Finite Group Databasebeta

← #6375239

Subgroups — #6375239

Order 512.

1437 conjugacy classes of subgroups.

The subgroup lattice has 1233 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34149C211yesmaximal, characteristic
2#22027C211yesmaximal, characteristic, complemented
3#22026C211yesmaximal, characteristic, complemented
4#22025C211yesmaximal, characteristic, complemented
5#22023C211yesmaximal, characteristic, complemented
6#22017C211yesmaximal, characteristic, complemented
7#22016C211yesmaximal, characteristic, complemented
8#22014C211yesmaximal, characteristic, complemented
9#22012C211yesmaximal, characteristic, complemented
10#22006C211yesmaximal, characteristic, complemented
11#22006C211yesmaximal, characteristic, complemented
12#22004C211yesmaximal, characteristic, complemented
13#22004C211yesmaximal, characteristic, complemented
14#22003C211yesmaximal, characteristic, complemented
15#22002C211yesmaximal, characteristic, complemented
16#22001C211yesmaximal, characteristic, complemented
17#22000C211yesmaximal, characteristic, complemented
18#21435C211yesmaximal, characteristic, complemented
19#21434C211yesmaximal, characteristic, complemented
20#21433C211yesmaximal, characteristic, complemented
21#21431C211yesmaximal, characteristic, complemented
22#21381C211yesmaximal, characteristic
23#21381C211yesmaximal, characteristic
24#21357C211yesmaximal, characteristic, complemented
25#21357C211yesmaximal, characteristic, complemented
26#20786C211yesmaximal, characteristic, complemented
27#20781C211yesmaximal, characteristic, complemented
28#20779C211yesmaximal, characteristic, complemented
29#20779C211yesmaximal, characteristic, complemented
30#20465C211yesmaximal, characteristic, complemented
31#20368C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C2×#433C2211yescharacteristic
34C2×#433C2211yescharacteristic
35C2×#405C2211yescharacteristic
36C2×#405C2211yescharacteristic
37#2373C411yescharacteristic
38#2373C411yescharacteristic
39#2373C411yescharacteristic
40#2373C411yescharacteristic
41#2372C411yescharacteristic
42#2372C411yescharacteristic
43#2371C411yescharacteristic
44#2371C411yescharacteristic
45#2368C411yescharacteristic
46#2368C411yescharacteristic
47#2364C411yescharacteristic
48#2364C411yescharacteristic
49#2359C411yescharacteristic
50#2359C411yescharacteristic
51#2359C411yescharacteristic
52#2359C411yescharacteristic
53#2298C2211yescharacteristic
54#2298C2211yescharacteristic
55#2295C2211yescharacteristic
56#2295C2211yescharacteristic
57#2290C2211yescharacteristic
58#2290C2211yescharacteristic
59#2290C2211yescharacteristic
60#2290C2211yescharacteristic
61C42×D4C2211yescharacteristic
62C42×D4C2211yescharacteristic
63C4×#117C2211yescharacteristic
64C4×#117C2211yescharacteristic
65C4×#117C2211yescharacteristic
66C2×#376C2211yescharacteristic
67#1985C2211yescharacteristic
68#1985C2211yescharacteristic
69#1984C2211yescharacteristic
70#1984C2211yescharacteristic
71#1955C2211yescharacteristic
72#1955C2211yescharacteristic
73#1954C2211yescharacteristic
74#1954C2211yescharacteristic
75#1940C2211yescharacteristic
76#1940C2211yescharacteristic
77#1940C2211yescharacteristic
78#1940C2211yescharacteristic
79#1939C2211yescharacteristic
80#1939C2211yescharacteristic
81#1939C2211yescharacteristic
82#1939C2211yescharacteristic
83#1924C2211yescharacteristic
84#1924C2211yescharacteristic
85#1924C2211yescharacteristic
86#1924C2211yescharacteristic
87#1924C2211yescharacteristic
