Finite Group Databasebeta

← D8×D1076 #46822561

Subgroups — D8×D1076 #46822561

Order 34432.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×D8×D269C212yesmaximal, complemented
2D4×D1076C212yesmaximal, complemented
3#31770982C211yesmaximal, characteristic, complemented
4#31770842C212yesmaximal, complemented
5#31770800C212yesmaximal, complemented
6#31770740C214yesmaximal, complemented
7C8×D1076C211yesmaximal, characteristic, complemented
8C4×D8×C269C211yesmaximal, characteristic, complemented
9C22×D1076—22no—
10C2×D4×D269C2214yescomplemented
11C2×D2152C2212yescomplemented
12C2×D2152C2212yescomplemented
13C2×#16864387C2214yescomplemented
14D8×D269—28no—
15C2×C8×D269C2212yescomplemented
16#22575450C2212yescomplemented
17#22575428C2214yescomplemented
18#22575427—22no—
19#22575423—24no—
20C4×D1076C2211yescharacteristic
21C4⋊#14524130C2211yescharacteristic, complemented
22#22575373C2214yescomplemented
23#22575365C2212yescomplemented
24C2×D8×C269C2211yescharacteristic
25C4×D4×C269C2212yescomplemented
26#107×C269C2211yescharacteristic, complemented
27#102×C269C2212yescomplemented
28C4×C8×C269C2211yescharacteristic, complemented
29C23×D269—24no—
30C2×D1076—24no—
31C2×D1076—22no—
32C2×D1076—22no—
33C2×D1076—48no—
34C2×D1076D411yescharacteristic
35C2×D1076C2314yes—
36C2×C22⋊D269—24no—
37D4×D269—28no—
38D4×D269—44no—
39C2×C4×D269C2312yes—
40D2152—24no—
41D2152—42no—
42#16864387—28no—
43C2×#14524130C2312yes—
44C8×D269—24no—
45C4⋊Dic269D411yescharacteristic
46#16864379—24no—
47#16864379D412yes—
48C2×D4×C269C2312yes—
49C22×C4×C269—22no—
50D8×C269D414yescomplemented
51C2×C8×C269C2311yescharacteristic
52C2×C8×C269C2311yescharacteristic
53C4⋊C4×C269C2312yes—
54C22⋊C4×C269—22no—
55C42×C269C2311yescharacteristic
56C22×D269—24no—
57C22×D269—48no—
58C22×D269—48no—
59C22×D269—84no—
60C22×D269C2×D412yes—
61D1076—24no—
62D1076—24no—
63D1076—48no—
64D1076—44no—
65D1076—82no—
66D1076D814yesdirect product factor
67C22⋊D269—48no—
68C2×Dic269C2×D412yes—
69C4×D269—22no—
70C4×D269—22no—
71#14524130—22no—
72C23×C269—22no—
73D4×C269—22no—
74D4×C269C2×D414yescomplemented
75C2×C4×C269—22no—
76C2×C4×C269—44no—
77C2×C4×C269C2×D411yescharacteristic
78C2×C4×C269C2×D411yescharacteristic
79C2×C4×C269C2411yescharacteristic
80C8×C269—21no—
81C8×C269C2×D412yescomplemented
82C22×C269—24no—
83C22×C269—42no—
84C22×C269—42no—
85C22×C269C22×D411yescharacteristic
86C2×D269—22no—
87C2×D269—22no—
88C2×D269—44no—
89C2×D269—44no—
90C2×D269—44no—
91C2×D269—816no—
92C2×D269C2×D814yescomplemented
93C4×C269—21no—
94C4×C269—42no—
95C4×C269C2×D812yescomplemented
96C4×C269C22×D411yescharacteristic
97C4×C269H(5,𝔽2)11yescharacteristic
98Dic269—22no—
99C2×C269—44no—
100C2×C269D4211yescharacteristic
101C2×C269C22×D811yescharacteristic
102C2×C269#57611yescharacteristic
103D269—24no—
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×D8D26911yescharacteristic, complemented
114C8×D4—2691no—
115C22×D4—2694no—
116C22×D4—5382no—
117C2×D8—2694no—
118C2×D8—2692no—
119C2×D8—2692no—
120C2×D8—5388no—
121C2×D8C2×D26911yescharacteristic
122C22×C8—2692no—
123#127—2692no—
