Finite Group Databasebeta

← #26105477

Subgroups — #26105477

Order 12032.

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

normal subgroups only

This group has 398 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#20251381C211yesmaximal, characteristic
2#20244931C211yesmaximal, characteristic
3#20244798C212yesmaximal
4#20241213C212yesmaximal
5C47×#1272C211yesmaximal, characteristic
6C2×#13093955—21no—
7C2×#13093949—22no—
8C2×#13093948—21no—
9#15689044—22no—
10#15689043—21no—
11#15689030—21no—
12#15689029C2212yes—
13#15689027—22no—
14#15688993C2211yescharacteristic
15#15688886—22no—
16#15688878C2211yescharacteristic
17C47×#391C2211yescharacteristic
18C47×#336C2212yes—
19C22×Dic94—21no—
20C22×Dic94D412yes—
21C22×C47⋊C8—21no—
22C2×C4⋊Dic47—21no—
23C2×C4⋊Dic47—22no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47D412yes—
26C2×Dic47⋊C4—22no—
27C2×C4×Dic47—21no—
28#13093955—42no—
29#13093949—44no—
30#13093948—42no—
31C47⋊#95—21no—
32C47⋊#95—22no—
33C47⋊#95—22no—
34C47⋊#95—22no—
35C22×Q8×C47D411yescharacteristic
36C22×C8×C47—22no—
37C2×C4⋊C4×C47D411yescharacteristic
38C2×C42×C47C2311yescharacteristic
39#95×C47—22no—
40C2×Q8×C47—21no—
41C2×Q8×C47—41no—
42C2×Q8×C47—41no—
43C2×Q8×C47Q1612yes—
44C22×C4×C47—21no—
45C22×C4×C47—21no—
46C22×C4×C47C2×D412yes—
47C22×C4×C47C2×D411yescharacteristic
48C22×Dic47—22no—
49C22×Dic47—22no—
50C22×Dic47—41no—
51C2×Dic94—22no—
52C2×Dic94—42no—
53C2×Dic94—42no—
54C2×Dic94—81no—
55C2×Dic94—82no—
56C2×Dic94SD1614yes—
57C2×C8×C47—42no—
58C2×C8×C47—42no—
59C2×C8×C47—42no—
60C4⋊C4×C47—41no—
61C42×C47—41no—
62C4⋊Dic47—42no—
63C4⋊Dic47—41no—
64C4⋊Dic47—41no—
65C4⋊Dic47—42no—
66C4⋊Dic47—42no—
67C4⋊Dic47—81no—
68Dic47⋊C4—82no—
69C4×Dic47—81no—
70C2×C47⋊C8—22no—
71C2×C47⋊C8—41no—
72C2×C47⋊C8—41no—
73C23×C47#12011yescharacteristic
74Q8×C47—42no—
75Q8×C47—81no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47—42no—
85C2×C4×C47C2×SD1612yes—
86C2×C4×C47C2×Q1611yescharacteristic
87C2×C4×C47#13712yes—
88C2×C4×C47#13711yescharacteristic
89C2×Dic47—24no—
90C2×Dic47—42no—
91C2×Dic47—42no—
92C2×Dic47—42no—
93C2×Dic47—42no—
94C2×Dic47—42no—
95C2×Dic47—82no—
96C2×Dic47—81no—
97Dic94—44no—
98Dic94—82no—
99Dic94—84no—
100C8×C47—82no—
101C47⋊C8—42no—
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—42no—
113C4×C47—81no—
114Dic47—44no—
115Dic47—82no—
116Dic47—161no—
117#2811—471no—
118#2096—471no—
119#2072—472no—
120#1272—472no—
121#1272D4711yescharacteristic
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—942no—
131#395—941no—
132#391—472no—
133#391—942no—
134#391—941no—
135#391C2×D4711yescharacteristic
136#384—471no—
137#340—942no—
138#336—471no—
139#336C2×D4712yes—
140C47#781211yescharacteristic, complemented, Sylow
141C22×Q8—472no—
142C22×Q8—941no—
143C22×Q8D18811yescharacteristic
144C22×C8—22no—
145C22×C8—941no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4—942no—
148C2×C4⋊C4—941no—
149C2×C4⋊C4—941no—
150C2×C4⋊C4—942no—
151C2×C4⋊C4D18811yescharacteristic
152C2×C42—941no—
153C2×C42C22×D4711yescharacteristic
154#106—1882no—
155#103—1884no—
156#103—1882no—
157#95—22no—
158#95—942no—
159#95—941no—
160#95—942no—
161#95—942no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—474no—
166C2×Q8—942no—
167C2×Q8—3761no—
168C2×Q8—3762no—
169C2×Q8—1882no—
170C2×Q8—1882no—
171C2×Q8Dic18812yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—942no—
175C22×C4—942no—
176C22×C4—1881no—
177C22×C4C2×D18811yescharacteristic
178C22×C4D4×D4712yes—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—942no—
183C2×C8—1881no—
184C2×C8—1881no—
185C4⋊C4—41no—
186C4⋊C4—3762no—
187C4⋊C4—3761no—
188C4⋊C4—1881no—
189C4⋊C4—1881no—
190C4⋊C4—1882no—
191C4⋊C4—1882no—
192C4⋊C4—1882no—
193C42—41no—
194C42—3761no—
195C23#1309399411yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—3762no—
199Q8—3764no—
200Q8—1884no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—944no—
211C2×C4—3762no—
212C2×C4—3761no—
213C2×C4—1882no—
214C2×C4—1882no—
215C2×C4—1882no—
216C2×C4—1882no—
217C2×C4—1882no—
218C2×C4SD16×D4712yes—
219C2×C4C2×Dic18811yescharacteristic
220C2×C4#1309405612yes—
221C2×C4#1309405711yescharacteristic
222C8—82no—
223C8—1882no—
224C22#1568926312yes—
225C22#1568928111yescharacteristic
226C22#1568929311yescharacteristic
227C22#1568930212yes—
228C22#1568931411yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—42no—
234C4—81no—
235C4—3762no—
236C4—1884no—
237C4—7521no—
238C2#2024238012yes—
239C2#2024241511yescharacteristic
240C2#2024246711yescharacteristic
241C2#2024261212yes—
242C2#2024269511yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1272C2
socle, prime radicalC23×C47#120
hypercenter#1272D47
hypocenterC47#7812
LCSG ▷ C2×C42×C47 ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

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
#202513812
#202449312
#202447982
#202412132
C47×#12722
#781247