Finite Group Databasebeta

← #7646720

Subgroups — #7646720

Order 512.

6566 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42929C214yesmaximal, complemented
4#42926C214yesmaximal, complemented
5#42179C218yesmaximal, complemented
6#39619C211yesmaximal, characteristic, complemented
7#39616C211yesmaximal, characteristic, complemented
8#39491C211yesmaximal, characteristic, complemented
9#39488C211yesmaximal, characteristic, complemented
10#39172C211yesmaximal, characteristic, complemented
11#39167C211yesmaximal, characteristic, complemented
12#38958C211yesmaximal, characteristic, complemented
13#38954C211yesmaximal, characteristic, complemented
14#38095C212yesmaximal, complemented
15#38091C212yesmaximal, complemented
16#37871C212yesmaximal, complemented
17#37868C212yesmaximal, complemented
18#37545C212yesmaximal, complemented
19#37542C212yesmaximal, complemented
20#36963C218yesmaximal, complemented
21#35665C214yesmaximal, complemented
22#35322C211yesmaximal, characteristic, complemented
23#35246C212yesmaximal, complemented
24#35241C211yesmaximal, characteristic, complemented
25#35179C212yesmaximal, complemented
26#35155C214yesmaximal, complemented
27#34947C211yesmaximal, characteristic, complemented
28#34910C211yesmaximal, characteristic, complemented
29#34060C211yesmaximal, characteristic, complemented
30#3518—216no—
31#3482—216no—
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#556C2211yescharacteristic
36C2×#556C2212yes—
37C2×#556C2214yes—
38C2×#556C2212yes—
39C2×#556C2212yes—
40C2×#555C2211yescharacteristic
41C2×#555C2212yes—
42C2×#552C2214yes—
43C2×#552C2212yes—
44C2×D4×Q8C2211yescharacteristic
45C2×D4×Q8C2211yescharacteristic
46C2×#548C2212yes—
47C2×#548C2212yes—
48C2×#547C2211yescharacteristic
49C2×#547C2212yes—
50C2×#542C2212yes—
51C2×#542C2214yes—
52C2×#533C2212yes—
53C2×#533C2211yescharacteristic
54C2×#533C2212yes—
55C2×#533C2211yescharacteristic
56C2×#529C2211yescharacteristic
57C2×#529C2212yes—
58C2×#529C2214yes—
59C2×#529C2212yes—
60C2×#519C2212yes—
61C2×C4×#41C2212yes—
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2211yescharacteristic
64C22×C4×Q8C2212yes—
65#2868C2211yescharacteristic
66#2862C2211yescharacteristic
67#2862C2211yescharacteristic
68#2862C2211yescharacteristic
69#2857C2212yes—
70#2855C2218yes—
71#2853C2218yes—
72#2850C2212yes—
73#2823C2218yes—
74#2814C2218yes—
75#2723C2218yes—
76#2722C2218yes—
77#2720C2218yes—
78#2718C2218yes—
79#2717C2218yes—
80#2716C2218yes—
81#2715C2218yes—
82#2715C2218yes—
83#2713C2218yes—
84#2712C2218yes—
85#2710C2218yes—
86#2708C2218yes—
87#2700C2218yes—
88#2698C2218yes—
89#2688C2218yes—
90#2686C2218yes—
91#2664C2214yes—
92#2660C2212yes—
93#2660C2212yes—
94#2640C2212yes—
95#2640C2212yes—
96#2638C2218yes—
97#2637C2218yes—
98#2637C2218yes—
99#2630C2218yes—
100#2630C2218yes—
101#2627C2218yes—
102#2621C2212yes—
103#2621C2214yes—
104#2620C2212yes—
105#2620C2212yes—
106#2619C2212yes—
107#2609C2218yes—
108#2602C2214yes—
109#2601C2214yes—
110#2599C2218yes—
111#2599C2218yes—
112#2582C2218yes—
113#2581C2218yes—
114#2579C2218yes—
115#2568C2212yes—
116#2568C2211yescharacteristic
117#2568C2211yescharacteristic
118#2568C2212yes—
119#2567C2211yescharacteristic
120#2567C2212yes—
121#2567C2212yes—
122#2566C2211yescharacteristic
123#2566C2212yes—
124#2566C2212yes—
125#2565C2211yescharacteristic
126#2565C2212yes—
127#2565C2212yes—
128#2565C2212yes—
129#2565C2212yes—
130#2565C2212yes—
131#2565C2214yes—
132#2564C2214yes—
133#2563C2211yescharacteristic
134#2547C2211yescharacteristic
