Finite Group Databasebeta

← #22626233

Subgroups — #22626233

Order 9344.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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#17989573C212yesmaximal
2#17989497C214yesmaximal, complemented
3#17989161C211yesmaximal, characteristic
4D73⋊M16—22no—
5#14556652C2214yes—
6#14556651—22no—
7C2×#11924028C2211yescharacteristic
8#14556589C2212yes—
9#14556580C412yes—
10#14556574—22no—
11#14556567—22no—
12#14556550C411yescharacteristic
13C22×Q8×C73C411yescharacteristic
14#11924038—42no—
15#11924037—24no—
16#11924036—42no—
17#11924028—42no—
18C2×Dic146C2311yescharacteristic
19C2×D292C2×C411yescharacteristic
20C2×C22⋊D73D412yes—
21C2×C4×D73D412yes—
22C4⋊Dic73—21no—
23#11924007—24no—
24C22⋊Dic73—21no—
25#11924005—24no—
26C4×Dic73C2×C412yes—
27C2×Q8×C73—21no—
28C2×Q8×C73—42no—
29C2×Q8×C73C2×C412yes—
30C22×C4×C73—21no—
31C22×C4×C73C2×C411yescharacteristic
32C23×C73C22⋊C411yescharacteristic
33C22×D73C22⋊C412yes—
34Q8×C73—42no—
35Q8×C73—42no—
36C2×C4×C73—22no—
37C2×C4×C73—22no—
38C2×C4×C73—42no—
39C2×C4×C73C22⋊C411yescharacteristic
40C2×C4×C73C22×C411yescharacteristic
41C22⋊D73—42no—
42C2×Dic73—22no—
43C2×Dic73C2×D412yes—
44D292—41no—
45C4×D73—22no—
46C4×D73—22no—
47Dic146—41no—
48#10596833—44no—
49C22×C73—21no—
50C22×C73—41no—
51C22×C73C2×C22⋊C411yescharacteristic
52C2×D73—22no—
53C2×D73—42no—
54C4×C73—21no—
55C4×C73—42no—
56C4×C73#9912yes—
57Dic73—22no—
58Dic73—42no—
59C2×C73—21no—
60C2×C73—41no—
61C2×C73C2×#9911yescharacteristic
62D73—42no—
63#2135—731nomaximal, Sylow
64C73#213511yescharacteristic, complemented, Sylow
65#536—731no—
66#413—732no—
67#356—734no—
68C2×#41—731no—
69C22×Q8#6440811yescharacteristic
70C2×M16—1462no—
71C4⋊Q8—732no—
72#124—732no—
73#123—1462no—
74C22⋊Q8—1462no—
75#117—731no—
76#101—734no—
77#100—1462no—
78#41—2922no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—731no—
82C2×Q8C2×#6440812yes—
83C2×D4—732no—
84C2×D4—731no—
85C22×C4—21no—
86C22×C4—732no—
87C22×C4C2×#6440811yescharacteristic
88M16—2922no—
89M16—1464no—
90C2×C8—2922no—
91C4⋊C4—1464no—
92C4⋊C4—1461no—
93C22⋊C4—1464no—
94C22⋊C4—1461no—
95C42—732no—
96C23—732no—
97C23C22⋊#6440811yescharacteristic
98Q8—42no—
99Q8—42no—
100Q8—2921no—
101D4—2921no—
102D4—2922no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—42no—
106C2×C4—732no—
107C2×C4—1462no—
108C2×C4—1462no—
109C2×C4—1462no—
110C2×C4C22⋊#6440811yescharacteristic
111C2×C4C22×#6440811yescharacteristic
112C8—2924no—
113C22—21no—
114C22—41no—
115C22—2922no—
116C22—1462no—
117C22C2×C22⋊#6440811yescharacteristic
118C4—21no—
119C4—42no—
120C4—2922no—
121C4—1462no—
122C4#1455664912yes—
123C2—21no—
124C2—41no—
125C2—2922no—
126C2C2×#1455664911yescharacteristic
subgroupG/H
centerC2C2×#14556649
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22×Q8×C73C4
socleC2×C73C2×#99
hypercenterC22×Q8#64408
hypocenterC73#2135
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #17989497C2semidirect
64. C73#2135semidirect