Finite Group Databasebeta

← 3−1+2×#611 #14517421

Subgroups — 3−1+2×#611 #14517421

Order 1944.

317 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 317 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C22×C9×3−1+2C211yesmaximal, characteristic, complemented
2C2×D9×3−1+2C211yesmaximal, characteristic, complemented
33−1+2×Dic9C211yesmaximal, characteristic, complemented
4#67×3−1+2—31nomaximal
5C32×#611C311yesmaximal, characteristic
6C9×#611C313yesmaximal, complemented
7C2×C9×3−1+2—21no—
8C2×C9×3−1+2C2211yescharacteristic
9D9×3−1+2—21no—
10C22×C3×3−1+2D311yescharacteristic
11C22×C32×C9C2×C311yescharacteristic
12C2×D3×3−1+2—31no—
13C2×C32×D9C2×C311yescharacteristic
14Dic3×3−1+2—31no—
15C32×Dic9C2×C311yescharacteristic
16C22×C9⋊C9—23no—
17C22×C32⋊C9—21no—
18C22×C92C2×C313yescomplemented
19C2×C9×D9C2×C313yescomplemented
20C9×Dic9C2×C313yescomplemented
21C9×3−1+2D411yescharacteristic, complemented, Sylow
22C32×#67—31no—
23D4×3−1+2—91no—
24C9×#67—33no—
25C3×#611—31no—
26C3×#611C3211yescharacteristic
27C2×C3×3−1+2—21no—
28C2×C3×3−1+2C2×D311yescharacteristic
29C2×C32×C9—21no—
30C2×C32×C9C22×C311yescharacteristic
31D3×3−1+2—61no—
32C32×D9—21no—
33C2×C9⋊C9—26no—
34C2×C9⋊C9—23no—
35C2×C32⋊C9—22no—
36C2×C32⋊C9—21no—
37C2×C92—23no—
38C2×C92C22×C313yes—
39C9×D9—23no—
40C22×C33C3×D311yescharacteristic
41C2×C32×D3—31no—
42C32×Dic3—31no—
43C22×3−1+2—21no—
44C22×3−1+2—23no—
45C22×3−1+2—91no—
46C22×3−1+2D911yescharacteristic, complemented
47C22×C3×C9—23no—
48C22×C3×C9—21no—
49C22×C3×C9—31no—
50C22×C3×C9—61no—
51C22×C3×C9C3×D313yes—
52C22×C3×C9C2×C3211yescharacteristic
53C2×D3×C9—33no—
54C2×C3×D9—31no—
55C2×C3×D9C2×C3211yescharacteristic
56C4×3−1+2—91no—
57C9×Dic3—33no—
58C3×Dic9—31no—
59C3×Dic9C2×C3211yescharacteristic
60C3×3−1+2#6711yescharacteristic
61C32×C9C3×D411yescharacteristic
62C9⋊C9—23no—
63C32⋊C9—21no—
64C92C3×D413yescomplemented
65C32×D4—91no—
66C3×#67—31no—
67C3×#67—91no—
68D4×C9—93no—
69#6113−1+211yescharacteristic, direct product factor
70C2×C33—21no—
71C2×C33C2×C3×D311yescharacteristic
72C32×D3—61no—
73C2×3−1+2—22no—
74C2×3−1+2—26no—
75C2×3−1+2—21no—
76C2×3−1+2—21no—
77C2×3−1+2—23no—
78C2×3−1+2—181no—
79C2×3−1+2C2×D911yescharacteristic
80C2×C3×C9—23no—
81C2×C3×C9—21no—
82C2×C3×C9—26no—
83C2×C3×C9—22no—
84C2×C3×C9—23no—
85C2×C3×C9—21no—
86C2×C3×C9—31no—
87C2×C3×C9—61no—
88C2×C3×C9—62no—
89C2×C3×C9—61no—
90C2×C3×C9C2×C3×D313yes—
91C2×C3×C9C22×C3211yescharacteristic
92D3×C9—63no—
93C3×D9—21no—
94C3×D9—61no—
95C22×C32—21no—
96C22×C32—31no—
97C22×C32—61no—
98C22×C32—91no—
99C22×C32C3×D911yescharacteristic
100C22×C32C32×D311yescharacteristic
101C2×C3×D3—31no—
102C2×C3×D3—91no—
103C32×C4—91no—
104C3×Dic3—31no—
105C3×Dic3—91no—
106C22×C9—23no—
107C22×C9—21no—
108C22×C9—63no—
109C22×C9—61no—
110C22×C9—93no—
111C22×C9C3×D913yescomplemented
112C22×C9C2×3−1+211yescharacteristic, complemented
