Finite Group Databasebeta

← #11781000

Subgroups — #11781000

Order 1152.

252 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 47 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
1Q8×#622C211yesmaximal, characteristic
2#10593450C211yesmaximal, characteristic
3#10591630C212yesmaximal
4#10590042C211yesmaximal, characteristic
5#10590039C212yesmaximal
6C2×#3776—21no—
7C2×#3776—21no—
8Q8×C3⋊Dic3C2211yescharacteristic
9#63919C2212yes—
10C4⋊#622—21no—
11C4⋊#622C2211yescharacteristic
12C4×#622—21no—
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#1670—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—21no—
41C32×Q8Q1612yescomplemented
42C2×C32×C4—21no—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3C2×D411yescharacteristic
46C2×C3⋊Dic3#4111yescharacteristic
47C2×C3×Dic3—42no—
48#627—42no—
49#627—42no—
50#622—21no—
51#622—41no—
52#622SD1612yes—
53C3×C3⋊C8—42no—
54#494—91no—
55#475—92no—
56C8×Q8—91no—
57#335—91no—
58#332—92no—
59C2×C3×Q8—22no—
60C2×Dic6—122no—
61C2×C3×C8—62no—
62C3×C4⋊C4—62no—
63C4⋊Dic3—22no—
64C4⋊Dic3—62no—
65C4⋊Dic3—122no—
66Dic3⋊C4—122no—
67C4×Dic3—62no—
68C4×Dic3—122no—
69C2×C3⋊C8—22no—
70C22×C32#12111yescharacteristic
71C32×C4—22no—
72C32×C4C2×Q1611yescharacteristic
73C32×C4#13511yescharacteristic
74C3⋊Dic3—21no—
75C3⋊Dic3—41no—
76C3⋊Dic3C2×SD1611yescharacteristic
77C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
78C3×Dic3—82no—
79C2×Q16—181no—
80C2×Q16—181no—
81C4⋊Q8—92no—
82C4×Q8—91no—
83#106—182no—
84C4⋊C8—92no—
85C4⋊C8—91no—
86C4⋊C8—181no—
87#103—62no—
88C4×C8—91no—
89C4×C8—181no—
90C3×Q8—24no—
91C3×Q8—42no—
92C2×C3×C4—22no—
93C2×C3×C4—42no—
94C2×C3×C4—122no—
95C2×Dic3—42no—
96C2×Dic3—62no—
97C2×Dic3—62no—
98C2×Dic3—122no—
99Dic6—242no—
100Dic6—242no—
101C3×C8—122no—
102C3⋊C8—42no—
103C2×C32#46011yescharacteristic
104C2×C32#46711yescharacteristic
105C2×C32#47311yescharacteristic
106C2×Q8—182no—
107C2×Q8GO+(4,𝔽2)11yescharacteristic
108Q16—362no—
109Q16—362no—
110C2×C8—62no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—181no—
114C4⋊C4—62no—
115C4⋊C4—91no—
116C4⋊C4—181no—
117C4⋊C4—182no—
118C42—91no—
119C42—181no—
120C22×C3—22no—
121C3×C4—22no—
122C3×C4—22no—
123C3×C4—44no—
124C3×C4—242no—
125Dic3—62no—
126Dic3—62no—
127Dic3—82no—
128Dic3—122no—
129Dic3—242no—
130C32#167011yescharacteristic, complemented, Sylow
131Q8—21no—
132Q8—362no—
133Q8—362no—
134Q8#377612yescomplemented
135C2×C4—21no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—122no—
139C2×C4—181no—
140C2×C4C2×GO+(4,𝔽2)11yescharacteristic
141C8—92no—
142C8—122no—
143C8—181no—
144C8—361no—
145C2×C3—22no—
146C2×C3—22no—
147C2×C3—22no—
148C22#6424211yescharacteristic
149C4—22no—
150C4—91no—
151C4—91no—
152C4—181no—
153C4—242no—
154C4—361no—
155C4#6423711yescharacteristic
156C4C2×#377611yescharacteristic
157C3—22no—
158C2#1059347611yescharacteristic
159C2#1059348211yescharacteristic
160C2#1059352711yescharacteristic
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#1670
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
41. C32×Q8Q16semidirect
130. C32#1670semidirect
134. Q8#3776semidirect

Maximal subgroups

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

subgroupindex
Q8×#6222
#105934502
#105916302
#105900422
#105900392
#16709