Finite Group Databasebeta

← C2×C3⋊#4623 #11921002

Subgroups — C2×C3⋊#4623 #11921002

Order 1152.

428 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 53 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⋊#4623C212yesmaximal, direct product factor
3C2×#4623—33nomaximal
4C2×#4523—31nomaximal
5C2×C3⋊SL(2,ℤ/4)—41nomaximal
6C2×C3×C42⋊C3C412yescomplemented
7C2×C3×C42⋊C3C2211yescharacteristic
8C22×C3×C42D311yescharacteristic
9C2×#926—31no—
10C22×#208—31no—
11C22×C42⋊C3D313yes—
12#4623—36no—
13#4523—32no—
14#4523—32no—
15C22×C3×A4—41no—
16C3⋊SL(2,ℤ/4)—42no—
17C3×C42⋊C3C2×C411yescharacteristic, complemented
18C2×#339—91noSylow
19C23×C3×C4—31no—
20C2×SL(2,ℤ/4)—123no—
21C2×C3×C42—31no—
22C2×C3×C42—32no—
23C2×C3×C42Dic312yescomplemented
24C2×C3×C42C2×D311yescharacteristic
25C2×#217—61no—
26#926—32no—
27#926—32no—
28#926—61no—
29#926—61no—
30C2×C4⋊Dic3—31no—
31C2×C4⋊Dic3—31no—
32C2×C4×Dic3—61no—
33C2×#208—34no—
34C2×#208—32no—
35C2×#208—61no—
36C2×#208—62no—
37C22×C3⋊C8—61no—
38C2×C42⋊C3Dic316yescomplemented
39C2×C42⋊C3C2×D313yes—
40C2×C3×A4—42no—
41C2×C3×A4—41no—
42C2×C3⋊Dic3—161no—
43C22×M16—91no—
44C2×#117—91no—
45C22×C42C3⋊D311yescharacteristic
46#339—92no—
47#339—92no—
48C24×C3S411yescharacteristic
49C22×A4—43no—
50C22×C3×C4—31no—
51C22×C3×C4—32no—
52C22×C3×C4—31no—
53C22×C3×C4—31no—
54C22×C3×C4—31no—
55C22×C3×C4—32no—
56C22×C3×C4—32no—
57C22×C3×C4—32no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×Dic3—61no—
61C22×Dic3—61no—
62SL(2,ℤ/4)—126no—
63C3×C42—32no—
64C3×C42—31no—
65C3×C42—61no—
66C3×C42C2×Dic311yescharacteristic, complemented
67#217—62no—
68#217—62no—
69C4⋊Dic3—32no—
70C4⋊Dic3—32no—
71C4⋊Dic3—61no—
72C4⋊Dic3—61no—
73C4×Dic3—62no—
74C4×Dic3—62no—
75#208—34no—
76#208—64no—
77#208—62no—
78C2×C3⋊C8—62no—
79C2×C3⋊C8—64no—
80C42⋊C3C2×Dic313yescomplemented
81C22×C32—161no—
82C3×A4—41no—
83C3⋊Dic3—162no—
84C23×C4—31no—
85C2×M16—92no—
86C2×M16—94no—
87C2×M16—181no—
88C2×M16—182no—
89C22×C8—181no—
90#117—92no—
91#117—92no—
92#117—181no—
93#117—181no—
94C2×C4⋊C4—91no—
95C2×C4⋊C4—91no—
96C2×C22⋊C4—181no—
97C2×C42—31no—
98C2×C42—32no—
99C2×C42—181no—
100C2×C42C3⋊Dic312yescomplemented
101C2×C42C2×C3⋊D311yescharacteristic
102C23×C3—31no—
103C23×C3—31no—
104C23×C3—32no—
105C23×C3SL(2,ℤ/4)12yes—
106C23×C3C2×S411yescharacteristic
107C2×A4—43no—
108C2×A4—46no—
109C2×C3×C4—31no—
110C2×C3×C4—32no—
111C2×C3×C4—31no—
112C2×C3×C4—32no—
113C2×C3×C4—31no—
114C2×C3×C4—31no—
115C2×C3×C4—31no—
116C2×C3×C4—32no—
117C2×C3×C4—32no—
118C2×C3×C4—32no—
119C2×C3×C4—32no—
120C2×C3×C4—31no—
121C2×C3×C4—32no—
122C2×C3×C4—32no—
123C2×C3×C4—32no—
124C2×C3×C4—31no—
125C2×C3×C4—31no—
126C2×C3×C4—32no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129C2×Dic3—122no—
130C2×Dic3—121no—
