Finite Group Databasebeta

← #26105463

Subgroups — #26105463

Order 12032.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#20244931C211yesmaximal, characteristic, complemented
2#20244791C212yesmaximal, complemented
3#20241214C211yesmaximal, characteristic, complemented
4#20241209C212yesmaximal, complemented
5C47×#2733C211yesmaximal, characteristic
6C2×#13093955—21no—
7C2×#13093948—21no—
8C2×#13093945—22no—
9#15688993C2211yescharacteristic
10#15688885—22no—
11#15688878C2212yes—
12#15688878C2211yescharacteristic
13C2×#124×C47—21no—
14C47×#394—21no—
15C47×#392—22no—
16C47×#391C2211yescharacteristic
17C47×#390C2212yes—
18C47×#388—22no—
19C22×C47⋊C8—21no—
20C22×C47⋊C8—22no—
21C2×C4⋊Dic47—22no—
22C2×C4⋊Dic47—21no—
23#13093955—42no—
24#13093948—42no—
25#13093945—44no—
26C22×Q8×C47D411yescharacteristic
27C22×D4×C47—21no—
28C22×D4×C47—21no—
29C22×D4×C47D412yes—
30#124×C47—42no—
31#124×C47—42no—
32C2×C4⋊C4×C47D412yes—
33C2×C4⋊C4×C47D411yescharacteristic
34C2×C22⋊C4×C47—22no—
35C2×C22⋊C4×C47—22no—
36C2×C22⋊C4×C47—22no—
37C2×C22⋊C4×C47—22no—
38C2×C42×C47—21no—
39C2×C42×C47C2311yescharacteristic
40#95×C47—21no—
41#95×C47—22no—
42C24×C47—22no—
43C2×Q8×C47—21no—
44C2×Q8×C47—41no—
45C2×Q8×C47—41no—
46C2×Q8×C47SD1612yes—
47C2×D4×C47—22no—
48C2×D4×C47—22no—
49C2×D4×C47—42no—
50C2×D4×C47—42no—
51C2×D4×C47—42no—
52C2×D4×C47—81no—
53C2×D4×C47—81no—
54C2×D4×C47—81no—
55C2×D4×C47—82no—
56C22×C4×C47—21no—
57C22×C4×C47—22no—
58C22×C4×C47—21no—
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47C2×D412yes—
61C22×Dic47—41no—
62C4⋊C4×C47—42no—
63C4⋊C4×C47—41no—
64C22⋊C4×C47—44no—
65C22⋊C4×C47—42no—
66C22⋊C4×C47—42no—
67C22⋊C4×C47—42no—
68C22⋊C4×C47—42no—
69C22⋊C4×C47—82no—
70C42×C47—41no—
71C42×C47—42no—
72C4⋊Dic47—41no—
73C4⋊Dic47—41no—
74C4⋊Dic47—42no—
75C4⋊Dic47—42no—
76C2×C47⋊C8—22no—
77C2×C47⋊C8—41no—
78C2×C47⋊C8—41no—
79C2×C47⋊C8—42no—
80C2×C47⋊C8—42no—
81C2×C47⋊C8—42no—
82C23×C47—42no—
83C23×C47—42no—
84C23×C47—42no—
85C23×C47—42no—
86C23×C47—42no—
87C23×C47—42no—
88C23×C47—42no—
89C23×C47#12011yescharacteristic
90Q8×C47—42no—
91Q8×C47—81no—
92D4×C47—44no—
93D4×C47—82no—
94D4×C47—84no—
95D4×C47—84no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—21no—
100C2×C4×C47—22no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47—42no—
104C2×C4×C47—42no—
105C2×C4×C47—41no—
106C2×C4×C47—42no—
107C2×C4×C47—42no—
108C2×C4×C47C2×SD1611yescharacteristic
109C2×C4×C47#13512yes—
110C2×C4×C47AGL(1,ℤ/8)12yes—
111C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
112C2×Dic47—82no—
113C2×Dic47—81no—
114C47⋊C8—42no—
115C47⋊C8—82no—
116#7810—471nomaximal, Sylow
117C22×C47—82no—
118C22×C47—82no—
119C22×C47—82no—
120C22×C47—82no—
121C22×C47—82no—
122C22×C47—82no—
123C22×C47—82no—
124C22×C47#44912yes—
125C22×C47#45011yescharacteristic
126C22×C47#45311yescharacteristic
127C22×C47#45512yes—
128C22×C47#45811yescharacteristic
129C4×C47—22no—
130C4×C47—22no—
131C4×C47—21no—
132C4×C47—21no—
