Finite Group Databasebeta

← #26104401

Subgroups — #26104401

Order 12032.

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

normal subgroups only

This group has 440 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
1C4×#13094024C211yesmaximal, characteristic
2#20243531C211yesmaximal, characteristic
3#20241210C214yesmaximal
4C47×#1839C211yesmaximal, characteristic
5C2×#13094024C411yescharacteristic
6C2×C4×Dic94—21no—
7#15689029—21no—
8#15689021—21no—
9#15689021C2212yes—
10#15688993C411yescharacteristic
11C4×C4⋊Dic47—21no—
12C4×C4⋊Dic47C412yes—
13#15688878—21no—
14#15688878—21no—
15#15688878C2212yes—
16C43×C47C2211yescharacteristic
17C47×#336—21no—
18C47×#336—21no—
19C47×#336C2212yes—
20C22×Dic94—21no—
21C22×C47⋊C8—22no—
22#13094024—22no—
23#13094024C814yescomplemented
24C4×Dic94—44no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47C2×C412yes—
29C2×C4⋊Dic47C2×C412yes—
30C2×Dic47⋊C4—22no—
31C2×C4×Dic47—22no—
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
42C22×C4×C47C22⋊C411yescharacteristic
43C22×C4×C47C22⋊C411yescharacteristic
44C22×C4×C47C22⋊C411yescharacteristic
45C22×C4×C47C22⋊C411yescharacteristic
46C22×C4×C47C22×C411yescharacteristic
47C22×C4×C47C2×D411yescharacteristic
48C22×C4×C47C2×D411yescharacteristic
49C22×Dic47—22no—
50C22×Dic47—22no—
51C2×Dic94—24no—
52C2×Dic94—42no—
53C2×Dic94—42no—
54C2×C8×C47—42no—
55C2×C8×C47—42no—
56C2×C8×C47—42no—
57C42×C47—22no—
58C42×C47—22no—
59C42×C47—22no—
60C42×C47—41no—
61C42×C47—41no—
62C42×C47—41no—
63C42×C47C2×C812yes—
64C42×C47M1612yes—
65C4⋊Dic47—24no—
66C4⋊Dic47—22no—
67C4⋊Dic47—42no—
68C4⋊Dic47—42no—
69C4⋊Dic47—42no—
70C4⋊Dic47C2×C814yes—
71Dic47⋊C4—44no—
72C4×Dic47—44no—
73C2×C47⋊C8—42no—
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×C47C22⋊C812yes—
93C2×C4×C47C22⋊C812yes—
94C2×C4×C47#10112yes—
95C2×C4×C47C22×C811yescharacteristic
96C2×C4×C47C2×M1611yescharacteristic
97C2×C4×C47AGL(1,ℤ/8)12yes—
98C2×C4×C47#13712yes—
99C2×Dic47—24no—
100C2×Dic47—42no—
101C2×Dic47—42no—
102C2×Dic47—42no—
103C2×Dic47—42no—
104C2×Dic47—42no—
105Dic94—48no—
106C8×C47—82no—
107C47⋊C8—82no—
108#7604—471nomaximal, Sylow
109C22×C47C2×C22⋊C811yescharacteristic
110C22×C47#41011yescharacteristic
111C22×C47C2×#10111yescharacteristic
112C22×C47#41811yescharacteristic
113C22×C47#41911yescharacteristic
114C22×C47#42111yescharacteristic
115C22×C47#42111yescharacteristic
116C4×C47—22no—
117C4×C47—21no—
118C4×C47—21no—
119C4×C47—22no—
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—22no—
123C4×C47—41no—
124Dic47—44no—
125Dic47—82no—
126C4×C4⋊Q8—471no—
127#1839—471no—
128#1839D4711yescharacteristic
129#1271—474no—
130C2×C47#146111yescharacteristic
131C2×C47#147811yescharacteristic
132C2×C47#147911yescharacteristic
133C2×C47#151411yescharacteristic
134C2×C47#151511yescharacteristic
135C2×C47#153711yescharacteristic
136C2×C47#155611yescharacteristic
