Finite Group Databasebeta

← #7086756

Subgroups — #7086756

Order 512.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59557C211yesmaximal, characteristic, complemented
2#39405C211yesmaximal, characteristic
3#32257C211yesmaximal, characteristic, complemented
4#32180C211yesmaximal, characteristic, complemented
5#32164C211yesmaximal, characteristic, complemented
6#32122C211yesmaximal, characteristic, complemented
7#31806C211yesmaximal, characteristic, complemented
8#31100C211yesmaximal, characteristic, complemented
9#30547C211yesmaximal, characteristic, complemented
10#30547C211yesmaximal, characteristic, complemented
11#29561C211yesmaximal, characteristic, complemented
12#29356C211yesmaximal, characteristic, complemented
13#29064C211yesmaximal, characteristic, complemented
14#28995C211yesmaximal, characteristic, complemented
15#28026C211yesmaximal, characteristic, complemented
16#27775C211yesmaximal, characteristic, complemented
17#27541C211yesmaximal, characteristic, complemented
18#27354C211yesmaximal, characteristic, complemented
19#27273C211yesmaximal, characteristic, complemented
20#26998C211yesmaximal, characteristic, complemented
21#26912C211yesmaximal, characteristic, complemented
22#26832C211yesmaximal, characteristic, complemented
23#26716C211yesmaximal, characteristic, complemented
24#26647C211yesmaximal, characteristic, complemented
25#25272C211yesmaximal, characteristic, complemented
26#24492C211yesmaximal, characteristic, complemented
27#23684C211yesmaximal, characteristic, complemented
28#23290C211yesmaximal, characteristic, complemented
29#23231C211yesmaximal, characteristic, complemented
30#22864C211yesmaximal, characteristic, complemented
31#22226C211yesmaximal, characteristic, complemented
32C2×#538—21no—
33C2×#490C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#474C2211yescharacteristic, complemented
38C2×#450C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic, complemented
41C2×#418C2211yescharacteristic
42#2858C2211yescharacteristic
43#2793—21no—
44#2762—21no—
45#2714—21no—
46#2678—21no—
47#2676—21no—
48#2670—21no—
49#2631—21no—
50#2594—21no—
51#2552C2211yescharacteristic, complemented
52#2541C2211yescharacteristic
53#2541C2211yescharacteristic
54#2533—21no—
55#2532—21no—
56#2524—21no—
57#2514C2211yescharacteristic, complemented
58#2512C2211yescharacteristic
59#2511C2211yescharacteristic, complemented
60#2497C2211yescharacteristic
61#2491C2211yescharacteristic
62#2489C2211yescharacteristic
63#2489C2211yescharacteristic
64#2469—21no—
65#2456—21no—
66#2452C2211yescharacteristic
67#2451C2211yescharacteristic, complemented
68#2445C2211yescharacteristic
69#2439C2211yescharacteristic
70#2433C2211yescharacteristic
71#2433C2211yescharacteristic
72#2428C2211yescharacteristic
73#2424—21no—
74#2422C2211yescharacteristic
75#2370C2211yescharacteristic, complemented
76#2366C2211yescharacteristic
77#2365C2211yescharacteristic, complemented
78#2362C2211yescharacteristic
79#2355—21no—
80#2347C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82C4×#127C2211yescharacteristic
83C4×#125C2211yescharacteristic, complemented
84C4×#126C2211yescharacteristic
85#2295C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2088C2211yescharacteristic, complemented
88#2083C2211yescharacteristic, complemented
89#2076C2211yescharacteristic
90#2076C2211yescharacteristic
91#2073C2211yescharacteristic
92#2073C2211yescharacteristic, complemented
93#2072C2211yescharacteristic, complemented
94#2071C2211yescharacteristic
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2057C2211yescharacteristic, complemented
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic, complemented
105#2055C2211yescharacteristic, complemented
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic, complemented
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic, complemented
116#2025C2211yescharacteristic, complemented
117#2024C2211yescharacteristic, complemented
118#2023C2211yescharacteristic
119#2014C2211yescharacteristic
120#2014C2211yescharacteristic
121#2014C2211yescharacteristic
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic, complemented
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1988C2211yescharacteristic, complemented
129#1988C2211yescharacteristic, complemented
130#1982C2211yescharacteristic
131#1982C2211yescharacteristic
132#1982C2211yescharacteristic
133#1982C2211yescharacteristic
