Finite Group Databasebeta

← #7657334

Subgroups — #7657334

Order 512.

6604 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C2×Q8×#41C211yesmaximal, characteristic, complemented
3#42813C212yesmaximal, complemented
4#42808C212yesmaximal, complemented
5#42786C214yesmaximal, complemented
6#42174C214yesmaximal, complemented
7#41988C214yesmaximal, complemented
8#40523C218yesmaximal, complemented
9#39727C212yesmaximal, complemented
10#39718C214yesmaximal, complemented
11#39598C212yesmaximal, complemented
12#39591C214yesmaximal, complemented
13#37640C211yesmaximal, characteristic, complemented
14#37635C211yesmaximal, characteristic, complemented
15#37622C212yesmaximal, complemented
16#37551C212yesmaximal, complemented
17#36579C212yesmaximal, complemented
18#36544C212yesmaximal, complemented
19#35949C212yesmaximal, complemented
20#35926C212yesmaximal, complemented
21#35688C214yesmaximal, complemented
22#35342C212yesmaximal, complemented
23#35297C211yesmaximal, characteristic, complemented
24#34614C212yesmaximal, complemented
25#34609C211yesmaximal, characteristic
26#34196C211yesmaximal, characteristic, complemented
27#3507—216no—
28C2×#559C2212yes—
29Q8×#41—216no—
30C2×Q82C2211yescharacteristic
31C2×#557C2212yes—
32C2×#557C2211yescharacteristic
33C2×#557C2212yes—
34C2×#556C2214yes—
35C2×#556C2211yescharacteristic
36C2×#556C2211yescharacteristic
37C2×#554C2212yes—
38C2×#554C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#554C2214yes—
41C2×#554C2211yescharacteristic
42C2×#554C2212yes—
43C2×#552C2212yes—
44C2×#552C2212yes—
45C2×D4×Q8C2212yes—
46C2×D4×Q8C2211yescharacteristic
47C2×#539C2214yes—
48C2×#536C2212yes—
49C2×#533C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#533C2214yes—
52C2×#533C2212yes—
53C2×#533C2212yes—
54C2×#532C2211yescharacteristic
55C2×#529C2212yes—
56C2×#529C2212yes—
57C2×#520C2212yes—
58C2×C4×#41C2212yes—
59C2×C4×#41C2211yescharacteristic
60C22×C4×Q8C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2857C2212yes—
64#2851C2214yes—
65#2850C2214yes—
66#2821C2214yes—
67#2821C2214yes—
68#2820C2214yes—
69#2817C2214yes—
70#2814C2218yes—
71#2734C2218yes—
72#2731C2218yes—
73#2730C2218yes—
74#2729C2218yes—
75#2725C2218yes—
76#2720C2218yes—
77#2713C2218yes—
78#2704C2218yes—
79#2702C2218yes—
80#2696C2218yes—
81#2683C2218yes—
82#2674C2218yes—
83#2664C2214yes—
84#2664C2214yes—
85#2663C2218yes—
86#2660C2212yes—
87#2642C2212yes—
88#2638C2218yes—
89#2637C2214yes—
90#2636C2214yes—
91#2635C2214yes—
92#2634C2214yes—
93#2632C2212yes—
94#2631C2212yes—
95#2630C2218yes—
96#2629C2214yes—
97#2628C2212yes—
98#2628C2214yes—
99#2625C2212yes—
100#2625C2212yes—
101#2625C2212yes—
102#2624C2212yes—
103#2624C2212yes—
104#2624C2211yescharacteristic
105#2624C2211yescharacteristic
106#2621C2214yes—
107#2620C2214yes—
108#2620C2214yes—
109#2619C2212yes—
110#2616C2214yes—
111#2616C2212yes—
112#2615C2211yescharacteristic
113#2615C2211yescharacteristic
114#2611C2214yes—
115#2611C2214yes—
116#2604C2214yes—
117#2603C2214yes—
118#2602C2218yes—
119#2600C2218yes—
120#2599C2214yes—
121#2598C2214yes—
122#2592C2214yes—
123#2592C2214yes—
124#2584C2212yes—
125#2584C2214yes—
126#2584C2214yes—
127#2582C2214yes—
128#2581C2214yes—
129#2581C2214yes—
130#2581C2212yes—
131#2580C2214yes—
132#2568C2212yes—
133#2567C2212yes—
134#2567C2212yes—
135#2562C2212yes—
136#2558C2218yes—
137#2556C2218yes—
138#2548C2212yes—
139#2547C2212yes—
140#2542C2212yes—
141#2538C2212yes—
142#2538C2212yes—
143#2538C2214yes—
144#2538C2214yes—
145#2536C2212yes—
146#2536C2214yes—
147#2506C2218yes—
148#2499C2214yes—
149#2485C2214yes—
150#2481C2218yes—
151#2469C2218yes—
