Finite Group Databasebeta

← C4×#92294 #14517505

Subgroups — C4×#92294 #14517505

Order 1944.

253 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 253 conjugacy classes of subgroups — too many to draw. Only its 75 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×#92294C211yesmaximal, characteristic
2C4×#6887C211yesmaximal, characteristic, complemented
3#11757598C211yesmaximal, characteristic, complemented
4C3×C4×C3⋊D9C311yesmaximal, characteristic
5C4×D9⋊C9—32nomaximal
6C4×(C3⋊D3)⋊C9—31nomaximal
7C4×C9×D9—31nomaximal
8C2×#6887C2211yescharacteristic
9#92294C412yesdirect product factor
10C2×C3×C3⋊D9C2×C311yescharacteristic
11C32×C4×C9C2×C311yescharacteristic
12C3×C3⋊Dic9C2×C311yescharacteristic
13C2×D9⋊C9—32no—
14C2×(C3⋊D3)⋊C9—31no—
15C2×C9×D9—31no—
16C4×C9⋊C9—22no—
17C4×C9⋊C9D312yescomplemented
18C4×C32⋊C9—21no—
19C4×C32⋊C9D311yescharacteristic
20C4×C92—21no—
21C4×C92D311yescharacteristic, complemented
22Dic9⋊C9—32no—
23(C3⋊Dic3)⋊C9—31no—
24C9×Dic9—31no—
25#6887C2×C411yescharacteristic, complemented, Sylow
26C3×C4×C3⋊D3—31no—
27C4×C3⋊D9C911yescharacteristic, complemented
28C4×D3×C9—91no—
29C3×C4×D9—31no—
30C3×C4×D9—32no—
31C2×C32×C9C22×C311yescharacteristic
32C3×C3⋊D9C3×C412yes—
33C2×C9⋊C9—22no—
34C2×C9⋊C9C2×D312yes—
35C2×C32⋊C9—21no—
36C2×C32⋊C9C2×D311yescharacteristic
37C2×C92—21no—
38C2×C92C2×D311yescharacteristic
39D9⋊C9—34no—
40(C3⋊D3)⋊C9—32no—
41C9×D9—32no—
42C2×C3×C3⋊D3—31no—
43C33×C4C3×D311yescharacteristic
44C3×C3⋊Dic3—31no—
45C2×C3⋊D9C2×C911yescharacteristic
46C2×D3×C9—91no—
47C2×C3×D9—31no—
48C2×C3×D9—32no—
49C3×C4×C9—21no—
50C3×C4×C9—22no—
51C3×C4×C9—21no—
52C3×C4×C9—22no—
53C3×C4×C9—21no—
54C3×C4×C9—21no—
55C3×C4×C9C2×C911yescharacteristic, complemented
56C3×C4×C9C3×D311yescharacteristic
57C3×C4×C9C3×D312yes—
58C3×C4×C9C3⋊D311yescharacteristic
59C3⋊Dic9C2×C911yescharacteristic, complemented
60C9×Dic3—91no—
61C3×Dic9—31no—
62C3×Dic9—32no—
63C32×C9C2×C3×C411yescharacteristic
64C9⋊C9—22no—
65C9⋊C9C4×D312yescomplemented
66C32⋊C9—21no—
67C32⋊C9C4×D311yescharacteristic
68C92—21no—
69C92C4×D311yescharacteristic, complemented
70C4×C3⋊D3—31no—
71C3×C4×D3—91no—
72C3×C4×D3—271no—
73C2×C4×C9—271no—
74C4×D9—31no—
75C4×D9—32no—
76C2×C33C2×C3×D311yescharacteristic
77C3×C3⋊D3—32no—
78C2×C3×C9—21no—
79C2×C3×C9—22no—
80C2×C3×C9—21no—
81C2×C3×C9—22no—
82C2×C3×C9—21no—
83C2×C3×C9—21no—
84C2×C3×C9C22×C911yescharacteristic
85C2×C3×C9C2×C3×D311yescharacteristic
86C2×C3×C9C2×C3×D312yes—
87C2×C3×C9C2×C3⋊D311yescharacteristic
88C3⋊D9C4×C912yescomplemented
89D3×C9—92no—
90C3×D9—32no—
91C3×D9—34no—
92C2×C3⋊D3—31no—
93C2×C3×D3—91no—
94C2×C3×D3—271no—
95C32×C4—21no—
96C32×C4—31no—
