Finite Group Databasebeta

← #11808490

Subgroups — #11808490

Order 1152.

1981 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 1981 conjugacy classes of subgroups — too many to draw. Only its 268 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×#63921C213yesmaximal
2C2×#63900C213yesmaximal, complemented
3C3⋊D3×#95C211yesmaximal, characteristic, complemented
4C3×#4677C212yesmaximal, complemented
5#10591324C216yesmaximal, complemented
6D3×#399—32nomaximal
7C23×D32C2211yescharacteristic
8C22×C4×C3⋊D3C2213yes—
9C22×#624C2213yes—
10C2×C3×(C2×D3)⋊C4C2216yes—
11C2×C3×C4⋊Dic3C2216yescomplemented
12C2×#3724C2216yescomplemented
13C2×(C2×D3)⋊Dic3C2216yes—
14#63921—212no—
15#63900—212no—
16C32×#95C2211yescharacteristic, complemented
17#63658C2213yescomplemented
18C2×D3×C4⋊C4—36no—
19C2×D3×C22⋊C4—36no—
20C3×#399—32no—
21#4993—36no—
22#4949—36no—
23#4677D312yescomplemented
24D3×#95—32no—
25D3×#95—61no—
26C23×C3⋊D3C2311yescharacteristic
27C23×C3×D3C2312yes—
28C22×D32—26no—
29C22×D32—26no—
30C22×D32Q814yes—
31C22×C32×C4C2313yes—
32C22×C3⋊Dic3C2313yes—
33C2×C4×C3⋊D3—212no—
34C2×C4×C3⋊D3D4112yes—
35C22×C3×Dic3C2316yes—
36C2×#624—212no—
37C2×#624—26no—
38C3×(C2×D3)⋊C4—212no—
39C3×C4⋊Dic3—212no—
40#3724—212no—
41(C2×D3)⋊Dic3—212no—
42C2×#399—91noSylow
43C24×D3—32no—
44C22×C4×D3—36no—
45C22×C4×D3—36no—
46C22×C4×D3—63no—
47C2×C3×C4⋊C4—36no—
48C2×C3×C22⋊C4—36no—
49C2×#217—36no—
50C2×(C2×D3)⋊C4—36no—
51C2×(C2×D3)⋊C4C2×D316yes—
52C2×C4⋊Dic3C2×D316yescomplemented
53C2×Dic3⋊C4—312no—
54D3×C4⋊C4—624no—
55D3×C22⋊C4—624no—
56C3×#95—21no—
57C3×#95C2×D312yescomplemented
58C3⋊#95—36no—
59C3⋊#95—63no—
60C23×C32C2411yescharacteristic
61C22×C3⋊D3C2×D416yes—
62C22×C3⋊D3C2×Q812yes—
63C22×C3⋊D3#4116yes—
64C22×C3×D3—26no—
65C22×C3×D3—26no—
66C22×C3×D3C2×Q814yes—
67C2×D32—224no—
68C2×D32—412no—
69C2×D32—44no—
70C2×C32×C4—26no—
71C2×C32×C4C2×D416yes—
72C2×C3⋊Dic3—26no—
73C2×C3⋊Dic3C2×D416yes—
74C4×C3⋊D3—224no—
75C2×C3×Dic3—26no—
76C2×C3×Dic3—212no—
77#624—412no—
78C22×C4⋊C4—93no—
79C22×C22⋊C4—93no—
80#399—32no—
81#399—96no—
82C2×#95—91no—
83C24×C3—32no—
84C23×D3—32no—
85C23×D3—38no—
86C23×D3—61no—
87C23×D3—612no—
88C23×D3—612no—
89C23×D3C22×D312yes—
90C22×C3×C4—23no—
91C22×C3×C4—36no—
92C22×C3×C4C22×D316yes—
93C22×Dic3—36no—
94C22×Dic3—63no—
95C22×Dic3C22×D316yes—
96C2×C4×D3—324no—
97C2×C4×D3—612no—
98C2×C4×D3—624no—
99C2×C4×D3—612no—
100C2×C4×D3—624no—
101C2×C4×D3—1212no—
102C3×C4⋊C4—612no—
103C3×C22⋊C4—612no—
104#217—612no—
105(C2×D3)⋊C4—212no—
106(C2×D3)⋊C4—612no—
107C4⋊Dic3—212no—
108Dic3⋊C4—624no—
109C22×C32C22×D413yes—
110C22×C32C22×Q811yescharacteristic
111C22×C32C2×#4113yes—
112C2×C3⋊D3C22⋊Q8112yes—
113C2×C3⋊D3#123112yes—
114C2×C3⋊D3#12714yes—
115C2×C3×D3—212no—
116C2×C3×D3—46no—
117C2×C3×D3—42no—
118D32—416no—
119C32×C4—26no—
120C3⋊Dic3—26no—
121C3×Dic3—46no—
122C25—91no—
123C23×C4—93no—
124C23×C4—93no—
125C2×C4⋊C4—36no—
126C2×C4⋊C4—96no—
127C2×C4⋊C4—1812no—
128C2×C22⋊C4—36no—
129C2×C22⋊C4—96no—
