Finite Group Databasebeta

← #22612111

Subgroups — #22612111

Order 9344.

150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#17988823C211yesmaximal, characteristic
2#17988412C212yesmaximal, complemented
3#17988387C212yesmaximal, complemented
4C22⋊#11924003C211yesmaximal, characteristic, complemented
5C2×#107×C73C211yesmaximal, characteristic, complemented
6C2×D584C2211yescharacteristic
7#14556565—21no—
8C2×#11924003C2212yes—
9#14556525C2211yescharacteristic
10#14556513—21no—
11C22×C8×C73C2211yescharacteristic
12C2×C4⋊C4×C73—21no—
13#107×C73—21no—
14#107×C73C2212yes—
15C2×D292—21no—
16C2×C22⋊D73—41no—
17D584—22no—
18C4⋊Dic73—21no—
19#11924005—41no—
20#11924003—22no—
21C22×C4×C73—41no—
22C22×C4×C73D411yescharacteristic
23C2×C8×C73—22no—
24C2×C8×C73D411yescharacteristic
25C2×C8×C73C2311yescharacteristic
26C4⋊C4×C73—22no—
27C4⋊C4×C73—41no—
28C23×C73D811yescharacteristic
29C22×D73—41no—
30C2×C4×C73—21no—
31C2×C4×C73—21no—
32C2×C4×C73—42no—
33C2×C4×C73—82no—
34C2×C4×C73D811yescharacteristic
35C2×C4×C73C2×D411yescharacteristic
36C22⋊D73—82no—
37C2×Dic73—41no—
38D292—41no—
39D292—41no—
40C8×C73—21no—
41C8×C73#4112yes—
42C22×C73—21no—
43C22×C73—21no—
44C22×C73D1612yes—
45C22×C73C2×D811yescharacteristic
46C2×D73—81no—
47C2×D73—81no—
48C2×D73—81no—
49C4×C73—21no—
50C4×C73—82no—
51C4×C73#12311yescharacteristic
52C4×C73#13711yescharacteristic
53Dic73—81no—
54C2×C73—22no—
55C2×C73#48011yescharacteristic
56C2×C73C2×D1611yescharacteristic
57C2×C73#51011yescharacteristic
58D73—161no—
59#2232—731nomaximal, Sylow
60C73#223211yescharacteristic, complemented, Sylow
61#466—731no—
62C2×#107D7311yescharacteristic, complemented
63#366—732no—
64#357—732no—
65C22⋊C16—731no—
66C2×D8—731no—
67C22×C8C2×D7311yescharacteristic
68#121—1461no—
69C2×C4⋊C4—21no—
70C2×C16—732no—
71#107—21no—
72#107—731no—
73#107C2×D7312yes—
74#102—1461no—
75C2×D4—2921no—
76C2×D4—1461no—
77C22×C4—41no—
78C22×C4C22⋊D7311yescharacteristic
79D8—1462no—
80C2×C8—22no—
81C2×C8C22⋊D7311yescharacteristic
82C2×C8C22×D7311yescharacteristic
83C4⋊C4—22no—
84C4⋊C4—41no—
85C4⋊C4—1461no—
86C22⋊C4—2921no—
87C16—1462no—
88C23—2921no—
89C23#1192401311yescharacteristic
90D4—2921no—
91D4—2921no—
92D4—5842no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—42no—
96C2×C4—82no—
97C2×C4—2921no—
98C2×C4#1192401311yescharacteristic
99C2×C4C2×C22⋊D7311yescharacteristic
100C8—21no—
101C8#1192402812yes—
102C22—21no—
103C22—21no—
104C22—5841no—
105C22—5841no—
106C22—5841no—
107C22#1455653212yes—
108C22C2×#1192401311yescharacteristic
109C4—21no—
110C4—82no—
111C4—5841no—
112C4#1455657411yescharacteristic
113C4#1455662211yescharacteristic
114C2—22no—
115C2—11681no—
116C2#1798890011yescharacteristic
117C2C2×#1455653211yescharacteristic
118C2#1798902811yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×#107×C73C2
socleC22×C73C2×D8
hypercenterC2×#107D73
hypocenterC73#2232
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #17988412C2semidirect
3. #17988387C2semidirect
4. C22⋊#11924003C2semidirect
5. C2×#107×C73C2semidirect
60. C73#2232semidirect
62. C2×#107D73semidirect