Finite Group Databasebeta

← #7658966

Subgroups — #7658966

Order 512.

6868 conjugacy classes of subgroups.

The subgroup lattice has 1296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3514C211yesmaximal, characteristic, complemented
3#42966C212yesmaximal, complemented
4#42943C212yesmaximal, complemented
5#42799C214yesmaximal, complemented
6#42484C212yesmaximal, complemented
7#42481C212yesmaximal, complemented
8#42308C214yesmaximal, complemented
9#42169C214yesmaximal, complemented
10#41989C214yesmaximal, complemented
11#41946C214yesmaximal, complemented
12#40529C218yesmaximal, complemented
13#37640C211yesmaximal, characteristic, complemented
14#37606C212yesmaximal, complemented
15#37546C211yesmaximal, characteristic, complemented
16#37546C212yesmaximal, complemented
17#37541C212yesmaximal, complemented
18#37536C211yesmaximal, characteristic, complemented
19#36699C211yesmaximal, characteristic, complemented
20#36684C212yesmaximal, complemented
21#36077C212yesmaximal, complemented
22#36048C212yesmaximal, complemented
23#36004C212yesmaximal, complemented
24#35956C212yesmaximal, complemented
25#35808C214yesmaximal, complemented
26#34193C211yesmaximal, characteristic, complemented
27#3514—216no—
28#3510—216no—
29C2×#559C2212yes—
30C2×#559C2212yes—
31C2×#559C2211yescharacteristic, complemented
32C2×#556C2212yescomplemented
33C2×#556C2211yescharacteristic, complemented
34C2×#556C2212yescomplemented
35C2×#555C2212yes—
36C2×#551C2214yescomplemented
37C2×#551C2214yescomplemented
38C2×#551C2214yescomplemented
39C2×D4×Q8C2211yescharacteristic, complemented
40C2×#548C2212yes—
41C2×#546C2212yes—
42C2×#546C2212yes—
43C2×D42C2211yescharacteristic, complemented
44C2×#542C2212yescomplemented
45C2×#542C2212yescomplemented
46C2×#542C2212yescomplemented
47C2×#538C2214yes—
48C2×#536C2211yescharacteristic
49C2×#535C2211yescharacteristic
50C2×#533C2211yescharacteristic, complemented
51C2×#532C2211yescharacteristic
52C2×#529C2211yescharacteristic
53C2×#529C2212yescomplemented
54C2×#529C2212yescomplemented
55C2×#529C2212yescomplemented
56C22×#124C2212yescomplemented
57C22×#124C2211yescharacteristic, complemented
58C2×#519C2211yescharacteristic, complemented
59C2×#518C2212yescomplemented
60C2×#518C2211yescharacteristic, complemented
61C2×C4×#41C2211yescharacteristic
62#2823C2218yescomplemented
63#2822C2211yescharacteristic, complemented
64#2822C2211yescharacteristic, complemented
65#2821C2212yescomplemented
66#2821C2212yescomplemented
67#2820C2212yescomplemented
68#2820C2212yescomplemented
69#2820C2212yescomplemented
70#2820C2211yescharacteristic, complemented
71#2820C2211yescharacteristic, complemented
72#2819C2212yes—
73#2819C2212yescomplemented
74#2819C2212yescomplemented
75#2817C2212yescomplemented
76#2816C2212yes—
77#2814C2214yescomplemented
78#2814C2214yescomplemented
79#2814C2214yescomplemented
80#2813C2214yescomplemented
81#2813C2214yescomplemented
82#2705C2218yescomplemented
83#2702C2218yescomplemented
84#2701C2218yescomplemented
85#2700C2218yescomplemented
86#2697C2218yescomplemented
87#2683C2218yescomplemented
88#2681C2218yescomplemented
89#2680C2218yescomplemented
90#2679C2218yescomplemented
91#2678C2218yescomplemented
92#2678C2218yescomplemented
