Finite Group Databasebeta

← #7657508

Subgroups — #7657508

Order 512.

6726 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3520C211yesmaximal, characteristic, complemented
2C2×#3475C211yesmaximal, characteristic, complemented
3#42673C214yesmaximal, complemented
4#42648C212yesmaximal, complemented
5#42647C212yesmaximal, complemented
6#41414C218yesmaximal, complemented
7#41383C214yesmaximal, complemented
8#41382C214yesmaximal, complemented
9#38920C212yesmaximal, complemented
10#38911C212yesmaximal, complemented
11#38048C214yesmaximal, complemented
12#38035C214yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37622C211yesmaximal, characteristic, complemented
15#37445C212yesmaximal, complemented
16#37438C212yesmaximal, complemented
17#36405C212yesmaximal, complemented
18#36404C212yesmaximal, complemented
19#36011C212yesmaximal, complemented
20#35846C212yesmaximal, complemented
21#35773C214yesmaximal, complemented
22#35311C212yesmaximal, complemented
23#35297C211yesmaximal, characteristic, complemented
24#34635C212yesmaximal, complemented
25#34614C211yesmaximal, characteristic, complemented
26#34186C211yesmaximal, characteristic, complemented
27#3520—216no—
28#3475—216no—
29C2×#556C2211yescharacteristic
30C2×#556C2211yescharacteristic
31C2×#555C2211yescharacteristic
32C2×#554C2212yes—
33C2×#554C2211yescharacteristic
34C2×#553C2212yes—
35C2×#552C2212yes—
36C2×#552C2212yes—
37C2×#552C2212yes—
38C2×#551C2214yes—
39C2×#551C2214yes—
40C2×D4×Q8C2211yescharacteristic
41C2×#548C2212yes—
42C2×#547C2211yescharacteristic
43C2×#547C2211yescharacteristic
44C2×#547C2211yescharacteristic
45C2×#546C2212yes—
46C2×#546C2212yes—
47C2×#542C2212yes—
48C2×#539C2214yes—
49C2×#533C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#529C2212yes—
52C2×#529C2211yescharacteristic
53C2×#529C2214yes—
54C2×#525C2212yes—
55C2×#525C2212yes—
56C22×C22⋊Q8C2212yes—
57C2×#520C2212yes—
58C2×C4×#41C2212yes—
59C2×C4×#41C2211yescharacteristic
60C22×C4×D4C2211yescharacteristic
61C22×#117C2212yes—
62#2857C2212yescomplemented
63#2857C2212yescomplemented
64#2855C2214yescomplemented
65#2855C2214yescomplemented
66#2822C2214yescomplemented
67#2817C2214yescomplemented
68#2816C2214yescomplemented
69#2814C2214yes—
70#2812C2218yes—
71#2724C2218yes—
72#2718C2218yescomplemented
73#2718C2218yescomplemented
74#2710C2218yescomplemented
75#2706C2218yescomplemented
76#2701C2218yes—
77#2701C2218yes—
78#2700C2218yescomplemented
79#2699C2218yes—
80#2698C2218yescomplemented
81#2689C2218yescomplemented
82#2687C2218yescomplemented
83#2664C2214yescomplemented
84#2663C2218yes—
85#2663C2214yescomplemented
86#2661C2214yescomplemented
87#2638C2214yescomplemented
88#2637C2212yescomplemented
89#2636C2212yescomplemented
90#2635C2214yescomplemented
91#2630C2214yes—
92#2629C2212yescomplemented
93#2628C2212yescomplemented
94#2625C2212yes—
95#2625C2212yes—
96#2625C2214yes—
97#2625C2211yescharacteristic
98#2625C2212yes—
99#2625C2212yes—
100#2625C2214yescomplemented
101#2624C2211yescharacteristic
102#2624C2212yes—
103#2624C2214yescomplemented
104#2623C2214yescomplemented
105#2623C2214yescomplemented
106#2622C2218yes—
107#2622C2218yes—
108#2621C2214yes—
109#2621C2212yescomplemented
110#2620C2212yescomplemented
111#2616C2211yescharacteristic
112#2616C2212yes—
113#2615C2211yescharacteristic
114#2602C2218yes—
115#2592C2212yescomplemented
116#2591C2214yescomplemented
117#2584C2212yescomplemented
118#2584C2212yescomplemented
119#2583C2214yescomplemented
120#2582C2214yescomplemented
121#2582C2212yescomplemented
122#2581C2212yescomplemented
123#2568C2212yescomplemented
124#2568C2212yescomplemented
125#2562C2212yescomplemented
126#2560C2218yescomplemented
