Finite Group Databasebeta

← #11771958

Subgroups — #11771958

Order 1152.

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

normal subgroups only

This group has 250 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#10592358C211yesmaximal, characteristic
2#10590208C211yesmaximal, characteristic
3#10590203C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C4⋊(C3⋊Dic3)C411yescharacteristic
6C2×#3750C2211yescharacteristic
7C22⋊#622—21no—
8C32×#95C411yescharacteristic
9#63658—21no—
10#63658—21no—
11#4659—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—
21C4⋊(C3⋊Dic3)—41no—
22#3750—41no—
23#1353—91nomaximal, Sylow
24C2×C4⋊Dic3—62no—
25C2×Dic3⋊C4—62no—
26C3×#95—22no—
27C3⋊#95—64no—
28C3⋊#95—64no—
29C23×C32C22⋊C411yescharacteristic
30C2×C32×C4—21no—
31C2×C32×C4—41no—
32C2×C32×C4—41no—
33C2×C32×C4—41no—
34C2×C32×C4—41no—
35C2×C3⋊Dic3—21no—
36C2×C3⋊Dic3—21no—
37C2×C3⋊Dic3—21no—
38C2×C3⋊Dic3—41no—
39C2×C3⋊Dic3—42no—
40C2×C3⋊Dic3—41no—
41C2×C3⋊Dic3SD1611yescharacteristic
42C2×C3⋊Dic3Q1611yescharacteristic
43#622—42no—
44#622—81no—
45#400—91no—
46#343—91no—
47#324—91no—
48C22×C3×C4—24no—
49C22×C3×C4—22no—
50C22×Dic3—62no—
51C22×Dic3—62no—
52C22×Dic3—64no—
53C4⋊Dic3—124no—
54Dic3⋊C4—124no—
55C22×C32—21no—
56C22×C32—21no—
57C22×C32#9911yescharacteristic
58C22×C32#10311yescharacteristic
59C22×C32#10411yescharacteristic
60C32×C4—41no—
61C32×C4—81no—
62C3⋊Dic3—21no—
63C3⋊Dic3—21no—
64C3⋊Dic3—41no—
65C3⋊Dic3—81no—
66C2×M16—181no—
67C2×C4⋊C4—91no—
68C2×C4⋊C4—91no—
69C22⋊C8—181no—
70#95—181no—
71#95—181no—
72#95#15711yescharacteristic
73C23×C3—22no—
74C2×C3×C4—24no—
75C2×C3×C4—44no—
76C2×C3×C4—44no—
77C2×C3×C4—44no—
78C2×C3×C4—44no—
79C2×Dic3—62no—
80C2×Dic3—62no—
81C2×Dic3—122no—
82C2×Dic3—122no—
83C2×Dic3—122no—
84C2×Dic3—124no—
85C2×Dic3—124no—
86C2×Dic3—128no—
87C2×C32—21no—
88C2×C32—21no—
89C2×C32#32811yescharacteristic
90C2×C32#35211yescharacteristic
91C2×C32#35511yescharacteristic
92C22×C4—21no—
93C22×C4—91no—
94C22×C4—91no—
95C22×C4—181no—
96C22×C4C2×#15711yescharacteristic
97M16—182no—
98M16—361no—
99C2×C8—361no—
100C2×C8—361no—
101C4⋊C4—361no—
102C4⋊C4—361no—
103C22×C3—24no—
104C22×C3—24no—
105C22×C3—22no—
106C22×C3—22no—
107C22×C3—22no—
108C3×C4—44no—
109C3×C4—84no—
110Dic3—122no—
111Dic3—122no—
112Dic3—242no—
113Dic3—244no—
114C32#135311yescharacteristic, complemented, Sylow
115C23C22⋊#15711yescharacteristic
116C2×C4—21no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—91no—
122C2×C4—91no—
123C2×C4—181no—
124C2×C4—181no—
125C2×C4—181no—
126C2×C4—361no—
127C2×C4—362no—
128C2×C4—361no—
129C8—362no—
130C8—721no—
131C2×C3—24no—
132C2×C3—24no—
133C2×C3—22no—
134C2×C3—22no—
135C2×C3—22no—
136C22—21no—
137C22—21no—
138C22#6377411yescharacteristic
139C22#6378311yescharacteristic
140C22#6378411yescharacteristic
141C4—41no—
142C4—81no—
143C4—181no—
144C4—181no—
145C4—361no—
146C4—721no—
147C3—22no—
148C2—21no—
149C2—21no—
150C2#1059014511yescharacteristic
151C2#1059015411yescharacteristic
152C2#1059015811yescharacteristic
subgroupG/H
centerC22#63774
commutatorC22×C32×C4C2×C4
FrattiniC22×C4C2×#157
FittingC32×#95C4
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×#3750C22
hypercenter#95#157
hypocenterC32#1353
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
114. C32#1353semidirect

Maximal subgroups

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

subgroupindex
#105923582
#105902082
#105902032
#13539