131C2×Dic3—121no—
132C2×Dic3—483no—
133C3⋊C8—64no—
134C2×C32—161no—
135C2×C32—162no—
136C24C3⋊S411yescharacteristic
137C22×C4—31no—
138C22×C4—31no—
139C22×C4—31no—
140C22×C4—31no—
141C22×C4—32no—
142C22×C4—32no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—32no—
146C22×C4—32no—
147C22×C4—181no—
148C22×C4—181no—
149M16—94no—
150M16—184no—
151M16—182no—
152C2×C8—182no—
153C2×C8—184no—
154C4⋊C4—92no—
155C4⋊C4—92no—
156C4⋊C4—181no—
157C4⋊C4—181no—
158C22⋊C4—182no—
159C22⋊C4—182no—
160C42—32no—
161C42—31no—
162C42—61no—
163C42—182no—
164C42—182no—
165C42C2×C3⋊Dic311yescharacteristic, complemented
166C22×C3—32no—
167C22×C3—31no—
168C22×C3—31no—
169C22×C3—31no—
170C22×C3—32no—
171C22×C3—32no—
172C22×C3—61no—
173C22×C3—163no—
174C22×C3#85711yescharacteristic
175C22×C3C2×SL(2,ℤ/4)11yescharacteristic
176A4—43no—
177C3×C4—31no—
178C3×C4—31no—
179C3×C4—32no—
180C3×C4—31no—
181C3×C4—32no—
182C3×C4—31no—
183Dic3—122no—
184Dic3—122no—
185Dic3—486no—
186C32—161noSylow
187C23—31no—
188C23—31no—
189C23—32no—
190C23C3⋊SL(2,ℤ/4)12yes—
191C23C2×C3⋊S411yescharacteristic
192C2×C4—31no—
193C2×C4—31no—
194C2×C4—31no—
195C2×C4—31no—
196C2×C4—32no—
197C2×C4—31no—
198C2×C4—32no—
199C2×C4—32no—
200C2×C4—31no—
201C2×C4—32no—
202C2×C4—32no—
203C2×C4—32no—
204C2×C4—32no—
205C2×C4—32no—
206C2×C4—32no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4—32no—
210C2×C4—182no—
211C2×C4—182no—
212C2×C4—362no—
213C2×C4—361no—
214C2×C4—361no—
215C8—184no—
216C2×C3—31no—
217C2×C3—31no—
218C2×C3—32no—
219C2×C3—163no—
220C2×C3—166no—
221C2×C3#462312yescomplemented
222C2×C3C2×#85711yescharacteristic
223C22—31no—
224C22—32no—
225C22—31no—
226C22—31no—
227C22—32no—
228C22—32no—
229C22—61no—
230C22C3⋊#85711yescharacteristic
231C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
232C4—31no—
233C4—31no—
234C4—32no—
235C4—31no—
236C4—31no—
237C4—32no—
238C4—362no—
239C4—362no—
240C3—163no—
241C3C2×#462311yescharacteristic, complemented
242C2—31no—
243C2—31no—
244C2—32no—
245C2C3⋊#462312yesdirect product factor
246C2C2×C3⋊#85711yescharacteristic
subgroupG/H
center, hypercenterC22C3⋊#857
commutator, hypocenterC3×C42⋊C3C2×C4
FrattiniC23C2×C3⋊S4
FittingC22×C3×C42D3
socleC24×C3S4
prime radicalC22×C3×C42⋊C3C2
cosocleC2×C3×C42⋊C3C22
LCSG ▷ C3×C42⋊C3
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C3⋊#4623C2direct (N × H)
6. C2×C3×C42⋊C3C4semidirect
17. C3×C42⋊C3C2×C4semidirect
23. C2×C3×C42Dic3semidirect
38. C2×C42⋊C3Dic3semidirect
66. C3×C42C2×Dic3semidirect
80. C42⋊C3C2×Dic3semidirect
100. C2×C42C3⋊Dic3semidirect
165. C42C2×C3⋊Dic3semidirect
221. C2×C3#4623semidirect
241. C3C2×#4623semidirect
245. C2C3⋊#4623direct (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⋊#46232
C2×#46233
C2×#45233
C2×C3⋊SL(2,ℤ/4)4