124#121—2694no—
125#121—5382no—
126#120—5384no—
127C4×D4—2691no—
128C4×D4C2×D26912yescomplemented
129#107C2×D26911yescharacteristic, complemented
130C4⋊C8—2691no—
131#102—2694no—
132#102C2×D26912yescomplemented
133C22⋊C8—2692no—
134C4×C8C2×D26911yescharacteristic, complemented
135C24—5384no—
136C2×D4—2691no—
137C2×D4—2694no—
138C2×D4—5384no—
139C2×D4—5384no—
140C2×D4—5388no—
141C2×D4—5382no—
142C2×D4—5382no—
143C2×D4—10768no—
144C2×D4—10764no—
145C2×D4C22×D26912yes—
146C22×C4—22no—
147C22×C4—2692no—
148D8—5388no—
149D8—5384no—
150D8—10762no—
151D8D107614yesdirect product factor
152C2×C8—2692no—
153C2×C8—5384no—
154C2×C8C22×D26911yescharacteristic
155C2×C8C22×D26911yescharacteristic
156C4⋊C4—2691no—
157C4⋊C4C22×D26912yes—
158C22⋊C4—22no—
159C22⋊C4—2692no—
160C22⋊C4—5384no—
161C42C22×D26911yescharacteristic
162C23—22no—
163C23—2692no—
164C23—5384no—
165C23—10768no—
166C23—10768no—
167C23—21524no—
168D4—22no—
169D4—2694no—
170D4—5384no—
171D4—5384no—
172D4—10768no—
173D4—10768no—
174D4—10764no—
175D4—21522no—
176D4C2×D107614yescomplemented
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—2692no—
180C2×C4—5382no—
181C2×C4—5382no—
182C2×C4D4×D26911yescharacteristic
183C2×C4D4×D26911yescharacteristic
184C2×C4C23×D26911yescharacteristic
185C8—21no—
186C8—5382no—
187C8C2×D107612yescomplemented
188C22—24no—
189C22—42no—
190C22—42no—
191C22—2694no—
192C22—5382no—
193C22—5382no—
194C22—10764no—
195C22—10764no—
196C22—10764no—
197C22—215216no—
198C22C2×D4×D26911yescharacteristic
199C4—21no—
200C4—42no—
201C4—5382no—
202C4D8×D26912yescomplemented
203C4C22×D107611yescharacteristic
204C4#2257549911yescharacteristic
205C2—44no—
206C2—5384no—
207C2—21524no—
208C2D4×D107611yescharacteristic
209C2C2×D8×D26911yescharacteristic
210C2#3177140711yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC4×D8×C269C2
socleC22×C269C22×D4
hypercenterC4×D8D269
hypocenterC269D4×D8
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D269C2semidirect
2. D4×D1076C2semidirect
3. #31770982C2semidirect
4. #31770842C2semidirect
5. #31770800C2semidirect
6. #31770740C2semidirect
7. C8×D1076C2semidirect
8. C4×D8×C269C2semidirect
10. C2×D4×D269C22semidirect
11. C2×D2152C22semidirect
12. C2×D2152C22semidirect
13. C2×#16864387C22semidirect
15. C2×C8×D269C22semidirect
16. #22575450C22semidirect
17. #22575428C22semidirect
21. C4⋊#14524130C22semidirect
22. #22575373C22semidirect
23. #22575365C22semidirect
25. C4×D4×C269C22semidirect
26. #107×C269C22semidirect
27. #102×C269C22semidirect
28. C4×C8×C269C22semidirect
50. D8×C269D4semidirect
66. D1076D8direct (N × H)
74. D4×C269C2×D4semidirect
81. C8×C269C2×D4semidirect
92. C2×D269C2×D8semidirect
95. C4×C269C2×D8semidirect
105. C269D4×D8semidirect
113. C4×D8D269semidirect
128. C4×D4C2×D269semidirect
129. #107C2×D269semidirect
132. #102C2×D269semidirect
134. C4×C8C2×D269semidirect
151. D8D1076direct (N × H)
176. D4C2×D1076semidirect
187. C8C2×D1076semidirect
202. C4D8×D269semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2692
D4×D10762
#317709822
#317708422
#317708002
#317707402
C8×D10762
C4×D8×C2692
D4×D8269