Finite Group Databasebeta

← #7654861

Subgroups — #7654861

Order 512.

6794 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42926C214yesmaximal, complemented
4#42176C218yesmaximal, complemented
5#39724C212yesmaximal, complemented
6#39596C212yesmaximal, complemented
7#38920C212yesmaximal, complemented
8#38915C214yesmaximal, complemented
9#38911C212yesmaximal, complemented
10#38903C214yesmaximal, complemented
11#38051C214yesmaximal, complemented
12#38032C214yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37622C212yesmaximal, complemented
15#36579C212yesmaximal, complemented
16#36545C212yesmaximal, complemented
17#36405C212yesmaximal, complemented
18#36404C212yesmaximal, complemented
19#35834C214yesmaximal, complemented
20#35280C211yesmaximal, characteristic, complemented
21#35280C211yesmaximal, characteristic, complemented
22#35189C212yesmaximal, complemented
23#35179C212yesmaximal, complemented
24#34976C211yesmaximal, characteristic, complemented
25#34952C212yesmaximal, complemented
26#34188C211yesmaximal, characteristic, complemented
27#3482—216no—
28#3482—216no—
29C2×#557C2211yescharacteristic
30C2×#557C2211yescharacteristic
31C2×#556C2211yescharacteristic
32C2×#556C2212yes—
33C2×#556C2211yescharacteristic
34C2×#556C2212yes—
35C2×#552C2212yes—
36C2×#552C2214yes—
37C2×#552C2214yes—
38C2×#552C2212yes—
39C2×D4×Q8C2211yescharacteristic
40C2×D4×Q8C2211yescharacteristic
41C2×#548C2212yes—
42C2×#548C2212yes—
43C2×#547C2211yescharacteristic
44C2×#547C2211yescharacteristic
45C2×#547C2212yes—
46C2×#547C2212yes—
47C2×#533C2211yescharacteristic
48C2×#533C2211yescharacteristic
49C2×#533C2212yes—
50C2×#533C2212yes—
51C2×#529C2214yes—
52C2×#529C2212yes—
53C2×#529C2212yes—
54C2×#529C2214yes—
55C2×C4×#41C2212yes—
56C2×C4×#41C2212yes—
57C2×C4×#41C2211yescharacteristic
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60C22×C4×Q8C2212yes—
61C22×C4×Q8C2212yes—
62#2857C2212yes—
63#2857C2212yes—
64#2857C2212yes—
65#2857C2212yes—
66#2855C2214yes—
67#2855C2214yes—
68#2851C2214yes—
69#2850C2214yes—
70#2822C2214yes—
71#2814C2218yes—
72#2720C2218yes—
73#2719C2218yes—
74#2718C2218yes—
75#2717C2218yes—
76#2708C2218yes—
77#2706C2218yes—
78#2692C2218yes—
79#2690C2218yes—
80#2689C2218yes—
81#2688C2218yes—
82#2687C2218yes—
83#2686C2218yes—
84#2664C2218yes—
85#2630C2218yes—
86#2629C2214yes—
87#2629C2214yes—
88#2628C2214yes—
89#2627C2218yes—
90#2625C2214yes—
91#2625C2214yes—
92#2625C2214yes—
93#2624C2214yes—
94#2621C2214yes—
95#2621C2214yes—
96#2609C2214yes—
97#2601C2218yes—
98#2592C2214yes—
99#2584C2214yes—
100#2582C2212yes—
101#2582C2212yes—
102#2582C2212yes—
103#2582C2211yescharacteristic
104#2582C2212yes—
105#2582C2212yes—
106#2582C2212yes—
107#2581C2214yes—
108#2581C2214yes—
109#2581C2214yes—
110#2580C2214yes—
111#2579C2218yes—
112#2568C2212yes—
113#2568C2212yes—
114#2568C2214yes—
115#2567C2214yes—
116#2565C2218yes—
117#2557C2218yes—
118#2553C2218yes—
119#2550C2214yes—
120#2546C2212yes—
121#2546C2212yes—
122#2542C2214yes—
123#2538C2212yes—
124#2538C2212yes—
125#2538C2212yes—
126#2538C2212yes—
127#2538C2211yescharacteristic
128#2538C2211yescharacteristic
129#2537C2211yescharacteristic
130#2521C2218yes—
131#2496C2218yes—
132#2492C2214yes—
133#2489C2214yes—
134#2487C2214yes—
135#2485C2212yes—
136#2485C2214yes—
137#2485C2212yes—
138#2481C2218yes—
139#2478C2218yes—
140#2473C2218yes—
141#2470C2218yes—
142#2469C2218yes—
143#2468C2218yes—
144#2462C2218yes—
145#2457C2218yes—
146#2447C2214yes—
147#2446C2214yes—
148#2434C2214yes—
149#2432C2214yes—
150#2421C2214yes—
151#2420C2214yes—
152#2417C2214yes—
153#2417C2214yes—
154#2417C2214yes—
155#2417C2214yes—
156#2415C2214yes—
157#2415C2214yes—
158#2415C2214yes—
