Finite Group Databasebeta

← #92308⋊C4 #14517124

Subgroups — #92308⋊C4 #14517124

Order 1944.

188 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 33 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
1C2×#92308C211yesmaximal, characteristic
2#11757613C211yesmaximal, characteristic, complemented
3#11757612C211yesmaximal, characteristic, complemented
4#4181⋊C4—31nomaximal
5((C3⋊D3)⋊C9)⋊C4—31nomaximal
6D9×Dic9—31nomaximal
7C2×#6896C2211yescharacteristic
8#92308C412yescomplemented
9C3⋊(3−1+2⋊C4)—61no—
10C2×#4181D311yescharacteristic
11C2×D9⋊C9—61no—
12C2×(C3⋊D3)⋊C9—31no—
13C2×C9×D9—31no—
14#66328D311yescharacteristic
15C9⋊Dic9D311yescharacteristic, complemented
16Dic9⋊C9—61no—
17#66316—31no—
18#66316—31no—
19(C3⋊Dic3)⋊C9—31no—
20C9×Dic9—31no—
21#6896C2×C411yescharacteristic, complemented, Sylow
22#6294—91no—
23D3×Dic9—91no—
24Dic3×D9—91no—
25C2×C3×3−1+2—21no—
26C2×C9⋊C9—21no—
27C2×C9⋊C9—21no—
28C2×C9⋊C9—41no—
29C2×C32⋊C9C2×D311yescharacteristic
30C2×C32⋊C9C2×D311yescharacteristic
31C2×C92C2×D311yescharacteristic
32#4181Dic312yes—
33D9⋊C9—62no—
34(C3⋊D3)⋊C9—32no—
35C9×D9—32no—
36C2×C3×C3⋊D3—31no—
37C3×C3⋊Dic3—31no—
38C3×C3⋊Dic3—91no—
39C2×D3×C9—91no—
40C2×C3×D9—31no—
41C2×C3×D9—61no—
42C3⋊Dic9—31no—
43C3⋊Dic9—31no—
44C3⋊Dic9—61no—
453−1+2⋊C4—183no—
46C9×Dic3—91no—
47C3×Dic9—31no—
48C3×Dic9—61no—
49C3×3−1+2—21no—
50C9⋊C9—21no—
51C9⋊C9—21no—
52C9⋊C9—41no—
53C32⋊C9C4×D311yescharacteristic
54C32⋊C9C2×Dic311yescharacteristic
55C92C4×D311yescharacteristic, complemented
56#624—271no—
57D3×Dic3—271no—
58D3×Dic3—271no—
59C2×Dic9—271no—
60C4×D9—271no—
61C2×C33D3211yescharacteristic
62C3×C3⋊D3—32no—
63C2×3−1+2—63no—
64C2×C3×C9—21no—
65C2×C3×C9—21no—
66C2×C3×C9—21no—
67C2×C3×C9—41no—
68C2×C3×C9D3211yescharacteristic
69C2×C3×C9D3211yescharacteristic
70D3×C9—92no—
71C3×D9—32no—
72C3×D9—62no—
73C2×C3⋊D3—31no—
74C2×C3×D3—91no—
75C2×C3×D3—271no—
76C3⋊Dic3—31no—
77C3⋊Dic3—91no—
78C3×Dic3—91no—
79C3×Dic3—271no—
80C3×Dic3—271no—
81C3×Dic3—271no—
82C3×Dic3—541no—
83C22×C9—271no—
84C2×D9—31no—
85C2×D9—61no—
86C4×C9—271no—
87Dic9—31no—
88Dic9—61no—
89Dic9—183no—
90Dic9—271no—
91Dic9—271no—
92C33D3×Dic311yescharacteristic
933−1+2—63no—
94C3×C9—21no—
95C3×C9—21no—
96C3×C9—21no—
97C3×C9—41no—
98C3×C9D3×Dic311yescharacteristic
99C3×C9#62411yescharacteristic
100C2×Dic3—811no—
101C4×D3—811no—
102C4×D3—811no—
103C2×C32—31no—
104C2×C32—31no—
105C2×C32—61no—
106C2×C32#111311yescharacteristic
107C3⋊D3—32no—
108C3×D3—92no—
109C3×D3—272no—
110C2×C9—23no—
111C2×C9—31no—
112C2×C9—31no—
113C2×C9—61no—
114C2×C9—61no—
115C2×C9—121no—
116C2×C9—272no—
117D9—32no—
118D9—62no—
119C22×C3—271no—
120C2×D3—91no—
121C2×D3—271no—
122C3×C4—271no—
123C3×C4—811no—
124Dic3—91no—
125Dic3—271no—
126Dic3—271no—
127Dic3—271no—
128Dic3—541no—
129C32—31no—
130C32—31no—
131C32—61no—
132C32#629411yescharacteristic
133C9—23no—
134C9—31no—
135C9—31no—
136C9—61no—
137C9—61no—
138C9—121no—
139C2×C4—2431noSylow
140C2×C3—21no—
141C2×C3—91no—
142C2×C3—272no—
143C2×C3#4207⋊C211yescharacteristic
144C2×C3#4207⋊C211yescharacteristic
145D3—92no—
146D3—272no—
147C22—271no—
148C4—271no—
149C4—811no—
150C3—21no—
151C3—91no—
152C3#4207⋊C411yescharacteristic
153C3#1061990811yescharacteristic
154C2—272no—
155C2#92308⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92308⋊C2
commutator, hypocenter#6896C2×C4
Frattini, socleC2×C32#1113
Fitting, cosocleC2×#6896C22
prime radicalC2×#4181D3
LCSG ▷ #6896
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757613C2semidirect
3. #11757612C2semidirect
8. #92308C4semidirect
15. C9⋊Dic9D3semidirect
21. #6896C2×C4semidirect
55. C92C4×D3semidirect

Maximal subgroups

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

subgroupindex
C2×#923082
#117576132
#117576122
#4181⋊C43
((C3⋊D3)⋊C9)⋊C43
D9×Dic93