Finite Group Databasebeta

← D4×#13050575 #24919136

Subgroups — D4×#13050575 #24919136

Order 10624.

620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13050575C212yesmaximal, complemented
2D4×D332C211yesmaximal, characteristic, complemented
3#19128077C211yesmaximal, characteristic, complemented
4#19127935C212yesmaximal, complemented
5#19127896C211yesmaximal, characteristic, complemented
6#19127893C211yesmaximal, characteristic, complemented
7#19127835C212yesmaximal, complemented
8#19127834C212yesmaximal, complemented
9C4×#13050575C211yesmaximal, characteristic, complemented
10D4×C83⋊C8C211yesmaximal, characteristic, complemented
11D42×C83C211yesmaximal, characteristic, complemented
12C22×D332C2212yescomplemented
13C2×D4×D83—21no—
14C2×#13050575—28no—
15C2×#13050575C2211yescharacteristic
16C2×#13050575C2212yescomplemented
17C2×#13050575C2212yescomplemented
18C2×#13050575C2212yescomplemented
19C2×#13050575C2212yescomplemented
20C22×C83⋊C8C2212yescomplemented
21#14581789C2211yescharacteristic, complemented
22#14581767—21no—
23#14581766C2212yescomplemented
24#14581762—22no—
25C4×D332C2211yescharacteristic, complemented
26#14581725C2211yescharacteristic, complemented
27C4⋊(C83⋊C8)C2211yescharacteristic, complemented
28#14581713C2211yescharacteristic, complemented
29#14581713C2212yescomplemented
30#14581712C2211yescharacteristic, complemented
31#14581712C2212yescomplemented
32C22⋊(C83⋊C8)C2212yescomplemented
33C4×C83⋊C8C2211yescharacteristic, complemented
34C22×D4×C83—21no—
35C22×D4×C83C2212yescomplemented
36#127×C83C2211yescharacteristic, complemented
37#121×C83—21no—
38#121×C83C2212yescomplemented
39#120×C83—22no—
40C4×D4×C83C2211yescharacteristic
41C4×D4×C83C2211yescharacteristic, complemented
42C23×D83—22no—
43C2×D332—24no—
44C2×D332—22no—
45C2×D332—21no—
46C2×D332—21no—
47C2×D332—42no—
48C2×D332C2312yes—
49C2×D332C2311yescharacteristic
50C2×C22⋊D83—22no—
51D4×D83—44no—
52C2×C4×D83—21no—
53#13050575—24no—
54#13050575—24no—
55#13050575—24no—
56#13050575—42no—
57#13050575D414yesdirect product factor
58C2×C83⋊C8—24no—
59C2×C83⋊C8C2312yes—
60C2×C83⋊C8C2311yescharacteristic
61C2×C83⋊C8C2311yescharacteristic
62C4⋊Dic83C2311yescharacteristic
63(C2×D83)⋊C4—21no—
64(C2×D83)⋊C4—22no—
65C24×C83—22no—
66C2×D4×C83—24no—
67C2×D4×C83—22no—
68C2×D4×C83—22no—
69C2×D4×C83—21no—
70C2×D4×C83—21no—
71C2×D4×C83—42no—
72C2×D4×C83—44no—
73C2×D4×C83D411yescharacteristic
74C2×D4×C83C2312yes—
75C2×D4×C83C2311yescharacteristic
76C22×C4×C83—21no—
77C22×C4×C83C2312yes—
78C4⋊C4×C83D411yescharacteristic
79C4⋊C4×C83C2311yescharacteristic
80C22⋊C4×C83—21no—
81C22⋊C4×C83—22no—
82C22⋊C4×C83D412yes—
83C42×C83C2311yescharacteristic
84C23×C83—21no—
85C23×C83—22no—
86C23×C83—44no—
87C23×C83—44no—
88C23×C83—82no—
89C23×C83C2×D412yes—
90C22×D83—21no—
91C22×D83—22no—
92C22×D83—44no—
93C22×D83—44no—
94C22×D83—82no—
