Finite Group Databasebeta

← #11808216

Subgroups — #11808216

Order 1152.

2832 conjugacy classes of subgroups; only the 319 normal subgroups are shown.

normal subgroups only

This group has 2832 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
1C22×#3832C211yesmaximal, characteristic, complemented
2C2×#64090C213yesmaximal, complemented
3C32×#393C211yesmaximal, characteristic, complemented
4#10592929C211yesmaximal, characteristic, complemented
5#10592659C213yesmaximal, complemented
6#10592371C213yesmaximal, complemented
7#10592365C213yesmaximal, complemented
8#76777—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#638C2213yes—
11C23×C3⋊Dic3C2211yescharacteristic
12C2×#3832—212no—
13C22×C4⋊(C3⋊D3)C2213yes—
14C22×C4×C3⋊D3C2213yes—
15C2×C32×C22⋊C4C2213yes—
16C2×#3752C2216yes—
17C2×#3752C2213yes—
18C2×#3750C2213yes—
19C2×C4×C3⋊Dic3C2213yes—
20#64090—212no—
21C32×#95C2213yes—
22#63658C2213yes—
23C22×#239—34no—
24C2×#67⋊C4—312no—
25C3×#393D314yescomplemented
26#5230—34no—
27#4960—312no—
28#4672—312no—
29#4666—312no—
30C24×C32C2311yescharacteristic
31C23×C3⋊D3C2313yes—
32C2×C32×Q8—26no—
33C22×C32×C4C2313yes—
34C22×C32×C4C2313yes—
35C2×#638—26no—
36C2×#638—26no—
37C2×#638—26no—
38C22×C3⋊Dic3—26no—
39C22×C3⋊Dic3C2311yescharacteristic
40C22×C3⋊Dic3C2313yes—
41C22×C3⋊Dic3C2311yescharacteristic
42#3832—232no—
43C2×C4⋊(C3⋊D3)—212no—
44C2×C4⋊(C3⋊D3)—26no—
45C2×C4×C3⋊D3—212no—
46C2×C4×C3⋊D3D4112yescomplemented
47C32×C22⋊C4—26no—
48#3752—26no—
49#3752—212no—
50#3750—26no—
51C4×C3⋊Dic3—26no—
52#2388—91noSylow
53C22×C3×Q8C2×D314yes—
54C22×#67—312no—
55C23×Dic3—34no—
56C2×#239—648no—
57C22×D12—312no—
58C22×C4×D3—312no—
59C2×C3×C22⋊C4C2×D3112yes—
60C2×(C2×D3)⋊C4—324no—
61C2×(C2×D3)⋊C4—312no—
62C2×Dic3⋊C4—312no—
63C2×C4×Dic3—312no—
64#67⋊C4—648no—
65C3×#95C2×D3112yes—
66C3⋊#95—312no—
67C23×C32—23no—
68C23×C32—23no—
69C23×C32#4112yescomplemented
70C23×C32C2411yescharacteristic
71C22×C3⋊D3—26no—
72C22×C3⋊D3—26no—
73C22×C3⋊D3—23no—
74C22×C3⋊D3—23no—
75C22×C3⋊D3C2×D416yes—
76C32×Q8—28no—
77C2×C32×C4—26no—
78C2×C32×C4—23no—
79C2×C32×C4—26no—
80C2×C32×C4C2×D416yes—
81#638—224no—
82C2×C3⋊Dic3—23no—
83C2×C3⋊Dic3—23no—
84C2×C3⋊Dic3—23no—
85C2×C3⋊Dic3—44no—
86C2×C3⋊Dic3C2×D416yes—
87C2×C3⋊Dic3#4116yescomplemented
88C4⋊(C3⋊D3)—224no—
89C4×C3⋊D3—224no—
90C22×#41—91no—
91C2×C4×D4—93no—
92#395—91no—
93#394—93no—
94#393C3⋊D311yescharacteristic, complemented
95#392—93no—
96C4×C22⋊C4—93no—
97C24×C3C22×D314yes—
98C23×D3—312no—
99C2×C3×Q8—224no—
100C22×C3×C4C22×D3112yes—
101C22×C3×C4C22×D3112yes—
102C2×#67—624no—
103C2×#67—624no—
104C2×#67—624no—
105C22×Dic3—34no—
106C22×Dic3—312no—
107C22×Dic3—34no—
108C22×Dic3—624no—
109#239—6128no—
110C2×D12—648no—
111C2×D12—624no—
112C2×C4×D3—348no—
113C2×C4×D3—648no—
114C3×C22⋊C4—224no—
115(C2×D3)⋊C4—648no—
116(C2×D3)⋊C4—624no—
117Dic3⋊C4—624no—
118C4×Dic3—624no—
119C22×C32—26no—
120C22×C32—41no—
121C22×C32—43no—
122C22×C32C22×D413yes—
123C22×C32C2×#4111yescharacteristic
124C22×C32C2×#4113yes—
125C2×C3⋊D3—26no—
126C2×C3⋊D3—26no—
127C2×C3⋊D3—26no—
128C2×C3⋊D3—46no—
129C2×C3⋊D3—46no—
130C32×C4—26no—
131C32×C4—43no—
132C3⋊Dic3—26no—
