Finite Group Databasebeta

← C2×C3⋊(#383⋊C3) #11921248

Subgroups — C2×C3⋊(#383⋊C3) #11921248

Order 1152.

303 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 303 conjugacy classes of subgroups — too many to draw. Only its 49 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
1C22×C3×C42⋊C3C211yesmaximal, characteristic
2C3⋊(#383⋊C3)C212yesmaximal, direct product factor
3C2×#4937C311yesmaximal, characteristic, complemented
4C2×#383⋊C3—31nomaximal
5C2×Dic3×A4—41nomaximal
6C2×C3×C42⋊C3C412yescomplemented
7C2×C3×C42⋊C3C2211yescharacteristic
8C22×C3×C42C2×C311yescharacteristic
9C22×C42⋊C3—21no—
10C22×C42⋊C3D311yescharacteristic
11C2×C3⋊#95—31no—
12C2×C3⋊#95—31no—
13#4937—32no—
14#4937C2×C312yescomplemented
15#383⋊C3—32no—
16C22×C3×A4—41no—
17Dic3×A4—42no—
18C3×C42⋊C3C2×C411yescharacteristic, complemented
19C2×#383—31noSylow
20C23×C3×C4—31no—
21C23×Dic3—31no—
22C23×Dic3A411yescharacteristic
23C2×C4×A4—121no—
24C2×C3×C42—31no—
25C2×C3×C42—32no—
26C2×C3×C42C3×C412yescomplemented
27C2×C3×C42C22×C311yescharacteristic
28C2×C42⋊C3—22no—
29C2×C42⋊C3—21no—
30C2×C42⋊C3Dic312yescomplemented
31C2×C42⋊C3C2×D311yescharacteristic
32C3⋊#95—32no—
33C3⋊#95—32no—
34C3⋊#95—32no—
35C3⋊#95—32no—
36C2×C3×A4—42no—
37C2×C3×A4—41no—
38C2×C3×Dic3—161no—
39C22×C42C3×D311yescharacteristic
40#383—32no—
41#383—92no—
42C2×#95—91no—
43C2×#95—91no—
44C24×C3C2×A411yescharacteristic
45C22×A4—41no—
46C22×A4—81no—
47C22×C3×C4—32no—
48C22×C3×C4—32no—
49C22×C3×C4—31no—
50C22×C3×C4—31no—
51C22×C3×C4—62no—
52C22×C3×C4—61no—
53C22×C3×C4—61no—
54C22×Dic3—32no—
55C22×Dic3—61no—
56C22×Dic3—64no—
57C22×Dic3—61no—
58C22×Dic3—61no—
59C22×Dic3—61no—
60C22×Dic3C2×A412yes—
61C4×A4—122no—
62C3×C42—32no—
63C3×C42—31no—
64C3×C42—32no—
65C3×C42C2×C3×C411yescharacteristic, complemented
66C42⋊C3—21no—
67C42⋊C3C2×Dic311yescharacteristic, complemented
68C22×C32—161no—
69C3×A4—41no—
70C3×Dic3—162no—
71C23×C4—31no—
72C23×C4—31no—
73C23×C4—91no—
74C2×C42—31no—
75C2×C42—32no—
76C2×C42C3×Dic312yescomplemented
77C2×C42C2×C3×D311yescharacteristic
78#95—92no—
79#95—92no—
80#95—92no—
81#95—92no—
82C23×C3—32no—
83C23×C3—31no—
84C23×C3—31no—
85C23×C3C4×A412yes—
86C23×C3C22×A411yescharacteristic
87C2×A4—41no—
88C2×A4—42no—
89C2×A4—81no—
90C2×A4—82no—
91C2×C3×C4—31no—
92C2×C3×C4—32no—
93C2×C3×C4—31no—
94C2×C3×C4—61no—
95C2×C3×C4—61no—
96C2×C3×C4—62no—
97C2×C3×C4—62no—
98C2×C3×C4—62no—
99C2×C3×C4—62no—
100C2×C3×C4—61no—
101C2×C3×C4—61no—
102C2×C3×C4—481no—
103C2×Dic3—41no—
104C2×Dic3—62no—
105C2×Dic3—64no—
106C2×Dic3—62no—
