Finite Group Databasebeta

← #26122600

Subgroups — #26122600

Order 12032.

1258 conjugacy classes of subgroups; only the 263 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 263 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×#15688984C213yesmaximal
2C2×#15688890C213yesmaximal
3C47×#2273C211yesmaximal, characteristic
4C24×Dic47C2211yescharacteristic
5C22×C22⋊Dic47C2213yes—
6#15688984—26no—
7#15688984C4112yescomplemented
8C2×C47⋊#95—26no—
9#15688890—26no—
10C22×C22⋊C4×C47C2213yes—
11C4×C22⋊C4×C47—26no—
12C23×Dic47—23no—
13C23×Dic47—23no—
14C23×Dic47—26no—
15C23×Dic47—23no—
16C23×Dic47C2×C416yes—
17C2×C22⋊Dic47—26no—
18C2×C22⋊Dic47—26no—
19C2×C22⋊Dic47—23no—
20C2×C22⋊Dic47C2×C416yes—
21C47⋊#95—224no—
22C25×C47C2311yescharacteristic
23C23×C4×C47D416yes—
24C2×C22⋊C4×C47—26no—
25C2×C22⋊C4×C47—26no—
26C2×C22⋊C4×C47C2×C416yes—
27C2×C22⋊C4×C47D416yes—
28C2×C42×C47—24no—
29#95×C47—24no—
30C24×C47—44no—
31C24×C47C22×C413yes—
32C24×C47C2×D413yes—
33C24×C47C2×D413yes—
34C24×C47#4116yes—
35C22×C4×C47—26no—
36C22×C4×C47—26no—
37C22×C4×C47—412no—
38C22×C4×C47C22⋊C4112yes—
39C22×Dic47—26no—
40C22×Dic47—26no—
41C22×Dic47—212no—
42C22×Dic47—212no—
43C22×Dic47—26no—
44C22×Dic47—41no—
45C22×Dic47—46no—
46C22×Dic47—43no—
47C22×Dic47—43no—
48C22×Dic47—42no—
49C22×Dic47—41no—
50C22×Dic47—412no—
51C22×Dic47—46no—
52C22×Dic47C4214yescomplemented
53C22⋊C4×C47—212no—
54C22⋊C4×C47—212no—
55C42×C47—84no—
56C22⋊Dic47—212no—
57C22⋊Dic47—43no—
58C22⋊Dic47—43no—
59C23×C47—212no—
60C23×C47—46no—
61C23×C47—46no—
62C23×C47—412no—
63C23×C47C2×C4211yescharacteristic
64C23×C47C2×C22⋊C413yes—
65C23×C47#11713yes—
66C23×C47C4×D416yes—
67C23×C47C4×D416yes—
68C23×C47#12011yescharacteristic
69C23×C47#12116yes—
70C23×C47#12313yes—
71C23×C47#12413yes—
72C23×C47#12612yes—
73C23×C47#12711yescharacteristic
74C2×C4×C47—212no—
75C2×C4×C47—412no—
76C2×C4×C47—412no—
77C2×C4×C47—86no—
78C2×Dic47—212no—
79C2×Dic47—46no—
80C2×Dic47—412no—
81C2×Dic47—46no—
82C2×Dic47—412no—
83C2×Dic47—46no—
84C2×Dic47—812no—
85#10936—471nomaximal, Sylow
86C22×C47—26no—
87C22×C47—212no—
88C22×C47—26no—
89C22×C47—212no—
90C22×C47—41no—
91C22×C47—43no—
92C22×C47—46no—
93C22×C47—43no—
94C22×C47—42no—
95C22×C47—41no—
96C22×C47C4×C22⋊C413yes—
97C22×C47#38613yes—
98C22×C47#38816yes—
99C22×C47#39013yes—
100C22×C47#45814yes—
101C4×C47—412no—
102Dic47—44no—
103Dic47—86no—
104C2×#381—473no—
105#2273D4711yescharacteristic
106C2×#342—473no—
107C2×C47—23no—
108C2×C47—23no—
109C2×C47—26no—
110C2×C47#143711yescharacteristic
111C2×C47#189016yes—
