Finite Group Databasebeta

← D8×D356 #26031928

Subgroups — D8×D356 #26031928

Order 11392.

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×D89C212yesmaximal, complemented
2D4×D356C212yesmaximal, complemented
3#19151975C211yesmaximal, characteristic, complemented
4#19151835C212yesmaximal, complemented
5#19151793C212yesmaximal, complemented
6#19151733C214yesmaximal, complemented
7C8×D356C211yesmaximal, characteristic, complemented
8C4×D8×C89C211yesmaximal, characteristic, complemented
9C22×D356—22no—
10C2×D4×D89C2214yescomplemented
11C2×D712C2212yescomplemented
12C2×D712C2212yescomplemented
13C2×#13083559C2214yescomplemented
14D8×D89—28no—
15C2×C8×D89C2212yescomplemented
16#15668009C2212yescomplemented
17#15667987C2214yescomplemented
18#15667986—22no—
19#15667982—24no—
20C4×D356C2211yescharacteristic
21C4⋊#10623494C2211yescharacteristic, complemented
22#15667932C2214yescomplemented
23#15667924C2212yescomplemented
24C2×D8×C89C2211yescharacteristic
25C4×D4×C89C2212yescomplemented
26#107×C89C2211yescharacteristic, complemented
27#102×C89C2212yescomplemented
28C4×C8×C89C2211yescharacteristic, complemented
29C23×D89—24no—
30C2×D356—24no—
31C2×D356—22no—
32C2×D356—22no—
33C2×D356—48no—
34C2×D356D411yescharacteristic
35C2×D356C2314yes—
36C2×C22⋊D89—24no—
37D4×D89—28no—
38D4×D89—44no—
39C2×C4×D89C2312yes—
40D712—24no—
41D712—42no—
42#13083559—28no—
43C2×#10623494C2312yes—
44C8×D89—24no—
45C4⋊Dic89D411yescharacteristic
46#13083551—24no—
47#13083551D412yes—
48C2×D4×C89C2312yes—
49C22×C4×C89—22no—
50D8×C89D414yescomplemented
51C2×C8×C89C2311yescharacteristic
52C2×C8×C89C2311yescharacteristic
53C4⋊C4×C89C2312yes—
54C22⋊C4×C89—22no—
55C42×C89C2311yescharacteristic
56C23×C89—22no—
57C22×D89—24no—
58C22×D89—48no—
59C22×D89—48no—
60C22×D89—84no—
61C22×D89C2×D412yes—
62D4×C89—22no—
63D4×C89C2×D414yescomplemented
64C2×C4×C89—22no—
65C2×C4×C89—44no—
66C2×C4×C89C2×D411yescharacteristic
67C2×C4×C89C2×D411yescharacteristic
68C2×C4×C89C2411yescharacteristic
69C22⋊D89—48no—
70C2×Dic89C2×D412yes—
71D356—24no—
72D356—24no—
73D356—48no—
74D356—44no—
75D356—82no—
76D356D814yesdirect product factor
77C4×D89—22no—
78C4×D89—22no—
79C8×C89—21no—
80C8×C89C2×D412yescomplemented
81#10623494—22no—
82C22×C89—24no—
83C22×C89—42no—
84C22×C89—42no—
85C22×C89C22×D411yescharacteristic
86C2×D89—22no—
87C2×D89—22no—
88C2×D89—44no—
89C2×D89—44no—
90C2×D89—44no—
91C2×D89—816no—
92C2×D89C2×D814yescomplemented
93C4×C89—21no—
94C4×C89—42no—
95C4×C89C2×D812yescomplemented
96C4×C89C22×D411yescharacteristic
97C4×C89H(5,𝔽2)11yescharacteristic
98Dic89—22no—
99C2×C89—44no—
100C2×C89D4211yescharacteristic
101C2×C89C22×D811yescharacteristic
102C2×C89#57611yescharacteristic
103D89—24no—
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×D8D8911yescharacteristic, complemented
114C8×D4—891no—
115C22×D4—894no—
116C22×D4—1782no—
117C2×D8—894no—
118C2×D8—892no—
119C2×D8—892no—
120C2×D8—1788no—
121C2×D8C2×D8911yescharacteristic
122C22×C8—892no—
123#127—892no—
124#121—894no—
