Finite Group Databasebeta

← #11923059

Subgroups — #11923059

Order 1152.

752 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C3×A4×#41C211yesmaximal, characteristic
2#10593643C213yesmaximal, complemented
3C2×C3⋊(A4⋊C8)C213yesmaximal, complemented
4#85511—33nomaximal
5#84075—31nomaximal
6C3×Q8×A4C411yescharacteristic
7C3×D4×A4C413yes—
8C2×C3×C4×A4C2213yes—
9#64157—41nomaximal
10C3⋊(A4⋊C8)C2211yescharacteristic
11C3⋊(A4⋊C8)C2213yes—
12C22×C3×#41D311yescharacteristic
13A4×#41D313yes—
14C2×#948—31no—
15C2×#948—31no—
16#5409—39no—
17C2×A4⋊C8—39no—
18#5234—33no—
19#5234—33no—
20#5207—33no—
21C2×#830—33no—
22C22×C3×A4C2×C413yes—
23C32×#41—41no—
24C3×C4×A4C2×C413yes—
25C3×C4×A4C2311yescharacteristic
26#3748—43no—
27C2×C3⋊(C3⋊C8)—43no—
28#2880—91noSylow
29C2×C3×#41—31no—
30C2×C3×#41—33no—
31C2×C3×#41—31no—
32C2×C3×#41—33no—
33C22×C3×Q8Dic311yescharacteristic
34C22×C3×D4Dic313yes—
35C23×C3×C4C2×D313yes—
36Q8×A4Dic313yes—
37D4×A4Dic319yes—
38C2×C4×A4C2×D319yes—
39#948—61no—
40#948—63no—
41#948—63no—
42#948—61no—
43#948—123no—
44C2×#208—33no—
45C2×#208—33no—
46C22×C3⋊C8—33no—
47C22×C3⋊C8—33no—
48A4⋊C8—33no—
49A4⋊C8—39no—
50#830—33no—
51#830—33no—
52#830—36no—
53#830—31no—
54#830—33no—
55C2×C3×A4—23no—
56C2×C3×A4C22×C411yescharacteristic
57C32×Q8—41no—
58C32×D4—43no—
59C2×C32×C4—43no—
60C3⋊(C3⋊C8)—41no—
61C3⋊(C3⋊C8)—43no—
62C22×#41C3⋊D311yescharacteristic
63C2×#131—91no—
64C2×#131—91no—
65#408—93no—
66#408—93no—
67#407—93no—
68C2×C22⋊C8—93no—
69C24×C3C2×Dic313yes—
70C22×A4C2×Dic319yes—
71C3×#41—31no—
72C3×#41—33no—
73C3×#41—33no—
74C3×#41—43no—
75C3×#41—61no—
76C3×#41—63no—
77C3×#41—63no—
78C3×#41S411yescharacteristic
79C2×C3×Q8—31no—
80C2×C3×Q8—33no—
81C2×C3×D4—33no—
82C2×C3×D4—33no—
83C2×C3×D4—36no—
84C22×C3×C4—33no—
85C22×C3×C4—33no—
86C22×C3×C4—33no—
87C22×C3×C4—33no—
88C22×C3×C4C2×Dic313yes—
89C22×C3×C4C22×D311yescharacteristic
90C4×A4C2×Dic319yes—
91C4×A4C22×D313yes—
92#208—63no—
93#208—63no—
94#208—63no—
95#208—63no—
96#208—129no—
97C2×C3⋊C8—31no—
98C2×C3⋊C8—31no—
99C2×C3⋊C8—33no—
100C2×C3⋊C8—33no—
101C2×C3⋊C8—63no—
102C2×C3⋊C8—63no—
103C2×C3⋊C8—63no—
104C2×C3⋊C8—63no—
105C2×C3⋊C8—129no—
106C22×C32—43no—
107C3×A4#13111yescharacteristic, complemented
108C32×C4—43no—
109C32×C4—41no—
110C2×#41—31no—
111C2×#41—33no—
112C2×#41—33no—
113C2×#41—31no—
114C22×Q8C3⋊Dic311yescharacteristic
115C22×D4C3⋊Dic313yes—
116C23×C4C2×C3⋊D313yes—
117#131—181no—
118#131—183no—
119#131—183no—
120#131—181no—
121C2×M16—93no—
122C2×M16—93no—
123C22×C8—93no—
124C22×C8—93no—
125C22⋊C8—93no—
126C22⋊C8—93no—
127C22⋊C8—96no—
128C22⋊C8—91no—
129C22⋊C8—93no—
130C23×C3—23no—
131C23×C3—33no—
132C23×C3—33no—
133C23×C3—63no—
134C23×C3C22×Dic311yescharacteristic
135C2×A4—29no—
136C2×A4C22×Dic313yes—
137C3×Q8—33no—
138C3×Q8—43no—
139C3×Q8—61no—
140C3×Q8SL(2,ℤ/4)11yescharacteristic