159#2414C2214yes—
160#2409C2214yes—
161#2409C2214yes—
162#2407C2214yes—
163#2407C2214yes—
164#2407C2212yes—
165#2407C2212yes—
166#2396C2218yes—
167#2392C2214yes—
168#2365C2214yes—
169#2362C2214yes—
170#2360C2214yes—
171#2355C2212yes—
172#2355C2212yes—
173#2354C2212yes—
174#2354C2212yes—
175#2352C2214yes—
176#2352C2214yes—
177#2352C2214yes—
178#2324C2214yes—
179#2323C2214yes—
180#2317C2214yes—
181#2316C2212yes—
182#2316C2212yes—
183#2314C2214yes—
184#2311C2212yes—
185#2311C2212yes—
186#2311C2212yes—
187#2310C2214yes—
188C4×C22⋊Q8C2214yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2214yes—
191C4×C22⋊Q8C2212yes—
192C4×#121C2212yes—
193C4×#121C2212yes—
194#2297C2214yes—
195#2296C2214yes—
196#2285C2211yescharacteristic
197#2285C2212yes—
198#2285C2212yes—
199C2×#384C2211yescharacteristic
200#2274C2212yes—
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2311yescharacteristic
206C23×Q8C2312yes—
207C23×Q8C2312yes—
208#557—28no—
209#557—28no—
210#556—28no—
211#556—28no—
212#556—216no—
213#556—216no—
214#552—216no—
215#552—232no—
216#552—232no—
217#552—216no—
218D4×Q8—28no—
219D4×Q8—28no—
220#548—216no—
221#548—216no—
222#547—216no—
223#547—28no—
224#547—28no—
225#547—216no—
226#533—216no—
227#533—216no—
228#533—28no—
229#533—28no—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239#529—232no—
240#529—216no—
241#529—232no—
242#529—216no—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2314yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2312yes—
253C2×#125C2314yes—
254C2×#125C2314yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#124C2312yes—
260C2×#124C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2312yes—
293C4×#41—216no—
294C4×#41—216no—
295C4×#41—28no—
296C4×#41—28no—
297C4×#41D4116yescomplemented
298C2×C4×Q8—216no—
299C2×C4×Q8—216no—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2311yescharacteristic
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2311yescharacteristic
343C2×#117C2311yescharacteristic
344C2×#117C2314yes—
345C2×#117C2314yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2314yes—
352C2×#117C2312yes—
353C2×#117C2314yes—
354C2×#117C2312yes—
355C2×#117C2311yescharacteristic
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2314yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2314yes—
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2312yes—
363C22×C42C2314yes—
364C22×C42C2314yes—
365C22×C42C2312yes—
366C22×C42C2312yes—
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369#400C2318yes—
370#400C2318yes—
371#400C2318yes—
372#400C2318yes—
373#400C2318yes—
374#400C2318yes—
375#399C2318yes—
376#399C2318yes—
377#398C2314yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#398C2318yes—
388#397C2318yes—
389#397C2318yes—
390#397C2318yes—
391#397C2318yes—
392#397C2318yes—
393#397C2318yes—
394#397C2318yes—
395#397C2314yes—
396#396C2314yes—
397#396C2318yes—
398#396C2318yes—
399#396C2314yes—
400#396C2318yes—
401#396C2318yes—
402#395C2318yes—
403#395C2318yes—
404#395C2318yes—
405#395C2318yes—
406#394C2314yes—
407#394C2318yes—
408#394C2318yes—
409#394C2318yes—
410#394C2318yes—
411#394C2314yes—
412#394C2314yes—
413#393C2318yes—
414#393C2318yes—
415#392C2318yes—
416#392C2314yes—
417#391C2318yes—
418#391C2318yes—
419#391C2312yes—
420#391C2314yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#390C2314yes—
435#390C2314yes—
436#390C2314yes—
437#390C2318yes—
438#390C2312yes—
439#390C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2314yes—
453#389C2314yes—
454#389C2318yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2318yes—
462#389C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2314yes—
472#388C2314yes—
473#387C2318yes—
