Finite Group Databasebeta

← #14518796

Subgroups — #14518796

Order 1944.

959 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 959 conjugacy classes of subgroups — too many to draw. Only its 94 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)C212yesmaximal, complemented
2C3⋊(C3⋊#1084)C211yesmaximal, characteristic, complemented
3#10620157—32nomaximal
4#10619884—36nomaximal
5C2×C32×H(3,𝔽3)C2211yescharacteristic
6C3×C3⋊((C3⋊D3)⋊C3)—22no—
7C2×C3×C3⋊(C3⋊D3)D312yescomplemented
8C2×C32×C3⋊D3—32no—
9C3×C3⋊(C3⋊Dic3)—32no—
10C3×C3⋊(C3⋊Dic3)—61no—
11C2×C3⋊((C3⋊D3)⋊C3)D316yescomplemented
12C2×C3×(C3⋊D3)⋊C3—36no—
13C3⋊#1084—36no—
14C3⋊#1084—69no—
15C3⋊#1084—66no—
16C32×H(3,𝔽3)D411yescharacteristic, complemented, Sylow
17#6295—96no—
18#6295—91no—
19#6291—92no—
20#6290—92no—
21#6198—99no—
22C2×C34—21no—
23C2×C34C2×D312yes—
24C3×C3⋊(C3⋊D3)—22no—
25C32×C3⋊D3—62no—
26C2×C3×H(3,𝔽3)—26no—
27C2×C3×H(3,𝔽3)—29no—
28C2×C3×H(3,𝔽3)C2×D316yes—
29C3⋊((C3⋊D3)⋊C3)—26no—
30C3×(C3⋊D3)⋊C3—66no—
31C2×C3⋊(C3⋊D3)C3⋊D312yescomplemented
32C2×C3×C3⋊D3—36no—
33C2×C3×C3⋊D3—32no—
34C2×C3×C3⋊D3—36no—
35C2×C3×C3⋊D3—92no—
36C2×C3×C3⋊D3—182no—
37C2×C32×D3—92no—
38C2×C32×D3—92no—
39C2×C32×D3—182no—
40C3⋊(C3⋊Dic3)—32no—
41C3⋊(C3⋊Dic3)—61no—
42C3×C3⋊Dic3—96no—
43C3×C3⋊Dic3—91no—
44C3×C3⋊Dic3—92no—
45C3×C3⋊Dic3—186no—
46C3×C3⋊Dic3—186no—
47C3×C3⋊Dic3—182no—
48C3×C3⋊Dic3—186no—
49C2×(C3⋊D3)⋊C3—318no—
50#1084—99no—
51#1084—1818no—
52#1084—1818no—
53C34—21no—
54C34#6712yescomplemented
55C3×H(3,𝔽3)—26no—
56C3×H(3,𝔽3)—29no—
57C3×H(3,𝔽3)#6716yescomplemented
58#638—272no—
59#626—276no—
60#626—272no—
61#625—271no—
62#625—276no—
63C2×C33—26no—
64C2×C33—26no—
65C2×C33—22no—
66C2×C33—26no—
67C2×C33—32no—
68C2×C33—62no—
69C2×C33—62no—
70C2×C33—61no—
71C2×C33—122no—
72C2×C33—122no—
73C2×C33—122no—
74C2×C33D3211yescharacteristic
75C2×C33D3216yes—
76C2×C33C2×C3⋊D312yes—
77C3⋊(C3⋊D3)—22no—
78C3×C3⋊D3—62no—
79C3×C3⋊D3—66no—
80C3×C3⋊D3—66no—
81C3×C3⋊D3—182no—
82C3×C3⋊D3—184no—
83C32×D3—182no—
84C32×D3—184no—
85C32×D3—182no—
86C2×H(3,𝔽3)—218no—
87C2×H(3,𝔽3)—218no—
88C2×H(3,𝔽3)D3219yes—
89(C3⋊D3)⋊C3—618no—
90C22×C32—272no—
91C2×C3⋊D3—32no—
92C2×C3⋊D3—36no—
93C2×C3⋊D3—92no—
94C2×C3⋊D3—182no—
95C2×C3×D3—96no—
96C2×C3×D3—92no—
97C2×C3×D3—96no—
98C2×C3×D3—92no—
99C2×C3×D3—182no—
100C2×C3×D3—186no—
101C2×C3×D3—276no—
102C3⋊Dic3—92no—
103C3⋊Dic3—96no—
104C3⋊Dic3—91no—
105C3⋊Dic3—186no—
106C3⋊Dic3—182no—
107C3⋊Dic3—186no—
108C3⋊Dic3—186no—
109C3×Dic3—276no—
110C3×Dic3—272no—
111C3×Dic3—549no—
112C3×Dic3—546no—