95D4×C83—22no—
96D4×C83—21no—
97D4×C83—22no—
98D4×C83—44no—
99D4×C83—44no—
100D4×C83—42no—
101D4×C83—81no—
102D4×C83D814yescomplemented
103D4×C83C2×D412yescomplemented
104C2×C4×C83—22no—
105C2×C4×C83—22no—
106C2×C4×C83—21no—
107C2×C4×C83—42no—
108C2×C4×C83C2×D411yescharacteristic
109C2×C4×C83C2×D412yes—
110C2×C4×C83C2×D411yescharacteristic
111C2×C4×C83C2411yescharacteristic
112C22⋊D83—44no—
113C2×Dic83—21no—
114D332—22no—
115D332—21no—
116D332—22no—
117D332—44no—
118D332—42no—
119D332—81no—
120D332C2×D412yescomplemented
121C4×D83—42no—
122C83⋊C8—22no—
123C83⋊C8—21no—
124C83⋊C8C2×D412yescomplemented
125C22×C83—22no—
126C22×C83—22no—
127C22×C83—22no—
128C22×C83—41no—
129C22×C83—41no—
130C22×C83—42no—
131C22×C83—42no—
132C22×C83—42no—
133C22×C83—88no—
134C22×C83C2×D814yescomplemented
135C22×C83C22×D411yescharacteristic
136C2×D83—22no—
137C2×D83—41no—
138C2×D83—41no—
139C2×D83—42no—
140C2×D83—42no—
141C2×D83—42no—
142C2×D83—88no—
143C4×C83—22no—
144C4×C83—21no—
145C4×C83—41no—
146C4×C83C2×D812yescomplemented
147C4×C83C22×D411yescharacteristic
148C4×C83H(5,𝔽2)11yescharacteristic
149Dic83—41no—
150C2×C83—24no—
151C2×C83—42no—
152C2×C83—82no—
153C2×C83D4211yescharacteristic
154C2×C83C22×D811yescharacteristic
155C2×C83#57611yescharacteristic
156D83—42no—
157D83—82no—
158D4×D8—831nomaximal, Sylow
159C83D4×D811yescharacteristic, complemented, Sylow
160C22×D8—832no—
161D42—831no—
162D42D8311yescharacteristic, complemented
163#493—831no—
164#466—832no—
165#459—831no—
166#459—831no—
167#447—832no—
168#447—832no—
169C4×D8—831no—
170C8×D4—831no—
171C22×D4—21no—
172C22×D4—832no—
173C22×D4—1661no—
174C22×D4C2×D8312yescomplemented
175C2×D8—832no—
176C2×D8—831no—
177C2×D8—832no—
178C2×D8—832no—
179C2×D8—832no—
180C2×D8—1668no—
181C22×C8—832no—
182#127—831no—
183#127C2×D8311yescharacteristic, complemented
184#121—21no—
185#121—832no—
186#121—1661no—
187#121C2×D8312yescomplemented
188#120—22no—
189#120—1662no—
190C4×D4—831no—
191C4×D4C2×D8311yescharacteristic
192C4×D4C2×D8311yescharacteristic, complemented
193#107—831no—
194C4⋊C8—831no—
195#102—831no—
196#102—832no—
197#102—831no—
198#102—832no—
199C22⋊C8—832no—
200C4×C8—831no—
201C24—22no—
202C24—1662no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—3322no—
211C2×D4—3324no—
212C2×D4—831no—
213C2×D4—832no—
214C2×D4—1664no—
215C2×D4—1662no—
216C2×D4—1662no—
217C2×D4—1661no—
218C2×D4—1661no—
219C2×D4C22⋊D8311yescharacteristic
220C2×D4C22×D8312yes—
221C2×D4C22×D8311yescharacteristic
222C22×C4—21no—
223C22×C4—1661no—
224C22×C4C22×D8312yes—
225D8—3322no—
226D8—834no—
227D8—1664no—
228D8—1664no—
229D8—1664no—
230C2×C8—831no—
231C2×C8—831no—
232C2×C8—832no—
233C2×C8—1664no—
234C4⋊C4—831no—
235C4⋊C4C22⋊D8311yescharacteristic
236C4⋊C4C22×D8311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—1661no—
240C22⋊C4—1662no—
241C22⋊C4C22⋊D8312yes—
