Finite Group Databasebeta

← C3×C3⋊#6258 #14519225

Subgroups — C3×C3⋊#6258 #14519225

Order 1944.

1030 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C32×C22⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C32×C3⋊S4—33nomaximal
3C32×#638—31nomaximal
4C3⋊#6258C311yesmaximal, characteristic, direct product factor
5C3×#6258—39nomaximal
6C3×C3⋊#272—41nomaximal
7C22×C34D311yescharacteristic, complemented
8C2×C32×C3⋊D3—31no—
9C33×A4D313yescomplemented
10C32×C3⋊Dic3—31no—
11C3×C22⋊H(3,𝔽3)—21no—
12C3×C22⋊H(3,𝔽3)—23no—
13C3×C22⋊H(3,𝔽3)—29no—
14C3×C22⋊H(3,𝔽3)D319yescomplemented
15C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic, complemented
16C32×H(3,𝔽3)—41noSylow
17C3×C3⋊S4—39no—
18C3×C3⋊S4—33no—
19C32×S4—99no—
20C3×#638—33no—
21C3×#638—31no—
22C32×#67—91no—
23C32×#67—93no—
24#6258—39no—
25C2×C34—31no—
26C32×C3⋊D3—61no—
27C32×C3⋊D3—123no—
28C3⋊#272—41no—
29C3×#272—129no—
30C22×C33—21no—
31C22×C33—23no—
32C22×C33—33no—
33C22×C33—63no—
34C22×C33C3×D311yescharacteristic, complemented
35C22×C33C3⋊D311yescharacteristic
36C22×C33C3⋊D313yescomplemented
37C2×C3×C3⋊D3—33no—
38C2×C3×C3⋊D3—31no—
39C2×C32×D3—91no—
40C2×C32×D3—93no—
41C32×A4—23no—
42C32×A4—29no—
43C32×A4—39no—
44C32×A4—69no—
45C32×A4C3×D313yescomplemented
46C32×A4C3⋊D319yescomplemented
47C3×C3⋊Dic3—33no—
48C3×C3⋊Dic3—31no—
49C32×Dic3—91no—
50C32×Dic3—93no—
51C22⋊H(3,𝔽3)—29no—
52C22⋊H(3,𝔽3)—227no—
53C22⋊H(3,𝔽3)C3×D319yescomplemented
54C34—43no—
55C34S411yescharacteristic, complemented
56C3×H(3,𝔽3)—41no—
57C3×H(3,𝔽3)—49no—
58C3×H(3,𝔽3)—89no—
59C3×H(3,𝔽3)—83no—
60C3×H(3,𝔽3)—81no—
61C3⋊S4—33no—
62C3×S4—927no—
63C3×S4—99no—
64C32×D4—271no—
65#638—31no—
66C3×#67—99no—
67C3×#67—93no—
68C3×#67—91no—
69C3×#67—93no—
70C2×C33—33no—
71C2×C33—31no—
72C2×C33—31no—
73C2×C33—33no—
74C2×C33—61no—
75C2×C33—63no—
76C2×C33—63no—
77C2×C33—69no—
78C3×C3⋊D3—63no—
79C3×C3⋊D3—61no—
80C3×C3⋊D3—123no—
81C3×C3⋊D3—129no—
82C32×D3—181no—
83C32×D3—183no—
84C32×D3—369no—
85#272—129no—
86C22×C32—23no—
87C22×C32—21no—
88C22×C32—23no—
89C22×C32—31no—
90C22×C32—39no—
91C22×C32—61no—
92C22×C32—69no—
93C22×C32—62no—
94C22×C32—61no—
95C22×C32—271no—
96C22×C32#27213yescomplemented
97C22×C32C3×C3⋊D311yescharacteristic
98C22×C32C3×C3⋊D313yescomplemented
99C22×C32C3⋊(C3⋊D3)11yescharacteristic
100C2×C3⋊D3—31no—
101C2×C3×D3—99no—
102C2×C3×D3—93no—
103C2×C3×D3—91no—
104C2×C3×D3—93no—
105C3×A4—29no—
106C3×A4—33no—
107C3×A4—327no—
108C3×A4—63no—
109C3×A4—627no—
110C3×A4—66no—
111C3×A4—63no—
112C3×A4C3×C3⋊D319yescomplemented
113C32×C4—271no—
114C3⋊Dic3—31no—
115C3×Dic3—99no—
116C3×Dic3—93no—
117C3×Dic3—91no—
118C3×Dic3—93no—
119C33—21no—
120C33—23no—
121C33—33no—
122C33—43no—
123C33—49no—
124C33—63no—
125C33—89no—
126C33—83no—
127C33—129no—
128C33—249no—
129C33C3×S411yescharacteristic, complemented
