Finite Group Databasebeta

← #11781820

Subgroups — #11781820

Order 1152.

248 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593835C211yesmaximal, characteristic
2#10593450C211yesmaximal, characteristic
3#10591630C212yesmaximal
4#10590041C211yesmaximal, characteristic
5#10590039C212yesmaximal
6C2×#3776—21no—
7C2×#3776—21no—
8Q8×C3⋊Dic3C2211yescharacteristic
9#63919C2212yes—
10#63779—21no—
11#63777—21no—
12C4⋊#622C2211yescharacteristic
13C4×#622C2211yescharacteristic
14C3×#835—22no—
15#63573—22no—
16#63572C2212yes—
17#4791—62no—
18C2×C32×Q8D411yescharacteristic
19C2×#627—22no—
20C2×#622—21no—
21C2×#622D411yescharacteristic
22C2×#622D411yescharacteristic
23#3776—42no—
24#3776—42no—
25C4⋊(C3⋊Dic3)—21no—
26C4⋊(C3⋊Dic3)D411yescharacteristic
27C4×C3⋊Dic3—21no—
28C4×C3⋊Dic3C2311yescharacteristic
29C3×C4⋊Dic3—22no—
30C2×C3×C3⋊C8—22no—
31#3724—22no—
32#1690—91nomaximal, Sylow
33Q8×Dic3—62no—
34#888—62no—
35C3×#103—62no—
36#835—22no—
37#817—62no—
38Dic3⋊C8—62no—
39#808—62no—
40C32×Q8—22no—
41C2×C32×C4—21no—
42C2×C32×C4C2×D411yescharacteristic
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3C2×D411yescharacteristic
45C2×C3⋊Dic3#4111yescharacteristic
46C2×C3×Dic3—42no—
47#627—42no—
48#627—42no—
49#622—21no—
50#622—41no—
51#622SD1612yes—
52C3×C3⋊C8—42no—
53#494—91no—
54#475—92no—
55#446—91no—
56#334—91no—
57#332—92no—
58C2×C3×Q8—22no—
59C2×Dic6—122no—
60C2×C3×C8—62no—
61C3×C4⋊C4—62no—
62C4⋊Dic3—22no—
63C4⋊Dic3—62no—
64C4⋊Dic3—122no—
65Dic3⋊C4—122no—
66C4×Dic3—62no—
67C4×Dic3—122no—
68C2×C3⋊C8—22no—
69C22×C32#12111yescharacteristic
70C32×C4—41no—
71C32×C4#13712yes—
72C3⋊Dic3—21no—
73C3⋊Dic3—41no—
74C3⋊Dic3C2×SD1611yescharacteristic
75C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
76C3×Dic3—82no—
77C2×Q16—181no—
78C2×Q16—181no—
79C4⋊Q8—92no—
80C4×Q8—91no—
81#106—182no—
82C4⋊C8—92no—
83C4⋊C8—91no—
84C4⋊C8—181no—
85#103—62no—
86#97—181no—
87C4×C8—91no—
88C3×Q8—24no—
89C3×Q8—42no—
90C2×C3×C4—22no—
91C2×C3×C4—42no—
92C2×C3×C4—122no—
93C2×Dic3—42no—
94C2×Dic3—62no—
95C2×Dic3—62no—
96C2×Dic3—122no—
97Dic6—242no—
98Dic6—242no—
99C3×C8—122no—
100C3⋊C8—42no—
101C2×C32#46011yescharacteristic
102C2×C32#47011yescharacteristic
103C2×C32#47311yescharacteristic
104C2×Q8—182no—
105C2×Q8GO+(4,𝔽2)11yescharacteristic
106Q16—362no—
107Q16—362no—
108C2×C8—62no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—181no—
112C4⋊C4—62no—
113C4⋊C4—91no—
114C4⋊C4—181no—
115C4⋊C4—182no—
116C42—91no—
117C42—181no—
118C22×C3—22no—
119C3×C4—22no—
120C3×C4—22no—
121C3×C4—44no—
122C3×C4—242no—
123Dic3—62no—
124Dic3—62no—
125Dic3—82no—
126Dic3—122no—
127Dic3—242no—
128C32#169011yescharacteristic, complemented, Sylow
129Q8—22no—
130Q8—362no—
131Q8—362no—
132C2×C4—21no—
133C2×C4—91no—
134C2×C4—91no—
135C2×C4—122no—
136C2×C4—181no—
137C2×C4C2×GO+(4,𝔽2)11yescharacteristic
138C8—92no—
139C8—122no—
140C8—181no—
141C8—361no—
142C2×C3—22no—
143C2×C3—22no—
144C2×C3—22no—
145C22#6424211yescharacteristic
146C4—41no—
147C4—91no—
148C4—91no—
149C4—181no—
150C4—242no—
151C4—361no—
152C4#6423912yes—
153C3—22no—
154C2#1059347611yescharacteristic
155C2#1059348211yescharacteristic
156C2#1059350811yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socle, prime radicalC22×C32#121
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1690
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
128. C32#1690semidirect

Maximal subgroups

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

subgroupindex
#105938352
#105934502
#105916302
#105900412
#105900392
#16909