Finite Group Databasebeta

← C2×#13092457 #15681980

Subgroups — C2×#13092457 #15681980

Order 2944.

536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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×#67267C211yesmaximal, characteristic
2C2×#10625097C211yesmaximal, characteristic
3#13092457C218yesmaximal, direct product factor
4C2×#10624989C212yesmaximal, complemented
5C2×#10624990C212yesmaximal, complemented
6C22×C4⋊C4×C23C211yesmaximal, characteristic
7C23×C4×C23—21no—
8C23×C4×C23C2211yescharacteristic
9C2×C4⋊C4×C23—21no—
10C2×C4⋊C4×C23—22no—
11C2×C4⋊C4×C23C2212yes—
12C2×C4⋊C4×C23C2214yes—
13C2×C22⋊Dic23—21no—
14#10625097—22no—
15#10625097C2214yes—
16C2×C4⋊Dic23C2211yescharacteristic
17C2×C4⋊Dic23C2211yescharacteristic
18C2×C4×Dic23—21no—
19C2×#67267C418yescomplemented
20C2×#67267C2214yes—
21C22×C23⋊C8C2212yes—
22#10624990C2218yescomplemented
23#10624989C2218yescomplemented
24C24×C23D411yescharacteristic
25C22×C4×C23—24no—
26C22×C4×C23—22no—
27C22×C4×C23—44no—
28C22×C4×C23C2×C414yes—
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D412yes—
31C22×C4×C23Q814yes—
32C22×C4×C23C2311yescharacteristic
33C22×C4×C23C2312yes—
34C22×Dic23—21no—
35C22×Dic23—21no—
36C4⋊C4×C23—24no—
37C4⋊C4×C23—22no—
38C4⋊C4×C23C2314yes—
39C22⋊Dic23—24no—
40C4⋊Dic23—21no—
41C4⋊Dic23—21no—
42C4⋊Dic23C2312yes—
43C4⋊Dic23C2312yes—
44C4×Dic23—24no—
45#67267C2×C4116yescomplemented
46C2×C23⋊C8C2×C418yescomplemented
47C2×C23⋊C8C2314yes—
48C23×C23—22no—
49C23×C23—22no—
50C23×C23C4⋊C414yes—
51C23×C23C2×D412yes—
52C23×C23C2×D411yescharacteristic
53C2×C4×C23—24no—
54C2×C4×C23—48no—
55C2×C4×C23—44no—
56C2×C4×C23C4⋊C418yes—
57C2×C4×C23C4⋊C414yes—
58C2×C4×C23C22×C412yes—
59C2×C4×C23C22×C414yes—
60C2×C4×C23C2×D412yes—
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×Q814yes—
63C2×C4×C23C2×Q812yes—
64C2×C4×C23C2411yescharacteristic
65C2×Dic23—22no—
66C2×Dic23—22no—
67C2×Dic23—42no—
68C2×Dic23—42no—
69C23⋊C8C22×C418yescomplemented
70C2×#428—231nomaximal, Sylow
71C22×C23—22no—
72C22×C23—22no—
73C22×C23—28no—
74C22×C23C2×C4⋊C414yes—
75C22×C23C2×C4⋊C412yes—
76C22×C23AGL(1,ℤ/8)12yes—
77C22×C23#13712yes—
78C22×C23C22×D411yescharacteristic
79C4×C23—44no—
80C4×C23C2×C4⋊C412yes—
81C4×C23C2×C4⋊C414yes—
82C4×C23C23×C411yescharacteristic
83C4×C23C22×Q811yescharacteristic
84Dic23—42no—
85Dic23—42no—
86C22×M16—231no—
87C2×#117—231no—
88C22×C4⋊C4D2311yescharacteristic
89#428—238no—
90C2×#107—232no—
91C2×#106—232no—
92C2×C23—24no—
93C2×C23#42814yescomplemented
94C2×C23C22×C4⋊C411yescharacteristic
95C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
96C2×C23C2×#13711yescharacteristic
97C23×C4—21no—
98C23×C4C2×D2311yescharacteristic
99C2×M16—238no—
100C2×M16—234no—
101C22×C8—232no—
102#117—234no—
103#117—462no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—231no—
107C2×C4⋊C4—231no—
108C2×C4⋊C4C2×D2312yes—
109C2×C4⋊C4C2×D2314yes—
110C2×C22⋊C4—461no—
111C2×C42—461no—
112#107—238no—
113#106—238no—
114C23C2×#42811yescharacteristic, complemented, Sylow
115C24C22⋊D2311yescharacteristic
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—461no—
120C22×C4—461no—
121C22×C4Dic4614yes—
122C22×C4C4×D2314yes—
123C22×C4C22⋊D2312yes—
124C22×C4C22⋊D2311yescharacteristic
125C22×C4C22×D2312yes—
126C22×C4C22×D2311yescharacteristic
127M16—2316no—
128C2×C8—238no—
129C2×C8—234no—
130C4⋊C4—24no—
131C4⋊C4—22no—
132C4⋊C4—232no—
133C4⋊C4—232no—
134C4⋊C4—461no—
135C4⋊C4—461no—
136C4⋊C4C22×D2314yes—
137C22⋊C4—464no—
138C42—464no—
139C23—22no—
140C23—22no—
141C23Dic23⋊C414yes—
142C23C2×C22⋊D2312yes—
143C23C2×C22⋊D2311yescharacteristic
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—462no—
148C2×C4—462no—
149C2×C4—922no—
150C2×C4—922no—
151C2×C4Dic23⋊C418yes—
152C2×C4Dic23⋊C414yes—
153C2×C4C2×Dic4614yes—
154C2×C4C2×Dic4612yes—
155C2×C4C2×C4×D2312yes—
156C2×C4C2×C4×D2314yes—
157C2×C4C2×C22⋊D2312yes—
158C2×C4C2×C22⋊D2311yescharacteristic
159C2×C4C23×D2311yescharacteristic
160C8—238no—
161C22—22no—
162C22—22no—
163C22—28no—
164C22C2×Dic23⋊C414yes—
165C22C2×Dic23⋊C412yes—
166C22#1062510312yes—
167C22#1062511312yes—
168C22C22×C22⋊D2311yescharacteristic
169C4—44no—
170C4—922no—
171C4—922no—
172C4C2×Dic23⋊C412yes—
173C4C2×Dic23⋊C414yes—
174C4C22×Dic4611yescharacteristic
175C4C22×C4×D2311yescharacteristic
176C2—24no—
177C2#1309245714yesdirect product factor
178C2C22×Dic23⋊C411yescharacteristic
179C2C2×#1062510311yescharacteristic
180C2C2×#1062511311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC22×C4⋊C4×C23C2
socleC23×C23C2×D4
prime radicalC24×C23D4
cosocleC2×C4×C23C24
hypercenterC22×C4⋊C4D23
hypocenterC23C2×#428
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13092457C2direct (N × H)
4. C2×#10624989C2semidirect
5. C2×#10624990C2semidirect
19. C2×#67267C4semidirect
22. #10624990C22semidirect
23. #10624989C22semidirect
45. #67267C2×C4semidirect
46. C2×C23⋊C8C2×C4semidirect
69. C23⋊C8C22×C4semidirect
93. C2×C23#428semidirect
114. C23C2×#428semidirect
177. C2#13092457direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#672672
C2×#106250972
#130924572
C2×#106249892
C2×#106249902
C22×C4⋊C4×C232
C2×#42823