Finite Group Databasebeta

← C2×#17989686 #22627106

Subgroups — C2×#17989686 #22627106

Order 9344.

236 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 71 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×#14556687C212yesmaximal, complemented
2#17989686C214yesmaximal, direct product factor
3C22×#11924038C211yesmaximal, characteristic
4#14556687—22no—
5#14556687C2214yescomplemented
6C2×#11924040—22no—
7C2×#11924038—22no—
8C2×#11924038—22no—
9C2×#11924038C412yes—
10C2×#11924038C2212yes—
11C22×#10596833C411yescharacteristic
12C22×#10596833C2211yescharacteristic
13C22×C4×D73C411yescharacteristic
14#11924040—24no—
15#11924038—24no—
16#11924038—24no—
17C2×#10596833—21no—
18C2×#10596833—21no—
19C2×#10596833C2×C412yes—
20C2×#10596833C2×C411yescharacteristic
21C2×#10596833D412yes—
22C2×#10596833D412yes—
23C2×#10596833C2311yescharacteristic
24C23×D73C811yescharacteristic
25C22×Dic73C2×C411yescharacteristic
26C2×C4×D73—21no—
27C2×C4×D73—21no—
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73C812yes—
31C2×C4×D73C2×C412yes—
32C22×C4×C73C811yescharacteristic
33C23×C73C2×C811yescharacteristic
34C22×D73—21no—
35C22×D73—21no—
36C22×D73—42no—
37C22×D73C2×C812yes—
38C2×C4×C73—21no—
39C2×C4×C73—21no—
40C2×C4×C73C2×C812yes—
41C2×Dic73C22⋊C411yescharacteristic
42C2×Dic73C22⋊C411yescharacteristic
43C2×Dic73C2×C811yescharacteristic
44C2×Dic73M1611yescharacteristic
45C2×Dic73M1611yescharacteristic
46C2×Dic73C22×C411yescharacteristic
47C4×D73—22no—
48C4×D73—22no—
49C4×D73—22no—
50C4×D73—22no—
51#10596833—22no—
52#10596833C22⋊C412yes—
53#10596833C2×D412yes—
54C22×C73—22no—
55C22×C73C22⋊C811yescharacteristic
56C22×C73C22⋊C811yescharacteristic
57C22×C73C22×C811yescharacteristic
58C2×D73—22no—
59C2×D73—42no—
60C2×D73—42no—
61C2×D73—42no—
62C4×C73—22no—
63Dic73C22⋊C811yescharacteristic
64Dic73C22⋊C811yescharacteristic
65Dic73C2×C22⋊C411yescharacteristic
66Dic73C2×M1611yescharacteristic
67C2×C73—21no—
68C2×C73—21no—
69C2×C73#34912yescomplemented
70C2×C73C2×C22⋊C811yescharacteristic
71D73—42no—
72C2×#349—731nomaximal, Sylow
73C73C2×#34911yescharacteristic, complemented, Sylow
74C22×M16—731no—
75C2×M32—732no—
76#349—734no—
77C23×C4—731no—
78C2×M16—732no—
79C2×M16—732no—
80C2×M16—1462no—
81C2×M16—1462no—
82C22×C8—731no—
83C22×C8—731no—
84M32—734no—
85M32—1462no—
86C2×C16—1462no—
87C24—731no—
88C22×C4—731no—
89C22×C4—732no—
90C22×C4—732no—
91C22×C4—1461no—
92C22×C4—1461no—
93C22×C4—1461no—
94C22×C4—1461no—
95C22×C4#1059684211yescharacteristic
96M16—1464no—
97M16—1464no—
98C2×C8—731no—
99C2×C8—732no—
100C2×C8—732no—
101C2×C8—731no—
102C2×C8—732no—
103C2×C8—1461no—
104C2×C8—1461no—
105C16—1464no—
106C23—2922no—
107C23—732no—
108C23—1461no—
109C23—1461no—
110C23C2×#1059684211yescharacteristic
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—731no—
114C2×C4—731no—
115C2×C4—731no—
116C2×C4—731no—
117C2×C4—731no—
118C2×C4—731no—
119C2×C4—1462no—
120C2×C4—1462no—
121C2×C4—1462no—
122C2×C4—1462no—
123C2×C4C2×#1059684212yes—
124C8—732no—
125C8—732no—
126C8—1462no—
127C22—22no—
128C22—2922no—
129C22—2922no—
130C22—2922no—
131C22—1462no—
132C22C22⋊#1059684211yescharacteristic
133C22C22⋊#1059684211yescharacteristic
134C22C22×#1059684211yescharacteristic
135C4—22no—
136C4—731no—
137C4—731no—
138C4—731no—
139C4—731no—
140C2—21no—
141C2—21no—
142C2—2922no—
143C2#1798968612yesdirect product factor
144C2C2×C22⋊#1059684211yescharacteristic
subgroupG/H
centerC22C22⋊#10596842
commutatorC22×C73C22×C8
FrattiniC22C22×#10596842
FittingC22×C4×C73C8
socleC22×C73C22⋊C8
hypercenterC22×C4#10596842
hypocenterC73C2×#349
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556687C2semidirect
2. #17989686C2direct (N × H)
5. #14556687C22semidirect
69. C2×C73#349semidirect
73. C73C2×#349semidirect
143. C2#17989686direct (N × H)