113C3×Dic3—541no—
114C33—26no—
115C33—22no—
116C33—26no—
117C33—26no—
118C33—32no—
119C33—62no—
120C33—62no—
121C33—61no—
122C33—122no—
123C33—122no—
124C33—122no—
125C33#62511yescharacteristic
126C33#62516yescomplemented
127C33#63812yescomplemented
128H(3,𝔽3)—218no—
129H(3,𝔽3)—218no—
130H(3,𝔽3)#62519yescomplemented
131#67—812no—
132#67—816no—
133D12—811no—
134C2×C32—22no—
135C2×C32—21no—
136C2×C32—26no—
137C2×C32—29no—
138C2×C32—32no—
139C2×C32—36no—
140C2×C32—41no—
141C2×C32—62no—
142C2×C32—66no—
143C2×C32—66no—
144C2×C32—66no—
145C2×C32—62no—
146C2×C32—66no—
147C2×C32—122no—
148C2×C32—126no—
149C2×C32—126no—
150C2×C32—126no—
151C2×C32—542no—
152C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
153C2×C32D3×C3⋊D312yes—
154C2×C32D3×C3⋊D316yes—
155C3⋊D3—62no—
156C3⋊D3—66no—
157C3⋊D3—182no—
158C3⋊D3—184no—
159C3×D3—184no—
160C3×D3—186no—
161C3×D3—1812no—
162C3×D3—182no—
163C3×D3—182no—
164C3×D3—186no—
165C3×D3—546no—
166C22×C3—276no—
167C22×C3—272no—
168C2×D3—92no—
169C2×D3—92no—
170C2×D3—182no—
171C2×D3—276no—
172C3×C4—811no—
173Dic3—276no—
174Dic3—272no—
175Dic3—541no—
176Dic3—546no—
177Dic3—549no—
178C32—22no—
179C32—21no—
180C32—26no—
181C32—29no—
182C32—32no—
183C32—36no—
184C32—41no—
185C32—62no—
186C32—66no—
187C32—66no—
188C32—66no—
189C32—62no—
190C32—66no—
191C32—122no—
192C32—126no—
193C32—126no—
194C32—126no—
195C32#619811yescharacteristic, complemented
196C32#629012yes—
197C32#629016yescomplemented
198D4—2431noSylow
199C2×C3—21no—
200C2×C3—22no—
201C2×C3—36no—
202C2×C3—41no—
203C2×C3—66no—
204C2×C3—69no—
205C2×C3—546no—
206C2×C3—542no—
207C2×C3((C3⋊D3)⋊C3)⋊D312yes—
208C2×C3C3⋊D3211yescharacteristic
209D3—184no—
210D3—182no—
211D3—182no—
212D3—546no—
213C22—272no—
214C4—811no—
215C3—22no—
216C3—21no—
217C3—36no—
218C3—41no—
219C3—66no—
220C3—69no—
221C3#1061988412yescomplemented
222C3#1062015111yescharacteristic
223C2—542no—
224C2#1175808411yescharacteristic
subgroupG/H
center, hypercenterC2#11758084
commutator, Fitting, cosocleC2×C32×H(3,𝔽3)C22
FrattiniC2×C3C3⋊D32
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. C3⋊(C3⋊#1084)C2semidirect
7. C2×C3×C3⋊(C3⋊D3)D3semidirect
11. C2×C3⋊((C3⋊D3)⋊C3)D3semidirect
16. C32×H(3,𝔽3)D4semidirect
31. C2×C3⋊(C3⋊D3)C3⋊D3semidirect
54. C34#67semidirect
57. C3×H(3,𝔽3)#67semidirect
126. C33#625semidirect
127. C33#638semidirect
130. H(3,𝔽3)#625semidirect
195. C32#6198semidirect
197. C32#6290semidirect
221. C3#10619884semidirect

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⋊#1084)2
#106201573
#106198843