134#1982C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1961C2211yescharacteristic
140#1957C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1939C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1936C2211yescharacteristic, complemented
149#1936C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic, complemented
161#1925C2211yescharacteristic, complemented
162#1925C2211yescharacteristic, complemented
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1921C2211yescharacteristic, complemented
167#1918C2211yescharacteristic, complemented
168#1918C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1895C2211yescharacteristic
173#1895C2211yescharacteristic
174#1894C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1875C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1864C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1854C2211yescharacteristic
187#1851C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1770C2211yescharacteristic, complemented
195#1767C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1745C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209#538—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126—21no—
218C2×#126D411yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C22⋊C4—21no—
250#490—24no—
251#490—24no—
252#486—42no—
253#482—42no—
254#474—42no—
255#450—24no—
256#440—42no—
257#440—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271#418—42no—
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#395—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#393—21no—
339#393—21no—
340#393—21no—
341#392—21no—
342#392—21no—
343#392—21no—
344#392—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#391—21no—
351#391—21no—
352#391—21no—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388D411yescharacteristic
394#388D411yescharacteristic
395#388D411yescharacteristic
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387D411yescharacteristic
412#387D411yescharacteristic
413#387D411yescharacteristic
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#385—21no—
421#385—21no—
422#384—21no—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#383—21no—
426#383—21no—
427#383D411yescharacteristic
428#382—21no—
429#382—21no—
430#382C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#379—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454#376—21no—
455C43C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2411yescharacteristic
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C4⋊Q8—22no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#127—22no—
548#127—22no—
549#127—41no—
550#127—41no—
551#127—41no—
552#127—41no—
553#127—41no—
554#127—41no—
555#127—41no—
556#127—41no—
557#126—24no—
558#126—44no—
559#125—22no—
560#125—22no—
561#125—41no—
562#125—41no—
563#124—44no—
564#124—44no—
565#124—82no—
566#123—44no—
567#123—44no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570C22⋊Q8—44no—
571#121—44no—
572#121—44no—
573#121—44no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—82no—
579#121—82no—
580#120—44no—
581#120—44no—
582#120—82no—
583#120—82no—
584C4×Q8—22no—
585C4×Q8—41no—
586C4×Q8—44no—
587C4×D4—44no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—44no—
597C4×D4—82no—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—44no—
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#107—22no—
696#107—22no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102#4114yes—
740C22⋊C8—22no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743#97—22no—
744#97—22no—
745#97—41no—
746#97—41no—
747#97—41no—
748C4×C8—41no—
749C4×C8—41no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—42no—
812C2×Q8—42no—
813C2×Q8—42no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—81no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—44no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4C2×#4112yes—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C2511yescharacteristic
928SD16—44no—
929SD16—44no—
930SD16—82no—
931SD16—82no—
932M16—82no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8C2×#4112yes—
957C4⋊C4—22no—
958C4⋊C4—22no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4AGL(1,ℤ/8)14yes—
1004C4⋊C4C2×#4112yes—
1005C4⋊C4H(5,𝔽2)12yes—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C42—22no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—41no—
1057C42—41no—
1058C42—41no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—42no—
