Finite Group Databasebeta

← #7732370

Subgroups — #7732370

Order 512.

6918 conjugacy classes of subgroups.

The subgroup lattice has 1269 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic, complemented
2C2×#3559C211yesmaximal, characteristic, complemented
3#51213C214yesmaximal, complemented
4#50899C214yesmaximal, complemented
5#47681C218yesmaximal, complemented
6#43979C218yesmaximal, complemented
7#39618C212yesmaximal, complemented
8#39163C212yesmaximal, complemented
9#38092C212yesmaximal, complemented
10#38082C212yesmaximal, complemented
11#37864C212yesmaximal, complemented
12#37862C212yesmaximal, complemented
13#37745C214yesmaximal, complemented
14#37702C214yesmaximal, complemented
15#37540C211yesmaximal, characteristic, complemented
16#37423C212yesmaximal, complemented
17#37301C212yesmaximal, complemented
18#36362C212yesmaximal, complemented
19#36164C212yesmaximal, complemented
20#35620C212yesmaximal, complemented
21#35534C212yesmaximal, complemented
22#35237C211yesmaximal, characteristic, complemented
23#35180C211yesmaximal, characteristic, complemented
24C2×#2566C211yesmaximal, characteristic, complemented
25#34083C211yesmaximal, characteristic, complemented
26#3559—216no—
27C2×#563C2212yescomplemented
28C2×#562C2212yescomplemented
29#3520—216no—
30C2×#556C2211yescharacteristic
31C2×#554C2212yes—
32C2×#554C2212yescomplemented
33C2×#553C2212yes—
34C2×#553C2212yescomplemented
35C2×#552C2212yes—
36C2×#551C2214yes—
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2212yes—
39C2×#547C2212yes—
40C2×#547C2214yes—
41C2×#547C2211yescharacteristic
42C2×#547C2211yescharacteristic
43C2×#546C2212yes—
44C2×#544C2212yescomplemented
45C2×#542C2212yes—
46C2×#540C2212yescomplemented
47C2×#539C2212yes—
48C2×#539C2214yes—
49C2×#539C2214yescomplemented
50C2×#537C2212yes—
51C2×#533C2211yescharacteristic
52C2×#532C2211yescharacteristic
53C2×#529C2211yescharacteristic
54C22×#125C2211yescharacteristic
55C2×#525C2212yes—
56C22×C22⋊Q8C2212yes—
57C2×#520C2212yes—
58C22×C4×D4C2211yescharacteristic
59#2862C2212yescomplemented
60#2861C2212yes—
61#2856C2212yes—
62#2850C2212yes—
63#2850C2212yes—
64#2850C2212yescomplemented
65#2847C2214yes—
66#2822C2214yescomplemented
67#2728C2218yescomplemented
68#2723C2218yescomplemented
69#2721C2218yescomplemented
70#2716C2218yescomplemented
71#2706C2218yescomplemented
72#2705C2218yescomplemented
73#2703C2218yes—
74#2702C2218yescomplemented
75#2700C2218yescomplemented
76#2696C2218yes—
77#2693C2218yescomplemented
78#2692C2218yescomplemented
79#2692C2218yescomplemented
80#2690C2218yescomplemented
81#2688C2218yescomplemented
82#2687C2218yescomplemented
83#2681C2218yescomplemented
84#2680C2218yescomplemented
85#2676C2218yescomplemented
86#2671C2218yescomplemented
87#2660C2212yescomplemented
88#2660C2212yescomplemented
89#2642C2212yescomplemented
90#2640C2212yes—
91#2639C2214yes—
92#2634C2214yescomplemented
93#2631C2214yes—
94#2627C2214yes—
95#2620C2212yescomplemented
96#2619C2212yes—
97#2592C2214yescomplemented
98#2568C2212yescomplemented
99#2568C2212yescomplemented
100#2566C2212yes—
101#2566C2214yes—
102#2566C2212yes—
103#2566C2212yes—
104#2566C2214yes—
105#2566C2212yes—
106#2566C2212yes—
107#2565C2212yescomplemented
108#2565C2212yescomplemented
109#2565C2212yescomplemented
110#2563C2211yescharacteristic
111#2563C2212yes—
112#2563C2211yescharacteristic
113#2563C2212yescomplemented
114#2563C2212yescomplemented
115#2562C2214yescomplemented
116#2554C2218yes—
117#2548C2212yescomplemented
118#2547C2212yescomplemented
119#2544C2212yes—
120#2544C2212yes—
121#2542C2212yescomplemented
122#2541C2211yescharacteristic
123#2541C2211yescharacteristic
