Finite Group Databasebeta

← #11781161

Subgroups — #11781161

Order 1152.

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

normal subgroups only

This group has 264 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#10593388C211yesmaximal, characteristic
3#10591633C212yesmaximal
4#10590042C211yesmaximal, characteristic
5#10590038C212yesmaximal
6Q8×C3⋊Dic3C2211yescharacteristic
7C2×C3×#216—22no—
8#63873C2212yes—
9C4⋊#622—21no—
10C4⋊#622C2211yescharacteristic
11C4×#622—21no—
12C4×#622C2211yescharacteristic
13#63743—21no—
14#63743—21no—
15#63572C2212yes—
16#63566—22no—
17#5182—62no—
18C2×C32×Q8D411yescharacteristic
19C2×C3×Dic6—22no—
20C2×#622—21no—
21C2×#622D411yescharacteristic
22C2×#622D411yescharacteristic
23C4⋊(C3⋊Dic3)—21no—
24C4⋊(C3⋊Dic3)D411yescharacteristic
25C4×C3⋊Dic3—21no—
26C4×C3⋊Dic3C2311yescharacteristic
27C3×#216—44no—
28C2×C3×C3⋊C8—22no—
29#3724—22no—
30#3724—22no—
31#1674—91nomaximal, Sylow
32C2×C3×Q16—62no—
33Q8×Dic3—62no—
34#944—62no—
35C2×#216—22no—
36#835—62no—
37#816—62no—
38Dic3⋊C8—62no—
39C32×Q8—21no—
40C32×Q8D812yes—
41C2×C32×C4—21no—
42C2×C32×C4C2×D411yescharacteristic
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3C2×D411yescharacteristic
45C2×C3⋊Dic3#4111yescharacteristic
46C2×C3×Dic3—42no—
47C3×Dic6—42no—
48C3×Dic6—42no—
49#622—21no—
50#622—41no—
51#622Q1612yescomplemented
52C3×C3⋊C8—42no—
53#500—91no—
54#462—92no—
55C8×Q8—91no—
56#335—91no—
57#332—92no—
58C2×C3×Q8—22no—
59C2×C3×Q8—62no—
60C2×Dic6—22no—
61C3×Q16—124no—
62C2×C3×C8—62no—
63#216—44no—
64C4⋊Dic3—62no—
65C4⋊Dic3—122no—
66Dic3⋊C4—122no—
67Dic3⋊C4—122no—
68C4×Dic3—62no—
69C4×Dic3—122no—
70C2×C3⋊C8—22no—
71C22×C32#12111yescharacteristic
72C32×C4—22no—
73C32×C4C2×D811yescharacteristic
74C32×C4#13511yescharacteristic
75C3⋊Dic3—21no—
76C3⋊Dic3—41no—
77C3⋊Dic3C2×Q1611yescharacteristic
78C3⋊Dic3#13711yescharacteristic
79C3×Dic3—82no—
80C2×Q16—62no—
81C4⋊Q8—92no—
82C4×Q8—91no—
83#107—181no—
84#107—181no—
85C4⋊C8—92no—
86C4⋊C8—91no—
87C4⋊C8—181no—
88#103—182no—
89C4×C8—91no—
90C4×C8—181no—
91C3×Q8—24no—
92C3×Q8—42no—
93C3×Q8—122no—
94C3×Q8—122no—
95C2×C3×C4—22no—
96C2×C3×C4—42no—
97C2×C3×C4—122no—
98C2×Dic3—42no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101C2×Dic3—122no—
102Dic6—42no—
103Dic6—42no—
104C3×C8—122no—
105C3⋊C8—42no—
106C2×C32#46211yescharacteristic
107C2×C32#46611yescharacteristic
108C2×C32#47311yescharacteristic
109C2×Q8—62no—
110C2×Q8GO+(4,𝔽2)11yescharacteristic
111Q16—124no—
112C2×C8—62no—
113C2×C8—91no—
114C2×C8—91no—
115C2×C8—181no—
116C4⋊C4—91no—
117C4⋊C4—181no—
118C4⋊C4—182no—
119C4⋊C4—182no—
120C42—91no—
121C42—181no—
122C22×C3—22no—
123C3×C4—22no—
124C3×C4—22no—
125C3×C4—44no—
126C3×C4—242no—
127Dic3—62no—
128Dic3—62no—
129Dic3—82no—
130Dic3—122no—
131Dic3—242no—
132C32#167411yescharacteristic, complemented, Sylow
133Q8—21no—
134Q8—122no—
135Q8—122no—
136Q8#377412yes—
137C2×C4—21no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4—122no—
141C2×C4—181no—
142C2×C4C2×GO+(4,𝔽2)11yescharacteristic
143C8—92no—
144C8—122no—
145C8—181no—
146C8—361no—
147C2×C3—22no—
148C2×C3—22no—
149C2×C3—22no—
150C22#6424211yescharacteristic
151C4—22no—
152C4—91no—
153C4—91no—
154C4—181no—
155C4—242no—
156C4—361no—
157C4C2×#377411yescharacteristic
158C4#6423711yescharacteristic
159C3—22no—
160C2#1059347711yescharacteristic
161C2#1059348211yescharacteristic
162C2#1059352011yescharacteristic
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#1674
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
51. #622Q16semidirect
132. C32#1674semidirect

Maximal subgroups

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

subgroupindex
Q8×#6222
#105933882
#105916332
#105900422
#105900382
#16749