Finite Group Databasebeta

← #7657658

Subgroups — #7657658

Order 512.

7978 conjugacy classes of subgroups.

The subgroup lattice has 1629 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3508C211yesmaximal, characteristic, complemented
2C2×#3514C211yesmaximal, characteristic, complemented
3#41958C214yesmaximal, complemented
4#41956C214yesmaximal, complemented
5#41945C214yesmaximal, complemented
6#41932C214yesmaximal, complemented
7#40501C214yesmaximal, complemented
8#40488C214yesmaximal, complemented
9#39741C212yesmaximal, complemented
10#39739C212yesmaximal, complemented
11#37683C212yesmaximal, complemented
12#37681C212yesmaximal, complemented
13#37676C212yesmaximal, complemented
14#37674C212yesmaximal, complemented
15#37618C211yesmaximal, characteristic, complemented
16#37614C211yesmaximal, characteristic, complemented
17#37544C211yesmaximal, characteristic, complemented
18#37544C211yesmaximal, characteristic, complemented
19#37537C211yesmaximal, characteristic, complemented
20#37536C211yesmaximal, characteristic, complemented
21#36124C212yesmaximal, complemented
22#36121C212yesmaximal, complemented
23#35692C214yesmaximal, complemented
24#35683C214yesmaximal, complemented
25#35329C211yesmaximal, characteristic, complemented
26#35326C211yesmaximal, characteristic, complemented
27#35303C211yesmaximal, characteristic, complemented
28#34641C211yesmaximal, characteristic, complemented
29#34624C211yesmaximal, characteristic, complemented
30C2×#2657C211yesmaximal, characteristic, complemented
31#34123C211yesmaximal, characteristic, complemented
32#3514—216no—
33#3508—216no—
34C2×#559C2211yescharacteristic, complemented
35C2×#559C2212yescomplemented
36C2×#559C2212yescomplemented
37C2×#556C2211yescharacteristic, complemented
38C2×#555C2212yescomplemented
39C2×#551C2212yes—
40C2×#551C2212yescomplemented
41C2×#550C2212yescomplemented
42C2×#550C2212yescomplemented
43C2×D4×Q8C2211yescharacteristic
44C2×#548C2211yescharacteristic
45C2×#548C2211yescharacteristic, complemented
46C2×#546C2211yescharacteristic
47C2×#546C2212yes—
48C2×#546C2212yes—
49C2×#546C2212yes—
50C2×#546C2212yescomplemented
51C2×#546C2212yescomplemented
52C2×#546C2211yescharacteristic, complemented
53C2×D42C2211yescharacteristic
54C2×#542C2212yescomplemented
55C2×#540C2212yescomplemented
56C2×#540C2212yescomplemented
57C2×#538C2212yes—
58C2×#538C2212yescomplemented
59C2×#536C2212yescomplemented
60C2×#535C2212yes—
61C2×#535C2212yescomplemented
62C2×#533C2211yescharacteristic, complemented
63C2×#532C2211yescharacteristic, complemented
64C2×#532C2211yescharacteristic, complemented
65C2×#532C2211yescharacteristic, complemented
66C2×#532C2211yescharacteristic, complemented
67C2×#532C2211yescharacteristic, complemented
68C2×#532C2212yescomplemented
69C2×#532C2212yescomplemented
70C22×#127C2212yes—
71C22×#127C2211yescharacteristic, complemented
72C2×#529C2211yescharacteristic
73C2×#529C2211yescharacteristic, complemented
74C2×#529C2211yescharacteristic, complemented
75C22×#124C2211yescharacteristic
76C22×#124C2211yescharacteristic, complemented
77C22×#124C2212yescomplemented
78C2×#518C2212yes—
79C2×#518C2212yescomplemented
80C2×C4×#41C2211yescharacteristic
81#2858C2212yescomplemented
82#2858C2212yescomplemented
83#2857C2212yescomplemented
84#2856C2212yescomplemented
85#2850C2212yes—
86#2850C2212yescomplemented
87#2820C2214yescomplemented
88#2819C2214yescomplemented
89#2818C2214yescomplemented
90#2815C2214yescomplemented
91#2813C2214yescomplemented
92#2813C2214yescomplemented
93#2733C2218yescomplemented
94#2730C2218yescomplemented
95#2705C2218yescomplemented
96#2682C2218yescomplemented
97#2676C2218yescomplemented
98#2675C2218yescomplemented
99#2674C2218yescomplemented
100#2673C2218yescomplemented
101#2673C2218yescomplemented
102#2672C2218yescomplemented
103#2669C2218yescomplemented
104#2669C2218yescomplemented
105#2662C2214yescomplemented
106#2661C2214yescomplemented
107#2660C2211yescharacteristic, complemented
108#2658C2211yescharacteristic, complemented
109#2658C2211yescharacteristic, complemented
110#2658C2212yescomplemented
111#2658C2211yescharacteristic, complemented
112#2657C2211yescharacteristic
113#2657C2212yes—
114#2657C2211yescharacteristic
115#2657C2211yescharacteristic, complemented
116#2657C2212yescomplemented
117#2657C2212yescomplemented
118#2657C2214yescomplemented
119#2657C2211yescharacteristic, complemented
120#2657C2211yescharacteristic, complemented
121#2657C2214yescomplemented
122#2657C2211yescharacteristic, complemented
123#2656C2214yescomplemented
124#2656C2214yescomplemented
125#2642C2211yescharacteristic, complemented
126#2641C2211yescharacteristic, complemented
127#2641C2211yescharacteristic, complemented
128#2640C2211yescharacteristic, complemented
