Finite Group Databasebeta

← #26105475

Subgroups — #26105475

Order 12032.

398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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
2#20244796C212yesmaximal
3#20241214C211yesmaximal, characteristic
4#20241214C212yesmaximal
5C47×#2811C211yesmaximal, characteristic
6C2×#13093955—21no—
7C2×#13093948—22no—
8C2×#13093948—21no—
9#15688993C2211yescharacteristic
10#15688885—22no—
11#15688878C2212yes—
12#15688878C2211yescharacteristic
13C47×#395—22no—
14C47×#395—21no—
15C47×#391—22no—
16C47×#391—21no—
17C47×#391C2212yes—
18C47×#391C2211yescharacteristic
19C22×C47⋊C8—21no—
20C22×C47⋊C8—22no—
21C2×C4⋊Dic47—22no—
22C2×C4⋊Dic47—21no—
23#13093955—42no—
24#13093948—42no—
25#13093948—44no—
26C22×Q8×C47—21no—
27C22×Q8×C47D412yes—
28C22×Q8×C47D411yescharacteristic
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47—22no—
31C2×C4⋊C4×C47D412yes—
32C2×C4⋊C4×C47D411yescharacteristic
33C2×C42×C47—21no—
34C2×C42×C47C2311yescharacteristic
35#95×C47—21no—
36#95×C47—22no—
37#95×C47—22no—
38#95×C47—22no—
39#95×C47—22no—
40C2×Q8×C47—22no—
41C2×Q8×C47—21no—
42C2×Q8×C47—42no—
43C2×Q8×C47—42no—
44C2×Q8×C47—41no—
45C2×Q8×C47—41no—
46C2×Q8×C47—81no—
47C2×Q8×C47—82no—
48C2×Q8×C47SD1614yes—
49C2×Q8×C47Q1612yes—
50C22×C4×C47—22no—
51C22×C4×C47—21no—
52C22×C4×C47—21no—
53C22×C4×C47—22no—
54C22×C4×C47C2×D412yes—
55C22×C4×C47C2×D411yescharacteristic
56C22×Dic47—41no—
57C4⋊C4×C47—42no—
58C4⋊C4×C47—41no—
59C4⋊C4×C47—81no—
60C4⋊C4×C47—82no—
61C42×C47—41no—
62C42×C47—81no—
63C4⋊Dic47—41no—
64C4⋊Dic47—41no—
65C4⋊Dic47—42no—
66C4⋊Dic47—42no—
67C2×C47⋊C8—22no—
68C2×C47⋊C8—41no—
69C2×C47⋊C8—41no—
70C2×C47⋊C8—42no—
71C2×C47⋊C8—42no—
72C2×C47⋊C8—42no—
73C23×C47#12011yescharacteristic
74Q8×C47—44no—
75Q8×C47—42no—
76Q8×C47—82no—
77Q8×C47—81no—
78Q8×C47—84no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—24no—
84C2×C4×C47—22no—
85C2×C4×C47—41no—
86C2×C4×C47—42no—
87C2×C4×C47—42no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47—42no—
91C2×C4×C47—42no—
92C2×C4×C47—42no—
93C2×C4×C47—42no—
94C2×C4×C47C2×SD1612yes—
95C2×C4×C47C2×Q1611yescharacteristic
96C2×C4×C47#13712yes—
97C2×C4×C47#13711yescharacteristic
98C2×Dic47—82no—
99C2×Dic47—81no—
100C47⋊C8—42no—
101C47⋊C8—82no—
102#7812—471nomaximal, Sylow
103C22×C47#44812yes—
104C22×C47#45111yescharacteristic
105C22×C47#45311yescharacteristic
106C22×C47#45512yes—
107C22×C47#45811yescharacteristic
108C4×C47—22no—
109C4×C47—22no—
110C4×C47—21no—
111C4×C47—21no—
112C4×C47—44no—
113C4×C47—42no—
114C4×C47—81no—
115C4×C47—82no—
116Dic47—161no—
117#2811D4711yescharacteristic
118#2096—471no—
119#2072—472no—
120#1272—471no—
121#1272—472no—
122C2×C47#160812yes—
123C2×C47#161411yescharacteristic
124C2×C47#162311yescharacteristic
125C2×C47#164512yes—
126C2×C47#165911yescharacteristic
127C2×#106—941no—
128C2×#103—942no—
129C2×#103—941no—
130#395—22no—
131#395—21no—
132#391—22no—
133#391—21no—
134#391C2×D4712yes—
135#391C2×D4711yescharacteristic
136#384—471no—
137#340—942no—
138#336—472no—
139#336—471no—
140C47#781211yescharacteristic, complemented, Sylow
141C22×Q8—21no—
142C22×Q8C22⋊D4712yes—
143C22×Q8C22⋊D4711yescharacteristic
144C22×C8—941no—
145C22×C8—942no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—942no—
149C2×C4⋊C4—941no—
150C2×C4⋊C4C22⋊D4712yes—
151C2×C4⋊C4C22⋊D4711yescharacteristic
152C2×C42—21no—
153C2×C42C22×D4711yescharacteristic
154#106—1882no—
155#103—1882no—
156#103—1884no—
157#95—21no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—22no—
162C2×Q8—22no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—82no—
170C2×Q8#1062533614yes—
171C2×Q8#1062533712yes—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—1881no—
177C22×C4C2×C22⋊D4712yes—
178C22×C4C2×C22⋊D4711yescharacteristic
179C2×C8—942no—
180C2×C8—1882no—
181C2×C8—1882no—
182C2×C8—1882no—
183C2×C8—1881no—
184C2×C8—1881no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—81no—
188C4⋊C4—82no—
189C4⋊C4—1881no—
190C4⋊C4—1881no—
191C4⋊C4—1882no—
192C4⋊C4—1882no—
193C42—41no—
194C42—81no—
195C23#1309399311yescharacteristic
196Q8—44no—
197Q8—42no—
198Q8—82no—
199Q8—81no—
200Q8—84no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—3762no—
217C2×C4—3761no—
218C2×C4C2×#1062533612yes—
219C2×C4C2×#1062533711yescharacteristic
220C2×C4#1309405512yes—
221C2×C4#1309405511yescharacteristic
222C8—3762no—
223C8—1882no—
224C22#1568926212yes—
225C22#1568927911yescharacteristic
226C22#1568929111yescharacteristic
227C22#1568930112yes—
228C22#1568931311yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—44no—
234C4—42no—
235C4—81no—
236C4—82no—
237C4—7521no—
238C2#2024237912yes—
239C2#2024241311yescharacteristic
240C2#2024246611yescharacteristic
241C2#2024260912yes—
242C2#2024269411yescharacteristic
subgroupG/H
centerC23#13093993
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#2811C2
socle, prime radicalC23×C47#120
hypercenter#2811D47
hypocenterC47#7812
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2811

Complements

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

NH ≅ G/Ntype
140. C47#7812semidirect

Maximal subgroups

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

subgroupindex
#202449312
#202447962
#202412142
C47×#28112
#781247