127#2556C2218yescomplemented
128#2550C2214yescomplemented
129#2546C2212yescomplemented
130#2546C2212yescomplemented
131#2542C2214yescomplemented
132#2538C2212yescomplemented
133#2536C2212yescomplemented
134#2519C2218yescomplemented
135#2506C2218yescomplemented
136#2503C2214yescomplemented
137#2502C2214yescomplemented
138#2499C2218yes—
139#2492C2214yescomplemented
140#2489C2214yescomplemented
141#2487C2214yescomplemented
142#2485C2214yes—
143#2485C2214yescomplemented
144#2484C2214yescomplemented
145#2484C2214yescomplemented
146#2483C2218yes—
147#2478C2218yescomplemented
148#2478C2218yescomplemented
149#2474C2218yescomplemented
150#2470C2218yescomplemented
151#2468C2218yescomplemented
152#2466C2218yescomplemented
153#2459C2218yescomplemented
154#2457C2218yescomplemented
155#2447C2214yes—
156#2447C2214yes—
157#2432C2214yes—
158#2432C2214yes—
159#2420C2214yes—
160#2420C2214yes—
161#2415C2214yes—
162#2415C2214yes—
163#2415C2214yescomplemented
164#2415C2214yescomplemented
165#2415C2214yescomplemented
166#2414C2214yescomplemented
167#2409C2214yescomplemented
168#2407C2214yes—
169#2407C2214yes—
170#2407C2214yescomplemented
171#2396C2212yescomplemented
172#2395C2218yes—
173#2395C2214yescomplemented
174#2395C2214yescomplemented
175#2392C2214yes—
176#2392C2212yescomplemented
177#2365C2214yescomplemented
178#2362C2214yescomplemented
179#2360C2214yescomplemented
180#2357C2212yes—
181#2357C2212yes—
182#2357C2214yes—
183#2354C2212yes—
184#2354C2212yes—
185#2354C2214yes—
186#2352C2214yescomplemented
187#2323C2214yescomplemented
188#2317C2214yescomplemented
189#2312C2214yes—
190#2310C2214yescomplemented
191#2309C2212yes—
192C4×C22⋊Q8C2212yescomplemented
193C4×#121C2212yescomplemented
194#2297C2214yescomplemented
195#2296C2214yescomplemented
196#2285C2211yescharacteristic
197#2285C2211yescharacteristic
198#2280C2212yes—
199#2280C2212yes—
200#2274C2212yes—
201C22×#41C2311yescharacteristic
202C22×#41C2312yes—
203C22×#41C2312yes—
204C22×#41C2312yes—
205C23×Q8C2312yes—
206C23×D4C2311yescharacteristic
207C24×C4C2312yes—
208#556—28no—
209#556—28no—
210#555—28no—
211#554—28no—
212#554—216no—
213#553—216no—
214#552—216no—
215#552—216no—
216#552—216no—
217#551—232no—
218#551—232no—
219D4×Q8—28no—
220#548—216no—
221#547—28no—
222#547—28no—
223#547—28no—
224#546—216no—
225#546—216no—
226#542—216no—
227#539—232no—
228#533—28no—
229#533—28no—
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2314yes—
236#529—232no—
237#529—216no—
238#529—28no—
239C2×#126C2314yes—
240C2×#126C2312yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2311yescharacteristic
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×#125C2314yes—
251C2×#124C2311yescharacteristic
252C2×#124C2312yes—
253C2×#124C2314yes—
254C2×#124C2312yes—
255C2×#124C2314yes—
256#525—216no—
257#525—216no—
258C2×#123C2314yes—
259C2×#123C2314yes—
260C2×#123C2312yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×C22⋊Q8—216no—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2311yescharacteristic
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2311yescharacteristic
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#120C2314yes—
299C2×#120C2314yes—
300#520—216no—
301C4×#41—216no—
302C4×#41—28no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×D4D4116yescomplemented
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2311yescharacteristic
327C2×C4×D4C2314yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×#117—216no—
335C2×#117C2314yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2311yescharacteristic
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2314yes—