88#1924C2211yescharacteristic
89#1924C2211yescharacteristic
90#1924C2211yescharacteristic
91#1924C2211yescharacteristic
92#1924C2211yescharacteristic
93#1924C2211yescharacteristic
94#1924C2211yescharacteristic
95#1923C2211yescharacteristic
96#1923C2211yescharacteristic
97#1923C2211yescharacteristic
98#1923C2211yescharacteristic
99#1917C2211yescharacteristic
100#1917C2211yescharacteristic
101#1917C2211yescharacteristic
102#1917C2211yescharacteristic
103#1917C2211yescharacteristic
104#1917C2211yescharacteristic
105#1917C2211yescharacteristic
106#1917C2211yescharacteristic
107#1917C2211yescharacteristic
108#1917C2211yescharacteristic
109#1917C2211yescharacteristic
110#1917C2211yescharacteristic
111#1916C2211yescharacteristic
112#1916C2211yescharacteristic
113#1916C2211yescharacteristic
114#1916C2211yescharacteristic
115#1870C2211yescharacteristic
116#1870C2211yescharacteristic
117#1870C2211yescharacteristic
118#1870C2211yescharacteristic
119#1869C2211yescharacteristic
120#1869C2211yescharacteristic
121#1869C2211yescharacteristic
122#1869C2211yescharacteristic
123#1851C2211yescharacteristic
124#1851C2211yescharacteristic
125#1851C2211yescharacteristic
126#1851C2211yescharacteristic
127#1850C2211yescharacteristic
128#1850C2211yescharacteristic
129#1850C2211yescharacteristic
130#1850C2211yescharacteristic
131#1840C2211yescharacteristic
132#1840C2211yescharacteristic
133#1840C2211yescharacteristic
134#1840C2211yescharacteristic
135#1840C2211yescharacteristic
136#1840C2211yescharacteristic
137#1839C2211yescharacteristic
138#1839C2211yescharacteristic
139#1832C2211yescharacteristic
140#1832C2211yescharacteristic
141#1832C2211yescharacteristic
142#1832C2211yescharacteristic
143#1832C2211yescharacteristic
144#1832C2211yescharacteristic
145#1831C2211yescharacteristic
146#1831C2211yescharacteristic
147#1818C2211yescharacteristic
148#1818C2211yescharacteristic
149#1817C2211yescharacteristic
150#1817C2211yescharacteristic
151#1817C2211yescharacteristic
152#1817C2211yescharacteristic
153#1817C2211yescharacteristic
154#1817C2211yescharacteristic
155#1798C2211yescharacteristic
156#1798C2211yescharacteristic
157#1797C2211yescharacteristic
158#1797C2211yescharacteristic
159#1797C2211yescharacteristic
160#1797C2211yescharacteristic
161#1797C2211yescharacteristic
162#1797C2211yescharacteristic
163#1768C2211yescharacteristic
164#1768C2211yescharacteristic
165#1768C2211yescharacteristic
166#1768C2211yescharacteristic
167#1768C2211yescharacteristic
168#1768C2211yescharacteristic
169#1767C2211yescharacteristic
170#1767C2211yescharacteristic
171#1767C2211yescharacteristic
172#1767C2211yescharacteristic
173C4×C4⋊C8C2211yescharacteristic
174C4×C4⋊C8C2211yescharacteristic
175#1750C2211yescharacteristic
176#1750C2211yescharacteristic
177#1750C2211yescharacteristic
178#1750C2211yescharacteristic
179#1750C2211yescharacteristic
180#1750C2211yescharacteristic
181#1749C2211yescharacteristic
182#1749C2211yescharacteristic
183#1749C2211yescharacteristic
184#1749C2211yescharacteristic
185C4×C22⋊C8C2211yescharacteristic
186C4×C22⋊C8C2211yescharacteristic
187#1746C2211yescharacteristic
188#1746C2211yescharacteristic
189#1746C2211yescharacteristic
190#1746C2211yescharacteristic
191#1746C2211yescharacteristic
192#1746C2211yescharacteristic
193#1745C2211yescharacteristic
194#1745C2211yescharacteristic
195#1744C2211yescharacteristic
196#1744C2211yescharacteristic
197#1729C2211yescharacteristic
198#1729C2211yescharacteristic