93#2670C2218yescomplemented
94#2663C2214yescomplemented
95#2662C2214yescomplemented
96#2662C2218yescomplemented
97#2662C2214yescomplemented
98#2662C2214yescomplemented
99#2661C2214yescomplemented
100#2657C2212yes—
101#2640C2212yescomplemented
102#2638C2214yescomplemented
103#2635C2214yescomplemented
104#2632C2214yescomplemented
105#2631C2214yescomplemented
106#2631C2214yescomplemented
107#2630C2218yescomplemented
108#2626C2214yescomplemented
109#2626C2212yescomplemented
110#2624C2212yescomplemented
111#2624C2212yescomplemented
112#2620C2214yescomplemented
113#2620C2218yescomplemented
114#2620C2214yescomplemented
115#2617C2212yes—
116#2617C2214yescomplemented
117#2617C2214yescomplemented
118#2616C2214yescomplemented
119#2614C2214yescomplemented
120#2613C2214yescomplemented
121#2610C2214yescomplemented
122#2610C2214yescomplemented
123#2604C2214yescomplemented
124#2603C2214yescomplemented
125#2601C2218yescomplemented
126#2599C2214yescomplemented
127#2598C2214yescomplemented
128#2592C2212yescomplemented
129#2592C2214yescomplemented
130#2567C2212yescomplemented
131#2561C2214yescomplemented
132#2560C2218yescomplemented
133#2554C2218yescomplemented
134#2548C2212yescomplemented
135#2548C2214yescomplemented
136#2547C2212yescomplemented
137#2545C2214yescomplemented
138#2544C2214yescomplemented
139#2542C2212yescomplemented
140#2540C2212yes—
141#2540C2214yescomplemented
142#2539C2214yescomplemented
143#2538C2214yescomplemented
144#2534C2218yescomplemented
145#2512C2218yescomplemented
146#2476C2218yescomplemented
147#2474C2218yescomplemented
148#2472C2218yescomplemented
149#2472C2218yescomplemented
150#2461C2218yescomplemented
151#2461C2218yescomplemented
152#2457C2218yescomplemented
153#2452C2214yescomplemented
154#2451C2214yescomplemented
155#2447C2214yescomplemented
156#2445C2214yes—
157#2436C2212yescomplemented
158#2435C2214yescomplemented
159#2433C2214yes—
160#2433C2212yescomplemented
161#2429C2214yescomplemented
162#2428C2214yes—
163#2426C2214yescomplemented
164#2426C2214yescomplemented
165#2424C2218yescomplemented
166#2418C2218yescomplemented
167#2411C2214yescomplemented
168#2411C2218yescomplemented
169#2409C2214yescomplemented
170#2409C2212yescomplemented
171#2408C2214yescomplemented
172#2408C2212yescomplemented
173#2404C2214yescomplemented
174#2399C2212yescomplemented
175#2398C2212yescomplemented
176#2396C2214yescomplemented
177#2396C2214yescomplemented
178#2396C2214yescomplemented
179#2395C2212yescomplemented
180#2395C2212yescomplemented
181#2392C2214yescomplemented
182#2392C2218yescomplemented
183#2392C2214yescomplemented
184#2367C2214yescomplemented
185#2366C2214yescomplemented
186#2363C2214yescomplemented
187#2362C2214yescomplemented
188#2354C2214yescomplemented
189#2354C2212yescomplemented
190Q8×C4⋊C4C2212yescomplemented
191#2347C2214yescomplemented
192#2347C2212yescomplemented
193#2341C2212yes—
194#2319C2214yescomplemented
195#2319C2212yescomplemented
196#2285C2211yescharacteristic, complemented
197#2285C2212yescomplemented
198#2283C2211yescharacteristic, complemented
199#2283C2212yescomplemented
200#2276C2212yescomplemented
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×Q8C2312yes—
205C23×D4C2311yescharacteristic