124#2535C2214yes—
125#2504C2212yes—
126#2504C2212yes—
127#2504C2212yescomplemented
128#2503C2212yes—
129#2503C2212yescomplemented
130#2502C2212yes—
131#2501C2212yescomplemented
132#2500C2212yes—
133#2499C2212yescomplemented
134#2489C2218yescomplemented
135#2488C2218yes—
136#2488C2218yescomplemented
137#2484C2214yes—
138#2481C2218yescomplemented
139#2481C2218yescomplemented
140#2477C2218yescomplemented
141#2471C2218yescomplemented
142#2464C2218yes—
143#2464C2218yescomplemented
144#2457C2218yescomplemented
145#2456C2218yescomplemented
146#2450C2218yescomplemented
147#2450C2218yescomplemented
148#2449C2218yes—
149#2443C2218yes—
150#2443C2218yescomplemented
151#2442C2218yescomplemented
152#2439C2218yescomplemented
153#2433C2212yes—
154#2431C2212yes—
155#2431C2212yes—
156#2430C2218yescomplemented
157#2425C2218yescomplemented
158#2424C2218yes—
159#2417C2218yescomplemented
160#2412C2218yes—
161#2409C2218yescomplemented
162#2404C2218yes—
163#2404C2214yes—
164C2×#396C2214yes—
165#2358C2218yes—
166#2339C2218yes—
167#2337C2212yescomplemented
168#2336C2212yescomplemented
169#2334C2214yescomplemented
170#2329C2212yes—
171#2328C2212yes—
172#2328C2212yes—
173#2328C2212yes—
174#2326C2212yescomplemented
175#2325C2212yes—
176#2322C2214yes—
177#2317C2212yescomplemented
178#2311C2212yes—
179#2311C2214yes—
180C4×#127C2212yes—
181C4×#124C2212yescomplemented
182#2298C2212yescomplemented
183#2297C2212yes—
184#2296C2212yescomplemented
185#2295C2212yescomplemented
186C2×#390C2211yescharacteristic
187C2×#390C2211yescharacteristic
188#2290C2212yes—
189#2290C2212yescomplemented
190C2×#385C2214yes—
191C2×#384C2211yescharacteristic
192#2283C2211yescharacteristic
193C2×#382C2211yescharacteristic
194C2×#382C2212yescomplemented
195C42×D4C2212yes—
196C2×C4×C4⋊C4C2211yescharacteristic
197C22×#41C2312yes—
198C22×#41C2312yes—
199C22×#41C2314yes—
200C22×#41C2312yes—
201C23×Q8C2312yes—
202C23×D4C2311yescharacteristic
203C24×C4C2312yes—
204#563—216no—
205#562—216no—
206#556—28no—
207#554—216no—
208#554—216no—
209#553—216no—
210#553—216no—
211#552—216no—
212#551—232no—
213D4×Q8—28no—
214#548—216no—
215#547—232no—
216#547—28no—
217#547—28no—
218#547—216no—
219#546—216no—
220#544—216no—
221#542—216no—
222#540—216no—
223#539—232no—
224#539—232no—
225#539—216no—
226#537—216no—
227#533—28no—
228#532—28no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2314yes—
235C2×#127C2312yes—
236C2×#127C2311yescharacteristic
237C2×#127C2312yes—
238#529D4116yescomplemented
239C2×#126C2314yes—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2312yes—
244C2×#125—28no—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2314yes—
253C2×#125C2311yescharacteristic
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2311yescharacteristic
260#525—216no—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2318yes—
272C2×#123C2312yes—
273C2×C22⋊Q8—216no—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2318yes—
291C2×C22⋊Q8C2311yescharacteristic
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2318yes—
306C2×#121C2311yescharacteristic
307C2×#120C2314yes—
308C2×#120C2318yes—
309#520—216no—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×D4—28no—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2318yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2314yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2314yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2314yes—
353C22×C22⋊C4C2314yes—
354C22×C22⋊C4C2312yes—
355C22×C22⋊C4C2314yes—
356C22×C22⋊C4C2314yes—
357C22×C42C2311yescharacteristic
358C22×C42C2311yescharacteristic
359C22×C42C2312yes—
360C22×C42C2311yescharacteristic
361#400C2318yes—