199#1728C2211yescharacteristic
200C2×#336C2211yescharacteristic
201C4×#97C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#529—24no—
208#529—24no—
209C2×#126C2×C411yescharacteristic
210C2×#126C2×C411yescharacteristic
211C2×#125C2×C411yescharacteristic
212C2×#124C2×C411yescharacteristic
213C2×#123C2×C411yescharacteristic
214C2×#123C2×C411yescharacteristic
215C2×C22⋊Q8C2×C411yescharacteristic
216C2×#121C2×C411yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4C2×C411yescharacteristic
219C2×C4×D4C2×C411yescharacteristic
220C2×C4×D4C2×C411yescharacteristic
221C2×C4×D4C2×C411yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117C2×C411yescharacteristic
226C2×#117C2×C411yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236#433—24no—
237#433—24no—
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C22⋊C8C2311yescharacteristic
259C2×C22⋊C8C2311yescharacteristic
260C2×C22⋊C8C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×C22⋊C8C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278#405—24no—
279#405—24no—
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#391C2×C411yescharacteristic
301#391C2×C411yescharacteristic
302#391C2×C411yescharacteristic
303#391C2×C411yescharacteristic
304#389C2×C411yescharacteristic
305#389C2×C411yescharacteristic
306#389C2×C411yescharacteristic
307#389C2×C411yescharacteristic
308#388C2×C411yescharacteristic
309#388C2×C411yescharacteristic
310#388C2×C411yescharacteristic
311#388C2×C411yescharacteristic
312#388C2×C411yescharacteristic
313#388C2×C411yescharacteristic
314#388C2×C411yescharacteristic
315#388C2×C411yescharacteristic
316#388C2×C411yescharacteristic
317#388C2×C411yescharacteristic
318#388C2×C411yescharacteristic
319#388C2×C411yescharacteristic
320#388C2×C411yescharacteristic
321#388C2×C411yescharacteristic
322#388C2×C411yescharacteristic
323#388C2×C411yescharacteristic
324#387C2×C411yescharacteristic
325#387C2×C411yescharacteristic
326#387C2×C411yescharacteristic
327#387C2×C411yescharacteristic
328#387C2×C411yescharacteristic
329#387C2×C411yescharacteristic
330#387C2×C411yescharacteristic
331#387C2×C411yescharacteristic
332#387C2×C411yescharacteristic
333#387C2×C411yescharacteristic
334#387C2×C411yescharacteristic
335#387C2×C411yescharacteristic
336#387C2×C411yescharacteristic
337#387C2×C411yescharacteristic
338#387C2×C411yescharacteristic
339#387C2×C411yescharacteristic
340#387C2×C411yescharacteristic
341#387C2×C411yescharacteristic
342#387C2×C411yescharacteristic
343#387C2×C411yescharacteristic
344#387C2×C411yescharacteristic
345#387C2×C411yescharacteristic
346#387C2×C411yescharacteristic
347#387C2×C411yescharacteristic
348#386C2×C411yescharacteristic
349#386C2×C411yescharacteristic
350#386C2×C411yescharacteristic
351#386C2×C411yescharacteristic
352#386C2×C411yescharacteristic
353#386C2×C411yescharacteristic
354#386C2×C411yescharacteristic
355#386C2×C411yescharacteristic
356#385C2×C411yescharacteristic
357#385C2×C411yescharacteristic
358#385C2×C411yescharacteristic
359#385C2×C411yescharacteristic
360#385C2×C411yescharacteristic
361#385C2×C411yescharacteristic
362#385C2×C411yescharacteristic
363#385C2×C411yescharacteristic
364C4×C4⋊C4C2×C411yescharacteristic
365C4×C4⋊C4C2×C411yescharacteristic
366C4×C4⋊C4C2×C411yescharacteristic
367C4×C4⋊C4C2×C411yescharacteristic
368C4×C4⋊C4C2×C411yescharacteristic
369C4×C4⋊C4C2×C411yescharacteristic
370C4×C4⋊C4C2×C411yescharacteristic
371C4×C4⋊C4C2×C411yescharacteristic
