Finite Group Databasebeta

← #26109621

Subgroups — #26109621

Order 12032.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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×#15688990C211yesmaximal, characteristic
2#20243454C212yesmaximal
3#20241231C211yesmaximal, characteristic
4#20241230C212yesmaximal
5C47×#1280C211yesmaximal, characteristic
6C22×C4×Dic47C2211yescharacteristic
7C2×C22⋊(C47⋊C8)C2212yes—
8#15688990—24no—
9C2×C47⋊#95C412yes—
10C2×C47⋊#95C412yes—
11C2×C47⋊#95C2211yescharacteristic
12#15688877—24no—
13C2×C22⋊C8×C47C2212yes—
14C2×#95×C47C2211yescharacteristic
15C23×Dic47C2×C411yescharacteristic
16C23×Dic47C2×C412yes—
17C23×Dic47C2×C411yescharacteristic
18C22×C47⋊C8—22no—
19C2×C4×Dic47—22no—
20C2×C4×Dic47—21no—
21C2×C4×Dic47—21no—
22C2×C4×Dic47D414yes—
23C22⋊(C47⋊C8)—22no—
24C22⋊(C47⋊C8)—22no—
25C47⋊#95—22no—
26C47⋊#95—24no—
27C47⋊#95—24no—
28C23×C4×C47C2×C412yes—
29C23×C4×C47C2311yescharacteristic
30C22×C8×C47—22no—
31C22⋊C8×C47—22no—
32C22⋊C8×C47—22no—
33#95×C47—22no—
34C24×C47C22×C411yescharacteristic
35C22×C4×C47—22no—
36C22×C4×C47—22no—
37C22×C4×C47—22no—
38C22×C4×C47—42no—
39C22×C4×C47—42no—
40C22×C4×C47—42no—
41C22×C4×C47C2×D412yes—
42C22×C4×C47#4112yes—
43C22×C4×C47#4111yescharacteristic
44C22×C4×C47#4111yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—21no—
47C22×Dic47—21no—
48C22×Dic47—21no—
49C22×Dic47—22no—
50C22×Dic47—22no—
51C22×Dic47—22no—
52C22×Dic47—22no—
53C22×Dic47—22no—
54C22×Dic47—41no—
55C22×Dic47—41no—
56C22×Dic47—42no—
57C22×Dic47—42no—
58C22×Dic47C22⋊C412yes—
59C22×Dic47C22⋊C412yes—
60C2×C8×C47—44no—
61C2×C8×C47—42no—
62C4×Dic47—24no—
63C4×Dic47—24no—
64C2×C47⋊C8—44no—
65C2×C47⋊C8—42no—
66C23×C47—22no—
67C23×C47—21no—
68C23×C47—21no—
69C23×C47C2×C22⋊C411yescharacteristic
70C23×C47#11711yescharacteristic
71C23×C47#11711yescharacteristic
72C23×C47#13112yes—
73C23×C47#13112yes—
74C2×C4×C47—24no—
75C2×C4×C47—42no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—42no—
81C2×C4×C47—82no—
82C2×C4×C47—82no—
83C2×C4×C47#12312yes—
84C2×C4×C47#12312yes—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—24no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—42no—
91C2×Dic47—42no—
92C2×Dic47—41no—
93C2×Dic47—42no—
94C2×Dic47—41no—
95C2×Dic47—42no—
96C2×Dic47—42no—
97C2×Dic47—42no—
98C2×Dic47—82no—
99C2×Dic47—82no—
100C8×C47—82no—
101C47⋊C8—82no—
102#8705—471nomaximal, Sylow
103C22×C47—21no—
104C22×C47—21no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—22no—
108C22×C47—22no—
109C22×C47—22no—
110C22×C47—22no—
111C22×C47#38111yescharacteristic
112C22×C47#40812yes—
113C22×C47#41012yes—
114C22×C47#41311yescharacteristic
115C22×C47#41311yescharacteristic
116C22×C47#43311yescharacteristic
117C22×C47#43312yes—
118C22×C47#43311yescharacteristic
119C4×C47—22no—
120C4×C47—22no—
121C4×C47—82no—
122Dic47—42no—
123Dic47—42no—
124Dic47—82no—
125C2×#383—471no—