362#400C2318yes—
363#400C2318yes—
364#400C2318yes—
365#400C2318yes—
366#400C2318yes—
367#399C2318yes—
368#399C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2318yes—
372#398C2318yes—
373#398C2318yes—
374#398C2318yes—
375#397C2318yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#397C2318yes—
380#397C2318yes—
381#396C2318yes—
382#396C2318yes—
383#396C2318yes—
384#396C2318yes—
385#396C2318yes—
386#396C2318yes—
387#395C2318yes—
388#395C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#394C2318yes—
395#393C2314yes—
396#393C2314yes—
397#393C2318yes—
398#393C2318yes—
399#393C2318yes—
400#393C2318yes—
401#392C2318yes—
402#392C2314yes—
403#392C2314yes—
404#392C2318yes—
405#392C2318yes—
406#392C2318yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2318yes—
413#391C2312yes—
414#391C2318yes—
415#391C2314yes—
416#391C2318yes—
417#391C2318yes—
418#390C2312yes—
419#390C2312yes—
420#390C2318yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2314yes—
429#390C2314yes—
430#390C2318yes—
431#390C2312yes—
432#390C2318yes—
433#389C2318yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#388C2318yes—
438#388C2318yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2318yes—
443#388C2314yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2318yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#386C2314yes—
463#386C2314yes—
464#386C2318yes—
465#386C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2318yes—
470#386C2318yes—
471#386C2318yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#386C2318yes—
477#386C2318yes—
478#386C2318yes—
479#385C2318yes—
480#385C2318yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2314yes—
486#385C2314yes—
487#385C2314yes—
488#385C2314yes—
489#385C2318yes—
490#385C2318yes—
491#384C2312yes—
492#384C2312yes—
493#384C2312yes—
494#384C2312yes—
495#384C2314yes—
496#383C2312yes—
497#382C2312yes—
498#382C2312yes—
499#382C2312yes—
500#382C2312yes—
501#382C2312yes—
502#382C2312yes—
503#382C2312yes—
504#382C2312yes—
505#382C2314yes—
506#382C2312yes—
507#382C2318yes—
508#381C2312yes—
509#381C2318yes—
510#381C2318yes—
511#380C2318yes—
512#380C2318yes—
513#380C2314yes—
514#380C2314yes—
515#380C2318yes—
516#380C2318yes—
517#380C2318yes—
518#380C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2311yescharacteristic
521C4×C4⋊C4C2311yescharacteristic
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2312yes—
525C4×C4⋊C4C2312yes—
526C4×C4⋊C4C2312yes—
527C4×C4⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2314yes—
530C4×C22⋊C4C2318yes—
531C4×C22⋊C4C2318yes—
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2312yes—
535#376C2312yes—
536#376C2312yes—
537C2×#95C2312yes—
538C2×#95C2314yes—
539C2×#95C2318yes—
540C43C2312yes—
541C25C2412yes—
542C2×#41—28no—
543C2×#41—216no—
544C2×#41—28no—
545C2×#41—28no—
546C2×#41—28no—
547C2×#41—48no—
548C2×#41—416no—
549C2×#41—44no—
550C2×#41—84no—
551C22×Q8—28no—
552C22×Q8—84no—
553C22×Q8C2412yes—
554C22×Q8C2412yes—
555C22×Q8C2414yes—
556C22×Q8C2414yes—
557C22×Q8C2412yes—
558C22×Q8C2411yescharacteristic
559C22×D4—24no—
560C22×D4—24no—
561C22×D4—42no—
562C22×D4C2412yes—
563C22×D4C2411yescharacteristic
564C22×D4C2414yes—
565C22×D4C2414yes—
566C22×D4C2412yes—
567C22×D4C2412yes—
568C22×D4C2411yescharacteristic
569C22×D4C2418yes—
570C22×D4C2414yes—
571C22×D4C2412yes—
572C22×D4C2414yes—
573C22×D4C2414yes—
574C22×D4C2412yes—
575C22×D4C2418yes—
576C22×D4C2411yescharacteristic
577C23×C4—28no—
578C23×C4—84no—
579C23×C4C2412yes—
580C23×C4C2414yes—
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2414yes—
589C23×C4C2412yes—
590C23×C4C2414yes—
591C23×C4C2414yes—
592C23×C4C2414yes—