474#387C2318yes—
475#387C2318yes—
476#387C2318yes—
477#387C2318yes—
478#387C2318yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2314yes—
484#387C2314yes—
485#386C2318yes—
486#386C2318yes—
487#386C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2314yes—
493#386C2314yes—
494#385C2318yes—
495#385C2318yes—
496#385C2318yes—
497#385C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2314yes—
503#385C2314yes—
504#384C2318yes—
505#384C2312yes—
506#384C2311yescharacteristic
507#384C2312yes—
508#384C2311yescharacteristic
509#384C2312yes—
510#384C2312yes—
511#382C2318yes—
512#382C2312yes—
513#382C2314yes—
514#382C2314yes—
515#382C2314yes—
516#381C2318yes—
517#381C2318yes—
518#380C2314yes—
519#380C2314yes—
520#380C2314yes—
521#380C2314yes—
522#380C2314yes—
523#380C2314yes—
524#380C2318yes—
525#380C2318yes—
526#380C2312yes—
527#380C2314yes—
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2312yes—
534#380C2312yes—
535#380C2314yes—
536#380C2312yes—
537#380C2312yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2318yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2318yes—
549C4×C22⋊C4C2318yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2314yes—
552C4×C22⋊C4C2318yes—
553C4×C22⋊C4C2314yes—
554C2×#41—24no—
555C2×#41—28no—
556C2×#41—24no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—24no—
560C2×#41—24no—
561C2×#41—42no—
562C2×#41—42no—
563C2×#41—42no—
564C2×#41—42no—
565C2×#41—44no—
566C2×#41—44no—
567C2×#41—44no—
568C2×#41C2×D418yes—
569C22×Q8—28no—
570C22×Q8—28no—
571C22×Q8—28no—
572C22×Q8—44no—
573C22×Q8—44no—
574C22×Q8—44no—
575C22×Q8C2412yes—
576C22×Q8C2412yes—
577C22×Q8C2412yes—
578C22×Q8C2412yes—
579C22×Q8C2411yescharacteristic
580C22×Q8C2414yes—
581C22×Q8C2411yescharacteristic
582C22×Q8C2411yescharacteristic
583C22×Q8C2414yes—
584C22×D4C2411yescharacteristic
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2412yes—
588C22×D4C2411yescharacteristic
589C22×D4C2411yescharacteristic
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2414yes—
598C23×C4C2412yes—
599C23×C4C2414yes—
600C23×C4C2412yes—
601C23×C4C2411yescharacteristic
602C23×C4C2411yescharacteristic
603C23×C4C2411yescharacteristic
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2412yes—
610C4⋊Q8—28no—
611C4⋊Q8—28no—
612C4⋊Q8—24no—
613C4⋊Q8—24no—
614C4⋊Q8—28no—
615C4⋊Q8—24no—
616C4⋊Q8—24no—
617C4⋊Q8—28no—
618C4⋊Q8—48no—
619#126—216no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—216no—
624#126—216no—
625#125—216no—
626#125—216no—
627#125—28no—
628#125—216no—
629#125—28no—
630#125—28no—
631#125—28no—
632#125—216no—
633#124—28no—
634#124—216no—
635#124—216no—
636#124—28no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—216no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—48no—
659C22⋊Q8—48no—
660C22⋊Q8—48no—
661C22⋊Q8—48no—
662C22⋊Q8—44no—
663#121—28no—
664#121—216no—
665#121—216no—
666#121—28no—
667#121—28no—
668#121—44no—
669C4×Q8—28no—
670C4×Q8—28no—
671C4×Q8—216no—
672C4×Q8—28no—
673C4×Q8—24no—
674C4×Q8—216no—
675C4×Q8—28no—
676C4×Q8—216no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—28no—
680C4×Q8—216no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—28no—
687C4×Q8C2×D418yes—
688C4×Q8C2×D418yes—
689C4×D4—28no—
690C4×D4—28no—
691C4×D4—216no—
692C4×D4—216no—
693C4×D4—28no—
694C4×D4—28no—
695C4×D4—28no—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—24no—
699C4×D4—24no—
700C4×D4—24no—
701C4×D4—28no—
702C4×D4—24no—
703C4×D4—48no—
704C4×D4C2×D418yes—
705C4×D4C2×D418yes—
706C4×D4C2×D4116yes—
707C4×D4C2×D4116yes—
708#117—24no—
709#117—28no—
710#117—24no—
711#117—216no—
712#117—28no—
713#117—28no—
714#117—28no—
715#117—216no—
716#117—28no—
717#117—28no—
