Finite Group Databasebeta

← #11771976

Subgroups — #11771976

Order 1152.

322 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 30 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#10592929C211yesmaximal, characteristic
2#10590208C211yesmaximal, characteristic
3#10590203C211yesmaximal, characteristic
4C22×C32×Q8C411yescharacteristic
5C2×#3792—21no—
6C2×#3750—21no—
7C2×#3750C2211yescharacteristic
8C22⋊#622—21no—
9#63658—21no—
10#63658C411yescharacteristic
11#5230—62no—
12C2×C32×Q8—42no—
13C2×C32×Q8—41no—
14C22×C32×C4—21no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C3⋊Dic3—21no—
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19#3792—22no—
20#3792—41no—
21C2×#622—41no—
22C2×#622—41no—
23#3750—41no—
24#3750—42no—
25#1354—91nomaximal, Sylow
26C22×C3×Q8—22no—
27C2×Dic3⋊C4—62no—
28C2×Dic3⋊C4—64no—
29C3⋊#95—62no—
30C3⋊#95—64no—
31C23×C32C22⋊C411yescharacteristic
32C32×Q8—42no—
33C32×Q8—42no—
34C2×C32×C4—22no—
35C2×C32×C4—21no—
36C2×C32×C4—41no—
37C2×C32×C4—41no—
38C2×C32×C4—41no—
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—21no—
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3—41no—
46C2×C3⋊Dic3SD1611yescharacteristic
47C2×C3⋊Dic3Q1611yescharacteristic
48#622—42no—
49#622—81no—
50#395—91no—
51#343—91no—
52#324—91no—
53C2×C3×Q8—48no—
54C2×C3×Q8—44no—
55C22×C3×C4—24no—
56C22×C3×C4—22no—
57C22×Dic3—62no—
58C22×Dic3—62no—
59C22×Dic3—64no—
60Dic3⋊C4—124no—
61Dic3⋊C4—128no—
62C22×C32—21no—
63C22×C32—21no—
64C22×C32#9911yescharacteristic
65C22×C32#10311yescharacteristic
66C22×C32#10411yescharacteristic
67C32×C4—42no—
68C32×C4—41no—
69C3⋊Dic3—21no—
70C3⋊Dic3—21no—
71C3⋊Dic3—42no—
72C3⋊Dic3—41no—
73C22×Q8#15711yescharacteristic
74C2×M16—181no—
75C2×C4⋊C4—91no—
76C2×C4⋊C4—181no—
77C22⋊C8—181no—
78#95—91no—
79#95—181no—
80C23×C3—22no—
81C3×Q8—48no—
82C3×Q8—48no—
83C2×C3×C4—28no—
84C2×C3×C4—24no—
85C2×C3×C4—44no—
86C2×C3×C4—44no—
87C2×C3×C4—44no—
88C2×Dic3—62no—
89C2×Dic3—62no—
90C2×Dic3—68no—
91C2×Dic3—122no—
92C2×Dic3—122no—
93C2×Dic3—122no—
94C2×Dic3—124no—
95C2×Dic3—124no—
96C2×Dic3—124no—
97C2×C32—21no—
98C2×C32—21no—
99C2×C32#32811yescharacteristic
100C2×C32AΣL(1,𝔽16)11yescharacteristic
101C2×C32#35611yescharacteristic
102C2×Q8—42no—
103C2×Q8—41no—
104C22×C4—21no—
105C22×C4—91no—
106C22×C4—91no—
107C22×C4—181no—
108C22×C4C2×#15711yescharacteristic
109M16—182no—
110M16—361no—
111C2×C8—361no—
112C2×C8—361no—
113C4⋊C4—361no—
114C4⋊C4—362no—
115C22×C3—24no—
116C22×C3—24no—
117C22×C3—22no—
118C22×C3—22no—
119C22×C3—22no—
120C3×C4—48no—
121C3×C4—44no—
122Dic3—122no—
123Dic3—122no—
124Dic3—128no—
125Dic3—242no—
126C32#135411yescharacteristic, complemented, Sylow
127C23C22⋊#15711yescharacteristic
128Q8—42no—
129Q8—42no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—91no—
136C2×C4—91no—
137C2×C4—181no—
138C2×C4—181no—
139C2×C4—182no—
140C2×C4—181no—
141C2×C4—361no—
142C2×C4—361no—
143C2×C4—361no—
144C8—362no—
145C8—721no—
146C2×C3—24no—
147C2×C3—24no—
148C2×C3—22no—
149C2×C3—22no—
150C2×C3—22no—
151C22—21no—
152C22—21no—
153C22#6378411yescharacteristic
154C22#6378511yescharacteristic
155C22#6378611yescharacteristic
156C4—42no—
157C4—41no—
158C4—181no—
159C4—181no—
160C4—362no—
161C4—361no—
162C3—22no—
163C2—21no—
164C2—21no—
165C2#1059021511yescharacteristic
166C2#1059021811yescharacteristic
167C2#1059022311yescharacteristic
subgroupG/H
centerC22#63786
commutatorC22×C32×C4C2×C4
FrattiniC22×C4C2×#157
FittingC22×C32×Q8C4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×#3750C22
hypercenterC22×Q8#157
hypocenterC32#1354
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
126. C32#1354semidirect

Maximal subgroups

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

subgroupindex
#105929292
#105902082
#105902032
#13549