372C4×C4⋊C4C2×C411yescharacteristic
373C4×C4⋊C4C2×C411yescharacteristic
374C4×C4⋊C4C2×C411yescharacteristic
375C4×C4⋊C4C2×C411yescharacteristic
376C4×C4⋊C4C2×C411yescharacteristic
377C4×C4⋊C4C2×C411yescharacteristic
378C4×C4⋊C4C2311yescharacteristic
379C4×C4⋊C4C2311yescharacteristic
380C4×C4⋊C4C2311yescharacteristic
381C4×C4⋊C4C2311yescharacteristic
382C4×C4⋊C4C2311yescharacteristic
383C4×C4⋊C4C2311yescharacteristic
384C4×C22⋊C4C2×C411yescharacteristic
385C4×C22⋊C4C2×C411yescharacteristic
386C4×C22⋊C4C2×C411yescharacteristic
387C4×C22⋊C4C2×C411yescharacteristic
388C4×C22⋊C4C2×C411yescharacteristic
389C4×C22⋊C4C2×C411yescharacteristic
390C4×C22⋊C4C2×C411yescharacteristic
391C4×C22⋊C4C2×C411yescharacteristic
392C4×C22⋊C4C2×C411yescharacteristic
393C4×C22⋊C4C2×C411yescharacteristic
394C4×C22⋊C4C2×C411yescharacteristic
395C4×C22⋊C4C2×C411yescharacteristic
396C4×C22⋊C4C2×C411yescharacteristic
397C4×C22⋊C4C2×C411yescharacteristic
398C4×C22⋊C4C2×C411yescharacteristic
399C4×C22⋊C4C2×C411yescharacteristic
400C4×C22⋊C4C2×C411yescharacteristic
401C4×C22⋊C4C2×C411yescharacteristic
402C4×C22⋊C4C2311yescharacteristic
403C4×C22⋊C4C2311yescharacteristic
404C4×C22⋊C4C2311yescharacteristic
405C4×C22⋊C4C2311yescharacteristic
406C4×C22⋊C4C2311yescharacteristic
407C4×C22⋊C4C2311yescharacteristic
408#376C2×C411yescharacteristic
409#376C2×C411yescharacteristic
410#376C2×C411yescharacteristic
411#376C2×C411yescharacteristic
412#376C2×C411yescharacteristic
413#376C2×C411yescharacteristic
414#376C2311yescharacteristic
415#376C2311yescharacteristic
416#376C2311yescharacteristic
417#376C2311yescharacteristic
418#376C2311yescharacteristic
419#376C2311yescharacteristic
420C2×#95C2×C411yescharacteristic
421C2×#95C2×C411yescharacteristic
422C2×#95C2×C411yescharacteristic
423C2×#95C2×C411yescharacteristic
424C43C2311yescharacteristic
425C43C2311yescharacteristic
426C43C2311yescharacteristic
427C43C2311yescharacteristic
428#336C2311yescharacteristic
429#336C2311yescharacteristic
430#336C2311yescharacteristic
431#336C2311yescharacteristic
432#336C2311yescharacteristic
433#336C2311yescharacteristic
434#336C2311yescharacteristic
435#336C2311yescharacteristic
436#336C2311yescharacteristic
437#336C2311yescharacteristic
438#336C2311yescharacteristic
439#336C2311yescharacteristic
440#336C2311yescharacteristic
441#336C2311yescharacteristic
442#336C2311yescharacteristic
443#336C2311yescharacteristic
444#336C2311yescharacteristic
445#336C2311yescharacteristic
446#336C2311yescharacteristic
447#336C2311yescharacteristic
448#336C2311yescharacteristic
449#336C2311yescharacteristic
450#336C2311yescharacteristic
451#336C2311yescharacteristic
452#336C2311yescharacteristic
453#336C2311yescharacteristic
454#336C2311yescharacteristic
455#336C2311yescharacteristic
456#336C2311yescharacteristic
457#336C2311yescharacteristic
458#336C2311yescharacteristic
459#336C2311yescharacteristic
460#336C2311yescharacteristic
461#336C2311yescharacteristic
462#336C2311yescharacteristic
463#336C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8C22×C411yescharacteristic
485C22×D4C22×C411yescharacteristic
486C22×D4C22×C411yescharacteristic
487C22×D4C22×C411yescharacteristic
488C23×C4C22×C411yescharacteristic
489C23×C4C22×C411yescharacteristic
490C23×C4C22×C411yescharacteristic
491C23×C4C22×C411yescharacteristic
492C23×C4C22×C411yescharacteristic
493C23×C4C22×C411yescharacteristic
494C23×C4C22×C411yescharacteristic
495C23×C4C22×C411yescharacteristic
