Finite Group Databasebeta

← D4×D712 #26031929

Subgroups — D4×D712 #26031929

Order 11392.

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×D712C212yesmaximal, complemented
2D4×D356C212yesmaximal, complemented
3#19151975C211yesmaximal, characteristic, complemented
4#19151834C212yesmaximal, complemented
5#19151794C212yesmaximal, complemented
6#19151734C214yesmaximal, complemented
7C4×D712C211yesmaximal, characteristic, complemented
8C8×D4×C89C211yesmaximal, characteristic, complemented
9C22×D356C2214yescomplemented
10C2×D4×D89—22no—
11C2×D712—28no—
12C2×D712C2211yescharacteristic
13C2×D712C2212yescomplemented
14C2×D712C2214yescomplemented
15C2×D712C2212yescomplemented
16#15668009C2212yescomplemented
17#15667987—22no—
18#15667986C2214yescomplemented
19#15667982—24no—
20C4×D356C2212yescomplemented
21#15667946C2211yescharacteristic, complemented
22#15667934C2212yescomplemented
23#15667934C2214yescomplemented
24C22×C8×C89C2212yescomplemented
25C4×D4×C89C2211yescharacteristic
26C4⋊C8×C89C2211yescharacteristic, complemented
27C22⋊C8×C89C2212yescomplemented
28C4×C8×C89C2211yescharacteristic, complemented
29C23×D89—24no—
30C2×D356—28no—
31C2×D356—24no—
32C2×D356—22no—
33C2×D356—22no—
34C2×D356—44no—
35C2×D356C2314yes—
36C2×D356C2312yes—
37C2×C22⋊D89—24no—
38D4×D89—48no—
39C2×C4×D89—22no—
40D712—28no—
41D712—24no—
42D712—42no—
43D712D414yesdirect product factor
44C4⋊Dic89C2312yes—
45#13083551—22no—
46#13083551—24no—
47C2×D4×C89D411yescharacteristic
48C22×C4×C89C2312yes—
49C2×C8×C89—24no—
50C2×C8×C89C2311yescharacteristic
51C2×C8×C89C2312yes—
52C2×C8×C89C2311yescharacteristic
53C4⋊C4×C89D411yescharacteristic
54C22⋊C4×C89D412yes—
55C42×C89C2311yescharacteristic
56C23×C89C2×D412yes—
57C22×D89—22no—
58C22×D89—24no—
59C22×D89—48no—
60C22×D89—48no—
61C22×D89—84no—
62D4×C89D814yescomplemented
63C2×C4×C89—22no—
64C2×C4×C89—22no—
65C2×C4×C89C2×D411yescharacteristic
66C2×C4×C89C2×D412yes—
67C2×C4×C89C2×D411yescharacteristic
68C2×C4×C89C2411yescharacteristic
69C22⋊D89—48no—
70C2×Dic89—22no—
71D356—24no—
72D356—22no—
73D356—24no—
74D356—48no—
75D356—44no—
76D356—82no—
77D356C2×D414yescomplemented
78C4×D89—44no—
79C8×C89—22no—
80C8×C89—21no—
81C8×C89C2×D412yescomplemented
82C22×C89—22no—
83C22×C89—22no—
84C22×C89C2×D814yescomplemented
85C22×C89C22×D411yescharacteristic
86C2×D89—24no—
87C2×D89—42no—
88C2×D89—42no—
89C2×D89—44no—
90C2×D89—44no—
91C2×D89—44no—
92C2×D89—816no—
93C4×C89—22no—
94C4×C89—21no—
95C4×C89C2×D812yescomplemented
96C4×C89C22×D411yescharacteristic
97C4×C89H(5,𝔽2)11yescharacteristic
98Dic89—42no—
99C2×C89—24no—
100C2×C89D4211yescharacteristic
101C2×C89C22×D811yescharacteristic
102C2×C89#57611yescharacteristic
103D89—44no—
104D89—84no—
105D4×D8—891nomaximal, Sylow
106C89D4×D811yescharacteristic, complemented, Sylow
107C22×D8—892no—
108D42—892no—
109#493—891no—
110#466—892no—
111#459—892no—
112#447—894no—
113C4×D8—891no—
114C8×D4D8911yescharacteristic, complemented
115C22×D4—894no—
116C22×D4—1782no—
117C2×D8—891no—
118C2×D8—892no—
119C2×D8—894no—
120C2×D8—892no—
121C2×D8—1788no—
122C22×C8C2×D8912yescomplemented
123#127—892no—
124#121—894no—