346C2×#117C2314yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2314yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2311yescharacteristic
358C22×C22⋊C4C2314yes—
359C22×C22⋊C4C2314yes—
360C22×C22⋊C4C2312yes—
361C22×C42C2314yes—
362C22×C42C2312yes—
363C22×C42C2311yescharacteristic
364#400C2314yes—
365#400C2314yes—
366#400C2318yes—
367#400C2314yes—
368#400C2314yes—
369#400C2318yes—
370#400C2318yes—
371#400C2312yes—
372#399C2318yes—
373#399C2312yes—
374#399C2314yes—
375#399C2318yes—
376#398C2318yes—
377#398C2314yes—
378#398C2314yes—
379#398C2318yes—
380#398C2314yes—
381#398C2318yes—
382#398C2318yes—
383#398C2314yes—
384#398C2314yes—
385#398C2318yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#397C2318yes—
390#397C2318yes—
391#397C2318yes—
392#397C2314yes—
393#397C2318yes—
394#397C2318yes—
395#397C2314yes—
396#397C2318yes—
397#397C2318yes—
398#397C2318yes—
399#397C2318yes—
400#397C2312yes—
401#397C2314yes—
402#397C2318yes—
403#397C2318yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2318yes—
409#395C2312yes—
410#395C2314yes—
411#395C2318yes—
412#395C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2318yes—
417#394C2318yes—
418#394C2318yes—
419#394C2318yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2318yes—
424#394C2318yes—
425#394C2318yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#393C2318yes—
430#393C2314yes—
431#393C2312yes—
432#392C2314yes—
433#392C2312yes—
434#392C2318yes—
435#392C2318yes—
436#391C2318yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2318yes—
442#391C2314yes—
443#391C2318yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#390C2318yes—
449#390C2314yes—
450#390C2314yes—
451#390C2318yes—
452#390C2314yes—
453#390C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2318yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2318yes—
464#389C2318yes—
465#389C2318yes—
466#389C2314yes—
467#389C2314yes—
468#389C2318yes—
469#389C2318yes—
470#389C2312yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2314yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2314yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2314yes—
497#385C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2314yes—
507#384C2318yes—
508#384C2312yes—
509#384C2312yes—
510#382C2312yes—
511#382C2314yes—
512#382C2318yes—
513#382C2312yes—
514#381C2314yes—
515#381C2318yes—
516#381C2318yes—
517#381C2318yes—
518#381C2318yes—
519#381C2314yes—
520#380C2314yes—
521#380C2314yes—
522#380C2312yes—
523#380C2312yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2311yescharacteristic
530#380C2312yes—
531#380C2311yescharacteristic
532#380C2312yes—
533#380C2312yes—
534#379C2314yes—
535#379C2314yes—
536C4×C4⋊C4C2318yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2318yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2314yes—
552C4×C22⋊C4C2314yes—
553C4×C22⋊C4C2314yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—24no—
558C2×#41—28no—
559C2×#41—44no—
560C2×#41—44no—
561C2×#41—44no—
562C2×#41—44no—
563C2×#41—44no—
564C2×#41—48no—
565C22×Q8—28no—
566C22×Q8—48no—
567C22×Q8C2412yes—
568C22×Q8C2412yes—
569C22×Q8C2411yescharacteristic
570C22×Q8C2412yes—
571C22×Q8C2411yescharacteristic
572C22×Q8C2412yes—
573C22×Q8C2414yes—
574C22×D4—42no—
575C22×D4—42no—
576C22×D4C2×D418yes—
577C22×D4C2411yescharacteristic
578C22×D4C2411yescharacteristic
579C22×D4C2411yescharacteristic
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2411yescharacteristic
585C22×D4C2414yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2412yes—
589C23×C4—48no—
590C23×C4C2×D4116yes—
591C23×C4C2412yes—
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2412yes—
608C4⋊Q8—28no—
609C4⋊Q8—24no—
610C4⋊Q8—24no—
611C4⋊Q8—24no—
612C4⋊Q8—24no—
613C4⋊Q8—48no—
