Finite Group Databasebeta

← C2×#11757563 #14517426

Subgroups — C2×#11757563 #14517426

Order 1944.

480 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 106 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×#6891C211yesmaximal, characteristic
2#11757563C212yesmaximal, direct product factor
3C2×C32×C3⋊Dic3C311yesmaximal, characteristic
4C2×Dic3×3−1+2—31nomaximal
5C2×(C3⋊Dic3)⋊C9C313yesmaximal, complemented
6C2×#6891C412yescomplemented
7C2×#6891C2211yescharacteristic
8C22×C34C2×C311yescharacteristic
9C32×C3⋊Dic3C2×C312yes—
10C22×C3×3−1+2—21no—
11C22×C3×3−1+2D311yescharacteristic
12Dic3×3−1+2—32no—
13C22×C32⋊C9—23no—
14C22×C32⋊C9C2×C313yes—
15(C3⋊Dic3)⋊C9C2×C316yescomplemented
16#6891C2×C411yescharacteristic, complemented, Sylow
17C2×C3×C3⋊Dic3—31no—
18C2×C3×C3⋊Dic3C3211yescharacteristic
19C2×C32×Dic3—31no—
20C2×C32×Dic3—91no—
21C2×C4×3−1+2—91no—
22C2×C9×Dic3—33no—
23C2×C34C3×C412yes—
24C2×C34C22×C311yescharacteristic
25C2×C3×3−1+2—22no—
26C2×C3×3−1+2—21no—
27C2×C3×3−1+2Dic312yescomplemented
28C2×C3×3−1+2C2×D311yescharacteristic
29C2×C32⋊C9—26no—
30C2×C32⋊C9—23no—
31C2×C32⋊C9C3×C416yescomplemented
32C2×C32⋊C9C22×C313yes—
33C22×C33—21no—
34C22×C33—31no—
35C22×C33—31no—
36C22×C33—63no—
37C22×C33—61no—
38C22×C33—61no—
39C22×C33C3×D311yescharacteristic
40C22×C33C2×C3211yescharacteristic
41C3×C3⋊Dic3—32no—
42C3×C3⋊Dic3C2×C3212yes—
43C32×Dic3—32no—
44C32×Dic3—92no—
45C22×3−1+2—31no—
46C22×3−1+2—61no—
47C22×3−1+2—62no—
48C22×3−1+2—61no—
49C22×C3×C9—23no—
50C22×C3×C9C3×D313yes—
51C4×3−1+2—92no—
52C9×Dic3—36no—
53C34C2×C3×C411yescharacteristic
54C3×3−1+2—21no—
55C3×3−1+2C2×Dic311yescharacteristic, complemented
56C32⋊C9—23no—
57C32⋊C9C2×C3×C413yescomplemented
58C2×C32×C4—91no—
59C2×C3⋊Dic33−1+211yescharacteristic, complemented
60C2×C3×Dic3—31no—
61C2×C3×Dic3—91no—
62C2×C3×Dic3—91no—
63C2×C3×Dic3—93no—
64C2×C4×C9—93no—
65C2×C33—22no—
66C2×C33—21no—
67C2×C33—32no—
68C2×C33—32no—
69C2×C33—31no—
70C2×C33—31no—
71C2×C33—66no—
72C2×C33—62no—
73C2×C33—62no—
74C2×C33—63no—
75C2×C33—61no—
76C2×C33—61no—
77C2×C33C3×Dic312yes—
78C2×C33C32×C412yes—
79C2×C33C2×C3×D311yescharacteristic
80C2×C33C22×C3211yescharacteristic
81C2×3−1+2—32no—
82C2×3−1+2—31no—
83C2×3−1+2—62no—
84C2×3−1+2—61no—
85C2×3−1+2—64no—
86C2×3−1+2—62no—
87C2×3−1+2—62no—
88C2×3−1+2—61no—
89C2×C3×C9—26no—
90C2×C3×C9—23no—
91C2×C3×C9C3×Dic316yescomplemented
92C2×C3×C9C2×C3×D313yes—
93C22×C32—23no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—33no—
97C22×C32—31no—
98C22×C32—31no—
99C22×C32—61no—
100C22×C32—61no—
101C22×C32—61no—
102C22×C32—63no—
103C22×C32—63no—
104C22×C32—63no—
105C22×C32—61no—
106C22×C32—61no—
107C22×C32—63no—
108C22×C32(C3⋊D3)⋊C311yescharacteristic
109C22×C32C2×3−1+211yescharacteristic
110C22×C32C32×D311yescharacteristic
111C32×C4—92no—
112C3⋊Dic3C2×3−1+212yescomplemented
113C3×Dic3—32no—
114C3×Dic3—92no—
115C3×Dic3—92no—
116C3×Dic3—96no—
117C22×C9—33no—
118C22×C9—63no—
119C4×C9—96no—
120C33—21no—
121C33—31no—
122C33—31no—
123C33—63no—
124C33—61no—
125C33—61no—
126C33C2×C3×Dic311yescharacteristic
127C33C2×C32×C411yescharacteristic
1283−1+2—31no—
