Finite Group Databasebeta

← #26117273

Subgroups — #26117273

Order 12032.

476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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#20253912C211yesmaximal, characteristic
2#20253427C212yesmaximal
3#20241790C212yesmaximal
4#20241219C211yesmaximal, characteristic
5C47×#1985C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689532—22no—
8#15689532—22no—
9#15689458—22no—
10#15689418—22no—
11#15689333—22no—
12#15689279—22no—
13C4×#10625337—24no—
14#15689176C2212yes—
15#15689161—22no—
16#15688853—24no—
17C2×C4×Q8×C47C2211yescharacteristic
18C2×C4⋊C8×C47C2211yescharacteristic
19C2×#97×C47C2211yescharacteristic
20C47×#336—22no—
21C2×#10625337—24no—
22#13094024D412yes—
23#13094024D412yes—
24#13094016—22no—
25#13094003—22no—
26#13094003—22no—
27C4×Dic94—22no—
28C4×Dic94—22no—
29#13093983—22no—
30#13093958—22no—
31#13093958—22no—
32#13093957—24no—
33#13093956—24no—
34C4⋊(C47⋊C8)—22no—
35#13093948—24no—
36#13093947—24no—
37C22⋊(C47⋊C8)—22no—
38C4×C47⋊C8D414yes—
39C22×Q8×C47D411yescharacteristic
40C22×C8×C47—21no—
41C22×C8×C47D412yes—
42C4×Q8×C47—22no—
43C4×Q8×C47—22no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47D411yescharacteristic
46C2×C42×C47—21no—
47C2×C42×C47C2311yescharacteristic
48C4⋊C8×C47—22no—
49#97×C47—22no—
50C2×Q8×C47—22no—
51C2×Q8×C47—42no—
52C22×C4×C47—21no—
53C22×C4×C47—21no—
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47#4111yescharacteristic
57C2×Dic94—22no—
58C2×Dic94—22no—
59C2×C8×C47—22no—
60C2×C8×C47—22no—
61C2×C8×C47—41no—
62C2×C8×C47—42no—
63C2×C8×C47Q1614yescomplemented
64C4⋊C4×C47—22no—
65C4⋊C4×C47—42no—
66C42×C47—41no—
67C42×C47—41no—
68C42×C47C2×D412yes—
69C42×C47C2×D412yes—
70C22⋊Dic47—42no—
71#10625337—48no—
72C4⋊Dic47—22no—
73C4⋊Dic47—22no—
74C4⋊Dic47—22no—
75C4⋊Dic47—22no—
76Dic47⋊C4—42no—
77Dic47⋊C4—42no—
78C4×Dic47—42no—
79C2×C47⋊C8—24no—
80C23×C47#12111yescharacteristic
81Q8×C47—24no—
82Q8×C47—42no—
83C2×C4×C47—22no—
84C2×C4×C47—41no—
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47—42no—
89C2×C4×C47—41no—
90C2×C4×C47#12011yescharacteristic
91C2×C4×C47#12012yes—
92C2×C4×C47#12112yes—
93C2×C4×C47#12711yescharacteristic
94C2×C4×C47C2×Q1612yes—
95C2×C4×C47#13712yes—
96C2×Dic47—42no—
97C2×Dic47—42no—
98Dic94—44no—
99Dic94—44no—
100C8×C47—24no—
101C8×C47—81no—
102C47⋊C8—44no—
103#10037—471nomaximal, Sylow
104C22×C47—21no—
105C22×C47—21no—
106C22×C47#39211yescharacteristic
107C22×C47#46212yes—
108C4×C47—22no—
109C4×C47—22no—
110C4×C47—42no—
111C4×C47—81no—
112C4×C47#45112yes—
113C4×C47#49411yescharacteristic
114C4×C47#49711yescharacteristic
115Dic47—82no—
116Dic47—82no—
117#3162—471no—
118#3104—472no—
119#1985D4711yescharacteristic
120#1481—472no—
121#1275—471no—
122C2×C47—22no—
123C2×C47#201011yescharacteristic
124C2×C47#201611yescharacteristic
125C2×C47#201711yescharacteristic
126#533—472no—
127C2×C4×Q8C2×D4711yescharacteristic
128#501—942no—
129#501—942no—
130#484—942no—
131#477—942no—
132#462—942no—
133#451—942no—
134C4×Q16—944no—
135#431—472no—
136#427—942no—
137C2×C4⋊C8C2×D4711yescharacteristic
138C2×#97C2×D4711yescharacteristic
139#336—22no—
140Q8⋊C8—944no—
141C47#1003711yescharacteristic, complemented, Sylow
142C22×Q8D18811yescharacteristic
143C2×Q16—944no—
144C22×C8—21no—
145C22×C8C22⋊D4712yes—
146C4⋊Q8—472no—
147C4⋊Q8—472no—
148#125—942no—
149C22⋊Q8—942no—
150C22⋊Q8—942no—
151C4×Q8—22no—
152C4×Q8—22no—
153C4×Q8—942no—
154C4×Q8—942no—
155#117—942no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D18811yescharacteristic
158C2×C42—21no—
159C2×C42C22×D4711yescharacteristic
160#107—944no—
161#107—942no—
162#107—942no—
163#106—944no—
164C4⋊C8—22no—
165C4⋊C8—942no—
166#103—944no—
167#103—944no—
168C22⋊C8—942no—
169#97—22no—
170C4×C8—474no—
171C2×Q8—22no—
172C2×Q8—42no—
173C2×Q8—942no—
174C2×Q8—942no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D18811yescharacteristic
178C22×C4#1062535011yescharacteristic
179C22×C4C2×C22⋊D4711yescharacteristic
180Q16—1888no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—944no—
186C2×C8#1062533714yescomplemented
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—942no—
190C4⋊C4—942no—
191C4⋊C4—942no—
192C4⋊C4—942no—
193C4⋊C4—1882no—
194C4⋊C4—1882no—
195C22⋊C4—1882no—
196C42—41no—
197C42—41no—
198C42—1882no—
199C42D4×D4712yes—
200C42D4×D4712yes—
201C23#1309399811yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—1884no—
205Q8—1884no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—1882no—
214C2×C4—1882no—
215C2×C4#1309399211yescharacteristic
216C2×C4#1309399412yes—
217C2×C4#1309399712yes—
218C2×C4#1309402011yescharacteristic
219C2×C4C2×#1062533712yes—
220C2×C4#1309405412yes—
221C8—24no—
222C8—81no—
223C8—1884no—
224C22—21no—
225C22—21no—
226C22#1568903211yescharacteristic
227C22#1568933312yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—81no—
232C4—3762no—
233C4—3762no—
234C4#1568927812yes—
235C4#1568950211yescharacteristic
236C4#1568951811yescharacteristic
237C2—22no—
238C2#2024445511yescharacteristic
239C2#2024448711yescharacteristic
240C2#2024449211yescharacteristic
subgroupG/H
centerC2×C4#13094020
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1985C2
socleC22×C47#392
prime radicalC23×C47#121
hypercenter#1985D47
hypocenterC47#10037
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
63. C2×C8×C47Q16semidirect
141. C47#10037semidirect
186. C2×C8#10625337semidirect

Maximal subgroups

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

subgroupindex
#202539122
#202534272
#202417902
#202412192
C47×#19852
#1003747