718#117—216no—
719#117—216no—
720#117—44no—
721#117—48no—
722#117—48no—
723#117C2×D4116yes—
724#117C2×D418yes—
725C2×C4⋊C4—28no—
726C2×C4⋊C4—216no—
727C2×C4⋊C4—28no—
728C2×C4⋊C4—216no—
729C2×C4⋊C4—44no—
730C2×C4⋊C4—44no—
731C2×C4⋊C4—44no—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2418yes—
779C2×C4⋊C4C2418yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2418yes—
782C2×C4⋊C4C2418yes—
783C2×C4⋊C4C2418yes—
784C2×C4⋊C4C2418yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
821C2×C42—216no—
822C2×C42—28no—
823C2×C42—216no—
824C2×C42—28no—
825C2×C42C2×D4116yes—
826C2×C42C2×D418yes—
827C2×C42C2412yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2412yes—
834C2×C42C2414yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2412yes—
840C2×C42C2418yes—
841C2×C42C2418yes—
842C2×C42C2411yescharacteristic
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2411yescharacteristic
846C2×C42C2411yescharacteristic
847C2×C42C2411yescharacteristic
848C2×C42C2412yes—
849#95C2418yes—
850#95C2418yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2414yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2418yes—
868#95C2418yes—
869#95C2418yes—
870#95C2418yes—
871#95C2418yes—
872#95C2418yes—
873#95C2418yes—
874#95C2418yes—
875C24C2512yes—
876C24C2512yes—
877C24C2511yescharacteristic
878C24C2512yes—
879#41—416no—
880#41—416no—
881#41—432no—
882#41—416no—
883#41—432no—
884C2×Q8—22no—
885C2×Q8—28no—
886C2×Q8—28no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—22no—
891C2×Q8—24no—
892C2×Q8—28no—
893C2×Q8—24no—
894C2×Q8—24no—
895C2×Q8—22no—
896C2×Q8—22no—
897C2×Q8—22no—
898C2×Q8—22no—
899C2×Q8—24no—
900C2×Q8—24no—
901C2×Q8—24no—
902C2×Q8—24no—
903C2×Q8—22no—
904C2×Q8—24no—
905C2×Q8—24no—
906C2×Q8—44no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—432no—
910C2×Q8—432no—
911C2×Q8C22×D414yes—
912C2×Q82−1+414yes—
913C2×D4—24no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—24no—
917C2×D4—28no—
918C2×D4—24no—
919C2×D4—28no—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—24no—
923C2×D4—22no—
924C2×D4—22no—
925C2×D4—22no—
926C2×D4—22no—
927C2×D4—22no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—44no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—44no—
937C2×D4C22×D414yes—
938C2×D4C22×D418yes—
939C2×D42−1+414yes—
940C22×C4—24no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—24no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—22no—
950C22×C4—28no—
951C22×C4—28no—
952C22×C4—28no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—28no—
956C22×C4—24no—
957C22×C4—28no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—28no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4C22×D418yes—
986C22×C4C22×D418yes—
987C22×C4C22×D414yes—
988C22×C4C22×D414yes—
989C22×C4C22×D414yes—
990C22×C4C22×D418yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2518yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2512yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C4⋊C4—24no—
1014C4⋊C4—22no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—22no—
1026C4⋊C4—24no—
1027C4⋊C4—22no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—22no—
1033C4⋊C4—24no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—48no—
1061C4⋊C4—48no—
1062C4⋊C4—48no—
1063C4⋊C4—48no—
1064C4⋊C4—48no—
1065C4⋊C4—48no—
1066C4⋊C4C22×D414yes—
1067C4⋊C4C22×D418yes—
1068C4⋊C4C22×D418yes—
1069C4⋊C4C22×D414yes—
1070C22⋊C4—28no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—28no—
1082C22⋊C4—24no—
1083C22⋊C4—24no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—44no—
1089C22⋊C4—48no—
1090C22⋊C4—48no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—48no—
1096C22⋊C4—48no—
1097C22⋊C4—48no—
