Finite Group Databasebeta

← C2×#17989483 #22626164

Subgroups — C2×#17989483 #22626164

Order 9344.

236 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 90 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×#14556665C212yesmaximal, complemented
2#17989483C214yesmaximal, direct product factor
3C22×#11924012C211yesmaximal, characteristic
4#14556665—22no—
5#14556665C2214yescomplemented
6C2×#11924031—22no—
7C2×#11924012—22no—
8C2×#11924012—22no—
9C2×#11924012C412yes—
10C2×#11924012C2212yes—
11C22×#10596831C411yescharacteristic
12C22×#10596831C2211yescharacteristic
13C23×C4×C73C411yescharacteristic
14#11924031—24no—
15#11924012—24no—
16#11924012—24no—
17C2×#10596831—21no—
18C2×#10596831—21no—
19C2×#10596831C2×C412yes—
20C2×#10596831C2×C411yescharacteristic
21C2×#10596831D412yes—
22C2×#10596831D412yes—
23C2×#10596831C2311yescharacteristic
24C24×C73C811yescharacteristic
25C22×C4×C73—21no—
26C22×C4×C73—21no—
27C22×C4×C73—21no—
28C22×C4×C73—21no—
29C22×C4×C73C811yescharacteristic
30C22×C4×C73C812yes—
31C22×C4×C73C2×C412yes—
32C22×C4×C73C2×C411yescharacteristic
33C23×C73—21no—
34C23×C73—21no—
35C23×C73—42no—
36C23×C73C2×C811yescharacteristic
37C23×C73C2×C812yes—
38C2×C4×C73—21no—
39C2×C4×C73—21no—
40C2×C4×C73—22no—
41C2×C4×C73—22no—
42C2×C4×C73—22no—
43C2×C4×C73—22no—
44C2×C4×C73C22⋊C411yescharacteristic
45C2×C4×C73C22⋊C411yescharacteristic
46C2×C4×C73C2×C812yes—
47C2×C4×C73C2×C811yescharacteristic
48C2×C4×C73M1611yescharacteristic
49C2×C4×C73M1611yescharacteristic
50C2×C4×C73C22×C411yescharacteristic
51#10596831—22no—
52#10596831C22⋊C412yes—
53#10596831C2×D412yes—
54C22×C73—22no—
55C22×C73—22no—
56C22×C73—42no—
57C22×C73—42no—
58C22×C73—42no—
59C22×C73C22⋊C811yescharacteristic
60C22×C73C22⋊C811yescharacteristic
61C22×C73C22×C811yescharacteristic
62C4×C73—22no—
63C4×C73C22⋊C811yescharacteristic
64C4×C73C22⋊C811yescharacteristic
65C4×C73C2×C22⋊C411yescharacteristic
66C4×C73C2×M1611yescharacteristic
67C2×C73—21no—
68C2×C73—21no—
69C2×C73—42no—
70C2×C73#34912yescomplemented
71C2×C73C2×C22⋊C811yescharacteristic
72C2×#349—731nomaximal, Sylow
73C73C2×#34911yescharacteristic, complemented, Sylow
74C22×M16—731no—
75C2×M32—732no—
76#349—734no—
77C23×C4#6440811yescharacteristic
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#1059683311yescharacteristic
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4#1059683311yescharacteristic
93C22×C4#1059683312yes—
94C22×C4C2×#6440812yes—
95C22×C4C2×#6440811yescharacteristic
96M16—1464no—
97M16—1464no—
98C2×C8—732no—
99C2×C8—732no—
100C2×C8—731no—
101C2×C8—731no—
102C2×C8—732no—
103C2×C8—1461no—
104C2×C8—1461no—
105C16—1464no—
106C23—21no—
107C23—21no—
108C23—42no—
109C23C2×#1059683311yescharacteristic
110C23C2×#1059683312yes—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4C22⋊#6440811yescharacteristic
118C2×C4C22⋊#6440811yescharacteristic
119C2×C4C2×#1059683312yes—
120C2×C4C2×#1059683311yescharacteristic
121C2×C4#1192403711yescharacteristic
122C2×C4#1192403711yescharacteristic
123C2×C4C22×#6440811yescharacteristic
124C8—732no—
125C8—732no—
126C8—1462no—
127C22—22no—
128C22—22no—
129C22—42no—
130C22—42no—
131C22—42no—
132C22C22⋊#1059683311yescharacteristic
133C22C22⋊#1059683311yescharacteristic
134C22C22×#1059683311yescharacteristic
135C4—22no—
136C4C22⋊#1059683311yescharacteristic
137C4C22⋊#1059683311yescharacteristic
138C4C2×C22⋊#6440811yescharacteristic
139C4C2×#1192403711yescharacteristic
140C2—21no—
141C2—21no—
142C2—42no—
143C2#1798948312yesdirect product factor
144C2C2×C22⋊#1059683311yescharacteristic
subgroupG/H
centerC2×C4C22⋊#64408
commutatorC22×C73C22×C8
FrattiniC2×C4C22×#64408
FittingC23×C4×C73C4
socleC22×C73C22⋊C8
hypercenterC23×C4#64408
hypocenterC73C2×#349
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556665C2semidirect
2. #17989483C2direct (N × H)
5. #14556665C22semidirect
70. C2×C73#349semidirect
73. C73C2×#349semidirect
143. C2#17989483direct (N × H)