Finite Group Databasebeta

← #11771040

Subgroups — #11771040

Order 1152.

302 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593845C212yesmaximal
2C2×C22⋊#622C211yesmaximal, characteristic
3C23×C3⋊Dic3C2211yescharacteristic
4C2×#3792—22no—
5C22×#622C412yes—
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—44no—
16C2×#622—22no—
17C2×#622—24no—
18C2×#622—42no—
19#1293—91nomaximal, Sylow
20C23×Dic3—121no—
21C23×C32—22no—
22C23×C32—41no—
23C23×C32—41no—
24C23×C32C4⋊C412yes—
25C23×C32C4⋊C411yescharacteristic
26C2×C3⋊Dic3—22no—
27C2×C3⋊Dic3—24no—
28C2×C3⋊Dic3—42no—
29C2×C3⋊Dic3—41no—
30C2×C3⋊Dic3C4211yescharacteristic
31C2×C3⋊Dic3C22⋊C412yes—
32C2×C3⋊Dic3C22⋊C411yescharacteristic
33#622—44no—
34#622—42no—
35#407—92no—
36C2×C22⋊C8—91no—
37C24×C3—41no—
38C22×Dic3—121no—
39C22×Dic3—122no—
40C22×Dic3—122no—
41C22×Dic3—121no—
42C22×Dic3—128no—
43C22×C32—21no—
44C22×C32—21no—
45C22×C32—22no—
46C22×C32—22no—
47C22×C32—22no—
48C22×C32—44no—
49C22×C32#9511yescharacteristic
50C22×C32#10812yes—
51C3⋊Dic3—22no—
52C3⋊Dic3—21no—
53C3⋊Dic3#9912yes—
54C23×C4—91no—
55C2×M16—182no—
56C22×C8—92no—
57C22⋊C8—94no—
58C22⋊C8—182no—
59C22⋊C8—182no—
60C23×C3—44no—
61C23×C3—44no—
62C23×C3—44no—
63C23×C3—42no—
64C23×C3—41no—
65C2×Dic3—121no—
66C2×Dic3—121no—
67C2×Dic3—122no—
68C2×Dic3—124no—
69C2×Dic3—128no—
70C2×Dic3—128no—
71C2×Dic3—124no—
72C2×C32—22no—
73C2×C32—42no—
74C2×C32#33811yescharacteristic
75C2×C32#34111yescharacteristic
76C2×C32#34211yescharacteristic
77C24PSU(3,𝔽2)11yescharacteristic
78C22×C4—92no—
79C22×C4—91no—
80C22×C4—92no—
81C22×C4—91no—
82C22×C4—362no—
83M16—364no—
84C2×C8—184no—
85C2×C8—182no—
86C2×C8—362no—
87C22×C3—42no—
88C22×C3—44no—
89C22×C3—42no—
90C22×C3—44no—
91C22×C3—44no—
92C22×C3—416no—
93C22×C3—41no—
94C22×C3—42no—
95Dic3—122no—
96Dic3—124no—
97Dic3—122no—
98C32#129311yescharacteristic, complemented, Sylow
99C23—22no—
100C23—41no—
101C23—41no—
102C23#377712yes—
103C23#377711yescharacteristic
104C2×C4—91no—
105C2×C4—92no—
106C2×C4—91no—
107C2×C4—182no—
108C2×C4—184no—
109C2×C4—361no—
110C2×C4—362no—
111C8—362no—
112C8—364no—
113C2×C3—44no—
114C2×C3—48no—
115C2×C3—41no—
116C2×C3—41no—
117C2×C3—41no—
118C22—21no—
119C22—21no—
120C22—22no—
121C22—22no—
122C22—22no—
123C22—44no—
124C22#6374711yescharacteristic
125C22#6374812yes—
126C4—92no—
127C4—182no—
128C4—181no—
129C3—41no—
130C2—22no—
131C2—42no—
132C2#1059009611yescharacteristic
133C2#1059009711yescharacteristic
134C2#1059009811yescharacteristic
subgroupG/H
centerC22#63747
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC24PSU(3,𝔽2)
Fitting, prime radicalC24×C32Q8
socleC22×C32#95
cosocleC23×C3⋊Dic3C22
hypocenterC32#1293
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
98. C32#1293semidirect

Maximal subgroups

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

subgroupindex
#105938452
C2×C22⋊#6222
#12939