1293−1+2—61no—
1303−1+2—62no—
1313−1+2—61no—
132C3×C9—23no—
133C3×C9C2×C3×Dic313yescomplemented
134C2×C3×C4—91no—
135C2×C3×C4—271no—
136C2×Dic3—31no—
137C2×Dic3—91no—
138C2×C32—23no—
139C2×C32—26no—
140C2×C32—22no—
141C2×C32—22no—
142C2×C32—21no—
143C2×C32—21no—
144C2×C32—33no—
145C2×C32—36no—
146C2×C32—32no—
147C2×C32—32no—
148C2×C32—31no—
149C2×C32—31no—
150C2×C32—62no—
151C2×C32—62no—
152C2×C32—61no—
153C2×C32—61no—
154C2×C32—61no—
155C2×C32—62no—
156C2×C32—63no—
157C2×C32—63no—
158C2×C32—66no—
159C2×C32—66no—
160C2×C32—63no—
161C2×C32—66no—
162C2×C32—62no—
163C2×C32—62no—
164C2×C32—61no—
165C2×C32—61no—
166C2×C32—63no—
167C2×C32—66no—
168C2×C32(C3⋊Dic3)⋊C312yes—
169C2×C32C4×3−1+212yescomplemented
170C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
171C2×C32C22×3−1+211yescharacteristic
172C2×C32C32×Dic312yes—
173C2×C32C2×C32×D311yescharacteristic
174C2×C9—36no—
175C2×C9—33no—
176C2×C9—66no—
177C2×C9—63no—
178C22×C3—21no—
179C22×C3—31no—
180C22×C3—31no—
181C22×C3—63no—
182C22×C3—61no—
183C22×C3—61no—
184C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
185C22×C3D3×3−1+211yescharacteristic
186C3×C4—92no—
187C3×C4—272no—
188Dic3—32no—
189Dic3—92no—
190C32—23no—
191C32—21no—
192C32—21no—
193C32—33no—
194C32—31no—
195C32—31no—
196C32—61no—
197C32—61no—
198C32—61no—
199C32—63no—
200C32—63no—
201C32—63no—
202C32—63no—
203C32—61no—
204C32—61no—
205C32C2×(C3⋊Dic3)⋊C311yescharacteristic
206C32C2×C4×3−1+211yescharacteristic, complemented
207C32C2×C32×Dic311yescharacteristic
208C9—33no—
209C9—63no—
210C2×C4—91noSylow
211C2×C3—21no—
212C2×C3—22no—
213C2×C3—31no—
214C2×C3—31no—
215C2×C3—32no—
216C2×C3—32no—
217C2×C3—63no—
218C2×C3—61no—
219C2×C3—61no—
220C2×C3—66no—
221C2×C3—62no—
222C2×C3—62no—
223C2×C3C3×(C3⋊Dic3)⋊C312yes—
224C2×C3Dic3×3−1+212yes—
225C2×C3C2×C3×(C3⋊D3)⋊C311yescharacteristic
226C2×C3C2×D3×3−1+211yescharacteristic
227C22#9225911yescharacteristic
228C4—92no—
229C3—21no—
230C3—31no—
231C3—31no—
232C3—63no—
233C3—61no—
234C3—61no—
235C3C2×C3×(C3⋊Dic3)⋊C311yescharacteristic
236C3C2×Dic3×3−1+211yescharacteristic
237C2#1175756312yesdirect product factor
238C2C2×#9225911yescharacteristic
subgroupG/H
centerC22×C3C3×(C3⋊D3)⋊C3
commutatorC33C2×C32×C4
FrattiniC2×C32C2×C32×D3
FittingC22×#6891C2
socleC22×C32C32×D3
prime radicalC22×C34C2×C3
cosocleC2×C33C22×C32
hypercenterC22×C32(C3⋊D3)⋊C3
hypocenterC32C2×C4×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C32

Complements

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

NH ≅ G/Ntype
2. #11757563C2direct (N × H)
5. C2×(C3⋊Dic3)⋊C9C3semidirect
6. C2×#6891C4semidirect
15. (C3⋊Dic3)⋊C9C2×C3semidirect
16. #6891C2×C4semidirect
27. C2×C3×3−1+2Dic3semidirect
31. C2×C32⋊C9C3×C4semidirect
55. C3×3−1+2C2×Dic3semidirect
57. C32⋊C9C2×C3×C4semidirect
59. C2×C3⋊Dic33−1+2semidirect
91. C2×C3×C9C3×Dic3semidirect
112. C3⋊Dic3C2×3−1+2semidirect
133. C3×C9C2×C3×Dic3semidirect
169. C2×C32C4×3−1+2semidirect
206. C32C2×C4×3−1+2semidirect
237. C2#11757563direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68912
#117575632
C2×C32×C3⋊Dic33
C2×Dic3×3−1+23
C2×(C3⋊Dic3)⋊C93