Finite Group Databasebeta

← C3×#88994 #13049589

Subgroups — C3×#88994 #13049589

Order 1296.

580 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 50 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×C32×C3⋊D3C211yesmaximal, characteristic
2C2×C3×C3⋊#157C212yesmaximal, complemented
3#88994C311yesmaximal, characteristic, direct product factor
4C3×C22⋊#157—31nomaximal
5C22×C34C411yescharacteristic, complemented
6C2×C32×C3⋊D3—22no—
7C2×C32×C3⋊D3C411yescharacteristic, complemented
8C2×C32×C3⋊D3C2211yescharacteristic
9C3×C3⋊#157—22no—
10C22×C3×C3⋊D3—21no—
11C22×C3×C3⋊D3D311yescharacteristic
12C22×C3×C3⋊D3C2×C311yescharacteristic
13C22×C32×D3—62no—
14C2×C3⋊#157C2×C312yescomplemented
15C2×C3×#157—32no—
16C2×C34—21no—
17C2×C34C2×C411yescharacteristic
18C32×C3⋊D3—21no—
19C32×C3⋊D3D412yes—
20C22⋊#157—31no—
21C3×#217—91nomaximal
22C22×C33—21no—
23C22×C33—22no—
24C22×C33—44no—
25C22×C33—42no—
26C22×C33—42no—
27C22×C33Dic311yescharacteristic, complemented
28C22×C33C3×C411yescharacteristic, complemented
29C2×C3×C3⋊D3—24no—
30C2×C3×C3⋊D3—21no—
31C2×C3×C3⋊D3—21no—
32C2×C3×C3⋊D3—22no—
33C2×C3×C3⋊D3—22no—
34C2×C3×C3⋊D3Dic311yescharacteristic, complemented
35C2×C3×C3⋊D3C3×C411yescharacteristic, complemented
36C2×C3×C3⋊D3C2×D311yescharacteristic
37C2×C3×C3⋊D3C22×C311yescharacteristic
38C2×C32×D3—62no—
39C2×C32×D3—62no—
40C2×C32×D3—68no—
41C3⋊#157—22no—
42C3×#157—62no—
43C34C22⋊C411yescharacteristic, complemented, Sylow
44C23×C32—91no—
45C22×C3⋊D3C3×D311yescharacteristic
46C22×C3×D3—62no—
47C22×C3×D3—62no—
48C22×C3×D3—64no—
49C2×#157—32no—
50C2×C3×Dic3—92no—
51C2×C33—24no—
52C2×C33—22no—
53C2×C33—21no—
54C2×C33—21no—
55C2×C33—21no—
56C2×C33—22no—
57C2×C33—48no—
58C2×C33—44no—
59C2×C33—44no—
60C2×C33—44no—
61C2×C33—42no—
62C2×C33—42no—
63C2×C33C2×Dic311yescharacteristic
64C2×C33C2×C3×C411yescharacteristic
65C3×C3⋊D3—22no—
66C3×C3⋊D3—21no—
67C3×C3⋊D3—21no—
68C3×C3⋊D3—22no—
69C3×C3⋊D3#6712yes—
70C3×C3⋊D3C3×D412yes—
71C32×D3—64no—
72C32×D3—64no—
73C3×C22⋊C4—271no—
74#217—91no—
75C22×C32—24no—
76C22×C32—22no—
77C22×C32—22no—
78C22×C32—44no—
79C22×C32—44no—
80C22×C32—42no—
81C22×C32—42no—
82C22×C32—48no—
83C22×C32—42no—
84C22×C32—42no—
85C22×C32—44no—
86C22×C32—91no—
87C22×C32—91no—
88C22×C32—182no—
89C22×C32C3×Dic311yescharacteristic, complemented
90C22×C32#15711yescharacteristic, complemented
91C2×C3⋊D3—22no—
92C2×C3⋊D3C3×Dic311yescharacteristic, complemented
93C2×C3⋊D3C2×C3×D311yescharacteristic
94C2×C3×D3—62no—
95C2×C3×D3—62no—
96C2×C3×D3—62no—
97C2×C3×D3—62no—
98C2×C3×D3—64no—
99C2×C3×D3—64no—
100C2×C3×D3—68no—
101C2×C3×D3—68no—
102C2×C3×D3—616no—
103#157—62no—
104C3×Dic3—182no—
105C33—21no—
106C33—22no—
107C33—44no—
108C33—42no—
109C33—42no—
110C33#21711yescharacteristic, complemented
111C33C3×C22⋊C411yescharacteristic, complemented
112C23×C3—91no—
113C23×C3—91no—
114C23×C3—181no—
115C22×D3—62no—
116C2×C3×C4—272no—
117C2×Dic3—92no—
118C2×C32—21no—
119C2×C32—21no—
120C2×C32—28no—
121C2×C32—24no—
122C2×C32—24no—
