269#95C2411yescharacteristic
1270#95C2411yescharacteristic
1271#95C2414yes—
1272#95C2414yes—
1273#95C2414yes—
1274#95C2414yes—
1275#95C2414yes—
1276#95C2414yes—
1277#95C2414yes—
1278#95C2414yes—
1279#95C2414yes—
1280#95C2414yes—
1281#95C2414yes—
1282#95C2414yes—
1283#95C2414yes—
1284#95C2414yes—
1285#95C2414yes—
1286#95C2414yes—
1287#95C2414yes—
1288#95C2414yes—
1289#95C2414yes—
1290#95C2414yes—
1291#95C2414yes—
1292#95C2414yes—
1293#95C2414yes—
1294#95C2414yes—
1295#95C2414yes—
1296#95C2414yes—
1297C24C2514yes—
1298C24C2511yescharacteristic
1299C24C2511yescharacteristic
1300C24C2511yescharacteristic
1301#41—816no—
1302C2×Q8—28no—
1303C2×Q8—24no—
1304C2×Q8—24no—
1305C2×Q8—28no—
1306C2×Q8—24no—
1307C2×Q8—24no—
1308C2×Q8—24no—
1309C2×Q8—22no—
1310C2×Q8—24no—
1311C2×Q8—24no—
1312C2×Q8—28no—
1313C2×Q8—24no—
1314C2×Q8—22no—
1315C2×Q8—44no—
1316C2×Q8—41no—
1317C2×Q8—44no—
1318C2×Q8—44no—
1319C2×Q8—44no—
1320C2×Q8—44no—
1321C2×Q8—44no—
1322C2×Q8—432no—
1323C2×Q8—816no—
1324C2×Q8C2×#4118yes—
1325C2×D4—22no—
1326C2×D4—22no—
1327C2×D4—22no—
1328C2×D4—22no—
1329C2×D4—28no—
1330C2×D4—28no—
1331C2×D4—24no—
1332C2×D4—24no—
1333C2×D4—24no—
1334C2×D4—28no—
1335C2×D4—22no—
1336C2×D4—24no—
1337C2×D4—24no—
1338C2×D4—22no—
1339C2×D4—24no—
1340C2×D4—24no—
1341C2×D4—24no—
1342C2×D4—24no—
1343C2×D4—41no—
1344C2×D4—41no—
1345C2×D4—41no—
1346C2×D4—44no—
1347C2×D4—44no—
1348C2×D4—44no—
1349C2×D4—44no—
1350C2×D4—44no—
1351C2×D4—44no—
1352C22×C4—22no—
1353C22×C4—22no—
1354C22×C4—22no—
1355C22×C4—22no—
1356C22×C4—28no—
1357C22×C4—22no—
1358C22×C4—22no—
1359C22×C4—22no—
1360C22×C4—22no—
1361C22×C4—22no—
1362C22×C4—22no—
1363C22×C4—22no—
1364C22×C4—28no—
1365C22×C4—22no—
1366C22×C4—22no—
1367C22×C4—22no—
1368C22×C4—22no—
1369C22×C4—22no—
1370C22×C4—22no—
1371C22×C4—22no—
1372C22×C4—22no—
1373C22×C4—22no—
1374C22×C4—22no—
1375C22×C4—22no—
1376C22×C4—22no—
1377C22×C4—22no—
1378C22×C4—22no—
1379C22×C4—28no—
1380C22×C4—28no—
1381C22×C4—28no—
1382C22×C4—44no—
1383C22×C4—44no—
1384C22×C4—44no—
1385C22×C4—44no—
1386C22×C4—44no—
1387C22×C4—44no—
1388C22×C4—44no—
1389C22×C4—44no—
1390C22×C4—44no—
1391C22×C4—44no—
1392C22×C4H(5,𝔽2)14yes—
1393C22×C42−1+414yes—
1394C22×C4C2511yescharacteristic
1395C22×C4C2511yescharacteristic
1396C22×C4C2511yescharacteristic
1397C22×C4C2511yescharacteristic
1398C22×C4C2511yescharacteristic
1399C22×C4C2511yescharacteristic
1400C22×C4C2511yescharacteristic
1401C22×C4C2511yescharacteristic
1402C22×C4C2511yescharacteristic
1403C22×C4C2511yescharacteristic
1404C22×C4C2514yes—
1405C22×C4C2511yescharacteristic
1406C22×C4C2514yes—
1407C22×C4C2511yescharacteristic
1408C22×C4C2511yescharacteristic
1409C22×C4C2511yescharacteristic
1410C22×C4C2511yescharacteristic
1411C22×C4C2511yescharacteristic
1412C22×C4C2511yescharacteristic
1413C22×C4C2514yes—
1414C22×C4C2514yes—
1415C22×C4C2511yescharacteristic
1416C22×C4C2514yes—
