Finite Group Databasebeta

← #11771115

Subgroups — #11771115

Order 1152.

308 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593845C211yesmaximal, characteristic
2C2×C22⋊#622C212yesmaximal
3C23×C3⋊Dic3C2211yescharacteristic
4C2×#3792C412yes—
5C22×#622—22no—
6C22⋊#622—22no—
7C22⋊#622—22no—
8C22⋊#622C414yes—
9C24×C32Q811yescharacteristic
10C22×C3⋊Dic3—42no—
11C22×C3⋊Dic3C2×C411yescharacteristic
12C22×C3⋊Dic3C2×C412yes—
13C22×C3⋊Dic3D412yes—
14C22×C3⋊Dic3D411yescharacteristic
15#3792—42no—
16C2×#622—24no—
17C2×#622—22no—
18C2×#622—44no—
19#1298—91nomaximal, Sylow
20C23×Dic3—121no—
21C23×C32—24no—
22C23×C32—41no—
23C23×C32C4⋊C411yescharacteristic
24C23×C32C4⋊C412yes—
25C2×C3⋊Dic3—24no—
26C2×C3⋊Dic3—22no—
27C2×C3⋊Dic3—42no—
28C2×C3⋊Dic3—41no—
29C2×C3⋊Dic3C4211yescharacteristic
30C2×C3⋊Dic3C22⋊C412yes—
31C2×C3⋊Dic3C22⋊C411yescharacteristic
32#622—44no—
33#622—42no—
34#407—91no—
35C2×C22⋊C8—92no—
36C24×C3—41no—
37C22×Dic3—121no—
38C22×Dic3—122no—
39C22×Dic3—122no—
40C22×Dic3—121no—
41C22×Dic3—128no—
42C22×C32—22no—
43C22×C32—22no—
44C22×C32—22no—
45C22×C32—21no—
46C22×C32—44no—
47C22×C32#9511yescharacteristic
48C22×C32#10814yes—
49C3⋊Dic3—22no—
50C3⋊Dic3—21no—
51C3⋊Dic3#9912yes—
52C23×C4—91no—
53C2×M16—92no—
54C22×C8—182no—
55C22⋊C8—94no—
56C22⋊C8—182no—
57C22⋊C8—182no—
58C23×C3—48no—
59C23×C3—44no—
60C23×C3—41no—
61C23×C3—42no—
62C2×Dic3—121no—
63C2×Dic3—121no—
64C2×Dic3—122no—
65C2×Dic3—128no—
66C2×Dic3—124no—
67C2×Dic3—128no—
68C2×Dic3—124no—
69C2×C32—24no—
70C2×C32—41no—
71C2×C32#34112yes—
72C2×C32#34211yescharacteristic
73C24PSU(3,𝔽2)11yescharacteristic
74C22×C4—92no—
75C22×C4—91no—
76C22×C4—92no—
77C22×C4—91no—
78C22×C4—362no—
79M16—362no—
80C2×C8—184no—
81C2×C8—182no—
82C2×C8—364no—
83C22×C3—44no—
84C22×C3—42no—
85C22×C3—44no—
86C22×C3—44no—
87C22×C3—416no—
88C22×C3—41no—
89C22×C3—44no—
90Dic3—122no—
91Dic3—124no—
92Dic3—122no—
93C32#129811yescharacteristic, complemented, Sylow
94C23—24no—
95C23—41no—
96C23#377711yescharacteristic
97C23#377712yes—
98C2×C4—91no—
99C2×C4—92no—
100C2×C4—91no—
101C2×C4—184no—
102C2×C4—182no—
103C2×C4—361no—
104C2×C4—362no—
105C8—362no—
106C8—364no—
107C2×C3—48no—
108C2×C3—44no—
109C2×C3—42no—
110C2×C3—41no—
111C22—22no—
112C22—22no—
113C22—22no—
114C22—21no—
115C22—44no—
116C22#6374711yescharacteristic
117C22#6374814yes—
118C4—92no—
119C4—182no—
120C4—181no—
121C3—41no—
122C2—24no—
123C2—41no—
124C2#1059009712yes—
125C2#1059009811yescharacteristic
subgroupG/H
centerC22#63747
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC24PSU(3,𝔽2)
Fitting, prime radicalC24×C32Q8
socleC22×C32#95
cosocleC23×C3⋊Dic3C22
hypocenterC32#1298
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
93. C32#1298semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105938452
C2×C22⋊#6222
#12989