Finite Group Databasebeta

← #11785742

Subgroups — #11785742

Order 1152.

602 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 66 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×#64086C211yesmaximal, characteristic
2#10593845C212yesmaximal
3#10590208C214yesmaximal, complemented
4C23×C3⋊Dic3C2211yescharacteristic
5C2×#3792C2214yes—
6C2×C32×C22⋊C4C411yescharacteristic
7C2×#3757C411yescharacteristic
8C2×#3750C2212yes—
9C2×C4×C3⋊Dic3C412yes—
10#64086—24no—
11C22⋊#622—24no—
12C2×#877—62no—
13C24×C32C2×C411yescharacteristic
14C22×C32×C4C2×C412yes—
15C22×C3⋊Dic3—24no—
16C22×C3⋊Dic3C2×C411yescharacteristic
17C22×C3⋊Dic3C2×C412yes—
18C22×C3⋊Dic3D414yes—
19C22×C3⋊Dic3C2311yescharacteristic
20#3792—28no—
21C2×#622—24no—
22C32×C22⋊C4—22no—
23#3757—22no—
24#3750—24no—
25C4×C3⋊Dic3—24no—
26#1822—91nomaximal, Sylow
27C23×Dic3—62no—
28C2×C3×C22⋊C4—22no—
29C2×#217—62no—
30C2×Dic3⋊C4—64no—
31C2×C4×Dic3—64no—
32#877—616no—
33C23×C32—22no—
34C23×C32—42no—
35C23×C32C22⋊C412yes—
36C23×C32C22×C411yescharacteristic
37C2×C32×C4—22no—
38C2×C32×C4—42no—
39C2×C3⋊Dic3—22no—
40C2×C3⋊Dic3—28no—
41C2×C3⋊Dic3—22no—
42C2×C3⋊Dic3—42no—
43C2×C3⋊Dic3C22⋊C412yes—
44C2×C3⋊Dic3C2×D412yes—
45C2×C3⋊Dic3#4114yes—
46#622—44no—
47C2×#117—91no—
48#407—92no—
49#343—94no—
50C24×C3—22no—
51C22×C3×C4—24no—
52C22×Dic3—68no—
53C22×Dic3—62no—
54C22×Dic3—62no—
55C22×Dic3—64no—
56C22×Dic3—616no—
57C3×C22⋊C4—28no—
58#217—68no—
59Dic3⋊C4—616no—
60C4×Dic3—616no—
61C22×C32—22no—
62C22×C32—22no—
63C22×C32—24no—
64C22×C32—44no—
65C22×C32C2×C22⋊C411yescharacteristic
66C22×C32#11712yes—
67C32×C4—42no—
68C3⋊Dic3—22no—
69C3⋊Dic3—42no—
70C3⋊Dic3#12314yes—
71C23×C4—91no—
72C2×M16—94no—
73#117—184no—
74C2×C4⋊C4—92no—
75C2×C22⋊C4—91no—
76C2×C22⋊C4#15711yescharacteristic
77C2×C42—92no—
78C22⋊C8—184no—
79C23×C3—28no—
80C23×C3—22no—
81C23×C3—24no—
82C23×C3—48no—
83C2×C3×C4—28no—
84C2×C3×C4—48no—
85C2×Dic3—64no—
86C2×Dic3—64no—
87C2×Dic3—68no—
88C2×Dic3—632no—
89C2×Dic3—68no—
90C2×Dic3—68no—
91C2×Dic3—128no—
92C2×C32—22no—
93C2×C32—42no—
94C2×C32#38111yescharacteristic
95C2×C32#41312yes—
96C24C2×#15711yescharacteristic
97C22×C4—91no—
98C22×C4—91no—
99C22×C4—94no—
100C22×C4—92no—
101C22×C4—184no—
102C22×C4C2×#15712yes—
103M16—188no—
104C2×C8—184no—
105C4⋊C4—184no—
106C22⋊C4—22no—
107C22⋊C4—182no—
108C42—184no—
109C22×C3—28no—
110C22×C3—28no—
111C22×C3—24no—
112C22×C3—22no—
113C22×C3—48no—
114C22×C3—416no—
115C3×C4—48no—
116Dic3—68no—
117Dic3—68no—
118Dic3—128no—
119C32#182211yescharacteristic, complemented, Sylow
120C23—22no—
121C23—42no—
122C23C22⋊#15712yes—
123C23C22×#15711yescharacteristic
124C2×C4—22no—
125C2×C4—42no—
126C2×C4—94no—
127C2×C4—92no—
128C2×C4—92no—
129C2×C4—188no—
130C2×C4—182no—
131C2×C4—182no—
132C2×C4—362no—
133C8—364no—
134C2×C3—28no—
135C2×C3—22no—
136C2×C3—24no—
137C2×C3—48no—
138C22—22no—
139C22—22no—
140C22—24no—
141C22—44no—
142C22#6428612yes—
143C22C2×C22⋊#15711yescharacteristic
144C4—42no—
145C4—94no—
146C4—182no—
147C4—362no—
148C3—22no—
149C2—22no—
150C2—42no—
151C2#1059381111yescharacteristic
152C2#1059382412yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C22⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1822
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10590208C2semidirect
119. C32#1822semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
#105938452
#105902082
#18229