614#126—216no—
615#126—216no—
616#126—216no—
617#126—216no—
618#126—216no—
619#126—28no—
620#125—216no—
621#125—28no—
622#125—216no—
623#125—24no—
624#125—28no—
625#125—28no—
626#124—28no—
627#124—28no—
628#124—216no—
629#124—216no—
630#124—24no—
631#123—216no—
632#123—216no—
633#123—216no—
634#123—216no—
635#123—28no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—216no—
640C22⋊Q8—24no—
641C22⋊Q8—28no—
642C22⋊Q8—216no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—216no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—28no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—44no—
658C22⋊Q8—48no—
659C22⋊Q8—48no—
660C22⋊Q8—48no—
661#121—216no—
662#121—28no—
663#121—216no—
664#121—28no—
665#121—24no—
666#121—28no—
667#121—28no—
668#121—28no—
669#121—44no—
670#120—216no—
671#120—216no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8—24no—
680C4×Q8—28no—
681C4×D4—28no—
682C4×D4—28no—
683C4×D4—216no—
684C4×D4—28no—
685C4×D4—28no—
686C4×D4—216no—
687C4×D4—216no—
688C4×D4—216no—
689C4×D4—28no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—24no—
693C4×D4—24no—
694C4×D4—24no—
695C4×D4—48no—
696C4×D4C2×D418yes—
697C4×D4C2×D418yes—
698C4×D4C2×D418yes—
699C4×D4C2×D4116yes—
700C4×D4C2×D4116yes—
701C4×D4C2×D418yes—
702#117—24no—
703#117—28no—
704#117—216no—
705#117—216no—
706#117—28no—
707#117—28no—
708#117—28no—
709#117—28no—
710#117—28no—
711#117—216no—
712#117—216no—
713#117—28no—
714#117—28no—
715#117—44no—
716#117—48no—
717#117—48no—
718#117—44no—
719C2×C4⋊C4—28no—
720C2×C4⋊C4—28no—
721C2×C4⋊C4—216no—
722C2×C4⋊C4—28no—
723C2×C4⋊C4—28no—
724C2×C4⋊C4C2×D418yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C22⋊C4—216no—
775C2×C22⋊C4—216no—
776C2×C22⋊C4C2×D4116yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2412yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2418yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2418yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2412yes—
819C2×C42—216no—
820C2×C42—28no—
821C2×C42C2×D418yes—
822C2×C42C2414yes—
823C2×C42C2412yes—
824C2×C42C2414yes—
825C2×C42C2414yes—
826C2×C42C2414yes—
827C2×C42C2414yes—
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2412yes—
832C2×C42C2418yes—
833C2×C42C2418yes—
834C2×C42C2414yes—
835C2×C42C2411yescharacteristic
836C2×C42C2411yescharacteristic
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839#95C2412yes—
840#95C2412yes—
841#95C2414yes—
842#95C2418yes—
843#95C2418yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866C24—44no—
867C24—42no—
868C24—42no—
869C24—44no—
870C24C22×D418yes—
871C24C2512yes—
872C24C2512yes—
873C24C2511yescharacteristic
874C24C2512yes—
875C24C2512yes—
876#41—416no—
877#41—432no—
878#41—432no—
879#41—816no—
880C2×Q8—22no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—22no—
884C2×Q8—24no—
885C2×Q8—24no—
886C2×Q8—28no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—28no—
891C2×Q8—24no—
892C2×Q8—24no—
893C2×Q8—42no—
894C2×Q8—48no—
895C2×Q8—44no—
896C2×Q8—816no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—28no—
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—22no—
908C2×D4—22no—
909C2×D4—24no—
910C2×D4—416no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—44no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—42no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—48no—
927C2×D4C22×D414yes—
928C2×D4C22×D414yes—
929C2×D4C22×D418yes—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—28no—
937C22×C4—28no—
938C22×C4—28no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—24no—
948C22×C4—24no—
949C22×C4—28no—
950C22×C4—432no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—42no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—48no—