496C23×C4C22×C411yescharacteristic
497C23×C4C22×C411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C2×M16—22no—
502C2×M16—22no—
503C2×M16—41no—
504C2×M16—41no—
505C2×M16—41no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529#126—24no—
530#126—24no—
531#125—24no—
532#124—24no—
533#123—24no—
534#123—24no—
535C22⋊Q8—24no—
536#121—24no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—42no—
546C4×D4—42no—
547C4×D4—42no—
548C4×D4—42no—
549#117—22no—
550#117—22no—
551#117—41no—
552#117—41no—
553#117—41no—
554#117—41no—
555#117—42no—
556#117—42no—
557#117#4114yes—
558#117#4114yes—
559C2×C4⋊C4C22×C411yescharacteristic
560C2×C4⋊C4C22×C411yescharacteristic
561C2×C4⋊C4C22×C411yescharacteristic
562C2×C4⋊C4C22×C411yescharacteristic
563C2×C4⋊C4C22×C411yescharacteristic
564C2×C4⋊C4C22×C411yescharacteristic
565C2×C4⋊C4C22×C411yescharacteristic
566C2×C4⋊C4C22×C411yescharacteristic
567C2×C4⋊C4C22×C411yescharacteristic
568C2×C4⋊C4C22×C411yescharacteristic
569C2×C4⋊C4C22×C411yescharacteristic
570C2×C4⋊C4C22×C411yescharacteristic
571C2×C4⋊C4C22×C411yescharacteristic
572C2×C4⋊C4C22×C411yescharacteristic
573C2×C4⋊C4C22×C411yescharacteristic
574C2×C4⋊C4C22×C411yescharacteristic
575C2×C4⋊C4C22×C411yescharacteristic
576C2×C4⋊C4C22×C411yescharacteristic
577C2×C4⋊C4C22×C411yescharacteristic
578C2×C4⋊C4C22×C411yescharacteristic
579C2×C4⋊C4C22×C411yescharacteristic
580C2×C4⋊C4C22×C411yescharacteristic
581C2×C4⋊C4C22×C411yescharacteristic
582C2×C4⋊C4C22×C411yescharacteristic
583C2×C4⋊C4C22×C411yescharacteristic
584C2×C4⋊C4C22×C411yescharacteristic
585C2×C22⋊C4C22×C411yescharacteristic
586C2×C22⋊C4C22×C411yescharacteristic
587C2×C22⋊C4C22×C411yescharacteristic
588C2×C22⋊C4C22×C411yescharacteristic
589C2×C22⋊C4C22×C411yescharacteristic
590C2×C22⋊C4C22×C411yescharacteristic
591C2×C22⋊C4C22×C411yescharacteristic
592C2×C22⋊C4C22×C411yescharacteristic
593C2×C22⋊C4C22×C411yescharacteristic
594C2×C22⋊C4C22×C411yescharacteristic
595C2×C22⋊C4C22×C411yescharacteristic
596C2×C22⋊C4C22×C411yescharacteristic
597C2×C22⋊C4C22×C411yescharacteristic
598C2×C22⋊C4C22×C411yescharacteristic
599C2×C22⋊C4C22×C411yescharacteristic
600C2×C22⋊C4C22×C411yescharacteristic
601C2×C22⋊C4C22×C411yescharacteristic
602C2×C22⋊C4C22×C411yescharacteristic
603C2×C22⋊C4C22×C411yescharacteristic
604C2×C22⋊C4C22×C411yescharacteristic
605C2×C22⋊C4C22×C411yescharacteristic
606C2×C22⋊C4C22×C411yescharacteristic
607C2×C22⋊C4C22×C411yescharacteristic
608C2×C22⋊C4C22×C411yescharacteristic
609C2×C22⋊C4C22×C411yescharacteristic
610C2×C22⋊C4C22×C411yescharacteristic
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—41no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42C22×C411yescharacteristic
622C2×C42C22×C411yescharacteristic
623C2×C42C22×C411yescharacteristic
624C2×C42C22×C411yescharacteristic
625C2×C42C22×C411yescharacteristic
626C2×C42C22×C411yescharacteristic
627C2×C42C22×C411yescharacteristic
628C2×C42C22×C411yescharacteristic
629C2×C42C22×C411yescharacteristic
630C2×C42C22×C411yescharacteristic
631C2×C42C22×C411yescharacteristic
632C2×C42C22×C411yescharacteristic
633C2×C42C22×C411yescharacteristic
634C2×C42C22×C411yescharacteristic
635C2×C42C22×C411yescharacteristic
636C2×C42C22×C411yescharacteristic
637C2×C42C22×C411yescharacteristic
638C2×C42C22×C411yescharacteristic
639C2×C42C22×C411yescharacteristic
640C2×C42C22×C411yescharacteristic
641C2×C42C22×C411yescharacteristic
642C2×C42C22×C411yescharacteristic
643C2×C42C22×C411yescharacteristic