152#2465C2218yes—
153#2465C2218yes—
154#2463C2218yes—
155#2462C2218yes—
156#2461C2218yes—
157#2460C2218yes—
158#2449C2218yes—
159#2440C2214yes—
160#2439C2214yes—
161#2429C2214yes—
162#2429C2214yes—
163#2423C2214yes—
164#2421C2214yes—
165#2417C2214yes—
166#2415C2214yes—
167#2415C2214yes—
168#2415C2218yes—
169#2409C2214yes—
170#2409C2214yes—
171#2398C2212yes—
172#2397C2212yes—
173#2396C2214yes—
174#2392C2214yes—
175#2392C2218yes—
176#2388C2214yes—
177#2362C2214yes—
178#2360C2214yes—
179#2355C2214yes—
180#2355C2212yes—
181#2352C2214yes—
182Q8×C4⋊C4C2212yes—
183D4×C4⋊C4C2214yes—
184#2344C2214yes—
185#2344C2212yes—
186Q8×C22⋊C4C2212yes—
187#2324C2214yes—
188#2323C2214yes—
189#2323C2214yes—
190#2320C2214yes—
191#2320C2212yes—
192C4×C22⋊Q8C2214yes—
193C4×#121C2214yes—
194C4×#121C2212yes—
195C4×#121C2212yes—
196#2285C2211yescharacteristic
197#2285C2212yes—
198#2283C2211yescharacteristic
199#2283C2212yes—
200#2276C2212yes—
201C22×#41C2311yescharacteristic
202C22×#41C2312yes—
203C23×Q8C2312yes—
204C23×Q8C2311yescharacteristic
205#559—216no—
206Q82—28no—
207#557—28no—
208#557—216no—
209#557—216no—
210#556—28no—
211#556—28no—
212#556—232no—
213#554—28no—
214#554—216no—
215#554—28no—
216#554—28no—
217#554—216no—
218#554—232no—
219#552—216no—
220#552—216no—
221D4×Q8—216no—
222D4×Q8—28no—
223#539—232no—
224#536—216no—
225#533—216no—
226#533—232no—
227#533—216no—
228#533—28no—
229#533—28no—
230#532—28no—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2314yes—
243C2×#127C2311yescharacteristic
244#529—216no—
245#529—216no—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2318yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299#520—216no—
300C4×#41—216no—
301C4×#41—28no—
302C2×C4×Q8—216no—
303C2×C4×Q8D4116yescomplemented
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2314yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2314yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2318yes—
346C2×#117C2312yes—
347C2×#117C2314yes—
348C2×#117C2314yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2312yes—
352C2×#117C2311yescharacteristic
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2314yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2314yes—
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2311yescharacteristic
362C22×C4⋊C4C2312yes—
363C22×C42C2314yes—
364C22×C42C2312yes—
365C22×C42C2312yes—
366C22×C42C2311yescharacteristic
367#400C2318yes—
368#400C2318yes—
369#400C2314yes—
370#400C2318yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#399C2314yes—
375#399C2314yes—
376#399C2312yes—
377#399C2318yes—
378#399C2312yes—
379#399C2314yes—
380#398C2314yes—
381#398C2318yes—
382#398C2314yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#398C2314yes—
387#398C2318yes—
388#398C2318yes—
389#397C2318yes—
390#397C2318yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2318yes—
395#397C2318yes—
396#397C2312yes—
397#397C2318yes—
398#396C2318yes—
399#396C2318yes—
400#396C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#396C2318yes—
405#396C2318yes—
406#395C2318yes—
407#395C2318yes—
408#395C2318yes—
409#395C2318yes—
410#395C2318yes—
411#395C2314yes—
412#395C2318yes—
413#395C2314yes—
414#394C2314yes—
415#394C2318yes—
416#394C2318yes—
417#394C2318yes—
418#394C2318yes—
419#394C2314yes—
420#394C2314yes—
421#394C2318yes—
422#394C2318yes—
423#394C2314yes—
424#394C2314yes—
425#393C2318yes—
426#393C2318yes—
427#393C2318yes—
428#393C2312yes—
429#393C2312yes—
430#393C2314yes—
431#392C2312yes—
432#392C2314yes—
433#392C2314yes—
434#392C2312yes—
435#392C2314yes—
436#392C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2318yes—
