Finite Group Databasebeta

← C2×#17985781 #22589958

Subgroups — C2×#17985781 #22589958

Order 9088.

236 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#14556068C212yesmaximal, complemented
2#17985781C214yesmaximal, direct product factor
3C22×M16×C71C211yesmaximal, characteristic
4#14556068—22no—
5#14556068C2214yescomplemented
6C2×C71⋊C16—22no—
7C23×C4×C71C411yescharacteristic
8C2×M16×C71—22no—
9C2×M16×C71—22no—
10C2×M16×C71C412yes—
11C2×M16×C71C2212yes—
12C22×C8×C71C411yescharacteristic
13C22×C8×C71C2211yescharacteristic
14C71⋊C16—24no—
15C24×C71C811yescharacteristic
16C22×C4×C71—21no—
17C22×C4×C71—21no—
18C22×C4×C71—21no—
19C22×C4×C71—21no—
20C22×C4×C71C811yescharacteristic
21C22×C4×C71C812yes—
22C22×C4×C71C2×C412yes—
23C22×C4×C71C2×C411yescharacteristic
24M16×C71—24no—
25M16×C71—24no—
26C2×C8×C71—21no—
27C2×C8×C71—21no—
28C2×C8×C71C2×C412yes—
29C2×C8×C71C2×C411yescharacteristic
30C2×C8×C71D412yes—
31C2×C8×C71D412yes—
32C2×C8×C71C2311yescharacteristic
33C23×C71—21no—
34C23×C71—21no—
35C23×C71—42no—
36C23×C71C2×C811yescharacteristic
37C23×C71C2×C812yes—
38C2×C4×C71—21no—
39C2×C4×C71—21no—
40C2×C4×C71—22no—
41C2×C4×C71—22no—
42C2×C4×C71—22no—
43C2×C4×C71—22no—
44C2×C4×C71C22⋊C411yescharacteristic
45C2×C4×C71C22⋊C411yescharacteristic
46C2×C4×C71C2×C812yes—
47C2×C4×C71C2×C811yescharacteristic
48C2×C4×C71M1611yescharacteristic
49C2×C4×C71M1611yescharacteristic
50C2×C4×C71C22×C411yescharacteristic
51C8×C71—22no—
52C8×C71C22⋊C412yes—
53C8×C71C2×D412yes—
54C22×C71—22no—
55C22×C71—22no—
56C22×C71—42no—
57C22×C71—42no—
58C22×C71—42no—
59C22×C71C22⋊C811yescharacteristic
60C22×C71C22⋊C811yescharacteristic
61C22×C71C22×C811yescharacteristic
62C4×C71—22no—
63C4×C71C22⋊C811yescharacteristic
64C4×C71C22⋊C811yescharacteristic
65C4×C71C2×C22⋊C411yescharacteristic
66C4×C71C2×M1611yescharacteristic
67C2×C71—21no—
68C2×C71—21no—
69C2×C71—42no—
70C2×C71#34912yescomplemented
71C2×C71C2×C22⋊C811yescharacteristic
72C2×#349—711nomaximal, Sylow
73C71C2×#34911yescharacteristic, complemented, Sylow
74C22×M16D7111yescharacteristic
75C2×M32—712no—
76#349—714no—
77C23×C4Dic7111yescharacteristic
78C2×M16—22no—
79C2×M16—22no—
80C2×M16Dic7112yes—
81C2×M16C2×D7112yes—
82C22×C8Dic7111yescharacteristic
83C22×C8C2×D7111yescharacteristic
84M32—714no—
85M32—1422no—
86C2×C16—1422no—
87C24C71⋊C811yescharacteristic
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4C71⋊C811yescharacteristic
93C22×C4C71⋊C812yes—
94C22×C4C2×Dic7112yes—
95C22×C4C2×Dic7111yescharacteristic
96M16—24no—
97M16—24no—
98C2×C8—21no—
99C2×C8—21no—
100C2×C8C2×Dic7112yes—
101C2×C8C2×Dic7111yescharacteristic
102C2×C8C22⋊D7112yes—
103C2×C8C22⋊D7112yes—
104C2×C8C22×D7111yescharacteristic
105C16—1424no—
106C23—21no—
107C23—21no—
108C23—42no—
109C23C2×C71⋊C811yescharacteristic
110C23C2×C71⋊C812yes—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4C22⋊Dic7111yescharacteristic
118C2×C4C22⋊Dic7111yescharacteristic
119C2×C4C2×C71⋊C812yes—
120C2×C4C2×C71⋊C811yescharacteristic
121C2×C4#1176584911yescharacteristic
122C2×C4#1176584911yescharacteristic
123C2×C4C22×Dic7111yescharacteristic
124C8—22no—
125C8C22⋊Dic7112yes—
126C8C2×C22⋊D7112yes—
127C22—22no—
128C22—22no—
129C22—42no—
130C22—42no—
131C22—42no—
132C22C22⋊(C71⋊C8)11yescharacteristic
133C22C22⋊(C71⋊C8)11yescharacteristic
134C22C22×C71⋊C811yescharacteristic
135C4—22no—
136C4C22⋊(C71⋊C8)11yescharacteristic
137C4C22⋊(C71⋊C8)11yescharacteristic
138C4C2×C22⋊Dic7111yescharacteristic
139C4C2×#1176584911yescharacteristic
140C2—21no—
141C2—21no—
142C2—42no—
143C2#1798578112yesdirect product factor
144C2C2×C22⋊(C71⋊C8)11yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic71
commutatorC22×C71C22×C8
FrattiniC2×C8C22×D71
FittingC22×M16×C71C2
socleC22×C71C22⋊C8
hypercenterC22×M16D71
hypocenterC71C2×#349
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
1. C2×#14556068C2semidirect
2. #17985781C2direct (N × H)
5. #14556068C22semidirect
70. C2×C71#349semidirect
73. C71C2×#349semidirect
143. C2#17985781direct (N × H)