1417C22×C4C2514yes—
1418C22×C4C2511yescharacteristic
1419C22×C4C2514yes—
1420C22×C4C2511yescharacteristic
1421C22×C4C2511yescharacteristic
1422C22×C4C2511yescharacteristic
1423C22×C4C2511yescharacteristic
1424C22×C4C2511yescharacteristic
1425C22×C4C2511yescharacteristic
1426C22×C4C2511yescharacteristic
1427C22×C4C2511yescharacteristic
1428C22×C4C2511yescharacteristic
1429C4⋊C4—28no—
1430C4⋊C4—28no—
1431C4⋊C4—28no—
1432C4⋊C4—28no—
1433C4⋊C4—24no—
1434C4⋊C4—24no—
1435C4⋊C4—24no—
1436C4⋊C4—24no—
1437C4⋊C4—22no—
1438C4⋊C4—22no—
1439C4⋊C4—22no—
1440C4⋊C4—22no—
1441C4⋊C4—22no—
1442C4⋊C4—24no—
1443C4⋊C4—28no—
1444C4⋊C4—24no—
1445C4⋊C4—28no—
1446C4⋊C4—22no—
1447C4⋊C4—22no—
1448C4⋊C4—22no—
1449C4⋊C4—24no—
1450C4⋊C4—22no—
1451C4⋊C4—22no—
1452C4⋊C4—24no—
1453C4⋊C4—28no—
1454C4⋊C4—22no—
1455C4⋊C4—22no—
1456C4⋊C4—22no—
1457C4⋊C4—22no—
1458C4⋊C4—22no—
1459C4⋊C4—22no—
1460C4⋊C4—22no—
1461C4⋊C4—24no—
1462C4⋊C4—22no—
1463C4⋊C4—22no—
1464C4⋊C4—22no—
1465C4⋊C4—24no—
1466C4⋊C4—24no—
1467C4⋊C4—24no—
1468C4⋊C4—24no—
1469C4⋊C4—24no—
1470C4⋊C4—24no—
1471C4⋊C4—24no—
1472C4⋊C4—41no—
1473C4⋊C4—41no—
1474C4⋊C4—41no—
1475C4⋊C4—41no—
1476C4⋊C4—44no—
1477C4⋊C4—44no—
1478C4⋊C4—44no—
1479C4⋊C4—41no—
1480C4⋊C4—41no—
1481C4⋊C4—41no—
1482C4⋊C4—44no—
1483C4⋊C4—44no—
1484C4⋊C4—44no—
1485C4⋊C4—41no—
1486C4⋊C4—41no—
1487C4⋊C4—41no—
1488C4⋊C4—44no—
1489C4⋊C4—44no—
1490C4⋊C4—44no—
1491C4⋊C4—44no—
1492C4⋊C4—44no—
1493C4⋊C4—44no—
1494C4⋊C4—44no—
1495C4⋊C4—44no—
1496C4⋊C4—44no—
1497C4⋊C4—44no—
1498C4⋊C4—44no—
1499C4⋊C4—44no—
1500C4⋊C4—44no—
1501C4⋊C4—44no—
1502C4⋊C4C2×#4118yes—
1503C4⋊C4C2×#4118yes—
1504C22⋊C4—22no—
1505C22⋊C4—22no—
1506C22⋊C4—22no—
1507C22⋊C4—22no—
1508C22⋊C4—28no—
1509C22⋊C4—22no—
1510C22⋊C4—22no—
1511C22⋊C4—22no—
1512C22⋊C4—22no—
1513C22⋊C4—28no—
1514C22⋊C4—28no—
1515C22⋊C4—22no—
1516C22⋊C4—22no—
1517C22⋊C4—28no—
1518C22⋊C4—22no—
1519C22⋊C4—22no—
1520C22⋊C4—22no—
1521C22⋊C4—22no—
1522C22⋊C4—28no—
1523C22⋊C4—28no—
1524C22⋊C4—22no—
1525C22⋊C4—22no—
1526C22⋊C4—22no—
1527C22⋊C4—22no—
1528C22⋊C4—28no—
1529C22⋊C4—22no—
1530C22⋊C4—22no—
1531C22⋊C4—28no—
1532C22⋊C4—41no—
1533C22⋊C4—41no—
1534C22⋊C4—41no—
1535C22⋊C4—41no—
1536C22⋊C4—44no—
1537C22⋊C4—44no—
1538C22⋊C4—44no—
1539C22⋊C4—44no—
1540C22⋊C4—44no—
1541C22⋊C4—44no—
1542C22⋊C4—44no—
1543C22⋊C4—41no—
1544C22⋊C4—41no—
1545C22⋊C4—41no—
1546C22⋊C4—41no—
1547C22⋊C4—41no—
1548C22⋊C4—41no—
1549C22⋊C4—44no—
1550C22⋊C4—44no—
1551C22⋊C4—44no—
1552C22⋊C4—44no—
1553C22⋊C4—44no—
1554C22⋊C4—44no—
1555C22⋊C4—44no—
1556C22⋊C4—44no—
1557C22⋊C4—44no—
1558C22⋊C4—44no—
1559C22⋊C4—44no—
1560C22⋊C4—44no—
1561C22⋊C4—44no—
1562C22⋊C4—44no—
1563C42—22no—
1564C42—22no—
1565C42—22no—
1566C42—22no—
1567C42—22no—
1568C42—22no—
1569C42—22no—
1570C42—22no—
1571C42—22no—
1572C42—22no—
1573C42—22no—
1574C42—22no—
1575C42—28no—
1576C42—28no—
1577C42—22no—
1578C42—22no—
1579C42—22no—
1580C42—22no—
1581C42—22no—
1582C42—22no—