135#2546C2211yescharacteristic
136#2545C2212yes—
137#2545C2211yescharacteristic
138#2545C2212yes—
139#2544C2211yescharacteristic
140#2544C2212yes—
141#2542C2211yescharacteristic
142#2542C2211yescharacteristic
143#2504C2212yes—
144#2502C2212yes—
145#2500C2212yes—
146#2500C2212yes—
147#2500C2211yescharacteristic
148#2499C2212yes—
149#2499C2212yes—
150#2499C2211yescharacteristic
151#2499C2214yes—
152#2499C2212yes—
153#2499C2212yes—
154#2498C2214yes—
155#2478C2218yes—
156#2477C2218yes—
157#2475C2218yes—
158#2474C2218yes—
159#2466C2218yes—
160#2465C2218yes—
161#2462C2218yes—
162#2459C2218yes—
163#2451C2214yes—
164#2451C2214yes—
165#2447C2214yes—
166#2446C2214yes—
167#2439C2214yes—
168#2439C2214yes—
169#2436C2212yes—
170#2434C2212yes—
171#2434C2214yes—
172#2432C2214yes—
173#2432C2211yescharacteristic
174#2431C2211yescharacteristic
175#2429C2214yes—
176#2429C2214yes—
177#2421C2214yes—
178#2420C2214yes—
179#2417C2214yes—
180#2417C2214yes—
181#2415C2214yes—
182#2415C2214yes—
183#2409C2214yes—
184#2407C2214yes—
185#2396C2214yes—
186#2392C2214yes—
187#2327C2212yes—
188#2327C2214yes—
189#2327C2212yes—
190#2326C2212yes—
191#2326C2212yes—
192#2323C2214yes—
193#2320C2212yes—
194#2319C2212yes—
195#2318C2214yes—
196#2317C2212yes—
197#2317C2212yes—
198#2317C2212yes—
199#2314C2214yes—
200#2311C2212yes—
201#2310C2212yes—
202#2310C2212yes—
203C4×C4⋊Q8C2211yescharacteristic
204C4×#127C2211yescharacteristic
205C4×#124C2211yescharacteristic
206C4×#124C2211yescharacteristic
207C4×C22⋊Q8C2214yes—
208#2297C2212yes—
209#2295C2211yescharacteristic
210#2295C2211yescharacteristic
211#2293C2211yescharacteristic
212#2293C2211yescharacteristic
213#2290C2212yes—
214#2290C2212yes—
215#2290C2214yes—
216#2285C2212yes—
217#2285C2212yes—
218#2283C2212yes—
219C4×#117C2211yescharacteristic
220C2×C4×C4⋊C4C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2311yescharacteristic
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226Q82—28no—
227#557—28no—
228#556—28no—
229#556—28no—
230#556—216no—
231#556—216no—
232#556—232no—
233#556—216no—
234#555—28no—
235#555—216no—
236#552—216no—
237#552—232no—
238D4×Q8—28no—
239D4×Q8—28no—
240#548—216no—
241#548—216no—
242#547—216no—
243#547—28no—
244#542—216no—
245#542—232no—
246#533—216no—
247#533—28no—
248#533—216no—
249#533—28no—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2314yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2314yes—
263C2×#127C2311yescharacteristic
264#529—232no—
265#529—216no—
266#529—216no—
267#529—28no—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#124C2311yescharacteristic
283C2×#124C2312yes—
284C2×#124C2311yescharacteristic
285C2×#124C2314yes—
286C2×#124C2314yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#123C2314yes—
294C2×#123C2312yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2311yescharacteristic
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×#121C2311yescharacteristic
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2314yes—
321#519—216no—
322C4×#41—216no—
323C4×#41—28no—
324C4×#41D4116yescomplemented
325C2×C4×Q8—216no—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2314yes—
336C2×C4×Q8C2314yes—
337C2×C4×Q8C2314yes—
338C2×C4×Q8C2314yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2314yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2312yes—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×#117C2312yes—
363C2×#117C2312yes—
364C2×#117C2312yes—
365C2×#117C2314yes—
366C2×#117C2314yes—
367C2×#117C2312yes—
368C2×#117C2312yes—