123C2×C32—24no—
124C2×C32—22no—
125C2×C32—22no—
126C2×C32—44no—
127C2×C32—44no—
128C2×C32—48no—
129C2×C32—48no—
130C2×C32—44no—
131C2×C32—44no—
132C2×C32—44no—
133C2×C32—44no—
134C2×C32—42no—
135C2×C32—42no—
136C2×C32—48no—
137C2×C32—416no—
138C2×C32—48no—
139C2×C32—42no—
140C2×C32—42no—
141C2×C32—44no—
142C2×C32—92no—
143C2×C32—181no—
144C2×C32C2×C3×Dic311yescharacteristic
145C2×C32C2×#15711yescharacteristic
146C3⋊D3—21no—
147C3⋊D3C3×#6712yes—
148C3×D3—64no—
149C3×D3—64no—
150C3×D3—68no—
151C3×D3—68no—
152C3×D3—64no—
153C3×D3—64no—
154C22⋊C4—271noSylow
155C22×C3—22no—
156C22×C3—21no—
157C22×C3—44no—
158C22×C3—42no—
159C22×C3—42no—
160C22×C3—91no—
161C22×C3—91no—
162C22×C3—91no—
163C22×C3—91no—
164C22×C3—181no—
165C22×C3—181no—
166C22×C3—182no—
167C22×C3—182no—
168C22×C3—184no—
169C22×C3C3×#15711yescharacteristic, complemented
170C22×C3C3⋊#15711yescharacteristic, complemented
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—68no—
174C3×C4—542no—
175Dic3—182no—
176C32—24no—
177C32—22no—
178C32—22no—
179C32—42no—
180C32—42no—
181C32—44no—
182C32—44no—
183C32—44no—
184C32—48no—
185C32—42no—
186C32—42no—
187C32C3×#21711yescharacteristic, complemented
188C32C22⋊#15711yescharacteristic, complemented
189C23—91no—
190C2×C4—272no—
191C2×C3—24no—
192C2×C3—22no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—22no—
196C2×C3—21no—
197C2×C3—48no—
198C2×C3—44no—
199C2×C3—44no—
200C2×C3—44no—
201C2×C3—42no—
202C2×C3—42no—
203C2×C3—92no—
204C2×C3—92no—
205C2×C3—182no—
206C2×C3—182no—
207C2×C3—181no—
208C2×C3—181no—
209C2×C3C2×C3×#15711yescharacteristic
210C2×C3C2×C3⋊#15711yescharacteristic
211D3—64no—
212D3—64no—
213C22—91no—
214C22—91no—
215C22—182no—
216C22C3×C3⋊#15711yescharacteristic, complemented
217C4—542no—
218C3—22no—
219C3—21no—
220C3—44no—
221C3—42no—
222C3—42no—
223C3C3×C22⋊#15711yescharacteristic, complemented
224C3#8899411yescharacteristic, direct product factor
225C2—21no—
226C2—92no—
227C2—181no—
228C2C2×C3×C3⋊#15711yescharacteristic
subgroupG/H
centerC2×C3C2×C3⋊#157
commutatorC2×C33C2×C3×C4
FrattiniC2C2×C3×C3⋊#157
FittingC22×C34C4
socleC2×C34C2×C4
prime radicalC22×C32×C3⋊D3C2
cosocleC2×C3×C3⋊D3C22×C3
hypercenterC22×C3C3⋊#157
hypocenterC33C3×C22⋊C4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×C3⋊#157C2semidirect
3. #88994C3direct (N × H)
5. C22×C34C4semidirect
7. C2×C32×C3⋊D3C4semidirect
14. C2×C3⋊#157C2×C3semidirect
27. C22×C33Dic3semidirect
28. C22×C33C3×C4semidirect
34. C2×C3×C3⋊D3Dic3semidirect
35. C2×C3×C3⋊D3C3×C4semidirect
43. C34C22⋊C4semidirect
89. C22×C32C3×Dic3semidirect
90. C22×C32#157semidirect
92. C2×C3⋊D3C3×Dic3semidirect
110. C33#217semidirect
111. C33C3×C22⋊C4semidirect
169. C22×C3C3×#157semidirect
170. C22×C3C3⋊#157semidirect
187. C32C3×#217semidirect
188. C32C22⋊#157semidirect
216. C22C3×C3⋊#157semidirect
223. C3C3×C22⋊#157semidirect
224. C3#88994direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C3⋊D32
C2×C3×C3⋊#1572
#889943
C3×C22⋊#1573
C3×#2179