Finite Group Databasebeta

← C2×C3⋊#4622 #11920940

Subgroups — C2×C3⋊#4622 #11920940

Order 1152.

434 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 35 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×#95⋊C3C211yesmaximal, characteristic, complemented
2C3⋊#4622C212yesmaximal, direct product factor
3C2×#4622—33nomaximal
4C2×#4451—31nomaximal
5C22×C3⋊S4—41nomaximal
6C3×#95⋊C3C2211yescharacteristic, complemented
7C2×#930—31no—
8C2×C3×#95D311yescharacteristic, complemented
9C2×#830—31no—
10C2×#95⋊C3D313yescomplemented
11#4622—36no—
12#4451—32no—
13#4451—32no—
14C22×C3×A4—41no—
15C2×C3⋊S4—42no—
16C2×C3⋊S4—44no—
17C2×#327—91noSylow
18C22×S4—123no—
19C23×C3×C4—31no—
20C22×#67—61no—
21C22×D12—31no—
22#930—32no—
23#930—32no—
24#930—61no—
25#930—61no—
26C2×(C2×D3)⋊C4—61no—
27C2×C4⋊Dic3—31no—
28C22×C3⋊C8—61no—
29C3×#95—31no—
30C3×#95C2×D311yescharacteristic, complemented
31#830—32no—
32#830—61no—
33#95⋊C3C2×D313yescomplemented
34C22×C3⋊D3—161no—
35C2×C3×A4—42no—
36C2×C3×A4—41no—
37C3⋊S4—44no—
38C2×#121—91no—
39C2×C22⋊C8—91no—
40C2×#95C3⋊D311yescharacteristic, complemented
41#327—92no—
42#327—92no—
43C24×C3S411yescharacteristic
44C23×D3—61no—
45C22×A4—43no—
46C2×S4—126no—
47C2×S4—1212no—
48C22×C3×C4—31no—
49C22×C3×C4—31no—
50C22×C3×C4—31no—
51C22×C3×C4—31no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—122no—
55C2×#67—62no—
56C2×#67—62no—
57C2×#67—122no—
58C2×#67—122no—
59C22×Dic3—61no—
60C2×D12—32no—
61C2×D12—61no—
62C2×D12—122no—
63(C2×D3)⋊C4—62no—
64(C2×D3)⋊C4—62no—
65C4⋊Dic3—32no—
66C4⋊Dic3—61no—
67C2×C3⋊C8—62no—
68C2×C3⋊C8—122no—
69C22×C32—161no—
70C2×C3⋊D3—162no—
71C2×C3⋊D3—164no—
72C3×A4—41no—
73C22×D4—91no—
74C22×D4—181no—
75C23×C4—31no—
76C22×C8—181no—
77#121—92no—
78#121—92no—
79#121—181no—
80#121—181no—
81C2×C4⋊C4—91no—
82C2×C22⋊C4—181no—
83C22⋊C8—92no—
84C22⋊C8—181no—
85#95—31no—
86#95C2×C3⋊D311yescharacteristic, complemented
87C23×C3—31no—
88C23×C3—31no—
89C23×C3—32no—
90C23×C3GL(2,𝔽3)12yes—
91C23×C3C2×S411yescharacteristic
92C22×D3—62no—
93C22×D3—122no—
94C22×D3—122no—
95C22×D3—121no—
96C22×D3—121no—
97C22×D3—483no—
98C2×A4—43no—
99C2×A4—46no—
100S4—1212no—
101C2×C3×C4—31no—
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—62no—
106C2×C3×C4—62no—
107C2×C3×C4—121no—
108C2×C3×C4—121no—
109C2×C3×C4—121no—
110C2×C3×C4—121no—
111#67—122no—
112#67—124no—
113#67—122no—
114C2×Dic3—62no—
115C2×Dic3—122no—
116D12—122no—
117D12—122no—
118C3⋊C8—122no—
119C2×C32—161no—
120C2×C32—162no—
121C3⋊D3—164no—
122C24—181no—
123C24C3⋊S411yescharacteristic
124C2×D4—92no—
125C2×D4—181no—
126C2×D4—182no—
127C2×D4—182no—
128C2×D4—362no—
129C2×D4—362no—
130C2×D4—362no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—31no—
136C22×C4—31no—
137C22×C4—122no—
138C22×C4—181no—
139C2×C8—182no—
140C2×C8—362no—
141C4⋊C4—92no—
142C4⋊C4—181no—
143C22⋊C4—182no—
144C22⋊C4—182no—
145C22×C3—31no—
146C22×C3—32no—
147C22×C3—31no—
148C22×C3—31no—
149C22×C3—32no—
150C22×C3—32no—
151C22×C3—61no—
152C22×C3—163no—
153C22×C3#85711yescharacteristic
154C22×C3C2×GL(2,𝔽3)11yescharacteristic
155C2×D3—122no—
156C2×D3—122no—
157C2×D3—122no—
158C2×D3—242no—
159C2×D3—242no—
160C2×D3—486no—
161C2×D3—4812no—
162A4—43no—
163C3×C4—61no—
164C3×C4—61no—
165C3×C4—61no—
166C3×C4—61no—
167Dic3—122no—
168C32—161noSylow
169C23—31no—
170C23—31no—
171C23—32no—
172C23—182no—
173C23—362no—
174C23—362no—
175C23—361no—
176C23—361no—
177C23C3⋊GL(2,𝔽3)12yes—
178C23C2×C3⋊S411yescharacteristic
179D4—362no—
180D4—362no—
181D4—362no—
182D4—364no—
183D4—362no—
184C2×C4—31no—
185C2×C4—31no—
186C2×C4—31no—
187C2×C4—31no—
188C2×C4—62no—
189C2×C4—62no—
190C2×C4—121no—
191C2×C4—121no—
192C2×C4—121no—
193C2×C4—121no—
194C2×C4—182no—
195C2×C4—362no—
196C8—362no—
197C2×C3—31no—
198C2×C3—31no—
199C2×C3—32no—
200C2×C3—163no—
201C2×C3—166no—
202C2×C3#462212yescomplemented
203C2×C3C2×#85711yescharacteristic
204D3—242no—
205D3—4812no—
206C22—31no—
207C22—32no—
208C22—31no—
209C22—31no—
210C22—32no—
211C22—32no—
212C22—61no—
213C22—362no—
214C22—362no—
215C22—362no—
216C22—722no—
217C22—722no—
218C22C3⋊#85711yescharacteristic
219C22C2×C3⋊GL(2,𝔽3)11yescharacteristic
220C4—61no—
221C4—61no—
222C4—61no—
223C4—61no—
224C4—362no—
225C3—163no—
226C3C2×#462211yescharacteristic, complemented
227C2—31no—
228C2—31no—
229C2—32no—
230C2—722no—
231C2C3⋊#462212yesdirect product factor
232C2C2×C3⋊#85711yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊#857
commutator, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC2×C3×#95D3
socleC24×C3S4
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×C3×#95⋊C3C2semidirect
2. C3⋊#4622C2direct (N × H)
6. C3×#95⋊C3C22semidirect
8. C2×C3×#95D3semidirect
10. C2×#95⋊C3D3semidirect
30. C3×#95C2×D3semidirect
33. #95⋊C3C2×D3semidirect
40. C2×#95C3⋊D3semidirect
86. #95C2×C3⋊D3semidirect
202. C2×C3#4622semidirect
226. C3C2×#4622semidirect
231. C2C3⋊#4622direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#95⋊C32
C3⋊#46222
C2×#46223
C2×#44513
C22×C3⋊S44