Finite Group Databasebeta

← #14518680

Subgroups — #14518680

Order 1944.

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

normal subgroups only

This group has 796 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⋊D3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×C32×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊((C3⋊Dic3)⋊C3))C211yesmaximal, characteristic, complemented
4#10620151C311yesmaximal, characteristic, complemented
5C3×#6290—31nomaximal
6#6290⋊C3—34nomaximal
7C2×C32×H(3,𝔽3)C2211yescharacteristic
8C3⋊D3×H(3,𝔽3)—21no—
9C32×(C3⋊D3)⋊C3—21no—
10C2×C32×C3⋊D3—21no—
11C2×C32×C3⋊D3D311yescharacteristic, complemented
12C2×C32×C3⋊D3C2×C311yescharacteristic, complemented
13C2×C32×C3⋊D3C2×C311yescharacteristic, complemented
14C2×C33×D3—31no—
15C3⋊(C3⋊(C3⋊Dic3))C2×C311yescharacteristic, complemented
16C3×C3⋊(C3⋊Dic3)—31no—
17C2×D3×H(3,𝔽3)—34no—
18C2×C3×(C3⋊D3)⋊C3—24no—
19C2×C3×(C3⋊D3)⋊C3D314yescomplemented
20C3⋊((C3⋊Dic3)⋊C3)—34no—
21C3⋊((C3⋊Dic3)⋊C3)—64no—
22C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
23C3×#638—91no—
24#6290—31no—
25#6290—34no—
26#6290—91no—
27C3×#625—94no—
28#638⋊C3—91no—
29C2×C34—21no—
30C2×C34C2×D311yescharacteristic
31C2×C34C22×C311yescharacteristic
32C32×C3⋊D3—22no—
33C32×C3⋊D3—21no—
34C32×C3⋊D3—21no—
35C32×C3⋊D3—21no—
36C33×D3—61no—
37C2×C3×H(3,𝔽3)—24no—
38C2×C3×H(3,𝔽3)—24no—
39C2×C3×H(3,𝔽3)—44no—
40C2×C3×H(3,𝔽3)C2×D314yes—
41D3×H(3,𝔽3)—64no—
42C3×(C3⋊D3)⋊C3—28no—
43C3×(C3⋊D3)⋊C3—24no—
44C22×C33—91no—
45C2×C3×C3⋊D3—31no—
46C2×C3×C3⋊D3—31no—
47C2×C3×C3⋊D3—61no—
48C2×C3×C3⋊D3C3×D311yescharacteristic
49C2×C3×C3⋊D3C3×D314yescomplemented
50C2×C32×D3—34no—
51C2×C32×D3—34no—
52C2×C32×D3—31no—
53C2×C32×D3—34no—
54C2×C32×D3—64no—
55C2×C32×D3—64no—
56C2×C32×D3—91no—
57C3⋊(C3⋊Dic3)—31no—
58C3⋊(C3⋊Dic3)—34no—
59C3⋊(C3⋊Dic3)—64no—
60C3⋊(C3⋊Dic3)—91no—
61C3⋊(C3⋊Dic3)—184no—
62C3×C3⋊Dic3—91no—
63C3×C3⋊Dic3—94no—
64C3×C3⋊Dic3—184no—
65C22×H(3,𝔽3)—91no—
66C2×(C3⋊D3)⋊C3—24no—
67C2×(C3⋊D3)⋊C3C3⋊D311yescharacteristic, complemented
68(C3⋊Dic3)⋊C3—91no—
69(C3⋊Dic3)⋊C3—184no—
70C34—21no—
71C34#6711yescharacteristic, 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—
78#638—91no—
79C3×#67—271no—
80C3×#67—274no—
81#625—94no—
82#625—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—21no—
98C3×C3⋊D3—24no—
99C3×C3⋊D3—61no—
100C3×C3⋊D3—61no—
101C3×C3⋊D3—62no—
102C32×D3—68no—
103C32×D3—64no—
104C32×D3—61no—
105C32×D3—68no—
106C32×D3—64no—
107C32×D3—64no—
108C32×D3—181no—
109C2×H(3,𝔽3)—24no—
110C2×H(3,𝔽3)—24no—
111C2×H(3,𝔽3)—44no—
112C2×H(3,𝔽3)—412no—
113C2×H(3,𝔽3)—181no—
114C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
115(C3⋊D3)⋊C3—28no—
116(C3⋊D3)⋊C3—21no—
117C22×C32—91no—
118C22×C32—94no—
119C22×C32—91no—
120C22×C32—91no—
121C22×C32—184no—
122C22×C32—181no—
123C2×C3⋊D3(C3⋊D3)⋊C311yescharacteristic, complemented
124C2×C3⋊D3C3×C3⋊D311yescharacteristic, complemented
125C2×C3×D3—34no—
126C2×C3×D3—34no—
127C2×C3×D3—31no—
128C2×C3×D3—64no—
129C2×C3×D3—94no—
130C2×C3×D3—94no—
131C2×C3×D3—94no—
132C2×C3×D3—184no—
133C3⋊Dic3—91no—
134C3⋊Dic3—94no—
135C3⋊Dic3—91no—
136C3⋊Dic3—184no—
137C3⋊Dic3—184no—
138C3⋊Dic3—274no—
139C3⋊Dic3—544no—
140C3⋊Dic3—544no—
141C3⋊Dic3—548no—
142C3×Dic3—274no—