444#391C2314yes—
445#391C2314yes—
446#391C2318yes—
447#390C2314yes—
448#390C2318yes—
449#390C2312yes—
450#390C2314yes—
451#390C2312yes—
452#390C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2318yes—
459#389C2314yes—
460#389C2318yes—
461#389C2318yes—
462#389C2312yes—
463#389C2314yes—
464#389C2312yes—
465#389C2318yes—
466#389C2314yes—
467#389C2314yes—
468#389C2318yes—
469#389C2318yes—
470#389C2318yes—
471#389C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2314yes—
485#388C2314yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#387C2318yes—
495#387C2318yes—
496#387C2318yes—
497#387C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2314yes—
503#386C2314yes—
504#385C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#384C2314yes—
511#384C2314yes—
512#384C2314yes—
513#384C2312yes—
514#383C2314yes—
515#383C2312yes—
516#382C2312yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#382C2312yes—
521#381C2312yes—
522#381C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2312yes—
526#380C2314yes—
527#380C2312yes—
528#380C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2311yescharacteristic
533#380C2311yescharacteristic
534#380C2312yes—
535#380C2312yes—
536#380C2318yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2318yes—
545C4×C4⋊C4C2318yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2314yes—
552#376C2314yes—
553#376C2312yes—
554C2×#41—24no—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—48no—
558C22×Q8—28no—
559C22×Q8—44no—
560C22×Q8—44no—
561C22×Q8—44no—
562C22×Q8C2×D418yes—
563C22×Q8C2411yescharacteristic
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2414yes—
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×Q8C2414yes—
572C22×Q8C2412yes—
573C22×Q8C2412yes—
574C22×D4C2411yescharacteristic
575C22×D4C2412yes—
576C22×D4C2411yescharacteristic
577C22×D4C2411yescharacteristic
578C22×D4C2414yes—
579C22×D4C2412yes—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2412yes—
583C22×D4C2414yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2412yes—
590C23×C4C2414yes—
591C23×C4C2412yes—
592C23×C4C2414yes—
593C23×C4C2414yes—
594C23×C4C2414yes—
595C23×C4C2412yes—
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C4⋊Q8—28no—
599C4⋊Q8—216no—
600C4⋊Q8—216no—
601C4⋊Q8—28no—
602C4⋊Q8—216no—
603C4⋊Q8—24no—
604C4⋊Q8—28no—
605C4⋊Q8—24no—
606C4⋊Q8—24no—
607C4⋊Q8—28no—
608C4⋊Q8—24no—
609C4⋊Q8—24no—
610#127—24no—
611#126—216no—
612#126—216no—
613#126—216no—
614#126—216no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—216no—
620#125—28no—
621#125—28no—
622#125—28no—
623#125—28no—
624#125—28no—
625#125—28no—
626#124—216no—
627#124—28no—
628#124—28no—
629#124—28no—
630#124—84no—
631#123—216no—
632#123—216no—
633#123—216no—
634#123—216no—
635C22⋊Q8—28no—
636C22⋊Q8—216no—
637C22⋊Q8—28no—
638C22⋊Q8—28no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—28no—
647C22⋊Q8—216no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—48no—
656C22⋊Q8—48no—
657C22⋊Q8—84no—
658C22⋊Q8—88no—
659#121—24no—
660#121—24no—
661#121—28no—
662#121—28no—
663#121—28no—
664C4×Q8—28no—
665C4×Q8—28no—
666C4×Q8—216no—
667C4×Q8—216no—
668C4×Q8—28no—
669C4×Q8—216no—
670C4×Q8—28no—
671C4×Q8—24no—
672C4×Q8—28no—
673C4×Q8—24no—
674C4×Q8—28no—
675C4×Q8—28no—
676C4×Q8—216no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—28no—
680C4×Q8—48no—
681C4×Q8C2×D418yes—
682C4×Q8C2×D418yes—
683C4×Q8C2×D4116yes—
684C4×Q8C2×D418yes—
685C4×Q8C2×D418yes—
686C4×Q8C2×D4116yes—
687C4×D4—28no—
688C4×D4—216no—
689C4×D4—216no—
690C4×D4—28no—
691C4×D4—216no—
692C4×D4—216no—
693C4×D4—216no—
694C4×D4—28no—
