Finite Group Databasebeta

← #26104549

Subgroups — #26104549

Order 12032.

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

normal subgroups only

This group has 468 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
1C4×#13094024C211yesmaximal, characteristic
2#20243137C211yesmaximal, characteristic
3#20241212C214yesmaximal
4C47×#1745C211yesmaximal, characteristic
5C2×#13094024C411yescharacteristic
6C2×C4×Dic94—21no—
7C2×#13093935—21no—
8#15689029—21no—
9#15689021—21no—
10#15689021C2212yes—
11#15688993C411yescharacteristic
12C4×C4⋊Dic47—21no—
13C4×C4⋊Dic47C412yes—
14#15688878—21no—
15#15688878C2212yes—
16C2×#97×C47—21no—
17C43×C47C2211yescharacteristic
18C47×#336—21no—
19C47×#336C2212yes—
20C22×Dic94—21no—
21C22×C47⋊C8—22no—
22#13094024—24no—
23C4×Dic94—44no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47C2×C412yes—
28C2×C4⋊Dic47C2×C412yes—
29C2×Dic47⋊C4—22no—
30C2×C4×Dic47—22no—
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—24no—
43C22×C4×C47C22⋊C411yescharacteristic
44C22×C4×C47C22⋊C411yescharacteristic
45C22×C4×C47C22⋊C411yescharacteristic
46C22×C4×C47C22⋊C411yescharacteristic
47C22×C4×C47C22×C411yescharacteristic
48C22×C4×C47C2×D411yescharacteristic
49C22×C4×C47C2×D411yescharacteristic
50C22×Dic47—22no—
51C22×Dic47—22no—
52C2×Dic94—24no—
53C2×Dic94—42no—
54C2×Dic94—42no—
55C2×C8×C47—24no—
56C2×C8×C47—42no—
57C2×C8×C47—42no—
58C42×C47—22no—
59C42×C47—22no—
60C42×C47—22no—
61C42×C47—22no—
62C42×C47—22no—
63C42×C47—22no—
64C42×C47—41no—
65C4⋊Dic47—24no—
66C4⋊Dic47—22no—
67C4⋊Dic47—42no—
68C4⋊Dic47—42no—
69C4⋊Dic47—42no—
70C4⋊Dic47M1614yes—
71Dic47⋊C4—44no—
72C4×Dic47—44no—
73C2×C47⋊C8—24no—
74C2×C47⋊C8—42no—
75C2×C47⋊C8—42no—
76C23×C47C2×C22⋊C411yescharacteristic
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—21no—
92C2×C4×C47#10112yes—
93C2×C4×C47#10412yes—
94C2×C4×C47#10412yes—
95C2×C4×C47C2×M1612yes—
96C2×C4×C47AGL(1,ℤ/8)12yes—
97C2×C4×C47#13712yes—
98C2×Dic47—24no—
99C2×Dic47—42no—
100C2×Dic47—42no—
101C2×Dic47—42no—
102C2×Dic47—42no—
103C2×Dic47—42no—
104Dic94—48no—
105C8×C47—44no—
106C47⋊C8—44no—
107#7638—471nomaximal, Sylow
108C22×C47#40711yescharacteristic
109C22×C47#41011yescharacteristic
110C22×C47C2×#10111yescharacteristic
111C22×C47#41811yescharacteristic
112C22×C47#41911yescharacteristic
113C22×C47C2×#10411yescharacteristic
114C22×C47C2×#10411yescharacteristic
115C4×C47—22no—
116C4×C47—22no—
117C4×C47—22no—
118C4×C47—22no—
119C4×C47—22no—
120C4×C47—22no—
121C4×C47—41no—
122Dic47—44no—
123Dic47—82no—
124C4×C4⋊Q8—471no—
125#1745—471no—
126#1745D4711yescharacteristic
127#1271—474no—
128C2×C47#146711yescharacteristic
129C2×C47#149011yescharacteristic
130C2×C47#149111yescharacteristic
131C2×C47#150511yescharacteristic
132C2×C47#150611yescharacteristic
133C2×C47#152611yescharacteristic
134C2×C47#155611yescharacteristic
