Finite Group Databasebeta

← #14518675

Subgroups — #14518675

Order 1944.

884 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 81 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×C3⋊(C3⋊((C3⋊D3)⋊C3))C211yesmaximal, characteristic, complemented
2C2×C32×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10620152C311yesmaximal, characteristic, complemented
5C3×#6291—31nomaximal
6#6292⋊C3—34nomaximal
7C2×C32×H(3,𝔽3)C2211yescharacteristic
8C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
9C32×(C3⋊D3)⋊C3—21no—
10C2×C3⋊(C3⋊(C3⋊D3))C2×C311yescharacteristic, complemented
11C2×C3×C3⋊(C3⋊D3)—31no—
12C2×C32×C3⋊D3C2×C311yescharacteristic, complemented
13C2×C33×D3—31no—
14C32×C3⋊Dic3—21no—
15C32×C3⋊Dic3D311yescharacteristic, complemented
16C32×C3⋊Dic3C2×C311yescharacteristic, complemented
17C2×C3⋊((C3⋊D3)⋊C3)—34no—
18C2×C3⋊((C3⋊D3)⋊C3)—64no—
19C2×C3×(C3⋊D3)⋊C3—24no—
20C2×C3×(C3⋊D3)⋊C3D314yescomplemented
21Dic3×H(3,𝔽3)—34no—
22C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
23C3×#638—91no—
24#6292—34no—
25#6291—31no—
26#6291—91no—
27C3×#626—94no—
28C4⋊((C3⋊D3)⋊C3)—91no—
29C2×C34—21no—
30C2×C34C2×D311yescharacteristic
31C2×C34C22×C311yescharacteristic
32C3⋊(C3⋊(C3⋊D3))—21no—
33C3×C3⋊(C3⋊D3)—61no—
34C32×C3⋊D3—21no—
35C33×D3—61no—
36C2×C3×H(3,𝔽3)—24no—
37C2×C3×H(3,𝔽3)—24no—
38C2×C3×H(3,𝔽3)—44no—
39C2×C3×H(3,𝔽3)C2×D314yes—
40C3⋊((C3⋊D3)⋊C3)—68no—
41C3⋊((C3⋊D3)⋊C3)—64no—
42C3×(C3⋊D3)⋊C3—28no—
43C3×(C3⋊D3)⋊C3—24no—
44C22×C33—91no—
45C2×C3⋊(C3⋊D3)—31no—
46C2×C3⋊(C3⋊D3)—34no—
47C2×C3⋊(C3⋊D3)—64no—
48C2×C3⋊(C3⋊D3)—91no—
49C2×C3⋊(C3⋊D3)—184no—
50C2×C3×C3⋊D3—91no—
51C2×C3×C3⋊D3—94no—
52C2×C3×C3⋊D3—184no—
53C2×C3×C3⋊D3C3×D314yescomplemented
54C2×C32×D3—34no—
55C2×C32×D3—31no—
56C2×C32×D3—64no—
57C2×C32×D3—91no—
58C3×C3⋊Dic3—31no—
59C3×C3⋊Dic3—31no—
60C3×C3⋊Dic3—61no—
61C3×C3⋊Dic3C3×D311yescharacteristic
62C32×Dic3—34no—
63C32×Dic3—34no—
64C32×Dic3—64no—
65C2×(C3⋊D3)⋊C3—24no—
66C2×(C3⋊D3)⋊C3—91no—
67C2×(C3⋊D3)⋊C3—184no—
68C2×(C3⋊D3)⋊C3C3⋊D311yescharacteristic, complemented
69C4×H(3,𝔽3)—91no—
70C34—21no—
71C34D1211yescharacteristic, complemented
72C34C3×D411yescharacteristic, complemented
73C3×H(3,𝔽3)—24no—
74C3×H(3,𝔽3)—24no—
75C3×H(3,𝔽3)—44no—
76C3×H(3,𝔽3)#6714yescomplemented
77#638—91no—
78C4⋊(C3⋊D3)—91no—
79C3×#67—274no—
80C3×D12—271no—
81#626—94no—
82#626—274no—
83C2×C33—24no—
84C2×C33—24no—
