Finite Group Databasebeta

← #22612023

Subgroups — #22612023

Order 9344.

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

normal subgroups only

This group has 154 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×Dic584C211yesmaximal, characteristic, complemented
2C2×C16×D73C211yesmaximal, characteristic
3#17988829C212yesmaximal
4#17988390C212yesmaximal, complemented
5#366×C73C211yesmaximal, characteristic, complemented
6C2×Dic292C2212yes—
7C2×C8×D73C2211yescharacteristic
8#14556571—22no—
9Dic584—22no—
10C2×#11924003C2211yescharacteristic
11C16×D73—22no—
12#14556514—22no—
13C2×C16×C73C2211yescharacteristic
14#107×C73C2212yes—
15C2×Dic146—22no—
16C2×C4×D73D411yescharacteristic
17Dic292—22no—
18Dic292—22no—
19C2×#10596831D411yescharacteristic
20C8×D73—21no—
21C8×D73—21no—
22C4⋊Dic73—42no—
23#11924005—42no—
24#11924003—21no—
25C2×C8×C73C2311yescharacteristic
26C4⋊C4×C73—22no—
27C16×C73D412yes—
28C22×D73D811yescharacteristic
29C2×C4×C73—42no—
30C2×C4×C73C2×D411yescharacteristic
31C2×Dic73—42no—
32C2×Dic73D811yescharacteristic
33C4×D73—21no—
34C4×D73—21no—
35Dic146—42no—
36Dic146—42no—
37C8×C73C2×D411yescharacteristic
38C8×C73#4111yescharacteristic
39#10596831—21no—
40C22×C73C2×D811yescharacteristic
41C2×D73—21no—
42C2×D73—21no—
43C2×D73Q3212yescomplemented
44C4×C73—82no—
45C4×C73#12111yescharacteristic
46C4×C73#13511yescharacteristic
47Dic73—21no—
48Dic73—82no—
49C2×C73#46611yescharacteristic
50C2×C73C2×Q3211yescharacteristic
51C2×C73#50811yescharacteristic
52D73—22no—
53#2216—731nomaximal, Sylow
54C73#221611yescharacteristic, complemented, Sylow
55C2×Q32—731no—
56C22×C16—731no—
57#467—732no—
58#366D7311yescharacteristic, complemented
59#358—732no—
60C2×Q16—732no—
61C22×C8—731no—
62C22⋊Q8—1462no—
63Q32—1462no—
64C2×C16—731no—
65C2×C16—1462no—
66C2×C16C2×D7311yescharacteristic
67#107C2×D7312yes—
68#103—1462no—
69C2×Q8—1462no—
70C22×C4—731no—
71Q16—1462no—
72Q16—1462no—
73C2×C8—731no—
74C2×C8—1461no—
75C2×C8—1461no—
76C2×C8C22×D7311yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—2922no—
79C22⋊C4—2922no—
80C16—1461no—
81C16D29212yes—
82C23—731no—
83Q8—2922no—
84Q8—2922no—
85C2×C4—42no—
86C2×C4—2922no—
87C2×C4—731no—
88C2×C4—1461no—
89C2×C4—1461no—
90C2×C4D4×D7311yescharacteristic
91C8—1461no—
92C8C2×D29211yescharacteristic
93C8#1192402911yescharacteristic
94C22—732no—
95C22—1461no—
96C22—1461no—
97C22D8×D7311yescharacteristic
98C4—82no—
99C4—5842no—
100C4—1461no—
101C4#1455656611yescharacteristic
102C4#1455661411yescharacteristic
103C2—1462no—
104C2#1798882411yescharacteristic
105C2Q32×D7311yescharacteristic
106C2#1798901611yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#366×C73C2
socleC22×C73C2×D8
hypercenter#366D73
hypocenterC73#2216
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×Dic584C2semidirect
4. #17988390C2semidirect
5. #366×C73C2semidirect
43. C2×D73Q32semidirect
54. C73#2216semidirect
58. #366D73semidirect