Finite Group Databasebeta

← #26116387

Subgroups — #26116387

Order 12032.

424 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 127 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#20251751C211yesmaximal, characteristic
2#20243241C211yesmaximal, characteristic
3#20241270C214yesmaximal
4C47×#1745C211yesmaximal, characteristic
5C2×#13094016C412yes—
6C2×C4⋊(C47⋊C8)—21no—
7C2×#13093935C2212yes—
8#15689021—21no—
9#15689021—21no—
10#15689021—21no—
11#15689021—21no—
12#15688993C411yescharacteristic
13#15688993C411yescharacteristic
14#15688989C2212yes—
15#15688878—21no—
16C2×#97×C47C2212yes—
17C43×C47C2211yescharacteristic
18C47×#336—21no—
19C47×#336—21no—
20C22×C47⋊C8—22no—
21#13094016—44no—
22C2×C4⋊Dic47—21no—
23C2×C4⋊Dic47—21no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47C2×C412yes—
27C2×C4⋊Dic47C2×C412yes—
28C2×Dic47⋊C4—22no—
29C2×Dic47⋊C4—22no—
30C4⋊(C47⋊C8)—24no—
31#13093935—24no—
32C47⋊#95—22no—
33C47⋊#95—22no—
34C22×C8×C47—22no—
35C2×C42×C47C2×C411yescharacteristic
36C2×C42×C47C2×C411yescharacteristic
37C2×C42×C47D411yescharacteristic
38C2×C42×C47D411yescharacteristic
39C2×C42×C47D411yescharacteristic
40C2×C42×C47D411yescharacteristic
41C2×C42×C47C2311yescharacteristic
42#97×C47—22no—
43#97×C47Q814yes—
44C22×C4×C47C22⋊C411yescharacteristic
45C22×C4×C47C22⋊C411yescharacteristic
46C22×C4×C47C22⋊C411yescharacteristic
47C22×C4×C47C22⋊C411yescharacteristic
48C22×C4×C47C22×C411yescharacteristic
49C22×C4×C47C2×D411yescharacteristic
50C22×C4×C47C2×D411yescharacteristic
51C22×Dic47—22no—
52C22×Dic47—22no—
53C2×C8×C47—24no—
54C2×C8×C47—42no—
55C2×C8×C47—42no—
56C42×C47—22no—
57C42×C47—22no—
58C42×C47—22no—
59C42×C47—41no—
60C42×C47—41no—
61C42×C47—41no—
62C42×C47C2×Q812yes—
63C42×C47#4112yes—
64C4⋊Dic47—42no—
65C4⋊Dic47—42no—
66C4⋊Dic47—42no—
67C4⋊Dic47—42no—
68C4⋊Dic47—42no—
69C4⋊Dic47—42no—
70Dic47⋊C4—44no—
71Dic47⋊C4—44no—
72C2×C47⋊C8—24no—
73C2×C47⋊C8—42no—
74C2×C47⋊C8—42no—
75C23×C47C2×C22⋊C411yescharacteristic
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47#10012yes—
92C2×C4×C47#10112yes—
93C2×C4×C47#10412yes—
94C2×C4×C47C4×Q812yes—
95C2×C4×C47C22⋊Q812yes—
96C2×C4×C47#12411yescharacteristic
97C2×C4×C47C4⋊Q811yescharacteristic
98C2×Dic47—42no—
99C2×Dic47—42no—
100C2×Dic47—42no—
101C2×Dic47—42no—
102C2×Dic47—42no—
103C2×Dic47—42no—
104C8×C47—44no—
105C47⋊C8—44no—
106#9894—471nomaximal, Sylow
107C22×C47#39111yescharacteristic
108C22×C47C2×#10011yescharacteristic
109C22×C47C2×#10111yescharacteristic
110C22×C47C2×#10411yescharacteristic
111C22×C47#42111yescharacteristic
112C22×C47#42111yescharacteristic
113C22×C47#42111yescharacteristic
114C4×C47—21no—
115C4×C47—21no—
116C4×C47—22no—
117C4×C47—22no—
118C4×C47—22no—
119C4×C47—22no—
120C4×C47—22no—
121C4×C47—41no—
122Dic47—82no—
123Dic47—82no—
124#2859—471no—
125#1767—471no—
126#1745D4711yescharacteristic
127#1295—474no—
128C2×C47#152811yescharacteristic
129C2×C47#153011yescharacteristic
130C2×C47#153411yescharacteristic
131C2×C47#153611yescharacteristic