964C22×C4—48no—
965C22×C4C22×D418yes—
966C22×C4C22×D414yes—
967C22×C4C22×D414yes—
968C22×C4C22×D418yes—
969C22×C4C22×D414yes—
970C22×C4C22×D418yes—
971C22×C4C22×D418yes—
972C22×C4C22×D418yes—
973C22×C4C2514yes—
974C22×C4C2512yes—
975C22×C4C2514yes—
976C22×C4C2518yes—
977C22×C4C2514yes—
978C22×C4C2512yes—
979C22×C4C2514yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2512yes—
983C22×C4C2514yes—
984C22×C4C2514yes—
985C22×C4C2512yes—
986C22×C4C2511yescharacteristic
987C22×C4C2512yes—
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2512yes—
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—22no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—24no—
1009C4⋊C4—22no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—24no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—24no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—24no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—48no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—48no—
1036C4⋊C4—48no—
1037C4⋊C4—48no—
1038C4⋊C4—48no—
1039C4⋊C4—48no—
1040C4⋊C4C22×D414yes—
1041C4⋊C4C22×D414yes—
1042C4⋊C4C22×D418yes—
1043C22⋊C4—24no—
1044C22⋊C4—24no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—24no—
1057C22⋊C4—28no—
1058C22⋊C4—24no—
1059C22⋊C4—24no—
1060C22⋊C4—24no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—24no—
1064C22⋊C4—48no—
1065C22⋊C4—48no—
1066C22⋊C4—44no—
1067C22⋊C4—48no—
1068C22⋊C4—44no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—48no—
1072C22⋊C4—48no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—48no—
1078C22⋊C4—44no—
1079C22⋊C4—48no—
1080C22⋊C4—48no—
1081C22⋊C4C22×D418yes—
1082C22⋊C4C22×D418yes—
1083C22⋊C4C22×D418yes—
1084C22⋊C4C22×D418yes—
1085C42—24no—
1086C42—28no—
1087C42—28no—
1088C42—28no—
1089C42—24no—
1090C42—24no—
1091C42—28no—
1092C42—28no—
1093C42—24no—
1094C42—28no—
1095C42—44no—
1096C42—48no—
1097C42—48no—
1098C42C22×D414yes—
1099C42C22×D414yes—
1100C42C22×D414yes—
1101C42C22×D414yes—
1102C23—21no—
1103C23—21no—
1104C23—24no—
1105C23—24no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—24no—
1112C23—24no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—24no—
1123C23—24no—
1124C23—22no—
1125C23—22no—
1126C23—48no—
1127C23—48no—
1128C23—48no—
1129C23—88no—
1130C23—88no—
1131C23C23×D412yes—
1132C23C23×D414yes—
1133C23C23×D414yes—
1134C23C2611yescharacteristic
1135Q8—44no—
1136Q8—48no—
1137Q8—48no—
1138Q8—44no—
1139Q8—48no—
1140Q8—84no—
1141Q8—88no—
1142D4—28no—
1143D4—28no—
1144D4—48no—
1145D4—44no—
1146D4—48no—
1147D4—48no—
1148D4—416no—
1149D4—416no—
1150D4—44no—
1151D4—88no—
1152D4—88no—
1153D4—88no—
1154C2×C4—21no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—28no—
1162C2×C4—28no—
1163C2×C4—216no—
1164C2×C4—216no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—28no—
1179C2×C4—24no—
1180C2×C4—28no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—28no—
1187C2×C4—24no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—28no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—48no—
1202C2×C4—48no—
1203C2×C4—48no—
1204C2×C4—44no—
1205C2×C4—416no—
1206C2×C4—416no—
1207C2×C4—48no—
1208C2×C4—48no—
1209C2×C4—48no—
1210C2×C4—84no—
1211C2×C4—88no—
1212C2×C4—88no—
1213C2×C4—88no—
1214C2×C4C23×D414yes—
1215C2×C4C23×D412yes—
1216C2×C4C23×D412yes—
1217C2×C4C23×D412yes—
1218C2×C4C23×D412yes—
1219C2×C4C23×D414yes—
1220C2×C4C23×D412yes—
1221C2×C4C23×D412yes—
1222C2×C4#58512yes—
1223C2×C4#58512yes—
1224C2×C4#58514yes—
1225C22—22no—
1226C22—24no—
1227C22—24no—
1228C22—22no—
1229C22—24no—
1230C22—24no—
1231C22—22no—
1232C22—24no—
1233C22—24no—
1234C22—44no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—44no—
