Finite Group Databasebeta

← #14518797

Subgroups — #14518797

Order 1944.

1177 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 1177 conjugacy classes of subgroups — too many to draw. Only its 96 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⋊#272)C211yesmaximal, characteristic
2C3×C3⋊((C3⋊Dic3)⋊C3)C212yesmaximal, complemented
3#10620154—32nomaximal
4#10619885—36nomaximal
5C2×C32×H(3,𝔽3)C2211yescharacteristic
6C3⋊(C3⋊#272)C412yescomplemented
7C2×C3×C3⋊(C3⋊D3)—32no—
8C2×C3×C3⋊(C3⋊D3)—61no—
9C3×C3⋊(C3⋊Dic3)D312yescomplemented
10C32×C3⋊Dic3—32no—
11C2×C3⋊#272—36no—
12C2×C3⋊#272—69no—
13C2×C3⋊#272—66no—
14C3⋊((C3⋊Dic3)⋊C3)D316yescomplemented
15C3×(C3⋊Dic3)⋊C3—36no—
16C32×H(3,𝔽3)C2×C411yescharacteristic, complemented, Sylow
17#6294—96no—
18#6294—91no—
19#6289—92no—
20Dic3×C3⋊D3—92no—
21#6199—99no—
22C2×C34—21no—
23C2×C34C2×D312yes—
24C3×C3⋊(C3⋊D3)—34no—
25C3×C3⋊(C3⋊D3)—62no—
26C2×C3×H(3,𝔽3)—26no—
27C2×C3×H(3,𝔽3)—29no—
28C2×C3×H(3,𝔽3)C2×D316yes—
29C3⋊#272—312no—
30C3⋊#272—618no—
31C3⋊#272—612no—
32C2×C3⋊(C3⋊D3)—32no—
33C2×C3⋊(C3⋊D3)—61no—
34C2×C3×C3⋊D3—96no—
35C2×C3×C3⋊D3—91no—
36C2×C3×C3⋊D3—92no—
37C2×C3×C3⋊D3—186no—
38C2×C3×C3⋊D3—186no—
39C2×C3×C3⋊D3—182no—
40C2×C3×C3⋊D3—186no—
41C3⋊(C3⋊Dic3)C3⋊D312yescomplemented
42C3×C3⋊Dic3—36no—
43C3×C3⋊Dic3—32no—
44C3×C3⋊Dic3—36no—
45C3×C3⋊Dic3—92no—
46C3×C3⋊Dic3—182no—
47C32×Dic3—92no—
48C32×Dic3—92no—
49C32×Dic3—182no—
50C2×#272—99no—
51C2×#272—1818no—
52C2×#272—1818no—
53(C3⋊Dic3)⋊C3—318no—
54C34—21no—
55C34C4×D312yescomplemented
56C3×H(3,𝔽3)—26no—
57C3×H(3,𝔽3)—29no—
58C3×H(3,𝔽3)C4×D316yescomplemented
59C4×C3⋊D3—272no—
60#624—271no—
61#624—276no—
62D3×Dic3—276no—
63D3×Dic3—272no—
64C2×C33—26no—
65C2×C33—26no—
66C2×C33—22no—
67C2×C33—26no—
68C2×C33—32no—
69C2×C33—62no—
70C2×C33—62no—
71C2×C33—61no—
72C2×C33—122no—
73C2×C33—122no—
74C2×C33—122no—
75C2×C33D3211yescharacteristic
76C2×C33D3216yes—
77C2×C33C2×C3⋊D312yes—
78C3⋊(C3⋊D3)—34no—
79C3⋊(C3⋊D3)—62no—
80C3×C3⋊D3—94no—
81C3×C3⋊D3—92no—
82C3×C3⋊D3—912no—
83C3×C3⋊D3—1812no—
84C3×C3⋊D3—184no—
85C3×C3⋊D3—1812no—
86C3×C3⋊D3—1812no—
87C2×H(3,𝔽3)—218no—
88C2×H(3,𝔽3)—218no—
89C2×H(3,𝔽3)D3219yes—
90#272—918no—
91#272—1836no—
92#272—1836no—
93C2×C3⋊D3—92no—
94C2×C3⋊D3—96no—
95C2×C3⋊D3—91no—
96C2×C3⋊D3—186no—
97C2×C3⋊D3—182no—
98C2×C3⋊D3—186no—
99C2×C3⋊D3—186no—
100C2×C3×D3—276no—
101C2×C3×D3—272no—
102C2×C3×D3—549no—
103C2×C3×D3—546no—
104C2×C3×D3—541no—
105C32×C4—272no—
106C3⋊Dic3—32no—
107C3⋊Dic3—36no—
108C3⋊Dic3—92no—
109C3⋊Dic3—182no—
110C3×Dic3—96no—
111C3×Dic3—92no—
112C3×Dic3—96no—
113C3×Dic3—92no—
114C3×Dic3—182no—
115C3×Dic3—186no—
116C3×Dic3—276no—