132C2×C47#198611yescharacteristic
133C2×C47#199511yescharacteristic
134C2×C47#199711yescharacteristic
135C2×#125—472no—
136C2×C4⋊C8—941no—
137C2×#97—472no—
138C2×#97C2×D4712yes—
139#389—941no—
140#389—941no—
141#389—941no—
142#389—941no—
143#384—471no—
144#384—471no—
145#382—472no—
146C43C2×D4711yescharacteristic
147#336—21no—
148#336—21no—
149#336—941no—
150C47#989411yescharacteristic, complemented, Sylow
151C22×C8—22no—
152C22×C8—942no—
153#125—1884no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—472no—
156C2×C4⋊C4—942no—
157C2×C4⋊C4—942no—
158C2×C4⋊C4—941no—
159C2×C4⋊C4—941no—
160C2×C4⋊C4—941no—
161C2×C4⋊C4—941no—
162C2×C42C4×D4711yescharacteristic
163C2×C42C4×D4711yescharacteristic
164C2×C42D18811yescharacteristic
165C2×C42D18811yescharacteristic
166C2×C42C22⋊D4711yescharacteristic
167C2×C42C22⋊D4711yescharacteristic
168C2×C42C22×D4711yescharacteristic
169C4⋊C8—944no—
170#97—22no—
171#97—944no—
172#97Dic9414yes—
173#95—942no—
174#95—942no—
175C22×C4—942no—
176C22×C4—942no—
177C22×C4(C2×D47)⋊C411yescharacteristic
178C22×C4(C2×D47)⋊C411yescharacteristic
179C22×C4(C2×D47)⋊C411yescharacteristic
180C22×C4(C2×D47)⋊C411yescharacteristic
181C22×C4C2×C4×D4711yescharacteristic
182C22×C4C2×D18811yescharacteristic
183C22×C4C2×C22⋊D4711yescharacteristic
184C2×C8—24no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—944no—
188C2×C8—1882no—
189C2×C8—1882no—
190C4⋊C4—1882no—
191C4⋊C4—1882no—
192C4⋊C4—1884no—
193C4⋊C4—1882no—
194C4⋊C4—1882no—
195C4⋊C4—1882no—
196C4⋊C4—1884no—
197C4⋊C4—1882no—
198C42—22no—
199C42—22no—
200C42—22no—
201C42—41no—
202C42—41no—
203C42—41no—
204C42C2×Dic9412yes—
205C42#1062535012yes—
206C23C2×(C2×D47)⋊C411yescharacteristic
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—1882no—
223C2×C4—1882no—
224C2×C4—1882no—
225C2×C4—1882no—
226C2×C4—1882no—
227C2×C4—1882no—
228C2×C4#1309394012yes—
229C2×C4#1309394212yes—
230C2×C4#1309395012yes—
231C2×C4C4×Dic9412yes—
232C2×C4#1309400312yes—
233C2×C4#1309401211yescharacteristic
234C2×C4#1309402411yescharacteristic
235C8—44no—
236C8—1884no—
237C22#1568902911yescharacteristic
238C22C2×#1309394011yescharacteristic
239C22C2×#1309394211yescharacteristic
240C22C2×#1309395011yescharacteristic
241C22#1568913911yescharacteristic
242C22#1568914111yescharacteristic
243C22#1568914111yescharacteristic
244C4—22no—
245C4—22no—
246C4—22no—
247C4—21no—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—3762no—
253C4—3762no—
254C2#2024199111yescharacteristic
255C2#2024200011yescharacteristic
256C2#2024201411yescharacteristic
257C2#2024202211yescharacteristic
258C2#2024433211yescharacteristic
259C2#2024436911yescharacteristic
260C2#2024437711yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1745C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1745D47
hypocenterC47#9894
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
150. C47#9894semidirect

Maximal subgroups

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

subgroupindex
#202517512
#202432412
#202412702
C47×#17452
#989447