Finite Group Databasebeta

← #22612167

Subgroups — #22612167

Order 9344.

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

normal subgroups only

This group has 142 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#17988992C211yesmaximal, characteristic, complemented
2#17988391C212yesmaximal, complemented
3#17988388C212yesmaximal
4#17988363C211yesmaximal, characteristic, complemented
5#495×C73C211yesmaximal, characteristic
6#14556591—21no—
7C2×#11924003C2212yes—
8#14556525—21no—
9#14556525C2212yes—
10C2×Q16×C73C2211yescharacteristic
11C2×SD16×C73—21no—
12C2×D8×C73C2211yescharacteristic
13#124×C73—21no—
14C4×C8×C73C2211yescharacteristic
15C2×Dic146—41no—
16C4⋊Dic73—22no—
17C4⋊Dic73—41no—
18#11924003—22no—
19C2×Q8×C73—21no—
20C2×D4×C73—21no—
21Q16×C73—22no—
22SD16×C73—42no—
23D8×C73—22no—
24C2×C8×C73D411yescharacteristic
25C2×C8×C73C2311yescharacteristic
26C22⋊C4×C73—41no—
27C22⋊C4×C73—41no—
28C42×C73D411yescharacteristic
29C23×C73—41no—
30Q8×C73—41no—
31Q8×C73—41no—
32D4×C73—41no—
33D4×C73—41no—
34C2×C4×C73—41no—
35C2×C4×C73D811yescharacteristic
36C2×C4×C73D811yescharacteristic
37C2×C4×C73C2×D411yescharacteristic
38C2×Dic73—42no—
39Dic146—82no—
40C8×C73SD1612yes—
41C8×C73#4112yes—
42C22×C73—81no—
43C22×C73—81no—
44C22×C73—81no—
45C22×C73C2×D811yescharacteristic
46C4×C73—21no—
47C4×C73—21no—
48C4×C73—81no—
49C4×C73#12411yescharacteristic
50C4×C73C2×SD1611yescharacteristic
51Dic73—82no—
52C2×C73—161no—
53C2×C73#48611yescharacteristic
54C2×C73#50911yescharacteristic
55C2×C73#51011yescharacteristic
56#2243—731nomaximal, Sylow
57C73#224311yescharacteristic, complemented, Sylow
58#500—731no—
59#495D7311yescharacteristic
60#358—732no—
61#357—732no—
62#346—731no—
63C2×Q16C2×D7311yescharacteristic
64C2×SD16—21no—
65C2×D8C2×D7311yescharacteristic
66C4⋊Q8—1461no—
67#124—21no—
68C2×C16—732no—
69#107—732no—
70#107—1461no—
71C4×C8C2×D7311yescharacteristic
72C2×Q8—21no—
73C2×Q8—2921no—
74C2×D4—21no—
75Q16—22no—
76SD16—42no—
77D8—22no—
78C2×C8C22⋊D7311yescharacteristic
79C2×C8C22×D7311yescharacteristic
80C4⋊C4—2921no—
81C4⋊C4—1462no—
82C22⋊C4—41no—
83C22⋊C4—41no—
84C42C22⋊D7311yescharacteristic
85C16—1462no—
86C23—41no—
87Q8—41no—
88Q8—41no—
89Q8—5842no—
90D4—41no—
91D4—41no—
92C2×C4—41no—
93C2×C4—2922no—
94C2×C4#1192401311yescharacteristic
95C2×C4#1192401311yescharacteristic
96C2×C4C2×C22⋊D7311yescharacteristic
97C8#1192401612yes—
98C8#1192402712yes—
99C22—81no—
100C22—81no—
101C22—81no—
102C22C2×#1192401311yescharacteristic
103C4—21no—
104C4—21no—
105C4—81no—
106C4—5842no—
107C4#1455657811yescharacteristic
108C4C2×#1192401611yescharacteristic
109C2—161no—
110C2#1798893311yescharacteristic
111C2#1798902211yescharacteristic
112C2#1798902711yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#495×C73C2
socleC22×C73C2×D8
hypercenter#495D73
hypocenterC73#2243
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #17988992C2semidirect
2. #17988391C2semidirect
4. #17988363C2semidirect
57. C73#2243semidirect