206C23×D4C2312yes—
207C23×D4C2312yes—
208#559—28no—
209#559—216no—
210#559—216no—
211#556—216no—
212#556—216no—
213#556—28no—
214#555—216no—
215#551—232no—
216#551—232no—
217#551—232no—
218D4×Q8—28no—
219#548—216no—
220#546—216no—
221#546—216no—
222D42—28no—
223#542—216no—
224#542—216no—
225#542—216no—
226#538—232no—
227#536—28no—
228#535—28no—
229#533—28no—
230#532—28no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×#127C2311yescharacteristic
237C2×#127C2312yes—
238C2×#127C2314yes—
239#529—28no—
240#529—216no—
241#529—216no—
242#529—216no—
243C2×#126C2314yes—
244C2×#126C2312yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2311yescharacteristic
251C2×#125C2311yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#124—28no—
254C2×#124—216no—
255C2×#124C2311yescharacteristic
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2312yes—
270C2×#124C2314yes—
271C2×#124C2314yes—
272C2×#124C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2318yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2318yes—
296C2×C22⋊Q8C2318yes—
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2318yes—
308C2×#120C2314yes—
309C2×#120C2314yes—
310C2×#120C2314yes—
311C2×#120C2318yes—
312C2×#120C2314yes—
313C2×#120C2318yes—
314C2×#120C2318yes—
315#519—28no—
316#518—216no—
317#518—28no—
318C4×#41D4116yescomplemented
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2314yes—
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2318yes—
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2312yes—
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2312yes—
350C2×#117C2314yes—
351C2×#117C2314yes—
352C2×#117C2314yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2311yescharacteristic
356C2×#117C2311yescharacteristic
357C2×#117C2314yes—
358C2×#117C2312yes—
359C2×#117C2314yes—
360C2×#117C2311yescharacteristic
361C2×#117C2312yes—
362C22×C22⋊C4C2314yes—
363C22×C22⋊C4C2312yes—
364C22×C22⋊C4C2312yes—
365C22×C22⋊C4C2314yes—
366C22×C22⋊C4C2314yes—
367C22×C22⋊C4C2314yes—
368C22×C42C2311yescharacteristic
369C22×C42C2312yes—
370#400C2314yes—
371#400C2312yes—
372#400C2312yes—
373#400C2312yes—
374#400C2312yes—
375#399C2314yes—
376#399C2312yes—
377#399C2312yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#398C2318yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2318yes—
390#397C2318yes—
391#397C2312yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2318yes—
400#397C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#396C2314yes—
405#396C2314yes—
406#396C2318yes—
407#396C2318yes—
408#396C2318yes—
409#396C2318yes—
410#396C2318yes—
411#396C2318yes—
412#396C2318yes—
413#395C2312yes—
414#395C2312yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2318yes—
421#394C2318yes—
422#394C2312yes—
423#394C2312yes—
424#394C2314yes—
425#394C2314yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2318yes—
441#394C2318yes—
442#394C2318yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2318yes—
452#392C2314yes—
453#392C2314yes—
454#392C2314yes—
455#392C2314yes—
456#392C2314yes—
457#392C2314yes—
458#392C2318yes—
459#392C2318yes—
460#392C2318yes—
461#392C2318yes—
462#391C2314yes—
463#391C2314yes—
464#391C2318yes—
465#391C2314yes—
466#390C2318yes—