593C23×C4C2412yes—
594C23×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2414yes—
599C23×C4C2411yescharacteristic
600C4⋊Q8—216no—
601C4⋊Q8—24no—
602C4⋊Q8—24no—
603C4⋊Q8—24no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606#127—28no—
607#127—24no—
608#127—44no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—216no—
613#126C2×D4116yes—
614#125—216no—
615#125—216no—
616#125—28no—
617#125—28no—
618#125—28no—
619#125—28no—
620#125—28no—
621#125—28no—
622#125C2×D418yes—
623#124—216no—
624#124—28no—
625#124—28no—
626#124—44no—
627#124—44no—
628#124C2×D418yes—
629#123—216no—
630#123—216no—
631#123—216no—
632#123—216no—
633#123—216no—
634#123—216no—
635#123—216no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—88no—
640#123C2×D4116yes—
641C22⋊Q8—28no—
642C22⋊Q8—216no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—216no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—88no—
658C22⋊Q8C2×D418yes—
659#121—28no—
660#121—216no—
661#121—216no—
662#121—28no—
663#121—28no—
664#121—28no—
665#121—28no—
666#121—28no—
667#121—216no—
668#121—216no—
669#121—216no—
670#121—88no—
671#121—84no—
672#121—84no—
673#121C2×D418yes—
674#120—216no—
675#120—416no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8C2×D418yes—
680C4×D4—216no—
681C4×D4—216no—
682C4×D4—216no—
683C4×D4—216no—
684C4×D4—216no—
685C4×D4—24no—
686C4×D4—28no—
687C4×D4—24no—
688C4×D4—24no—
689C4×D4—24no—
690C4×D4—28no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4—28no—
695C4×D4—28no—
696C4×D4—48no—
697C4×D4—88no—
698C4×D4C2×D4116yes—
699C4×D4C2×D418yes—
700#117—28no—
701#117—28no—
702#117—216no—
703#117—28no—
704#117—44no—
705#117C2×D4116yes—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—28no—
709C2×C4⋊C4—24no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—24no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—216no—
714C2×C4⋊C4—28no—
715C2×C4⋊C4—216no—
716C2×C4⋊C4—44no—
717C2×C4⋊C4—84no—
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2418yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2411yescharacteristic
761C2×C4⋊C4C2412yes—
762C2×C22⋊C4—28no—
763C2×C22⋊C4—216no—
764C2×C22⋊C4—48no—
765C2×C22⋊C4—84no—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C42—42no—
805C2×C42—44no—
806C2×C42—42no—
807C2×C42C2×D418yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2412yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2411yescharacteristic
821C2×C42C2412yes—
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825#95C2418yes—
826#95C2414yes—
827#95C2414yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2418yes—
840#95C2418yes—
841#95C2414yes—
842#95C2418yes—
843#95C2412yes—
844#95C2412yes—
845#95C2414yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852C24—24no—
853C24—24no—
854C24—28no—
855C24—44no—
856C24—42no—
857C24C2512yes—
858C24C2514yes—
859C24C2512yes—
860C24C2512yes—
861C24C2511yescharacteristic
862#41—432no—
863#41—816no—
864#41—832no—
865#41—816no—
866C2×Q8—24no—
867C2×Q8—24no—
868C2×Q8—28no—
869C2×Q8—28no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—24no—
873C2×Q8—42no—
874C2×Q8—44no—
875C2×Q8—48no—
876C2×Q8—48no—
877C2×Q8—44no—
878C2×Q8—816no—
879C2×Q8C22×D414yes—
880C2×D4—28no—
881C2×D4—28no—
882C2×D4—28no—
883C2×D4—24no—
884C2×D4—28no—
885C2×D4—216no—
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—216no—
890C2×D4—22no—
891C2×D4—24no—
892C2×D4—24no—
893C2×D4—22no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—24no—
900C2×D4—22no—
901C2×D4—416no—
902C2×D4—42no—
903C2×D4—44no—
904C2×D4—42no—
905C2×D4—48no—
906C2×D4—48no—
907C2×D4—44no—
908C2×D4—48no—
909C2×D4—48no—
910C2×D4—44no—
911C2×D4—48no—