242C42C22×D8311yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—3324no—
249C23—3324no—
250C23—6642no—
251C23—1662no—
252C23—1661no—
253C23C2×C22⋊D8312yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—3324no—
262D4—3324no—
263D4—3322no—
264D4—832no—
265D4—6641no—
266D4—1662no—
267D4—1662no—
268D4—1661no—
269D4#1305057514yesdirect product factor
270D4D4×D8312yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—3322no—
276C2×C4—1661no—
277C2×C4C2×C22⋊D8311yescharacteristic
278C2×C4C2×C22⋊D8312yes—
279C2×C4C2×C22⋊D8311yescharacteristic
280C2×C4C23×D8311yescharacteristic
281C8—832no—
282C8—1662no—
283C8—1661no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—3321no—
294C22—3321no—
295C22—3322no—
296C22—3322no—
297C22—3322no—
298C22—6648no—
299C22—1662no—
300C22C2×#1305057514yescomplemented
301C22C22×C22⋊D8311yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—3321no—
306C4C2×#1305057512yescomplemented
307C4C2×D4×D8311yescharacteristic
308C4#1458183711yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—3322no—
313C2—6642no—
314C2D4×C22⋊D8311yescharacteristic
315C2C22×#1305057511yescharacteristic
316C2#1912850411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingD42×C83C2
socleC22×C83C22×D4
hypercenterD42D83
hypocenterC83D4×D8
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#13050575C2semidirect
2. D4×D332C2semidirect
3. #19128077C2semidirect
4. #19127935C2semidirect
5. #19127896C2semidirect
6. #19127893C2semidirect
7. #19127835C2semidirect
8. #19127834C2semidirect
9. C4×#13050575C2semidirect
10. D4×C83⋊C8C2semidirect
11. D42×C83C2semidirect
12. C22×D332C22semidirect
16. C2×#13050575C22semidirect
17. C2×#13050575C22semidirect
18. C2×#13050575C22semidirect
19. C2×#13050575C22semidirect
20. C22×C83⋊C8C22semidirect
21. #14581789C22semidirect
23. #14581766C22semidirect
25. C4×D332C22semidirect
26. #14581725C22semidirect
27. C4⋊(C83⋊C8)C22semidirect
28. #14581713C22semidirect
29. #14581713C22semidirect
30. #14581712C22semidirect
31. #14581712C22semidirect
32. C22⋊(C83⋊C8)C22semidirect
33. C4×C83⋊C8C22semidirect
35. C22×D4×C83C22semidirect
36. #127×C83C22semidirect
38. #121×C83C22semidirect
41. C4×D4×C83C22semidirect
57. #13050575D4direct (N × H)
102. D4×C83D8semidirect
103. D4×C83C2×D4semidirect
120. D332C2×D4semidirect
124. C83⋊C8C2×D4semidirect
134. C22×C83C2×D8semidirect
146. C4×C83C2×D8semidirect
159. C83D4×D8semidirect
162. D42D83semidirect
174. C22×D4C2×D83semidirect
183. #127C2×D83semidirect
187. #121C2×D83semidirect
192. C4×D4C2×D83semidirect
269. D4#13050575direct (N × H)
270. D4D4×D83semidirect
300. C22C2×#13050575semidirect
306. C4C2×#13050575semidirect

Maximal subgroups

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

subgroupindex
C22×#130505752
D4×D3322
#191280772
#191279352
#191278962
#191278932
#191278352
#191278342
C4×#130505752
D4×C83⋊C82
D42×C832
D4×D883