Finite Group Databasebeta

← #14518831

Subgroups — #14518831

Order 1944.

1148 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 107 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
2C3⋊(C3⋊((C3⋊Dic3)⋊C3))C211yesmaximal, characteristic, complemented
3C32×#1084C211yesmaximal, characteristic, complemented
4#10620144—31nomaximal
5Dic3×C3⋊(C3⋊D3)—31nomaximal
6#10619901—34nomaximal
7C2×C32×H(3,𝔽3)C2211yescharacteristic
8C3⋊(C3⋊((C3⋊D3)⋊C3))C412yescomplemented
9C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic
10C2×C3×C3⋊(C3⋊D3)—31no—
11C3⋊(C3⋊(C3⋊Dic3))D311yescharacteristic, complemented
12C3×C3⋊(C3⋊Dic3)—31no—
13C33×Dic3—31no—
14C33×Dic3—31no—
15C33×Dic3—61no—
16C2×C3⋊((C3⋊D3)⋊C3)—34no—
17C2×C3⋊((C3⋊D3)⋊C3)—64no—
18C3×#1084D314yescomplemented
19C3⋊((C3⋊Dic3)⋊C3)—34no—
20C3⋊((C3⋊Dic3)⋊C3)—64no—
21C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
22C4×C3⋊(C3⋊D3)—91no—
23#6289—94no—
24#6289—99no—
25Dic3×C3⋊D3—94no—
26Dic3×C3⋊D3—99no—
27((C3⋊D3)⋊C3)⋊C4—91no—
28C2×C34—21no—
29C2×C34C2×D311yescharacteristic
30C2×C34C2×D311yescharacteristic
31C3⋊(C3⋊(C3⋊D3))Dic312yescomplemented
32C3×C3⋊(C3⋊D3)—32no—
33C2×C3×H(3,𝔽3)—24no—
34C2×C3×H(3,𝔽3)—24no—
35C2×C3×H(3,𝔽3)—44no—
36C2×C3×H(3,𝔽3)C2×D314yes—
37C3⋊((C3⋊D3)⋊C3)—38no—
38C3⋊((C3⋊D3)⋊C3)—68no—
39C2×C3⋊(C3⋊D3)—31no—
40C2×C3⋊(C3⋊D3)—34no—
41C2×C3⋊(C3⋊D3)—64no—
42C2×C3⋊(C3⋊D3)—99no—
43C2×C3×C3⋊D3—99no—
44C2×C3×C3⋊D3—94no—
45C33×C4—91no—
46C3⋊(C3⋊Dic3)—31no—
47C3⋊(C3⋊Dic3)—34no—
48C3⋊(C3⋊Dic3)—64no—
49C3⋊(C3⋊Dic3)—99no—
50C3×C3⋊Dic3—99no—
51C3×C3⋊Dic3—94no—
52C32×Dic3—39no—
53C32×Dic3—39no—
54C32×Dic3—34no—
55C32×Dic3—34no—
56C32×Dic3—64no—
57C32×Dic3—69no—
58C2×(C3⋊D3)⋊C3—91no—
59C2×(C3⋊D3)⋊C3—184no—
60#1084C3⋊D311yescharacteristic, complemented
61(C3⋊Dic3)⋊C3—91no—
62(C3⋊Dic3)⋊C3—184no—
63C34—21no—
64C34C4×D311yescharacteristic, complemented
65C34C2×Dic311yescharacteristic, complemented
66C3×H(3,𝔽3)—24no—
67C3×H(3,𝔽3)—24no—
68C3×H(3,𝔽3)—44no—
69C3×H(3,𝔽3)C4×D314yescomplemented
70C4×C3⋊D3—279no—
71C4×C3⋊D3—274no—
72#624—271no—
73#624—2712no—
74D3×Dic3—271no—
75D3×Dic3—2712no—
76C2×C33—24no—
77C2×C33—24no—
78C2×C33—24no—
79C2×C33—39no—
80C2×C33—39no—
81C2×C33—44no—
82C2×C33—69no—
83C2×C33D3214yes—
84C2×C33D3214yes—
85C2×C33D3211yescharacteristic
86C3⋊(C3⋊D3)—32no—
87C3⋊(C3⋊D3)—38no—
88C3⋊(C3⋊D3)—68no—
89C3⋊(C3⋊D3)—918no—
90C3×C3⋊D3—918no—
91C3×C3⋊D3—98no—
92C2×H(3,𝔽3)—24no—
93C2×H(3,𝔽3)—24no—
94C2×H(3,𝔽3)—44no—
95C2×H(3,𝔽3)—412no—
96C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
97(C3⋊D3)⋊C3—92no—
98(C3⋊D3)⋊C3—188no—
99C2×C3⋊D3—99no—
100C2×C3⋊D3—94no—
101C2×C3⋊D3—91no—
102C2×C3⋊D3—184no—
103C2×C3⋊D3—2712no—
104C2×C3⋊D3—5412no—
105C2×C3×D3—2712no—
106C2×C3×D3—271no—
107C32×C4—99no—
108C32×C4—94no—
109C3⋊Dic3—99no—
110C3⋊Dic3—94no—
111C3⋊Dic3—91no—
112C3⋊Dic3—184no—
113C3⋊Dic3—2712no—
114C3⋊Dic3—5412no—
115C3×Dic3—312no—
