Finite Group Databasebeta

← D82×C61 #29523400

Subgroups — D82×C61 #29523400

Order 15616.

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×C61C214yesmaximal, complemented
2C61×#1712C211yesmaximal, characteristic, complemented
3C61×#1667C214yesmaximal, complemented
4C61×#1619C214yesmaximal, complemented
5C8×D8×C61C212yesmaximal, complemented
6C22×D8×C61—24no—
7D42×C61C2214yescomplemented
8C61×#493C2214yescomplemented
9C61×#493C2212yescomplemented
10C61×#466—24no—
11C61×#459C2218yescomplemented
12C61×#447—28no—
13C4×D8×C61C2212yes—
14C8×D4×C61C2214yescomplemented
15C61×#335C2212yescomplemented
16C61×#331C2214yescomplemented
17C61×D4⋊C8C2214yescomplemented
18C82×C61C2211yescharacteristic, complemented
19C22×D4×C61—28no—
20C2×D8×C61—28no—
21C2×D8×C61—24no—
22C2×D8×C61—24no—
23C2×D8×C61—42no—
24C2×D8×C61—416no—
25C2×D8×C61D412yes—
26C22×C8×C61—24no—
27#127×C61C2314yes—
28#121×C61—28no—
29#120×C61—44no—
30C4×D4×C61C2314yes—
31#107×C61D412yes—
32C4⋊C8×C61C2314yes—
33#102×C61—28no—
34#102×C61D414yes—
35C22⋊C8×C61—24no—
36C4×C8×C61C2311yescharacteristic
37C4×C8×C61C2312yes—
38C24×C61—44no—
39C2×D4×C61—28no—
40C2×D4×C61—24no—
41C2×D4×C61—48no—
42C2×D4×C61—416no—
43C2×D4×C61—88no—
44C2×D4×C61C2×D414yes—
45C22×C4×C61—24no—
46D8×C61—416no—
47D8×C61—48no—
48D8×C61—84no—
49D8×C61—84no—
50D8×C61D818yesdirect product factor
51C2×C8×C61—21no—
52C2×C8×C61—24no—
53C2×C8×C61—48no—
54C2×C8×C61C2×D412yes—
55C2×C8×C61C2×D412yes—
56C4⋊C4×C61C2×D414yes—
57C22⋊C4×C61—24no—
58C22⋊C4×C61—44no—
59C42×C61C2411yescharacteristic
60C23×C61—24no—
61C23×C61—44no—
62C23×C61—816no—
63C23×C61—164no—
64D4×C61—24no—
65D4×C61—48no—
66D4×C61—48no—
67D4×C61—84no—
68D4×C61—816no—
69D4×C61C2×D818yescomplemented
70C2×C4×C61—24no—
71C2×C4×C61—44no—
72C2×C4×C61—44no—
73C2×C4×C61C22×D412yes—
74C2×C4×C61H(5,𝔽2)11yescharacteristic
75C8×C61—22no—
76C8×C61—22no—
77C8×C61—44no—
78C8×C61C2×D814yescomplemented
79D82C6111yesmaximal, characteristic, direct product factor, Sylow
80C22×C61—28no—
81C22×C61—44no—
82C22×C61—44no—
83C22×C61—88no—
84C22×C61—84no—
85C22×C61—1616no—
86C22×C61D4211yescharacteristic
87C4×C61—21no—
88C4×C61—44no—
89C4×C61C22×D812yes—
90C4×C61#57612yes—
91D4×D8C2×C6114yescomplemented
92#1712C2×C6111yescharacteristic, complemented
93#1667C2×C6114yescomplemented
94#1619C2×C6114yescomplemented
95C8×D8C2×C6112yescomplemented
96C2×C61—48no—
97C2×C61—164no—
98C2×C61D4×D812yes—
99C2×C61#329211yescharacteristic
100C22×D8—24no—
101D42C22×C6114yescomplemented
102#493C22×C6114yescomplemented
103#493C22×C6112yescomplemented
104#466—24no—
105#459C22×C6118yescomplemented
106#447—28no—
107C4×D8C22×C6112yes—
108C8×D4C22×C6114yescomplemented
