Finite Group Databasebeta

← #11771024

Subgroups — #11771024

Order 1152.

278 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×C4⋊#622C211yesmaximal, characteristic
2#10591120C212yesmaximal
3C22×#622C412yes—
4C2×C4×C3⋊Dic3C2211yescharacteristic
5C2×C3×#208—22no—
6C4⋊#622—22no—
7#63572—22no—
8#63572C414yes—
9#5118—62no—
10C22×C32×C4D411yescharacteristic
11C22×C3⋊Dic3C2×C411yescharacteristic
12C22×C3⋊Dic3Q811yescharacteristic
13C2×#622—22no—
14C2×#622—42no—
15C4×C3⋊Dic3C2×C412yes—
16C4×C3⋊Dic3D412yes—
17C3×#208—42no—
18C3×#208—42no—
19C2×C3×C3⋊C8—24no—
20#1292—91nomaximal, Sylow
21C2×C3×M16—62no—
22C2×C4×Dic3—62no—
23C2×#208—22no—
24Dic3⋊C8—64no—
25Dic3⋊C8—64no—
26C23×C32C4⋊C411yescharacteristic
27C2×C32×C4C22⋊C412yes—
28C2×C32×C4D811yescharacteristic
29C2×C32×C4SD1612yes—
30C2×C32×C4Q1611yescharacteristic
31C2×C3⋊Dic3—21no—
32C2×C3⋊Dic3—21no—
33C2×C3⋊Dic3—41no—
34C2×C3⋊Dic3C4211yescharacteristic
35C2×C3⋊Dic3C22⋊C411yescharacteristic
36C2×C3⋊Dic3C4⋊C412yes—
37#622—42no—
38C3×C3⋊C8—44no—
39#423—92no—
40C2×C4⋊C8—91no—
41C22×C3×C4—22no—
42C22×Dic3—62no—
43C22×Dic3—62no—
44C3×M16—122no—
45C3×M16—122no—
46C2×C3×C8—64no—
47C4×Dic3—62no—
48C4×Dic3—62no—
49C4×Dic3—62no—
50C4×Dic3—62no—
51#208—42no—
52#208—42no—
53C2×C3⋊C8—24no—
54C22×C32—21no—
55C22×C32—21no—
56C22×C32#9511yescharacteristic
57C22×C32#10611yescharacteristic
58C22×C32#10711yescharacteristic
59C32×C4#10212yes—
60C32×C4#10312yes—
61C3⋊Dic3—22no—
62C3⋊Dic3—21no—
63C3⋊Dic3#10011yescharacteristic
64C3⋊Dic3#10111yescharacteristic
65C2×M16—62no—
66C22×C8—92no—
67C2×C42—91no—
68C4⋊C8—94no—
69C4⋊C8—182no—
70C4⋊C8—182no—
71C23×C3—22no—
72C2×C3×C4—22no—
73C2×C3×C4—22no—
74C2×C3×C4—22no—
75C2×C3×C4—22no—
76C2×C3×C4—22no—
77C2×C3×C4—22no—
78C2×Dic3—62no—
79C2×Dic3—62no—
80C2×Dic3—62no—
81C2×Dic3—62no—
82C2×Dic3—122no—
83C2×Dic3—122no—
84C2×Dic3—124no—
85C3×C8—124no—
86C3⋊C8—44no—
87C2×C32—21no—
88C2×C32—21no—
89C2×C32#33811yescharacteristic
90C2×C32#34011yescharacteristic
91C2×C32#34311yescharacteristic
92C22×C4—91no—
93C22×C4—91no—
94C22×C4GO+(4,𝔽2)11yescharacteristic
95M16—122no—
96M16—122no—
97C2×C8—64no—
98C2×C8—182no—
99C2×C8—362no—
100C42—92no—
101C42—92no—
102C22×C3—22no—
103C22×C3—22no—
104C22×C3—22no—
105C22×C3—42no—
106C22×C3—42no—
107C3×C4—22no—
108C3×C4—22no—
109C3×C4—22no—
110C3×C4—22no—
111Dic3—62no—
112Dic3—62no—
113Dic3—64no—
114Dic3—122no—
115Dic3—122no—
116C32#129211yescharacteristic, complemented, Sylow
117C23#377311yescharacteristic
118C2×C4—91no—
119C2×C4—92no—
120C2×C4—91no—
121C2×C4—181no—
122C2×C4—181no—
123C2×C4—361no—
124C2×C4D32⋊C412yes—
125C2×C4#377411yescharacteristic
126C2×C4#377512yes—
127C2×C4#377611yescharacteristic
128C8—124no—
129C8—362no—
130C2×C3—22no—
131C2×C3—22no—
132C2×C3—22no—
133C2×C3—42no—
134C2×C3—42no—
135C22—21no—
136C22—21no—
137C22#6373711yescharacteristic
138C22#6374211yescharacteristic
139C22#6374311yescharacteristic
140C4—91no—
141C4—91no—
142C4—182no—
143C4—181no—
144C4#6373912yes—
145C4#6374012yes—
146C3—22no—
147C2—21no—
148C2—21no—
149C2#1059004611yescharacteristic
150C2#1059005311yescharacteristic
151C2#1059007511yescharacteristic
subgroupG/H
centerC22#63737
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C32C4⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypocenterC32#1292
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
116. C32#1292semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#6222
#105911202
#12929