Finite Group Databasebeta

← C2×#15690724 #20260705

Subgroups — C2×#15690724 #20260705

Order 6208.

210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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×C22⋊D97C211yesmaximal, characteristic
2C2×C22⋊Dic97C211yesmaximal, characteristic, complemented
3#15690724C214yesmaximal, direct product factor
4C2×C22⋊C4×C97C211yesmaximal, characteristic, complemented
5C23×D97C411yescharacteristic, complemented
6C2×C22⋊D97—21no—
7C2×C22⋊D97—21no—
8C2×C22⋊D97—21no—
9C2×C22⋊D97—21no—
10C2×C22⋊D97C412yescomplemented
11C2×C22⋊D97C2212yes—
12C22×Dic97—21no—
13C22×Dic97C411yescharacteristic, complemented
14C22⋊Dic97—21no—
15C22⋊Dic97C2212yescomplemented
16C24×C97C2211yescharacteristic
17C22×C4×C97—21no—
18C22⋊C4×C97—21no—
19C22⋊C4×C97C2212yescomplemented
20C23×C97—42no—
21C23×C97C2×C411yescharacteristic
22C23×C97C2×C411yescharacteristic
23C23×C97D411yescharacteristic
24C23×C97D411yescharacteristic
25C23×C97D411yescharacteristic
26C23×C97D411yescharacteristic
27C23×C97C2311yescharacteristic
28C22×D97—21no—
29C22×D97—21no—
30C22×D97—42no—
31C22×D97C2×C412yescomplemented
32C2×C4×C97—22no—
33C2×C4×C97—42no—
34C22⋊D97—22no—
35C22⋊D97—22no—
36C22⋊D97—22no—
37C22⋊D97—22no—
38C2×Dic97—21no—
39C2×Dic97—21no—
40C2×Dic97—22no—
41C2×Dic97—42no—
42C2×Dic97C2×C412yescomplemented
43C22×C97—22no—
44C22×C97—22no—
45C22×C97—22no—
46C22×C97—41no—
47C22×C97—41no—
48C22×C97—41no—
49C22×C97—41no—
50C22×C97C22⋊C411yescharacteristic
51C22×C97C22⋊C411yescharacteristic
52C22×C97C22⋊C411yescharacteristic
53C22×C97C22⋊C411yescharacteristic
54C22×C97C22×C411yescharacteristic
55C22×C97C2×D411yescharacteristic
56C22×C97C2×D411yescharacteristic
57C2×D97—22no—
58C2×D97—42no—
59C2×D97—42no—
60C2×D97—42no—
61C4×C97—42no—
62Dic97—22no—
63Dic97—42no—
64C2×C97—21no—
65C2×C97—21no—
66C2×C97—21no—
67C2×C97—21no—
68C2×C97—21no—
69C2×C97—21no—
70C2×C97#9912yescomplemented
71C2×C97C2×C22⋊C411yescharacteristic
72D97—42no—
73C97C2×#9911yescharacteristic, complemented, Sylow
74C2×#99—971nomaximal, Sylow
75C22×D4—971no—
76C2×C22⋊C4—971no—
77C2×C22⋊C4D9711yescharacteristic, complemented
78#99—974no—
79C24—971no—
80C24C2×D9711yescharacteristic
81C2×D4—972no—
82C2×D4—972no—
83C2×D4—1941no—
84C2×D4—1941no—
85C2×D4—1941no—
86C2×D4—1941no—
87C22×C4—21no—
88C22×C4—971no—
89C22×C4—1941no—
90C22⋊C4—21no—
91C22⋊C4—972no—
92C22⋊C4—1941no—
93C22⋊C4C2×D9712yescomplemented
94C23—42no—
95C23—972no—
96C23—3882no—
97C23—1941no—
98C23—1941no—
99C23C4×D9711yescharacteristic
100C23C4×D9711yescharacteristic
101C23D38811yescharacteristic
102C23D38811yescharacteristic
103C23C22⋊D9711yescharacteristic
104C23C22⋊D9711yescharacteristic
105C23C22×D9711yescharacteristic
106D4—1942no—
107D4—1942no—
108D4—1942no—
109D4—1942no—
110C2×C4—22no—
111C2×C4—42no—
112C2×C4—972no—
113C2×C4—3882no—
114C2×C4—1942no—
115C2×C4—1941no—
116C2×C4—1941no—
117C22—22no—
118C22—22no—
119C22—22no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—41no—
124C22—3882no—
125C22—3882no—
126C22—3882no—
127C22—1942no—
128C22#1309548811yescharacteristic
129C22#1309548811yescharacteristic
130C22#1309548811yescharacteristic
131C22#1309548811yescharacteristic
132C22C2×C4×D9711yescharacteristic
133C22C2×C22⋊D9711yescharacteristic
134C22C2×D38811yescharacteristic
135C4—42no—
136C4—3882no—
137C4—1942no—
138C2—21no—
139C2—21no—
140C2—21no—
141C2—21no—
142C2—21no—
143C2—21no—
144C2—3882no—
145C2#1569072412yesdirect product factor
146C2C2×#1309548811yescharacteristic
subgroupG/H
centerC22#13095488
commutatorC22×C97C22×C4
FrattiniC23C22×D97
FittingC2×C22⋊C4×C97C2
socleC22×C97C22⋊C4
hypercenterC2×C22⋊C4D97
hypocenterC97C2×#99
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Dic97C2semidirect
3. #15690724C2direct (N × H)
4. C2×C22⋊C4×C97C2semidirect
5. C23×D97C4semidirect
10. C2×C22⋊D97C4semidirect
13. C22×Dic97C4semidirect
15. C22⋊Dic97C22semidirect
19. C22⋊C4×C97C22semidirect
31. C22×D97C2×C4semidirect
42. C2×Dic97C2×C4semidirect
70. C2×C97#99semidirect
73. C97C2×#99semidirect
77. C2×C22⋊C4D97semidirect
93. C22⋊C4C2×D97semidirect
145. C2#15690724direct (N × H)