Finite Group Databasebeta

← #26105409

Subgroups — #26105409

Order 12032.

366 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 87 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#20244931C211yesmaximal, characteristic
2#20244859C212yesmaximal
3#20241214C211yesmaximal, characteristic
4#20241211C212yesmaximal
5C47×#2809C211yesmaximal, characteristic
6C2×#13093957—22no—
7C2×#13093955—21no—
8C2×#13093948—21no—
9#15688993C2211yescharacteristic
10#15688885—22no—
11#15688878C2211yescharacteristic
12#15688878C2212yes—
13C47×#400—21no—
14C47×#398—22no—
15C47×#391—21no—
16C47×#391C2211yescharacteristic
17C47×#389C2212yes—
18C47×#387—22no—
19C22×C47⋊C8—21no—
20C22×C47⋊C8—22no—
21C2×C4⋊Dic47—21no—
22C2×C4⋊Dic47—22no—
23#13093957—44no—
24#13093955—42no—
25#13093948—42no—
26C22×Q8×C47D411yescharacteristic
27C2×C4⋊C4×C47—22no—
28C2×C4⋊C4×C47—21no—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47D412yes—
31C2×C4⋊C4×C47D412yes—
32C2×C4⋊C4×C47D411yescharacteristic
33C2×C42×C47—21no—
34C2×C42×C47C2311yescharacteristic
35#95×C47—21no—
36#95×C47—22no—
37#95×C47—22no—
38#95×C47—22no—
39#95×C47—22no—
40C2×Q8×C47—21no—
41C2×Q8×C47—41no—
42C2×Q8×C47—41no—
43C2×Q8×C47Q1612yes—
44C22×C4×C47—21no—
45C22×C4×C47—22no—
46C22×C4×C47—22no—
47C22×C4×C47—21no—
48C22×C4×C47C2×D411yescharacteristic
49C22×C4×C47C2×D412yes—
50C22×Dic47—41no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—42no—
54C4⋊C4×C47—41no—
55C4⋊C4×C47—42no—
56C4⋊C4×C47—42no—
57C4⋊C4×C47—81no—
58C4⋊C4×C47—81no—
59C42×C47—41no—
60C42×C47—81no—
61C4⋊Dic47—41no—
62C4⋊Dic47—41no—
63C4⋊Dic47—42no—
64C4⋊Dic47—42no—
65C2×C47⋊C8—22no—
66C2×C47⋊C8—24no—
67C2×C47⋊C8—42no—
68C2×C47⋊C8—41no—
69C2×C47⋊C8—42no—
70C2×C47⋊C8—41no—
71C23×C47#12011yescharacteristic
72Q8×C47—42no—
73Q8×C47—81no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47—41no—
85C2×C4×C47—42no—
86C2×C4×C47—42no—
87C2×C4×C47—42no—
88C2×C4×C47—42no—
89C2×C4×C47C2×Q1611yescharacteristic
90C2×C4×C47#13512yes—
91C2×C4×C47AGL(1,ℤ/8)12yes—
92C2×C4×C47#13711yescharacteristic
93C2×Dic47—82no—
94C2×Dic47—81no—
95C47⋊C8—44no—
96C47⋊C8—42no—
97#7802—471nomaximal, Sylow
98C22×C47#44912yes—
99C22×C47#45111yescharacteristic
100C22×C47#45311yescharacteristic
101C22×C47#45612yes—
102C22×C47#45811yescharacteristic
103C4×C47—22no—
104C4×C47—22no—
105C4×C47—21no—
106C4×C47—21no—
107C4×C47—42no—
108C4×C47—82no—
109C4×C47—82no—
110C4×C47—81no—
111Dic47—161no—
112#2809D4711yescharacteristic
113#2096—471no—
114#2083—472no—
115#1272—471no—
116#1271—472no—
117C2×C47#160912yes—
118C2×C47#161411yescharacteristic
119C2×C47#162411yescharacteristic
120C2×C47#164812yes—
121C2×C47#166011yescharacteristic
122C2×#107—942no—
123C2×#106—941no—
124C2×#103—941no—
125#400—21no—
126#398—22no—
127#391—21no—
128#391C2×D4711yescharacteristic
129#389C2×D4712yes—
130#387—22no—
131#384—471no—
132#340—942no—
133#336—472no—
134#336—471no—
135C47#780211yescharacteristic, complemented, Sylow
136C22×Q8C22⋊D4711yescharacteristic
137C22×C8—942no—
138C22×C8—941no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—942no—
143C2×C4⋊C4—941no—
144C2×C4⋊C4C22⋊D4712yes—
145C2×C4⋊C4C22⋊D4712yes—
146C2×C4⋊C4C22⋊D4711yescharacteristic
147C2×C42—21no—
148C2×C42C22×D4711yescharacteristic
149#107—1884no—
150#106—1882no—
151#103—1882no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156#95—22no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8#1062533712yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—1881no—
166C22×C4C2×C22⋊D4711yescharacteristic
167C22×C4C2×C22⋊D4712yes—
168C2×C8—942no—
169C2×C8—944no—
170C2×C8—1882no—
171C2×C8—1881no—
172C2×C8—1882no—
173C2×C8—1881no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—81no—
181C4⋊C4—81no—
182C4⋊C4—1881no—
183C4⋊C4—1881no—
184C4⋊C4—1882no—
185C4⋊C4—1882no—
186C42—41no—
187C42—81no—
188C23#1309399311yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—3762no—
207C2×C4—3761no—
208C2×C4C2×#1062533711yescharacteristic
209C2×C4#1309404412yes—
210C2×C4#1309404912yes—
211C2×C4#1309405511yescharacteristic
212C8—1884no—
213C8—1882no—
214C22#1568926812yes—
215C22#1568927911yescharacteristic
216C22#1568929111yescharacteristic
217C22#1568930612yes—
218C22#1568931311yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—42no—
224C4—81no—
225C4—82no—
226C4—82no—
227C4—7521no—
228C2#2024238512yes—
229C2#2024241311yescharacteristic
230C2#2024247111yescharacteristic
231C2#2024263012yes—
232C2#2024269911yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2809C2
socle, prime radicalC23×C47#120
hypercenter#2809D47
hypocenterC47#7802
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
135. C47#7802semidirect

Maximal subgroups

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

subgroupindex
#202449312
#202448592
#202412142
#202412112
C47×#28092
#780247