Finite Group Databasebeta

← #22612155

Subgroups — #22612155

Order 9344.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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#17988992C211yesmaximal, characteristic, complemented
2#17988964C211yesmaximal, characteristic
3#17988389C214yesmaximal, complemented
4C4×C16×C73C211yesmaximal, characteristic, complemented
5C2×D584—21no—
6C2×D584C2212yes—
7#14556591—21no—
8#14556588—21no—
9#14556525—21no—
10#14556525C2212yes—
11C2×C16×C73C2212yes—
12C4×C8×C73C2211yescharacteristic
13C2×Dic146—41no—
14C2×D292—22no—
15C2×D292—41no—
16C2×D292—41no—
17D584—24no—
18D584—42no—
19C4⋊Dic73—22no—
20C4⋊Dic73—41no—
21C2×C8×C73D411yescharacteristic
22C2×C8×C73C2311yescharacteristic
23C42×C73D411yescharacteristic
24C16×C73—22no—
25C22×D73—42no—
26C2×C4×C73D811yescharacteristic
27C2×C4×C73D811yescharacteristic
28C2×C4×C73C2×D411yescharacteristic
29C2×Dic73—42no—
30D292—42no—
31D292—42no—
32D292—82no—
33D292—82no—
34Dic146—82no—
35C8×C73SD1612yes—
36C8×C73#4112yes—
37C22×C73C2×D811yescharacteristic
38C2×D73—82no—
39C2×D73—82no—
40C2×D73—82no—
41C4×C73D1612yes—
42C4×C73SD3212yes—
43C4×C73#12411yescharacteristic
44C4×C73C2×SD1611yescharacteristic
45Dic73—82no—
46C2×C73#48611yescharacteristic
47C2×C73C2×D1611yescharacteristic
48C2×C73C2×SD3211yescharacteristic
49D73—162no—
50#2240—731nomaximal, Sylow
51C73#224011yescharacteristic, complemented, Sylow
52#500—731no—
53#493—731no—
54#357—734no—
55C4×C16D7311yescharacteristic, complemented
56C2×D8—732no—
57C2×D8—1461no—
58C4⋊Q8—1461no—
59#127—1461no—
60C2×C16C2×D7312yes—
61#107—732no—
62#107—1461no—
63C4×C8C2×D7311yescharacteristic
64C2×Q8—2921no—
65C2×D4—2921no—
66C2×D4—2921no—
67C2×D4—1462no—
68D8—2922no—
69D8—1464no—
70C2×C8D29211yescharacteristic
71C2×C8C22×D7311yescharacteristic
72C4⋊C4—2921no—
73C4⋊C4—1462no—
74C42D29211yescharacteristic
75C16—22no—
76C23—2922no—
77Q8—5842no—
78D4—2922no—
79D4—2922no—
80D4—5842no—
81D4—5842no—
82C2×C4—2922no—
83C2×C4D58411yescharacteristic
84C2×C4D58411yescharacteristic
85C2×C4C2×D29211yescharacteristic
86C8#1192401712yes—
87C8#1192402812yes—
88C22—5842no—
89C22—5842no—
90C22—5842no—
91C22C2×D58411yescharacteristic
92C4—5842no—
93C4D116812yes—
94C4#1455653612yes—
95C4#1455657911yescharacteristic
96C4C2×#1192401711yescharacteristic
97C2—11682no—
98C2#1798893411yescharacteristic
99C2C2×D116811yescharacteristic
100C2C2×#1455653611yescharacteristic
subgroupG/H
centerC22C2×D584
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC4×C16×C73C2
socleC22×C73C2×D8
hypercenterC4×C16D73
hypocenterC73#2240
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×C16

Complements

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

NH ≅ G/Ntype
1. #17988992C2semidirect
3. #17988389C2semidirect
4. C4×C16×C73C2semidirect
51. C73#2240semidirect
55. C4×C16D73semidirect