Finite Group Databasebeta

← #26107631

Subgroups — #26107631

Order 12032.

810 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C22×#13094016C211yesmaximal, characteristic
2#20243456C211yesmaximal, characteristic
3C2×#15688848C214yesmaximal
4C47×#1817C211yesmaximal, characteristic
5C2×#13094016—28no—
6C2×#13094016—22no—
7C2×#13094016—22no—
8C22×C4⋊Dic47C411yescharacteristic
9C22×C4⋊Dic47C411yescharacteristic
10C22×Dic47⋊C4C412yes—
11C22×Dic47⋊C4C2212yes—
12C2×C22⋊(C47⋊C8)C2212yes—
13#15688878—22no—
14#15688848—28no—
15C22×C42×C47C2211yescharacteristic
16C2×C22⋊C8×C47C2212yes—
17C47×#336—22no—
18C23×Dic47C2×C412yes—
19C23×Dic47C2×C412yes—
20C22×C47⋊C8—22no—
21#13094016—216no—
22#13094016—216no—
23C2×C4⋊Dic47—22no—
24C2×C4⋊Dic47—22no—
25C2×C4⋊Dic47—24no—
26C2×C4⋊Dic47—24no—
27C2×Dic47⋊C4—24no—
28C2×Dic47⋊C4—22no—
29C2×Dic47⋊C4—22no—
30C2×Dic47⋊C4—24no—
31C2×Dic47⋊C4—24no—
32C2×Dic47⋊C4—24no—
33C2×Dic47⋊C4D418yes—
34C22⋊(C47⋊C8)—24no—
35C23×C4×C47C2×C411yescharacteristic
36C23×C4×C47C2×C411yescharacteristic
37C23×C4×C47C2311yescharacteristic
38C22×C8×C47—22no—
39C2×C42×C47—24no—
40C2×C42×C47D412yes—
41C2×C42×C47D412yes—
42C22⋊C8×C47—24no—
43C24×C47C22×C411yescharacteristic
44C22×C4×C47—22no—
45C22×C4×C47—24no—
46C22×C4×C47—22no—
47C22×C4×C47—22no—
48C22×C4×C47—22no—
49C22×C4×C47—42no—
50C22×C4×C47C22⋊C412yes—
51C22×C4×C47C22⋊C412yes—
52C22×C4×C47C2×D411yescharacteristic
53C22×C4×C47C2×D411yescharacteristic
54C22×C4×C47C2×D414yes—
55C22×Dic47—22no—
56C22×Dic47—22no—
57C22×Dic47—22no—
58C22×Dic47—22no—
59C22×Dic47—24no—
60C22×Dic47—24no—
61C22×Dic47—44no—
62C22×Dic47C22⋊C414yes—
63C22×Dic47C22⋊C414yes—
64C2×C8×C47—44no—
65C2×C8×C47—42no—
66C42×C47—24no—
67C42×C47—24no—
68C4⋊Dic47—28no—
69C4⋊Dic47—28no—
70Dic47⋊C4—216no—
71Dic47⋊C4—28no—
72Dic47⋊C4—28no—
73C2×C47⋊C8—44no—
74C2×C47⋊C8—42no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47C2×C22⋊C412yes—
78C23×C47C2×C22⋊C411yescharacteristic
79C23×C47#13112yes—
80C23×C47#13112yes—
81C2×C4×C47—28no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—44no—
90C2×C4×C47—44no—
91C2×C4×C47#10114yes—
92C2×C4×C47#12012yes—
93C2×C4×C47#12012yes—
94C2×Dic47—24no—
95C2×Dic47—24no—
96C2×Dic47—28no—
97C2×Dic47—44no—
98C2×Dic47—44no—
99C2×Dic47—42no—
100C2×Dic47—42no—
101C2×Dic47—44no—
102C2×Dic47—44no—
103C8×C47—82no—
104C47⋊C8—82no—
105#8306—471nomaximal, Sylow
106C22×C47—24no—
107C22×C47—24no—
108C22×C47—22no—
109C22×C47—22no—
110C22×C47#37911yescharacteristic
111C22×C47#40814yes—
112C22×C47#40811yescharacteristic
113C22×C47#40811yescharacteristic
114C22×C47#41012yes—
115C22×C47C2×#10112yes—
116C4×C47—22no—
117C4×C47—22no—
118C4×C47—24no—
119C4×C47—42no—
120Dic47—44no—
121Dic47—44no—
122C22×#125—471no—
123#1817—471no—
124#1817D4711yescharacteristic
125C2×#324—474no—
126C2×C47—24no—
127C2×C47#147012yes—
128C2×C47#147012yes—