695C4×D4—24no—
696C4×D4—28no—
697C4×D4—24no—
698C4×D4—28no—
699C4×D4—28no—
700C4×D4—28no—
701C4×D4—24no—
702C4×D4—24no—
703C4×D4—48no—
704C4×D4—48no—
705C4×D4—88no—
706#117—28no—
707#117—24no—
708#117—28no—
709#117—28no—
710#117—28no—
711#117—216no—
712#117—28no—
713#117—216no—
714#117—216no—
715#117—84no—
716#117—82no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—216no—
719C2×C4⋊C4—28no—
720C2×C4⋊C4—28no—
721C2×C4⋊C4C2×D418yes—
722C2×C4⋊C4C2×D4116yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2414yes—
812C2×C42—28no—
813C2×C42—216no—
814C2×C42C2×D4116yes—
815C2×C42C2×D418yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2414yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2414yes—
826C2×C42C2418yes—
827C2×C42C2414yes—
828C2×C42C2418yes—
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2412yes—
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835C2×C42C2411yescharacteristic
836C2×C42C2412yes—
837#95C2412yes—
838#95C2412yes—
839#95C2414yes—
840#95C2418yes—
841#95C2414yes—
842#95C2414yes—
843#95C2418yes—
844#95C2418yes—
845#95C2414yes—
846#95C2418yes—
847#95C2418yes—
848#95C2414yes—
849#95C2418yes—
850#95C2414yes—
851#95C2414yes—
852#95C2418yes—
853#95C2414yes—
854#95C2418yes—
855#95C2414yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864C24C2512yes—
865C24C2512yes—
866C24C2511yescharacteristic
867C24C2512yes—
868#41—232no—
869#41—432no—
870C2×Q8—22no—
871C2×Q8—24no—
872C2×Q8—28no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—28no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—44no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—44no—
892C2×Q8—42no—
893C2×Q8—42no—
894C2×Q8—416no—
895C2×Q8—432no—
896C2×Q8C22×D414yes—
897C2×Q8C22×D414yes—
898C2×Q8C22×D418yes—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—22no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—24no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—44no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—28no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—28no—
934C22×C4—28no—
935C22×C4—28no—
936C22×C4—24no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—42no—
940C22×C4—41no—
941C22×C4—42no—
942C22×C4—41no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—42no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—42no—
953C22×C4—44no—
954C22×C4C22×D414yes—
955C22×C4C22×D414yes—
956C22×C4C22×D418yes—
957C22×C4C22×D414yes—
958C22×C4C22×D418yes—
959C22×C42−1+418yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2518yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2514yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2514yes—
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2511yescharacteristic
976C22×C4C2512yes—
977C22×C4C2511yescharacteristic
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—22no—
998C4⋊C4—22no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—216no—
1019C4⋊C4—28no—
1020C4⋊C4—48no—
1021C4⋊C4—44no—
1022C4⋊C4—48no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—48no—
1026C4⋊C4—48no—
1027C4⋊C4—48no—
1028C4⋊C4—48no—
1029C4⋊C4—48no—
1030C4⋊C4C22×D414yes—
1031C4⋊C4C22×D414yes—
1032C4⋊C4C22×D418yes—
1033C4⋊C4C22×D418yes—
1034C4⋊C4C22×D418yes—
1035C4⋊C4C22×D418yes—
1036C4⋊C4C22×D418yes—
1037C22⋊C4—28no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—216no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—24no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—24no—
1052C22⋊C4—24no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—42no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—42no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—48no—