125#121—1782no—
126#120—1784no—
127C4×D4—892no—
128C4×D4C2×D8911yescharacteristic
129#107—891no—
130C4⋊C8C2×D8911yescharacteristic, complemented
131#102—892no—
132#102—894no—
133C22⋊C8C2×D8912yescomplemented
134C4×C8C2×D8911yescharacteristic, complemented
135C24—1784no—
136C2×D4—892no—
137C2×D4—894no—
138C2×D4—3564no—
139C2×D4—3568no—
140C2×D4—1788no—
141C2×D4—1784no—
142C2×D4—1784no—
143C2×D4—1782no—
144C2×D4—1782no—
145C2×D4D35611yescharacteristic
146C22×C4—1782no—
147C22×C4C22×D8912yes—
148D8—894no—
149D8—3562no—
150D8—1788no—
151D8—1784no—
152C2×C8—24no—
153C2×C8C22×D8911yescharacteristic
154C2×C8C22×D8912yes—
155C2×C8C22×D8911yescharacteristic
156C4⋊C4—892no—
157C4⋊C4D35611yescharacteristic
158C22⋊C4—1782no—
159C22⋊C4—1784no—
160C22⋊C4D35612yes—
161C42C22×D8911yescharacteristic
162C23—3568no—
163C23—3568no—
164C23—1784no—
165C23—1782no—
166C23—7124no—
167C23C2×D35612yes—
168D4—894no—
169D4—3568no—
170D4—3568no—
171D4—3564no—
172D4—1784no—
173D4—1784no—
174D4—1782no—
175D4—7122no—
176D4D71214yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3564no—
180C2×C4—1782no—
181C2×C4C2×D35611yescharacteristic
182C2×C4C2×D35612yes—
183C2×C4C2×D35611yescharacteristic
184C2×C4C23×D8911yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D8912yescomplemented
188C22—22no—
189C22—22no—
190C22—3562no—
191C22—3562no—
192C22—3564no—
193C22—3564no—
194C22—3564no—
195C22—1784no—
196C22—71216no—
197C22C2×D71214yescomplemented
198C22C22×D35611yescharacteristic
199C4—21no—
200C4—22no—
201C4—3562no—
202C4C2×D71212yescomplemented
203C4C2×D4×D8911yescharacteristic
204C4#1566805811yescharacteristic
205C2—24no—
206C2—3564no—
207C2—7124no—
208C2D4×D35611yescharacteristic
209C2C22×D71211yescharacteristic
210C2#1915240311yescharacteristic
subgroupG/H
centerC22C22×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC8×D4×C89C2
socleC22×C89C22×D4
hypercenterC8×D4D89
hypocenterC89D4×D8
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D712C2semidirect
2. D4×D356C2semidirect
3. #19151975C2semidirect
4. #19151834C2semidirect
5. #19151794C2semidirect
6. #19151734C2semidirect
7. C4×D712C2semidirect
8. C8×D4×C89C2semidirect
9. C22×D356C22semidirect
13. C2×D712C22semidirect
14. C2×D712C22semidirect
15. C2×D712C22semidirect
16. #15668009C22semidirect
18. #15667986C22semidirect
20. C4×D356C22semidirect
21. #15667946C22semidirect
22. #15667934C22semidirect
23. #15667934C22semidirect
24. C22×C8×C89C22semidirect
26. C4⋊C8×C89C22semidirect
27. C22⋊C8×C89C22semidirect
28. C4×C8×C89C22semidirect
43. D712D4direct (N × H)
62. D4×C89D8semidirect
77. D356C2×D4semidirect
81. C8×C89C2×D4semidirect
84. C22×C89C2×D8semidirect
95. C4×C89C2×D8semidirect
106. C89D4×D8semidirect
114. C8×D4D89semidirect
122. C22×C8C2×D89semidirect
130. C4⋊C8C2×D89semidirect
133. C22⋊C8C2×D89semidirect
134. C4×C8C2×D89semidirect
176. D4D712direct (N × H)
187. C8D4×D89semidirect
197. C22C2×D712semidirect
202. C4C2×D712semidirect

Maximal subgroups

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

subgroupindex
C22×D7122
D4×D3562
#191519752
#191518342
#191517942
#191517342
C4×D7122
C8×D4×C892
D4×D889