467#390C2318yes—
468#390C2314yes—
469#390C2314yes—
470#390C2318yes—
471#390C2318yes—
472#390C2318yes—
473#390C2318yes—
474#390C2314yes—
475#390C2318yes—
476#390C2314yes—
477#390C2314yes—
478#390C2318yes—
479#390C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2318yes—
483#389C2314yes—
484#389C2318yes—
485#388C2318yes—
486#388C2318yes—
487#388C2318yes—
488#388C2318yes—
489#388C2318yes—
490#388C2318yes—
491#388C2318yes—
492#388C2318yes—
493#388C2318yes—
494#388C2318yes—
495#388C2318yes—
496#388C2318yes—
497#388C2318yes—
498#388C2318yes—
499#387C2318yes—
500#387C2318yes—
501#386C2318yes—
502#386C2318yes—
503#386C2318yes—
504#386C2318yes—
505#386C2314yes—
506#386C2318yes—
507#386C2318yes—
508#386C2318yes—
509#386C2318yes—
510#385C2318yes—
511#385C2318yes—
512#385C2318yes—
513#385C2314yes—
514#384C2314yes—
515#384C2314yes—
516#384C2312yes—
517#383C2312yes—
518#383C2314yes—
519#382C2312yes—
520#382C2311yescharacteristic
521#382C2311yescharacteristic
522#381C2312yes—
523#381C2318yes—
524#381C2314yes—
525#380C2312yes—
526#380C2314yes—
527#380C2314yes—
528#380C2312yes—
529#380C2312yes—
530#380C2314yes—
531#380C2318yes—
532#379C2318yes—
533#379C2314yes—
534#379C2318yes—
535C4×C4⋊C4C2318yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2312yes—
543C4×C4⋊C4C2318yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2318yes—
552#376C2314yes—
553#376C2312yes—
554C25C2412yes—
555C25C2414yes—
556C2×#41—28no—
557C2×#41—44no—
558C2×#41—84no—
559C2×#41C2×D418yes—
560C22×Q8—24no—
561C22×Q8—28no—
562C22×Q8—44no—
563C22×Q8—84no—
564C22×Q8C2412yes—
565C22×Q8C2411yescharacteristic
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2411yescharacteristic
570C22×Q8C2412yes—
571C22×Q8C2414yes—
572C22×D4—28no—
573C22×D4—24no—
574C22×D4—28no—
575C22×D4—44no—
576C22×D4—48no—
577C22×D4—84no—
578C22×D4C2412yes—
579C22×D4C2412yes—
580C22×D4C2411yescharacteristic
581C22×D4C2414yes—
582C22×D4C2412yes—
583C22×D4C2412yes—
584C22×D4C2414yes—
585C22×D4C2414yes—
586C22×D4C2412yes—
587C22×D4C2411yescharacteristic
588C22×D4C2412yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2418yes—
592C22×D4C2418yes—
593C22×D4C2418yes—
594C22×D4C2412yes—
595C23×C4C2412yes—
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2411yescharacteristic
607C23×C4C2412yes—
608C4⋊Q8—28no—
609C4⋊Q8—28no—
610C4⋊Q8—24no—
611C4⋊Q8—24no—
612C4⋊Q8—24no—
613#127—28no—
614#127—24no—
615#127—48no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—216no—
620#126—28no—
621#126—216no—
622#126—216no—
623#125—24no—
624#125—24no—
625#125—24no—
626#124—28no—
627#124—28no—
628#124—28no—
629#124—216no—
630#124—216no—
631#124—216no—
632#124—24no—
633#124—28no—
634#124—28no—
635#124—216no—
636#124—28no—
637#124—28no—
638#124—28no—
639#124—216no—
640#124—28no—
641#124—28no—
642#124—48no—
643#124—84no—
644#123—216no—
645#123—28no—
646#123—216no—
647#123—216no—
648#123—216no—
649#123—216no—
650#123—216no—
651#123—216no—
652#123—216no—
653#123—88no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—24no—
659C22⋊Q8—28no—
660C22⋊Q8—28no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—216no—
664C22⋊Q8—216no—
665C22⋊Q8—48no—
666C22⋊Q8—88no—
667C22⋊Q8—88no—
668#121—216no—
669#121—28no—
670#121—28no—