107C2×Dic3—121no—
108C2×Dic3—122no—
109C2×Dic3—122no—
110C2×C32—162no—
111C2×C32—161no—
112C24D3×A411yescharacteristic
113C22×C4—31no—
114C22×C4—31no—
115C22×C4—32no—
116C22×C4—32no—
117C22×C4—32no—
118C22×C4—62no—
119C22×C4—61no—
120C22×C4—61no—
121C22×C4—92no—
122C22×C4—181no—
123C22×C4—184no—
124C22×C4—181no—
125C22×C4—181no—
126C22×C4—181no—
127C42—32no—
128C42—31no—
129C42—32no—
130C42C2×C3×Dic311yescharacteristic, complemented
131C22×C3—31no—
132C22×C3—32no—
133C22×C3—32no—
134C22×C3—32no—
135C22×C3—32no—
136C22×C3—31no—
137C22×C3—31no—
138C22×C3—161no—
139C22×C3—321no—
140C22×C3#126⋊C311yescharacteristic
141C22×C3C2×C4×A411yescharacteristic
142A4—41no—
143A4—81no—
144C3×C4—61no—
145C3×C4—62no—
146C3×C4—61no—
147C3×C4—482no—
148Dic3—42no—
149Dic3—122no—
150C32—161noSylow
151C23—32no—
152C23—31no—
153C23—31no—
154C23Dic3×A412yes—
155C23C2×D3×A411yescharacteristic
156C2×C4—31no—
157C2×C4—32no—
158C2×C4—31no—
159C2×C4—61no—
160C2×C4—61no—
161C2×C4—62no—
162C2×C4—62no—
163C2×C4—61no—
164C2×C4—61no—
165C2×C4—62no—
166C2×C4—62no—
167C2×C4—121no—
168C2×C4—182no—
169C2×C4—184no—
170C2×C4—182no—
171C2×C4—361no—
172C2×C4—362no—
173C2×C4—362no—
174C2×C3—31no—
175C2×C3—31no—
176C2×C3—32no—
177C2×C3—161no—
178C2×C3—162no—
179C2×C3—321no—
180C2×C3—322no—
181C2×C3#383⋊C312yescomplemented
182C2×C3C2×#126⋊C311yescharacteristic
183C22—31no—
184C22—32no—
185C22—32no—
186C22—31no—
187C22—31no—
188C22—32no—
189C22—32no—
190C22C3⋊(#126⋊C3)11yescharacteristic
191C22C2×Dic3×A411yescharacteristic
192C4—61no—
193C4—62no—
194C4—61no—
195C4—122no—
196C4—362no—
197C3—161no—
198C3—321no—
199C3C2×#383⋊C311yescharacteristic, complemented
200C2—31no—
201C2—31no—
202C2—32no—
203C2C3⋊(#383⋊C3)12yesdirect product factor
204C2C2×C3⋊(#126⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊(#126⋊C3)
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC22×C3×C42C2×C3
socleC24×C3C2×A4
prime radicalC22×C3×C42⋊C3C2
cosocleC2×C3×C42C22×C3
LCSG ▷ C3×C42
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C3⋊(#383⋊C3)C2direct (N × H)
3. C2×#4937C3semidirect
6. C2×C3×C42⋊C3C4semidirect
14. #4937C2×C3semidirect
18. C3×C42⋊C3C2×C4semidirect
26. C2×C3×C42C3×C4semidirect
30. C2×C42⋊C3Dic3semidirect
65. C3×C42C2×C3×C4semidirect
67. C42⋊C3C2×Dic3semidirect
76. C2×C42C3×Dic3semidirect
130. C42C2×C3×Dic3semidirect
181. C2×C3#383⋊C3semidirect
199. C3C2×#383⋊C3semidirect
203. C2C3⋊(#383⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C42⋊C32
C3⋊(#383⋊C3)2
C2×#49373
C2×#383⋊C33
C2×Dic3×A44