129#2640C2211yescharacteristic, complemented
130#2640C2211yescharacteristic, complemented
131#2636C2214yescomplemented
132#2636C2214yescomplemented
133#2635C2214yescomplemented
134#2635C2214yescomplemented
135#2632C2214yescomplemented
136#2631C2214yescomplemented
137#2631C2214yescomplemented
138#2626C2214yescomplemented
139#2620C2212yescomplemented
140#2619C2212yescomplemented
141#2619C2214yescomplemented
142#2617C2214yescomplemented
143#2615C2214yescomplemented
144#2613C2214yescomplemented
145#2611C2214yescomplemented
146#2610C2214yescomplemented
147#2604C2214yescomplemented
148#2603C2214yescomplemented
149#2598C2214yescomplemented
150#2598C2214yescomplemented
151#2564C2214yescomplemented
152#2555C2218yescomplemented
153#2548C2212yescomplemented
154#2547C2212yescomplemented
155#2545C2212yescomplemented
156#2545C2212yescomplemented
157#2545C2212yescomplemented
158#2545C2212yescomplemented
159#2544C2212yescomplemented
160#2544C2212yescomplemented
161#2544C2212yescomplemented
162#2544C2212yescomplemented
163#2543C2214yescomplemented
164#2541C2212yescomplemented
165#2541C2212yescomplemented
166#2540C2214yescomplemented
167#2540C2214yescomplemented
168#2539C2214yescomplemented
169#2539C2214yescomplemented
170#2535C2214yescomplemented
171#2498C2214yescomplemented
172#2482C2214yescomplemented
173#2471C2218yescomplemented
174#2467C2218yescomplemented
175#2463C2218yescomplemented
176#2461C2218yescomplemented
177#2456C2218yescomplemented
178#2456C2218yescomplemented
179#2456C2218yescomplemented
180#2456C2218yescomplemented
181#2445C2218yescomplemented
182#2437C2218yescomplemented
183#2436C2212yescomplemented
184#2435C2212yes—
185#2435C2212yescomplemented
186#2434C2212yescomplemented
187#2433C2212yes—
188#2433C2212yescomplemented
189#2432C2212yescomplemented
190#2432C2212yescomplemented
191#2431C2212yescomplemented
192#2431C2212yescomplemented
193#2431C2212yescomplemented
194#2431C2212yescomplemented
195#2430C2214yescomplemented
196#2428C2218yescomplemented
197#2424C2218yescomplemented
198#2424C2218yescomplemented
199#2418C2218yes—
200#2410C2218yes—
201#2408C2218yescomplemented
202#2408C2214yescomplemented
203#2404C2214yescomplemented
204#2403C2218yes—
205#2397C2214yescomplemented
206#2397C2214yescomplemented
207#2392C2214yescomplemented
208#2388C2214yescomplemented
209C2×#392C2214yescomplemented
210C2×#392C2214yescomplemented
211#2358C2218yescomplemented
212#2356C2212yescomplemented
213#2353C2212yes—
214#2353C2212yescomplemented
215#2349C2212yescomplemented
216#2346C2212yescomplemented
217#2343C2212yescomplemented
218#2343C2212yescomplemented
219#2339C2212yes—
220D4×C22⋊C4C2218yescomplemented
221#2328C2212yescomplemented
222#2327C2212yescomplemented
223#2326C2212yescomplemented
224#2326C2212yescomplemented
225C4×#127C2212yescomplemented
226C4×#124C2212yescomplemented
227#2295C2212yescomplemented
228#2290C2212yes—
229#2290C2212yescomplemented
230#2283C2211yescharacteristic, complemented
231#2283C2211yescharacteristic, complemented
232#2283C2211yescharacteristic, complemented
233C42×D4C2212yescomplemented
234C4×#117C2211yescharacteristic, complemented
235C2×#376C2211yescharacteristic, complemented
236C2×#376C2211yescharacteristic, complemented
237C22×#41C2311yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2312yes—
240C22×#41C2312yes—
241C22×#41C2312yes—
242C22×#41C2312yes—
243C22×#41C2311yescharacteristic
244C23×Q8C2311yescharacteristic
245C23×Q8C2311yescharacteristic
246C23×D4C2312yes—
247C23×D4C2312yes—
248C23×D4C2311yescharacteristic
249C23×D4C2312yes—
250C23×D4C2311yescharacteristic
251C23×D4C2312yes—
252C23×D4C2318yes—
253#559—216no—
254#559—216no—
255#559—28no—
256#556—28no—
257#555—216no—
258#551—216no—
259#551—216no—
260#550—216no—
261#550—216no—
262D4×Q8—28no—
263#548—28no—
264#548—28no—
265#546—216no—
266#546—216no—
267#546—216no—
268#546—28no—
269#546—216no—
270#546—216no—
271#546—28no—
272D42—28no—
273#542—216no—
274#540—216no—
275#540—216no—
276#538—216no—
277#538—216no—
278#536—48no—
279#535—216no—
280#535—48no—
281#533—28no—
282#532—28no—
283#532—28no—
284#532—28no—
285#532—28no—
286#532—28no—
287#532—48no—
288#532—48no—
289C2×C4⋊Q8C2312yes—
290C2×C4⋊Q8C2311yescharacteristic
291C2×C4⋊Q8C2311yescharacteristic
292C2×C4⋊Q8C2311yescharacteristic
293C2×C4⋊Q8C2312yes—
294C2×C4⋊Q8C2312yes—
295C2×C4⋊Q8C2312yes—
296C2×#127—28no—
297C2×#127—48no—
298C2×#127C2312yes—
299C2×#127C2312yes—
300C2×#127C2312yes—
301C2×#127C2312yes—
302C2×#127C2311yescharacteristic
303C2×#127C2311yescharacteristic
304C2×#127C2312yes—
305C2×#127C2311yescharacteristic
306C2×#127C2314yes—
307C2×#127C2312yes—
308C2×#127C2312yes—
309C2×#127C2318yes—
310C2×#127C2312yes—
311C2×#127C2312yes—
312#529—28no—
313#529—28no—
314#529—28no—
315C2×#126C2312yes—
316C2×#126C2312yes—