85C2×C33—24no—
86C2×C33—31no—
87C2×C33—31no—
88C2×C33—44no—
89C2×C33—64no—
90C2×C33—64no—
91C2×C33—61no—
92C2×C33—124no—
93C2×C33—181no—
94C2×C33D3214yes—
95C2×C33C2×C3×D311yescharacteristic
96C2×C33C2×C3×D314yes—
97C3⋊(C3⋊D3)—61no—
98C3⋊(C3⋊D3)—68no—
99C3⋊(C3⋊D3)—64no—
100C3⋊(C3⋊D3)—181no—
101C3⋊(C3⋊D3)—188no—
102C3×C3⋊D3—24no—
103C3×C3⋊D3—181no—
104C3×C3⋊D3—188no—
105C3×C3⋊D3—184no—
106C32×D3—68no—
107C32×D3—64no—
108C32×D3—61no—
109C32×D3—181no—
110C2×H(3,𝔽3)—24no—
111C2×H(3,𝔽3)—24no—
112C2×H(3,𝔽3)—44no—
113C2×H(3,𝔽3)—412no—
114C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
115(C3⋊D3)⋊C3—28no—
116(C3⋊D3)⋊C3—21no—
117(C3⋊D3)⋊C3—188no—
118(C3⋊D3)⋊C3—181no—
119C22×C32—91no—
120C22×C32—94no—
121C22×C32—184no—
122C2×C3⋊D3—91no—
123C2×C3⋊D3—94no—
124C2×C3⋊D3—91no—
125C2×C3⋊D3—184no—
126C2×C3⋊D3—184no—
127C2×C3⋊D3—274no—
128C2×C3⋊D3—544no—
129C2×C3⋊D3—544no—
130C2×C3⋊D3—548no—
131C2×C3⋊D3C3×C3⋊D311yescharacteristic, complemented
132C2×C3×D3—34no—
133C2×C3×D3—31no—
134C2×C3×D3—64no—
135C2×C3×D3—94no—
136C2×C3×D3—274no—
137C2×C3×D3—271no—
138C2×C3×D3—544no—
139C32×C4—91no—
140C32×C4—91no—
141C32×C4—181no—
142C3⋊Dic3(C3⋊D3)⋊C311yescharacteristic, complemented
143C3×Dic3—34no—
144C3×Dic3—94no—
145C3×Dic3—94no—
146C3×Dic3—184no—
147C33—24no—
148C33—24no—
149C33—24no—
150C33—31no—
151C33—31no—
152C33—44no—
153C33—64no—
154C33—64no—
155C33—61no—
156C33—124no—
157C33#62614yescomplemented
158C33C3×D1211yescharacteristic
159C33C3×#6714yescomplemented
160H(3,𝔽3)—24no—
161H(3,𝔽3)—24no—
162H(3,𝔽3)—44no—
163H(3,𝔽3)—412no—
164H(3,𝔽3)#63811yescharacteristic, complemented
165C3×D4—811no—
166#67—274no—
167D12—271no—
168D12—811no—
169C2×C32—24no—
170C2×C32—24no—
171C2×C32—24no—
172C2×C32—21no—
173C2×C32—34no—
174C2×C32—34no—
175C2×C32—44no—
176C2×C32—64no—
177C2×C32—64no—
178C2×C32—68no—
179C2×C32—64no—
180C2×C32—64no—
181C2×C32—64no—
182C2×C32—124no—
183C2×C32—124no—
184C2×C32—128no—
185C2×C32—124no—
186C2×C32—184no—
187C2×C32—188no—
188C2×C32—181no—
189C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
190C2×C32C3×D3214yes—
191C2×C32D3×C3⋊D311yescharacteristic
192C2×C32C2×C3×C3⋊D311yescharacteristic
193C3⋊D3—21no—
194C3⋊D3—188no—
195C3⋊D3—181no—
196C3⋊D3—184no—
197C3⋊D3—188no—
198C3⋊D3—181no—
199C3⋊D3—544no—
200C3⋊D3—548no—
201C3⋊D3—5416no—
202C3⋊D3—548no—
203C3×D3—68no—
204C3×D3—64no—
205C3×D3—61no—
