Finite Group Databasebeta

← #11771967

Subgroups — #11771967

Order 1152.

420 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 95 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#10592678C211yesmaximal, characteristic
2C32×#343C211yesmaximal, characteristic
3#10589394C211yesmaximal, characteristic
4#67494—34nomaximal
5C22×#634C411yescharacteristic
6C2×C32×M16—21no—
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3750—21no—
9#63658—21no—
10#63658C411yescharacteristic
11#63657—21no—
12#4979—34no—
13C3×#343D314yes—
14#4528—34no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C32×C4D411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3—21no—
20C2×#634—41no—
21C2×#634—42no—
22C32×M16—22no—
23C32×M16—41no—
24C2×C32×C8—41no—
25C32×C4⋊C4—41no—
26#3750—42no—
27C2×C3⋊(C3⋊C8)—41no—
28#1354—91noSylow
29C22×Dic6—34no—
30C2×C3×M16—24no—
31C2×C3×C4⋊C4C2×D314yes—
32C2×Dic3⋊C4—64no—
33C3⋊#95—34no—
34C3⋊#95—64no—
35#830—64no—
36C23×C32C22⋊C411yescharacteristic
37C2×C32×C4—21no—
38C2×C32×C4—21no—
39C2×C32×C4—21no—
40C2×C32×C4—21no—
41C2×C32×C4—41no—
42C2×C32×C4—41no—
43C2×C32×C4SD1611yescharacteristic
44C2×C32×C4Q1611yescharacteristic
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3—41no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3—41no—
51#634—42no—
52#634—42no—
53C32×C8—42no—
54C3⋊(C3⋊C8)—81no—
55#395—91no—
56#343C3⋊D311yescharacteristic
57#324—91no—
58C22×C3×C4C4×D314yes—
59C22×C3×C4D1214yes—
60C22×C3×C4#6714yes—
61C22×Dic3—64no—
62C22×Dic3—64no—
63C2×Dic6—124no—
64C2×Dic6—128no—
65C3×M16—28no—
66C3×M16—44no—
67C2×C3×C8—44no—
68C3×C4⋊C4—44no—
69Dic3⋊C4—128no—
70C2×C3⋊C8—124no—
71C22×C32—21no—
72C22×C32—21no—
73C22×C32#9911yescharacteristic
74C22×C32#10311yescharacteristic
75C22×C32#10411yescharacteristic
76C32×C4—21no—
77C32×C4—21no—
78C32×C4—41no—
79C32×C4—41no—
80C3⋊Dic3—42no—
81C3⋊Dic3—42no—
82C22×Q8—91no—
83C2×M16—21no—
84C2×C4⋊C4—181no—
85C2×C4⋊C4C2×C3⋊D311yescharacteristic
86C22⋊C8—181no—
87#95—91no—
88#95—181no—
89C23×C3(C2×D3)⋊C414yes—
90C2×C3×C4—24no—
91C2×C3×C4—24no—
92C2×C3×C4—24no—
93C2×C3×C4—24no—
94C2×C3×C4—44no—
95C2×C3×C4—44no—
96C2×C3×C4#21414yes—
97C2×C3×C4#21614yes—
98C2×Dic3—68no—
99C2×Dic3—68no—
100C2×Dic3—124no—
101C2×Dic3—124no—
102C2×Dic3—124no—
103C2×Dic3—124no—
104Dic6—128no—
105Dic6—128no—
106C3×C8—48no—
107C3⋊C8—244no—
108C2×C32—21no—
109C2×C32—21no—
110C2×C32#32811yescharacteristic
111C2×C32AΣL(1,𝔽16)11yescharacteristic
112C2×C32#35611yescharacteristic
113C2×Q8—361no—
114C2×Q8—362no—
115C22×C4—181no—
116C22×C4—181no—
117C22×C4C4×C3⋊D311yescharacteristic
118C22×C4C4⋊(C3⋊D3)11yescharacteristic
119C22×C4#63811yescharacteristic
120M16—22no—
121M16—41no—
122C2×C8—41no—
123C2×C8—361no—
124C4⋊C4—41no—
125C4⋊C4—362no—
126C22×C3—24no—
127C22×C3—24no—
128C22×C3#80514yes—
129C22×C3#80614yes—
130C22×C3#81014yes—
131C3×C4—24no—
132C3×C4—24no—
133C3×C4—44no—
134C3×C4—44no—
135Dic3—128no—
136Dic3—128no—
137C32#135411yescharacteristic, complemented, Sylow
138C23#375211yescharacteristic
139Q8—362no—
140Q8—362no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—182no—
148C2×C4—182no—
149C2×C4—361no—
150C2×C4—361no—
151C2×C4—361no—
152C2×C4—361no—
153C2×C4#375411yescharacteristic
154C2×C4#375611yescharacteristic
155C8—42no—
156C8—721no—
157C2×C3—24no—
158C2×C3—24no—
159C2×C3#445214yes—
160C2×C3#447514yes—
161C2×C3#447814yes—
162C22—21no—
163C22—21no—
164C22#6363211yescharacteristic
165C22#6363311yescharacteristic
166C22#6363711yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—362no—
172C4—362no—
173C3#6749414yescomplemented
174C2—21no—
175C2—21no—
176C2#1058931811yescharacteristic
177C2#1058934111yescharacteristic
178C2#1058934411yescharacteristic
subgroupG/H
centerC22#63633
commutatorC22×C32×C4C2×C4
FrattiniC2×C4⋊C4C2×C3⋊D3
FittingC32×#343C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C32×C4⋊C4C22
hypercenter#343C3⋊D3
hypocenterC32#1354
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
137. C32#1354semidirect
173. C3#67494semidirect

Maximal subgroups

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

subgroupindex
#105926782
C32×#3432
#105893942
#674943