1252C22—816no—
1253C22C24×D411yescharacteristic
1254C22C2×#58512yes—
1255C22C2×#58511yescharacteristic
1256C22C2×#58511yescharacteristic
1257C222−1+612yes—
1258C4—22no—
1259C4—24no—
1260C4—24no—
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—42no—
1265C4—44no—
1266C4—42no—
1267C4—42no—
1268C4—44no—
1269C4—42no—
1270C4—44no—
1271C4—44no—
1272C4—42no—
1273C4—42no—
1274C4—44no—
1275C4—44no—
1276C4—48no—
1277C4#344914yes—
1278C4#348514yes—
1279C2—44no—
1280C2—44no—
1281C2—42no—
1282C2—82no—
1283C2—82no—
1284C2C2×#344911yescharacteristic
1285C2C2×#348511yescharacteristic
1286C2#6285911yescharacteristic
1287C2#6293612yes—
1288C2#6296712yes—
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×#3475C2semidirect
3. #42673C2semidirect
4. #42648C2semidirect
5. #42647C2semidirect
6. #41414C2semidirect
7. #41383C2semidirect
8. #41382C2semidirect
9. #38920C2semidirect
10. #38911C2semidirect
11. #38048C2semidirect
12. #38035C2semidirect
13. #37641C2semidirect
14. #37622C2semidirect
15. #37445C2semidirect
16. #37438C2semidirect
17. #36405C2semidirect
18. #36404C2semidirect
19. #36011C2semidirect
20. #35846C2semidirect
21. #35773C2semidirect
22. #35311C2semidirect
23. #35297C2semidirect
24. #34635C2semidirect
25. #34614C2semidirect
26. #34186C2semidirect
62. #2857C22semidirect
63. #2857C22semidirect
64. #2855C22semidirect
65. #2855C22semidirect
66. #2822C22semidirect
67. #2817C22semidirect
68. #2816C22semidirect
72. #2718C22semidirect
73. #2718C22semidirect
74. #2710C22semidirect
75. #2706C22semidirect
78. #2700C22semidirect
80. #2698C22semidirect
81. #2689C22semidirect
82. #2687C22semidirect
83. #2664C22semidirect
85. #2663C22semidirect
86. #2661C22semidirect
87. #2638C22semidirect
88. #2637C22semidirect
89. #2636C22semidirect
90. #2635C22semidirect
92. #2629C22semidirect
93. #2628C22semidirect
100. #2625C22semidirect
103. #2624C22semidirect
104. #2623C22semidirect
105. #2623C22semidirect
109. #2621C22semidirect
110. #2620C22semidirect
115. #2592C22semidirect
116. #2591C22semidirect
117. #2584C22semidirect
118. #2584C22semidirect
119. #2583C22semidirect
120. #2582C22semidirect
121. #2582C22semidirect
122. #2581C22semidirect
123. #2568C22semidirect
124. #2568C22semidirect
125. #2562C22semidirect
126. #2560C22semidirect
127. #2556C22semidirect
128. #2550C22semidirect
129. #2546C22semidirect
130. #2546C22semidirect
131. #2542C22semidirect
132. #2538C22semidirect
133. #2536C22semidirect
134. #2519C22semidirect
135. #2506C22semidirect
136. #2503C22semidirect
137. #2502C22semidirect
139. #2492C22semidirect
140. #2489C22semidirect
141. #2487C22semidirect
143. #2485C22semidirect
144. #2484C22semidirect
145. #2484C22semidirect
147. #2478C22semidirect
148. #2478C22semidirect
149. #2474C22semidirect
150. #2470C22semidirect
151. #2468C22semidirect
152. #2466C22semidirect
153. #2459C22semidirect
154. #2457C22semidirect
163. #2415C22semidirect
164. #2415C22semidirect
165. #2415C22semidirect
166. #2414C22semidirect
167. #2409C22semidirect
170. #2407C22semidirect
171. #2396C22semidirect
173. #2395C22semidirect
174. #2395C22semidirect
176. #2392C22semidirect
177. #2365C22semidirect
178. #2362C22semidirect
179. #2360C22semidirect
186. #2352C22semidirect
187. #2323C22semidirect
188. #2317C22semidirect
190. #2310C22semidirect
192. C4×C22⋊Q8C22semidirect
193. C4×#121C22semidirect
194. #2297C22semidirect
195. #2296C22semidirect
312. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35202
C2×#34752
#426732
#426482
#426472
#414142
#413832
#413822
#389202
#389112
#380482
#380352
#376412
#376222
#374452
#374382
#364052
#364042
#360112
#358462
#357732
#353112
#352972
#346352
#346142
#341862