Finite Group Databasebeta

← #11808736

Subgroups — #11808736

Order 1152.

2520 conjugacy classes of subgroups; only the 339 normal subgroups are shown.

normal subgroups only

This group has 2520 conjugacy classes of subgroups — too many to draw. Only its 339 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×D4×C3⋊Dic3C213yesmaximal, complemented
2C2×#64090C213yesmaximal, complemented
3C32×#392C211yesmaximal, characteristic, complemented
4#10592922C213yesmaximal, complemented
5#10592648C213yesmaximal, complemented
6#10592376C211yesmaximal, characteristic, complemented
7#10592347C211yesmaximal, characteristic, complemented
8#76667—34nomaximal
9C22×C32×D4C2213yes—
10C22×#638C2213yes—
11C23×C3⋊Dic3C2213yes—
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C32×C22⋊C4C2213yes—
14C2×#3757C2216yes—
15D4×C3⋊Dic3—212no—
16C2×#3752C2213yes—
17C2×C4⋊(C3⋊Dic3)C2213yes—
18C2×#3750C2213yes—
19C2×C4×C3⋊Dic3C2213yes—
20#64090—212no—
21C32×#95C2211yescharacteristic
22#63658C2213yes—
23C2×D4×Dic3—312no—
24C2×#67⋊C4—312no—
25C3×#392D314yescomplemented
26#5223—312no—
27#4949—312no—
28#4677—34no—
29#4648—34no—
30C24×C32C2313yes—
31C23×C3⋊D3C2311yescharacteristic
32C2×C32×D4—212no—
33C2×C32×D4—26no—
34C22×C32×C4C2311yescharacteristic
35C22×C32×C4C2313yes—
36C2×#638—26no—
37C2×#638—26no—
38C2×#638—26no—
39C22×C3⋊Dic3—26no—
40C22×C3⋊Dic3—212no—
41C22×C3⋊Dic3C2313yes—
42C22×C3⋊Dic3C2313yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C2×C4×C3⋊D3—26no—
45C32×C22⋊C4—26no—
46#3757—212no—
47#3752—26no—
48C4⋊(C3⋊Dic3)—26no—
49#3750—26no—
50C4×C3⋊Dic3D4112yescomplemented
51#2397—91noSylow
52C22×C3×D4C2×D3112yes—
53C22×#67—312no—
54C23×Dic3—312no—
55C22×C4×D3—34no—
56C2×C3×C22⋊C4C2×D3112yes—
57C2×#217—324no—
58D4×Dic3—648no—
59C2×(C2×D3)⋊C4—312no—
60C2×C4⋊Dic3—312no—
61C2×Dic3⋊C4—312no—
62C2×C4×Dic3—312no—
63#67⋊C4—648no—
64C3×#95C2×D314yes—
65C3⋊#95—312no—
66C23×C32—26no—
67C23×C32—23no—
68C23×C32—23no—
69C23×C32—26no—
70C23×C32#4116yes—
71C23×C32C2411yescharacteristic
72C22×C3⋊D3—23no—
73C22×C3⋊D3—23no—
74C22×C3⋊D3#4112yes—
75C32×D4—224no—
76C2×C32×C4—26no—
77C2×C32×C4—23no—
78C2×C32×C4C2×D416yes—
79#638—224no—
80C2×C3⋊Dic3—23no—
81C2×C3⋊Dic3—23no—
82C2×C3⋊Dic3—23no—
83C2×C3⋊Dic3—26no—
84C2×C3⋊Dic3—412no—
85C2×C3⋊Dic3C2×D416yes—
86C2×C3⋊Dic3C2×D416yes—
87C4×C3⋊D3—44no—
88C2×C4×D4—93no—
89C2×C4×D4—93no—
90#399—93no—
91#399—91no—
92#392—93no—
93#392C3⋊D311yescharacteristic, complemented
94#376—91no—
95C24×C3C22×D3112yes—
96C23×D3—34no—
97C2×C3×D4—248no—
98C2×C3×D4—224no—
99C22×C3×C4C22×D314yes—
100C22×C3×C4C22×D3112yes—
101C2×#67—624no—
102C2×#67—624no—
103C2×#67—624no—
104C22×Dic3—34no—
105C22×Dic3—312no—
106C22×Dic3—312no—
107C22×Dic3—624no—
108C22×Dic3—648no—
109C2×C4×D3—624no—
110C3×C22⋊C4—224no—
111#217—648no—
112(C2×D3)⋊C4—624no—
113C4⋊Dic3—624no—
114Dic3⋊C4—624no—
115C4×Dic3—348no—
116C22×C32—26no—
117C22×C32—212no—
118C22×C32—43no—
119C22×C32—46no—
120C22×C32—43no—
121C22×C32C22×D413yes—
122C22×C32C2×#4113yes—