317C2×#126C2312yes—
318C2×#126C2312yes—
319C2×#126C2312yes—
320C2×#125C2312yes—
321C2×#125C2311yescharacteristic
322C2×#124—28no—
323C2×#124—28no—
324C2×#124—48no—
325C2×#124C2312yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2312yes—
330C2×#124C2311yescharacteristic
331C2×#124C2311yescharacteristic
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2311yescharacteristic
338C2×#124C2311yescharacteristic
339C2×#124C2311yescharacteristic
340C2×#124C2311yescharacteristic
341C2×#124C2311yescharacteristic
342C2×#124C2312yes—
343C2×#124C2312yes—
344C2×#124C2314yes—
345C2×#124C2312yes—
346C2×#124C2312yes—
347C2×#124C2312yes—
348C2×#124C2312yes—
349C2×#124C2312yes—
350C2×#124C2312yes—
351C2×#124C2318yes—
352C2×#124C2312yes—
353C2×#124C2312yes—
354C2×#123C2312yes—
355C2×#123C2312yes—
356C2×#123C2312yes—
357C2×#123C2314yes—
358C2×#123C2312yes—
359C2×#123C2314yes—
360C2×#123C2312yes—
361C2×#123C2314yes—
362C2×#123C2314yes—
363C2×#123C2312yes—
364C2×#123C2312yes—
365C2×#123C2318yes—
366C2×C22⋊Q8C2312yes—
367C2×C22⋊Q8C2312yes—
368C2×C22⋊Q8C2311yescharacteristic
369C2×C22⋊Q8C2311yescharacteristic
370C2×C22⋊Q8C2311yescharacteristic
371C2×C22⋊Q8C2312yes—
372C2×C22⋊Q8C2312yes—
373C2×C22⋊Q8C2312yes—
374C2×C22⋊Q8C2312yes—
375C2×C22⋊Q8C2312yes—
376C2×C22⋊Q8C2318yes—
377C2×#121C2311yescharacteristic
378C2×#121C2312yes—
379C2×#121C2311yescharacteristic
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×#121C2311yescharacteristic
383C2×#121C2312yes—
384C2×#121C2312yes—
385C2×#121C2312yes—
386C2×#121C2312yes—
387C2×#121C2312yes—
388C2×#121C2314yes—
389C2×#121C2312yes—
390C2×#121C2312yes—
391C2×#121C2312yes—
392C2×#121C2312yes—
393C2×#121C2312yes—
394C2×#121C2314yes—
395C2×#121C2312yes—
396C2×#121C2314yes—
397C2×#121C2312yes—
398C2×#121C2314yes—
399C2×#121C2318yes—
400C2×#121C2318yes—
401C2×#121C2318yes—
402C2×#121C2318yes—
403C2×#121C2318yes—
404C2×#121C2318yes—
405C2×#120C2314yes—
406C2×#120C2312yes—
407C2×#120C2314yes—
408C2×#120C2312yes—
409C2×#120C2312yes—
410C2×#120C2312yes—
411C2×#120C2318yes—
412C2×#120C2318yes—
413C2×#120C2318yes—
414#518—216no—
415#518—216no—
416C4×#41D4116yescomplemented
417C2×C4×Q8C2311yescharacteristic
418C2×C4×Q8C2312yes—
419C2×C4×Q8C2311yescharacteristic
420C2×C4×Q8C2312yes—
421C2×C4×Q8C2311yescharacteristic
422C2×C4×Q8C2311yescharacteristic
423C2×C4×Q8C2311yescharacteristic
424C2×C4×D4C2311yescharacteristic
425C2×C4×D4C2312yes—
426C2×C4×D4C2312yes—
427C2×C4×D4C2311yescharacteristic
428C2×C4×D4C2312yes—
429C2×C4×D4C2311yescharacteristic
430C2×C4×D4C2312yes—
431C2×C4×D4C2312yes—
432C2×C4×D4C2312yes—
433C2×C4×D4C2312yes—
434C2×C4×D4C2312yes—
435C2×C4×D4C2312yes—
436C2×C4×D4C2312yes—
437C2×C4×D4C2312yes—
438C2×C4×D4C2312yes—
439C2×C4×D4C2312yes—
440C2×C4×D4C2312yes—
441C2×C4×D4C2312yes—
442C2×C4×D4C2312yes—
443C2×C4×D4C2312yes—
444C2×C4×D4C2314yes—
445C2×C4×D4C2314yes—
446C2×C4×D4C2318yes—
447C2×C4×D4C2314yes—
448C2×C4×D4C2318yes—
449C2×C4×D4C2318yes—
450C2×C4×D4C2311yescharacteristic
451C2×C4×D4C2311yescharacteristic
452C2×C4×D4C2311yescharacteristic
453C2×C4×D4C2311yescharacteristic
454C2×C4×D4C2311yescharacteristic
455C2×C4×D4C2311yescharacteristic
456C2×#117C2312yes—
457C2×#117C2312yes—
458C2×#117C2312yes—
459C2×#117C2312yes—
460C2×#117C2312yes—
461C2×#117C2312yes—
462C2×#117C2311yescharacteristic
463C2×#117C2311yescharacteristic
464C2×#117C2311yescharacteristic
465C22×C22⋊C4C2312yes—
466C22×C22⋊C4C2314yes—
467C22×C22⋊C4C2312yes—
468C22×C22⋊C4C2312yes—
469C22×C22⋊C4C2312yes—
470C22×C22⋊C4C2312yes—
471C22×C22⋊C4C2312yes—
472C22×C22⋊C4C2314yes—
473C22×C22⋊C4C2318yes—
474C22×C42C2312yes—
475C22×C42C2312yes—
476C22×C42C2311yescharacteristic
477C22×C42C2311yescharacteristic
478C22×C42C2311yescharacteristic
479#400C2314yes—
480#400C2314yes—
481#399C2314yes—
482#399C2314yes—
483#399C2314yes—
484#399C2314yes—
485#399C2314yes—
486#399C2314yes—
487#399C2318yes—
488#399C2318yes—
489#398C2314yes—
490#397C2314yes—
491#397C2314yes—
492#397C2314yes—
493#397C2318yes—
494#396C2318yes—
495#396C2318yes—
496#396C2318yes—
497#396C2318yes—
498#396C2318yes—
499#395C2314yes—
500#395C2318yes—
501#394C2314yes—
502#394C2314yes—
503#394C2318yes—
504#394C2318yes—
505#394C2318yes—
506#394C2318yes—
507#394C2318yes—
508#394C2314yes—
509#394C2314yes—
510#394C2318yes—
511#394C2318yes—
512#394C2318yes—
513#394C2318yes—
514#394C2318yes—
515#394C2318yes—
516#393C2314yes—
517#393C2314yes—
518#393C2318yes—
519#393C2314yes—
520#392C2314yes—
521#392C2318yes—
522#392C2314yes—
523#392C2318yes—
524#392C2314yes—
525#392C2318yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#392C2314yes—
531#392C2314yes—
532#392C2318yes—
533#392C2318yes—
534#392C2314yes—
535#392C2318yes—
536#392C2318yes—
537#392C2318yes—
538#392C2318yes—
539#392C2314yes—
540#392C2314yes—
541#392C2318yes—
