Finite Group Databasebeta

← #14518839

Subgroups — #14518839

Order 1944.

1204 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 1204 conjugacy classes of subgroups — too many to draw. Only its 103 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×#272C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊((C3⋊Dic3)⋊C3))C211yesmaximal, characteristic, complemented
4#10620146—31nomaximal
5#10620145—31nomaximal
6#10619904—34nomaximal
7C2×C32×H(3,𝔽3)C2211yescharacteristic
8C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
9C32×#272—21no—
10C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic, complemented
11C2×C3×C3⋊(C3⋊D3)—31no—
12C2×C33×D3—31no—
13C2×C33×D3—31no—
14C2×C33×D3—61no—
15C3⋊(C3⋊(C3⋊Dic3))D311yescharacteristic, complemented
16C3×C3⋊(C3⋊Dic3)—31no—
17C2×C3×#272D314yescomplemented
18C2×C3⋊((C3⋊D3)⋊C3)—34no—
19C2×C3⋊((C3⋊D3)⋊C3)—64no—
20C3⋊((C3⋊Dic3)⋊C3)—34no—
21C3⋊((C3⋊Dic3)⋊C3)—64no—
22C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
23#6312—91no—
24#6291—94no—
25#6291—99no—
26#6290—94no—
27#6290—99no—
28#6200—91no—
29C2×C34—21no—
30C2×C34C2×D311yescharacteristic
31C2×C34C2×D311yescharacteristic
32C3⋊(C3⋊(C3⋊D3))—21no—
33C3×C3⋊(C3⋊D3)—61no—
34C33×D3—62no—
35C33×D3—61no—
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—
41C3×#272—24no—
42C3⋊((C3⋊D3)⋊C3)—68no—
43C3⋊((C3⋊D3)⋊C3)—64no—
44C22×C33—91no—
45C2×C3⋊(C3⋊D3)—31no—
46C2×C3⋊(C3⋊D3)—34no—
47C2×C3⋊(C3⋊D3)—64no—
48C2×C3⋊(C3⋊D3)—99no—
49C2×C3×C3⋊D3—99no—
50C2×C3×C3⋊D3—94no—
51C2×C32×D3—39no—
52C2×C32×D3—39no—
53C2×C32×D3—34no—
54C2×C32×D3—34no—
55C2×C32×D3—64no—
56C2×C32×D3—69no—
57C3⋊(C3⋊Dic3)—31no—
58C3⋊(C3⋊Dic3)—34no—
59C3⋊(C3⋊Dic3)—64no—
60C3⋊(C3⋊Dic3)—99no—
61C3×C3⋊Dic3—99no—
62C3×C3⋊Dic3—94no—
63C2×#272C3⋊D311yescharacteristic, complemented
64C2×(C3⋊D3)⋊C3—91no—
65C2×(C3⋊D3)⋊C3—184no—
66(C3⋊Dic3)⋊C3—91no—
67(C3⋊Dic3)⋊C3—184no—
68C34—21no—
69C34D1211yescharacteristic, complemented
70C34#6711yescharacteristic, complemented
71C3×H(3,𝔽3)—24no—
72C3×H(3,𝔽3)—24no—
73C3×H(3,𝔽3)—44no—
74C3×H(3,𝔽3)#6714yescomplemented
75#638—279no—
76#638—274no—
77#626—271no—
78#626—2712no—
79#625—271no—
80#625—2712no—
81C2×C33—24no—
82C2×C33—24no—
83C2×C33—24no—
84C2×C33—39no—
85C2×C33—39no—
86C2×C33—44no—
87C2×C33—69no—
88C2×C33—181no—
89C2×C33D3214yes—
90C2×C33D3214yes—
91C2×C33D3211yescharacteristic
92C3⋊(C3⋊D3)—61no—
93C3⋊(C3⋊D3)—68no—
94C3⋊(C3⋊D3)—64no—
95C3⋊(C3⋊D3)—189no—
96C3×C3⋊D3—189no—
97C3×C3⋊D3—184no—
98C32×D3—68no—
99C32×D3—69no—
100C32×D3—69no—
101C32×D3—618no—
102C32×D3—64no—
103C32×D3—64no—
104C2×H(3,𝔽3)—24no—
105C2×H(3,𝔽3)—24no—
106C2×H(3,𝔽3)—44no—
107C2×H(3,𝔽3)—412no—
108C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
109#272—21no—
110(C3⋊D3)⋊C3—188no—
111(C3⋊D3)⋊C3—181no—
112C22×C32—99no—
113C22×C32—94no—
114C2×C3⋊D3—99no—
115C2×C3⋊D3—94no—
116C2×C3⋊D3—91no—
117C2×C3⋊D3—184no—
118C2×C3⋊D3—2712no—
119C2×C3⋊D3—5412no—
120C2×C3×D3—312no—
121C2×C3×D3—312no—
122C2×C3×D3—31no—
123C2×C3×D3—31no—
124C2×C3×D3—61no—
125C2×C3×D3—612no—
