Finite Group Databasebeta

← D82×C103 #39925242

Subgroups — D82×C103 #39925242

Order 26368.

918 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 238 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
1D4×D8×C103C214yesmaximal, complemented
2C103×#1712C211yesmaximal, characteristic, complemented
3C103×#1667C214yesmaximal, complemented
4C103×#1619C214yesmaximal, complemented
5C8×D8×C103C212yesmaximal, complemented
6C22×D8×C103—24no—
7D42×C103C2214yescomplemented
8#493×C103C2214yescomplemented
9#493×C103C2212yescomplemented
10#466×C103—24no—
11#459×C103C2218yescomplemented
12#447×C103—28no—
13C4×D8×C103C2212yes—
14C8×D4×C103C2214yescomplemented
15#335×C103C2212yescomplemented
16#331×C103C2214yescomplemented
17D4⋊C8×C103C2214yescomplemented
18C82×C103C2211yescharacteristic, complemented
19C22×D4×C103—28no—
20C2×D8×C103—28no—
21C2×D8×C103—24no—
22C2×D8×C103—24no—
23C2×D8×C103—42no—
24C2×D8×C103—416no—
25C2×D8×C103D412yes—
26C22×C8×C103—24no—
27#127×C103C2314yes—
28#121×C103—28no—
29#120×C103—44no—
30C4×D4×C103C2314yes—
31#107×C103D412yes—
32C4⋊C8×C103C2314yes—
33#102×C103—28no—
34#102×C103D414yes—
35C22⋊C8×C103—24no—
36C4×C8×C103C2311yescharacteristic
37C4×C8×C103C2312yes—
38C24×C103—44no—
39C2×D4×C103—28no—
40C2×D4×C103—24no—
41C2×D4×C103—48no—
42C2×D4×C103—416no—
43C2×D4×C103—88no—
44C2×D4×C103C2×D414yes—
45C22×C4×C103—24no—
46D8×C103—416no—
47D8×C103—48no—
48D8×C103—84no—
49D8×C103—84no—
50D8×C103D818yesdirect product factor
51C2×C8×C103—21no—
52C2×C8×C103—24no—
53C2×C8×C103—48no—
54C2×C8×C103C2×D412yes—
55C2×C8×C103C2×D412yes—
56C4⋊C4×C103C2×D414yes—
57C22⋊C4×C103—24no—
58C22⋊C4×C103—44no—
59C42×C103C2411yescharacteristic
60C23×C103—24no—
61C23×C103—44no—
62C23×C103—816no—
63C23×C103—164no—
64D4×C103—24no—
65D4×C103—48no—
66D4×C103—48no—
67D4×C103—84no—
68D4×C103—816no—
69D4×C103C2×D818yescomplemented
70C2×C4×C103—24no—
71C2×C4×C103—44no—
72C2×C4×C103—44no—
73C2×C4×C103C22×D412yes—
74C2×C4×C103H(5,𝔽2)11yescharacteristic
75C8×C103—22no—
76C8×C103—22no—
77C8×C103—44no—
78C8×C103C2×D814yescomplemented
79C22×C103—28no—
80C22×C103—44no—
81C22×C103—44no—
82C22×C103—88no—
83C22×C103—84no—
84C22×C103—1616no—
85C22×C103D4211yescharacteristic
86C4×C103—21no—
87C4×C103—44no—
88C4×C103C22×D812yes—
89C4×C103#57612yes—
90D82C10311yesmaximal, characteristic, direct product factor, Sylow
91C2×C103—48no—
92C2×C103—164no—
93C2×C103D4×D812yes—
94C2×C103#329211yescharacteristic
95D4×D8C2×C10314yescomplemented
96#1712C2×C10311yescharacteristic, complemented
97#1667C2×C10314yescomplemented
98#1619C2×C10314yescomplemented
99C8×D8C2×C10312yescomplemented
100C103D8211yescharacteristic, direct product factor, Sylow
101C22×D8—24no—
102D42C22×C10314yescomplemented
103#493C22×C10314yescomplemented
104#493C22×C10312yescomplemented
105#466—24no—
106#459C22×C10318yescomplemented