112C24×C4—471no—
113C22×C22⋊C4—473no—
114C22×C22⋊C4C2×D4713yes—
115#381—4712no—
116#381—946no—
117C4×C22⋊C4—26no—
118C2×#95—946no—
119#342—946no—
120C47#1093611yescharacteristic, complemented, Sylow
121C25C22×D4711yescharacteristic
122C23×C4—476no—
123C23×C4—943no—
124C23×C4—946no—
125C23×C4—943no—
126C23×C4—943no—
127C23×C4C22⋊D4716yes—
128C2×C22⋊C4—26no—
129C2×C22⋊C4—26no—
130C2×C22⋊C4—476no—
131C2×C22⋊C4—946no—
132C2×C22⋊C4—946no—
133C2×C22⋊C4—943no—
134C2×C22⋊C4C4×D4716yes—
135C2×C22⋊C4D18816yes—
136C2×C42—24no—
137#95—24no—
138#95—9424no—
139C24—44no—
140C24C2×C4×D4713yes—
141C24C2×D18813yes—
142C24#1062535016yes—
143C24C2×C22⋊D4713yes—
144C22×C4—26no—
145C22×C4—26no—
146C22×C4—412no—
147C22×C4—474no—
148C22×C4—946no—
149C22×C4—946no—
150C22×C4—9412no—
151C22×C4—9412no—
152C22×C4—946no—
153C22×C4—18812no—
154C22×C4—1886no—
155C22×C4—1881no—
156C22×C4—1886no—
157C22×C4—1883no—
158C22×C4—1883no—
159C22×C4—1882no—
160C22×C4—1881no—
161C22×C4(C2×D47)⋊C4112yes—
162C22⋊C4—212no—
163C22⋊C4—212no—
164C22⋊C4—9412no—
165C22⋊C4—1883no—
166C22⋊C4—1883no—
167C42—84no—
168C23—212no—
169C23—46no—
170C23—46no—
171C23—412no—
172C23C42×D4711yescharacteristic
173C23C2×(C2×D47)⋊C413yes—
174C23#1309398113yes—
175C23C4×C22⋊D4716yes—
176C23C4×D18816yes—
177C23#1309399311yescharacteristic
178C23#1309399816yes—
179C23#1309400713yes—
180C23#1309401213yes—
181C23#1309401812yes—
182C23#1309402111yescharacteristic
183C2×C4—212no—
184C2×C4—412no—
185C2×C4—412no—
186C2×C4—86no—
187C2×C4—9412no—
188C2×C4—37612no—
189C2×C4—18812no—
190C2×C4—1886no—
191C2×C4—1886no—
192C2×C4—18812no—
193C2×C4—1886no—
194C22—26no—
195C22—26no—
196C22—212no—
197C22—212no—
198C22—41no—
199C22—43no—
200C22—46no—
201C22—43no—
202C22—42no—
203C22—41no—
204C22C4×(C2×D47)⋊C413yes—
205C22#1568900213yes—
206C22#1568901416yes—
207C22#1568902513yes—
208C22#1568931314yes—
209C4—412no—
210C4—3766no—
211C4—1884no—
212C2—23no—
213C2—23no—
214C2—26no—
215C2#2024162611yescharacteristic
216C2#2024380116yes—
subgroupG/H
centerC23#13093993
commutatorC23×C47C2×C42
FrattiniC25C22×D47
FittingC47×#2273C2
socleC23×C47#120
prime radical, cosocleC25×C47C23
hypercenter#2273D47
hypocenterC47#10936
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ #2273

Complements

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

NH ≅ G/Ntype
7. #15688984C4semidirect
52. C22×Dic47C42semidirect
120. C47#10936semidirect

Maximal subgroups

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

subgroupindex
C2×#156889842
C2×#156888902
C47×#22732
#1093647