130C33C3⋊S411yescharacteristic
131C33C3⋊S413yescomplemented
132H(3,𝔽3)—49no—
133H(3,𝔽3)—827no—
134H(3,𝔽3)—89no—
135S4—99no—
136C3×D4—273no—
137C3×D4—271no—
138#67—93no—
139#67—91no—
140C2×C32—31no—
141C2×C32—31no—
142C2×C32—39no—
143C2×C32—33no—
144C2×C32—31no—
145C2×C32—33no—
146C2×C32—61no—
147C2×C32—63no—
148C2×C32—63no—
149C2×C32—61no—
150C2×C32—69no—
151C2×C32—63no—
152C2×C32—69no—
153C2×C32—63no—
154C2×C32—618no—
155C2×C32—66no—
156C2×C32—541no—
157C3⋊D3—61no—
158C3⋊D3—123no—
159C3×D3—189no—
160C3×D3—183no—
161C3×D3—181no—
162C3×D3—183no—
163C3×D3—369no—
164C3×D3—3627no—
165C22×C3—23no—
166C22×C3—21no—
167C22×C3—33no—
168C22×C3—63no—
169C22×C3—271no—
170C22×C3—273no—
171C22×C3C3×#27211yescharacteristic, complemented
172C22×C3C3⋊#27213yescomplemented
173C22×C3C3×C3⋊(C3⋊D3)11yescharacteristic
174C2×D3—93no—
175C2×D3—91no—
176A4—39no—
177A4—69no—
178C3×C4—271no—
179C3×C4—273no—
180Dic3—93no—
181Dic3—91no—
182C32—21no—
183C32—23no—
184C32—23no—
185C32—31no—
186C32—39no—
187C32—49no—
188C32—61no—
189C32—69no—
190C32—62no—
191C32—61no—
192C32—89no—
193C32—123no—
194C32—1227no—
195C32—243no—
196C32—2427no—
197C32—246no—
198C32—243no—
199C32#625813yescomplemented
200C32C3×C3⋊S411yescharacteristic
201C32C3×C3⋊S413yescomplemented
202C32C3⋊(C3⋊S4)11yescharacteristic
203D4—271noSylow
204C2×C3—33no—
205C2×C3—31no—
206C2×C3—31no—
207C2×C3—33no—
208C2×C3—63no—
209C2×C3—61no—
210C2×C3—63no—
211C2×C3—69no—
212C2×C3—541no—
213C2×C3—543no—
214D3—183no—
215D3—181no—
216D3—369no—
217C22—271no—
218C22C3×C3⋊#27211yescharacteristic, complemented
219C4—271no—
220C3—23no—
221C3—21no—
222C3—33no—
223C3—63no—
224C3—129no—
225C3—249no—
226C3C3×#625811yescharacteristic, complemented
227C3C3⋊#625813yesdirect product factor
228C3C3×C3⋊(C3⋊S4)11yescharacteristic
229C2—31no—
230C2—541no—
subgroupG/H
center, hypercenterC32C3⋊(C3⋊S4)
commutator, cosocle, hypocenterC3×C22⋊H(3,𝔽3)C2×C3
FrattiniC3C3×C3⋊(C3⋊S4)
FittingC22×C34D3
socleC22×C33C3⋊D3
LCSG ▷ C3×C22⋊H(3,𝔽3)
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C22⋊H(3,𝔽3)C2semidirect
4. C3⋊#6258C3direct (N × H)
7. C22×C34D3semidirect
9. C33×A4D3semidirect
14. C3×C22⋊H(3,𝔽3)D3semidirect
15. C3×C22⋊H(3,𝔽3)C2×C3semidirect
34. C22×C33C3×D3semidirect
36. C22×C33C3⋊D3semidirect
45. C32×A4C3×D3semidirect
46. C32×A4C3⋊D3semidirect
53. C22⋊H(3,𝔽3)C3×D3semidirect
55. C34S4semidirect
96. C22×C32#272semidirect
98. C22×C32C3×C3⋊D3semidirect
112. C3×A4C3×C3⋊D3semidirect
129. C33C3×S4semidirect
131. C33C3⋊S4semidirect
171. C22×C3C3×#272semidirect
172. C22×C3C3⋊#272semidirect
199. C32#6258semidirect
201. C32C3×C3⋊S4semidirect
218. C22C3×C3⋊#272semidirect
226. C3C3×#6258semidirect
227. C3C3⋊#6258direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C22⋊H(3,𝔽3)2
C32×C3⋊S43
C32×#6383
C3⋊#62583
C3×#62583
C3×C3⋊#2724