Finite Group Databasebeta

← #26129338

Subgroups — #26129338

Order 12032.

342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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#20244733C211yesmaximal, characteristic
2#20242429C212yesmaximal
3#20241415C212yesmaximal
4#20241334C211yesmaximal, characteristic
5C47×#2571C211yesmaximal, characteristic
6#15689754C2211yescharacteristic
7#15689458—22no—
8#15689163—21no—
9#15688892C2211yescharacteristic
10#15688883—21no—
11#15688859—22no—
12#15688849C2212yes—
13C47×#400—21no—
14C47×#400C2212yes—
15C47×#389—22no—
16C47×#384C2211yescharacteristic
17C47×#382—22no—
18C4×C4⋊C4×C47—21no—
19C2×#10625329—21no—
20#13094023—41no—
21#13094015—41no—
22#13094003—22no—
23#13093983—21no—
24#13093957—41no—
25#13093957—42no—
26#13093955—41no—
27#13093947—42no—
28C22⋊(C47⋊C8)—22no—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47—21no—
31C2×C4⋊C4×C47—22no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47D411yescharacteristic
34C2×C4⋊C4×C47D412yes—
35C2×C4⋊C4×C47C2311yescharacteristic
36C2×C42×C47—22no—
37C2×C42×C47D411yescharacteristic
38#95×C47—21no—
39#95×C47—22no—
40#95×C47—22no—
41#95×C47—22no—
42#95×C47D412yes—
43C22×C4×C47—21no—
44C22×C4×C47—22no—
45C22×C4×C47—22no—
46C22×C4×C47—21no—
47C22×C4×C47C2×D411yescharacteristic
48C22×C4×C47C2×D412yes—
49C2×Dic94—22no—
50C4⋊C4×C47—41no—
51C4⋊C4×C47—42no—
52C4⋊C4×C47—44no—
53C4⋊C4×C47—42no—
54C4⋊C4×C47—42no—
55C4⋊C4×C47—41no—
56C4⋊C4×C47—81no—
57C42×C47—21no—
58C42×C47—44no—
59C42×C47Q1612yes—
60C22⋊Dic47—41no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64Dic47⋊C4—42no—
65C4×Dic47—41no—
66#10625329—22no—
67#10625329—41no—
68C2×C47⋊C8—41no—
69C2×C47⋊C8—42no—
70C23×C47#12011yescharacteristic
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—42no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47—42no—
84C2×C4×C47—41no—
85C2×C4×C47—42no—
86C2×C4×C47C2×Q1611yescharacteristic
87C2×C4×C47#13711yescharacteristic
88C2×Dic47—41no—
89C2×Dic47—41no—
90Dic94—82no—
91C47⋊C8—42no—
92C47⋊C8—82no—
93#12257—471nomaximal, Sylow
94C22×C47—21no—
95C22×C47—21no—
96C22×C47#45111yescharacteristic
97C22×C47#45611yescharacteristic
98C22×C47B(4,𝔽2)11yescharacteristic
99C4×C47—24no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—42no—
103C4×C47—82no—
104C4×C47—81no—
105C4×C47—82no—
106Dic47—81no—
107Dic47—81no—
108#2571D4711yescharacteristic
109#2060—471no—
110#1617—472no—
111#1353—472no—
112#1325—471no—
113C2×C47—21no—
114C2×C47—21no—
115C2×C47#160511yescharacteristic
116C2×C47#219811yescharacteristic
117C2×C47#220411yescharacteristic
118#544—471no—
119#484—942no—
120#428—941no—
121#400—21no—
122#400C2×D4712yes—
123#389—22no—
124#384C2×D4711yescharacteristic
125#382—22no—
126C4×C4⋊C4—21no—
127#343—471no—
128#339—941no—
129#328—942no—
130#324—472no—
131C47#1225711yescharacteristic, complemented, Sylow
132C2×M16—941no—
133C4⋊Q8—1881no—
134#125—1881no—
135C22⋊Q8—942no—
136#117—941no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4C22⋊D4711yescharacteristic
142C2×C4⋊C4C22⋊D4712yes—
143C2×C4⋊C4C22×D4711yescharacteristic
144C2×C42—22no—
145C2×C42C22⋊D4711yescharacteristic
146#107—1881no—
147#107—1882no—
148#106—1881no—
149#103—1882no—
150C22⋊C8—942no—
151#95—21no—
152#95—22no—
153#95—22no—
154#95—22no—
155#95C22⋊D4712yes—
156C2×Q8—942no—
157C22×C4—21no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—21no—
161C22×C4C2×C22⋊D4711yescharacteristic
162C22×C4C2×C22⋊D4712yes—
163M16—942no—
164M16—1881no—
165C2×C8—1882no—
166C2×C8—1881no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—44no—
172C4⋊C4—42no—
173C4⋊C4—81no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4—942no—
177C4⋊C4—1882no—
178C22⋊C4—1881no—
179C42—21no—
180C42—44no—
181C42—1881no—
182C42#1062533712yes—
183C23#1309399311yescharacteristic
184Q8—3762no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—1881no—
201C2×C4—1881no—
202C2×C4C2×#1062533711yescharacteristic
203C2×C4#1309405511yescharacteristic
204C8—3762no—
205C8—1882no—
206C22—21no—
207C22—21no—
208C22#1568927911yescharacteristic
209C22#1568930611yescharacteristic
210C22#1568931011yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—82no—
216C4—81no—
217C4—82no—
218C4—3761no—
219C4—3761no—
220C2—21no—
221C2—21no—
222C2#2024236211yescharacteristic
223C2#2024538411yescharacteristic
224C2#2024541411yescharacteristic
subgroupG/H
centerC22#15689310
commutator, cosocleC2×C4⋊C4×C47C23
FrattiniC2×C4⋊C4C22×D47
FittingC47×#2571C2
socleC22×C47B(4,𝔽2)
prime radicalC23×C47#120
hypercenter#2571D47
hypocenterC47#12257
LCSG ▷ C2×C4⋊C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
131. C47#12257semidirect

Maximal subgroups

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

subgroupindex
#202447332
#202424292
#202414152
#202413342
C47×#25712
#1225747