117C33—26no—
118C33—22no—
119C33—26no—
120C33—26no—
121C33—32no—
122C33—62no—
123C33—62no—
124C33—61no—
125C33—122no—
126C33—122no—
127C33—122no—
128C33#62411yescharacteristic
129C33#62416yescomplemented
130C33C4×C3⋊D312yescomplemented
131H(3,𝔽3)—218no—
132H(3,𝔽3)—218no—
133H(3,𝔽3)#62419yescomplemented
134C2×Dic3—811no—
135C4×D3—812no—
136C4×D3—816no—
137C2×C32—22no—
138C2×C32—21no—
139C2×C32—26no—
140C2×C32—29no—
141C2×C32—32no—
142C2×C32—36no—
143C2×C32—41no—
144C2×C32—62no—
145C2×C32—66no—
146C2×C32—66no—
147C2×C32—66no—
148C2×C32—62no—
149C2×C32—66no—
150C2×C32—122no—
151C2×C32—126no—
152C2×C32—126no—
153C2×C32—126no—
154C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
155C2×C32D3×C3⋊D312yes—
156C2×C32D3×C3⋊D316yes—
157C3⋊D3—94no—
158C3⋊D3—912no—
159C3⋊D3—92no—
160C3⋊D3—1812no—
161C3⋊D3—184no—
162C3⋊D3—1812no—
163C3⋊D3—1812no—
164C3×D3—274no—
165C3×D3—2712no—
166C3×D3—5418no—
167C3×D3—5412no—
168C3×D3—542no—
169C22×C3—811no—
170C2×D3—276no—
171C2×D3—272no—
172C2×D3—541no—
173C2×D3—546no—
174C2×D3—549no—
175C3×C4—276no—
176C3×C4—272no—
177Dic3—92no—
178Dic3—92no—
179Dic3—182no—
180Dic3—276no—
181C32—22no—
182C32—21no—
183C32—26no—
184C32—29no—
185C32—32no—
186C32—36no—
187C32—41no—
188C32—62no—
189C32—66no—
190C32—66no—
191C32—66no—
192C32—62no—
193C32—66no—
194C32—122no—
195C32—126no—
196C32—126no—
197C32—126no—
198C32#619911yescharacteristic, complemented
199C32#628912yes—
200C32#628916yescomplemented
201C2×C4—2431noSylow
202C2×C3—22no—
203C2×C3—21no—
204C2×C3—36no—
205C2×C3—41no—
206C2×C3—66no—
207C2×C3—69no—
208C2×C3—812no—
209C2×C3((C3⋊D3)⋊C3)⋊D312yes—
210C2×C3C3⋊D3211yescharacteristic
211D3—2712no—
212D3—274no—
213D3—542no—
214D3—5412no—
215D3—5418no—
216C22—811no—
217C4—272no—
218C3—21no—
219C3—22no—
220C3—36no—
221C3—41no—
222C3—66no—
223C3—69no—
224C3#1061988512yescomplemented
225C3#1062015011yescharacteristic
226C2—812no—
227C2#1175808411yescharacteristic
subgroupG/H
center, hypercenterC2#11758084
commutator, hypocenterC32×H(3,𝔽3)C2×C4
FrattiniC2×C3C3⋊D32
Fitting, cosocleC2×C32×H(3,𝔽3)C22
socleC2×C33D32
prime radicalC2×C3⋊(C3⋊#272)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
6. C3⋊(C3⋊#272)C4semidirect
9. C3×C3⋊(C3⋊Dic3)D3semidirect
14. C3⋊((C3⋊Dic3)⋊C3)D3semidirect
16. C32×H(3,𝔽3)C2×C4semidirect
41. C3⋊(C3⋊Dic3)C3⋊D3semidirect
55. C34C4×D3semidirect
58. C3×H(3,𝔽3)C4×D3semidirect
129. C33#624semidirect
130. C33C4×C3⋊D3semidirect
133. H(3,𝔽3)#624semidirect
198. C32#6199semidirect
200. C32#6289semidirect
224. C3#10619885semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊#272)2
C3×C3⋊((C3⋊Dic3)⋊C3)2
#106201543
#106198853