129C2×C47#178011yescharacteristic
130C2×C47#178211yescharacteristic
131C2×C47#178411yescharacteristic
132C2×#125—948no—
133C2×#125—942no—
134C2×#125—942no—
135C22×C4⋊C4—472no—
136C22×C4⋊C4—472no—
137C22×C4⋊C4—471no—
138C22×C4⋊C4—471no—
139C22×C42C2×D4711yescharacteristic
140C2×C22⋊C8—472no—
141C2×C22⋊C8C2×D4712yes—
142#336—22no—
143#336—942no—
144#324—948no—
145C47#830611yescharacteristic, complemented, Sylow
146C23×C4—472no—
147C23×C4—472no—
148C23×C4C4×D4711yescharacteristic
149C23×C4C4×D4711yescharacteristic
150C23×C4C22×D4711yescharacteristic
151C22×C8—22no—
152C22×C8—942no—
153#125—9416no—
154#125—9416no—
155C2×C4⋊C4—478no—
156C2×C4⋊C4—944no—
157C2×C4⋊C4—944no—
158C2×C4⋊C4—944no—
159C2×C4⋊C4—944no—
160C2×C4⋊C4—944no—
161C2×C4⋊C4—942no—
162C2×C4⋊C4—942no—
163C2×C4⋊C4—942no—
164C2×C4⋊C4—944no—
165C2×C4⋊C4—942no—
166C2×C42—24no—
167C2×C42D18812yes—
168C2×C42C22⋊D4712yes—
169C22⋊C8—24no—
170C22⋊C8—944no—
171C24C2×C4×D4711yescharacteristic
172C22×C4—22no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—474no—
179C22×C4—474no—
180C22×C4—942no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4—942no—
184C22×C4—944no—
185C22×C4—944no—
186C22×C4—1884no—
187C22×C4(C2×D47)⋊C412yes—
188C22×C4(C2×D47)⋊C412yes—
189C22×C4C2×D18811yescharacteristic
190C22×C4D4×D4714yes—
191C22×C4C2×C22⋊D4711yescharacteristic
192C2×C8—44no—
193C2×C8—42no—
194C2×C8—1884no—
195C2×C8—1882no—
196C4⋊C4—9416no—
197C4⋊C4—948no—
198C4⋊C4—948no—
199C4⋊C4—948no—
200C4⋊C4—948no—
201C42—24no—
202C42—24no—
203C23—22no—
204C23—22no—
205C23C22⋊C4×D4712yes—
206C23C2×(C2×D47)⋊C411yescharacteristic
207C23#1309403012yes—
208C23#1309403212yes—
209C2×C4—28no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—44no—
218C2×C4—44no—
219C2×C4—944no—
220C2×C4—944no—
221C2×C4—948no—
222C2×C4—1884no—
223C2×C4—1884no—
224C2×C4—1882no—
225C2×C4—1882no—
226C2×C4—1884no—
227C2×C4—1884no—
228C2×C4#1309394214yes—
229C2×C4#1309399212yes—
230C2×C4#1309399412yes—
231C8—82no—
232C8—3762no—
233C22—24no—
234C22—24no—
235C22—22no—
236C22—22no—
237C22#1568897811yescharacteristic
238C22#1568908814yes—
239C22#1568908911yescharacteristic
240C22#1568909111yescharacteristic
241C22#1568909612yes—
242C22C2×#1309394212yes—
243C4—22no—
244C4—22no—
245C4—24no—
246C4—42no—
247C4—1884no—
248C4—1884no—
249C2—24no—
250C2#2024174312yes—
251C2#2024174512yes—
252C2#2024329911yescharacteristic
253C2#2024330511yescharacteristic
254C2#2024331111yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutator, prime radicalC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1817C2
socleC23×C47C2×C22⋊C4
cosocleC23×C4×C47C23
hypercenter#1817D47
hypocenterC47#8306
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
145. C47#8306semidirect

Maximal subgroups

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

subgroupindex
C22×#130940162
#202434562
C2×#156888482
C47×#18172
#830647