1583C42—22no—
1584C42—22no—
1585C42—22no—
1586C42—22no—
1587C42—22no—
1588C42—22no—
1589C42—22no—
1590C42—22no—
1591C42—22no—
1592C42—22no—
1593C42—22no—
1594C42—22no—
1595C42—22no—
1596C42—44no—
1597C42—44no—
1598C42—44no—
1599C42—44no—
1600C42—44no—
1601C42—44no—
1602C42—44no—
1603C42—44no—
1604C42—44no—
1605C42C2×#4114yes—
1606C42H(5,𝔽2)14yes—
1607C422−1+414yes—
1608C23—21no—
1609C23—21no—
1610C23—21no—
1611C23—21no—
1612C23—21no—
1613C23—21no—
1614C23—21no—
1615C23—21no—
1616C23—21no—
1617C23—21no—
1618C23—21no—
1619C23—21no—
1620C23—24no—
1621C23—21no—
1622C23—24no—
1623C23—24no—
1624C23—21no—
1625C23—21no—
1626C23—21no—
1627C23—21no—
1628C23—24no—
1629C23—24no—
1630C23—21no—
1631C23—21no—
1632C23—24no—
1633C23—24no—
1634C23C2×H(5,𝔽2)12yes—
1635C23C2×2−1+412yes—
1636C23C2611yescharacteristic
1637Q8—216no—
1638Q8—44no—
1639Q8—416no—
1640Q8—48no—
1641Q8—48no—
1642Q8—88no—
1643Q8—164no—
1644D4—28no—
1645D4—44no—
1646D4—44no—
1647D4—48no—
1648D4—48no—
1649D4—48no—
1650D4—88no—
1651D4—88no—
1652D4—88no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—24no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—24no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—28no—
1668C2×C4—28no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—21no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—21no—
1676C2×C4—24no—
1677C2×C4—24no—
1678C2×C4—21no—
1679C2×C4—21no—
1680C2×C4—21no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—24no—
1684C2×C4—24no—
1685C2×C4—24no—
1686C2×C4—21no—
1687C2×C4—21no—
1688C2×C4—21no—
1689C2×C4—21no—
1690C2×C4—21no—
1691C2×C4—21no—
1692C2×C4—21no—
1693C2×C4—24no—
1694C2×C4—24no—
1695C2×C4—24no—
1696C2×C4—24no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—24no—
1702C2×C4—21no—
1703C2×C4—21no—
1704C2×C4—21no—
1705C2×C4—21no—
1706C2×C4—21no—
1707C2×C4—21no—
1708C2×C4—21no—
1709C2×C4—21no—
1710C2×C4—21no—
1711C2×C4—21no—
1712C2×C4—21no—
1713C2×C4—21no—
1714C2×C4—21no—
1715C2×C4—21no—
1716C2×C4—21no—
1717C2×C4—24no—
1718C2×C4—24no—
1719C2×C4—21no—
1720C2×C4—21no—
1721C2×C4—21no—
1722C2×C4—21no—
1723C2×C4—21no—
1724C2×C4—21no—
1725C2×C4—21no—
1726C2×C4—21no—
1727C2×C4—21no—
1728C2×C4—21no—
1729C2×C4—21no—
1730C2×C4—21no—
1731C2×C4—21no—
1732C2×C4—21no—
1733C2×C4—21no—
1734C2×C4—24no—
1735C2×C4—24no—
1736C2×C4—24no—
1737C2×C4—21no—
1738C2×C4—21no—
1739C2×C4—21no—
1740C2×C4—21no—
1741C2×C4—24no—
1742C2×C4—24no—
1743C2×C4—24no—
1744C2×C4—416no—
1745C2×C4—44no—
1746C2×C4—44no—
1747C2×C4—44no—
1748C2×C4—44no—
1749C2×C4—44no—
1750C2×C4—44no—
1751C2×C4—44no—
1752C2×C4—88no—
1753C2×C4—88no—
1754C2×C4—88no—
1755C2×C4—164no—
1756C2×C4C22×#4118yes—
1757C2×C4C22×#4112yes—
1758C2×C4C22×#4112yes—
1759C2×C4C22×#4112yes—
1760C2×C4C2×H(5,𝔽2)12yes—
1761C2×C4C2×H(5,𝔽2)12yes—
1762C2×C4C2×H(5,𝔽2)12yes—
1763C2×C4C2×H(5,𝔽2)12yes—
1764C2×C4C2×H(5,𝔽2)12yes—
1765C2×C4C2×2−1+412yes—