369C2×#117C2314yes—
370C2×#117C2311yescharacteristic
371C2×#117C2312yes—
372C2×#117C2314yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2311yescharacteristic
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2314yes—
382C22×C4⋊C4C2312yes—
383C22×C42C2314yes—
384C22×C42C2312yes—
385C22×C42C2312yes—
386C22×C42C2312yes—
387C22×C42C2311yescharacteristic
388#400C2314yes—
389#400C2318yes—
390#400C2318yes—
391#400C2314yes—
392#399C2314yes—
393#399C2314yes—
394#398C2318yes—
395#398C2318yes—
396#398C2318yes—
397#398C2318yes—
398#398C2314yes—
399#398C2318yes—
400#398C2318yes—
401#398C2318yes—
402#398C2318yes—
403#398C2318yes—
404#398C2314yes—
405#397C2318yes—
406#397C2318yes—
407#397C2314yes—
408#397C2318yes—
409#397C2318yes—
410#397C2318yes—
411#397C2318yes—
412#397C2318yes—
413#397C2318yes—
414#397C2314yes—
415#396C2318yes—
416#396C2318yes—
417#396C2314yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#396C2318yes—
422#396C2314yes—
423#395C2314yes—
424#395C2318yes—
425#395C2318yes—
426#395C2318yes—
427#395C2318yes—
428#395C2318yes—
429#394C2314yes—
430#394C2318yes—
431#394C2318yes—
432#394C2314yes—
433#394C2314yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#393C2314yes—
439#393C2318yes—
440#393C2318yes—
441#393C2318yes—
442#392C2314yes—
443#392C2318yes—
444#391C2311yescharacteristic
445#391C2311yescharacteristic
446#391C2311yescharacteristic
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2314yes—
458#391C2318yes—
459#391C2318yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2318yes—
464#391C2318yes—
465#391C2314yes—
466#391C2311yescharacteristic
467#391C2314yes—
468#391C2314yes—
469#390C2311yescharacteristic
470#390C2311yescharacteristic
471#390C2314yes—
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2312yes—
475#390C2312yes—
476#390C2311yescharacteristic
477#390C2312yes—
478#390C2312yes—
479#389C2314yes—
480#389C2318yes—
481#389C2318yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2318yes—
488#389C2318yes—
489#389C2318yes—
490#389C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2318yes—
496#388C2318yes—
497#388C2318yes—
498#388C2318yes—
499#388C2314yes—
500#388C2318yes—
501#388C2318yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2318yes—
506#387C2318yes—
507#387C2318yes—
508#387C2314yes—
509#387C2318yes—
510#387C2318yes—
511#387C2318yes—
512#387C2318yes—
513#387C2318yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2318yes—
519#387C2318yes—
520#387C2318yes—
521#387C2318yes—
522#387C2318yes—
523#387C2318yes—
524#387C2314yes—
525#386C2318yes—
526#386C2314yes—
527#386C2314yes—
528#386C2318yes—
529#386C2318yes—
530#386C2318yes—
531#386C2314yes—
532#386C2314yes—
533#386C2318yes—
534#385C2318yes—
535#385C2314yes—
536#385C2318yes—
537#385C2314yes—
538#385C2314yes—
539#385C2318yes—
540#385C2318yes—
541#385C2318yes—
542#385C2318yes—
543#385C2318yes—
544#385C2318yes—
545#385C2314yes—
546#384C2311yescharacteristic
547#384C2311yescharacteristic
548#384C2312yes—
549#384C2312yes—
550#384C2312yes—
551#384C2312yes—
552#384C2312yes—
553#384C2314yes—
554#384C2314yes—
555#383C2314yes—
556#382C2312yes—
557#382C2312yes—
558#382C2311yescharacteristic
559#382C2312yes—
560#382C2312yes—
561#382C2314yes—
562#382C2312yes—
563#382C2311yescharacteristic
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#381C2318yes—
568#381C2318yes—
569#381C2314yes—
570#380C2314yes—
571#380C2318yes—
572#380C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2314yes—
576#380C2318yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2311yescharacteristic