123C22×C32C2×#4111yescharacteristic
124C2×C3⋊D3—26no—
125C2×C3⋊D3—43no—
126C2×C3⋊D3—41no—
127C32×C4—26no—
128C32×C4—41no—
129C3⋊Dic3—26no—
130C3⋊Dic3—43no—
131C3⋊Dic3#12714yes—
132C22×D4—93no—
133C22×D4C2×C3⋊D313yes—
134C23×C4—93no—
135C23×C4—91no—
136C4×D4—1812no—
137C4×D4—1812no—
138C2×C4⋊C4—93no—
139C2×C4⋊C4—93no—
140C2×C22⋊C4—96no—
141C2×C22⋊C4—93no—
142C2×C22⋊C4C2×C3⋊D313yes—
143C2×C42—93no—
144#95—93no—
145#95C2×C3⋊D311yescharacteristic
146C23×C3—224no—
147C23×C3—212no—
148C23×C3—224no—
149C23×C3—212no—
150C23×C3#237124yes—
151C23×C3C23×D314yes—
152C22×D3—38no—
153C22×D3—612no—
154C22×D3—612no—
155C3×D4—296no—
156C2×C3×C4—224no—
157C2×C3×C4—212no—
158C2×C3×C4D3×D4124yes—
159#67—696no—
160C2×Dic3—324no—
161C2×Dic3—324no—
162C2×Dic3—612no—
163C2×Dic3—612no—
164C2×Dic3—612no—
165C2×Dic3—624no—
166C2×Dic3—1248no—
167C4×D3—1216no—
168C2×C32—46no—
169C2×C32#52513yes—
170C2×C32#52513yes—
171C2×C32C2×#12711yescharacteristic
172C3⋊D3—42no—
173C24—91no—
174C24C22×C3⋊D313yes—
175C2×D4—212no—
176C2×D4—26no—
177C2×D4—186no—
178C2×D4—186no—
179C2×D4—186no—
180C22×C4—91no—
181C22×C4—93no—
182C22×C4—93no—
183C22×C4—186no—
184C22×C4—186no—
185C22×C4—1812no—
186C22×C4C22×C3⋊D311yescharacteristic
187C22×C4C22×C3⋊D313yes—
188C4⋊C4—186no—
189C4⋊C4—186no—
190C22⋊C4—26no—
191C22⋊C4—1812no—
192C22⋊C4—186no—
193C42—912no—
194C22×C3—248no—
195C22×C3—224no—
196C22×C3—412no—
197C22×C3—412no—
198C22×C3—424no—
199C22×C3C2×D3×D4112yes—
200C22×C3C2×#237112yes—
201C22×C3D3×#4114yes—
202C2×D3—624no—
203C2×D3—124no—
204C2×D3—1212no—
205C3×C4—224no—
206C3×C4—44no—
207Dic3—316no—
208Dic3—624no—
209Dic3—1212no—
210C32#239711yescharacteristic, complemented, Sylow
211C23—23no—
212C23—26no—
213C23—26no—
214C23—23no—
215C23—92no—
216C23—183no—
217C23—183no—
218C23#383016yes—
219C23C23×C3⋊D311yescharacteristic
220D4—224no—
221D4—1824no—
222C2×C4—26no—
223C2×C4—23no—
224C2×C4—96no—
225C2×C4—96no—
226C2×C4—183no—
227C2×C4—183no—
228C2×C4—186no—
229C2×C4—183no—
230C2×C4—364no—
231C2×C4—3612no—
232C2×C4D4×C3⋊D316yes—
233C2×C3—424no—
234C2×C3#5586112yes—
235C2×C3#5606112yes—
236C2×C3D3×#12714yes—
237D3—128no—
238C22—212no—
239C22—26no—
240C22—43no—
241C22—43no—
242C22—46no—
243C22—186no—
244C22—361no—
245C22—363no—
246C22C2×D4×C3⋊D313yes—
247C22C2×#383013yes—
248C22#41×C3⋊D311yescharacteristic
249C4—26no—
250C4—41no—
251C4—94no—
252C4—186no—
253C4—363no—
254C3#7666714yescomplemented
255C2—46no—
256C2—362no—
257C2#1059605713yes—
258C2#1059607713yes—
259C2C3⋊D3×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#392C2
hypercenter#392C3⋊D3
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C2×#64090C2semidirect
3. C32×#392C2semidirect
4. #10592922C2semidirect
5. #10592648C2semidirect
6. #10592376C2semidirect
7. #10592347C2semidirect
25. C3×#392D3semidirect
50. C4×C3⋊Dic3D4semidirect
93. #392C3⋊D3semidirect
210. C32#2397semidirect
254. C3#76667semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×#640902
C32×#3922
#105929222
#105926482
#105923762
#105923472
#766673