912C2×D4—48no—
913C2×D4—48no—
914C2×D4—48no—
915C2×D4C22×D418yes—
916C2×D4C22×D414yes—
917C2×D42−1+414yes—
918C22×C4—24no—
919C22×C4—22no—
920C22×C4—24no—
921C22×C4—22no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—28no—
925C22×C4—24no—
926C22×C4—28no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—28no—
930C22×C4—28no—
931C22×C4—24no—
932C22×C4—28no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—24no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—28no—
940C22×C4—24no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—42no—
948C22×C4—44no—
949C22×C4—42no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—48no—
954C22×C4—48no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—48no—
959C22×C4—48no—
960C22×C4—48no—
961C22×C4—48no—
962C22×C4—816no—
963C22×C4C22×D414yes—
964C22×C4C22×D414yes—
965C22×C4C22×D418yes—
966C22×C4C22×D414yes—
967C22×C4C2514yes—
968C22×C4C2514yes—
969C22×C4C2514yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2514yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2512yes—
977C22×C4C2514yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2512yes—
984C22×C4C2511yescharacteristic
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C4⋊C4—22no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—48no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—48no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—48no—
1024C4⋊C4—44no—
1025C4⋊C4C22×D418yes—
1026C4⋊C4C22×D414yes—
1027C4⋊C4C22×D418yes—
1028C4⋊C4C22×D418yes—
1029C4⋊C4C22×D414yes—
1030C4⋊C4C22×D418yes—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—48no—
1050C22⋊C4—48no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—44no—
1062C22⋊C4—48no—
1063C22⋊C4—48no—
1064C22⋊C4C22×D418yes—
1065C22⋊C4C22×D418yes—
1066C22⋊C4C22×D418yes—
1067C22⋊C4C22×D418yes—
1068C22⋊C4C22×D418yes—
1069C42—28no—
1070C42—28no—
1071C42—28no—
1072C42—24no—
1073C42—24no—
1074C42—24no—
1075C42—24no—
1076C42—42no—
1077C42—42no—
1078C42—44no—
1079C42—44no—
1080C42—44no—
1081C42C22×D414yes—
1082C42C22×D414yes—
1083C42C22×D414yes—
1084C42C22×D414yes—
1085C42C22×D418yes—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—24no—
1092C23—22no—
1093C23—24no—
1094C23—22no—
1095C23—24no—
1096C23—24no—
1097C23—22no—
1098C23—24no—
1099C23—24no—
1100C23—22no—
1101C23—24no—
1102C23—24no—
1103C23—28no—
1104C23—22no—
1105C23—28no—
1106C23—24no—
1107C23—48no—
1108C23—416no—
1109C23—48no—
1110C23—84no—
1111C23—88no—
1112C23C23×D414yes—
1113C23C23×D412yes—
1114C23C2×2−1+414yes—
1115C23#58514yes—
1116C23C2611yescharacteristic
1117Q8—44no—
1118Q8—48no—
1119Q8—48no—
1120Q8—88no—
1121Q8—84no—
1122Q8—88no—
1123D4—216no—
1124D4—28no—
1125D4—44no—
1126D4—48no—
1127D4—416no—
1128D4—416no—
1129D4—48no—
1130D4—44no—
1131D4—84no—
1132D4—84no—
1133D4—88no—
1134D4—816no—
1135D4—88no—
1136D4—88no—
1137D4—168no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—28no—
1149C2×C4—28no—
1150C2×C4—216no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—28no—
1169C2×C4—28no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—28no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—28no—
1178C2×C4—44no—
1179C2×C4—416no—
1180C2×C4—48no—
1181C2×C4—48no—
1182C2×C4—48no—
1183C2×C4—48no—
1184C2×C4—88no—
1185C2×C4—84no—
1186C2×C4—84no—
1187C2×C4—88no—
1188C2×C4—88no—
1189C2×C4—88no—
1190C2×C4—84no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—88no—
1194C2×C4—88no—
1195C2×C4—88no—
1196C2×C4C23×D412yes—
1197C2×C4C23×D414yes—
1198C2×C4C23×D414yes—
1199C2×C4C23×D412yes—
1200C2×C4C23×D412yes—
1201C2×C4C23×D412yes—
1202C2×C4C23×D412yes—
1203C2×C4C23×D414yes—
1204C2×C4C23×D412yes—
1205C2×C4C2×2−1+412yes—
