Finite Group Databasebeta

← D82×C31 #21476726

Subgroups — D82×C31 #21476726

Order 7936.

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×C31C214yesmaximal, complemented
2C31×#1712C211yesmaximal, characteristic, complemented
3C31×#1667C214yesmaximal, complemented
4C31×#1619C214yesmaximal, complemented
5C8×D8×C31C212yesmaximal, complemented
6C22×D8×C31—24no—
7D42×C31C2214yescomplemented
8C31×#493C2214yescomplemented
9C31×#493C2212yescomplemented
10C31×#466—24no—
11C31×#459C2218yescomplemented
12C31×#447—28no—
13C4×D8×C31C2212yes—
14C8×D4×C31C2214yescomplemented
15C31×#335C2212yescomplemented
16C31×#331C2214yescomplemented
17C31×D4⋊C8C2214yescomplemented
18C82×C31C2211yescharacteristic, complemented
19C22×D4×C31—28no—
20C2×D8×C31—28no—
21C2×D8×C31—24no—
22C2×D8×C31—24no—
23C2×D8×C31—42no—
24C2×D8×C31—416no—
25C2×D8×C31D412yes—
26C22×C8×C31—24no—
27C31×#127C2314yes—
28C31×#121—28no—
29C31×#120—44no—
30C4×D4×C31C2314yes—
31C31×#107D412yes—
32C31×C4⋊C8C2314yes—
33C31×#102—28no—
34C31×#102D414yes—
35C31×C22⋊C8—24no—
36C4×C8×C31C2311yescharacteristic
37C4×C8×C31C2312yes—
38C24×C31—44no—
39C2×D4×C31—28no—
40C2×D4×C31—24no—
41C2×D4×C31—48no—
42C2×D4×C31—416no—
43C2×D4×C31—88no—
44C2×D4×C31C2×D414yes—
45C22×C4×C31—24no—
46D8×C31—416no—
47D8×C31—48no—
48D8×C31—84no—
49D8×C31—84no—
50D8×C31D818yesdirect product factor
51C2×C8×C31—21no—
52C2×C8×C31—24no—
53C2×C8×C31—48no—
54C2×C8×C31C2×D412yes—
55C2×C8×C31C2×D412yes—
56C4⋊C4×C31C2×D414yes—
57C22⋊C4×C31—24no—
58C22⋊C4×C31—44no—
59C42×C31C2411yescharacteristic
60D82C3111yesmaximal, characteristic, direct product factor, Sylow
61C23×C31—24no—
62C23×C31—44no—
63C23×C31—816no—
64C23×C31—164no—
65D4×C31—24no—
66D4×C31—48no—
67D4×C31—48no—
68D4×C31—84no—
69D4×C31—816no—
70D4×C31C2×D818yescomplemented
71C2×C4×C31—24no—
72C2×C4×C31—44no—
73C2×C4×C31—44no—
74C2×C4×C31C22×D412yes—
75C2×C4×C31H(5,𝔽2)11yescharacteristic
76C8×C31—22no—
77C8×C31—22no—
78C8×C31—44no—
79C8×C31C2×D814yescomplemented
80D4×D8C2×C3114yescomplemented
81#1712C2×C3111yescharacteristic, complemented
82#1667C2×C3114yescomplemented
83#1619C2×C3114yescomplemented
84C8×D8C2×C3112yescomplemented
85C22×C31—28no—
86C22×C31—44no—
87C22×C31—44no—
88C22×C31—88no—
89C22×C31—84no—
90C22×C31—1616no—
91C22×C31D4211yescharacteristic
92C4×C31—21no—
93C4×C31—44no—
94C4×C31C22×D812yes—
95C4×C31#57612yes—
96C22×D8—24no—
97D42C22×C3114yescomplemented
98#493C22×C3114yescomplemented
99#493C22×C3112yescomplemented
100#466—24no—
101#459C22×C3118yescomplemented
102#447—28no—
103C4×D8C22×C3112yes—
104C8×D4C22×C3114yescomplemented
105#335C22×C3112yescomplemented
106#331C22×C3114yescomplemented
107D4⋊C8C22×C3114yescomplemented
108C82C22×C3111yescharacteristic, complemented