644C2×C42C22×C411yescharacteristic
645C2×C42C22×C411yescharacteristic
646C2×C42C22×C411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681C22⋊C8—22no—
682C22⋊C8—22no—
683C22⋊C8—41no—
684C22⋊C8—41no—
685C22⋊C8—41no—
686C22⋊C8—41no—
687C22⋊C8—41no—
688C22⋊C8—41no—
689C22⋊C8—41no—
690C22⋊C8—41no—
691C22⋊C8—41no—
692C22⋊C8—41no—
693C22⋊C8—41no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698C22⋊C8—41no—
699#97—22no—
700#97—22no—
701#97—22no—
702#97—22no—
703#97—22no—
704#97—22no—
705#97—41no—
706#97—41no—
707#97—41no—
708#97—41no—
709#97—41no—
710#97—41no—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8—22no—
714C4×C8—22no—
715C4×C8—22no—
716C4×C8—22no—
717C4×C8—41no—
718C4×C8—41no—
719#95C22×C411yescharacteristic
720#95C22×C411yescharacteristic
721#95C22×C411yescharacteristic
722#95C22×C411yescharacteristic
723#95C22×C411yescharacteristic
724#95C22×C411yescharacteristic
725#95C22×C411yescharacteristic
726#95C22×C411yescharacteristic
727#95C22×C411yescharacteristic
728#95C22×C411yescharacteristic
729#95C22×C411yescharacteristic
730#95C22×C411yescharacteristic
731#95C22×C411yescharacteristic
732#95C22×C411yescharacteristic
733#95C22×C411yescharacteristic
734#95C22×C411yescharacteristic
735#95C22×C411yescharacteristic
736#95C22×C411yescharacteristic
737#95C22×C411yescharacteristic
738#95C22×C411yescharacteristic
739#95C22×C411yescharacteristic
740#95C22×C411yescharacteristic
741#95C22×C411yescharacteristic
742#95C22×C411yescharacteristic
743#95C22×C411yescharacteristic
744#95C22×C411yescharacteristic
745#95C22×C411yescharacteristic
746#95C22×C411yescharacteristic
747#95C22×C411yescharacteristic
748#95C22×C411yescharacteristic
749#95C22×C411yescharacteristic
750#95C22×C411yescharacteristic
751#95C22×C411yescharacteristic
752#95C22×C411yescharacteristic
753#95C22×C411yescharacteristic
754#95C22×C411yescharacteristic
755#95C22×C411yescharacteristic
756#95C22×C411yescharacteristic
757#95C22×C411yescharacteristic
758#95C22×C411yescharacteristic
759#95C22×C411yescharacteristic
760#95C22×C411yescharacteristic
761#95C22×C411yescharacteristic
762#95C22×C411yescharacteristic
763#95C22×C411yescharacteristic
764#95C22×C411yescharacteristic
765#95C22×C411yescharacteristic
766#95C22×C411yescharacteristic
767C24C23×C411yescharacteristic
768C24C23×C411yescharacteristic
769C24C23×C411yescharacteristic
770C2×Q8—22no—
771C2×Q8—41no—
772C2×Q8—41no—
773C2×D4—22no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—41no—
779C2×D4—41no—
780C2×D4—41no—
781C2×D4—41no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4C23×C411yescharacteristic
829C22×C4C23×C411yescharacteristic
830C22×C4C23×C411yescharacteristic
831C22×C4C23×C411yescharacteristic
832C22×C4C23×C411yescharacteristic
833C22×C4C23×C411yescharacteristic
834C22×C4C23×C411yescharacteristic
835C22×C4C23×C411yescharacteristic
836C22×C4C23×C411yescharacteristic
837C22×C4C23×C411yescharacteristic
838C22×C4C23×C411yescharacteristic
839C22×C4C23×C411yescharacteristic
840C22×C4C23×C411yescharacteristic
841C22×C4C23×C411yescharacteristic
842C22×C4C23×C411yescharacteristic
843C22×C4C23×C411yescharacteristic
844C22×C4C23×C411yescharacteristic
845C22×C4C23×C411yescharacteristic
846C22×C4C23×C411yescharacteristic
847C22×C4C23×C411yescharacteristic
848C22×C4C23×C411yescharacteristic
849C22×C4C23×C411yescharacteristic
850C22×C4C23×C411yescharacteristic
851C22×C4C23×C411yescharacteristic
852C22×C4C23×C411yescharacteristic
853C22×C4C23×C411yescharacteristic