1766C2×C4C2×2−1+412yes—
1767C2×C4C2×2−1+412yes—
1768C2×C4C2×2−1+412yes—
1769C2×C4C2×2−1+412yes—
1770C2×C4#58512yes—
1771C2×C4#58512yes—
1772C22—22no—
1773C22—22no—
1774C22—22no—
1775C22—22no—
1776C22—22no—
1777C22—22no—
1778C22—41no—
1779C22—41no—
1780C22—41no—
1781C22—41no—
1782C22—41no—
1783C22—41no—
1784C22—41no—
1785C22—41no—
1786C22—41no—
1787C22—44no—
1788C22—41no—
1789C22—44no—
1790C22—41no—
1791C22—44no—
1792C22—44no—
1793C22—41no—
1794C22—44no—
1795C22—41no—
1796C22—44no—
1797C22—41no—
1798C22—44no—
1799C22—41no—
1800C22C23×#4111yescharacteristic
1801C22C22×H(5,𝔽2)11yescharacteristic
1802C22C22×H(5,𝔽2)11yescharacteristic
1803C22C22×2−1+411yescharacteristic
1804C22C22×2−1+411yescharacteristic
1805C22C2×#58511yescharacteristic
1806C22C2×#58511yescharacteristic
1807C4—22no—
1808C4—28no—
1809C4—22no—
1810C4—22no—
1811C4—22no—
1812C4—22no—
1813C4—22no—
1814C4—41no—
1815C4—44no—
1816C4—41no—
1817C4—44no—
1818C4—41no—
1819C4—41no—
1820C4—41no—
1821C4—41no—
1822C4—41no—
1823C4—41no—
1824C4—41no—
1825C4—41no—
1826C4—41no—
1827C4—41no—
1828C4—41no—
1829C4—41no—
1830C4—44no—
1831C4—44no—
1832C4—41no—
1833C4—41no—
1834C4—41no—
1835C4—44no—
1836C4—41no—
1837C4—44no—
1838C4—41no—
1839C4#351614yes—
1840C4#351814yes—
1841C4#351914yes—
1842C2—42no—
1843C2—42no—
1844C2—81no—
1845C2—84no—
1846C2C2×#351911yescharacteristic
1847C2C2×#351611yescharacteristic
1848C2C2×#351811yescharacteristic
1849C2#6283311yescharacteristic
1850C2#6283511yescharacteristic
1851C2#6283511yescharacteristic
1852C2#6283611yescharacteristic
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. #45360C2semidirect
2. #45311C2semidirect
3. #45307C2semidirect
4. #45289C2semidirect
5. #45156C2semidirect
6. #45095C2semidirect
7. #45040C2semidirect
8. #45037C2semidirect
9. #45032C2semidirect
10. #45027C2semidirect
11. #44975C2semidirect
12. #44925C2semidirect
13. #42857C2semidirect
14. #42847C2semidirect
15. #42618C2semidirect
16. #42614C2semidirect
17. #42583C2semidirect
18. #42579C2semidirect
19. #36594C2semidirect
20. #36563C2semidirect
21. #36211C2semidirect
22. #36210C2semidirect
23. #36194C2semidirect
24. #36122C2semidirect
25. #36122C2semidirect
26. D4×C4⋊Q8C2semidirect
27. #36000C2semidirect
28. #35905C2semidirect
29. #35871C2semidirect
30. #35817C2semidirect
31. #35771C2semidirect
32. #35722C2semidirect
33. #35288C2semidirect
34. #35284C2semidirect
35. #35277C2semidirect
36. #34551C2semidirect
37. #34226C2semidirect
38. #34216C2semidirect
39. #34209C2semidirect

Maximal subgroups

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

subgroupindex
#453602
#453112
#453072
#452892
#451562
#450952
#450402
#450372
#450322
#450272
#449752
#449252
#428572
#428472
#426182
#426142
#425832
#425792
#365942
#365632
#362112
#362102
#361942
#361222
D4×C4⋊Q82
#360002
#359052
#358712
#358172
#357712
#357222
#352882
#352842
#352772
#345512
#342262
#342162
#342092