109C2×C31—48no—
110C2×C31—164no—
111C2×C31D4×D812yes—
112C2×C31#329211yescharacteristic
113C22×D4—28no—
114C2×D8—28no—
115C2×D8—24no—
116C2×D8—24no—
117C2×D8—42no—
118C2×D8—416no—
119C2×D8D4×C3112yes—
120C22×C8—24no—
121#127C23×C3114yes—
122#121—28no—
123#120—44no—
124C4×D4C23×C3114yes—
125#107D4×C3112yes—
126C4⋊C8C23×C3114yes—
127#102—28no—
128#102D4×C3114yes—
129C22⋊C8—24no—
130C4×C8C23×C3111yescharacteristic
131C4×C8C23×C3112yes—
132C31D8211yescharacteristic, direct product factor, Sylow
133C24—44no—
134C2×D4—28no—
135C2×D4—24no—
136C2×D4—48no—
137C2×D4—416no—
138C2×D4—88no—
139C2×D4C2×D4×C3114yes—
140C22×C4—24no—
141D8—416no—
142D8—48no—
143D8—84no—
144D8—84no—
145D8D8×C3118yesdirect product factor
146C2×C8—21no—
147C2×C8—24no—
148C2×C8—48no—
149C2×C8C2×D4×C3112yes—
150C2×C8C2×D4×C3112yes—
151C4⋊C4C2×D4×C3114yes—
152C22⋊C4—24no—
153C22⋊C4—44no—
154C42C24×C3111yescharacteristic
155C23—24no—
156C23—44no—
157C23—816no—
158C23—164no—
159D4—24no—
160D4—48no—
161D4—48no—
162D4—84no—
163D4—816no—
164D4C2×D8×C3118yescomplemented
165C2×C4—24no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4C22×D4×C3112yes—
169C2×C4C31×H(5,𝔽2)11yescharacteristic
170C8—22no—
171C8—22no—
172C8—44no—
173C8C2×D8×C3114yescomplemented
174C22—28no—
175C22—44no—
176C22—44no—
177C22—88no—
178C22—84no—
179C22—1616no—
180C22D42×C3111yescharacteristic
181C4—21no—
182C4—44no—
183C4C22×D8×C3112yes—
184C4C31×#57612yes—
185C2—48no—
186C2—164no—
187C2D4×D8×C3112yes—
188C2C31×#329211yescharacteristic
subgroupG/H
center, socleC22×C31D42
commutator, Frattini, cosocleC42C24×C31
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. D4×D8×C31C2semidirect
2. C31×#1712C2semidirect
3. C31×#1667C2semidirect
4. C31×#1619C2semidirect
5. C8×D8×C31C2semidirect
7. D42×C31C22semidirect
8. C31×#493C22semidirect
9. C31×#493C22semidirect
11. C31×#459C22semidirect
14. C8×D4×C31C22semidirect
15. C31×#335C22semidirect
16. C31×#331C22semidirect
17. C31×D4⋊C8C22semidirect
18. C82×C31C22semidirect
50. D8×C31D8direct (N × H)
60. D82C31direct (N × H)
70. D4×C31C2×D8semidirect
79. C8×C31C2×D8semidirect
80. D4×D8C2×C31semidirect
81. #1712C2×C31semidirect
82. #1667C2×C31semidirect
83. #1619C2×C31semidirect
84. C8×D8C2×C31semidirect
97. D42C22×C31semidirect
98. #493C22×C31semidirect
99. #493C22×C31semidirect
101. #459C22×C31semidirect
104. C8×D4C22×C31semidirect
105. #335C22×C31semidirect
106. #331C22×C31semidirect
107. D4⋊C8C22×C31semidirect
108. C82C22×C31semidirect
132. C31D82direct (N × H)
145. D8D8×C31direct (N × H)
164. D4C2×D8×C31semidirect
173. C8C2×D8×C31semidirect

Maximal subgroups

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

subgroupindex
D4×D8×C312
C31×#17122
C31×#16672
C31×#16192
C8×D8×C312
D8231