Finite Group Databasebeta

← #11772592

Subgroups — #11772592

Order 1152.

308 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 37 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#10593834C211yesmaximal, characteristic
2#10591640C212yesmaximal
3C2×#3832C2211yescharacteristic
4C2×#3788C411yescharacteristic
5C2×#3787C411yescharacteristic
6#63818—22no—
7#63778—22no—
8C3×#836—22no—
9#63559C414yes—
10#4751—62no—
11C2×C32×Q8D411yescharacteristic
12#3832—41no—
13#3832—41no—
14C2×C4⋊(C3⋊D3)C2×C412yes—
15C2×C4⋊(C3⋊D3)Q811yescharacteristic
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D412yes—
18C2×#622—21no—
19C2×#622—21no—
20#3788—41no—
21#3787—41no—
22C3×#208—24no—
23#3712—42no—
24#3710—42no—
25#1392—91nomaximal, Sylow
26C2×#239—62no—
27D3×M16—64no—
28C3×#101—62no—
29#836—22no—
30#823—64no—
31C22×C3⋊D3C4211yescharacteristic
32C22×C3⋊D3C4⋊C412yes—
33C32×Q8—41no—
34C2×C32×C4C22⋊C412yes—
35C2×C32×C4C4⋊C411yescharacteristic
36C2×C3⋊Dic3C22⋊C411yescharacteristic
37C4⋊(C3⋊D3)—42no—
38C4⋊(C3⋊D3)—41no—
39C4×C3⋊D3—22no—
40C4×C3⋊D3—22no—
41C4×C3⋊D3—21no—
42C4×C3⋊D3—21no—
43#622—41no—
44#622—41no—
45C3×C3⋊C8—44no—
46#413—92no—
47#408—91no—
48C2×C3×Q8—22no—
49#239—124no—
50#239—124no—
51C2×D12—62no—
52C2×D12—62no—
53C2×D12—62no—
54C2×C4×D3—62no—
55C2×C4×D3—62no—
56C2×C4×D3—62no—
57C3×M16—64no—
58#208—24no—
59ΓL(1,𝔽25)—124no—
60D3×C8—124no—
61C22×C32#9511yescharacteristic
62C2×C3⋊D3—22no—
63C2×C3⋊D3—21no—
64C2×C3⋊D3—41no—
65C2×C3⋊D3—42no—
66C32×C4—22no—
67C32×C4—21no—
68C3⋊Dic3#9911yescharacteristic
69C3⋊Dic3#9911yescharacteristic
70C2×#41—91no—
71C2×M16—91no—
72C2×M16—182no—
73C22×C8—91no—
74#101—62no—
75#100—94no—
76C22⋊C8—182no—
77C22×D3—62no—
78C22×D3—62no—
79C22×D3—62no—
80C3×Q8—44no—
81C2×C3×C4—22no—
82C2×C3×C4—22no—
83C2×C3×C4—22no—
84C2×Dic3—62no—
85D12—124no—
86D12—124no—
87D12—124no—
88C4×D3—64no—
89C4×D3—64no—
90C4×D3—122no—
91C4×D3—122no—
92C4×D3—122no—
93C4×D3—122no—
94C3×C8—124no—
95C3⋊C8—44no—
96C2×C32—21no—
97C2×C32#34211yescharacteristic
98C3⋊D3—42no—
99C3⋊D3—41no—
100#41—361no—
101#41—361no—
102C2×Q8GO+(4,𝔽2)11yescharacteristic
103C2×D4—92no—
104C2×D4—91no—
105C22×C4—92no—
106C22×C4—91no—
107M16—64no—
108M16—362no—
109M16—361no—
110C2×C8—181no—
111C2×C8—181no—
112C2×C8—362no—
113C2×C8—361no—
114C22×C3—22no—
115C2×D3—64no—
116C2×D3—122no—
117C2×D3—122no—
118C2×D3—242no—
119C2×D3—242no—
120C2×D3—242no—
121C3×C4—24no—
122C3×C4—42no—
123C3×C4—42no—
124Dic3—62no—
125Dic3—62no—
126C32#139211yescharacteristic, complemented, Sylow
127C23—92no—
128C23—91no—
129Q8—41no—
130D4—362no—
131D4—361no—
132C2×C4—91no—
133C2×C4—182no—
134C2×C4—181no—
135C2×C4—182no—
136C2×C4—181no—
137C2×C4D32⋊C412yes—
138C2×C4#377311yescharacteristic
139C8—124no—
140C8—361no—
141C8—361no—
142C2×C3—22no—
143C2×C3—42no—
144D3—124no—
145D3—242no—
146D3—242no—
147C22—182no—
148C22—181no—
149C22—362no—
150C22—361no—
151C22#6373711yescharacteristic
152C4—22no—
153C4—21no—
154C4—91no—
155C4—91no—
156C3—22no—
157C2—21no—
158C2—362no—
159C2—361no—
160C2#1059007711yescharacteristic
subgroupG/H
centerC2#10590077
commutatorC22×C3⋊D3C42
Frattini, hypercenterC2×Q8GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC2×C32#342
prime radical, cosocleC2×#3832C22
hypocenterC32#1392
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
126. C32#1392semidirect

Maximal subgroups

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

subgroupindex
#105938342
#105916402
#13929