1066C22⋊C4—48no—
1067C22⋊C4—48no—
1068C22⋊C4—48no—
1069C22⋊C4—44no—
1070C22⋊C4—48no—
1071C42—24no—
1072C42—28no—
1073C42—28no—
1074C42—24no—
1075C42—28no—
1076C42—24no—
1077C42—28no—
1078C42—28no—
1079C42—28no—
1080C42—28no—
1081C42—48no—
1082C42—44no—
1083C42—48no—
1084C42C22×D414yes—
1085C42C22×D418yes—
1086C42C22×D418yes—
1087C42C22×D418yes—
1088C42C22×D418yes—
1089C42C22×D414yes—
1090C42C22×D414yes—
1091C42C22×D414yes—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—21no—
1099C23—22no—
1100C23—21no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—24no—
1105C23—24no—
1106C23—24no—
1107C23—24no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23C23×D412yes—
1113C23C2×2−1+414yes—
1114C23C2611yescharacteristic
1115Q8—28no—
1116Q8—28no—
1117Q8—28no—
1118Q8—48no—
1119Q8—416no—
1120Q8—48no—
1121Q8—48no—
1122Q8—48no—
1123Q8—84no—
1124Q8—88no—
1125Q8—84no—
1126D4—28no—
1127D4—216no—
1128D4—48no—
1129D4—416no—
1130D4—48no—
1131D4—48no—
1132D4—44no—
1133D4—44no—
1134D4—84no—
1135D4—88no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—28no—
1151C2×C4—28no—
1152C2×C4—216no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—28no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—28no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—28no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—28no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—48no—
1184C2×C4—44no—
1185C2×C4—48no—
1186C2×C4—416no—
1187C2×C4—48no—
1188C2×C4—48no—
1189C2×C4—48no—
1190C2×C4—88no—
1191C2×C4—88no—
1192C2×C4—88no—
1193C2×C4—84no—
1194C2×C4C23×D414yes—
1195C2×C4C23×D412yes—
1196C2×C4C23×D412yes—
1197C2×C4C23×D414yes—
1198C2×C4C23×D414yes—
1199C2×C4C23×D412yes—
1200C2×C4C23×D414yes—
1201C2×C4C23×D412yes—
1202C2×C4C23×D412yes—
1203C2×C4C23×D412yes—
1204C2×C4C2×2−1+414yes—
1205C2×C4C2×2−1+414yes—
1206C2×C4#58514yes—
1207C22—22no—
1208C22—24no—
1209C22—22no—
1210C22—24no—
1211C22—24no—
1212C22—22no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22C24×D411yescharacteristic
1230C22C22×2−1+412yes—
1231C22C2×#58512yes—
1232C22H(7,𝔽2)11yescharacteristic
1233C222−1+611yescharacteristic
1234C4—22no—
1235C4—24no—
1236C4—24no—
1237C4—24no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—24no—
1242C4—24no—
1243C4—44no—
1244C4—44no—
1245C4—44no—
1246C4—42no—
1247C4—48no—
1248C4—44no—
1249C4—44no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—44no—
1254C4#344914yes—
1255C4#348614yes—
1256C2—42no—
1257C2—44no—
1258C2—82no—
1259C2—82no—
1260C2C2×#344911yescharacteristic
1261C2C2×#348611yescharacteristic
1262C2#6285311yescharacteristic
1263C2#6292612yes—
1264C2#6293212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34609C2
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×#3507C2semidirect
2. C2×Q8×#41C2semidirect
3. #42813C2semidirect
4. #42808C2semidirect
5. #42786C2semidirect
6. #42174C2semidirect
7. #41988C2semidirect
8. #40523C2semidirect
9. #39727C2semidirect
10. #39718C2semidirect
11. #39598C2semidirect
12. #39591C2semidirect
13. #37640C2semidirect
14. #37635C2semidirect
15. #37622C2semidirect
16. #37551C2semidirect
17. #36579C2semidirect
18. #36544C2semidirect
19. #35949C2semidirect
20. #35926C2semidirect
21. #35688C2semidirect
22. #35342C2semidirect
23. #35297C2semidirect
24. #34614C2semidirect
26. #34196C2semidirect
303. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C2×Q8×#412
#428132
#428082
#427862
#421742
#419882
#405232
#397272
#397182
#395982
#395912
#376402
#376352
#376222
#375512
#365792
#365442
#359492
#359262
#356882
#353422
#352972
#346142
#346092
#341962