671#121—28no—
672#121—24no—
673#121—28no—
674#121—28no—
675#121—28no—
676#121—216no—
677#121—48no—
678#121—88no—
679#120—216no—
680#120—216no—
681#120—216no—
682#120—84no—
683#120—88no—
684#120—88no—
685#120—88no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×Q8—28no—
689C4×Q8—28no—
690C4×Q8—28no—
691C4×Q8—24no—
692C4×Q8—28no—
693C4×Q8—28no—
694C4×Q8—48no—
695C4×Q8C2×D418yes—
696C4×Q8C2×D418yes—
697C4×D4—28no—
698C4×D4—216no—
699C4×D4—28no—
700C4×D4—216no—
701C4×D4—216no—
702C4×D4—28no—
703C4×D4—28no—
704C4×D4—28no—
705C4×D4—216no—
706C4×D4—28no—
707C4×D4—28no—
708C4×D4—28no—
709C4×D4—24no—
710C4×D4—28no—
711C4×D4—28no—
712C4×D4—88no—
713C4×D4C2×D418yes—
714C4×D4C2×D4116yes—
715C4×D4C2×D418yes—
716C4×D4C2×D4116yes—
717#117—24no—
718#117—24no—
719#117—28no—
720#117—216no—
721#117—28no—
722#117—216no—
723#117—216no—
724#117—216no—
725#117—84no—
726#117—82no—
727#117C2×D418yes—
728#117C2×D4116yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C22⋊C4—216no—
772C2×C22⋊C4—216no—
773C2×C22⋊C4—28no—
774C2×C22⋊C4—28no—
775C2×C22⋊C4—216no—
776C2×C22⋊C4—216no—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2418yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2418yes—
818C2×C22⋊C4C2418yes—
819C2×C22⋊C4C2418yes—
820C2×C22⋊C4C2418yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C42C2×D4116yes—
827C2×C42C2×D418yes—
828C2×C42C2414yes—
829C2×C42C2414yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2412yes—
833C2×C42C2412yes—
834C2×C42C2414yes—
835C2×C42C2418yes—
836C2×C42C2414yes—
837C2×C42C2418yes—
838C2×C42C2412yes—
839C2×C42C2411yescharacteristic
840C2×C42C2412yes—
841C2×C42C2411yescharacteristic
842C2×C42C2412yes—
843C2×C42C2411yescharacteristic
844C2×C42C2411yescharacteristic
845#95C2412yes—
846#95C2412yes—
847#95C2414yes—
848#95C2418yes—
849#95C2414yes—
850#95C2412yes—
851#95C2414yes—
852#95C2414yes—
853#95C2412yes—
854#95C2414yes—
855#95C2414yes—
856#95C2418yes—
857#95C2418yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2418yes—
862#95C2414yes—
863#95C2414yes—
864#95C2418yes—
865#95C2414yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24—24no—
870C24—28no—
871C24—44no—
872C24—48no—
873C24—44no—
874C24—42no—
875C24—44no—
876C24—48no—
877C24—44no—
878C24—42no—
879C24C2512yes—
880C24C2514yes—
881C24C2514yes—
882C24C2511yescharacteristic
883C24C2512yes—
884#41—416no—
885#41—816no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—22no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—28no—
893C2×Q8—24no—
894C2×Q8—28no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—44no—
898C2×Q8—44no—
899C2×Q8—48no—
900C2×Q8—42no—
901C2×Q8—42no—
902C2×Q8—416no—
903C2×Q8—816no—
904C2×Q8C22×D414yes—
905C2×D4—28no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—22no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—28no—
917C2×D4—24no—
918C2×D4—28no—
919C2×D4—28no—
920C2×D4—44no—
921C2×D4—48no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—416no—
926C2×D4—48no—
927C2×D4—44no—
928C2×D4—42no—
929C2×D4—48no—
930C2×D4—48no—
931C2×D4—48no—
932C2×D4—48no—
933C2×D4—42no—
934C2×D4—48no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—44no—
938C2×D4—48no—
939C2×D4—48no—
940C2×D4—48no—
