Finite Group Databasebeta

← D4×D2152 #46822562

Subgroups — D4×D2152 #46822562

Order 34432.

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×D2152C212yesmaximal, complemented
2D4×D1076C212yesmaximal, complemented
3#31770982C211yesmaximal, characteristic, complemented
4#31770841C212yesmaximal, complemented
5#31770801C212yesmaximal, complemented
6#31770741C214yesmaximal, complemented
7C4×D2152C211yesmaximal, characteristic, complemented
8C8×D4×C269C211yesmaximal, characteristic, complemented
9C22×D1076C2214yescomplemented
10C2×D4×D269—22no—
11C2×D2152—28no—
12C2×D2152C2211yescharacteristic
13C2×D2152C2212yescomplemented
14C2×D2152C2214yescomplemented
15C2×D2152C2212yescomplemented
16#22575450C2212yescomplemented
17#22575428—22no—
18#22575427C2214yescomplemented
19#22575423—24no—
20C4×D1076C2212yescomplemented
21#22575387C2211yescharacteristic, complemented
22#22575375C2212yescomplemented
23#22575375C2214yescomplemented
24C22×C8×C269C2212yescomplemented
25C4×D4×C269C2211yescharacteristic
26C4⋊C8×C269C2211yescharacteristic, complemented
27C22⋊C8×C269C2212yescomplemented
28C4×C8×C269C2211yescharacteristic, complemented
29C23×D269—24no—
30C2×D1076—28no—
31C2×D1076—24no—
32C2×D1076—22no—
33C2×D1076—22no—
34C2×D1076—44no—
35C2×D1076C2314yes—
36C2×D1076C2312yes—
37C2×C22⋊D269—24no—
38D4×D269—48no—
39C2×C4×D269—22no—
40D2152—28no—
41D2152—24no—
42D2152—42no—
43D2152D414yesdirect product factor
44C4⋊Dic269C2312yes—
45#16864379—22no—
46#16864379—24no—
47C2×D4×C269D411yescharacteristic
48C22×C4×C269C2312yes—
49C2×C8×C269—24no—
50C2×C8×C269C2311yescharacteristic
51C2×C8×C269C2312yes—
52C2×C8×C269C2311yescharacteristic
53C4⋊C4×C269D411yescharacteristic
54C22⋊C4×C269D412yes—
55C42×C269C2311yescharacteristic
56C22×D269—22no—
57C22×D269—24no—
58C22×D269—48no—
59C22×D269—48no—
60C22×D269—84no—
61D1076—24no—
62D1076—22no—
63D1076—24no—
64D1076—48no—
65D1076—44no—
66D1076—82no—
67D1076C2×D414yescomplemented
68C22⋊D269—48no—
69C2×Dic269—22no—
70C4×D269—44no—
71C23×C269C2×D412yes—
72D4×C269D814yescomplemented
73C2×C4×C269—22no—
74C2×C4×C269—22no—
75C2×C4×C269C2×D411yescharacteristic
76C2×C4×C269C2×D412yes—
77C2×C4×C269C2×D411yescharacteristic
78C2×C4×C269C2411yescharacteristic
79C8×C269—22no—
80C8×C269—21no—
81C8×C269C2×D412yescomplemented
82C22×C269—22no—
83C22×C269—22no—
84C22×C269C2×D814yescomplemented
85C22×C269C22×D411yescharacteristic
86C2×D269—24no—
87C2×D269—42no—
88C2×D269—42no—
89C2×D269—44no—
90C2×D269—44no—
91C2×D269—44no—
92C2×D269—816no—
93C4×C269—22no—
94C4×C269—21no—
95C4×C269C2×D812yescomplemented
96C4×C269C22×D411yescharacteristic
97C4×C269H(5,𝔽2)11yescharacteristic
98Dic269—42no—
99C2×C269—24no—
100C2×C269D4211yescharacteristic
101C2×C269C22×D811yescharacteristic
102C2×C269#57611yescharacteristic
103D269—44no—
104D269—84no—
105C269D4×D811yescharacteristic, complemented, Sylow
106D4×D8—2691nomaximal, Sylow
107C22×D8—2692no—
108D42—2692no—
109#493—2691no—
110#466—2692no—
111#459—2692no—
112#447—2694no—
113C4×D8—2691no—
114C8×D4D26911yescharacteristic, complemented
115C22×D4—2694no—
116C22×D4—5382no—
117C2×D8—2691no—
118C2×D8—2694no—
119C2×D8—2692no—
120C2×D8—2692no—
121C2×D8—5388no—
122C22×C8C2×D26912yescomplemented
