Finite Group Databasebeta

← C4⋊#92304 #14517537

Subgroups — C4⋊#92304 #14517537

Order 1944.

377 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 377 conjugacy classes of subgroups — too many to draw. Only its 60 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×#92304C212yesmaximal, complemented
2C4×#6893C211yesmaximal, characteristic, complemented
3C3×C4⋊AGL(1,ℤ/9)—32nomaximal
4C3×C4⋊((C3⋊D3)⋊C3)—31nomaximal
5C32×D36—31nomaximal
6C4⋊#4181C311yesmaximal, characteristic, complemented
7C2×#6893C2211yescharacteristic
8#92304—22no—
9C2×C3×AGL(1,ℤ/9)—34no—
10C2×C3×(C3⋊D3)⋊C3—32no—
11C2×C32×D9—32no—
12C3×C4×3−1+2D312yescomplemented
13C3×C4×H(3,𝔽3)D311yescharacteristic
14C32×C4×C9D311yescharacteristic, complemented
15C2×#4181C2×C312yescomplemented
16C4×C32⋊C9—21no—
17C4×C32⋊C9—22no—
18C4×C32⋊C9—21no—
19C4×C32⋊C9C2×C311yescharacteristic, complemented
20#6893D411yescharacteristic, complemented, Sylow
21C3×C4⋊(C3⋊D3)—31no—
22C32×D12—91no—
23C4⋊AGL(1,ℤ/9)—36no—
24C4⋊((C3⋊D3)⋊C3)—33no—
25C3×D36—33no—
26C3×D36—31no—
27C3×D36—32no—
28C2×C3×3−1+2C2×D312yes—
29C2×C3×H(3,𝔽3)C2×D311yescharacteristic
30C2×C32×C9C2×D311yescharacteristic
31C3×AGL(1,ℤ/9)—64no—
32C3×(C3⋊D3)⋊C3—62no—
33C32×D9—62no—
34C2×C32⋊C9—21no—
35C2×C32⋊C9—22no—
36C2×C32⋊C9—21no—
37C2×C32⋊C9C22×C311yescharacteristic
38#4181—22no—
39C2×C3×C3⋊D3—32no—
40C2×C32×D3—92no—
41C33×C4—21no—
42C33×C4C3×D311yescharacteristic
43C33×C4C3⋊D311yescharacteristic
44C2×AGL(1,ℤ/9)—312no—
45C2×(C3⋊D3)⋊C3—36no—
46C2×C3×D9—36no—
47C2×C3×D9—32no—
48C2×C3×D9—34no—
49C4×3−1+2—36no—
50C4×H(3,𝔽3)—33no—
51C3×C4×C9—21no—
52C3×C4×C9—22no—
53C3×C4×C9—33no—
54C3×C4×C9C3×D311yescharacteristic
55C3×C4×C9C3×D312yes—
56C3×3−1+2D1212yescomplemented
57C3×H(3,𝔽3)D1211yescharacteristic
58C32×C9D1211yescharacteristic, complemented
59C32⋊C9—21no—
60C32⋊C9—22no—
61C32⋊C9—21no—
62C32⋊C9C3×D411yescharacteristic, complemented
63C32×D4—271no—
64C4⋊(C3⋊D3)—31no—
65C3×D12—93no—
66C3×D12—91no—
67C3×D12—271no—
68D36—31no—
69D36—32no—
70C2×C33—21no—
71C2×C33C2×C3×D311yescharacteristic
72C2×C33C2×C3⋊D311yescharacteristic
73C3×C3⋊D3—62no—
74C32×D3—182no—
75C2×3−1+2—36no—
76C2×H(3,𝔽3)—33no—
77C2×C3×C9—21no—
78C2×C3×C9—22no—
79C2×C3×C9—33no—
80C2×C3×C9C2×C3×D311yescharacteristic
81C2×C3×C9C2×C3×D312yes—
82AGL(1,ℤ/9)—612no—
83(C3⋊D3)⋊C3—66no—
84C3×D9—66no—
85C3×D9—62no—
86C3×D9—64no—
87C22×C32—272no—
88C2×C3⋊D3—32no—
89C2×C3×D3—96no—
90C2×C3×D3—92no—
91C2×C3×D3—272no—
92C32×C4—31no—
