Finite Group Databasebeta

← #11920941

Subgroups — #11920941

Order 1152.

316 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 27 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⋊#4622C211yesmaximal, characteristic, complemented
3C3⋊#4621C211yesmaximal, characteristic, complemented
4#72985—33nomaximal
5#69398—31nomaximal
6#64269—41nomaximal
7C3×#95⋊C3C2211yescharacteristic
8#5791—31no—
9C2×C3×#95D311yescharacteristic, complemented
10#5207—31no—
11C2×#95⋊C3D313yescomplemented
12#4622—33no—
13#4621—33no—
14#4452—31no—
15#4452—31no—
16#4451—31no—
17#4451—31no—
18C22×C3×A4—41no—
19C2×C3⋊S4—41no—
20C3⋊SL(2,ℤ/4)—41no—
21#1504—91noSylow
22C23×C3×C4—31no—
23C2×#235—31no—
24GL(2,ℤ/4)—123no—
25#953—61no—
26#930—31no—
27#930—31no—
28#929—61no—
29C4×#67—61no—
30C4×#67—61no—
31#926—31no—
32#924—31no—
33#924—31no—
34C2×#208—61no—
35C3×#95—31no—
36C3×#95C2×D311yescharacteristic
37#830—31no—
38#830—31no—
39#830—61no—
40#95⋊C3C2×D313yes—
41C2×C3×A4—41no—
42C2×C3×A4—81no—
43C3⋊S4—81no—
44#638—161no—
45#525—91no—
46#407—91no—
47C2×#95C3⋊D311yescharacteristic, complemented
48#328—91no—
49#328—91no—
50#327—91no—
51#327—91no—
52C24×C3S411yescharacteristic
53C22×A4—43no—
54C2×S4—123no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4—122no—
62C2×#67—61no—
63C2×#67—61no—
64C2×#67—61no—
65#235—122no—
66C2×D12—31no—
67C2×C4×D3—61no—
68C2×Dic6—31no—
69SL(2,ℤ/4)—123no—
70#217—61no—
71#217—61no—
72#217—61no—
73(C2×D3)⋊C4—61no—
74(C2×D3)⋊C4—61no—
75C4⋊Dic3—31no—
76C4⋊Dic3—31no—
77Dic3⋊C4—61no—
78Dic3⋊C4—61no—
79C4×Dic3—61no—
80#208—122no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C22×C32—161no—
84C2×C3⋊D3—161no—
85C3×A4—41no—
86C3⋊Dic3—161no—
87C2×#41—91no—
88C23×C4—31no—
89C2×M16—181no—
90#123—181no—
91C22⋊Q8—91no—
92C22⋊Q8—91no—
93#121—91no—
94#121—91no—
95#120—181no—
96C4×D4—181no—
97C4×D4—181no—
98#117—91no—
99C22⋊C8—91no—
100C22⋊C8—91no—
101C22⋊C8—181no—
102#95—31no—
103#95C2×C3⋊D311yescharacteristic
104C23×C3—21no—
105C23×C3—31no—
106C23×C3—31no—
107C23×C3—61no—
108C23×C3C2×S411yescharacteristic
109C22×D3—61no—
110C2×A4—43no—
111C2×A4—83no—
112S4—243no—
113C2×C3×C4—31no—
114C2×C3×C4—31no—
115C2×C3×C4—31no—
116C2×C3×C4—31no—
117C2×C3×C4—62no—
118C2×C3×C4—62no—
119C2×C3×C4—121no—
120C2×C3×C4—121no—
121C2×C3×C4—121no—
122C2×C3×C4—121no—
123#67—122no—
124#67—121no—
125#67—121no—
126#67—121no—
127#67—121no—
128#67—483no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C2×Dic3—61no—
132D12—121no—
133C4×D3—122no—
134Dic6—121no—
135C3⋊C8—121no—
136C3⋊C8—121no—
137C2×C32—161no—
138C2×C32—321no—
139C3⋊D3—321no—
140C24C3⋊S411yescharacteristic
141#41—362no—
142C2×Q8—91no—
143C2×D4—91no—
144C2×D4—181no—
145C2×D4—181no—
146C2×D4—181no—
147C22×C4—31no—
148C22×C4—31no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—122no—
154C22×C4—181no—
155M16—362no—
156C2×C8—181no—
157C2×C8—181no—
158C4⋊C4—91no—
159C4⋊C4—91no—
160C4⋊C4—181no—
161C4⋊C4—181no—
162C22⋊C4—181no—
163C22⋊C4—181no—
164C22⋊C4—181no—
165C22⋊C4—181no—
166C22⋊C4—181no—
167C42—181no—
168C22×C3—31no—
169C22×C3—31no—
170C22×C3—32no—
171C22×C3—31no—
172C22×C3—61no—
173C22×C3—61no—
174C22×C3—61no—
175C22×C3—163no—
176C22×C3#85711yescharacteristic
177C22×C3#98311yescharacteristic
178C2×D3—121no—
179C2×D3—121no—
180C2×D3—121no—
181C2×D3—483no—
182A4—43no—
183C3×C4—61no—
184C3×C4—61no—
185C3×C4—61no—
186C3×C4—61no—
187Dic3—121no—
188Dic3—121no—
189Dic3—121no—
190Dic3—483no—
191C32—161noSylow
192C23—21no—
193C23—31no—
194C23—31no—
195C23—61no—
196C23—181no—
197C23C2×C3⋊S411yescharacteristic
198Q8—361no—
199D4—361no—
200D4—362no—
201D4—361no—
202D4—361no—
203D4—361no—
204D4—361no—
205C2×C4—31no—
206C2×C4—31no—
207C2×C4—31no—
208C2×C4—31no—
209C2×C4—62no—
210C2×C4—62no—
211C2×C4—121no—
212C2×C4—121no—
213C2×C4—121no—
214C2×C4—121no—
215C2×C4—181no—
216C2×C4—181no—
217C2×C4—181no—
218C2×C4—362no—
219C8—361no—
220C8—361no—
221C2×C3—21no—
222C2×C3—31no—
223C2×C3—31no—
224C2×C3—61no—
225C2×C3—163no—
226C2×C3—323no—
227C2×C3C2×#85711yescharacteristic
228D3—241no—
229D3—963no—
230C22—31no—
231C22—31no—
232C22—32no—
233C22—31no—
234C22—61no—
235C22—61no—
236C22—61no—
237C22—361no—
238C22—361no—
239C22—361no—
240C22C3⋊#85711yescharacteristic
241C22#6426411yescharacteristic
242C4—61no—
243C4—61no—
244C4—61no—
245C4—61no—
246C4—361no—
247C4—361no—
248C4—361no—
249C3—163no—
250C3#7298511yescharacteristic, complemented
251C2—21no—
252C2—31no—
253C2—31no—
254C2—61no—
255C2—721no—
256C2C2×C3⋊#85711yescharacteristic
subgroupG/H
centerC2C2×C3⋊#857
commutator, cosocle, hypocenterC3×#95⋊C3C22
FrattiniC23C2×C3⋊S4
FittingC2×C3×#95D3
socleC23×C3C2×S4
hypercenterC22C3⋊#857
LCSG ▷ C3×#95⋊C3
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×C3×#95⋊C3C2semidirect
2. C3⋊#4622C2semidirect
3. C3⋊#4621C2semidirect
9. C2×C3×#95D3semidirect
11. C2×#95⋊C3D3semidirect
47. C2×#95C3⋊D3semidirect
250. C3#72985semidirect

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
C3⋊#46212
#729853
#693983
#642694