Finite Group Databasebeta

← #7681047

Subgroups — #7681047

Order 512.

10774 conjugacy classes of subgroups.

The subgroup lattice has 1691 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3489C211yesmaximal, characteristic, complemented
3C2×#3486C211yesmaximal, characteristic, complemented
4C22×#536C211yesmaximal, characteristic, complemented
5#59002C214yesmaximal, complemented
6#58998C214yesmaximal, complemented
7#58995C218yesmaximal, complemented
8#45321C214yesmaximal, complemented
9#45091C214yesmaximal, complemented
10#44758C218yesmaximal, complemented
11#39360C212yesmaximal, complemented
12#39356C212yesmaximal, complemented
13#37680C212yesmaximal, complemented
14#37676C212yesmaximal, complemented
15#37675C212yesmaximal, complemented
16#37675C212yesmaximal, complemented
17#36124C212yesmaximal, complemented
18D4×C4⋊Q8C212yesmaximal, complemented
19#35667C211yesmaximal, characteristic, complemented
20#35666C211yesmaximal, characteristic, complemented
21#35660C211yesmaximal, characteristic, complemented
22#35621C211yesmaximal, characteristic, complemented
23#35317C211yesmaximal, characteristic, complemented
24#35308C211yesmaximal, characteristic, complemented
25#35306C211yesmaximal, characteristic, complemented
26#34738C211yesmaximal, characteristic, complemented
27C2×#2434C211yesmaximal, characteristic, complemented
28#34276C211yesmaximal, characteristic, complemented
29#34136C211yesmaximal, characteristic, complemented
30C22×2−1+4C2211yescharacteristic
31C22×2−1+4C2211yescharacteristic, complemented
32C23×#41C2211yescharacteristic
33C24×Q8C2211yescharacteristic
34#3499—216no—
35#3489—216no—
36#3486—216no—
37C2×D4×Q8C2212yes—
38C2×D4×Q8C2212yes—
39C2×D4×Q8C2212yes—
40C2×D4×Q8C2212yescomplemented
41C2×D4×Q8C2214yescomplemented
42C2×D4×Q8C2212yescomplemented
43C2×#548C2212yes—
44C2×#548C2212yes—
45C2×#548C2212yes—
46C2×#548C2212yescomplemented
47C2×#548C2212yescomplemented
48C2×#547C2212yes—
49C2×#547C2214yes—
50C2×#547C2214yescomplemented
51C2×#547C2218yescomplemented
52C2×#546C2212yes—
53C2×#546C2214yes—
54C2×#537C2212yes—
55C2×#537C2211yescharacteristic
56C2×#536—216no—
57C2×#536C2212yes—
58C2×#536C2214yes—
59C2×#536C2211yescharacteristic
60C2×#536C2212yes—
61C2×#536C2212yes—
62C2×#536C2211yescharacteristic
63C2×#536C2211yescharacteristic
64C2×#536C2214yes—
65C2×#536C2211yescharacteristic
66C2×#536C2211yescharacteristic
67C2×#536C2211yescharacteristic, complemented
68C2×#536C2212yescomplemented
69C2×#536C2212yescomplemented
70C2×#536C2211yescharacteristic, complemented
71C2×#536C2214yescomplemented
72C2×#536C2211yescharacteristic, complemented
73C2×#532C2211yescharacteristic
74C2×#532C2211yescharacteristic
75C2×#532C2212yescomplemented
76C22×C4⋊Q8C2212yes—
77C22×C4⋊Q8C2212yescomplemented
78C22×C4⋊Q8C2211yescharacteristic, complemented
79C22×C4⋊Q8C2211yescharacteristic, complemented
80C22×#124C2212yes—
81C2×#525C2214yes—
82C2×#525C2211yescharacteristic
83C2×#525C2212yes—
84C2×#525C2211yescharacteristic
85C22×#123C2214yes—
86C22×C22⋊Q8C2212yes—
87C22×C22⋊Q8C2211yescharacteristic
88C22×C22⋊Q8C2214yes—
89C2×#520C2211yescharacteristic
90C2×#519C2211yescharacteristic, complemented
91C2×C4×#41C2211yescharacteristic, complemented
92C22×#117C2211yescharacteristic
93#2868C2212yescomplemented
94#2858C2212yescomplemented
95#2857C2212yes—
96#2857C2212yescomplemented
97#2850C2212yes—
98#2850C2212yescomplemented
99#2683C2218yescomplemented
100#2682C2218yescomplemented
101#2680C2218yescomplemented
102#2680C2218yescomplemented
103#2677C2218yescomplemented
104#2677C2218yescomplemented
105#2674C2218yescomplemented
106#2674C2218yescomplemented
107#2674C2218yescomplemented
108#2672C2218yescomplemented
109#2672C2218yescomplemented
110#2671C2218yescomplemented
111#2658C2212yescomplemented
112#2658C2212yescomplemented
113#2621C2212yescomplemented
114#2621C2212yescomplemented
115#2620C2212yescomplemented
116#2620C2212yescomplemented
117#2555C2218yescomplemented
118#2551C2218yescomplemented
119#2547C2212yescomplemented
120#2546C2212yescomplemented
121#2546C2212yescomplemented
122#2546C2212yescomplemented
123#2545C2212yescomplemented
124#2545C2212yescomplemented
125#2545C2212yescomplemented
126#2544C2212yescomplemented
127#2542C2214yescomplemented
128#2542C2214yescomplemented
129#2501C2218yescomplemented
130#2461C2218yescomplemented
131#2461C2218yescomplemented
132#2461C2218yescomplemented
133#2455C2218yescomplemented
134#2449C2218yes—
135#2449C2218yescomplemented
136#2449C2218yescomplemented
137#2443C2218yes—