542#392C2318yes—
543#392C2318yes—
544#392C2318yes—
545#392C2318yes—
546#392C2318yes—
547#391C2312yes—
548#391C2312yes—
549#391C2312yes—
550#391C2312yes—
551#391C2314yes—
552#391C2312yes—
553#390C2312yes—
554#390C2312yes—
555#390C2318yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2312yes—
560#390C2318yes—
561#390C2318yes—
562#390C2318yes—
563#390C2318yes—
564#390C2318yes—
565#390C2312yes—
566#390C2318yes—
567#389C2318yes—
568#389C2314yes—
569#388C2318yes—
570#388C2318yes—
571#388C2318yes—
572#388C2318yes—
573#388C2318yes—
574#388C2318yes—
575#388C2314yes—
576#388C2314yes—
577#388C2318yes—
578#388C2318yes—
579#388C2318yes—
580#387C2318yes—
581#387C2318yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#386C2318yes—
587#386C2318yes—
588#386C2318yes—
589#386C2318yes—
590#386C2318yes—
591#386C2318yes—
592#386C2318yes—
593#386C2318yes—
594#386C2314yes—
595#386C2314yes—
596#386C2318yes—
597#386C2318yes—
598#386C2318yes—
599#386C2318yes—
600#386C2318yes—
601#385C2318yes—
602#385C2318yes—
603#385C2318yes—
604#385C2318yes—
605#385C2314yes—
606#385C2314yes—
607#385C2318yes—
608#384C2312yes—
609#383C2312yes—
610#383C2312yes—
611#383C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2312yes—
615#382C2312yes—
616#381C2312yes—
617#381C2312yes—
618#381C2312yes—
619#380C2318yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2318yes—
624#379C2318yes—
625#379C2318yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C22⋊C4C2314yes—
633C4×C22⋊C4C2312yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2318yes—
637C4×C22⋊C4C2312yes—
638C4×C22⋊C4C2312yes—
639C4×C22⋊C4C2312yes—
640#376C2312yes—
641#376C2312yes—
642#376C2312yes—
643#376C2312yes—
644#376C2312yes—
645#376C2312yes—
646#376C2311yescharacteristic
647#376C2311yescharacteristic
648#376C2311yescharacteristic
649#376C2311yescharacteristic
650C2×#95C2312yes—
651C2×#95C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C43C2312yes—
655C25C2414yes—
656C25C2412yes—
657C25C2412yes—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—28no—
661C2×#41—28no—
662C2×#41—28no—
663C2×#41—28no—
664C2×#41—44no—
665C2×#41—44no—
666C2×#41—44no—
667C2×#41—44no—
668C2×#41—44no—
669C2×#41—44no—
670C2×#41—44no—
671C2×#41—84no—
672C2×#41—84no—
673C2×#41C2×D418yes—
674C22×Q8—24no—
675C22×Q8—24no—
676C22×Q8—44no—
677C22×Q8—44no—
678C22×Q8C2411yescharacteristic
679C22×Q8C2411yescharacteristic
680C22×Q8C2411yescharacteristic
681C22×Q8C2412yes—
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2412yes—
685C22×Q8C2411yescharacteristic
686C22×D4—28no—
687C22×D4—28no—
688C22×D4—24no—
689C22×D4—24no—
690C22×D4—28no—
691C22×D4—28no—
692C22×D4—44no—
693C22×D4—44no—
694C22×D4—44no—
695C22×D4—416no—
696C22×D4—44no—
697C22×D4—48no—
698C22×D4—416no—
699C22×D4—48no—
700C22×D4—88no—
701C22×D4—84no—
702C22×D4C2412yes—
703C22×D4C2411yescharacteristic
704C22×D4C2411yescharacteristic
705C22×D4C2411yescharacteristic
706C22×D4C2412yes—
707C22×D4C2412yes—
708C22×D4C2411yescharacteristic
709C22×D4C2411yescharacteristic
710C22×D4C2412yes—
711C22×D4C2412yes—
712C22×D4C2412yes—
713C22×D4C2412yes—
714C22×D4C2418yes—
715C22×D4C2414yes—
716C22×D4C2412yes—
717C22×D4C2412yes—
718C22×D4C2412yes—
719C22×D4C2412yes—
720C22×D4C2414yes—
721C22×D4C2414yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C22×D4C2414yes—
725C22×D4C2412yes—
726C22×D4C2414yes—
727C22×D4C2412yes—
728C22×D4C2418yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2418yes—
732C22×D4C2418yes—
733C22×D4C2418yes—
734C22×D4C2418yes—
735C22×D4C2411yescharacteristic
736C23×C4C2414yes—
737C23×C4C2411yescharacteristic
738C23×C4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2412yes—
752C23×C4C2414yes—
753C23×C4C2411yescharacteristic
754C23×C4C2411yescharacteristic
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C4⋊Q8—28no—
759C4⋊Q8—24no—
760C4⋊Q8—24no—
761C4⋊Q8—24no—
762C4⋊Q8—28no—
763C4⋊Q8—44no—
764C4⋊Q8—44no—
765#127—216no—
766#127—24no—
767#127—24no—
768#127—28no—
769#127—28no—
770#127—28no—
771#127—24no—
772#127—28no—
773#127—28no—
774#127—416no—
775#127—44no—
776#127—44no—
777#127—44no—
778#127—44no—
779#126—28no—
780#126—28no—
781#126—28no—
782#126—28no—
783#126—28no—
784#125—24no—
785#125—28no—
786#124—216no—
787#124—28no—
788#124—28no—
789#124—28no—
790#124—24no—
791#124—24no—
792#124—24no—
793#124—28no—
794#124—28no—
795#124—24no—
796#124—24no—
797#124—24no—
798#124—24no—
799#124—28no—
800#124—28no—
801#124—28no—
802#124—28no—
803#124—28no—
804#124—28no—
805#124—28no—
806#124—28no—
807#124—28no—
808#124—416no—
809#124—44no—
810#124—44no—
811#124—44no—
812#124—44no—
813#124—44no—
814#124—44no—
815#123—28no—
816#123—28no—
817#123—28no—
818#123—28no—
819#123—28no—
820#123—216no—
821#123—216no—
822#123—216no—
823#123—216no—
824#123—28no—
825#123—28no—
