Finite Group Databasebeta

← C2×C3⋊(#384⋊C3) #11921247

Subgroups — C2×C3⋊(#384⋊C3) #11921247

Order 1152.

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

normal subgroups only

This group has 391 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⋊(#384⋊C3)C212yesmaximal, direct product factor
3C2×#4935C311yesmaximal, characteristic, complemented
4C2×#384⋊C3—31nomaximal
5C2×Dic3×A4—41nomaximal
6C2×C3×C42⋊C3C412yescomplemented
7C2×C3×C42⋊C3C2211yescharacteristic
8C22×C3×C42C2×C311yescharacteristic
9C22×C4⋊Dic3—31no—
10C22×C4⋊Dic3—31no—
11C22×C42⋊C3—21no—
12C22×C42⋊C3D311yescharacteristic
13#4935—32no—
14#4935C2×C312yescomplemented
15#384⋊C3—32no—
16C22×C3×A4—41no—
17Dic3×A4—42no—
18C3×C42⋊C3C2×C411yescharacteristic, complemented
19C2×#384—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×C4⋊Dic3—32no—
29C2×C4⋊Dic3—32no—
30C2×C4⋊Dic3—32no—
31C2×C4⋊Dic3—32no—
32C2×C4⋊Dic3—62no—
33C2×C4⋊Dic3—62no—
34C2×C4⋊Dic3—62no—
35C2×C4⋊Dic3—62no—
36C2×C42⋊C3—22no—
37C2×C42⋊C3—21no—
38C2×C42⋊C3Dic312yescomplemented
39C2×C42⋊C3C2×D311yescharacteristic
40C2×C3×A4—42no—
41C2×C3×A4—41no—
42C2×C3×Dic3—161no—
43C22×C4⋊C4—91no—
44C22×C4⋊C4—91no—
45C22×C42C3×D311yescharacteristic
46#384—32no—
47#384—92no—
48C24×C3C2×A411yescharacteristic
49C22×A4—41no—
50C22×A4—81no—
51C22×C3×C4—32no—
52C22×C3×C4—32no—
53C22×C3×C4—34no—
54C22×C3×C4—32no—
55C22×C3×C4—32no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×Dic3—32no—
59C22×Dic3—61no—
60C22×Dic3—62no—
61C22×Dic3—61no—
62C22×Dic3—61no—
63C22×Dic3—62no—
64C22×Dic3—61no—
65C22×Dic3C2×A412yes—
66C4×A4—122no—
67C3×C42—32no—
68C3×C42—31no—
69C3×C42—32no—
70C3×C42C2×C3×C411yescharacteristic, complemented
71C4⋊Dic3—64no—
72C4⋊Dic3—64no—
73C4⋊Dic3—64no—
74C4⋊Dic3—64no—
75C42⋊C3—21no—
76C42⋊C3C2×Dic311yescharacteristic, complemented
77C22×C32—161no—
78C3×A4—41no—
79C3×Dic3—162no—
80C23×C4—31no—
81C23×C4—31no—
82C23×C4—91no—
83C2×C4⋊C4—92no—
84C2×C4⋊C4—92no—
85C2×C4⋊C4—92no—
86C2×C4⋊C4—92no—
87C2×C4⋊C4—182no—
88C2×C4⋊C4—182no—
89C2×C4⋊C4—182no—
90C2×C4⋊C4—182no—
91C2×C42—31no—
92C2×C42—32no—
93C2×C42C3×Dic312yescomplemented
94C2×C42C2×C3×D311yescharacteristic
95C23×C3—31no—
96C23×C3—32no—
97C23×C3—31no—
98C23×C3C4×A412yes—
99C23×C3C22×A411yescharacteristic
100C2×A4—41no—
101C2×A4—42no—
102C2×A4—81no—
103C2×A4—82no—
104C2×C3×C4—32no—
105C2×C3×C4—32no—
106C2×C3×C4—34no—
107C2×C3×C4—34no—
108C2×C3×C4—32no—
109C2×C3×C4—32no—
110C2×C3×C4—34no—
111C2×C3×C4—34no—
112C2×C3×C4—31no—
113C2×C3×C4—32no—
114C2×C3×C4—31no—
115C2×C3×C4—481no—
