Finite Group Databasebeta

← #26129276

Subgroups — #26129276

Order 12032.

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

normal subgroups only

This group has 394 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#20242395C212yesmaximal
3#20241394C212yesmaximal
4#20241334C211yesmaximal, characteristic
5C47×#2582C211yesmaximal, characteristic
6#15689754C2211yescharacteristic
7#15689453—22no—
8#15689163—21no—
9#15688892C2211yescharacteristic
10#15688883—21no—
11#15688859—22no—
12#15688849C2212yes—
13C2×C4×Q8×C47—21no—
14C47×#398—21no—
15C47×#398C2212yes—
16C47×#391—22no—
17C47×#389—22no—
18C47×#384C2211yescharacteristic
19C2×#10625329—21no—
20#13094023—41no—
21#13094015—41no—
22#13094003—22no—
23#13093983—21no—
24#13093957—41no—
25#13093955—41no—
26#13093955—42no—
27#13093947—42no—
28C22⋊(C47⋊C8)—22no—
29C22×Q8×C47—21no—
30C4×Q8×C47—42no—
31C4×Q8×C47—42no—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47—21no—
36C2×C4⋊C4×C47D411yescharacteristic
37C2×C4⋊C4×C47D412yes—
38C2×C4⋊C4×C47C2311yescharacteristic
39C2×C42×C47—22no—
40C2×C42×C47D411yescharacteristic
41#95×C47—22no—
42#95×C47—21no—
43#95×C47—22no—
44#95×C47D412yes—
45C2×Q8×C47—24no—
46C2×Q8×C47—42no—
47C2×Q8×C47—42no—
48C22×C4×C47—21no—
49C22×C4×C47—22no—
50C22×C4×C47—22no—
51C22×C4×C47—21no—
52C22×C4×C47C2×D411yescharacteristic
53C22×C4×C47C2×D412yes—
54C2×Dic94—22no—
55C4⋊C4×C47—41no—
56C4⋊C4×C47—44no—
57C4⋊C4×C47—42no—
58C4⋊C4×C47—42no—
59C4⋊C4×C47—41no—
60C4⋊C4×C47—42no—
61C4⋊C4×C47—42no—
62C4⋊C4×C47—81no—
63C42×C47—21no—
64C42×C47—44no—
65C42×C47SD1612yes—
66C22⋊Dic47—41no—
67C4⋊Dic47—21no—
68C4⋊Dic47—22no—
69C4⋊Dic47—21no—
70Dic47⋊C4—42no—
71C4×Dic47—41no—
72#10625329—22no—
73#10625329—41no—
74C2×C47⋊C8—41no—
75C2×C47⋊C8—42no—
76C23×C47#12011yescharacteristic
77Q8×C47—48no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—24no—
84C2×C4×C47—22no—
85C2×C4×C47—42no—
86C2×C4×C47—42no—
87C2×C4×C47—42no—
88C2×C4×C47—42no—
89C2×C4×C47—42no—
90C2×C4×C47—42no—
91C2×C4×C47—42no—
92C2×C4×C47—41no—
93C2×C4×C47C2×SD1611yescharacteristic
94C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
95C2×Dic47—41no—
96C2×Dic47—41no—
97Dic94—82no—
98C47⋊C8—42no—
99C47⋊C8—82no—
100#12247—471nomaximal, Sylow
101C22×C47—21no—
102C22×C47—21no—
103C22×C47#45011yescharacteristic
104C22×C47#45611yescharacteristic
105C22×C47B(4,𝔽2)11yescharacteristic
106C4×C47—24no—
107C4×C47—21no—
108C4×C47—21no—
109C4×C47—44no—
110C4×C47—42no—
111C4×C47—82no—
112C4×C47—81no—
113Dic47—81no—
114Dic47—81no—
115#2582D4711yescharacteristic
116#2060—471no—
117#1611—472no—
118#1346—472no—
119#1325—471no—
120C2×C47—21no—
121C2×C47—21no—
122C2×C47#160411yescharacteristic
123C2×C47#219811yescharacteristic
124C2×C47#220511yescharacteristic
125#544—471no—
126C2×C4×Q8—21no—
127#483—942no—
128#428—941no—
129#398—21no—
130#398C2×D4712yes—
131#391—22no—
132#389—22no—
133#384C2×D4711yescharacteristic
134#343—471no—
135#339—941no—
136#328—942no—
137#324—472no—
138C47#1224711yescharacteristic, complemented, Sylow
139C22×Q8—21no—
140C2×M16—941no—
141C4⋊Q8—1881no—
142#125—1881no—
143C22⋊Q8—942no—
144C4×Q8—42no—
145C4×Q8—42no—
146#117—941no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C22⋊D4711yescharacteristic
152C2×C4⋊C4C22⋊D4712yes—
153C2×C4⋊C4C22×D4711yescharacteristic
154C2×C42—22no—
155C2×C42C22⋊D4711yescharacteristic
156#107—1881no—
157#106—1881no—
158#106—1882no—
159#103—1882no—
160C22⋊C8—942no—
161#95—22no—
162#95—21no—
163#95—22no—
164#95C22⋊D4712yes—
165C2×Q8—24no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—942no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4C2×C22⋊D4711yescharacteristic
174C22×C4C2×C22⋊D4712yes—
175M16—942no—
176M16—1881no—
177C2×C8—1882no—
178C2×C8—1881no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—41no—
182C4⋊C4—44no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—81no—
187C4⋊C4—941no—
188C4⋊C4—942no—
189C4⋊C4—941no—
190C4⋊C4—1882no—
191C22⋊C4—1881no—
192C42—21no—
193C42—44no—
194C42—1881no—
195C42#1062533512yes—
196C23#1309399311yescharacteristic
197Q8—48no—
198Q8—3762no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—1881no—
215C2×C4—1881no—
216C2×C4C2×#1062533511yescharacteristic
217C2×C4#1309405011yescharacteristic
218C8—3762no—
219C8—1882no—
220C22—21no—
221C22—21no—
222C22#1568927411yescharacteristic
223C22#1568930611yescharacteristic
224C22#1568931011yescharacteristic
225C4—24no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4—3761no—
233C4—3761no—
234C2—21no—
235C2—21no—
236C2#2024235711yescharacteristic
237C2#2024538411yescharacteristic
238C2#2024541811yescharacteristic
subgroupG/H
centerC22#15689310
commutator, cosocleC2×C4⋊C4×C47C23
FrattiniC2×C4⋊C4C22×D47
FittingC47×#2582C2
socleC22×C47B(4,𝔽2)
prime radicalC23×C47#120
hypercenter#2582D47
hypocenterC47#12247
LCSG ▷ C2×C4⋊C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2582

Complements

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

NH ≅ G/Ntype
138. C47#12247semidirect

Maximal subgroups

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

subgroupindex
#202447332
#202423952
#202413942
#202413342
C47×#25822
#1224747