130C2×C22⋊C4—1812no—
131#95—93no—
132#95D3211yescharacteristic, complemented
133C23×C3—21no—
134C23×C3—34no—
135C23×C3—66no—
136C23×C3—66no—
137C23×C3C23×D312yes—
138C22×D3—26no—
139C22×D3—26no—
140C22×D3—312no—
141C22×D3—34no—
142C22×D3—312no—
143C22×D3—66no—
144C22×D3—62no—
145C22×D3—66no—
146C22×D3—648no—
147C22×D3—1224no—
148C22×D3—128no—
149C22×D3D3×Q814yes—
150C2×C3×C4—212no—
151C2×C3×C4—26no—
152C2×C3×C4—46no—
153C2×C3×C4—612no—
154C2×C3×C4—66no—
155C2×C3×C4D3×D4112yes—
156C2×Dic3—212no—
157C2×Dic3—26no—
158C2×Dic3—312no—
159C2×Dic3—66no—
160C2×Dic3—612no—
161C2×Dic3—126no—
162C4×D3—648no—
163C4×D3—1224no—
164C4×D3—1224no—
165C2×C32C2×C22⋊Q813yes—
166C2×C32C2×#12313yes—
167C2×C32C2×#12711yescharacteristic
168C3⋊D3#39918yescomplemented
169C3×D3—44no—
170C24—32no—
171C24—94no—
172C24—91no—
173C24—186no—
174C24—186no—
175C22×C4—36no—
176C22×C4—93no—
177C22×C4—912no—
178C22×C4—1812no—
179C22×C4—186no—
180C22×C4—1812no—
181C22×C4C2×D3213yes—
182C4⋊C4—612no—
183C4⋊C4—1812no—
184C22⋊C4—612no—
185C22⋊C4—1812no—
186C22×C3—23no—
187C22×C3—23no—
188C22×C3—21no—
189C22×C3—612no—
190C22×C3—126no—
191C22×C3—122no—
192C22×C3C2×D3×D416yes—
193C22×C3C2×D3×Q812yes—
194C22×C3D3×#4116yes—
195C2×D3—212no—
196C2×D3—324no—
197C2×D3—38no—
198C2×D3—324no—
199C2×D3—46no—
200C2×D3—42no—
201C2×D3—612no—
202C2×D3—612no—
203C2×D3—64no—
204C2×D3—1232no—
205C3×C4—212no—
206C3×C4—46no—
207C3×C4—126no—
208Dic3—46no—
209Dic3—612no—
210Dic3—126no—
211C32C2×#39911yescharacteristic, complemented, Sylow
212C23—34no—
213C23—66no—
214C23—66no—
215C23—96no—
216C23—96no—
217C23—92no—
218C23—1824no—
219C23—364no—
220C23—3612no—
221C23C22×D3211yescharacteristic
222C2×C4—26no—
223C2×C4—66no—
224C2×C4—612no—
225C2×C4—96no—
226C2×C4—1824no—
227C2×C4—186no—
228C2×C4—3612no—
229C2×C4#380216yes—
230C2×C3—23no—
231C2×C3—21no—
232C2×C3—23no—
233C2×C3—124no—
234C2×C3D3×C22⋊Q816yes—
235C2×C3D3×#12316yes—
236C2×C3D3×#12712yes—
237D3—316no—
238D3—44no—
239D3—68no—
240C22—612no—
241C22—912no—
242C22—94no—
243C22—912no—
244C22—122no—
245C22—126no—
246C22—3616no—
247C22C2×#380213yes—
248C22#6431213yes—
249C22D32×Q811yescharacteristic
250C4—26no—
251C4—126no—
252C4—186no—
253C3—21no—
254C3D3×#39912yescomplemented
255C2—98no—
256C2—124no—
257C2#1059400811yescharacteristic
258C2#1059429513yes—
259C2#1059463113yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×D32C22
hypercenter#95D32
hypocenterC32C2×#399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63900C2semidirect
3. C3⋊D3×#95C2semidirect
4. C3×#4677C2semidirect
5. #10591324C2semidirect
11. C2×C3×C4⋊Dic3C22semidirect
12. C2×#3724C22semidirect
16. C32×#95C22semidirect
17. #63658C22semidirect
23. #4677D3semidirect
52. C2×C4⋊Dic3C2×D3semidirect
57. C3×#95C2×D3semidirect
132. #95D32semidirect
168. C3⋊D3#399semidirect
211. C32C2×#399semidirect
254. C3D3×#399semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
C2×#639002
C3⋊D3×#952
C3×#46772
#105913242
D3×#3993