116C2×Dic3—41no—
117C2×Dic3—62no—
118C2×Dic3—62no—
119C2×Dic3—64no—
120C2×Dic3—121no—
121C2×Dic3—121no—
122C2×Dic3—122no—
123C2×Dic3—121no—
124C2×C32—162no—
125C2×C32—161no—
126C24D3×A411yescharacteristic
127C22×C4—32no—
128C22×C4—32no—
129C22×C4—34no—
130C22×C4—31no—
131C22×C4—31no—
132C22×C4—32no—
133C22×C4—32no—
134C22×C4—32no—
135C22×C4—92no—
136C22×C4—181no—
137C22×C4—182no—
138C22×C4—181no—
139C22×C4—181no—
140C22×C4—182no—
141C22×C4—181no—
142C4⋊C4—184no—
143C4⋊C4—184no—
144C4⋊C4—184no—
145C4⋊C4—184no—
146C42—32no—
147C42—31no—
148C42—32no—
149C42C2×C3×Dic311yescharacteristic, complemented
150C22×C3—32no—
151C22×C3—31no—
152C22×C3—32no—
153C22×C3—32no—
154C22×C3—32no—
155C22×C3—31no—
156C22×C3—31no—
157C22×C3—161no—
158C22×C3—321no—
159C22×C3#127⋊C311yescharacteristic
160C22×C3C2×C4×A411yescharacteristic
161A4—41no—
162A4—81no—
163C3×C4—32no—
164C3×C4—32no—
165C3×C4—34no—
166C3×C4—482no—
167Dic3—42no—
168Dic3—122no—
169C32—161noSylow
170C23—31no—
171C23—32no—
172C23—31no—
173C23Dic3×A412yes—
174C23C2×D3×A411yescharacteristic
175C2×C4—32no—
176C2×C4—32no—
177C2×C4—32no—
178C2×C4—32no—
179C2×C4—34no—
180C2×C4—34no—
181C2×C4—34no—
182C2×C4—34no—
183C2×C4—31no—
184C2×C4—32no—
185C2×C4—31no—
186C2×C4—121no—
187C2×C4—182no—
188C2×C4—182no—
189C2×C4—184no—
190C2×C4—361no—
191C2×C4—361no—
192C2×C4—362no—
193C2×C4—361no—
194C2×C3—31no—
195C2×C3—32no—
196C2×C3—31no—
197C2×C3—161no—
198C2×C3—162no—
199C2×C3—321no—
200C2×C3—322no—
201C2×C3#384⋊C312yescomplemented
202C2×C3C2×#127⋊C311yescharacteristic
203C22—31no—
204C22—32no—
205C22—32no—
206C22—31no—
207C22—31no—
208C22—32no—
209C22—32no—
210C22C3⋊(#127⋊C3)11yescharacteristic
211C22C2×Dic3×A411yescharacteristic
212C4—32no—
213C4—32no—
214C4—34no—
215C4—122no—
216C4—362no—
217C3—161no—
218C3—321no—
219C3C2×#384⋊C311yescharacteristic, complemented
220C2—31no—
221C2—31no—
222C2—32no—
223C2C3⋊(#384⋊C3)12yesdirect product factor
224C2C2×C3⋊(#127⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊(#127⋊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⋊(#384⋊C3)C2direct (N × H)
3. C2×#4935C3semidirect
6. C2×C3×C42⋊C3C4semidirect
14. #4935C2×C3semidirect
18. C3×C42⋊C3C2×C4semidirect
26. C2×C3×C42C3×C4semidirect
38. C2×C42⋊C3Dic3semidirect
70. C3×C42C2×C3×C4semidirect
76. C42⋊C3C2×Dic3semidirect
93. C2×C42C3×Dic3semidirect
149. C42C2×C3×Dic3semidirect
201. C2×C3#384⋊C3semidirect
219. C3C2×#384⋊C3semidirect
223. C2C3⋊(#384⋊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⋊(#384⋊C3)2
C2×#49353
C2×#384⋊C33
C2×Dic3×A44