123#127—2692no—
124#121—2694no—
125#121—5382no—
126#120—5384no—
127C4×D4—2692no—
128C4×D4C2×D26911yescharacteristic
129#107—2691no—
130C4⋊C8C2×D26911yescharacteristic, complemented
131#102—2692no—
132#102—2694no—
133C22⋊C8C2×D26912yescomplemented
134C4×C8C2×D26911yescharacteristic, complemented
135C24—5384no—
136C2×D4—2692no—
137C2×D4—2694no—
138C2×D4—5388no—
139C2×D4—5384no—
140C2×D4—5384no—
141C2×D4—5382no—
142C2×D4—5382no—
143C2×D4—10764no—
144C2×D4—10768no—
145C2×D4D107611yescharacteristic
146C22×C4—5382no—
147C22×C4C22×D26912yes—
148D8—2694no—
149D8—5388no—
150D8—5384no—
151D8—10762no—
152C2×C8—24no—
153C2×C8C22×D26911yescharacteristic
154C2×C8C22×D26912yes—
155C2×C8C22×D26911yescharacteristic
156C4⋊C4—2692no—
157C4⋊C4D107611yescharacteristic
158C22⋊C4—5382no—
159C22⋊C4—5384no—
160C22⋊C4D107612yes—
161C42C22×D26911yescharacteristic
162C23—5382no—
163C23—5384no—
164C23—10768no—
165C23—10768no—
166C23—21524no—
167C23C2×D107612yes—
168D4—2694no—
169D4—5384no—
170D4—5382no—
171D4—5384no—
172D4—10768no—
173D4—10768no—
174D4—10764no—
175D4—21522no—
176D4D215214yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—5382no—
180C2×C4—10764no—
181C2×C4C2×D107611yescharacteristic
182C2×C4C2×D107612yes—
183C2×C4C2×D107611yescharacteristic
184C2×C4C23×D26911yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D26912yescomplemented
188C22—22no—
189C22—22no—
190C22—5384no—
191C22—10762no—
192C22—10762no—
193C22—10764no—
194C22—10764no—
195C22—10764no—
196C22—215216no—
197C22C2×D215214yescomplemented
198C22C22×D107611yescharacteristic
199C4—21no—
200C4—22no—
201C4—10762no—
202C4C2×D215212yescomplemented
203C4C2×D4×D26911yescharacteristic
204C4#2257549911yescharacteristic
205C2—24no—
206C2—10764no—
207C2—21524no—
208C2D4×D107611yescharacteristic
209C2C22×D215211yescharacteristic
210C2#3177141011yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC8×D4×C269C2
socleC22×C269C22×D4
hypercenterC8×D4D269
hypocenterC269D4×D8
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D2152C2semidirect
2. D4×D1076C2semidirect
3. #31770982C2semidirect
4. #31770841C2semidirect
5. #31770801C2semidirect
6. #31770741C2semidirect
7. C4×D2152C2semidirect
8. C8×D4×C269C2semidirect
9. C22×D1076C22semidirect
13. C2×D2152C22semidirect
14. C2×D2152C22semidirect
15. C2×D2152C22semidirect
16. #22575450C22semidirect
18. #22575427C22semidirect
20. C4×D1076C22semidirect
21. #22575387C22semidirect
22. #22575375C22semidirect
23. #22575375C22semidirect
24. C22×C8×C269C22semidirect
26. C4⋊C8×C269C22semidirect
27. C22⋊C8×C269C22semidirect
28. C4×C8×C269C22semidirect
43. D2152D4direct (N × H)
67. D1076C2×D4semidirect
72. D4×C269D8semidirect
81. C8×C269C2×D4semidirect
84. C22×C269C2×D8semidirect
95. C4×C269C2×D8semidirect
105. C269D4×D8semidirect
114. C8×D4D269semidirect
122. C22×C8C2×D269semidirect
130. C4⋊C8C2×D269semidirect
133. C22⋊C8C2×D269semidirect
134. C4×C8C2×D269semidirect
176. D4D2152direct (N × H)
187. C8D4×D269semidirect
197. C22C2×D2152semidirect
202. C4C2×D2152semidirect

Maximal subgroups

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

subgroupindex
C22×D21522
D4×D10762
#317709822
#317708412
#317708012
#317707412
C4×D21522
C8×D4×C2692
D4×D8269