Finite Group Databasebeta

← #22612018

Subgroups — #22612018

Order 9344.

174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 51 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×D1168C211yesmaximal, characteristic, complemented
2C2×C16×D73C211yesmaximal, characteristic, complemented
3#17988824C212yesmaximal, complemented
4#17988387C212yesmaximal, complemented
5#366×C73C211yesmaximal, characteristic, complemented
6C2×D584C2212yes—
7C2×C8×D73C2211yescharacteristic
8#14556566—22no—
9D1168—22no—
10C2×#11924003C2211yescharacteristic
11C16×D73—22no—
12#14556511—22no—
13C2×C16×C73C2211yescharacteristic
14#107×C73C2212yes—
15C2×D292—22no—
16C2×D292—42no—
17C2×C4×D73D411yescharacteristic
18D584—22no—
19D584—22no—
20C2×#10596831D411yescharacteristic
21C8×D73—21no—
22C8×D73—21no—
23#11924005—42no—
24#11924003—21no—
25C2×C8×C73C2311yescharacteristic
26C4⋊C4×C73—22no—
27C16×C73D412yescomplemented
28C22×D73—42no—
29C22×D73D811yescharacteristic
30C2×C4×C73—42no—
31C2×C4×C73C2×D411yescharacteristic
32C2×Dic73D811yescharacteristic
33D292—42no—
34D292—42no—
35D292—84no—
36C4×D73—21no—
37C4×D73—21no—
38C8×C73C2×D411yescharacteristic
39C8×C73#4111yescharacteristic
40#10596831—21no—
41C22×C73C2×D811yescharacteristic
42C2×D73—21no—
43C2×D73—21no—
44C2×D73—82no—
45C2×D73—82no—
46C2×D73—82no—
47C2×D73D1612yescomplemented
48C4×C73—82no—
49C4×C73#12111yescharacteristic
50C4×C73#13511yescharacteristic
51Dic73—21no—
52C2×C73#46611yescharacteristic
53C2×C73C2×D1611yescharacteristic
54C2×C73#50811yescharacteristic
55D73—22no—
56D73—162no—
57#2215—731nomaximal, Sylow
58C73#221511yescharacteristic, complemented, Sylow
59C2×D16—731no—
60C22×C16—731no—
61#466—732no—
62#366D7311yescharacteristic, complemented
63#357—732no—
64C2×D8—732no—
65C22×C8—731no—
66#121—1462no—
67D16—1462no—
68C2×C16—731no—
69C2×C16—1462no—
70C2×C16C2×D7311yescharacteristic
71#107C2×D7312yes—
72#102—1462no—
73C2×D4—2922no—
74C2×D4—1462no—
75C22×C4—731no—
76D8—1462no—
77D8—1462no—
78C2×C8—731no—
79C2×C8—1461no—
80C2×C8—1461no—
81C2×C8C22×D7311yescharacteristic
82C4⋊C4—22no—
83C22⋊C4—2922no—
84C16—1461no—
85C16D29212yescomplemented
86C23—2922no—
87C23—731no—
88D4—2922no—
89D4—2922no—
90D4—5844no—
91C2×C4—42no—
92C2×C4—731no—
93C2×C4—1461no—
94C2×C4—1461no—
95C2×C4D4×D7311yescharacteristic
96C8—1461no—
97C8C2×D29211yescharacteristic
98C8#1192402911yescharacteristic
99C22—5842no—
100C22—5842no—
101C22—5842no—
102C22—732no—
103C22—1461no—
104C22—1461no—
105C22D8×D7311yescharacteristic
106C4—82no—
107C4—1461no—
108C4#1455656611yescharacteristic
109C4#1455661411yescharacteristic
110C2—11682no—
111C2—1462no—
112C2#1798882411yescharacteristic
113C2D16×D7311yescharacteristic
114C2#1798902011yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#366×C73C2
socleC22×C73C2×D8
hypercenter#366D73
hypocenterC73#2215
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. C2×D1168C2semidirect
2. C2×C16×D73C2semidirect
3. #17988824C2semidirect
4. #17988387C2semidirect
5. #366×C73C2semidirect
27. C16×C73D4semidirect
47. C2×D73D16semidirect
58. C73#2215semidirect
62. #366D73semidirect
85. C16D292semidirect