125#121—1782no—
126#120—1784no—
127C4×D4—891no—
128C4×D4C2×D8912yescomplemented
129#107C2×D8911yescharacteristic, complemented
130C4⋊C8—891no—
131#102—894no—
132#102C2×D8912yescomplemented
133C22⋊C8—892no—
134C4×C8C2×D8911yescharacteristic, complemented
135C24—1784no—
136C2×D4—891no—
137C2×D4—894no—
138C2×D4—3568no—
139C2×D4—3564no—
140C2×D4—1784no—
141C2×D4—1784no—
142C2×D4—1788no—
143C2×D4—1782no—
144C2×D4—1782no—
145C2×D4C22×D8912yes—
146C22×C4—22no—
147C22×C4—892no—
148D8—3562no—
149D8—1788no—
150D8—1784no—
151D8D35614yesdirect product factor
152C2×C8—892no—
153C2×C8—1784no—
154C2×C8C22×D8911yescharacteristic
155C2×C8C22×D8911yescharacteristic
156C4⋊C4—891no—
157C4⋊C4C22×D8912yes—
158C22⋊C4—22no—
159C22⋊C4—892no—
160C22⋊C4—1784no—
161C42C22×D8911yescharacteristic
162C23—22no—
163C23—892no—
164C23—3568no—
165C23—3568no—
166C23—1784no—
167C23—7124no—
168D4—22no—
169D4—894no—
170D4—3568no—
171D4—3568no—
172D4—3564no—
173D4—1784no—
174D4—1784no—
175D4—7122no—
176D4C2×D35614yescomplemented
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—892no—
180C2×C4—1782no—
181C2×C4—1782no—
182C2×C4D4×D8911yescharacteristic
183C2×C4D4×D8911yescharacteristic
184C2×C4C23×D8911yescharacteristic
185C8—21no—
186C8—1782no—
187C8C2×D35612yescomplemented
188C22—24no—
189C22—42no—
190C22—42no—
191C22—894no—
192C22—3564no—
193C22—3564no—
194C22—3564no—
195C22—1782no—
196C22—1782no—
197C22—71216no—
198C22C2×D4×D8911yescharacteristic
199C4—21no—
200C4—42no—
201C4—1782no—
202C4D8×D8912yescomplemented
203C4C22×D35611yescharacteristic
204C4#1566805811yescharacteristic
205C2—44no—
206C2—1784no—
207C2—7124no—
208C2D4×D35611yescharacteristic
209C2C2×D8×D8911yescharacteristic
210C2#1915240011yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC4×D8×C89C2
socleC22×C89C22×D4
hypercenterC4×D8D89
hypocenterC89D4×D8
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D89C2semidirect
2. D4×D356C2semidirect
3. #19151975C2semidirect
4. #19151835C2semidirect
5. #19151793C2semidirect
6. #19151733C2semidirect
7. C8×D356C2semidirect
8. C4×D8×C89C2semidirect
10. C2×D4×D89C22semidirect
11. C2×D712C22semidirect
12. C2×D712C22semidirect
13. C2×#13083559C22semidirect
15. C2×C8×D89C22semidirect
16. #15668009C22semidirect
17. #15667987C22semidirect
21. C4⋊#10623494C22semidirect
22. #15667932C22semidirect
23. #15667924C22semidirect
25. C4×D4×C89C22semidirect
26. #107×C89C22semidirect
27. #102×C89C22semidirect
28. C4×C8×C89C22semidirect
50. D8×C89D4semidirect
63. D4×C89C2×D4semidirect
76. D356D8direct (N × H)
80. C8×C89C2×D4semidirect
92. C2×D89C2×D8semidirect
95. C4×C89C2×D8semidirect
106. C89D4×D8semidirect
113. C4×D8D89semidirect
128. C4×D4C2×D89semidirect
129. #107C2×D89semidirect
132. #102C2×D89semidirect
134. C4×C8C2×D89semidirect
151. D8D356direct (N × H)
176. D4C2×D356semidirect
187. C8C2×D356semidirect
202. C4D8×D89semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D892
D4×D3562
#191519752
#191518352
#191517932
#191517332
C8×D3562
C4×D8×C892
D4×D889