113C2×D9C2×3−1+211yescharacteristic, complemented
114C4×C9—93no—
115Dic9C2×3−1+211yescharacteristic, complemented
116C33C3×#6711yescharacteristic
1173−1+2—21no—
1183−1+2—23no—
1193−1+2#61111yescharacteristic, direct product factor
120C3×C9—23no—
121C3×C9—21no—
122C3×C9—31no—
123C3×C9—61no—
124C3×C9C3×#6713yes—
125C3×C9C32×D411yescharacteristic
126C3×D4—91no—
127C3×D4—271no—
128#67—31no—
129C2×C32—21no—
130C2×C32—22no—
131C2×C32—21no—
132C2×C32—21no—
133C2×C32—31no—
134C2×C32—61no—
135C2×C32—61no—
136C2×C32—62no—
137C2×C32—181no—
138C2×C32C2×C3×D911yescharacteristic
139C2×C32C2×C32×D311yescharacteristic
140C3×D3—61no—
141C3×D3—181no—
142C2×C9—22no—
143C2×C9—26no—
144C2×C9—23no—
145C2×C9—21no—
146C2×C9—23no—
147C2×C9—21no—
148C2×C9—62no—
149C2×C9—66no—
150C2×C9—63no—
151C2×C9—61no—
152C2×C9—183no—
153C2×C9C2×C3×D913yes—
154C2×C9C22×3−1+211yescharacteristic
155D9—21no—
156C22×C3—21no—
157C22×C3—31no—
158C22×C3—61no—
159C22×C3—91no—
160C22×C3—271no—
161C22×C3C32×D911yescharacteristic
162C22×C3D3×3−1+211yescharacteristic
163C2×D3—31no—
164C3×C4—91no—
165C3×C4—271no—
166Dic3—31no—
167C32—21no—
168C32—31no—
169C32—61no—
170C32C3×#61111yescharacteristic
171C32C32×#6711yescharacteristic
172C9—23no—
173C9—21no—
174C9—63no—
175C9—61no—
176C9C3×#61113yescomplemented
177C9D4×3−1+211yescharacteristic, complemented
178D4—91noSylow
179C2×C3—22no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—31no—
184C2×C3—61no—
185C2×C3—62no—
186C2×C3—61no—
187C2×C3—181no—
188C2×C3—541no—
189C2×C3C2×C32×D911yescharacteristic
190C2×C3C2×D3×3−1+211yescharacteristic
191D3—61no—
192C22—91no—
193C22D9×3−1+211yescharacteristic, complemented
194C4—91no—
195C3—21no—
196C3—31no—
197C3—61no—
198C3C32×#61111yescharacteristic
199C3#67×3−1+211yescharacteristic
200C2—21no—
201C2—181no—
202C2C2×D9×3−1+211yescharacteristic
subgroupG/H
centerC2×C3C2×C32×D9
commutator, cosocleC2×C3×C9C22×C32
Frattini, socleC2×C32C2×C32×D3
FittingC22×C9×3−1+2C2
prime radicalC32×#611C3
hypercenterC22×3−1+2D9
hypocenterC9D4×3−1+2
LCSG ▷ C2×C3×C9 ▷ C9
UCSC1 ◁ C2×C3 ◁ C22×3−1+2

Complements

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

NH ≅ G/Ntype
1. C22×C9×3−1+2C2semidirect
2. C2×D9×3−1+2C2semidirect
3. 3−1+2×Dic9C2semidirect
6. C9×#611C3semidirect
18. C22×C92C2×C3semidirect
19. C2×C9×D9C2×C3semidirect
20. C9×Dic9C2×C3semidirect
21. C9×3−1+2D4semidirect
46. C22×3−1+2D9semidirect
64. C92C3×D4semidirect
69. #6113−1+2direct (N × H)
111. C22×C9C3×D9semidirect
112. C22×C9C2×3−1+2semidirect
113. C2×D9C2×3−1+2semidirect
115. Dic9C2×3−1+2semidirect
119. 3−1+2#611direct (N × H)
176. C9C3×#611semidirect
177. C9D4×3−1+2semidirect
193. C22D9×3−1+2semidirect

Maximal subgroups

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

subgroupindex
C22×C9×3−1+22
C2×D9×3−1+22
3−1+2×Dic92
#67×3−1+23
C32×#6113
C9×#6113