138#2443C2218yescomplemented
139#2440C2218yes—
140#2440C2218yescomplemented
141#2440C2218yescomplemented
142#2437C2218yes—
143#2436C2211yescharacteristic
144#2436C2212yescomplemented
145#2435C2211yescharacteristic
146#2434C2211yescharacteristic
147#2434C2212yes—
148#2434C2212yes—
149#2434C2214yes—
150#2434C2214yescomplemented
151#2434C2214yescomplemented
152#2434C2212yescomplemented
153#2434C2212yescomplemented
154#2434C2212yescomplemented
155#2434C2212yescomplemented
156#2434C2212yescomplemented
157#2433C2211yescharacteristic
158#2432C2211yescharacteristic
159#2432C2211yescharacteristic
160#2432C2212yescomplemented
161#2432C2214yescomplemented
162#2432C2212yescomplemented
163#2432C2212yescomplemented
164#2431C2211yescharacteristic
165#2431C2211yescharacteristic
166#2431C2212yescomplemented
167#2430C2214yes—
168#2430C2218yescomplemented
169#2429C2214yescomplemented
170#2429C2214yescomplemented
171#2429C2214yescomplemented
172#2427C2214yescomplemented
173#2425C2218yescomplemented
174#2425C2218yescomplemented
175#2424C2218yes—
176#2422C2218yescomplemented
177#2418C2218yes—
178#2417C2214yes—
179#2417C2214yescomplemented
180#2415C2214yescomplemented
181#2415C2214yescomplemented
182#2413C2218yescomplemented
183#2413C2214yescomplemented
184#2412C2214yes—
185#2410C2214yes—
186#2409C2214yescomplemented
187#2407C2214yescomplemented
188#2406C2218yescomplemented
189#2388C2214yes—
190C2×#395C2214yescomplemented
191#2363C2212yescomplemented
192#2362C2212yescomplemented
193#2362C2214yescomplemented
194#2361C2212yes—
195#2360C2212yes—
196#2360C2214yescomplemented
197#2359C2214yescomplemented
198#2359C2218yescomplemented
199#2358C2218yes—
200#2358C2214yes—
201D4×C4⋊C4C2218yes—
202#2327C2212yescomplemented
203#2326C2212yescomplemented
204#2317C2211yescharacteristic, complemented
205#2311C2211yescharacteristic, complemented
206#2310C2211yescharacteristic, complemented
207C4×C4⋊Q8C2212yescomplemented
208C4×#124C2212yescomplemented
209C4×#120C2214yes—
210#2297C2211yescharacteristic
211#2297C2211yescharacteristic
212#2297C2211yescharacteristic, complemented
213#2296C2211yescharacteristic, complemented
214C2×#391C2211yescharacteristic, complemented
215C2×#391C2211yescharacteristic, complemented
216#2293C2212yescomplemented
217#2290C2212yes—
218#2290C2212yescomplemented
219C2×#385C2214yes—
220C42×D4C2212yes—
221C4×#117C2211yescharacteristic, complemented
222C2×C4×C22⋊C4C2211yescharacteristic
223C2×2−1+4—28no—
224C2×2−1+4—28no—
225C2×2−1+4—28no—
226C2×2−1+4—28no—
227C2×2−1+4—44no—
228C2×2−1+4—44no—
229C22×#41—28no—
230C22×#41—28no—
231C22×#41—44no—
232C22×#41C2311yescharacteristic
233C22×#41C2311yescharacteristic
234C22×#41C2312yes—
235C22×#41C2312yes—
236C22×#41C2311yescharacteristic
237C22×#41C2311yescharacteristic
238C22×#41C2314yes—
239C22×#41C2312yes—
240C22×#41C2312yes—
241C22×#41C2312yes—
242C22×#41C2314yes—
243C22×#41C2312yes—
244C22×#41C2311yescharacteristic
245C22×#41C2311yescharacteristic
246C23×Q8—28no—
247C23×Q8—28no—
248C23×Q8—44no—
249C23×Q8C2311yescharacteristic
250C23×Q8C2311yescharacteristic
251C23×Q8C2312yes—
252C23×Q8C2312yes—
253C23×Q8C2312yes—
254C23×Q8C2312yes—
255C23×Q8C2312yes—
256C23×Q8C2311yescharacteristic
257C23×Q8C2312yes—
258C23×Q8C2312yes—
259C23×Q8C2312yes—
260C23×Q8C2312yes—
261C23×Q8C2311yescharacteristic
262C23×D4C2312yes—
263C23×D4C2311yescharacteristic
264C24×C4C2312yes—
265C24×C4C2312yes—
266C24×C4C2311yescharacteristic
267D4×Q8—216no—
268D4×Q8—216no—
269D4×Q8—232no—
270D4×Q8—216no—
271D4×Q8—216no—
272D4×Q8—216no—
273#548—216no—
274#548—216no—
275#548—216no—
276#548—216no—
277#548—216no—
278#547—232no—
279#547—264no—
280#547—232no—
281#547—216no—
282#546—232no—
283#546—216no—
284#537—28no—
285#537—216no—
286#536—28no—
287#536—28no—
288#536—28no—
289#536—216no—
290#536—216no—
291#536—216no—
292#536—216no—
293#536—232no—
294#536—232no—
295#536—232no—
296#536—216no—
297#536—28no—
298#536—28no—
299#536—28no—
300#536—28no—
301#536D4116yescomplemented
302#532—28no—
303#532—216no—
304#532—44no—
305C2×C4⋊Q8—28no—
306C2×C4⋊Q8—216no—
307C2×C4⋊Q8—216no—
308C2×C4⋊Q8—44no—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2318yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2318yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2314yes—
321C2×C4⋊Q8C2314yes—
322C2×C4⋊Q8C2314yes—
323C2×C4⋊Q8C2314yes—
324C2×C4⋊Q8C2312yes—
325C2×C4⋊Q8C2312yes—
326C2×C4⋊Q8C2311yescharacteristic
327C2×C4⋊Q8C2312yes—
328C2×C4⋊Q8C2314yes—
329C2×C4⋊Q8C2312yes—
330C2×#127C2311yescharacteristic