133C3⋊Dic3—41no—
134C3⋊Dic3#12014yes—
135C2×#41—1812no—
136C22×Q8C2×C3⋊D311yescharacteristic
137C22×D4—93no—
138C22×D4—93no—
139C23×C4—93no—
140C23×C4—91no—
141C4×D4—1812no—
142C2×C4⋊C4—93no—
143C2×C22⋊C4—93no—
144C2×C22⋊C4—96no—
145C2×C22⋊C4C2×C3⋊D313yes—
146C2×C42—93no—
147#95—93no—
148#95C2×C3⋊D313yes—
149C23×C3—212no—
150C23×C3—212no—
151C23×C3#23918yescomplemented
152C23×C3C23×D314yes—
153C22×D3—324no—
154C22×D3—624no—
155C22×D3—612no—
156C22×D3—624no—
157C22×D3—612no—
158C3×Q8—232no—
159C2×C3×C4—224no—
160C2×C3×C4—212no—
161C2×C3×C4—224no—
162C2×C3×C4D3×D4124yes—
163#67—696no—
164C2×Dic3—324no—
165C2×Dic3—324no—
166C2×Dic3—612no—
167C2×Dic3—612no—
168C2×Dic3—612no—
169C2×Dic3—1216no—
170D12—696no—
171C4×D3—696no—
172C2×C32—42no—
173C2×C32C2×#12011yescharacteristic
174C2×C32#52513yes—
175C2×C32#53213yes—
176C3⋊D3—46no—
177C24—93no—
178C24C22×C3⋊D311yescharacteristic
179#41—1832no—
180C2×Q8—26no—
181C2×D4—1812no—
182C2×D4—186no—
183C2×D4—186no—
184C2×D4—186no—
185C2×D4—186no—
186C22×C4—91no—
187C22×C4—93no—
188C22×C4—912no—
189C22×C4—91no—
190C22×C4—1812no—
191C22×C4—186no—
192C22×C4C22×C3⋊D313yes—
193C22×C4C22×C3⋊D313yes—
194C4⋊C4—186no—
195C22⋊C4—26no—
196C22⋊C4—1812no—
197C22⋊C4—186no—
198C42—186no—
199C22×C3—224no—
200C22×C3—412no—
201C22×C3—44no—
202C22×C3C2×D3×D4112yes—
203C22×C3C2×#23914yes—
204C22×C3D3×#41112yes—
205C2×D3—624no—
206C2×D3—624no—
207C2×D3—624no—
208C2×D3—1224no—
209C2×D3—1224no—
210C3×C4—224no—
211C3×C4—412no—
212Dic3—316no—
213Dic3—624no—
214Dic3—124no—
215C32#238811yescharacteristic, complemented, Sylow
216C23—23no—
217C23—23no—
218C23—96no—
219C23—186no—
220C23—183no—
221C23—186no—
222C23—183no—
223C23#383212yescomplemented
224C23C23×C3⋊D311yescharacteristic
225Q8—28no—
226D4—1824no—
227D4—1824no—
228C2×C4—26no—
229C2×C4—23no—
230C2×C4—26no—
231C2×C4—96no—
232C2×C4—96no—
233C2×C4—1824no—
234C2×C4—183no—
235C2×C4—183no—
236C2×C4—183no—
237C2×C4—364no—
238C2×C4D4×C3⋊D316yes—
239C2×C3—48no—
240C2×C3D3×#12014yes—
241C2×C3#5627112yes—
242C2×C3#5668112yes—
243D3—1224no—
244C22—26no—
245C22—43no—
246C22—41no—
247C22—186no—
248C22—186no—
249C22—186no—
250C22—366no—
251C22—366no—
252C22C2×D4×C3⋊D313yes—
253C22C2×#383211yescharacteristic
254C22#41×C3⋊D313yes—
255C4—26no—
256C4—43no—
257C4—94no—
258C4—186no—
259C4—361no—
260C3#7677714yescomplemented
261C2—42no—
262C2—366no—
263C2C3⋊D3×#12011yescharacteristic
264C2#1059609813yes—
265C2#1059613913yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#393C2
hypercenter#393C3⋊D3
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C2×#64090C2semidirect
3. C32×#393C2semidirect
4. #10592929C2semidirect
5. #10592659C2semidirect
6. #10592371C2semidirect
7. #10592365C2semidirect
25. C3×#393D3semidirect
46. C2×C4×C3⋊D3D4semidirect
69. C23×C32#41semidirect
87. C2×C3⋊Dic3#41semidirect
94. #393C3⋊D3semidirect
151. C23×C3#239semidirect
215. C32#2388semidirect
223. C23#3832semidirect
260. C3#76777semidirect

Maximal subgroups

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

subgroupindex
C22×#38322
C2×#640902
C32×#3932
#105929292
#105926592
#105923712
#105923652
#767773