941C2×D4—48no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4—432no—
945C2×D4—816no—
946C2×D4C22×D414yes—
947C2×D4C22×D418yes—
948C22×C4—24no—
949C22×C4—24no—
950C22×C4—28no—
951C22×C4—24no—
952C22×C4—28no—
953C22×C4—28no—
954C22×C4—28no—
955C22×C4—28no—
956C22×C4—28no—
957C22×C4—42no—
958C22×C4—41no—
959C22×C4—42no—
960C22×C4—41no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—42no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—48no—
968C22×C4—48no—
969C22×C4—48no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4C22×D414yes—
973C22×C4C22×D418yes—
974C22×C4C22×D418yes—
975C22×C4C22×D414yes—
976C22×C4C22×D414yes—
977C22×C4C22×D418yes—
978C22×C4C2514yes—
979C22×C4C2514yes—
980C22×C4C2518yes—
981C22×C4C2512yes—
982C22×C4C2514yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2514yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2511yescharacteristic
991C22×C4C2511yescharacteristic
992C22×C4C2512yes—
993C22×C4C2511yescharacteristic
994C22×C4C2512yes—
995C22×C4C2511yescharacteristic
996C22×C4C2512yes—
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—24no—
1002C4⋊C4—24no—
1003C4⋊C4—24no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—24no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—22no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—22no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—24no—
1022C4⋊C4—24no—
1023C4⋊C4—28no—
1024C4⋊C4—42no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—42no—
1028C4⋊C4—44no—
1029C4⋊C4—48no—
1030C4⋊C4—48no—
1031C4⋊C4—48no—
1032C4⋊C4—44no—
1033C4⋊C4—48no—
1034C4⋊C4—44no—
1035C4⋊C4—48no—
1036C4⋊C4—44no—
1037C4⋊C4C22×D414yes—
1038C4⋊C4C22×D414yes—
1039C4⋊C4C22×D418yes—
1040C4⋊C4C22×D418yes—
1041C22⋊C4—24no—
1042C22⋊C4—28no—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—24no—
1048C22⋊C4—28no—
1049C22⋊C4—24no—
1050C22⋊C4—24no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—24no—
1066C22⋊C4—28no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—48no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—48no—
1076C22⋊C4—48no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4—48no—
1081C22⋊C4—44no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—48no—
1086C22⋊C4—48no—
1087C22⋊C4C22×D418yes—
1088C22⋊C4C22×D418yes—
1089C22⋊C4C22×D418yes—
1090C42—28no—
1091C42—28no—
1092C42—28no—
1093C42—24no—
1094C42—24no—
1095C42—24no—
1096C42—28no—
1097C42—48no—
1098C42—44no—
1099C42—48no—
1100C42C22×D414yes—
1101C42C22×D418yes—
1102C42C22×D414yes—
1103C42C22×D418yes—
1104C42C22×D418yes—
1105C42C22×D414yes—
1106C42C22×D414yes—
1107C23—22no—
1108C23—24no—
1109C23—21no—
1110C23—22no—
1111C23—24no—
1112C23—22no—
1113C23—21no—
1114C23—22no—
1115C23—24no—
1116C23—22no—
1117C23—24no—
1118C23—24no—
1119C23—28no—
1120C23—28no—
1121C23—24no—
1122C23—28no—
1123C23—24no—
1124C23—28no—
1125C23—22no—
1126C23—24no—
1127C23—22no—
1128C23—24no—
1129C23—24no—
1130C23—48no—
1131C23—416no—
1132C23—88no—
1133C23—84no—
1134C23—84no—
1135C23—88no—
1136C23—164no—
1137C23—168no—
1138C23—164no—
1139C23—168no—
1140C23C23×D414yes—
1141C23C23×D412yes—
1142C23C2611yescharacteristic
1143Q8—28no—
1144Q8—48no—
1145Q8—44no—
1146Q8—48no—
1147Q8—48no—
1148Q8—84no—
1149Q8—84no—
1150Q8—88no—