331C2×#127C2311yescharacteristic
332C2×#124—216no—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2318yes—
338C2×#124C2312yes—
339C2×#124C2312yes—
340C2×#124C2314yes—
341C2×#124C2314yes—
342C2×#124C2314yes—
343C2×#124C2311yescharacteristic
344C2×#124C2311yescharacteristic
345C2×#124C2312yes—
346C2×#124C2311yescharacteristic
347C2×#124C2311yescharacteristic
348C2×#124C2312yes—
349#525—28no—
350#525—216no—
351#525—232no—
352#525D4116yescomplemented
353C2×#123—232no—
354C2×#123C2314yes—
355C2×#123C2314yes—
356C2×#123C2314yes—
357C2×#123C2318yes—
358C2×#123C2318yes—
359C2×#123C2314yes—
360C2×#123C2312yes—
361C2×#123C2314yes—
362C2×#123C2314yes—
363C2×#123C2314yes—
364C2×#123C2314yes—
365C2×#123C2318yes—
366C2×#123C2314yes—
367C2×#123C2318yes—
368C2×#123C2314yes—
369C2×#123C2314yes—
370C2×#123C2312yes—
371C2×C22⋊Q8—28no—
372C2×C22⋊Q8—232no—
373C2×C22⋊Q8—216no—
374C2×C22⋊Q8C2312yes—
375C2×C22⋊Q8C2312yes—
376C2×C22⋊Q8C2311yescharacteristic
377C2×C22⋊Q8C2312yes—
378C2×C22⋊Q8C2312yes—
379C2×C22⋊Q8C2312yes—
380C2×C22⋊Q8C2311yescharacteristic
381C2×C22⋊Q8C2314yes—
382C2×C22⋊Q8C2312yes—
383C2×C22⋊Q8C2312yes—
384C2×C22⋊Q8C2312yes—
385C2×C22⋊Q8C2314yes—
386C2×C22⋊Q8C2318yes—
387C2×C22⋊Q8C2314yes—
388C2×C22⋊Q8C2318yes—
389C2×C22⋊Q8C2314yes—
390C2×C22⋊Q8C2312yes—
391C2×C22⋊Q8C2314yes—
392C2×C22⋊Q8C2314yes—
393C2×C22⋊Q8C2312yes—
394C2×C22⋊Q8C2314yes—
395C2×C22⋊Q8C2312yes—
396C2×C22⋊Q8C2314yes—
397C2×C22⋊Q8C2314yes—
398C2×C22⋊Q8C2312yes—
399C2×C22⋊Q8C2314yes—
400C2×C22⋊Q8C2318yes—
401C2×C22⋊Q8C2314yes—
402C2×C22⋊Q8C2318yes—
403C2×C22⋊Q8C2314yes—
404C2×C22⋊Q8C2314yes—
405C2×C22⋊Q8C2311yescharacteristic
406C2×C22⋊Q8C2314yes—
407C2×C22⋊Q8C2311yescharacteristic
408C2×#121C2311yescharacteristic
409C2×#121C2312yes—
410C2×#121C2311yescharacteristic
411C2×#121C2312yes—
412C2×#121C2314yes—
413C2×#121C2314yes—
414C2×#121C2314yes—
415C2×#121C2314yes—
416C2×#121C2318yes—
417C2×#121C2314yes—
418C2×#121C2314yes—
419C2×#121C2314yes—
420C2×#121C2314yes—
421C2×#121C2311yescharacteristic
422C2×#121C2311yescharacteristic
423C2×#120C2314yes—
424C2×#120C2312yes—
425C2×#120C2314yes—
426C2×#120C2312yes—
427#520—28no—
428#519—28no—
429C4×#41—28no—
430C2×C4×Q8C2312yes—
431C2×C4×Q8C2312yes—
432C2×C4×Q8C2312yes—
433C2×C4×Q8C2312yes—
434C2×C4×Q8C2312yes—
435C2×C4×Q8C2312yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2314yes—
438C2×C4×D4C2314yes—
439C2×C4×D4C2314yes—
440C2×C4×D4C2314yes—
441C2×C4×D4C2314yes—
442C2×C4×D4C2318yes—
443C2×C4×D4C2314yes—
444C2×C4×D4C2312yes—
445C2×C4×D4C2312yes—
446C2×C4×D4C2314yes—
447C2×C4×D4C2312yes—
448C2×C4×D4C2314yes—
449C2×C4×D4C2314yes—
450C2×C4×D4C2314yes—
451C2×C4×D4C2314yes—
452C2×C4×D4C2312yes—
453C2×C4×D4C2312yes—
454C2×#117—28no—
455C2×#117C2311yescharacteristic
456C2×#117C2311yescharacteristic
457C2×#117C2312yes—
458C2×#117C2314yes—
459C2×#117C2312yes—
460C2×#117C2312yes—
461C2×#117C2312yes—
462C2×#117C2312yes—
463C2×#117C2311yescharacteristic
464C2×#117C2311yescharacteristic
465C22×C4⋊C4C2311yescharacteristic
466C22×C4⋊C4C2318yes—
467C22×C4⋊C4C2318yes—
468C22×C4⋊C4C2312yes—
469C22×C4⋊C4C2312yes—
470C22×C4⋊C4C2312yes—
471C22×C4⋊C4C2314yes—
472C22×C4⋊C4C2314yes—
473C22×C4⋊C4C2314yes—
474C22×C22⋊C4C2312yes—
475C22×C22⋊C4C2314yes—
476C22×C22⋊C4C2312yes—
477C22×C22⋊C4C2318yes—
478C22×C22⋊C4C2312yes—
479C22×C42C2312yes—
480C22×C42C2312yes—
481C22×C42C2311yescharacteristic
482C22×C42C2311yescharacteristic
483#399C2318yes—
484#399C2318yes—
485#399C2318yes—
486#399C2318yes—
487#398C2318yes—
488#398C2318yes—
489#398C2318yes—
490#398C2318yes—
491#398C2318yes—
492#397C2318yes—
493#397C2318yes—
494#397C2318yes—
495#396C2318yes—
496#396C2318yes—
497#396C2318yes—
498#396C2318yes—
499#396C2318yes—
500#395C2318yes—
501#395C2318yes—
502#395C2318yes—
503#395C2318yes—
504#395C2314yes—
505#395C2318yes—
506#395C2318yes—
507#395C2318yes—
508#394C2318yes—
509#394C2318yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2318yes—
514#394C2318yes—
515#394C2318yes—
516#394C2318yes—
517#393C2314yes—
518#393C2318yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2318yes—
523#391C2311yescharacteristic
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2314yes—
528#391C2312yes—
529#391C2312yes—
530#391C2311yescharacteristic
531#391C2312yes—
532#391C2311yescharacteristic
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2311yescharacteristic
537#391C2314yes—
538#390C2312yes—
539#390C2311yescharacteristic
540#390C2311yescharacteristic
541#390C2318yes—
542#390C2318yes—
543#390C2314yes—
544#390C2312yes—