826#123—416no—
827C22⋊Q8—28no—
828C22⋊Q8—24no—
829C22⋊Q8—24no—
830C22⋊Q8—24no—
831C22⋊Q8—28no—
832C22⋊Q8—28no—
833C22⋊Q8—28no—
834C22⋊Q8—28no—
835C22⋊Q8—28no—
836C22⋊Q8—28no—
837C22⋊Q8—416no—
838#121—28no—
839#121—28no—
840#121—24no—
841#121—24no—
842#121—24no—
843#121—28no—
844#121—28no—
845#121—28no—
846#121—28no—
847#121—28no—
848#121—28no—
849#121—28no—
850#121—28no—
851#121—28no—
852#121—28no—
853#121—28no—
854#121—28no—
855#121—28no—
856#121—216no—
857#121—216no—
858#121—216no—
859#121—216no—
860#121—416no—
861#121—416no—
862#121—416no—
863#121—88no—
864#121—88no—
865#121—88no—
866#120—216no—
867#120—216no—
868#120—28no—
869#120—28no—
870#120—28no—
871#120—28no—
872#120—416no—
873#120—416no—
874#120—88no—
875C4×Q8—24no—
876C4×Q8—24no—
877C4×Q8—24no—
878C4×Q8—28no—
879C4×Q8—28no—
880C4×Q8C2×D418yescomplemented
881C4×Q8C2×D418yescomplemented
882C4×D4—28no—
883C4×D4—28no—
884C4×D4—28no—
885C4×D4—28no—
886C4×D4—216no—
887C4×D4—216no—
888C4×D4—28no—
889C4×D4—28no—
890C4×D4—28no—
891C4×D4—28no—
892C4×D4—28no—
893C4×D4—28no—
894C4×D4—28no—
895C4×D4—28no—
896C4×D4—24no—
897C4×D4—24no—
898C4×D4—24no—
899C4×D4—28no—
900C4×D4—28no—
901C4×D4—28no—
902C4×D4—28no—
903C4×D4—28no—
904C4×D4—416no—
905C4×D4—416no—
906C4×D4—48no—
907C4×D4—88no—
908C4×D4C2×D418yes—
909C4×D4C2×D418yes—
910C4×D4C2×D418yes—
911C4×D4C2×D418yes—
912C4×D4C2×D418yescomplemented
913C4×D4C2×D418yescomplemented
914#117—28no—
915#117—28no—
916#117—28no—
917#117—28no—
918#117—28no—
919#117—28no—
920#117C2×D418yes—
921#117C2×D418yescomplemented
922#117C2×D418yescomplemented
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2411yescharacteristic
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2418yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2418yes—
944C2×C4⋊C4C2418yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2418yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C22⋊C4—28no—
956C2×C22⋊C4—28no—
957C2×C22⋊C4—28no—
958C2×C22⋊C4—28no—
959C2×C22⋊C4—216no—
960C2×C22⋊C4—216no—
961C2×C22⋊C4—28no—
962C2×C22⋊C4—28no—
963C2×C22⋊C4—416no—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2418yes—
983C2×C22⋊C4C2412yes—
984C2×C22⋊C4C2412yes—
985C2×C22⋊C4C2412yes—
986C2×C22⋊C4C2412yes—
987C2×C22⋊C4C2418yes—
988C2×C22⋊C4C2414yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2412yes—
991C2×C22⋊C4C2412yes—
992C2×C22⋊C4C2414yes—
993C2×C22⋊C4C2418yes—
994C2×C22⋊C4C2414yes—
995C2×C22⋊C4C2414yes—
996C2×C22⋊C4C2414yes—
997C2×C22⋊C4C2414yes—
998C2×C22⋊C4C2412yes—
999C2×C22⋊C4C2412yes—
1000C2×C22⋊C4C2412yes—
1001C2×C22⋊C4C2418yes—
1002C2×C22⋊C4C2418yes—
1003C2×C22⋊C4C2418yes—
1004C2×C22⋊C4C2418yes—
1005C2×C22⋊C4C2418yes—
1006C2×C22⋊C4C2418yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2414yes—
1009C2×C22⋊C4C2418yes—
1010C2×C22⋊C4C2418yes—
1011C2×C22⋊C4C2418yes—
1012C2×C22⋊C4C2418yes—
1013C2×C22⋊C4C2418yes—
1014C2×C22⋊C4C2418yes—
1015C2×C22⋊C4C2418yes—
1016C2×C22⋊C4C2411yescharacteristic
1017C2×C22⋊C4C2411yescharacteristic
1018C2×C22⋊C4C2411yescharacteristic
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C42—28no—
1023C2×C42—28no—
1024C2×C42C2×D418yes—
1025C2×C42C2×D418yescomplemented
1026C2×C42C2×D418yescomplemented
1027C2×C42C2412yes—
1028C2×C42C2412yes—
1029C2×C42C2412yes—
1030C2×C42C2414yes—
1031C2×C42C2412yes—
1032C2×C42C2414yes—
1033C2×C42C2412yes—
1034C2×C42C2414yes—
1035C2×C42C2412yes—
1036C2×C42C2414yes—
1037C2×C42C2414yes—
1038C2×C42C2411yescharacteristic
1039C2×C42C2411yescharacteristic
1040C2×C42C2411yescharacteristic
1041C2×C42C2411yescharacteristic
1042C2×C42C2411yescharacteristic
1043C2×C42C2411yescharacteristic
1044C2×C42C2411yescharacteristic
1045C2×C42C2411yescharacteristic
1046C2×C42C2411yescharacteristic
1047C2×C42C2411yescharacteristic
1048C2×C42C2412yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2412yes—
1052#95C2412yes—
1053#95C2412yes—
1054#95C2412yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2414yes—
1062#95C2414yes—
1063#95C2414yes—
1064#95C2418yes—
1065#95C2414yes—
1066#95C2418yes—
1067#95C2414yes—
1068#95C2414yes—
1069#95C2418yes—
1070#95C2418yes—
1071#95C2418yes—
1072#95C2418yes—
1073C24—24no—
1074C24—24no—
1075C24—28no—
1076C24—216no—
1077C24—28no—
1078C24—44no—
1079C24—44no—
1080C24—44no—
1081C24—44no—
1082C24—44no—
1083C24—48no—
1084C24—44no—
1085C24—44no—
1086C24C2512yes—
1087C24C2512yes—
1088C24C2512yes—
1089C24C2514yes—
1090C24C2514yes—
1091C24C2511yescharacteristic
1092C24C2511yescharacteristic
1093C24C2511yescharacteristic
1094#41—416no—
1095#41—816no—
1096#41—88no—
1097#41—88no—
1098#41—816no—
1099#41—816no—
1100#41—816no—
1101C2×Q8—22no—
1102C2×Q8—22no—
1103C2×Q8—22no—
1104C2×Q8—24no—
1105C2×Q8—24no—
1106C2×Q8—24no—
1107C2×Q8—24no—
1108C2×Q8—24no—
1109C2×Q8—24no—
1110C2×Q8—24no—
1111C2×Q8—24no—