126C2×C3×D3—2712no—
127C2×C3×D3—271no—
128C3⋊Dic3—99no—
129C3⋊Dic3—94no—
130C3⋊Dic3—91no—
131C3⋊Dic3—184no—
132C3⋊Dic3—2712no—
133C3⋊Dic3—5412no—
134C3×Dic3—2712no—
135C3×Dic3—271no—
136C33—24no—
137C33—24no—
138C33—24no—
139C33—39no—
140C33—39no—
141C33—44no—
142C33—69no—
143C33#62514yescomplemented
144C33#62611yescharacteristic
145C33#62614yescomplemented
146H(3,𝔽3)—24no—
147H(3,𝔽3)—24no—
148H(3,𝔽3)—44no—
149H(3,𝔽3)—412no—
150H(3,𝔽3)#63811yescharacteristic, complemented
151#67—8112no—
152#67—811no—
153#67—811no—
154D12—811no—
155C2×C32—24no—
156C2×C32—24no—
157C2×C32—21no—
158C2×C32—312no—
159C2×C32—312no—
160C2×C32—44no—
161C2×C32—612no—
162C2×C32—612no—
163C2×C32—612no—
164C2×C32—1212no—
165C2×C32—189no—
166C2×C32—184no—
167C2×C32((C3⋊D3)⋊C3)⋊C219yes—
168C2×C32D3×C3⋊D311yescharacteristic
169C2×C32D3×C3⋊D311yescharacteristic
170C2×C32#111314yes—
171C3⋊D3—189no—
172C3⋊D3—184no—
173C3⋊D3—188no—
174C3⋊D3—181no—
175C3⋊D3—5412no—
176C3⋊D3—5424no—
177C3×D3—62no—
178C3×D3—612no—
179C3×D3—612no—
180C3×D3—624no—
181C3×D3—61no—
182C3×D3—61no—
183C3×D3—5412no—
184C3×D3—541no—
185C22×C3—912no—
186C22×C3—91no—
187C22×C3—811no—
188C2×D3—31no—
189C2×D3—31no—
190C2×D3—61no—
191C2×D3—2712no—
192C2×D3—271no—
193C2×D3—811no—
194C2×D3—1624no—
195C3×C4—811no—
196Dic3—2712no—
197Dic3—271no—
198Dic3—811no—
199Dic3—1624no—
200C32—21no—
201C32—24no—
202C32—24no—
203C32—312no—
204C32—312no—
205C32—44no—
206C32—612no—
207C32—612no—
208C32—612no—
209C32—1212no—
210C32#620019yescomplemented
211C32#629011yescharacteristic, complemented
212C32#629111yescharacteristic, complemented
213C32#629514yes—
214D4—2431noSylow
215C2×C3—31no—
216C2×C3—31no—
217C2×C3—64no—
218C2×C3—61no—
219C2×C3—64no—
220C2×C3—124no—
221C2×C3—1812no—
222C2×C3—181no—
223C2×C3—1621no—
224C2×C3#66432112yes—
225C2×C3C3⋊#111311yescharacteristic
226D3—61no—
227D3—61no—
228D3—62no—
229D3—5412no—
230D3—541no—
231D3—1621no—
232D3—1628no—
233C22—91no—
234C22—811no—
235C4—811no—
236C3—31no—
237C3—31no—
238C3—61no—
239C3—64no—
240C3—64no—
241C3—124no—
242C3#10619904112yescomplemented
243C3#1062015711yescharacteristic
244C2—181no—
245C2—1621no—
246C2#1175809111yescharacteristic
subgroupG/H
center, hypercenterC2#11758091
commutator, Fitting, cosocleC2×C32×H(3,𝔽3)C22
FrattiniC2×C3C3⋊#1113
socleC2×C33D32
hypocenterC32×H(3,𝔽3)D4
LCSG ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3)
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×#272C2semidirect
3. C3⋊(C3⋊((C3⋊Dic3)⋊C3))C2semidirect
10. C2×C3⋊(C3⋊(C3⋊D3))D3semidirect
15. C3⋊(C3⋊(C3⋊Dic3))D3semidirect
17. C2×C3×#272D3semidirect
22. C32×H(3,𝔽3)D4semidirect
63. C2×#272C3⋊D3semidirect
69. C34D12semidirect
70. C34#67semidirect
74. C3×H(3,𝔽3)#67semidirect
143. C33#625semidirect
145. C33#626semidirect
150. H(3,𝔽3)#638semidirect
210. C32#6200semidirect
211. C32#6290semidirect
212. C32#6291semidirect
242. C3#10619904semidirect

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×#2722
C3⋊(C3⋊((C3⋊Dic3)⋊C3))2
#106201463
#106201453
#106199043