126#1817—472no—
127#1280—472no—
128#1280—471no—
129#1280D4711yescharacteristic
130C2×C47—21no—
131C2×C47—22no—
132C2×C47—21no—
133C2×C47#147312yes—
134C2×C47#147312yes—
135C2×C47#181811yescharacteristic
136C2×C47#182011yescharacteristic
137C2×C47#182211yescharacteristic
138C22×C42—471no—
139C2×C22⋊C8—472no—
140C2×C22⋊C8C2×D4712yes—
141#383—944no—
142C2×#95—472no—
143C2×#95—472no—
144C2×#95—471no—
145C2×#95C2×D4711yescharacteristic
146#336—944no—
147C47#870511yescharacteristic, complemented, Sylow
148C23×C4—471no—
149C23×C4—471no—
150C23×C4—472no—
151C23×C4C4×D4712yes—
152C23×C4C22×D4711yescharacteristic
153C22×C8—22no—
154C22×C8—942no—
155C2×C42—474no—
156C2×C42—942no—
157C2×C42—941no—
158C2×C42—941no—
159C22⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—942no—
162C22⋊C8—942no—
163#95—22no—
164#95—944no—
165#95—944no—
166#95—942no—
167C24C2×C4×D4711yescharacteristic
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—472no—
175C22×C4—472no—
176C22×C4—941no—
177C22×C4—941no—
178C22×C4—941no—
179C22×C4—941no—
180C22×C4—942no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4—942no—
184C22×C4—942no—
185C22×C4—1881no—
186C22×C4—1881no—
187C22×C4—1882no—
188C22×C4—1882no—
189C22×C4#1062535012yes—
190C22×C4D4×D4712yes—
191C22×C4#1062535211yescharacteristic
192C22×C4#1062535411yescharacteristic
193C2×C8—44no—
194C2×C8—42no—
195C2×C8—1884no—
196C2×C8—1882no—
197C42—944no—
198C42—944no—
199C23—22no—
200C23—21no—
201C23—21no—
202C23C22⋊C4×D4711yescharacteristic
203C23#1309398111yescharacteristic
204C23#1309398211yescharacteristic
205C23#1309403012yes—
206C23#1309403212yes—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—944no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—3762no—
222C2×C4—3762no—
223C2×C4—1882no—
224C2×C4—1882no—
225C2×C4—1882no—
226C2×C4—1882no—
227C2×C4—1882no—
228C2×C4—1881no—
229C2×C4—1882no—
230C2×C4—1881no—
231C2×C4#1309400612yes—
232C2×C4#1309400912yes—
233C8—82no—
234C8—3762no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22#1568898511yescharacteristic
244C22#1568908812yes—
245C22#1568909512yes—
246C22#1568910411yescharacteristic
247C22#1568910611yescharacteristic
248C22#1568918211yescharacteristic
249C22#1568918312yes—
250C22#1568918511yescharacteristic
251C4—22no—
252C4—22no—
253C4—82no—
254C4—3762no—
255C4—1882no—
256C4—1882no—
257C2—21no—
258C2—22no—
259C2—21no—
260C2#2024175412yes—
261C2#2024175612yes—
262C2#2024345811yescharacteristic
263C2#2024346411yescharacteristic
264C2#2024347011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1280C2
socleC23×C47C2×C22⋊C4
cosocleC23×C4×C47C23
hypercenter#1280D47
hypocenterC47#8705
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
147. C47#8705semidirect

Maximal subgroups

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

subgroupindex
C2×#156889902
#202434542
#202412312
#202412302
C47×#12802
#870547