1112C2×Q8—24no—
1113C2×Q8—42no—
1114C2×Q8—44no—
1115C2×Q8—44no—
1116C2×Q8—44no—
1117C2×Q8—88no—
1118C2×Q8—88no—
1119C2×Q8C22×D414yes—
1120C2×D4—24no—
1121C2×D4—24no—
1122C2×D4—24no—
1123C2×D4—24no—
1124C2×D4—28no—
1125C2×D4—24no—
1126C2×D4—24no—
1127C2×D4—24no—
1128C2×D4—28no—
1129C2×D4—28no—
1130C2×D4—28no—
1131C2×D4—28no—
1132C2×D4—24no—
1133C2×D4—24no—
1134C2×D4—24no—
1135C2×D4—28no—
1136C2×D4—22no—
1137C2×D4—22no—
1138C2×D4—22no—
1139C2×D4—24no—
1140C2×D4—24no—
1141C2×D4—24no—
1142C2×D4—24no—
1143C2×D4—24no—
1144C2×D4—24no—
1145C2×D4—24no—
1146C2×D4—28no—
1147C2×D4—28no—
1148C2×D4—216no—
1149C2×D4—24no—
1150C2×D4—24no—
1151C2×D4—24no—
1152C2×D4—24no—
1153C2×D4—24no—
1154C2×D4—24no—
1155C2×D4—24no—
1156C2×D4—216no—
1157C2×D4—48no—
1158C2×D4—48no—
1159C2×D4—44no—
1160C2×D4—44no—
1161C2×D4—48no—
1162C2×D4—44no—
1163C2×D4—44no—
1164C2×D4—44no—
1165C2×D4—44no—
1166C2×D4—42no—
1167C2×D4—432no—
1168C2×D4—48no—
1169C2×D4—44no—
1170C2×D4—48no—
1171C2×D4—48no—
1172C2×D4—48no—
1173C2×D4—48no—
1174C2×D4—44no—
1175C2×D4—44no—
1176C2×D4—44no—
1177C2×D4—44no—
1178C2×D4—44no—
1179C2×D4—44no—
1180C2×D4—44no—
1181C2×D4—48no—
1182C2×D4—48no—
1183C2×D4—48no—
1184C2×D4—48no—
1185C2×D4—44no—
1186C2×D4—44no—
1187C2×D4—44no—
1188C2×D4—44no—
1189C2×D4—48no—
1190C2×D4—48no—
1191C2×D4—48no—
1192C2×D4—48no—
1193C2×D4—48no—
1194C2×D4—48no—
1195C2×D4—48no—
1196C2×D4—48no—
1197C2×D4—432no—
1198C2×D4—88no—
1199C2×D4—816no—
1200C2×D4—88no—
1201C2×D4—816no—
1202C2×D4—864no—
1203C2×D4C22×D414yes—
1204C2×D4C22×D414yes—
1205C2×D4C22×D414yes—
1206C22×C4—24no—
1207C22×C4—24no—
1208C22×C4—24no—
1209C22×C4—24no—
1210C22×C4—28no—
1211C22×C4—24no—
1212C22×C4—24no—
1213C22×C4—24no—
1214C22×C4—28no—
1215C22×C4—24no—
1216C22×C4—24no—
1217C22×C4—28no—
1218C22×C4—28no—
1219C22×C4—28no—
1220C22×C4—28no—
1221C22×C4—24no—
1222C22×C4—24no—
1223C22×C4—28no—
1224C22×C4—44no—
1225C22×C4—44no—
1226C22×C4—42no—
1227C22×C4—42no—
1228C22×C4—42no—
1229C22×C4—42no—
1230C22×C4—42no—
1231C22×C4—44no—
1232C22×C4—44no—
1233C22×C4—44no—
1234C22×C4—44no—
1235C22×C4—44no—
1236C22×C4—44no—
1237C22×C4—44no—
1238C22×C4—48no—
1239C22×C4—44no—
1240C22×C4—44no—
1241C22×C4—44no—
1242C22×C4—48no—
1243C22×C4—44no—
1244C22×C4—44no—
1245C22×C4C22×D414yes—
1246C22×C4C22×D414yes—
1247C22×C4C22×D414yes—
1248C22×C4C22×D414yes—
1249C22×C4C22×D414yes—
1250C22×C4C22×D414yes—
1251C22×C4C22×D414yes—
1252C22×C4C22×D414yes—
1253C22×C4C22×D414yes—
1254C22×C4C2514yes—
1255C22×C4C2514yes—
1256C22×C4C2514yes—
1257C22×C4C2512yes—
1258C22×C4C2514yes—
1259C22×C4C2512yes—
1260C22×C4C2512yes—
1261C22×C4C2512yes—
1262C22×C4C2512yes—
1263C22×C4C2514yes—
1264C22×C4C2511yescharacteristic
1265C22×C4C2511yescharacteristic
1266C22×C4C2511yescharacteristic
1267C22×C4C2511yescharacteristic
1268C22×C4C2511yescharacteristic
1269C22×C4C2511yescharacteristic
1270C22×C4C2511yescharacteristic
1271C22×C4C2511yescharacteristic
1272C22×C4C2511yescharacteristic
1273C22×C4C2511yescharacteristic
1274C22×C4C2511yescharacteristic
1275C22×C4C2514yes—
1276C22×C4C2511yescharacteristic
1277C4⋊C4—24no—
1278C4⋊C4—24no—
1279C4⋊C4—24no—
1280C4⋊C4—24no—
1281C4⋊C4—24no—
1282C4⋊C4—24no—
1283C4⋊C4—24no—
1284C4⋊C4—24no—
1285C4⋊C4—24no—
1286C4⋊C4—24no—
1287C4⋊C4—22no—
1288C4⋊C4—22no—
1289C4⋊C4—24no—
1290C4⋊C4—28no—
1291C4⋊C4—28no—
1292C4⋊C4—24no—
1293C4⋊C4—24no—
1294C4⋊C4—24no—
1295C4⋊C4—28no—
1296C4⋊C4—216no—
1297C4⋊C4—44no—
1298C4⋊C4—48no—
1299C4⋊C4—48no—
1300C4⋊C4—44no—
1301C4⋊C4—44no—
1302C4⋊C4—48no—
1303C4⋊C4C22×D414yes—
1304C4⋊C4C22×D414yes—
1305C4⋊C4C22×D414yes—
1306C4⋊C4C22×D414yes—
1307C4⋊C4C22×D414yes—
1308C4⋊C4C22×D414yes—
1309C22⋊C4—28no—
1310C22⋊C4—24no—
1311C22⋊C4—24no—
1312C22⋊C4—24no—
1313C22⋊C4—28no—
1314C22⋊C4—24no—
1315C22⋊C4—24no—
1316C22⋊C4—24no—
1317C22⋊C4—24no—
1318C22⋊C4—24no—
1319C22⋊C4—24no—
1320C22⋊C4—24no—
1321C22⋊C4—28no—
1322C22⋊C4—28no—
1323C22⋊C4—28no—
1324C22⋊C4—28no—
1325C22⋊C4—24no—
1326C22⋊C4—24no—
1327C22⋊C4—24no—
1328C22⋊C4—24no—
1329C22⋊C4—24no—
1330C22⋊C4—24no—
1331C22⋊C4—24no—
1332C22⋊C4—24no—
1333C22⋊C4—24no—
1334C22⋊C4—24no—
1335C22⋊C4—24no—
1336C22⋊C4—28no—
1337C22⋊C4—28no—
1338C22⋊C4—28no—
1339C22⋊C4—28no—
1340C22⋊C4—24no—
1341C22⋊C4—24no—
1342C22⋊C4—216no—
1343C22⋊C4—216no—
1344C22⋊C4—28no—
1345C22⋊C4—216no—
1346C22⋊C4—48no—
1347C22⋊C4—48no—
1348C22⋊C4—44no—
1349C22⋊C4—48no—
1350C22⋊C4—48no—
1351C22⋊C4—48no—
1352C22⋊C4—48no—
1353C22⋊C4—48no—
1354C22⋊C4—48no—
1355C22⋊C4—48no—
1356C22⋊C4—44no—
1357C22⋊C4—48no—
1358C22⋊C4—48no—
1359C22⋊C4—48no—
1360C22⋊C4—48no—
1361C22⋊C4C22×D414yes—
1362C22⋊C4C22×D414yes—
1363C22⋊C4C22×D414yes—
1364C22⋊C4C22×D414yes—
1365C22⋊C4C22×D414yes—
1366C22⋊C4C22×D414yes—
1367C42—24no—
1368C42—24no—
1369C42—24no—
1370C42—28no—
1371C42—28no—
1372C42—28no—
1373C42—24no—
1374C42—24no—
1375C42—24no—
1376C42—44no—
