Finite Group Databasebeta

← #11874933

Subgroups — #11874933

Order 1152.

586 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 586 conjugacy classes of subgroups — too many to draw. Only its 127 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#10593948C212yesmaximal
2C4×#3787C211yesmaximal, characteristic
3#10593396C212yesmaximal
4#10593390C218yesmaximal, complemented
5#10593387C212yesmaximal
6C2×#3787C2211yescharacteristic
7C2×#3787C2211yescharacteristic
8C42×C3⋊D3C2211yescharacteristic
9C3×#870—22no—
10#63900C2214yes—
11#63883—24no—
12#63872—22no—
13#63870C2218yes—
14C4×#622C2214yes—
15#63743C2218yes—
16#63742C2218yes—
17D3×#125—62no—
18C2×C4×C3⋊D3D412yes—
19C2×C4×C3⋊D3C2311yescharacteristic
20C2×#624—24no—
21C2×#622C2312yes—
22C2×#622C2312yes—
23#3787Q814yes—
24#3787Q814yes—
25C32×C42D411yescharacteristic
26C4×C3⋊Dic3D411yescharacteristic
27C4×C3⋊Dic3C2312yes—
28C3×C4⋊Dic3—24no—
29C3×Dic3⋊C4—28no—
30#3724C2318yes—
31Dic3⋊Dic3—28no—
32C2×#499—91nomaximal, Sylow
33C3×#125—62no—
34D3×C4⋊C4—64no—
35D3×C4⋊C4—68no—
36#890—64no—
37#889—68no—
38C42×D3—62no—
39#870—22no—
40C22×C3⋊D3C2×D411yescharacteristic
41C2×C32×C4C2×D412yes—
42C2×C32×C4C2×D411yescharacteristic
43C2×C3⋊Dic3C2×D412yes—
44C2×C3⋊Dic3C2411yescharacteristic
45C4×C3⋊D3—24no—
46C4×C3⋊D3C2×Q812yes—
47C4×C3⋊D3C2×Q812yes—
48C2×C3×Dic3—28no—
49#624—48no—
50#622C2×Q814yes—
51#622C2×Q814yes—
52C2×#125—92no—
53#499—98no—
54C2×#107—92no—
55C2×#106—92no—
56C2×C4×C8—91no—
57C2×C4×D3—62no—
58C2×C4×D3—64no—
59C2×C4×D3—68no—
60C3×C4⋊C4—68no—
61C3×C4⋊C4—64no—
62C3×C42—22no—
63C4⋊Dic3—24no—
64C4⋊Dic3—68no—
65Dic3⋊C4—28no—
66Dic3⋊C4—68no—
67Dic3⋊C4—68no—
68C4×Dic3—64no—
69C4×Dic3—62no—
70C22×C32C22×D411yescharacteristic
71C2×C3⋊D3C4⋊Q812yes—
72C2×C3⋊D3#13514yes—
73C32×C4—22no—
74C32×C4C4⋊Q812yes—
75C3⋊Dic3—22no—
76C3⋊Dic3C22×Q811yescharacteristic
77C3⋊Dic3C22×Q811yescharacteristic
78C3×Dic3—48no—
79C22×C8—91no—
80C22×C8—91no—
81#125—62no—
82#125—98no—
83#125—182no—
84C2×C4⋊C4—94no—
85C2×C4⋊C4—184no—
86C2×C42—91no—
87#107—98no—
88#106—98no—
89C4×C8—94no—
90C22×D3—62no—
91C2×C3×C4—22no—
92C2×C3×C4—24no—
93C2×C3×C4—68no—
94C2×Dic3—28no—
95C2×Dic3—62no—
96C2×Dic3—64no—
97C4×D3—64no—
98C4×D3—64no—
99C4×D3—128no—
100C4×D3—1216no—
101C2×C32C2×C4⋊Q811yescharacteristic
102C2×C32C2×#13512yes—
103C3⋊D3#49914yescomplemented
104C22×C4—91no—
105C22×C4—92no—
106C22×C4—184no—
107C2×C8—92no—
108C2×C8—92no—
109C2×C8—94no—
110C2×C8—94no—
111C4⋊C4—64no—
112C4⋊C4—68no—
113C4⋊C4—98no—
114C4⋊C4—188no—
115C42—92no—
116C42—91no—
117C42GO+(4,𝔽2)11yescharacteristic
118C22×C3—22no—
119C2×D3—64no—
120C2×D3—68no—
121C3×C4—24no—
122C3×C4—44no—
123C3×C4—128no—
124Dic3—48no—
125Dic3—62no—
126Dic3—62no—
127Dic3—124no—
128C32C2×#49911yescharacteristic, complemented, Sylow
129C23—91no—
130C2×C4—68no—
131C2×C4—91no—
132C2×C4—92no—
133C2×C4—92no—
134C2×C4—92no—
135C2×C4—184no—
136C2×C4—368no—
137C2×C4C2×GO+(4,𝔽2)12yes—
138C2×C4C2×GO+(4,𝔽2)11yescharacteristic
139C8—94no—
140C8—94no—
141C2×C3—22no—
142C2×C3—24no—
143D3—68no—
144C22—92no—
145C22—94no—
146C22C22×GO+(4,𝔽2)11yescharacteristic
147C4—22no—
148C4—91no—
149C4—91no—
150C4—128no—
151C4—182no—
152C4#6422212yes—
153C3—22no—
154C2—94no—
155C2C2×#6422211yescharacteristic
156C2#1059650012yes—
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#499
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10593390C2semidirect
103. C3⋊D3#499semidirect
128. C32C2×#499semidirect

Maximal subgroups

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

subgroupindex
#105939482
C4×#37872
#105933962
#105933902
#105933872
C2×#4999