109#335C22×C6112yescomplemented
110#331C22×C6114yescomplemented
111D4⋊C8C22×C6114yescomplemented
112C82C22×C6111yescharacteristic, complemented
113C61D8211yescharacteristic, direct product factor, Sylow
114C22×D4—28no—
115C2×D8—28no—
116C2×D8—24no—
117C2×D8—24no—
118C2×D8—42no—
119C2×D8—416no—
120C2×D8D4×C6112yes—
121C22×C8—24no—
122#127C23×C6114yes—
123#121—28no—
124#120—44no—
125C4×D4C23×C6114yes—
126#107D4×C6112yes—
127C4⋊C8C23×C6114yes—
128#102—28no—
129#102D4×C6114yes—
130C22⋊C8—24no—
131C4×C8C23×C6111yescharacteristic
132C4×C8C23×C6112yes—
133C24—44no—
134C2×D4—28no—
135C2×D4—24no—
136C2×D4—48no—
137C2×D4—416no—
138C2×D4—88no—
139C2×D4C2×D4×C6114yes—
140C22×C4—24no—
141D8—416no—
142D8—48no—
143D8—84no—
144D8—84no—
145D8D8×C6118yesdirect product factor
146C2×C8—21no—
147C2×C8—24no—
148C2×C8—48no—
149C2×C8C2×D4×C6112yes—
150C2×C8C2×D4×C6112yes—
151C4⋊C4C2×D4×C6114yes—
152C22⋊C4—24no—
153C22⋊C4—44no—
154C42C24×C6111yescharacteristic
155C23—24no—
156C23—44no—
157C23—816no—
158C23—164no—
159D4—24no—
160D4—48no—
161D4—48no—
162D4—84no—
163D4—816no—
164D4C2×D8×C6118yescomplemented
165C2×C4—24no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4C22×D4×C6112yes—
169C2×C4H(5,𝔽2)×C6111yescharacteristic
170C8—22no—
171C8—22no—
172C8—44no—
173C8C2×D8×C6114yescomplemented
174C22—28no—
175C22—44no—
176C22—44no—
177C22—84no—
178C22—88no—
179C22—1616no—
180C22D42×C6111yescharacteristic
181C4—21no—
182C4—44no—
183C4C22×D8×C6112yes—
184C4C61×#57612yes—
185C2—48no—
186C2—164no—
187C2D4×D8×C6112yes—
188C2C61×#329211yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. D4×D8×C61C2semidirect
2. C61×#1712C2semidirect
3. C61×#1667C2semidirect
4. C61×#1619C2semidirect
5. C8×D8×C61C2semidirect
7. D42×C61C22semidirect
8. C61×#493C22semidirect
9. C61×#493C22semidirect
11. C61×#459C22semidirect
14. C8×D4×C61C22semidirect
15. C61×#335C22semidirect
16. C61×#331C22semidirect
17. C61×D4⋊C8C22semidirect
18. C82×C61C22semidirect
50. D8×C61D8direct (N × H)
69. D4×C61C2×D8semidirect
78. C8×C61C2×D8semidirect
79. D82C61direct (N × H)
91. D4×D8C2×C61semidirect
92. #1712C2×C61semidirect
93. #1667C2×C61semidirect
94. #1619C2×C61semidirect
95. C8×D8C2×C61semidirect
101. D42C22×C61semidirect
102. #493C22×C61semidirect
103. #493C22×C61semidirect
105. #459C22×C61semidirect
108. C8×D4C22×C61semidirect
109. #335C22×C61semidirect
110. #331C22×C61semidirect
111. D4⋊C8C22×C61semidirect
112. C82C22×C61semidirect
113. C61D82direct (N × H)
145. D8D8×C61direct (N × H)
164. D4C2×D8×C61semidirect
173. C8C2×D8×C61semidirect

Maximal subgroups

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

subgroupindex
D4×D8×C612
C61×#17122
C61×#16672
C61×#16192
C8×D8×C612
D8261