Finite Group Databasebeta

← C4⋊(#126⋊C9) #11919509

Subgroups — C4⋊(#126⋊C9) #11919509

Order 1152.

228 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 36 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×#126⋊C9C212yesmaximal, complemented
2C4×C42⋊C9C211yesmaximal, characteristic, complemented
3C3×#2860C311yesmaximal, characteristic
4D4×C22⋊C9—41nomaximal
5#126⋊C9—22no—
6C2×C42⋊C9C2211yescharacteristic
7C2×C3×#126C2×C312yes—
8C3×#390—31no—
9C3×#389—31no—
10C3×#388—32no—
11C3×C43C2×C311yescharacteristic
12C22×C22⋊C9—42no—
13C4×C22⋊C9—41no—
14C42⋊C9D411yescharacteristic, complemented
15#2860C911yescharacteristic, complemented, Sylow
16C22×C3×D4A411yescharacteristic
17C3×#126—22no—
18C3×#126—62no—
19C2×C3×C4⋊C4—32no—
20C2×C3×C4⋊C4—31no—
21C2×C3×C22⋊C4—32no—
22C2×C3×C22⋊C4—32no—
23C2×C3×C42—31no—
24C2×C3×C42—31no—
25C2×C3×C42C22×C311yescharacteristic
26C3×#95—32no—
27C2×C22⋊C9—41no—
28C2×C22⋊C9—82no—
29D4×C9—161no—
30C2×#126C2×C912yescomplemented
31#390—31no—
32#389—31no—
33#388—32no—
34C43C2×C911yescharacteristic, complemented
35C24×C3C2×A412yes—
36C2×C3×D4—61no—
37C2×C3×D4—61no—
38C22×C3×C4—31no—
39C22×C3×C4—31no—
40C22×C3×C4—32no—
41C22×C3×C4C2×A411yescharacteristic
42C3×C4⋊C4—62no—
43C3×C4⋊C4—62no—
44C3×C4⋊C4—61no—
45C3×C4⋊C4—61no—
46C3×C22⋊C4—62no—
47C3×C22⋊C4—62no—
48C3×C22⋊C4—64no—
49C3×C42—31no—
50C3×C42—61no—
51C3×C42—61no—
52C3×C42—62no—
53C3×C42C3×D411yescharacteristic
54C22×C9—162no—
55C22⋊C9—41no—
56C4×C9—161no—
57C22×D4C22⋊C911yescharacteristic
58#126—22no—
59#126—62no—
60C2×C4⋊C4—32no—
61C2×C4⋊C4—31no—
62C2×C22⋊C4—32no—
63C2×C22⋊C4—32no—
64C2×C42—31no—
65C2×C42—31no—
66C2×C42C22×C911yescharacteristic
67#95—32no—
68C23×C3—22no—
69C23×C3—62no—
70C23×C3—62no—
71C23×C3C22×A411yescharacteristic
72C3×D4—41no—
73C3×D4—121no—
74C2×C3×C4—31no—
75C2×C3×C4—31no—
76C2×C3×C4—32no—
77C2×C3×C4—31no—
78C2×C3×C4—31no—
79C2×C3×C4—61no—
80C2×C3×C4—61no—
81C2×C3×C4—61no—
82C2×C3×C4—61no—
83C2×C3×C4—62no—
84C2×C3×C4—62no—
85C2×C3×C4—62no—
86C2×C9—161no—
87C2×C9—322no—
88C24C2×C22⋊C912yes—
89C2×D4—61no—
90C2×D4—61no—
91C22×C4—31no—
92C22×C4—31no—
93C22×C4—32no—
94C22×C4C2×C22⋊C911yescharacteristic
95C4⋊C4—62no—
96C4⋊C4—62no—
97C4⋊C4—61no—
98C4⋊C4—61no—
99C22⋊C4—62no—
100C22⋊C4—62no—
101C22⋊C4—64no—
102C42—31no—
103C42—61no—
104C42—61no—
105C42—62no—
106C42D4×C911yescharacteristic, complemented
107C22×C3—31no—
108C22×C3—31no—
109C22×C3—42no—
110C22×C3—122no—
111C22×C3—122no—
112C22×C3D4×A411yescharacteristic
113C3×C4—31no—
114C3×C4—61no—
115C3×C4—61no—
116C3×C4—62no—
117C3×C4—122no—
118C3×C4#126⋊C311yescharacteristic
119C9—161noSylow
120C23—22no—
121C23—62no—
122C23—62no—
123C23C22×C22⋊C911yescharacteristic
124D4—41no—
125D4—121no—
126C2×C4—31no—
127C2×C4—31no—
128C2×C4—32no—
129C2×C4—31no—
130C2×C4—31no—
131C2×C4—61no—
132C2×C4—61no—
133C2×C4—61no—
134C2×C4—61no—
135C2×C4—62no—
136C2×C4—62no—
137C2×C4—62no—
138C2×C3—31no—
139C2×C3—31no—
140C2×C3—82no—
141C2×C3C2×#126⋊C311yescharacteristic
142C22—31no—
143C22—31no—
144C22—42no—
145C22—122no—
146C22—122no—
147C22D4×C22⋊C911yescharacteristic
148C4—31no—
149C4—61no—
150C4—61no—
151C4—62no—
152C4—122no—
153C4#126⋊C911yescharacteristic, complemented
154C3C4⋊(#126⋊C3)11yescharacteristic
155C2—31no—
156C2—31no—
157C2—82no—
158C2C2×#126⋊C911yescharacteristic
subgroupG/H
centerC2×C3C2×#126⋊C3
commutatorC2×C42C22×C9
Frattini, socleC23×C3C22×A4
FittingC3×#2860C3
prime radicalC22×C3×D4A4
cosocleC2×C3×C42C22×C3
hypercenterC3×C4#126⋊C3
hypocenterC42D4×C9
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×#126⋊C9C2semidirect
2. C4×C42⋊C9C2semidirect
14. C42⋊C9D4semidirect
15. #2860C9semidirect
30. C2×#126C2×C9semidirect
34. C43C2×C9semidirect
106. C42D4×C9semidirect
153. C4#126⋊C9semidirect

Maximal subgroups

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

subgroupindex
C2×#126⋊C92
C4×C42⋊C92
C3×#28603
D4×C22⋊C94