Finite Group Databasebeta

← #22611720

Subgroups — #22611720

Order 9344.

156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556531C211yesmaximal, characteristic
2C2×#14556525C211yesmaximal, characteristic
3#17988414C212yesmaximal, complemented
4#17988412C212yesmaximal, complemented
5#427×C73C211yesmaximal, characteristic
6C2×C4⋊Dic73—21no—
7#14556531C414yescomplemented
8C2×#11924003C2212yes—
9#14556525—21no—
10#14556525C2212yes—
11C22×C8×C73C2211yescharacteristic
12#117×C73—21no—
13#107×C73C2211yescharacteristic
14#107×C73C2211yescharacteristic
15#106×C73—21no—
16C22×Dic73—41no—
17C4⋊Dic73—22no—
18C4⋊Dic73—41no—
19#11924003C2×C414yescomplemented
20C22×C4×C73D411yescharacteristic
21C2×C8×C73C2×C412yes—
22C2×C8×C73D411yescharacteristic
23C2×C8×C73Q812yes—
24C2×C8×C73C2311yescharacteristic
25C4⋊C4×C73—21no—
26C4⋊C4×C73—21no—
27C22⋊C4×C73—41no—
28C42×C73—41no—
29C23×C73D811yescharacteristic
30C2×C4×C73—41no—
31C2×C4×C73—41no—
32C2×C4×C73C4⋊C412yes—
33C2×C4×C73D811yescharacteristic
34C2×C4×C73Q1612yes—
35C2×C4×C73C2×D411yescharacteristic
36C2×Dic73—42no—
37C2×Dic73—82no—
38C8×C73C4⋊C412yes—
39C8×C73C22×C411yescharacteristic
40C8×C73C2×Q811yescharacteristic
41C22×C73—21no—
42C22×C73—21no—
43C22×C73#10712yes—
44C22×C73C2×D811yescharacteristic
45C4×C73—81no—
46C4×C73—81no—
47C4×C73#10712yes—
48C4×C73C2×C4⋊C411yescharacteristic
49C4×C73C2×Q1611yescharacteristic
50Dic73—82no—
51C2×C73—22no—
52C2×C73C2×#10711yescharacteristic
53C2×C73#50911yescharacteristic
54C2×C73#51011yescharacteristic
55#2159—731nomaximal, Sylow
56C73#215911yescharacteristic, complemented, Sylow
57C2×M32—731no—
58#427D7311yescharacteristic
59C2×#107—731no—
60#367—732no—
61#366—732no—
62C22×C8C2×D7311yescharacteristic
63#117—21no—
64C2×C4⋊C4—1461no—
65M32—734no—
66C2×C16—732no—
67#107—732no—
68#107—1461no—
69#107C2×D7311yescharacteristic
70#107C2×D7311yescharacteristic
71#106—21no—
72C22×C4—2921no—
73C22×C4C22⋊D7311yescharacteristic
74C2×C8Dic14612yes—
75C2×C8C4×D7312yes—
76C2×C8C22⋊D7311yescharacteristic
77C2×C8C22×D7311yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—21no—
80C4⋊C4—2921no—
81C4⋊C4—1462no—
82C22⋊C4—41no—
83C42—41no—
84C16—734no—
85C23#1192401311yescharacteristic
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—2922no—
89C2×C4—5842no—
90C2×C4#1192400712yes—
91C2×C4#1192401311yescharacteristic
92C2×C4#1192401812yes—
93C2×C4C2×C22⋊D7311yescharacteristic
94C8#1192400712yes—
95C8C2×C4×D7311yescharacteristic
96C8C2×Dic14611yescharacteristic
97C22—21no—
98C22—21no—
99C22#1455652412yes—
100C22C2×#1192401311yescharacteristic
101C4—81no—
102C4—81no—
103C4—5842no—
104C4#1455652412yes—
105C4C2×#1192400711yescharacteristic
106C4C2×#1192401811yescharacteristic
107C2—22no—
108C2C2×#1455652411yescharacteristic
109C2#1798902211yescharacteristic
110C2#1798902711yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
Fitting#427×C73C2
socleC22×C73C2×D8
hypercenter#427D73
hypocenterC73#2159
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #17988414C2semidirect
4. #17988412C2semidirect
7. #14556531C4semidirect
19. #11924003C2×C4semidirect
56. C73#2159semidirect