Finite Group Databasebeta

← #11771839

Subgroups — #11771839

Order 1152.

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

normal subgroups only

This group has 274 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#10592682C211yesmaximal, characteristic
2#10590208C211yesmaximal, characteristic
3#10590203C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C32×C4⋊C4C411yescharacteristic
6C2×#3750—21no—
7C2×#3750C2211yescharacteristic
8C22⋊#622—21no—
9#63658—21no—
10#63658C411yescharacteristic
11#4983—62no—
12C22×C32×C4—21no—
13C22×C32×C4C2×C411yescharacteristic
14C22×C3⋊Dic3—21no—
15C22×C3⋊Dic3D411yescharacteristic
16C22×C3⋊Dic3D411yescharacteristic
17#3792—22no—
18#3792—41no—
19C2×#622—41no—
20C2×#622—41no—
21C32×C4⋊C4—41no—
22#3750—41no—
23#3750—41no—
24#3750—41no—
25#1346—91nomaximal, Sylow
26C2×C3×C4⋊C4—22no—
27C2×Dic3⋊C4—62no—
28C2×Dic3⋊C4—64no—
29C3⋊#95—62no—
30C3⋊#95—64no—
31C23×C32C22⋊C411yescharacteristic
32C2×C32×C4—21no—
33C2×C32×C4—41no—
34C2×C32×C4—41no—
35C2×C32×C4—41no—
36C2×C32×C4—41no—
37C2×C3⋊Dic3—22no—
38C2×C3⋊Dic3—21no—
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—21no—
41C2×C3⋊Dic3—41no—
42C2×C3⋊Dic3—41no—
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3D811yescharacteristic
45C2×C3⋊Dic3SD1611yescharacteristic
46#622—42no—
47#622—81no—
48#398—91no—
49#343—91no—
50#324—91no—
51C22×C3×C4—24no—
52C22×C3×C4—22no—
53C22×Dic3—62no—
54C22×Dic3—62no—
55C22×Dic3—64no—
56C3×C4⋊C4—44no—
57Dic3⋊C4—124no—
58Dic3⋊C4—124no—
59Dic3⋊C4—124no—
60C22×C32—21no—
61C22×C32—21no—
62C22×C32#9911yescharacteristic
63C22×C32#10211yescharacteristic
64C22×C32#10411yescharacteristic
65C32×C4—41no—
66C32×C4—81no—
67C3⋊Dic3—21no—
68C3⋊Dic3—21no—
69C3⋊Dic3—42no—
70C3⋊Dic3—41no—
71C2×M16—181no—
72C2×C4⋊C4—91no—
73C2×C4⋊C4—181no—
74C2×C4⋊C4#15711yescharacteristic
75C22⋊C8—181no—
76#95—91no—
77#95—181no—
78C23×C3—22no—
79C2×C3×C4—24no—
80C2×C3×C4—44no—
81C2×C3×C4—44no—
82C2×C3×C4—44no—
83C2×C3×C4—44no—
84C2×Dic3—62no—
85C2×Dic3—62no—
86C2×Dic3—68no—
87C2×Dic3—122no—
88C2×Dic3—122no—
89C2×Dic3—122no—
90C2×Dic3—124no—
91C2×Dic3—124no—
92C2×Dic3—124no—
93C2×C32—21no—
94C2×C32—21no—
95C2×C32#32711yescharacteristic
96C2×C32#35211yescharacteristic
97C2×C32#35611yescharacteristic
98C22×C4—21no—
99C22×C4—91no—
100C22×C4—91no—
101C22×C4—181no—
102C22×C4C2×#15711yescharacteristic
103M16—182no—
104M16—361no—
105C2×C8—361no—
106C2×C8—361no—
107C4⋊C4—41no—
108C4⋊C4—361no—
109C4⋊C4—361no—
110C4⋊C4—361no—
111C22×C3—24no—
112C22×C3—24no—
113C22×C3—22no—
114C22×C3—22no—
115C22×C3—22no—
116C3×C4—44no—
117C3×C4—84no—
118Dic3—122no—
119Dic3—122no—
120Dic3—128no—
121Dic3—242no—
122C32#134611yescharacteristic, complemented, Sylow
123C23C22⋊#15711yescharacteristic
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—91no—
130C2×C4—91no—
131C2×C4—181no—
132C2×C4—181no—
133C2×C4—182no—
134C2×C4—181no—
135C2×C4—361no—
136C2×C4—361no—
137C2×C4—361no—
138C8—362no—
139C8—721no—
140C2×C3—24no—
141C2×C3—24no—
142C2×C3—22no—
143C2×C3—22no—
144C2×C3—22no—
145C22—21no—
146C22—21no—
147C22#6378211yescharacteristic
148C22#6378311yescharacteristic
149C22#6378611yescharacteristic
150C4—41no—
151C4—81no—
152C4—181no—
153C4—181no—
154C4—362no—
155C4—361no—
156C3—22no—
157C2—21no—
158C2—21no—
159C2#1059020511yescharacteristic
160C2#1059020911yescharacteristic
161C2#1059021811yescharacteristic
subgroupG/H
centerC22#63786
commutatorC22×C32×C4C2×C4
FrattiniC22×C4C2×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×#3750C22
hypercenterC2×C4⋊C4#157
hypocenterC32#1346
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
122. C32#1346semidirect

Maximal subgroups

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

subgroupindex
#105926822
#105902082
#105902032
#13469