Finite Group Databasebeta

← #26120719

Subgroups — #26120719

Order 12032.

494 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 137 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
1#20248417C211yesmaximal, characteristic
2#20244152C212yesmaximal
3#20243544C211yesmaximal, characteristic
4#20241227C212yesmaximal
5C47×#1296C211yesmaximal, characteristic
6C2×#13094023—22no—
7C2×#13093956—22no—
8C2×#13093955—22no—
9C2×C4×C47⋊C8C2211yescharacteristic
10#15689043—22no—
11#15689019—22no—
12#15688993C2211yescharacteristic
13C4×C4⋊Dic47C2212yes—
14#15688886—22no—
15C2×C4⋊C8×C47C2212yes—
16C47×#384C2211yescharacteristic
17C22×Dic94—22no—
18C22×C47⋊C8—21no—
19#13094023—44no—
20#13094023—44no—
21C2×C4⋊Dic47—22no—
22C2×C4⋊Dic47—21no—
23C2×C4⋊Dic47D412yes—
24C2×C4⋊Dic47D412yes—
25C2×Dic47⋊C4—24no—
26C2×C4×Dic47—22no—
27#13093956—44no—
28#13093955—44no—
29C4×C47⋊C8—21no—
30C4×C47⋊C8Q812yescomplemented
31C47⋊#95—22no—
32C47⋊#95—22no—
33C22×C8×C47—22no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47D412yes—
36C2×C42×C47C2311yescharacteristic
37C4⋊C8×C47—22no—
38C4⋊C8×C47Q814yescomplemented
39C22×C4×C47—22no—
40C22×C4×C47C2×D411yescharacteristic
41C22×C4×C47C2×D412yes—
42C22×Dic47—22no—
43C22×Dic47—22no—
44C22×Dic47—41no—
45C2×Dic94—48no—
46C2×Dic94—82no—
47C2×C8×C47—24no—
48C2×C8×C47—42no—
49C2×C8×C47—42no—
50C4⋊C4×C47—42no—
51C4⋊C4×C47—42no—
52C4⋊C4×C47—42no—
53C42×C47C2×Q812yes—
54C42×C47C2×Q811yescharacteristic
55C42×C47#4111yescharacteristic
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—42no—
59C4⋊Dic47—42no—
60C4⋊Dic47—42no—
61C4⋊Dic47SD1614yes—
62C4⋊Dic47SD1614yes—
63Dic47⋊C4—48no—
64C4×Dic47—42no—
65C4×Dic47—42no—
66C2×C47⋊C8—22no—
67C2×C47⋊C8—22no—
68C2×C47⋊C8—22no—
69C23×C47#12011yescharacteristic
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—44no—
73C2×C4×C47—42no—
74C2×C4×C47C22⋊Q812yes—
75C2×C4×C47C22⋊Q811yescharacteristic
76C2×C4×C47C4⋊Q812yes—
77C2×C4×C47C4⋊Q811yescharacteristic
78C2×C4×C47C2×SD1612yes—
79C2×C4×C47C2×SD1612yes—
80C2×C4×C47AGL(1,ℤ/8)12yes—
81C2×C4×C47#13712yes—
82C2×Dic47—24no—
83C2×Dic47—24no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—82no—
89C2×Dic47—81no—
90Dic94—88no—
91C8×C47—44no—
92C47⋊C8—24no—
93#10574—471nomaximal, Sylow
94C22×C47#39511yescharacteristic
95C22×C47#44812yes—
96C22×C47#45012yes—
97C22×C47#45311yescharacteristic
98C22×C47#45611yescharacteristic
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—82no—
102C4×C47#47512yes—
103C4×C47#47612yes—
104C4×C47#49812yes—
105C4×C47#50112yes—
106Dic47—44no—
107Dic47—44no—
108Dic47—161no—
109#2551—471no—
110#1948—472no—
111#1844—471no—
112#1296D4711yescharacteristic
113#1279—472no—
114C2×C47#162311yescharacteristic
115C2×C47#162911yescharacteristic
116C2×C47#165112yes—
117C2×C47#205812yes—
118C2×C47#206011yescharacteristic
119C2×C4⋊Q8—942no—
120C2×#106—942no—
121C2×#106—942no—
122C2×C4⋊C8C2×D4712yes—
123C2×C4×C8—471no—
124#395—942no—
125#389—942no—
126#384—471no—
127#384C2×D4711yescharacteristic
128C4×C4⋊C4—472no—
129#340—942no—
130C47#1057411yescharacteristic, complemented, Sylow
131C22×Q8—942no—
132C22×C8—22no—
133C22×C8—941no—
134C4⋊Q8—1884no—
135C4⋊Q8—1884no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—472no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—944no—
140C2×C4⋊C4—941no—
141C2×C4⋊C4—942no—
142C2×C4⋊C4D18812yes—
143C2×C42—942no—
144C2×C42C22×D4711yescharacteristic
145#106—1884no—
146#106—1884no—
147C4⋊C8—22no—
148C4⋊C8Dic9414yescomplemented
149C4×C8—472no—
150C4×C8—941no—
151#95—942no—
152#95—942no—
153C2×Q8—3762no—
154C2×Q8—1888no—
155C22×C4—22no—
156C22×C4—942no—
157C22×C4—942no—
158C22×C4—1881no—
159C22×C4C2×D18811yescharacteristic
160C22×C4D4×D4712yes—
161C2×C8—24no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—942no—
165C2×C8—942no—
166C2×C8—942no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—474no—
171C4⋊C4—474no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—1882no—
175C4⋊C4—1888no—
176C4⋊C4—1882no—
177C4⋊C4—1882no—
178C42—1882no—
179C42—1882no—
180C42C2×Dic9412yes—
181C42#1062535211yescharacteristic
182C42Q8×D4711yescharacteristic
183C23#1309399411yescharacteristic
184Q8—3768no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—944no—
190C2×C4—944no—
191C2×C4—3762no—
192C2×C4—3761no—
193C2×C4—1882no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4#1309400112yes—
198C2×C4#1309400411yescharacteristic
199C2×C4#1309402312yes—
200C2×C4#1309402411yescharacteristic
201C2×C4SD16×D4712yes—
202C2×C4SD16×D4712yes—
203C2×C4#1309404812yes—
204C2×C4#1309405612yes—
205C8—44no—
206C8—944no—
207C22#1568904411yescharacteristic
208C22#1568926312yes—
209C22#1568927512yes—
210C22#1568929311yescharacteristic
211C22#1568930811yescharacteristic
212C4—21no—
213C4—21no—
214C4—82no—
215C4—1884no—
216C4—1884no—
217C4—7521no—
218C4#1568940612yes—
219C4#1568941112yes—
220C4#1568952012yes—
221C4#1568953112yes—
222C2#2024246711yescharacteristic
223C2#2024250511yescharacteristic
224C2#2024265212yes—
225C2#2024472012yes—
226C2#2024473411yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1296C2
socle, prime radicalC23×C47#120
hypercenter#1296D47
hypocenterC47#10574
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
30. C4×C47⋊C8Q8semidirect
38. C4⋊C8×C47Q8semidirect
130. C47#10574semidirect
148. C4⋊C8Dic94semidirect

Maximal subgroups

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

subgroupindex
#202484172
#202441522
#202435442
#202412272
C47×#12962
#1057447