1064C42—42no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—22no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—84no—
1104C23—84no—
1105C23—162no—
1106C23—162no—
1107C23—162no—
1108C23—162no—
1109C23—162no—
1110C23C23×D411yescharacteristic
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—84no—
1116Q8—162no—
1117D4—22no—
1118D4—22no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—84no—
1134D4—84no—
1135D4—84no—
1136D4—84no—
1137D4—162no—
1138D4—162no—
1139D4—162no—
1140D4—162no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144D4—162no—
1145D4—162no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4C2×AGL(1,ℤ/8)12yes—
1227C2×C4C2×AGL(1,ℤ/8)12yes—
1228C2×C4C2×AGL(1,ℤ/8)12yes—
1229C2×C4C22×#4111yescharacteristic
1230C2×C4C2×H(5,𝔽2)11yescharacteristic
1231C2×C4#58511yescharacteristic
1232C2×C4#58511yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C8—22no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C22—41no—
1244C22—42no—
1245C22—41no—
1246C22—42no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—42no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—168no—
1279C22D4×#4111yescharacteristic
1280C22#348811yescharacteristic
1281C22#350011yescharacteristic
1282C22C22×AGL(1,ℤ/8)11yescharacteristic
1283C22#358511yescharacteristic
1284C22#358511yescharacteristic
1285C22#358611yescharacteristic
1286C4—22no—
1287C4—22no—
1288C4—22no—
1289C4—41no—
1290C4—42no—
1291C4—41no—
1292C4—41no—
1293C4—42no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4#350611yescharacteristic
1312C4#352111yescharacteristic
1313C4#354011yescharacteristic
1314C4#356811yescharacteristic
1315C2—81no—
1316C2—82no—
1317C2—161no—
1318C2—161no—
1319C2—161no—
1320C2#4418211yescharacteristic
1321C2#6146611yescharacteristic
1322C2#6150411yescharacteristic
1323C2#6195911yescharacteristic
1324C2#6208511yescharacteristic
1325C2#6256811yescharacteristic
1326C2#6257611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39405C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59557C2semidirect
3. #32257C2semidirect
4. #32180C2semidirect
5. #32164C2semidirect
6. #32122C2semidirect
7. #31806C2semidirect
8. #31100C2semidirect
9. #30547C2semidirect
10. #30547C2semidirect
11. #29561C2semidirect
12. #29356C2semidirect
13. #29064C2semidirect
14. #28995C2semidirect
15. #28026C2semidirect
16. #27775C2semidirect
17. #27541C2semidirect
18. #27354C2semidirect
19. #27273C2semidirect
20. #26998C2semidirect
21. #26912C2semidirect
22. #26832C2semidirect
23. #26716C2semidirect
24. #26647C2semidirect
25. #25272C2semidirect
26. #24492C2semidirect
27. #23684C2semidirect
28. #23290C2semidirect
29. #23231C2semidirect
30. #22864C2semidirect
31. #22226C2semidirect
37. C2×#474C22semidirect
40. C2×#440C22semidirect
51. #2552C22semidirect
57. #2514C22semidirect
59. #2511C22semidirect
67. #2451C22semidirect
75. #2370C22semidirect
77. #2365C22semidirect
83. C4×#125C22semidirect
85. #2295C22semidirect
86. #2100C22semidirect
87. #2088C22semidirect
88. #2083C22semidirect
92. #2073C22semidirect
93. #2072C22semidirect
98. #2067C22semidirect
99. #2066C22semidirect
100. #2057C22semidirect
101. #2057C22semidirect
104. #2055C22semidirect
105. #2055C22semidirect
110. #2041C22semidirect
115. #2025C22semidirect
116. #2025C22semidirect
117. #2024C22semidirect
123. #2014C22semidirect
126. #1992C22semidirect
127. #1989C22semidirect
128. #1988C22semidirect
129. #1988C22semidirect
134. #1982C22semidirect
137. #1973C22semidirect
140. #1957C22semidirect
141. #1942C22semidirect
142. #1939C22semidirect
146. #1936C22semidirect
147. #1936C22semidirect
148. #1936C22semidirect
149. #1936C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
155. #1926C22semidirect
160. #1925C22semidirect
161. #1925C22semidirect
162. #1925C22semidirect
166. #1921C22semidirect
167. #1918C22semidirect
168. #1918C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
176. #1880C22semidirect
178. #1877C22semidirect
181. #1864C22semidirect
182. #1864C22semidirect
185. #1862C22semidirect
188. #1847C22semidirect
192. #1776C22semidirect
193. #1771C22semidirect
194. #1770C22semidirect
195. #1767C22semidirect
197. #1762C22semidirect
199. C4×#102C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#595572
#394052
#322572
#321802
#321642
#321222
#318062
#311002
#305472
#295612
#293562
#290642
#289952
#280262
#277752
#275412
#273542
#272732
#269982
#269122
#268322
#267162
#266472
#252722
#244922
#236842
#232902
#232312
#228642
#222262