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2311yescharacteristic
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2311yescharacteristic
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2318yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2318yes—
593C4×C22⋊C4C2311yescharacteristic
594C4×C22⋊C4C2311yescharacteristic
595C4×C22⋊C4C2312yes—
596C4×C22⋊C4C2312yes—
597#376C2312yes—
598#376C2312yes—
599#376C2312yes—
600C2×#95C2312yes—
601C43C2311yescharacteristic
602C43C2311yescharacteristic
603C2×#41—24no—
604C2×#41—28no—
605C2×#41—24no—
606C2×#41—42no—
607C2×#41—44no—
608C2×#41—48no—
609C2×#41C2×D418yes—
610C22×Q8—28no—
611C22×Q8—28no—
612C22×Q8—28no—
613C22×Q8—44no—
614C22×Q8—48no—
615C22×Q8C2411yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2412yes—
618C22×Q8C2412yes—
619C22×Q8C2414yes—
620C22×Q8C2411yescharacteristic
621C22×Q8C2411yescharacteristic
622C22×Q8C2414yes—
623C22×Q8C2412yes—
624C22×Q8C2414yes—
625C22×D4C2411yescharacteristic
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C22×D4C2411yescharacteristic
629C22×D4C2414yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C23×C4C2412yes—
635C23×C4C2412yes—
636C23×C4C2414yes—
637C23×C4C2412yes—
638C23×C4C2411yescharacteristic
639C23×C4C2412yes—
640C23×C4C2411yescharacteristic
641C23×C4C2414yes—
642C23×C4C2412yes—
643C23×C4C2414yes—
644C23×C4C2414yes—
645C23×C4C2412yes—
646C23×C4C2411yescharacteristic
647C23×C4C2412yes—
648C4⋊Q8—28no—
649C4⋊Q8—24no—
650C4⋊Q8—28no—
651C4⋊Q8—28no—
652C4⋊Q8—216no—
653C4⋊Q8—24no—
654C4⋊Q8—24no—
655C4⋊Q8—24no—
656C4⋊Q8—28no—
657C4⋊Q8—24no—
658C4⋊Q8—28no—
659C4⋊Q8—44no—
660C4⋊Q8—48no—
661#127—42no—
662#126—216no—
663#126—216no—
664#126—216no—
665#126—216no—
666#126—216no—
667#126—216no—
668#126—28no—
669#126—216no—
670#125—216no—
671#125—216no—
672#125—24no—
673#125—28no—
674#125—28no—
675#125—28no—
676#124—24no—
677#124—28no—
678#124—216no—
679#124—216no—
680#124—216no—
681#124—216no—
682#124—216no—
683#124—24no—
684#124—28no—
685#124—44no—
686#124—42no—
687#123—216no—
688#123—216no—
689#123—28no—
690#123—216no—
691#123—216no—
692C22⋊Q8—28no—
693C22⋊Q8—28no—
694C22⋊Q8—28no—
695C22⋊Q8—24no—
696C22⋊Q8—216no—
697C22⋊Q8—28no—
698C22⋊Q8—28no—
699C22⋊Q8—28no—
700C22⋊Q8—28no—
701C22⋊Q8—216no—
702C22⋊Q8—28no—
703C22⋊Q8—216no—
704C22⋊Q8—28no—
705C22⋊Q8—216no—
706C22⋊Q8—216no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709#121—216no—
710#121—28no—
711#121—216no—
712#121—28no—
713#121—28no—
714#121—24no—
715C4×Q8—28no—
716C4×Q8—28no—
717C4×Q8—216no—
718C4×Q8—28no—
719C4×Q8—24no—
720C4×Q8—216no—
721C4×Q8—28no—
722C4×Q8—28no—
723C4×Q8—28no—
724C4×Q8—216no—
725C4×Q8—28no—
726C4×Q8—24no—
727C4×Q8—28no—
728C4×Q8—216no—
729C4×Q8—24no—
730C4×Q8—28no—
731C4×Q8—28no—
732C4×Q8—216no—
733C4×Q8C2×D418yes—
734C4×Q8C2×D418yes—
735C4×D4—28no—
736C4×D4—28no—
737C4×D4—216no—
738C4×D4—28no—
739C4×D4—28no—
740C4×D4—216no—
741C4×D4—216no—
742C4×D4—24no—
743C4×D4—24no—
744C4×D4—24no—
745C4×D4—28no—
746C4×D4—48no—
747C4×D4C2×D418yes—
748C4×D4C2×D4116yes—
749C4×D4C2×D418yes—
750C4×D4C2×D4116yes—
751#117—24no—
752#117—28no—
753#117—28no—
754#117—28no—
755#117—28no—
756#117—28no—
757#117—216no—
758#117—28no—
759#117—216no—
760#117—28no—
761#117—28no—
762#117—216no—
763#117—216no—
764#117—44no—
765#117—44no—
766#117—44no—
767#117C2×D4116yes—
768#117C2×D418yes—
769C2×C4⋊C4—28no—
770C2×C4⋊C4—216no—
771C2×C4⋊C4—44no—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2418yes—
814C2×C4⋊C4C2418yes—
815C2×C4⋊C4C2418yes—