137C2×C4⋊Q8—471no—
138C2×C4×Q8—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—21no—
148#336—472no—
149#336—941no—
150#336—941no—
151#336C2×D4712yes—
152C47#760411yescharacteristic, complemented, Sylow
153C22×Q8—941no—
154C22×C8—22no—
155C22×C8—942no—
156C4⋊Q8—474no—
157C4⋊Q8—942no—
158C4×Q8—1884no—
159C2×C4⋊C4—472no—
160C2×C4⋊C4—472no—
161C2×C4⋊C4—941no—
162C2×C4⋊C4—941no—
163C2×C4⋊C4—941no—
164C2×C4⋊C4—942no—
165C2×C42—942no—
166C2×C42C4×D4711yescharacteristic
167C2×C42C4×D4711yescharacteristic
168C2×C42D18811yescharacteristic
169C2×C42D18811yescharacteristic
170C2×C42C22⋊D4711yescharacteristic
171C2×C42C22⋊D4711yescharacteristic
172C2×C42C22×D4711yescharacteristic
173#95—942no—
174#95—942no—
175C2×Q8—944no—
176C2×Q8—1882no—
177C2×Q8—1882no—
178C22×C4—942no—
179C22×C4—942no—
180C22×C4(C2×D47)⋊C411yescharacteristic
181C22×C4(C2×D47)⋊C411yescharacteristic
182C22×C4(C2×D47)⋊C411yescharacteristic
183C22×C4(C2×D47)⋊C411yescharacteristic
184C22×C4C2×C4×D4711yescharacteristic
185C22×C4C2×D18811yescharacteristic
186C22×C4C2×C22⋊D4711yescharacteristic
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—1882no—
191C2×C8—1882no—
192C2×C8—1882no—
193C4⋊C4—474no—
194C4⋊C4—944no—
195C4⋊C4—942no—
196C4⋊C4—1882no—
197C4⋊C4—1882no—
198C4⋊C4—1882no—
199C4⋊C4—1884no—
200C42—22no—
201C42—22no—
202C42—22no—
203C42—41no—
204C42—41no—
205C42—41no—
206C42—1884no—
207C42C8×D4712yes—
208C42#1062532412yes—
209C23C2×(C2×D47)⋊C411yescharacteristic
210Q8—1888no—
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—21no—
225C2×C4—21no—
226C2×C4—944no—
227C2×C4—1882no—
228C2×C4—1882no—
229C2×C4—1882no—
230C2×C4—1882no—
231C2×C4—1882no—
232C2×C4(C2×D47)⋊C812yes—
233C2×C4(C2×D47)⋊C812yes—
234C2×C4#1309394212yes—
235C2×C4C2×C8×D4711yescharacteristic
236C2×C4C2×#1062532411yescharacteristic
237C2×C4#1309405212yes—
238C2×C4#1309405412yes—
239C8—82no—
240C8—3762no—
241C22C2×(C2×D47)⋊C811yescharacteristic
242C22#1568909611yescharacteristic
243C22C2×#1309394211yescharacteristic
244C22#1568912911yescharacteristic
245C22#1568913111yescharacteristic
246C22#1568913911yescharacteristic
247C22#1568914111yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—21no—
252C4—22no—
253C4—22no—
254C4—22no—
255C4—41no—
256C4—3762no—
257C4—1884no—
258C2#2024171111yescharacteristic
259C2#2024178011yescharacteristic
260C2#2024178211yescharacteristic
261C2#2024193611yescharacteristic
262C2#2024193811yescharacteristic
263C2#2024202511yescharacteristic
264C2#2024210411yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1839C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1839D47
hypocenterC47#7604
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
23. #13094024C8semidirect
152. C47#7604semidirect

Maximal subgroups

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

subgroupindex
C4×#130940242
#202435312
#202412102
C47×#18392
#760447