1206C2×C4#58512yes—
1207C22—22no—
1208C22—22no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—28no—
1216C22—42no—
1217C22—42no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—44no—
1228C22—48no—
1229C22—48no—
1230C22—44no—
1231C22—816no—
1232C22#350014yes—
1233C22C24×D411yescharacteristic
1234C22C22×2−1+411yescharacteristic
1235C22C2×#58511yescharacteristic
1236C22C2×#58512yes—
1237C22H(7,𝔽2)12yes—
1238C4—24no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—24no—
1243C4—22no—
1244C4—22no—
1245C4—24no—
1246C4—44no—
1247C4—44no—
1248C4—44no—
1249C4—42no—
1250C4—42no—
1251C4—44no—
1252C4—44no—
1253C4—44no—
1254C4—44no—
1255C4—44no—
1256C4—44no—
1257C4#348914yes—
1258C2—24no—
1259C2—44no—
1260C2—44no—
1261C2—84no—
1262C2—82no—
1263C2C2×#348911yescharacteristic
1264C2C2×#350011yescharacteristic
1265C2#6285211yescharacteristic
1266C2#6290812yes—
1267C2#6294812yes—
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×#3520C2semidirect
2. C2×#3559C2semidirect
3. #51213C2semidirect
4. #50899C2semidirect
5. #47681C2semidirect
6. #43979C2semidirect
7. #39618C2semidirect
8. #39163C2semidirect
9. #38092C2semidirect
10. #38082C2semidirect
11. #37864C2semidirect
12. #37862C2semidirect
13. #37745C2semidirect
14. #37702C2semidirect
15. #37540C2semidirect
16. #37423C2semidirect
17. #37301C2semidirect
18. #36362C2semidirect
19. #36164C2semidirect
20. #35620C2semidirect
21. #35534C2semidirect
22. #35237C2semidirect
23. #35180C2semidirect
24. C2×#2566C2semidirect
25. #34083C2semidirect
27. C2×#563C22semidirect
28. C2×#562C22semidirect
32. C2×#554C22semidirect
34. C2×#553C22semidirect
44. C2×#544C22semidirect
46. C2×#540C22semidirect
49. C2×#539C22semidirect
59. #2862C22semidirect
64. #2850C22semidirect
66. #2822C22semidirect
67. #2728C22semidirect
68. #2723C22semidirect
69. #2721C22semidirect
70. #2716C22semidirect
71. #2706C22semidirect
72. #2705C22semidirect
74. #2702C22semidirect
75. #2700C22semidirect
77. #2693C22semidirect
78. #2692C22semidirect
79. #2692C22semidirect
80. #2690C22semidirect
81. #2688C22semidirect
82. #2687C22semidirect
83. #2681C22semidirect
84. #2680C22semidirect
85. #2676C22semidirect
86. #2671C22semidirect
87. #2660C22semidirect
88. #2660C22semidirect
89. #2642C22semidirect
92. #2634C22semidirect
95. #2620C22semidirect
97. #2592C22semidirect
98. #2568C22semidirect
99. #2568C22semidirect
107. #2565C22semidirect
108. #2565C22semidirect
109. #2565C22semidirect
113. #2563C22semidirect
114. #2563C22semidirect
115. #2562C22semidirect
117. #2548C22semidirect
118. #2547C22semidirect
121. #2542C22semidirect
127. #2504C22semidirect
129. #2503C22semidirect
131. #2501C22semidirect
133. #2499C22semidirect
134. #2489C22semidirect
136. #2488C22semidirect
138. #2481C22semidirect
139. #2481C22semidirect
140. #2477C22semidirect
141. #2471C22semidirect
143. #2464C22semidirect
144. #2457C22semidirect
145. #2456C22semidirect
146. #2450C22semidirect
147. #2450C22semidirect
150. #2443C22semidirect
151. #2442C22semidirect
152. #2439C22semidirect
156. #2430C22semidirect
157. #2425C22semidirect
159. #2417C22semidirect
161. #2409C22semidirect
167. #2337C22semidirect
168. #2336C22semidirect
169. #2334C22semidirect
174. #2326C22semidirect
177. #2317C22semidirect
181. C4×#124C22semidirect
182. #2298C22semidirect
184. #2296C22semidirect
185. #2295C22semidirect
189. #2290C22semidirect
194. C2×#382C22semidirect
238. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#35592
#512132
#508992
#476812
#439792
#396182
#391632
#380922
#380822
#378642
#378622
#377452
#377022
#375402
#374232
#373012
#363622
#361642
#356202
#355342
#352372
#351802
C2×#25662
#340832