1377C42—44no—
1378C42C22×D414yes—
1379C42C22×D414yes—
1380C42C22×D414yes—
1381C42C22×D414yes—
1382C42C22×D414yes—
1383C42C22×D414yes—
1384C42C22×D414yes—
1385C42C22×D414yes—
1386C42C22×D414yes—
1387C42C22×D414yes—
1388C42H(5,𝔽2)18yes—
1389C23—22no—
1390C23—22no—
1391C23—22no—
1392C23—22no—
1393C23—22no—
1394C23—22no—
1395C23—22no—
1396C23—22no—
1397C23—22no—
1398C23—22no—
1399C23—22no—
1400C23—24no—
1401C23—24no—
1402C23—24no—
1403C23—24no—
1404C23—24no—
1405C23—24no—
1406C23—24no—
1407C23—24no—
1408C23—24no—
1409C23—28no—
1410C23—28no—
1411C23—24no—
1412C23—24no—
1413C23—24no—
1414C23—24no—
1415C23—24no—
1416C23—24no—
1417C23—28no—
1418C23—28no—
1419C23—48no—
1420C23—48no—
1421C23—416no—
1422C23—88no—
1423C23—84no—
1424C23—88no—
1425C23—816no—
1426C23—816no—
1427C23—84no—
1428C23—84no—
1429C23—816no—
1430C23—84no—
1431C23—168no—
1432C23C23×D412yes—
1433C23C23×D412yes—
1434C23C23×D412yes—
1435C23#58514yes—
1436C23C2611yescharacteristic
1437Q8—44no—
1438Q8—48no—
1439Q8—44no—
1440Q8—44no—
1441Q8—44no—
1442Q8—48no—
1443Q8—84no—
1444Q8—84no—
1445D4—28no—
1446D4—28no—
1447D4—44no—
1448D4—48no—
1449D4—48no—
1450D4—416no—
1451D4—48no—
1452D4—432no—
1453D4—48no—
1454D4—48no—
1455D4—48no—
1456D4—48no—
1457D4—44no—
1458D4—44no—
1459D4—44no—
1460D4—48no—
1461D4—48no—
1462D4—84no—
1463D4—84no—
1464D4—88no—
1465D4—84no—
1466D4—88no—
1467D4—816no—
1468D4—84no—
1469D4—88no—
1470D4—88no—
1471D4—84no—
1472D4—84no—
1473D4—88no—
1474D4—88no—
1475D4—816no—
1476D4—816no—
1477D4—816no—
1478D4—168no—
1479C2×C4—22no—
1480C2×C4—22no—
1481C2×C4—22no—
1482C2×C4—22no—
1483C2×C4—24no—
1484C2×C4—22no—
1485C2×C4—22no—
1486C2×C4—22no—
1487C2×C4—22no—
1488C2×C4—24no—
1489C2×C4—22no—
1490C2×C4—22no—
1491C2×C4—22no—
1492C2×C4—28no—
1493C2×C4—28no—
1494C2×C4—28no—
1495C2×C4—28no—
1496C2×C4—22no—
1497C2×C4—22no—
1498C2×C4—22no—
1499C2×C4—24no—
1500C2×C4—24no—
1501C2×C4—22no—
1502C2×C4—22no—
1503C2×C4—24no—
1504C2×C4—24no—
1505C2×C4—24no—
1506C2×C4—24no—
1507C2×C4—24no—
1508C2×C4—24no—
1509C2×C4—24no—
1510C2×C4—24no—
1511C2×C4—24no—
1512C2×C4—24no—
1513C2×C4—24no—
1514C2×C4—24no—
1515C2×C4—24no—
1516C2×C4—24no—
1517C2×C4—24no—
1518C2×C4—28no—
1519C2×C4—24no—
1520C2×C4—44no—
1521C2×C4—44no—
1522C2×C4—44no—
1523C2×C4—44no—
1524C2×C4—44no—
1525C2×C4—416no—
1526C2×C4—48no—
1527C2×C4—84no—
1528C2×C4—84no—
1529C2×C4—88no—
1530C2×C4—88no—
1531C2×C4—84no—
1532C2×C4—84no—
1533C2×C4—88no—
1534C2×C4—88no—
1535C2×C4—88no—
1536C2×C4—84no—
1537C2×C4—84no—
1538C2×C4C23×D412yes—
1539C2×C4C23×D412yes—
1540C2×C4C23×D412yes—
1541C2×C4C23×D412yes—
1542C2×C4C23×D412yes—
1543C2×C4C23×D412yes—
1544C2×C4C23×D412yes—
1545C2×C4C23×D412yes—
1546C2×C4C23×D412yes—
1547C2×C4C23×D412yes—
1548C2×C4C23×D412yes—
1549C2×C4C23×D412yes—
1550C2×C4C2×H(5,𝔽2)18yes—
1551C2×C4C2×H(5,𝔽2)14yes—
1552C22—22no—
1553C22—22no—
1554C22—28no—
1555C22—22no—
1556C22—22no—
1557C22—22no—
1558C22—22no—
1559C22—22no—
1560C22—22no—
1561C22—44no—
1562C22—44no—
1563C22—42no—
1564C22—42no—
1565C22—44no—
1566C22—44no—
1567C22—42no—
1568C22—44no—
1569C22—44no—
1570C22—42no—
1571C22—42no—
1572C22—42no—
1573C22—48no—
1574C22—48no—
1575C22—48no—
1576C22—48no—
1577C22—48no—
1578C22—48no—
1579C22—48no—
1580C22—42no—
1581C22—44no—
1582C22—44no—
1583C22—42no—
1584C22—42no—
1585C22—1616no—
1586C22—168no—
1587C22—168no—
1588C22#344914yes—
1589C22C24×D411yescharacteristic
1590C22C22×H(5,𝔽2)12yes—
1591C22C2×#58512yes—
1592C22H(7,𝔽2)12yes—
1593C4—22no—
1594C4—22no—
1595C4—22no—
1596C4—22no—
1597C4—22no—
1598C4—22no—
1599C4—22no—
1600C4—28no—
1601C4—22no—
1602C4—22no—
1603C4—22no—
1604C4—22no—
1605C4—44no—
1606C4—42no—
1607C4—42no—
1608C4—42no—
1609C4—42no—
1610C4—44no—
1611C4—44no—
1612C4—44no—
1613C4—44no—
1614C4—42no—
1615C4#349814yes—
1616C2—24no—
1617C2—42no—
1618C2—42no—
1619C2—84no—
1620C2—84no—
1621C2—82no—
1622C2—82no—
1623C2—82no—
1624C2C2×#344911yescharacteristic
1625C2C2×#349811yescharacteristic
1626C2#6285211yescharacteristic
1627C2#6292414yes—
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×#3508C2semidirect
2. C2×#3514C2semidirect
3. #41958C2semidirect
4. #41956C2semidirect
5. #41945C2semidirect
6. #41932C2semidirect
7. #40501C2semidirect
8. #40488C2semidirect
9. #39741C2semidirect
10. #39739C2semidirect
11. #37683C2semidirect
12. #37681C2semidirect
13. #37676C2semidirect
14. #37674C2semidirect
15. #37618C2semidirect
16. #37614C2semidirect
17. #37544C2semidirect
18. #37544C2semidirect
19. #37537C2semidirect
20. #37536C2semidirect
21. #36124C2semidirect
22. #36121C2semidirect
23. #35692C2semidirect
24. #35683C2semidirect
25. #35329C2semidirect
26. #35326C2semidirect
27. #35303C2semidirect
28. #34641C2semidirect
29. #34624C2semidirect
30. C2×#2657C2semidirect
31. #34123C2semidirect
34. C2×#559C22semidirect
35. C2×#559C22semidirect
