Finite Group Databasebeta

← #11808742

Subgroups — #11808742

Order 1152.

2520 conjugacy classes of subgroups; only the 319 normal subgroups are shown.

normal subgroups only

This group has 2520 conjugacy classes of subgroups — too many to draw. Only its 319 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×#64102C213yesmaximal, complemented
2C2×#64090C213yesmaximal, complemented
3C32×#399C211yesmaximal, characteristic, complemented
4#10592692C213yesmaximal, complemented
5#10592659C213yesmaximal, complemented
6#10592370C211yesmaximal, characteristic, complemented
7#10592347C211yesmaximal, characteristic, complemented
8#78019—34nomaximal
9C22×#638C2213yes—
10C23×C3⋊Dic3C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2213yes—
12C22×C4×C3⋊D3C2213yes—
13C2×C32×C4⋊C4C2213yes—
14C2×C32×C22⋊C4C2213yes—
15C2×#3752C2213yes—
16C2×#3752C2216yes—
17C2×#3750C2213yes—
18C2×C4×C3⋊Dic3C2213yes—
19#64102—212no—
20#64090—212no—
21C32×#95C2211yescharacteristic
22#63658C2213yes—
23C2×#893—312no—
24C2×#67⋊C4—312no—
25C3×#399D314yescomplemented
26#4993—312no—
27#4960—312no—
28#4671—34no—
29#4648—34no—
30C24×C32C2311yescharacteristic
31C23×C3⋊D3C2313yes—
32C22×C32×C4C2313yes—
33C22×C32×C4C2313yes—
34C2×#638—26no—
35C2×#638—26no—
36C2×#638—26no—
37C22×C3⋊Dic3—26no—
38C22×C3⋊Dic3C2311yescharacteristic
39C22×C3⋊Dic3C2313yes—
40C22×C3⋊Dic3C2311yescharacteristic
41C2×C4⋊(C3⋊D3)—212no—
42C2×C4⋊(C3⋊D3)—26no—
43C2×C4×C3⋊D3—26no—
44C2×C4×C3⋊D3—212no—
45C32×C4⋊C4—26no—
46C32×C22⋊C4—26no—
47#3752—26no—
48#3752—212no—
49#3750—26no—
50C4×C3⋊Dic3D4112yescomplemented
51#2397—91noSylow
52C22×#67—312no—
53C23×Dic3—34no—
54C22×D12—312no—
55C22×C4×D3—312no—
56C2×C3×C4⋊C4C2×D3112yes—
57C2×C3×C22⋊C4C2×D3112yes—
58C2×(C2×D3)⋊C4—312no—
59C2×(C2×D3)⋊C4—324no—
60C2×Dic3⋊C4—312no—
61C2×C4×Dic3—312no—
62#893—648no—
63#67⋊C4—648no—
64C3×#95C2×D314yes—
65C3⋊#95—312no—
66C23×C32—23no—
67C23×C32—23no—
68C23×C32#4112yes—
69C23×C32C2411yescharacteristic
70C22×C3⋊D3—26no—
71C22×C3⋊D3—23no—
72C22×C3⋊D3—26no—
73C22×C3⋊D3—23no—
74C22×C3⋊D3#4116yes—
75C2×C32×C4—26no—
76C2×C32×C4—23no—
77C2×C32×C4—26no—
78C2×C32×C4C2×D416yes—
79#638—224no—
80C2×C3⋊Dic3—23no—
81C2×C3⋊Dic3—23no—
82C2×C3⋊Dic3—23no—
83C2×C3⋊Dic3—44no—
84C2×C3⋊Dic3C2×D416yes—
85C2×C3⋊Dic3C2×D416yes—
86C4⋊(C3⋊D3)—224no—
87C4×C3⋊D3—412no—
88C2×C4×D4—93no—
89C2×C4×D4—93no—
90#399—93no—
91#399C3⋊D311yescharacteristic, complemented
92#392—93no—
93#392—91no—
94#376—91no—
95C24×C3C22×D314yes—
96C23×D3—312no—
97C22×C3×C4C22×D3112yes—
98C22×C3×C4C22×D3112yes—
99C2×#67—624no—
100C2×#67—624no—
101C2×#67—624no—
102C22×Dic3—34no—
103C22×Dic3—312no—
104C22×Dic3—34no—
105C22×Dic3—624no—
106C2×D12—648no—
107C2×D12—624no—
108C2×C4×D3—624no—
109C2×C4×D3—648no—
110C3×C4⋊C4—224no—
111C3×C22⋊C4—224no—
112(C2×D3)⋊C4—648no—
113(C2×D3)⋊C4—624no—
114Dic3⋊C4—624no—
115C4×Dic3—348no—
116C22×C32—26no—
117C22×C32—43no—
118C22×C32—41no—
119C22×C32C22×D413yes—
120C22×C32C2×#4111yescharacteristic