545#390C2311yescharacteristic
546#390C2311yescharacteristic
547#389C2318yes—
548#389C2314yes—
549#389C2318yes—
550#389C2318yes—
551#389C2318yes—
552#389C2318yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2318yes—
557#388C2318yes—
558#388C2318yes—
559#388C2318yes—
560#388C2314yes—
561#388C2314yes—
562#388C2318yes—
563#388C2314yes—
564#388C2318yes—
565#388C2314yes—
566#388C2318yes—
567#388C2318yes—
568#387C2318yes—
569#387C2318yes—
570#387C2314yes—
571#387C2314yes—
572#386C2314yes—
573#386C2318yes—
574#386C2318yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2318yes—
579#386C2318yes—
580#386C2314yes—
581#386C2318yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#385C2314yes—
587#385C2318yes—
588#385C2314yes—
589#385C2318yes—
590#385C2318yes—
591#385C2318yes—
592#385C2314yes—
593#385C2314yes—
594#385C2318yes—
595#385C2314yes—
596#385C2318yes—
597#385C2318yes—
598#385C2318yes—
599#385C2318yes—
600#385C2318yes—
601#385C2314yes—
602#385C2318yes—
603#385C2314yes—
604#384C2312yes—
605#384C2318yes—
606#384C2318yes—
607#382C2312yes—
608#381C2314yes—
609#380C2314yes—
610#380C2318yes—
611#380C2318yes—
612#380C2318yes—
613#379C2314yes—
614C4×C4⋊C4C2318yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2318yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2312yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2311yescharacteristic
629C4×C22⋊C4C2311yescharacteristic
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2311yescharacteristic
633C4×C22⋊C4C2311yescharacteristic
634#376C2312yes—
635C2×#95C2312yes—
636C2×#95C2314yes—
637C2×#95C2314yes—
638C43C2312yes—
639C25C2412yes—
640C25C2411yescharacteristic
6412−1+4—464no—
6422−1+4—464no—
643C2×#41—28no—
644C2×#41—24no—
645C2×#41—28no—
646C2×#41—216no—
647C2×#41—28no—
648C2×#41—28no—
649C2×#41—28no—
650C2×#41—24no—
651C2×#41—216no—
652C2×#41—216no—
653C2×#41—28no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—28no—
659C2×#41—24no—
660C2×#41—28no—
661C2×#41—24no—
662C2×#41—28no—
663C2×#41—24no—
664C2×#41—28no—
665C2×#41—28no—
666C2×#41—216no—
667C2×#41—24no—
668C2×#41—28no—
669C2×#41—24no—
670C2×#41—24no—
671C2×#41—24no—
672C2×#41—24no—
673C2×#41—44no—
674C2×#41—44no—
675C2×#41—48no—
676C2×#41—48no—
677C2×#41—42no—
678C2×#41—42no—
679C2×#41—44no—
680C2×#41—44no—
681C2×#41—44no—
682C2×#41—44no—
683C2×#41—464no—
684C2×#41C2×D418yes—
685C2×#41C2×D418yes—
686C22×Q8—28no—
687C22×Q8—28no—
688C22×Q8—28no—
689C22×Q8—24no—
690C22×Q8—28no—
691C22×Q8—28no—
692C22×Q8—28no—
693C22×Q8—28no—
694C22×Q8—28no—
695C22×Q8—28no—
696C22×Q8—24no—
697C22×Q8—24no—
698C22×Q8—24no—
699C22×Q8—28no—
700C22×Q8—28no—
701C22×Q8—24no—
702C22×Q8—24no—
703C22×Q8—28no—
704C22×Q8—28no—
705C22×Q8—28no—
706C22×Q8—28no—
707C22×Q8—28no—
708C22×Q8—24no—
709C22×Q8—28no—
710C22×Q8—28no—
711C22×Q8—24no—
712C22×Q8—24no—
713C22×Q8—24no—
714C22×Q8—44no—
715C22×Q8—44no—
716C22×Q8—44no—
717C22×Q8—44no—
718C22×Q8—44no—
719C22×Q8—42no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8—44no—
723C22×Q8—44no—
724C22×Q8—464no—
725C22×Q8C2×D418yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2412yes—
729C22×Q8C2412yes—
730C22×Q8C2411yescharacteristic
731C22×Q8C2411yescharacteristic
732C22×Q8C2414yes—
733C22×Q8C2414yes—
734C22×Q8C2414yes—
735C22×Q8C2414yes—
736C22×Q8C2412yes—
737C22×Q8C2412yes—
738C22×Q8C2411yescharacteristic
739C22×Q8C2412yes—
740C22×Q8C2411yescharacteristic
741C22×D4—28no—
742C22×D4—28no—
743C22×D4—24no—
744C22×D4—24no—
745C22×D4—42no—
746C22×D4—44no—
747C22×D4C2412yes—
748C22×D4C2412yes—
749C22×D4C2412yes—
750C22×D4C2411yescharacteristic
751C22×D4C2411yescharacteristic
752C22×D4C2414yes—
753C22×D4C2414yes—
754C22×D4C2414yes—
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2412yes—
760C22×D4C2411yescharacteristic
761C22×D4C2412yes—
762C22×D4C2411yescharacteristic
763C22×D4C2412yes—
764C22×D4C2414yes—
765C22×D4C2414yes—
766C22×D4C2412yes—
767C23×C4—24no—
768C23×C4—24no—
769C23×C4—28no—
770C23×C4—28no—
771C23×C4—28no—
772C23×C4—28no—
773C23×C4—44no—
774C23×C4—44no—
775C23×C4C2×D418yes—
776C23×C4C2412yes—
777C23×C4C2412yes—
778C23×C4C2412yes—
779C23×C4C2412yes—
780C23×C4C2414yes—
781C23×C4C2414yes—
782C23×C4C2412yes—
783C23×C4C2412yes—
784C23×C4C2414yes—
785C23×C4C2412yes—
786C23×C4C2414yes—
787C23×C4C2414yes—
788C23×C4C2414yes—
789C23×C4C2412yes—
790C23×C4C2414yes—
791C23×C4C2414yes—
792C23×C4C2412yes—
793C23×C4C2411yescharacteristic
794C23×C4C2412yes—
795C23×C4C2411yescharacteristic
796C23×C4C2412yes—
797C23×C4C2411yescharacteristic