36. C2×#559C22semidirect
37. C2×#556C22semidirect
38. C2×#555C22semidirect
40. C2×#551C22semidirect
41. C2×#550C22semidirect
42. C2×#550C22semidirect
45. C2×#548C22semidirect
50. C2×#546C22semidirect
51. C2×#546C22semidirect
52. C2×#546C22semidirect
54. C2×#542C22semidirect
55. C2×#540C22semidirect
56. C2×#540C22semidirect
58. C2×#538C22semidirect
59. C2×#536C22semidirect
61. C2×#535C22semidirect
62. C2×#533C22semidirect
63. C2×#532C22semidirect
64. C2×#532C22semidirect
65. C2×#532C22semidirect
66. C2×#532C22semidirect
67. C2×#532C22semidirect
68. C2×#532C22semidirect
69. C2×#532C22semidirect
71. C22×#127C22semidirect
73. C2×#529C22semidirect
74. C2×#529C22semidirect
76. C22×#124C22semidirect
77. C22×#124C22semidirect
79. C2×#518C22semidirect
81. #2858C22semidirect
82. #2858C22semidirect
83. #2857C22semidirect
84. #2856C22semidirect
86. #2850C22semidirect
87. #2820C22semidirect
88. #2819C22semidirect
89. #2818C22semidirect
90. #2815C22semidirect
91. #2813C22semidirect
92. #2813C22semidirect
93. #2733C22semidirect
94. #2730C22semidirect
95. #2705C22semidirect
96. #2682C22semidirect
97. #2676C22semidirect
98. #2675C22semidirect
99. #2674C22semidirect
100. #2673C22semidirect
101. #2673C22semidirect
102. #2672C22semidirect
103. #2669C22semidirect
104. #2669C22semidirect
105. #2662C22semidirect
106. #2661C22semidirect
107. #2660C22semidirect
108. #2658C22semidirect
109. #2658C22semidirect
110. #2658C22semidirect
111. #2658C22semidirect
115. #2657C22semidirect
116. #2657C22semidirect
117. #2657C22semidirect
118. #2657C22semidirect
119. #2657C22semidirect
120. #2657C22semidirect
121. #2657C22semidirect
122. #2657C22semidirect
123. #2656C22semidirect
124. #2656C22semidirect
125. #2642C22semidirect
126. #2641C22semidirect
127. #2641C22semidirect
128. #2640C22semidirect
129. #2640C22semidirect
130. #2640C22semidirect
131. #2636C22semidirect
132. #2636C22semidirect
133. #2635C22semidirect
134. #2635C22semidirect
135. #2632C22semidirect
136. #2631C22semidirect
137. #2631C22semidirect
138. #2626C22semidirect
139. #2620C22semidirect
140. #2619C22semidirect
141. #2619C22semidirect
142. #2617C22semidirect
143. #2615C22semidirect
144. #2613C22semidirect
145. #2611C22semidirect
146. #2610C22semidirect
147. #2604C22semidirect
148. #2603C22semidirect
149. #2598C22semidirect
150. #2598C22semidirect
151. #2564C22semidirect
152. #2555C22semidirect
153. #2548C22semidirect
154. #2547C22semidirect
155. #2545C22semidirect
156. #2545C22semidirect
157. #2545C22semidirect
158. #2545C22semidirect
159. #2544C22semidirect
160. #2544C22semidirect
161. #2544C22semidirect
162. #2544C22semidirect
163. #2543C22semidirect
164. #2541C22semidirect
165. #2541C22semidirect
166. #2540C22semidirect
167. #2540C22semidirect
168. #2539C22semidirect
169. #2539C22semidirect
170. #2535C22semidirect
171. #2498C22semidirect
172. #2482C22semidirect
173. #2471C22semidirect
174. #2467C22semidirect
175. #2463C22semidirect
176. #2461C22semidirect
177. #2456C22semidirect
178. #2456C22semidirect
179. #2456C22semidirect
180. #2456C22semidirect
181. #2445C22semidirect
182. #2437C22semidirect
183. #2436C22semidirect
185. #2435C22semidirect
186. #2434C22semidirect
188. #2433C22semidirect
189. #2432C22semidirect
190. #2432C22semidirect
191. #2431C22semidirect
192. #2431C22semidirect
193. #2431C22semidirect
194. #2431C22semidirect
195. #2430C22semidirect
196. #2428C22semidirect
197. #2424C22semidirect
198. #2424C22semidirect
201. #2408C22semidirect
202. #2408C22semidirect
203. #2404C22semidirect
205. #2397C22semidirect
206. #2397C22semidirect
207. #2392C22semidirect
208. #2388C22semidirect
209. C2×#392C22semidirect
210. C2×#392C22semidirect
211. #2358C22semidirect
212. #2356C22semidirect
214. #2353C22semidirect
215. #2349C22semidirect
216. #2346C22semidirect
217. #2343C22semidirect
218. #2343C22semidirect
220. D4×C22⋊C4C22semidirect
221. #2328C22semidirect
222. #2327C22semidirect
223. #2326C22semidirect
224. #2326C22semidirect
225. C4×#127C22semidirect
226. C4×#124C22semidirect
227. #2295C22semidirect
229. #2290C22semidirect
230. #2283C22semidirect
231. #2283C22semidirect
232. #2283C22semidirect
233. C42×D4C22semidirect
234. C4×#117C22semidirect
235. C2×#376C22semidirect
236. C2×#376C22semidirect
416. C4×#41D4semidirect
880. C4×Q8C2×D4semidirect
881. C4×Q8C2×D4semidirect
912. C4×D4C2×D4semidirect
913. C4×D4C2×D4semidirect
921. #117C2×D4semidirect
922. #117C2×D4semidirect
1025. C2×C42C2×D4semidirect
1026. C2×C42C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35082
C2×#35142
#419582
#419562
#419452
#419322
#405012
#404882
#397412
#397392
#376832
#376812
#376762
#376742
#376182
#376142
#375442
#375372
#375362
#361242
#361212
#356922
#356832
#353292
#353262
#353032
#346412
#346242
C2×#26572
#341232