816C2×C4⋊C4C2418yes—
817C2×C4⋊C4C2418yes—
818C2×C4⋊C4C2418yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2418yes—
853C2×C22⋊C4C2418yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2418yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2418yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C42—216no—
865C2×C42—28no—
866C2×C42—44no—
867C2×C42C2×D4116yes—
868C2×C42C2×D418yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2411yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898#95C2414yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2418yes—
911#95C2418yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2418yes—
918#95C2414yes—
919#95C2418yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2418yes—
924#95C2418yes—
925#95C2418yes—
926#95C2418yes—
927#95C2418yes—
928#95C2418yes—
929#95C2418yes—
930#95C2418yes—
931#95C2418yes—
932#95C2418yes—
933C24C2512yes—
934C24C2512yes—
935C24C2512yes—
936C24C2511yescharacteristic
937#41—416no—
938#41—416no—
939#41—432no—
940C2×Q8—22no—
941C2×Q8—22no—
942C2×Q8—28no—
943C2×Q8—28no—
944C2×Q8—24no—
945C2×Q8—24no—
946C2×Q8—24no—
947C2×Q8—28no—
948C2×Q8—24no—
949C2×Q8—22no—
950C2×Q8—28no—
951C2×Q8—24no—
952C2×Q8—24no—
953C2×Q8—22no—
954C2×Q8—28no—
955C2×Q8—28no—
956C2×Q8—22no—
957C2×Q8—24no—
958C2×Q8—44no—
959C2×Q8—48no—
960C2×Q8—44no—
961C2×Q8—48no—
962C2×Q8—432no—
963C2×Q8—432no—
964C2×Q8C22×D414yes—
965C2×Q82−1+414yes—
966C2×D4—28no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—28no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—24no—
974C2×D4—22no—
975C2×D4—24no—
976C2×D4—22no—
977C2×D4—22no—
978C2×D4—44no—
979C2×D4—42no—
980C2×D4—48no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—48no—
985C2×D4—44no—
986C2×D4C22×D414yes—
987C2×D4C22×D418yes—
988C22×C4—24no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—24no—
993C22×C4—28no—
994C22×C4—28no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—24no—
998C22×C4—28no—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—24no—
1002C22×C4—28no—
1003C22×C4—28no—
1004C22×C4—42no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—48no—
1009C22×C4—42no—
1010C22×C4—44no—
1011C22×C4—48no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4C22×D418yes—
1016C22×C4C22×D414yes—
1017C22×C4C22×D414yes—
1018C22×C4C22×D418yes—
1019C22×C4C22×D418yes—
1020C22×C4C22×D414yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2514yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C4⋊C4—24no—
1047C4⋊C4—22no—
1048C4⋊C4—28no—
1049C4⋊C4—24no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—22no—
1054C4⋊C4—24no—
1055C4⋊C4—22no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—22no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—28no—
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—48no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—48no—
1092C4⋊C4—48no—
1093C4⋊C4—48no—
1094C4⋊C4—48no—
1095C4⋊C4—48no—
1096C4⋊C4C22×D418yes—
1097C4⋊C4C22×D414yes—
1098C4⋊C4C22×D414yes—
1099C4⋊C4C22×D418yes—
1100C22⋊C4—28no—
1101C22⋊C4—24no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—24no—
1109C22⋊C4—28no—
1110C22⋊C4—24no—
1111C22⋊C4—24no—
1112C22⋊C4—24no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—24no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—48no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—48no—
1132C22⋊C4—48no—
1133C22⋊C4—48no—
1134C22⋊C4—44no—
1135C22⋊C4C22×D418yes—
1136C22⋊C4C22×D418yes—
1137C22⋊C4C22×D418yes—
1138C42—24no—
1139C42—24no—
1140C42—28no—
1141C42—28no—