97C32×C4—61no—
98C32×C4D3×C911yescharacteristic
99C32×C4C3×C3⋊D311yescharacteristic
100C3⋊Dic3—31no—
101C3×Dic3—91no—
102C3×Dic3—271no—
103C22×C9—271no—
104C2×D9—31no—
105C2×D9—32no—
106C4×C9—21no—
107C4×C9—22no—
108C4×C9—31no—
109C4×C9—62no—
110C4×C9—61no—
111C4×C9—61no—
112C4×C9—271no—
113C4×C9D3×C911yescharacteristic
114C4×C9D3×C912yes—
115Dic9—31no—
116Dic9—32no—
117C33C3×C4×D311yescharacteristic
118C3×C9—21no—
119C3×C9—22no—
120C3×C9—21no—
121C3×C9—22no—
122C3×C9—21no—
123C3×C9—21no—
124C3×C9C2×C4×C911yescharacteristic, complemented
125C3×C9C3×C4×D311yescharacteristic
126C3×C9C3×C4×D312yes—
127C3×C9C4×C3⋊D311yescharacteristic
128C2×C3×C4—271no—
129C4×D3—91no—
130C4×D3—271no—
131C2×C32—21no—
132C2×C32—31no—
133C2×C32—61no—
134C2×C32C2×D3×C911yescharacteristic
135C2×C32C2×C3×C3⋊D311yescharacteristic
136C3⋊D3—32no—
137C3×D3—92no—
138C3×D3—272no—
139C2×C9—21no—
140C2×C9—22no—
141C2×C9—31no—
142C2×C9—62no—
143C2×C9—61no—
144C2×C9—61no—
145C2×C9—272no—
146C2×C9C2×D3×C911yescharacteristic
147C2×C9C2×D3×C912yes—
148D9—32no—
149D9—34no—
150C22×C3—271no—
151C2×D3—91no—
152C2×D3—271no—
153C3×C4—21no—
154C3×C4—31no—
155C3×C4—61no—
156C3×C4—271no—
157C3×C4C9×C3⋊D311yescharacteristic
158C3×C4#420711yescharacteristic
159Dic3—91no—
160Dic3—271no—
161C32—21no—
162C32—31no—
163C32—61no—
164C32C4×D3×C911yescharacteristic
165C32C3×C4×C3⋊D311yescharacteristic
166C9—21no—
167C9—22no—
168C9—31no—
169C9—62no—
170C9—61no—
171C9—61no—
172C9C4×D3×C911yescharacteristic
173C9C4×D3×C912yes—
174C2×C4—271noSylow
175C2×C3—21no—
176C2×C3—31no—
177C2×C3—61no—
178C2×C3—272no—
179C2×C3C2×C9×C3⋊D311yescharacteristic
180C2×C3C2×#420711yescharacteristic
181D3—92no—
182D3—272no—
183C22—271no—
184C4—271no—
185C4#9229411yescharacteristic, direct product factor
186C3—21no—
187C3—31no—
188C3—61no—
189C3C4×C9×C3⋊D311yescharacteristic
190C3C4×#420711yescharacteristic
191C2—272no—
192C2C2×#9229411yescharacteristic
subgroupG/H
center, hypercenterC3×C4#4207
commutator, hypocenterC3×C9C2×C4×C9
Frattini, socleC2×C32C2×C3×C3⋊D3
FittingC4×#6887C2
prime radicalC2×C3×C3⋊D9C2×C3
cosocleC2×C32×C9C22×C3
LCSG ▷ C3×C9
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6887C2semidirect
3. #11757598C2semidirect
9. #92294C4direct (N × H)
17. C4×C9⋊C9D3semidirect
21. C4×C92D3semidirect
25. #6887C2×C4semidirect
27. C4×C3⋊D9C9semidirect
55. C3×C4×C9C2×C9semidirect
59. C3⋊Dic9C2×C9semidirect
65. C9⋊C9C4×D3semidirect
69. C92C4×D3semidirect
88. C3⋊D9C4×C9semidirect
124. C3×C9C2×C4×C9semidirect
185. C4#92294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#922942
C4×#68872
#117575982
C3×C4×C3⋊D93
C4×D9⋊C93
C4×(C3⋊D3)⋊C93
C4×C9×D93