798C23×C4C2411yescharacteristic
799C23×C4C2412yes—
800C23×C4C2411yescharacteristic
801C23×C4C2412yes—
802C23×C4C2414yes—
803C23×C4C2411yescharacteristic
804C4⋊Q8—28no—
805C4⋊Q8—24no—
806C4⋊Q8—28no—
807C4⋊Q8—28no—
808C4⋊Q8—28no—
809C4⋊Q8—216no—
810C4⋊Q8—28no—
811C4⋊Q8—232no—
812C4⋊Q8—232no—
813C4⋊Q8—216no—
814C4⋊Q8—216no—
815C4⋊Q8—216no—
816C4⋊Q8—28no—
817C4⋊Q8—28no—
818C4⋊Q8—28no—
819C4⋊Q8—28no—
820C4⋊Q8—48no—
821C4⋊Q8—44no—
822C4⋊Q8—44no—
823C4⋊Q8—42no—
824C4⋊Q8C2×D4116yes—
825#127—24no—
826#127—42no—
827#124—28no—
828#124—24no—
829#124—28no—
830#124—24no—
831#124—28no—
832#124—232no—
833#124—216no—
834#124—216no—
835#124—216no—
836#124—28no—
837#124—28no—
838#124—28no—
839#124—28no—
840#124—42no—
841#124—42no—
842#124C2×D4116yes—
843#123—216no—
844#123—216no—
845#123—216no—
846#123—28no—
847#123—232no—
848#123—216no—
849#123—232no—
850#123—232no—
851#123—216no—
852#123—216no—
853#123—216no—
854#123—216no—
855#123—216no—
856#123—232no—
857#123—216no—
858#123C2×D4132yes—
859#123C2×D4116yes—
860C22⋊Q8—216no—
861C22⋊Q8—28no—
862C22⋊Q8—28no—
863C22⋊Q8—216no—
864C22⋊Q8—28no—
865C22⋊Q8—28no—
866C22⋊Q8—28no—
867C22⋊Q8—24no—
868C22⋊Q8—24no—
869C22⋊Q8—28no—
870C22⋊Q8—28no—
871C22⋊Q8—28no—
872C22⋊Q8—232no—
873C22⋊Q8—216no—
874C22⋊Q8—28no—
875C22⋊Q8—216no—
876C22⋊Q8—28no—
877C22⋊Q8—216no—
878C22⋊Q8—232no—
879C22⋊Q8—216no—
880C22⋊Q8—216no—
881C22⋊Q8—28no—
882C22⋊Q8—28no—
883C22⋊Q8—232no—
884C22⋊Q8—216no—
885C22⋊Q8—216no—
886C22⋊Q8—216no—
887C22⋊Q8—232no—
888C22⋊Q8—216no—
889C22⋊Q8—216no—
890C22⋊Q8—216no—
891C22⋊Q8C2×D418yes—
892C22⋊Q8C2×D4132yes—
893C22⋊Q8C2×D418yes—
894#121—28no—
895#121—216no—
896#121—216no—
897#121—216no—
898#121—216no—
899#121—216no—
900#121—216no—
901#121—24no—
902#121—24no—
903#121—28no—
904#121—232no—
905#121—216no—
906#121—48no—
907#121C2×D418yes—
908#121C2×D418yes—
909#120—28no—
910#120—216no—
911#120—216no—
912#120C2×D4116yes—
913C4×Q8—28no—
914C4×Q8—28no—
915C4×Q8—28no—
916C4×Q8—28no—
917C4×Q8—28no—
918C4×Q8—28no—
919C4×D4—216no—
920C4×D4—216no—
921C4×D4—216no—
922C4×D4—28no—
923C4×D4—28no—
924C4×D4—216no—
925C4×D4—28no—
926C4×D4—216no—
927C4×D4—216no—
928C4×D4—216no—
929C4×D4—216no—
930C4×D4—216no—
931C4×D4—232no—
932C4×D4—216no—
933C4×D4—28no—
934C4×D4—48no—
935C4×D4C2×D4116yes—
936C4×D4C2×D4116yes—
937#117—24no—
938#117—24no—
939#117—28no—
940#117—28no—
941#117—28no—
942#117—216no—
943#117—28no—
944#117—28no—
945#117C2×D418yes—
946#117C2×D418yes—
947C2×C4⋊C4—24no—
948C2×C4⋊C4—28no—
949C2×C4⋊C4—216no—
950C2×C4⋊C4—28no—
951C2×C4⋊C4—28no—
952C2×C4⋊C4—232no—
953C2×C4⋊C4—216no—
954C2×C4⋊C4—232no—
955C2×C4⋊C4—48no—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2418yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2418yes—
968C2×C4⋊C4C2418yes—
969C2×C4⋊C4C2418yes—
970C2×C4⋊C4C2418yes—
971C2×C4⋊C4C2418yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2418yes—
986C2×C4⋊C4C2418yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2418yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2418yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C22⋊C4—28no—
997C2×C22⋊C4—28no—
998C2×C22⋊C4—232no—
999C2×C22⋊C4—216no—
1000C2×C22⋊C4—28no—
1001C2×C22⋊C4C2414yes—
1002C2×C22⋊C4C2412yes—
1003C2×C22⋊C4C2414yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2414yes—
1007C2×C22⋊C4C2418yes—
1008C2×C22⋊C4C2418yes—
1009C2×C22⋊C4C2418yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2418yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2418yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2418yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C42—24no—
1047C2×C42—24no—
1048C2×C42—28no—
1049C2×C42—28no—
1050C2×C42C2412yes—
1051C2×C42C2411yescharacteristic
1052C2×C42C2414yes—
1053C2×C42C2414yes—
1054C2×C42C2412yes—
1055C2×C42C2414yes—
1056C2×C42C2414yes—
1057C2×C42C2412yes—
1058C2×C42C2414yes—
1059C2×C42C2412yes—
1060C2×C42C2414yes—
1061C2×C42C2411yescharacteristic
1062C2×C42C2411yescharacteristic
1063C2×C42C2411yescharacteristic
1064C2×C42C2414yes—
1065C2×C42C2412yes—
1066C2×C42C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2418yes—
1072#95C2418yes—
1073#95C2418yes—
1074#95C2418yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2418yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2418yes—
1087#95C2418yes—
1088#95C2418yes—
1089C24—22no—
1090C24—22no—
1091C24—24no—
1092C24—24no—
1093C24—24no—
1094C24—28no—
1095C24—42no—
1096C24—42no—
1097C24—44no—
1098C24C22×D414yes—
1099C24C2512yes—
1100C24C2512yes—
1101C24C2511yescharacteristic
1102C24C2512yes—