1142C42—24no—
1143C42—28no—
1144C42—28no—
1145C42—28no—
1146C42—28no—
1147C42—28no—
1148C42—24no—
1149C42—22no—
1150C42—22no—
1151C42—24no—
1152C42—24no—
1153C42—22no—
1154C42—22no—
1155C42—24no—
1156C42—24no—
1157C42—44no—
1158C42—42no—
1159C42—42no—
1160C42C22×D414yes—
1161C42C22×D414yes—
1162C42C22×D418yes—
1163C42C22×D414yes—
1164C42C22×D418yes—
1165C42C22×D414yes—
1166C42C22×D418yes—
1167C23—22no—
1168C23—21no—
1169C23—22no—
1170C23—22no—
1171C23—21no—
1172C23—24no—
1173C23—24no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—24no—
1181C23—24no—
1182C23—22no—
1183C23—24no—
1184C23—24no—
1185C23C23×D412yes—
1186C23C23×D414yes—
1187C23C2611yescharacteristic
1188Q8—28no—
1189Q8—28no—
1190Q8—416no—
1191Q8—416no—
1192Q8—48no—
1193Q8—48no—
1194Q8—44no—
1195Q8—48no—
1196Q8—84no—
1197Q8—88no—
1198D4—28no—
1199D4—48no—
1200D4—48no—
1201D4—416no—
1202D4—44no—
1203D4—44no—
1204D4—88no—
1205D4—84no—
1206D4—88no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—28no—
1219C2×C4—216no—
1220C2×C4—28no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—28no—
1249C2×C4—28no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—28no—
1259C2×C4—48no—
1260C2×C4—44no—
1261C2×C4—48no—
1262C2×C4—48no—
1263C2×C4—416no—
1264C2×C4—48no—
1265C2×C4—416no—
1266C2×C4—416no—
1267C2×C4—48no—
1268C2×C4—48no—
1269C2×C4—88no—
1270C2×C4C23×D412yes—
1271C2×C4C23×D412yes—
1272C2×C4C23×D414yes—
1273C2×C4C23×D414yes—
1274C2×C4C23×D414yes—
1275C2×C4C23×D412yes—
1276C2×C4C23×D412yes—
1277C2×C4C23×D412yes—
1278C2×C4C23×D412yes—
1279C2×C4C2×2−1+414yes—
1280C2×C4C2×2−1+412yes—
1281C2×C4#58514yes—
1282C2×C4#58512yes—
1283C22—24no—
1284C22—22no—
1285C22—24no—
1286C22—22no—
1287C22—22no—
1288C22—24no—
1289C22—42no—
1290C22—44no—
1291C22—44no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—44no—
1298C22—44no—
1299C22—42no—
1300C22—42no—
1301C22—44no—
1302C22—44no—
1303C22C24×D411yescharacteristic
1304C22C22×2−1+411yescharacteristic
1305C22C2×#58511yescharacteristic
1306C22C2×#58512yes—
1307C222−1+612yes—
1308C4—22no—
1309C4—24no—
1310C4—24no—
1311C4—22no—
1312C4—22no—
1313C4—24no—
1314C4—22no—
1315C4—24no—
1316C4—44no—
1317C4—42no—
1318C4—42no—
1319C4—44no—
1320C4—42no—
1321C4—42no—
1322C4—44no—
1323C4—44no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4—42no—
1331C4#344914yes—
1332C4#348914yes—
1333C2—44no—
1334C2—42no—
1335C2—82no—
1336C2—82no—
1337C2C2×#344911yescharacteristic
1338C2C2×#348911yescharacteristic
1339C2#6285911yescharacteristic
1340C2#6293612yes—
1341C2#6295312yes—
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×#3518C2semidirect
2. C2×#3482C2semidirect
3. #42929C2semidirect
4. #42926C2semidirect
5. #42179C2semidirect
6. #39619C2semidirect
7. #39616C2semidirect
8. #39491C2semidirect
9. #39488C2semidirect
10. #39172C2semidirect
11. #39167C2semidirect
12. #38958C2semidirect
13. #38954C2semidirect
14. #38095C2semidirect
15. #38091C2semidirect
16. #37871C2semidirect
17. #37868C2semidirect
18. #37545C2semidirect
19. #37542C2semidirect
20. #36963C2semidirect
21. #35665C2semidirect
22. #35322C2semidirect
23. #35246C2semidirect
24. #35241C2semidirect
25. #35179C2semidirect
26. #35155C2semidirect
27. #34947C2semidirect
28. #34910C2semidirect
29. #34060C2semidirect
324. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#34822
#429292
#429262
#421792
#396192
#396162
#394912
#394882
#391722
#391672
#389582
#389542
#380952
#380912
#378712
#378682
#375452
#375422
#369632
#356652
#353222
#352462
#352412
#351792
#351552
#349472
#349102
#340602