854C22×C4C23×C411yescharacteristic
855C22×C4C2×#4112yes—
856C22×C4C2×#4112yes—
857C22×C4C2511yescharacteristic
858M16—44no—
859M16—44no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—44no—
909C2×C8—44no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—22no—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—41no—
925C4⋊C4—41no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4#11714yes—
935C4⋊C4#11714yes—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4#11714yes—
961C22⋊C4#11714yes—
962C42—22no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—41no—
987C42—41no—
988C42—41no—
989C42—41no—
990C42—41no—
991C42—41no—
992C42—41no—
993C42—41no—
994C42—41no—
995C42—41no—
996C42—41no—
997C42—41no—
998C42—41no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42—41no—
1008C42C2×#4112yes—
1009C42C2×#4112yes—
1010C42C2×#4112yes—
1011C42C2×#4112yes—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23C2×#11712yes—
1032C23#56812yes—
1033C23C24×C411yescharacteristic
1034Q8—82no—
1035D4—44no—
1036D4—44no—
1037D4—82no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—44no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—82no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—82no—
1130C2×C4—82no—
1131C2×C4—82no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4—82no—
1135C2×C4C2×#11712yes—
1136C2×C4C2×#11712yes—
1137C2×C4C2×#11712yes—
1138C2×C4C2×#11712yes—
1139C2×C4C2×#11712yes—
1140C2×C4#56812yes—
1141C2×C4C22×#4111yescharacteristic
1142C2×C4C22×#4111yescharacteristic
1143C2×C4#58511yescharacteristic
1144C2×C4#58511yescharacteristic
1145C2×C4#58511yescharacteristic
1146C2×C4#58511yescharacteristic
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22C22×#11711yescharacteristic
1185C22#342811yescharacteristic
1186C22#342811yescharacteristic
1187C22C2×#56811yescharacteristic
1188C22C2×#56811yescharacteristic
1189C22#357311yescharacteristic
1190C22#357311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—22no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4#345511yescharacteristic
1219C4#345511yescharacteristic
1220C4#345511yescharacteristic
1221C4#345511yescharacteristic
1222C2—42no—
1223C2—42no—
1224C2—81no—
1225C2#3405611yescharacteristic
1226C2#6012811yescharacteristic
1227C2#6012911yescharacteristic
1228C2#6029911yescharacteristic
1229C2#6029911yescharacteristic
1230C2#6029911yescharacteristic
1231C2#6030011yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC2×#121C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #22027C2semidirect
3. #22026C2semidirect
4. #22025C2semidirect
5. #22023C2semidirect
6. #22017C2semidirect
7. #22016C2semidirect
8. #22014C2semidirect
9. #22012C2semidirect
10. #22006C2semidirect
11. #22006C2semidirect
12. #22004C2semidirect
13. #22004C2semidirect
14. #22003C2semidirect
15. #22002C2semidirect
16. #22001C2semidirect
17. #22000C2semidirect
18. #21435C2semidirect
19. #21434C2semidirect
20. #21433C2semidirect
21. #21431C2semidirect
24. #21357C2semidirect
25. #21357C2semidirect
26. #20786C2semidirect
27. #20781C2semidirect
28. #20779C2semidirect
29. #20779C2semidirect
30. #20465C2semidirect
31. #20368C2semidirect

Maximal subgroups

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

subgroupindex
#341492
#220272
#220262
#220252
#220232
#220172
#220162
#220142
#220122
#220062
#220042
#220032
#220022
#220012
#220002
#214352
#214342
#214332
#214312
#213812
#213572
#207862
#207812
#207792
#204652
#203682