1151D4—28no—
1152D4—48no—
1153D4—48no—
1154D4—44no—
1155D4—48no—
1156D4—416no—
1157D4—48no—
1158D4—48no—
1159D4—84no—
1160D4—88no—
1161D4—88no—
1162D4—84no—
1163D4—88no—
1164D4—88no—
1165D4—816no—
1166D4—168no—
1167D4—168no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—28no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—28no—
1192C2×C4—28no—
1193C2×C4—24no—
1194C2×C4—28no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—28no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—28no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—48no—
1211C2×C4—44no—
1212C2×C4—48no—
1213C2×C4—48no—
1214C2×C4—44no—
1215C2×C4—48no—
1216C2×C4—48no—
1217C2×C4—88no—
1218C2×C4—88no—
1219C2×C4—88no—
1220C2×C4—88no—
1221C2×C4—88no—
1222C2×C4C23×D414yes—
1223C2×C4C23×D414yes—
1224C2×C4C23×D412yes—
1225C2×C4C23×D412yes—
1226C2×C4C23×D412yes—
1227C2×C4C23×D414yes—
1228C2×C4C23×D412yes—
1229C2×C4C23×D412yes—
1230C2×C4C23×D412yes—
1231C2×C4#58514yes—
1232C22—24no—
1233C22—22no—
1234C22—24no—
1235C22—22no—
1236C22—22no—
1237C22—24no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—48no—
1243C22—48no—
1244C22—44no—
1245C22—48no—
1246C22—48no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—44no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—44no—
1257C22—168no—
1258C22—1616no—
1259C22C24×D411yescharacteristic
1260C22C2×#58512yes—
1261C22H(7,𝔽2)11yescharacteristic
1262C22H(7,𝔽2)12yes—
1263C222−1+611yescharacteristic
1264C4—22no—
1265C4—22no—
1266C4—24no—
1267C4—22no—
1268C4—24no—
1269C4—22no—
1270C4—22no—
1271C4—24no—
1272C4—44no—
1273C4—48no—
1274C4—44no—
1275C4—44no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—44no—
1284C4#344914yes—
1285C2—44no—
1286C2—42no—
1287C2—84no—
1288C2—84no—
1289C2—82no—
1290C2C2×#344911yescharacteristic
1291C2#6285211yescharacteristic
1292C2#6285311yescharacteristic
1293C2#6306012yes—
1294C2#6306912yes—
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×#3510C2semidirect
2. C2×#3514C2semidirect
3. #42966C2semidirect
4. #42943C2semidirect
5. #42799C2semidirect
6. #42484C2semidirect
7. #42481C2semidirect
8. #42308C2semidirect
9. #42169C2semidirect
10. #41989C2semidirect
11. #41946C2semidirect
12. #40529C2semidirect
13. #37640C2semidirect
14. #37606C2semidirect
15. #37546C2semidirect
16. #37546C2semidirect
17. #37541C2semidirect
18. #37536C2semidirect
19. #36699C2semidirect
20. #36684C2semidirect
21. #36077C2semidirect
22. #36048C2semidirect
23. #36004C2semidirect
24. #35956C2semidirect
25. #35808C2semidirect
26. #34193C2semidirect
31. C2×#559C22semidirect
32. C2×#556C22semidirect
33. C2×#556C22semidirect
34. C2×#556C22semidirect
36. C2×#551C22semidirect
37. C2×#551C22semidirect
38. C2×#551C22semidirect
39. C2×D4×Q8C22semidirect
43. C2×D42C22semidirect
44. C2×#542C22semidirect
45. C2×#542C22semidirect
46. C2×#542C22semidirect
50. C2×#533C22semidirect
53. C2×#529C22semidirect
54. C2×#529C22semidirect
55. C2×#529C22semidirect
56. C22×#124C22semidirect
57. C22×#124C22semidirect
58. C2×#519C22semidirect
59. C2×#518C22semidirect
60. C2×#518C22semidirect
62. #2823C22semidirect
63. #2822C22semidirect
64. #2822C22semidirect
65. #2821C22semidirect
66. #2821C22semidirect
67. #2820C22semidirect