93C32×C4—31no—
94C32×C4—31no—
95C32×C4—61no—
96C32×C4—61no—
97C32×C4—62no—
98C32×C4—61no—
99C32×C4—61no—
100C32×C4#27213yes—
101C32×C4C3×C3⋊D311yescharacteristic
102C2×D9—32no—
103C2×D9—34no—
104C4×C9—31no—
105C4×C9—32no—
106C4×C9—61no—
107C4×C9—62no—
108C33—21no—
109C33C3×D1211yescharacteristic
110C33C4⋊(C3⋊D3)11yescharacteristic
1113−1+2—36no—
112H(3,𝔽3)—33no—
113C3×C9—21no—
114C3×C9—22no—
115C3×C9—33no—
116C3×C9C3×D1211yescharacteristic
117C3×C9C3×D1212yes—
118C3×D4—273no—
119C3×D4—271no—
120D12—91no—
121D12—271no—
122C2×C32—31no—
123C2×C32—31no—
124C2×C32—31no—
125C2×C32—61no—
126C2×C32—61no—
127C2×C32—62no—
128C2×C32—61no—
129C2×C32—61no—
130C2×C32—542no—
131C2×C32C2×#27213yes—
132C2×C32C2×C3×C3⋊D311yescharacteristic
133C3⋊D3—62no—
134C3×D3—186no—
135C3×D3—182no—
136C3×D3—542no—
137C2×C9—31no—
138C2×C9—32no—
139C2×C9—61no—
140C2×C9—62no—
141D9—62no—
142D9—64no—
143C22×C3—276no—
144C22×C3—272no—
145C2×D3—92no—
146C2×D3—272no—
147C3×C4—21no—
148C3×C4—33no—
149C3×C4—91no—
150C3×C4—181no—
151C3×C4C3×#27211yescharacteristic
152C3×C4#420711yescharacteristic
153C32—31no—
154C32—31no—
155C32—31no—
156C32—61no—
157C32—61no—
158C32—62no—
159C32—61no—
160C32—61no—
161C32C4⋊#27213yes—
162C32C3×C4⋊(C3⋊D3)11yescharacteristic
163C9—31no—
164C9—32no—
165C9—61no—
166C9—62no—
167D4—271noSylow
168C2×C3—21no—
169C2×C3—33no—
170C2×C3—91no—
171C2×C3—181no—
172C2×C3—546no—
173C2×C3—542no—
174C2×C3C2×C3×#27211yescharacteristic
175C2×C3C2×#420711yescharacteristic
176D3—182no—
177D3—542no—
178C22—272no—
179C4#9230411yescharacteristic, complemented
180C3—21no—
181C3—33no—
182C3—91no—
183C3—181no—
184C3C3×C4⋊#27211yescharacteristic
185C3C4⋊#420711yescharacteristic
186C2—542no—
187C2C2×#9230411yescharacteristic
subgroupG/H
centerC2×C3C2×#4207
commutator, cosocleC2×C32⋊C9C22×C3
Frattini, socleC2×C32C2×C3×C3⋊D3
FittingC4×#6893C2
hypercenterC3×C4#4207
hypocenterC32⋊C9C3×D4
LCSG ▷ C2×C32⋊C9 ▷ C32⋊C9
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×#92304C2semidirect
2. C4×#6893C2semidirect
6. C4⋊#4181C3semidirect
12. C3×C4×3−1+2D3semidirect
14. C32×C4×C9D3semidirect
15. C2×#4181C2×C3semidirect
19. C4×C32⋊C9C2×C3semidirect
20. #6893D4semidirect
56. C3×3−1+2D12semidirect
58. C32×C9D12semidirect
62. C32⋊C9C3×D4semidirect
179. C4#92304semidirect

Maximal subgroups

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

subgroupindex
C2×#923042
C4×#68932
C3×C4⋊AGL(1,ℤ/9)3
C3×C4⋊((C3⋊D3)⋊C3)3
C32×D363
C4⋊#41813