116C3×Dic3—312no—
117C3×Dic3—31no—
118C3×Dic3—31no—
119C3×Dic3—61no—
120C3×Dic3—612no—
121C3×Dic3—2712no—
122C3×Dic3—271no—
123C33—24no—
124C33—24no—
125C33—24no—
126C33—39no—
127C33—39no—
128C33—44no—
129C33—69no—
130C33D3×Dic311yescharacteristic
131C33D3×Dic314yescomplemented
132C33#62414yescomplemented
133H(3,𝔽3)—24no—
134H(3,𝔽3)—24no—
135H(3,𝔽3)—44no—
136H(3,𝔽3)—412no—
137H(3,𝔽3)C4×C3⋊D311yescharacteristic, complemented
138C2×Dic3—811no—
139C4×D3—811no—
140C4×D3—8112no—
141C4×D3—811no—
142C2×C32—24no—
143C2×C32—24no—
144C2×C32—21no—
145C2×C32—312no—
146C2×C32—312no—
147C2×C32—44no—
148C2×C32—612no—
149C2×C32—612no—
150C2×C32—612no—
151C2×C32—1212no—
152C2×C32((C3⋊D3)⋊C3)⋊C219yes—
153C2×C32D3×C3⋊D311yescharacteristic
154C2×C32D3×C3⋊D311yescharacteristic
155C2×C32#111314yes—
156C3⋊D3—918no—
157C3⋊D3—98no—
158C3⋊D3—92no—
159C3⋊D3—188no—
160C3⋊D3—2724no—
161C3⋊D3—5424no—
162C3×D3—2724no—
163C3×D3—272no—
164C22×C3—811no—
165C2×D3—2712no—
166C2×D3—271no—
167C2×D3—811no—
168C2×D3—1624no—
169C3×C4—912no—
170C3×C4—91no—
171C3×C4—811no—
172Dic3—31no—
173Dic3—31no—
174Dic3—61no—
175Dic3—2712no—
176Dic3—271no—
177Dic3—811no—
178Dic3—1624no—
179C32—24no—
180C32—24no—
181C32—21no—
182C32—312no—
183C32—312no—
184C32—44no—
185C32—612no—
186C32—612no—
187C32—612no—
188C32—1212no—
189C32((C3⋊D3)⋊C3)⋊C419yescomplemented
190C32Dic3×C3⋊D311yescharacteristic, complemented
191C32#628911yescharacteristic, complemented
192C32#629414yes—
193C2×C4—2431noSylow
194C2×C3—31no—
195C2×C3—31no—
196C2×C3—61no—
197C2×C3—64no—
198C2×C3—64no—
199C2×C3—124no—
200C2×C3—812no—
201C2×C3#66432112yes—
202C2×C3C3⋊#111311yescharacteristic
203D3—272no—
204D3—2724no—
205D3—812no—
206D3—1628no—
207C22—811no—
208C4—91no—
209C4—811no—
210C3—31no—
211C3—31no—
212C3—64no—
213C3—64no—
214C3—61no—
215C3—124no—
216C3#10619901112yescomplemented
217C3#1062015411yescharacteristic
218C2—812no—
219C2#1175809111yescharacteristic
subgroupG/H
center, hypercenterC2#11758091
commutator, hypocenterC32×H(3,𝔽3)C2×C4
FrattiniC2×C3C3⋊#1113
Fitting, cosocleC2×C32×H(3,𝔽3)C22
socleC2×C33D32
prime radicalC2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2
LCSG ▷ C32×H(3,𝔽3)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊(C3⋊((C3⋊Dic3)⋊C3))C2semidirect
3. C32×#1084C2semidirect
8. C3⋊(C3⋊((C3⋊D3)⋊C3))C4semidirect
11. C3⋊(C3⋊(C3⋊Dic3))D3semidirect
18. C3×#1084D3semidirect
21. C32×H(3,𝔽3)C2×C4semidirect
31. C3⋊(C3⋊(C3⋊D3))Dic3semidirect
60. #1084C3⋊D3semidirect
64. C34C4×D3semidirect
65. C34C2×Dic3semidirect
69. C3×H(3,𝔽3)C4×D3semidirect
131. C33D3×Dic3semidirect
132. C33#624semidirect
137. H(3,𝔽3)C4×C3⋊D3semidirect
189. C32((C3⋊D3)⋊C3)⋊C4semidirect
190. C32Dic3×C3⋊D3semidirect
191. C32#6289semidirect
216. C3#10619901semidirect

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
C3⋊(C3⋊((C3⋊Dic3)⋊C3))2
C32×#10842
#106201443
Dic3×C3⋊(C3⋊D3)3
#106199013