68. #2820C22semidirect
69. #2820C22semidirect
70. #2820C22semidirect
71. #2820C22semidirect
73. #2819C22semidirect
74. #2819C22semidirect
75. #2817C22semidirect
77. #2814C22semidirect
78. #2814C22semidirect
79. #2814C22semidirect
80. #2813C22semidirect
81. #2813C22semidirect
82. #2705C22semidirect
83. #2702C22semidirect
84. #2701C22semidirect
85. #2700C22semidirect
86. #2697C22semidirect
87. #2683C22semidirect
88. #2681C22semidirect
89. #2680C22semidirect
90. #2679C22semidirect
91. #2678C22semidirect
92. #2678C22semidirect
93. #2670C22semidirect
94. #2663C22semidirect
95. #2662C22semidirect
96. #2662C22semidirect
97. #2662C22semidirect
98. #2662C22semidirect
99. #2661C22semidirect
101. #2640C22semidirect
102. #2638C22semidirect
103. #2635C22semidirect
104. #2632C22semidirect
105. #2631C22semidirect
106. #2631C22semidirect
107. #2630C22semidirect
108. #2626C22semidirect
109. #2626C22semidirect
110. #2624C22semidirect
111. #2624C22semidirect
112. #2620C22semidirect
113. #2620C22semidirect
114. #2620C22semidirect
116. #2617C22semidirect
117. #2617C22semidirect
118. #2616C22semidirect
119. #2614C22semidirect
120. #2613C22semidirect
121. #2610C22semidirect
122. #2610C22semidirect
123. #2604C22semidirect
124. #2603C22semidirect
125. #2601C22semidirect
126. #2599C22semidirect
127. #2598C22semidirect
128. #2592C22semidirect
129. #2592C22semidirect
130. #2567C22semidirect
131. #2561C22semidirect
132. #2560C22semidirect
133. #2554C22semidirect
134. #2548C22semidirect
135. #2548C22semidirect
136. #2547C22semidirect
137. #2545C22semidirect
138. #2544C22semidirect
139. #2542C22semidirect
141. #2540C22semidirect
142. #2539C22semidirect
143. #2538C22semidirect
144. #2534C22semidirect
145. #2512C22semidirect
146. #2476C22semidirect
147. #2474C22semidirect
148. #2472C22semidirect
149. #2472C22semidirect
150. #2461C22semidirect
151. #2461C22semidirect
152. #2457C22semidirect
153. #2452C22semidirect
154. #2451C22semidirect
155. #2447C22semidirect
157. #2436C22semidirect
158. #2435C22semidirect
160. #2433C22semidirect
161. #2429C22semidirect
163. #2426C22semidirect
164. #2426C22semidirect
165. #2424C22semidirect
166. #2418C22semidirect
167. #2411C22semidirect
168. #2411C22semidirect
169. #2409C22semidirect
170. #2409C22semidirect
171. #2408C22semidirect
172. #2408C22semidirect
173. #2404C22semidirect
174. #2399C22semidirect
175. #2398C22semidirect
176. #2396C22semidirect
177. #2396C22semidirect
178. #2396C22semidirect
179. #2395C22semidirect
180. #2395C22semidirect
181. #2392C22semidirect
182. #2392C22semidirect
183. #2392C22semidirect
184. #2367C22semidirect
185. #2366C22semidirect
186. #2363C22semidirect
187. #2362C22semidirect
188. #2354C22semidirect
189. #2354C22semidirect
190. Q8×C4⋊C4C22semidirect
191. #2347C22semidirect
192. #2347C22semidirect
194. #2319C22semidirect
195. #2319C22semidirect
196. #2285C22semidirect
197. #2285C22semidirect
198. #2283C22semidirect
199. #2283C22semidirect
200. #2276C22semidirect
318. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35142
#429662
#429432
#427992
#424842
#424812
#423082
#421692
#419892
#419462
#405292
#376402
#376062
#375462
#375412
#375362
#366992
#366842
#360772
#360482
#360042
#359562
#358082
#341932