1103C24C2512yes—
1104C24C2511yescharacteristic
1105C24C2511yescharacteristic
1106#41—232no—
1107#41—232no—
1108#41—432no—
1109#41—432no—
1110#41—416no—
1111#41—464no—
1112#41—432no—
1113#41—432no—
1114#41—416no—
1115#41—432no—
1116#41—464no—
1117#41—432no—
1118#41—416no—
1119#41—416no—
1120C2×Q8—232no—
1121C2×Q8—22no—
1122C2×Q8—24no—
1123C2×Q8—24no—
1124C2×Q8—22no—
1125C2×Q8—28no—
1126C2×Q8—24no—
1127C2×Q8—24no—
1128C2×Q8—28no—
1129C2×Q8—28no—
1130C2×Q8—24no—
1131C2×Q8—24no—
1132C2×Q8—28no—
1133C2×Q8—24no—
1134C2×Q8—28no—
1135C2×Q8—28no—
1136C2×Q8—28no—
1137C2×Q8—24no—
1138C2×Q8—22no—
1139C2×Q8—24no—
1140C2×Q8—22no—
1141C2×Q8—28no—
1142C2×Q8—24no—
1143C2×Q8—22no—
1144C2×Q8—24no—
1145C2×Q8—24no—
1146C2×Q8—22no—
1147C2×Q8—24no—
1148C2×Q8—24no—
1149C2×Q8—22no—
1150C2×Q8—22no—
1151C2×Q8—22no—
1152C2×Q8—22no—
1153C2×Q8—24no—
1154C2×Q8—24no—
1155C2×Q8—24no—
1156C2×Q8—24no—
1157C2×Q8—44no—
1158C2×Q8—44no—
1159C2×Q8—44no—
1160C2×Q8—44no—
1161C2×Q8—42no—
1162C2×Q8—432no—
1163C2×Q8—432no—
1164C2×Q8—432no—
1165C2×Q8—432no—
1166C2×Q8—432no—
1167C2×Q8—416no—
1168C2×Q8—432no—
1169C2×Q8—432no—
1170C2×Q8—432no—
1171C2×Q8—432no—
1172C2×Q8—416no—
1173C2×Q8—416no—
1174C2×Q8C22×D414yes—
1175C2×Q8C22×D418yes—
1176C2×Q8C22×D418yes—
1177C2×Q8C22×D414yes—
1178C2×D4—24no—
1179C2×D4—24no—
1180C2×D4—24no—
1181C2×D4—24no—
1182C2×D4—28no—
1183C2×D4—24no—
1184C2×D4—24no—
1185C2×D4—28no—
1186C2×D4—28no—
1187C2×D4—24no—
1188C2×D4—24no—
1189C2×D4—24no—
1190C2×D4—28no—
1191C2×D4—24no—
1192C2×D4—24no—
1193C2×D4—28no—
1194C2×D4—24no—
1195C2×D4—24no—
1196C2×D4—24no—
1197C2×D4—24no—
1198C2×D4—24no—
1199C2×D4—28no—
1200C2×D4—28no—
1201C2×D4—22no—
1202C2×D4—22no—
1203C2×D4—24no—
1204C2×D4—28no—
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—24no—
1208C2×D4—22no—
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—28no—
1215C2×D4—28no—
1216C2×D4—416no—
1217C2×D4—42no—
1218C2×D4—42no—
1219C2×D4—42no—
1220C2×D4—44no—
1221C2×D4—44no—
1222C2×D4—44no—
1223C2×D4—44no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4—48no—
1228C2×D4—432no—
1229C2×D4C22×D418yes—
1230C2×D4C22×D418yes—
1231C2×D4C22×D414yes—
1232C2×D4C22×D418yes—
1233C2×D4C22×D414yes—
1234C2×D4C22×D418yes—
1235C22×C4—22no—
1236C22×C4—24no—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—232no—
1240C22×C4—22no—
1241C22×C4—24no—
1242C22×C4—22no—
1243C22×C4—24no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—24no—
1254C22×C4—24no—
1255C22×C4—28no—
1256C22×C4—28no—
1257C22×C4—28no—
1258C22×C4—24no—
1259C22×C4—28no—
1260C22×C4—28no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—28no—
1268C22×C4—24no—
1269C22×C4—28no—
1270C22×C4—28no—
1271C22×C4—28no—
1272C22×C4—28no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—28no—
1276C22×C4—28no—
1277C22×C4—24no—
1278C22×C4—28no—
1279C22×C4—28no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—24no—
1285C22×C4—28no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—28no—
1291C22×C4—28no—
1292C22×C4—42no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—44no—
1299C22×C4—44no—
1300C22×C4—42no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—432no—
1306C22×C4—48no—
1307C22×C4—44no—
1308C22×C4—432no—
1309C22×C4C22×D418yes—
1310C22×C4C22×D414yes—
1311C22×C4C22×D414yes—
1312C22×C4C22×D414yes—
1313C22×C4C22×D418yes—
1314C22×C4C22×D414yes—
1315C22×C4C22×D414yes—
1316C22×C4C22×D418yes—
1317C22×C4C22×D414yes—
1318C22×C4C22×D414yes—
1319C22×C4H(5,𝔽2)14yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2514yes—
1323C22×C4C2512yes—
1324C22×C4C2514yes—
1325C22×C4C2512yes—
1326C22×C4C2514yes—
1327C22×C4C2514yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2514yes—
1332C22×C4C2512yes—
1333C22×C4C2511yescharacteristic
1334C22×C4C2512yes—
1335C22×C4C2514yes—
1336C22×C4C2512yes—
1337C22×C4C2511yescharacteristic
1338C22×C4C2512yes—
1339C22×C4C2512yes—
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C4⋊C4—24no—
1343C4⋊C4—216no—
1344C4⋊C4—28no—
1345C4⋊C4—28no—
1346C4⋊C4—28no—
1347C4⋊C4—24no—
1348C4⋊C4—28no—
1349C4⋊C4—24no—
1350C4⋊C4—28no—
1351C4⋊C4—28no—
1352C4⋊C4—28no—
1353C4⋊C4—216no—
1354C4⋊C4—216no—
1355C4⋊C4—216no—
1356C4⋊C4—216no—
1357C4⋊C4—216no—
1358C4⋊C4—28no—
1359C4⋊C4—28no—
1360C4⋊C4—28no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—28no—
1364C4⋊C4—28no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—28no—
1368C4⋊C4—28no—
1369C4⋊C4—28no—
1370C4⋊C4—28no—
1371C4⋊C4—48no—
1372C4⋊C4—48no—
1373C4⋊C4—48no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4C22×D414yes—
1377C4⋊C4C22×D418yes—