141C3×D4—36no—
142C3×D4—33no—
143C3×D4—49no—
144C3×D4—63no—
145C3×D4SL(2,ℤ/4)13yes—
146C2×C3×C4—33no—
147C2×C3×C4—33no—
148C2×C3×C4—33no—
149C2×C3×C4—31no—
150C2×C3×C4—33no—
151C2×C3×C4—31no—
152C2×C3×C4—33no—
153C2×C3×C4—49no—
154C2×C3×C4—63no—
155C2×C3×C4C2×S413yes—
156C3⋊C8—61no—
157C3⋊C8—63no—
158C3⋊C8—61no—
159C3⋊C8—63no—
160C3⋊C8—123no—
161C3⋊C8—129no—
162C2×C32—41no—
163C2×C32—83no—
164C24C2×C3⋊Dic313yes—
165#41—31no—
166#41—33no—
167#41—33no—
168#41—61no—
169#41—63no—
170#41—63no—
171#41C3⋊S411yescharacteristic
172C2×Q8—31no—
173C2×Q8—33no—
174C2×D4—33no—
175C2×D4—33no—
176C2×D4—36no—
177C22×C4—33no—
178C22×C4—33no—
179C22×C4—33no—
180C22×C4—33no—
181C22×C4C2×C3⋊Dic313yes—
182C22×C4C22×C3⋊D311yescharacteristic
183M16—183no—
184M16—183no—
185M16—183no—
186M16—183no—
187C2×C8—91no—
188C2×C8—91no—
189C2×C8—93no—
190C2×C8—93no—
191C2×C8—183no—
192C2×C8—183no—
193C2×C8—183no—
194C2×C8—183no—
195C22×C3—31no—
196C22×C3—31no—
197C22×C3—33no—
198C22×C3—49no—
199C22×C3—63no—
200C22×C3—63no—
201C22×C3—63no—
202C22×C3—63no—
203C22×C3#94811yescharacteristic, complemented
204C22×C3C2×SL(2,ℤ/4)13yes—
205A4#94813yescomplemented
206C3×C4—31no—
207C3×C4—33no—
208C3×C4—49no—
209C3×C4—43no—
210C3×C4C2×SL(2,ℤ/4)13yes—
211C3×C4C22×S411yescharacteristic
212C32—41noSylow
213C23—23no—
214C23—33no—
215C23—33no—
216C23—63no—
217C23C22×C3⋊Dic311yescharacteristic
218Q8—33no—
219Q8—61no—
220Q8C3⋊SL(2,ℤ/4)11yescharacteristic
221D4—36no—
222D4—33no—
223D4—63no—
224D4C3⋊SL(2,ℤ/4)13yes—
225C2×C4—33no—
226C2×C4—33no—
227C2×C4—33no—
228C2×C4—31no—
229C2×C4—33no—
230C2×C4—31no—
231C2×C4—33no—
232C2×C4—63no—
233C2×C4C2×C3⋊S413yes—
234C8—181no—
235C8—183no—
236C8—181no—
237C8—183no—
238C2×C3—23no—
239C2×C3—31no—
240C2×C3—31no—
241C2×C3—43no—
242C2×C3—63no—
243C2×C3—89no—
244C2×C3C22×SL(2,ℤ/4)11yescharacteristic
245C22—31no—
246C22—31no—
247C22—33no—
248C22—63no—
249C22—63no—
250C22—63no—
251C22—63no—
252C22#6415711yescharacteristic, complemented
253C22C2×C3⋊SL(2,ℤ/4)13yes—
254C4—31no—
255C4—33no—
256C4C2×C3⋊SL(2,ℤ/4)13yes—
257C4C22×C3⋊S411yescharacteristic
258C3—43no—
259C3#8551111yescharacteristic, complemented
260C2—23no—
261C2—31no—
262C2—31no—
263C2—63no—
264C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC4C22×C3⋊S4
commutatorC2×C3×A4C22×C4
FittingC22×C3×#41D3
socleC23×C3C22×Dic3
prime radicalC3×A4×#41C2
cosocleC3×C4×A4C23
hypercenter#41C3⋊S4
hypocenterC3×A4#131
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. #10593643C2semidirect
3. C2×C3⋊(A4⋊C8)C2semidirect
107. C3×A4#131semidirect
203. C22×C3#948semidirect
205. A4#948semidirect
252. C22#64157semidirect
259. C3#85511semidirect

Maximal subgroups

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

subgroupindex
C3×A4×#412
#105936432
C2×C3⋊(A4⋊C8)2
#855113
#840753
#641574