133C4×C47—42no—
134C4×C47—82no—
135C4×C47—81no—
136Dic47—161no—
137#2733D4711yescharacteristic
138#2096—471no—
139#2071—472no—
140#1272—471no—
141#1270—472no—
142C2×C47—162no—
143C2×C47#161212yes—
144C2×C47#161311yescharacteristic
145C2×C47#162411yescharacteristic
146C2×C47#164212yes—
147C2×C47#165911yescharacteristic
148C2×#124—21no—
149C2×#106—941no—
150C2×#103—941no—
151C2×#102—942no—
152#394—21no—
153#392—22no—
154#391C2×D4711yescharacteristic
155#390C2×D4712yes—
156#388—22no—
157#384—471no—
158#340—942no—
159#336—472no—
160#336—471no—
161C47#781011yescharacteristic, complemented, Sylow
162C22×Q8C22⋊D4711yescharacteristic
163C22×D4—21no—
164C22×D4—21no—
165C22×D4C22⋊D4712yes—
166C22×C8—941no—
167C22×C8—942no—
168#124—42no—
169#124—42no—
170C2×C4⋊C4—942no—
171C2×C4⋊C4—941no—
172C2×C4⋊C4C22⋊D4712yes—
173C2×C4⋊C4C22⋊D4711yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C42—21no—
179C2×C42C22×D4711yescharacteristic
180#106—1882no—
181#103—1882no—
182#102—1884no—
183#95—21no—
184#95—22no—
185C24—22no—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8#1062533512yes—
190C2×D4—22no—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—42no—
195C2×D4—81no—
196C2×D4—81no—
197C2×D4—81no—
198C2×D4—82no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—1881no—
203C22×C4C2×C22⋊D4711yescharacteristic
204C22×C4C2×C22⋊D4712yes—
205C2×C8—942no—
206C2×C8—1882no—
207C2×C8—1882no—
208C2×C8—1882no—
209C2×C8—1881no—
210C2×C8—1881no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—1881no—
214C4⋊C4—1881no—
215C4⋊C4—1882no—
216C4⋊C4—1882no—
217C22⋊C4—44no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—82no—
223C42—41no—
224C42—42no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23#1309399311yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—44no—
236D4—82no—
237D4—84no—
238D4—84no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—3762no—
252C2×C4—3761no—
253C2×C4C2×#1062533511yescharacteristic
254C2×C4#1309404412yes—
255C2×C4#1309404912yes—
256C2×C4#1309405011yescharacteristic
257C8—3762no—
258C8—1882no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22#1568926812yes—
267C22#1568927411yescharacteristic
268C22#1568929111yescharacteristic
269C22#1568930112yes—
270C22#1568931311yescharacteristic
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—82no—
278C4—7521no—
279C2—162no—
280C2#2024240212yes—
281C2#2024240811yescharacteristic
282C2#2024247111yescharacteristic
283C2#2024258812yes—
284C2#2024269411yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#2733C2
socleC23×C47#120
hypercenter#2733D47
hypocenterC47#7810
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #20244931C2semidirect
2. #20244791C2semidirect
3. #20241214C2semidirect
4. #20241209C2semidirect
161. C47#7810semidirect

Maximal subgroups

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

subgroupindex
#202449312
#202447912
#202412142
#202412092
C47×#27332
#781047