1378C4⋊C4C22×D4132yes—
1379C4⋊C4C22×D418yes—
1380C4⋊C4C22×D414yes—
1381C4⋊C4C22×D418yes—
1382C22⋊C4—28no—
1383C22⋊C4—24no—
1384C22⋊C4—28no—
1385C22⋊C4—216no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—28no—
1390C22⋊C4—28no—
1391C22⋊C4—28no—
1392C22⋊C4—28no—
1393C22⋊C4—24no—
1394C22⋊C4—28no—
1395C22⋊C4—28no—
1396C22⋊C4—28no—
1397C22⋊C4—216no—
1398C22⋊C4—216no—
1399C22⋊C4—28no—
1400C22⋊C4—28no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—216no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—28no—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—28no—
1411C22⋊C4—28no—
1412C22⋊C4—28no—
1413C22⋊C4—44no—
1414C22⋊C4—44no—
1415C22⋊C4—48no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4C22×D418yes—
1420C22⋊C4C22×D418yes—
1421C22⋊C4C22×D4132yes—
1422C22⋊C4C22×D418yes—
1423C22⋊C4C22×D418yes—
1424C22⋊C4C22×D418yes—
1425C22⋊C4C22×D418yes—
1426C22⋊C42−1+418yescomplemented
1427C42—22no—
1428C42—28no—
1429C42—22no—
1430C42—24no—
1431C42—28no—
1432C42—24no—
1433C42—28no—
1434C42—28no—
1435C42—28no—
1436C42—24no—
1437C42—24no—
1438C42—22no—
1439C42—22no—
1440C42—28no—
1441C42—44no—
1442C42C22×D418yes—
1443C42C22×D418yes—
1444C23—21no—
1445C23—21no—
1446C23—22no—
1447C23—22no—
1448C23—22no—
1449C23—21no—
1450C23—22no—
1451C23—22no—
1452C23—21no—
1453C23—22no—
1454C23—22no—
1455C23—22no—
1456C23—24no—
1457C23—24no—
1458C23—24no—
1459C23—24no—
1460C23—22no—
1461C23—28no—
1462C23—28no—
1463C23—22no—
1464C23—22no—
1465C23—22no—
1466C23—22no—
1467C23—22no—
1468C23—22no—
1469C23—24no—
1470C23—24no—
1471C23—24no—
1472C23—24no—
1473C23—44no—
1474C23—48no—
1475C23—48no—
1476C23—48no—
1477C23—416no—
1478C23—48no—
1479C23—84no—
1480C23—88no—
1481C23C23×D414yes—
1482C23C23×D412yes—
1483C23C23×D414yes—
1484C23C23×D412yes—
1485C23C23×D412yes—
1486C23C23×D412yes—
1487C23C2×H(5,𝔽2)12yes—
1488C23C2×2−1+414yes—
1489C23C2611yescharacteristic
1490Q8—216no—
1491Q8—216no—
1492Q8—28no—
1493Q8—28no—
1494Q8—416no—
1495Q8—416no—
1496Q8—416no—
1497Q8—416no—
1498Q8—48no—
1499Q8—48no—
1500Q8—48no—
1501Q8—48no—
1502Q8—48no—
1503Q8—44no—
1504Q8—44no—
1505D4—216no—
1506D4—216no—
1507D4—216no—
1508D4—28no—
1509D4—28no—
1510D4—48no—
1511D4—416no—
1512D4—48no—
1513D4—48no—
1514D4—416no—
1515D4—48no—
1516D4—416no—
1517D4—48no—
1518D4—48no—
1519D4—48no—
1520D4—48no—
1521D4—44no—
1522D4—44no—
1523D4—88no—
1524D4—88no—
1525C2×C4—22no—
1526C2×C4—21no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—24no—
1530C2×C4—21no—
1531C2×C4—22no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—24no—
1537C2×C4—24no—
1538C2×C4—24no—
1539C2×C4—22no—
1540C2×C4—24no—
1541C2×C4—24no—
1542C2×C4—22no—
1543C2×C4—28no—
1544C2×C4—216no—
1545C2×C4—28no—
1546C2×C4—28no—
1547C2×C4—28no—
1548C2×C4—28no—
1549C2×C4—216no—
1550C2×C4—216no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—24no—
1554C2×C4—22no—
1555C2×C4—24no—
1556C2×C4—24no—
1557C2×C4—24no—
1558C2×C4—24no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—24no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—24no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—24no—
1572C2×C4—24no—
1573C2×C4—22no—
1574C2×C4—24no—
1575C2×C4—22no—
1576C2×C4—24no—
1577C2×C4—28no—
1578C2×C4—416no—
1579C2×C4—48no—
1580C2×C4—416no—
1581C2×C4—48no—
1582C2×C4—416no—
1583C2×C4—48no—
1584C2×C4—48no—
1585C2×C4—416no—
1586C2×C4—416no—
1587C2×C4—48no—
1588C2×C4—416no—
1589C2×C4—416no—
1590C2×C4—416no—
1591C2×C4—48no—
1592C2×C4—48no—
1593C2×C4—48no—
1594C2×C4—48no—
1595C2×C4—88no—
1596C2×C4—84no—
1597C2×C4D42116yes—
1598C2×C4C23×D414yes—
1599C2×C4C23×D418yes—
1600C2×C4C23×D414yes—
1601C2×C4C23×D412yes—
1602C2×C4C23×D418yes—
1603C2×C4C23×D414yes—
1604C2×C4C23×D412yes—
1605C2×C4C23×D414yes—
1606C2×C4C23×D412yes—
1607C2×C4C23×D412yes—
1608C2×C4C23×D412yes—
1609C2×C4C23×D412yes—
1610C2×C4C2×H(5,𝔽2)12yes—
1611C2×C4C2×H(5,𝔽2)12yes—
1612C2×C4C2×2−1+414yes—
1613C2×C4C2×2−1+414yes—
1614C22—24no—
1615C22—24no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—24no—
1620C22—24no—
1621C22—22no—
1622C22—28no—
1623C22—24no—
1624C22—22no—
1625C22—22no—
1626C22—24no—
1627C22—22no—
1628C22—24no—
1629C22—24no—
1630C22—416no—
1631C22—44no—
1632C22—42no—
1633C22—42no—
1634C22—42no—
1635C22—44no—
1636C22—42no—
1637C22—44no—
1638C22—44no—
1639C22—44no—
1640C22—42no—
1641C22—42no—
1642C22—42no—
1643C22—42no—
1644C22—44no—
1645C22—44no—
1646C22—42no—
1647C22—42no—
1648C22—816no—
1649C22C2×D4214yes—
1650C22#349914yescomplemented
1651C22C24×D411yescharacteristic
1652C22C24×D411yescharacteristic