135C2×C4⋊Q8—471no—
136C2×C4×Q8—941no—
137C2×#97—21no—
138C2×#97—941no—
139#391—941no—
140#389—472no—
141#389—941no—
142#384—471no—
143C4×C4⋊C4—472no—
144C4×C4⋊C4—941no—
145C43C2×D4711yescharacteristic
146#336—21no—
147#336—472no—
148#336—941no—
149#336C2×D4712yes—
150C47#763811yescharacteristic, complemented, Sylow
151C22×Q8—941no—
152C22×C8—22no—
153C22×C8—942no—
154C4⋊Q8—944no—
155C4×Q8—1884no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4—941no—
159C2×C4⋊C4—941no—
160C2×C4⋊C4—941no—
161C2×C4⋊C4—942no—
162C2×C42—942no—
163C2×C42C4×D4711yescharacteristic
164C2×C42C4×D4711yescharacteristic
165C2×C42D18811yescharacteristic
166C2×C42D18811yescharacteristic
167C2×C42C22⋊D4711yescharacteristic
168C2×C42C22⋊D4711yescharacteristic
169C2×C42C22×D4711yescharacteristic
170#97—24no—
171#97—944no—
172#95—942no—
173#95—942no—
174C2×Q8—944no—
175C2×Q8—1882no—
176C2×Q8—1882no—
177C22×C4—942no—
178C22×C4—942no—
179C22×C4(C2×D47)⋊C411yescharacteristic
180C22×C4(C2×D47)⋊C411yescharacteristic
181C22×C4(C2×D47)⋊C411yescharacteristic
182C22×C4(C2×D47)⋊C411yescharacteristic
183C22×C4C2×C4×D4711yescharacteristic
184C22×C4C2×D18811yescharacteristic
185C22×C4C2×C22⋊D4711yescharacteristic
186C2×C8—24no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—944no—
190C2×C8—1882no—
191C2×C8—1882no—
192C4⋊C4—474no—
193C4⋊C4—944no—
194C4⋊C4—942no—
195C4⋊C4—1882no—
196C4⋊C4—1882no—
197C4⋊C4—1882no—
198C4⋊C4—1884no—
199C42—22no—
200C42—22no—
201C42—22no—
202C42—22no—
203C42—22no—
204C42—22no—
205C42—41no—
206C42—1884no—
207C23C2×(C2×D47)⋊C411yescharacteristic
208Q8—1888no—
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—21no—
223C2×C4—21no—
224C2×C4—944no—
225C2×C4—1882no—
226C2×C4—1882no—
227C2×C4—1882no—
228C2×C4—1882no—
229C2×C4—1882no—
230C2×C4#1309394212yes—
231C2×C4#1309395012yes—
232C2×C4#1309395212yes—
233C2×C4M16×D4712yes—
234C2×C4#1309404912yes—
235C2×C4#1309405712yes—
236C8—44no—
237C8—1884no—
238C22#1568908611yescharacteristic
239C22#1568909611yescharacteristic
240C22C2×#1309394211yescharacteristic
241C22#1568912711yescharacteristic
242C22#1568913311yescharacteristic
243C22C2×#1309395011yescharacteristic
244C22C2×#1309395211yescharacteristic
245C4—22no—
246C4—22no—
247C4—22no—
248C4—22no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—3762no—
253C4—1884no—
254C2#2024173111yescharacteristic
255C2#2024183011yescharacteristic
256C2#2024183611yescharacteristic
257C2#2024189511yescharacteristic
258C2#2024190111yescharacteristic
259C2#2024198211yescharacteristic
260C2#2024210611yescharacteristic
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#7638
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#7638semidirect

Maximal subgroups

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

subgroupindex
C4×#130940242
#202431372
#202412122
C47×#17452
#763847