107#447—28no—
108C4×D8C22×C10312yes—
109C8×D4C22×C10314yescomplemented
110#335C22×C10312yescomplemented
111#331C22×C10314yescomplemented
112D4⋊C8C22×C10314yescomplemented
113C82C22×C10311yescharacteristic, complemented
114C22×D4—28no—
115C2×D8—28no—
116C2×D8—24no—
117C2×D8—24no—
118C2×D8—42no—
119C2×D8—416no—
120C2×D8D4×C10312yes—
121C22×C8—24no—
122#127C23×C10314yes—
123#121—28no—
124#120—44no—
125C4×D4C23×C10314yes—
126#107D4×C10312yes—
127C4⋊C8C23×C10314yes—
128#102—28no—
129#102D4×C10314yes—
130C22⋊C8—24no—
131C4×C8C23×C10311yescharacteristic
132C4×C8C23×C10312yes—
133C24—44no—
134C2×D4—28no—
135C2×D4—24no—
136C2×D4—48no—
137C2×D4—416no—
138C2×D4—88no—
139C2×D4C2×D4×C10314yes—
140C22×C4—24no—
141D8—416no—
142D8—48no—
143D8—84no—
144D8—84no—
145D8D8×C10318yesdirect product factor
146C2×C8—21no—
147C2×C8—24no—
148C2×C8—48no—
149C2×C8C2×D4×C10312yes—
150C2×C8C2×D4×C10312yes—
151C4⋊C4C2×D4×C10314yes—
152C22⋊C4—24no—
153C22⋊C4—44no—
154C42C24×C10311yescharacteristic
155C23—24no—
156C23—44no—
157C23—816no—
158C23—164no—
159D4—24no—
160D4—48no—
161D4—48no—
162D4—84no—
163D4—816no—
164D4C2×D8×C10318yescomplemented
165C2×C4—24no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4C22×D4×C10312yes—
169C2×C4H(5,𝔽2)×C10311yescharacteristic
170C8—22no—
171C8—22no—
172C8—44no—
173C8C2×D8×C10314yescomplemented
174C22—28no—
175C22—44no—
176C22—44no—
177C22—88no—
178C22—84no—
179C22—1616no—
180C22D42×C10311yescharacteristic
181C4—21no—
182C4—44no—
183C4C22×D8×C10312yes—
184C4#576×C10312yes—
185C2—48no—
186C2—164no—
187C2D4×D8×C10312yes—
188C2C103×#329211yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC42C24×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. D4×D8×C103C2semidirect
2. C103×#1712C2semidirect
3. C103×#1667C2semidirect
4. C103×#1619C2semidirect
5. C8×D8×C103C2semidirect
7. D42×C103C22semidirect
8. #493×C103C22semidirect
9. #493×C103C22semidirect
11. #459×C103C22semidirect
14. C8×D4×C103C22semidirect
15. #335×C103C22semidirect
16. #331×C103C22semidirect
17. D4⋊C8×C103C22semidirect
18. C82×C103C22semidirect
50. D8×C103D8direct (N × H)
69. D4×C103C2×D8semidirect
78. C8×C103C2×D8semidirect
90. D82C103direct (N × H)
95. D4×D8C2×C103semidirect
96. #1712C2×C103semidirect
97. #1667C2×C103semidirect
98. #1619C2×C103semidirect
99. C8×D8C2×C103semidirect
100. C103D82direct (N × H)
102. D42C22×C103semidirect
103. #493C22×C103semidirect
104. #493C22×C103semidirect
106. #459C22×C103semidirect
109. C8×D4C22×C103semidirect
110. #335C22×C103semidirect
111. #331C22×C103semidirect
112. D4⋊C8C22×C103semidirect
113. C82C22×C103semidirect
145. D8D8×C103direct (N × H)
164. D4C2×D8×C103semidirect
173. C8C2×D8×C103semidirect

Maximal subgroups

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

subgroupindex
D4×D8×C1032
C103×#17122
C103×#16672
C103×#16192
C8×D8×C1032
D82103