1653C22C22×H(5,𝔽2)11yescharacteristic
1654C22C22×2−1+412yes—
1655C222−1+612yes—
1656C4—24no—
1657C4—28no—
1658C4—24no—
1659C4—24no—
1660C4—24no—
1661C4—22no—
1662C4—22no—
1663C4—24no—
1664C4—24no—
1665C4—28no—
1666C4—42no—
1667C4—44no—
1668C4—42no—
1669C4—44no—
1670C4—42no—
1671C4—42no—
1672C4—42no—
1673C4—44no—
1674C4—42no—
1675C4—44no—
1676C4C2×D4214yes—
1677C4C2×D4214yes—
1678C2—24no—
1679C2—24no—
1680C2—44no—
1681C2—42no—
1682C2—44no—
1683C2—82no—
1684C2—82no—
1685C2C22×D4211yescharacteristic
1686C2C2×#349911yescharacteristic
1687C2#6285911yescharacteristic
1688C2#6294212yes—
1689C2D4×2−1+412yes—
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. C2×#3499C2semidirect
2. C2×#3489C2semidirect
3. C2×#3486C2semidirect
4. C22×#536C2semidirect
5. #59002C2semidirect
6. #58998C2semidirect
7. #58995C2semidirect
8. #45321C2semidirect
9. #45091C2semidirect
10. #44758C2semidirect
11. #39360C2semidirect
12. #39356C2semidirect
13. #37680C2semidirect
14. #37676C2semidirect
15. #37675C2semidirect
16. #37675C2semidirect
17. #36124C2semidirect
18. D4×C4⋊Q8C2semidirect
19. #35667C2semidirect
20. #35666C2semidirect
21. #35660C2semidirect
22. #35621C2semidirect
23. #35317C2semidirect
24. #35308C2semidirect
25. #35306C2semidirect
26. #34738C2semidirect
27. C2×#2434C2semidirect
28. #34276C2semidirect
29. #34136C2semidirect
31. C22×2−1+4C22semidirect
40. C2×D4×Q8C22semidirect
41. C2×D4×Q8C22semidirect
42. C2×D4×Q8C22semidirect
46. C2×#548C22semidirect
47. C2×#548C22semidirect
50. C2×#547C22semidirect
51. C2×#547C22semidirect
67. C2×#536C22semidirect
68. C2×#536C22semidirect
69. C2×#536C22semidirect
70. C2×#536C22semidirect
71. C2×#536C22semidirect
72. C2×#536C22semidirect
75. C2×#532C22semidirect
77. C22×C4⋊Q8C22semidirect
78. C22×C4⋊Q8C22semidirect
79. C22×C4⋊Q8C22semidirect
90. C2×#519C22semidirect
91. C2×C4×#41C22semidirect
93. #2868C22semidirect
94. #2858C22semidirect
96. #2857C22semidirect
98. #2850C22semidirect
99. #2683C22semidirect
100. #2682C22semidirect
101. #2680C22semidirect
102. #2680C22semidirect
103. #2677C22semidirect
104. #2677C22semidirect
105. #2674C22semidirect
106. #2674C22semidirect
107. #2674C22semidirect
108. #2672C22semidirect
109. #2672C22semidirect
110. #2671C22semidirect
111. #2658C22semidirect
112. #2658C22semidirect
113. #2621C22semidirect
114. #2621C22semidirect
115. #2620C22semidirect
116. #2620C22semidirect
117. #2555C22semidirect
118. #2551C22semidirect
119. #2547C22semidirect
120. #2546C22semidirect
121. #2546C22semidirect
122. #2546C22semidirect
123. #2545C22semidirect
124. #2545C22semidirect
125. #2545C22semidirect
126. #2544C22semidirect
127. #2542C22semidirect
128. #2542C22semidirect
129. #2501C22semidirect
130. #2461C22semidirect
131. #2461C22semidirect
132. #2461C22semidirect
133. #2455C22semidirect
135. #2449C22semidirect
136. #2449C22semidirect
138. #2443C22semidirect
140. #2440C22semidirect
141. #2440C22semidirect
144. #2436C22semidirect
150. #2434C22semidirect
151. #2434C22semidirect
152. #2434C22semidirect
153. #2434C22semidirect
154. #2434C22semidirect
155. #2434C22semidirect
156. #2434C22semidirect
160. #2432C22semidirect
161. #2432C22semidirect
162. #2432C22semidirect
163. #2432C22semidirect
166. #2431C22semidirect
168. #2430C22semidirect
169. #2429C22semidirect
170. #2429C22semidirect
171. #2429C22semidirect
172. #2427C22semidirect
173. #2425C22semidirect
174. #2425C22semidirect
176. #2422C22semidirect
179. #2417C22semidirect
180. #2415C22semidirect
181. #2415C22semidirect
182. #2413C22semidirect
183. #2413C22semidirect
186. #2409C22semidirect
187. #2407C22semidirect
188. #2406C22semidirect
190. C2×#395C22semidirect
191. #2363C22semidirect
192. #2362C22semidirect
193. #2362C22semidirect
196. #2360C22semidirect
197. #2359C22semidirect
198. #2359C22semidirect
202. #2327C22semidirect
203. #2326C22semidirect
204. #2317C22semidirect
205. #2311C22semidirect
206. #2310C22semidirect
207. C4×C4⋊Q8C22semidirect
208. C4×#124C22semidirect
212. #2297C22semidirect
213. #2296C22semidirect
214. C2×#391C22semidirect
215. C2×#391C22semidirect
216. #2293C22semidirect
218. #2290C22semidirect
221. C4×#117C22semidirect
301. #536D4semidirect
352. #525D4semidirect
1426. C22⋊C42−1+4semidirect
1650. C22#3499semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#34892
C2×#34862
C22×#5362
#590022
#589982
#589952
#453212
#450912
#447582
#393602
#393562
#376802
#376762
#376752
#361242
D4×C4⋊Q82
#356672
#356662
#356602
#356212
#353172
#353082
#353062
#347382
C2×#24342
#342762
#341362