121C22×C32C2×#4113yes—
122C2×C3⋊D3—212no—
123C2×C3⋊D3—26no—
124C2×C3⋊D3—43no—
125C2×C3⋊D3—46no—
126C2×C3⋊D3—43no—
127C32×C4—26no—
128C32×C4—43no—
129C3⋊Dic3—26no—
130C3⋊Dic3—41no—
131C3⋊Dic3#12714yes—
132C22×D4—93no—
133C22×D4—93no—
134C23×C4—91no—
135C23×C4—93no—
136C4×D4—1812no—
137C4×D4—1812no—
138C2×C4⋊C4—93no—
139C2×C4⋊C4C2×C3⋊D313yes—
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—212no—
147C23×C3—212no—
148C23×C3#23918yes—
149C23×C3C23×D314yes—
150C22×D3—324no—
151C22×D3—624no—
152C22×D3—612no—
153C22×D3—612no—
154C22×D3—624no—
155C2×C3×C4—224no—
156C2×C3×C4—212no—
157C2×C3×C4—224no—
158C2×C3×C4D3×D4124yes—
159#67—696no—
160C2×Dic3—324no—
161C2×Dic3—324no—
162C2×Dic3—612no—
163C2×Dic3—612no—
164C2×Dic3—612no—
165C2×Dic3—1216no—
166D12—696no—
167C4×D3—1248no—
168C2×C32—42no—
169C2×C32#52513yes—
170C2×C32#52513yes—
171C2×C32C2×#12711yescharacteristic
172C3⋊D3—46no—
173C24—93no—
174C24C22×C3⋊D311yescharacteristic
175C2×D4—1812no—
176C2×D4—186no—
177C2×D4—186no—
178C2×D4—186no—
179C2×D4—186no—
180C22×C4—91no—
181C22×C4—93no—
182C22×C4—91no—
183C22×C4—186no—
184C22×C4—1812no—
185C22×C4—186no—
186C22×C4C22×C3⋊D313yes—
187C22×C4C22×C3⋊D313yes—
188C4⋊C4—26no—
189C4⋊C4—186no—
190C22⋊C4—26no—
191C22⋊C4—1812no—
192C22⋊C4—186no—
193C42—912no—
194C22×C3—224no—
195C22×C3—412no—
196C22×C3—44no—
197C22×C3C2×D3×D4112yes—
198C22×C3C2×#23914yes—
199C22×C3D3×#41112yes—
200C2×D3—648no—
201C2×D3—624no—
202C2×D3—1212no—
203C2×D3—1212no—
204C2×D3—1224no—
205C3×C4—224no—
206C3×C4—412no—
207Dic3—316no—
208Dic3—624no—
209Dic3—124no—
210C32#239711yescharacteristic, complemented, Sylow
211C23—23no—
212C23—23no—
213C23—96no—
214C23—183no—
215C23—186no—
216C23—183no—
217C23—186no—
218C23#383212yes—
219C23C23×C3⋊D311yescharacteristic
220D4—1824no—
221D4—1824no—
222C2×C4—26no—
223C2×C4—23no—
224C2×C4—26no—
225C2×C4—96no—
226C2×C4—96no—
227C2×C4—183no—
228C2×C4—183no—
229C2×C4—183no—
230C2×C4—3612no—
231C2×C4—364no—
232C2×C4D4×C3⋊D316yes—
233C2×C3—48no—
234C2×C3#5627112yes—
235C2×C3#5656112yes—
236C2×C3D3×#12714yes—
237D3—1224no—
238C22—26no—
239C22—43no—
240C22—41no—
241C22—186no—
242C22—1812no—
243C22—366no—
244C22—363no—
245C22—363no—
246C22C2×D4×C3⋊D313yes—
247C22C2×#383211yescharacteristic
248C22#41×C3⋊D313yes—
249C4—26no—
250C4—43no—
251C4—94no—
252C4—186no—
253C4—361no—
254C3#7801914yescomplemented
255C2—42no—
256C2—366no—
257C2#1059609813yes—
258C2#1059612713yes—
259C2C3⋊D3×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#399C2
hypercenter#399C3⋊D3
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
2. C2×#64090C2semidirect
3. C32×#399C2semidirect
4. #10592692C2semidirect
5. #10592659C2semidirect
6. #10592370C2semidirect
7. #10592347C2semidirect
25. C3×#399D3semidirect
50. C4×C3⋊Dic3D4semidirect
91. #399C3⋊D3semidirect
210. C32#2397semidirect
254. C3#78019semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#640902
C32×#3992
#105926922
#105926592
#105923702
#105923472
#780193