1098C22⋊C4—48no—
1099C22⋊C4C22×D418yes—
1100C22⋊C4C22×D418yes—
1101C22⋊C4C22×D418yes—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—24no—
1106C42—28no—
1107C42—28no—
1108C42—24no—
1109C42—28no—
1110C42—24no—
1111C42—28no—
1112C42—28no—
1113C42—24no—
1114C42—28no—
1115C42—48no—
1116C42—48no—
1117C42C22×D414yes—
1118C42C22×D414yes—
1119C42C22×D418yes—
1120C42C22×D414yes—
1121C42C22×D414yes—
1122C42C22×D418yes—
1123C42C22×D418yes—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—21no—
1129C23—21no—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—21no—
1135C23—22no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23C23×D412yes—
1150C23C23×D414yes—
1151C23C2×2−1+414yes—
1152C23C2611yescharacteristic
1153Q8—28no—
1154Q8—28no—
1155Q8—416no—
1156Q8—416no—
1157Q8—48no—
1158Q8—48no—
1159Q8—48no—
1160Q8—44no—
1161Q8—48no—
1162D4—28no—
1163D4—28no—
1164D4—48no—
1165D4—48no—
1166D4—416no—
1167D4—48no—
1168D4—416no—
1169D4—44no—
1170D4—88no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—28no—
1186C2×C4—216no—
1187C2×C4—28no—
1188C2×C4—216no—
1189C2×C4—28no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—28no—
1211C2×C4—28no—
1212C2×C4—28no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—48no—
1227C2×C4—48no—
1228C2×C4—416no—
1229C2×C4—416no—
1230C2×C4—48no—
1231C2×C4—416no—
1232C2×C4—416no—
1233C2×C4—48no—
1234C2×C4—48no—
1235C2×C4—48no—
1236C2×C4—48no—
1237C2×C4—164no—
1238C2×C4C23×D414yes—
1239C2×C4C23×D412yes—
1240C2×C4C23×D412yes—
1241C2×C4C23×D414yes—
1242C2×C4C23×D412yes—
1243C2×C4C23×D414yes—
1244C2×C4C23×D412yes—
1245C2×C4C23×D412yes—
1246C2×C4C23×D412yes—
1247C2×C4C2×2−1+414yes—
1248C2×C4C2×2−1+412yes—
1249C2×C4C2×2−1+412yes—
1250C2×C4#58512yes—
1251C2×C4#58512yes—
1252C2×C4#58512yes—
1253C2×C4#58512yes—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—22no—
1258C22—24no—
1259C22—22no—
1260C22—24no—
1261C22—22no—
1262C22—24no—
1263C22—42no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22C24×D411yescharacteristic
1283C22C22×2−1+411yescharacteristic
1284C22C22×2−1+411yescharacteristic
1285C22C2×#58511yescharacteristic
1286C22C2×#58511yescharacteristic
1287C22C2×#58511yescharacteristic
1288C22C2×#58511yescharacteristic
1289C4—22no—
1290C4—24no—
1291C4—22no—
1292C4—24no—
1293C4—24no—
1294C4—22no—
1295C4—24no—
1296C4—44no—
1297C4—44no—
1298C4—48no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—44no—
1304C4—42no—
1305C4—44no—
1306C4—42no—
1307C4—44no—
1308C4#344914yes—
1309C4#348914yes—
1310C4#348914yes—
1311C2—44no—
1312C2—44no—
1313C2—42no—
1314C2—82no—
1315C2C2×#344911yescharacteristic
1316C2C2×#348911yescharacteristic
1317C2C2×#348911yescharacteristic
1318C2#6302511yescharacteristic
1319C2#6303211yescharacteristic
1320C2#6303411yescharacteristic
1321C2#6303611yescharacteristic
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×#3482C2semidirect
2. C2×#3482C2semidirect
3. #42926C2semidirect
4. #42176C2semidirect
5. #39724C2semidirect
6. #39596C2semidirect
7. #38920C2semidirect
8. #38915C2semidirect
9. #38911C2semidirect
10. #38903C2semidirect
11. #38051C2semidirect
12. #38032C2semidirect
13. #37641C2semidirect
14. #37622C2semidirect
15. #36579C2semidirect
16. #36545C2semidirect
17. #36405C2semidirect
18. #36404C2semidirect
19. #35834C2semidirect
20. #35280C2semidirect
21. #35280C2semidirect
22. #35189C2semidirect
23. #35179C2semidirect
24. #34976C2semidirect
25. #34952C2semidirect
26. #34188C2semidirect
297. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
#429262
#421762
#397242
#395962
#389202
#389152
#389112
#389032
#380512
#380322
#376412
#376222
#365792
#365452
#364052
#364042
#358342
#352802
#351892
#351792
#349762
#349522
#341882