Finite Group Databasebeta

← #22626958

Subgroups — #22626958

Order 9344.

170 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 27 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#17989673C212yesmaximal, complemented
2#17989539C211yesmaximal, characteristic
3C22⋊#10596842—22no—
4C2×C4⋊#64408C2211yescharacteristic
5C2×C22⋊#64408—22no—
6C2×C4×#64408C411yescharacteristic
7C2×D4×D73C411yescharacteristic
8C2×#10596842—42no—
9C22×#64408—21no—
10C22×#64408D412yes—
11C4⋊#64408—41no—
12C22⋊#64408—44no—
13C4×#64408—41no—
14C23×D73—21no—
15C2×D292C811yescharacteristic, complemented
16C2×C22⋊D73—21no—
17D4×D73—41no—
18D4×D73—41no—
19C2×C4×D73C2×C411yescharacteristic
20C2×D4×C73C811yescharacteristic, complemented
21C23×C73—21no—
22C22×D73—21no—
23C22×D73—42no—
24C22×D73—42no—
25C22×D73—41no—
26C22×D73—41no—
27C22×D73C22⋊C411yescharacteristic
28C2×#64408—22no—
29C2×#64408—22no—
30C2×#64408—41no—
31C2×#64408—41no—
32C2×#64408—42no—
33#10596842—82no—
34D4×C73—41no—
35C2×C4×C73C2×C811yescharacteristic
36C22⋊D73—42no—
37C2×Dic73M1611yescharacteristic
38D292—41no—
39C4×D73—21no—
40C4×D73—21no—
41C22×C73—42no—
42C22×C73—41no—
43C22×C73C22⋊C811yescharacteristic
44C2×D73—21no—
45C2×D73—21no—
46C2×D73—42no—
47C2×D73—41no—
48C2×D73—82no—
49C2×D73—81no—
50C2×D73—81no—
51C2×D73#9911yescharacteristic
52C2×D73#10011yescharacteristic
53#64408—42no—
54#64408—42no—
55C4×C73—21no—
56Dic73—21no—
57C2×C73—21no—
58C2×C73—81no—
59C2×C73#32311yescharacteristic
60D73—21no—
61D73—81no—
62D73#35311yescharacteristic
63D73#35511yescharacteristic
64#1318—731nomaximal, Sylow
65C73#131811yescharacteristic, complemented, Sylow
66#390—731no—
67#324—732no—
68C22×D4—731no—
69C2×C4⋊C4—731no—
70C2×C22⋊C4—1462no—
71C2×C42—731no—
72C22⋊C8—1462no—
73C24—1461no—
74C2×D4—2921no—
75C2×D4—2921no—
76C2×D4—731no—
77C2×D4—1461no—
78C2×D4#1059684211yescharacteristic, complemented
79C22×C4—732no—
80C22×C4—731no—
81C22×C4—1461no—
82C2×C8—2922no—
83C4⋊C4—2921no—
84C22⋊C4—2924no—
85C42—2921no—
86C23—21no—
87C23—2921no—
88C23—2921no—
89C23—2922no—
90C23—2922no—
91C23—731no—
92C23—1461no—
93D4—41no—
94D4—2921no—
95D4—2922no—
96C2×C4—2921no—
97C2×C4—2921no—
98C2×C4—2922no—
99C2×C4—731no—
100C2×C4—1461no—
101C2×C4—1461no—
102C2×C4—1462no—
103C2×C4—1462no—
104C2×C4C2×#1059684211yescharacteristic
105C8—5842no—
106C22—42no—
107C22—41no—
108C22—2922no—
109C22—2921no—
110C22—5841no—
111C22—5841no—
112C22—5842no—
113C22—731no—
114C22—731no—
115C22—1461no—
116C22—1461no—
117C22C22⋊#1059684211yescharacteristic
118C4—21no—
119C4—2922no—
120C4—2922no—
121C4—1461no—
122C2—21no—
123C2—81no—
124C2—5841no—
125C2—731no—
126C2—731no—
127C2—1461no—
128C2#1798967211yescharacteristic
subgroupG/H
centerC2#17989672
commutatorC2×C4×C73C2×C8
FrattiniC2×C4C2×#10596842
FittingC2×D4×C73C8
socleC2×C73#323
hypercenterC2×D4#10596842
hypocenterC73#1318
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #17989673C2semidirect
15. C2×D292C8semidirect
20. C2×D4×C73C8semidirect
65. C73#1318semidirect
78. C2×D4#10596842semidirect