Finite Group Databasebeta

← C2×#17988412 #22611707

Subgroups — C2×#17988412 #22611707

Order 9344.

168 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11924003C211yesmaximal, characteristic
2C2×#14556525C211yesmaximal, characteristic
3#17988412C214yesmaximal, direct product factor
4C2×#107×C73C211yesmaximal, characteristic
5C2×C4⋊Dic73—21no—
6C2×#11924003C414yescomplemented
7C2×#11924003C2212yes—
8#14556525—21no—
9#14556525C2212yes—
10C22×C8×C73C2211yescharacteristic
11C2×C4⋊C4×C73—21no—
12#107×C73—21no—
13#107×C73C2212yes—
14C22×Dic73—41no—
15C4⋊Dic73—22no—
16C4⋊Dic73—41no—
17#11924003C2×C414yescomplemented
18C22×C4×C73—41no—
19C22×C4×C73D411yescharacteristic
20C2×C8×C73C2×C412yes—
21C2×C8×C73D411yescharacteristic
22C2×C8×C73Q812yes—
23C2×C8×C73C2311yescharacteristic
24C4⋊C4×C73—22no—
25C4⋊C4×C73—41no—
26C23×C73D811yescharacteristic
27C2×C4×C73—42no—
28C2×C4×C73—82no—
29C2×C4×C73C4⋊C412yes—
30C2×C4×C73D811yescharacteristic
31C2×C4×C73Q1612yes—
32C2×C4×C73C2×D411yescharacteristic
33C2×Dic73—42no—
34C2×Dic73—82no—
35C8×C73C4⋊C412yes—
36C8×C73C22×C411yescharacteristic
37C8×C73C2×Q811yescharacteristic
38C22×C73#10712yes—
39C22×C73D1612yes—
40C22×C73Q3212yes—
41C22×C73C2×D811yescharacteristic
42C4×C73—82no—
43C4×C73#10712yes—
44C4×C73C2×C4⋊C411yescharacteristic
45C4×C73C2×Q1611yescharacteristic
46Dic73—82no—
47C2×C73#36614yescomplemented
48C2×C73C2×#10711yescharacteristic
49C2×C73C2×D1611yescharacteristic
50C2×C73C2×Q3211yescharacteristic
51C2×#366—731nomaximal, Sylow
52C73C2×#36611yescharacteristic, complemented, Sylow
53C22×C16—731no—
54C2×#107—731no—
55C2×#107D7311yescharacteristic
56#366—734no—
57C22×C8C2×D7311yescharacteristic
58C2×C4⋊C4—21no—
59C2×C4⋊C4—1461no—
60C2×C16—734no—
61C2×C16—732no—
62#107—21no—
63#107—732no—
64#107—1461no—
65#107C2×D7312yes—
66C22×C4—41no—
67C22×C4—2921no—
68C22×C4C22⋊D7311yescharacteristic
69C2×C8Dic14612yes—
70C2×C8C4×D7312yes—
71C2×C8C22⋊D7311yescharacteristic
72C2×C8C22×D7311yescharacteristic
73C4⋊C4—22no—
74C4⋊C4—41no—
75C4⋊C4—2921no—
76C4⋊C4—1462no—
77C16—734no—
78C23#1192401311yescharacteristic
79C2×C4—42no—
80C2×C4—82no—
81C2×C4—2922no—
82C2×C4—5842no—
83C2×C4#1192400712yes—
84C2×C4#1192401311yescharacteristic
85C2×C4#1192401812yes—
86C2×C4C2×C22⋊D7311yescharacteristic
87C8#1192400712yes—
88C8C2×C4×D7311yescharacteristic
89C8C2×Dic14611yescharacteristic
90C22#1455652412yes—
91C22#1455653212yes—
92C22#1455653712yes—
93C22C2×#1192401311yescharacteristic
94C4—82no—
95C4—5842no—
96C4#1455652412yes—
97C4C2×#1192400711yescharacteristic
98C4C2×#1192401811yescharacteristic
99C2#1798841214yesdirect product factor
100C2C2×#1455652411yescharacteristic
101C2C2×#1455653211yescharacteristic
102C2C2×#1455653711yescharacteristic
subgroupG/H
centerC23#11924013
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
FittingC2×#107×C73C2
socleC23×C73D8
hypercenterC2×#107D73
hypocenterC73C2×#366
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #17988412C2direct (N × H)
6. C2×#11924003C4semidirect
17. #11924003C2×C4semidirect
47. C2×C73#366semidirect
52. C73C2×#366semidirect
99. C2#17988412direct (N × H)