143C3×Dic3—271no—
144C3×Dic3—544no—
145C33—24no—
146C33—24no—
147C33—24no—
148C33—31no—
149C33—31no—
150C33—44no—
151C33—64no—
152C33—64no—
153C33—61no—
154C33—124no—
155C33#62514yescomplemented
156C33C3×#6711yescharacteristic
157C33C3×#6714yescomplemented
158H(3,𝔽3)—24no—
159H(3,𝔽3)—24no—
160H(3,𝔽3)—44no—
161H(3,𝔽3)—412no—
162H(3,𝔽3)#63811yescharacteristic, complemented
163C3×D4—811no—
164#67—271no—
165#67—274no—
166#67—811no—
167C2×C32—24no—
168C2×C32—24no—
169C2×C32—24no—
170C2×C32—21no—
171C2×C32—34no—
172C2×C32—34no—
173C2×C32—44no—
174C2×C32—64no—
175C2×C32—64no—
176C2×C32—68no—
177C2×C32—64no—
178C2×C32—64no—
179C2×C32—64no—
180C2×C32—124no—
181C2×C32—124no—
182C2×C32—128no—
183C2×C32—124no—
184C2×C32—184no—
185C2×C32—188no—
186C2×C32—181no—
187C2×C32—182no—
188C2×C32—181no—
189C2×C32—181no—
190C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
191C2×C32C3×D3214yes—
192C2×C32D3×C3⋊D311yescharacteristic
193C2×C32C2×C3×C3⋊D311yescharacteristic
194C3⋊D3—21no—
195C3⋊D3—21no—
196C3×D3—68no—
197C3×D3—64no—
198C3×D3—64no—
199C3×D3—61no—
200C3×D3—184no—
201C3×D3—184no—
202C3×D3—188no—
203C3×D3—184no—
204C22×C3—91no—
205C22×C3—94no—
206C22×C3—91no—
207C22×C3—184no—
208C22×C3—271no—
209C22×C3—271no—
210C22×C3—541no—
211C2×D3—34no—
212C2×D3—31no—
213C2×D3—91no—
214C3×C4—811no—
215Dic3—274no—
216Dic3—271no—
217Dic3—544no—
218Dic3—811no—
219Dic3—1624no—
220C32—24no—
221C32—24no—
222C32—21no—
223C32—24no—
224C32—34no—
225C32—34no—
226C32—44no—
227C32—64no—
228C32—64no—
229C32—68no—
230C32—64no—
231C32—64no—
232C32—64no—
233C32—124no—
234C32—124no—
235C32—128no—
236C32—124no—
237C32#638⋊C311yescharacteristic, complemented
238C32C3×#62514yes—
239C32#629011yescharacteristic, complemented
240C32C3×#63811yescharacteristic, complemented
241D4—811noSylow
242C2×C3—24no—
243C2×C3—31no—
244C2×C3—31no—
245C2×C3—64no—
246C2×C3—64no—
247C2×C3—61no—
248C2×C3—124no—
249C2×C3—181no—
250C2×C3—188no—
251C2×C3—184no—
252C2×C3—181no—
253C2×C3—541no—
254C2×C3—541no—
255C2×C3—542no—
256C2×C3D3×(C3⋊D3)⋊C314yes—
257C2×C3C3×D3×C3⋊D311yescharacteristic
258D3—64no—
259D3—61no—
260D3—181no—
261C22—91no—
262C22—91no—
263C4—811no—
264C3—24no—
265C3—31no—
266C3—31no—
267C3—64no—
268C3—61no—
269C3—64no—
270C3—124no—
271C3#6290⋊C314yescomplemented
272C3C3×#629011yescharacteristic
273C2—181no—
274C2—181no—
275C2C3⋊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⋊D3×H(3,𝔽3)C2semidirect
2. C2×C32×(C3⋊D3)⋊C3C2semidirect
3. C3⋊(C3⋊((C3⋊Dic3)⋊C3))C2semidirect
4. #10620151C3semidirect
11. C2×C32×C3⋊D3D3semidirect
12. C2×C32×C3⋊D3C2×C3semidirect
13. C2×C32×C3⋊D3C2×C3semidirect
15. C3⋊(C3⋊(C3⋊Dic3))C2×C3semidirect
19. C2×C3×(C3⋊D3)⋊C3D3semidirect
22. C32×H(3,𝔽3)D4semidirect
49. C2×C3×C3⋊D3C3×D3semidirect
67. C2×(C3⋊D3)⋊C3C3⋊D3semidirect
71. C34#67semidirect
72. C34C3×D4semidirect
76. C3×H(3,𝔽3)#67semidirect
123. C2×C3⋊D3(C3⋊D3)⋊C3semidirect
124. C2×C3⋊D3C3×C3⋊D3semidirect
155. C33#625semidirect
157. C33C3×#67semidirect
162. H(3,𝔽3)#638semidirect
237. C32#638⋊C3semidirect
239. C32#6290semidirect
240. C32C3×#638semidirect
271. C3#6290⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×H(3,𝔽3)2
C2×C32×(C3⋊D3)⋊C32
C3⋊(C3⋊((C3⋊Dic3)⋊C3))2
#106201513
C3×#62903
#6290⋊C33