206C3×D3—184no—
207C3×D3—544no—
208C3×D3—548no—
209C3×D3—541no—
210C22×C3—91no—
211C22×C3—94no—
212C22×C3—184no—
213C22×C3—811no—
214C2×D3—31no—
215C2×D3—91no—
216C2×D3—274no—
217C2×D3—271no—
218C2×D3—544no—
219C2×D3—811no—
220C2×D3—1624no—
221C3×C4—91no—
222C3×C4—271no—
223C3×C4—271no—
224C3×C4—541no—
225Dic3—34no—
226C32—24no—
227C32—24no—
228C32—24no—
229C32—21no—
230C32—34no—
231C32—34no—
232C32—44no—
233C32—64no—
234C32—64no—
235C32—68no—
236C32—64no—
237C32—64no—
238C32—64no—
239C32—124no—
240C32—124no—
241C32—128no—
242C32—124no—
243C32C4⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
244C32C3×#62614yes—
245C32#629111yescharacteristic, complemented
246C32C3×#63811yescharacteristic, complemented
247D4—811noSylow
248C2×C3—24no—
249C2×C3—31no—
250C2×C3—31no—
251C2×C3—61no—
252C2×C3—64no—
253C2×C3—64no—
254C2×C3—124no—
255C2×C3—181no—
256C2×C3—188no—
257C2×C3—184no—
258C2×C3—1621no—
259C2×C3D3×(C3⋊D3)⋊C314yes—
260C2×C3C3×D3×C3⋊D311yescharacteristic
261D3—61no—
262D3—181no—
263D3—548no—
264D3—544no—
265D3—541no—
266D3—1621no—
267D3—1628no—
268C22—91no—
269C22—811no—
270C4—91no—
271C3—24no—
272C3—31no—
273C3—31no—
274C3—64no—
275C3—64no—
276C3—61no—
277C3—124no—
278C3#6292⋊C314yescomplemented
279C3C3×#629111yescharacteristic
280C2—181no—
281C2—1621no—
282C2C3⋊D3×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊D3×(C3⋊D3)⋊C3
commutator, cosocleC2×C34C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×H(3,𝔽3)C22
socleC2×C33C2×C3×D3
hypocenterC34C3×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2semidirect
2. C2×C32×(C3⋊D3)⋊C3C2semidirect
3. H(3,𝔽3)×C3⋊Dic3C2semidirect
4. #10620152C3semidirect
10. C2×C3⋊(C3⋊(C3⋊D3))C2×C3semidirect
12. C2×C32×C3⋊D3C2×C3semidirect
15. C32×C3⋊Dic3D3semidirect
16. C32×C3⋊Dic3C2×C3semidirect
20. C2×C3×(C3⋊D3)⋊C3D3semidirect
22. C32×H(3,𝔽3)D4semidirect
53. C2×C3×C3⋊D3C3×D3semidirect
68. C2×(C3⋊D3)⋊C3C3⋊D3semidirect
71. C34D12semidirect
72. C34C3×D4semidirect
76. C3×H(3,𝔽3)#67semidirect
131. C2×C3⋊D3C3×C3⋊D3semidirect
142. C3⋊Dic3(C3⋊D3)⋊C3semidirect
157. C33#626semidirect
159. C33C3×#67semidirect
164. H(3,𝔽3)#638semidirect
243. C32C4⋊((C3⋊D3)⋊C3)semidirect
245. C32#6291semidirect
246. C32C3×#638semidirect
278. C3#6292⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊((C3⋊D3)⋊C3))2
C2×C32×(C3⋊D3)⋊C32
H(3,𝔽3)×C3⋊Dic32
#106201523
C3×#62913
#6292⋊C33