Finite Group Databasebeta

← #26118569

Subgroups — #26118569

Order 12032.

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

normal subgroups only

This group has 466 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#20254532C212yesmaximal
2#20253912C211yesmaximal, characteristic
3#20241951C212yesmaximal
4#20241233C211yesmaximal, characteristic
5C47×#1960C211yesmaximal, characteristic
6#15689680C2212yes—
7#15689532—22no—
8#15689532—22no—
9#15689519—22no—
10#15689475—22no—
11#15689453—24no—
12#15689405—24no—
13#15689176C2212yes—
14#15689161—22no—
15#15688859—24no—
16C2×C4⋊Q8×C47C2211yescharacteristic
17C2×#103×C47—22no—
18C2×#97×C47C2211yescharacteristic
19C47×#382C2211yescharacteristic
20#13094024D412yes—
21#13094024D412yes—
22#13094016—22no—
23#13094003—22no—
24#13094003—22no—
25C4×Dic94—22no—
26C4×Dic94—22no—
27#13093983—22no—
28#13093958—24no—
29#13093956—22no—
30#13093956—22no—
31#13093955—28no—
32C4⋊(C47⋊C8)—22no—
33#13093947—28no—
34C22⋊(C47⋊C8)D414yes—
35C4×C47⋊C8—22no—
36C22×Q8×C47—21no—
37C22×C8×C47D412yes—
38C4⋊Q8×C47—22no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47D412yes—
41C2×C4⋊C4×C47—22no—
42C2×C4⋊C4×C47—21no—
43C2×C42×C47C2311yescharacteristic
44#103×C47—44no—
45#97×C47—22no—
46#95×C47—22no—
47C2×Q8×C47—22no—
48C2×Q8×C47—41no—
49C2×Q8×C47—42no—
50C2×Q8×C47—42no—
51C22×C4×C47—41no—
52C22×C4×C47—41no—
53C22×C4×C47C2×D412yes—
54C22×C4×C47C2×D411yescharacteristic
55C2×Dic94—22no—
56C2×Dic94—22no—
57C2×C8×C47—22no—
58C2×C8×C47—22no—
59C2×C8×C47SD1614yes—
60C4⋊C4×C47—24no—
61C4⋊C4×C47—42no—
62C4⋊C4×C47—42no—
63C42×C47C2×D411yescharacteristic
64C42×C47C2×D412yes—
65C42×C47#4111yescharacteristic
66C22⋊Dic47—42no—
67C4⋊Dic47—22no—
68C4⋊Dic47—22no—
69C4⋊Dic47—22no—
70C4⋊Dic47—22no—
71Dic47⋊C4—42no—
72Dic47⋊C4—42no—
73C4×Dic47—42no—
74C2×C47⋊C8—24no—
75C23×C47#12711yescharacteristic
76Q8×C47—44no—
77Q8×C47—82no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—81no—
81C2×C4×C47—81no—
82C2×C4×C47—82no—
83C2×C4×C47—81no—
84C2×C4×C47#12011yescharacteristic
85C2×C4×C47#12012yes—
86C2×C4×C47#12112yes—
87C2×C4×C47#12111yescharacteristic
88C2×C4×C47C2×SD1612yes—
89C2×C4×C47#13712yes—
90C2×Dic47—42no—
91C2×Dic47—42no—
92Dic94—44no—
93Dic94—82no—
94C8×C47—24no—
95C47⋊C8—44no—
96#10227—471nomaximal, Sylow
97C22×C47—22no—
98C22×C47#39211yescharacteristic
99C22×C47#49211yescharacteristic
100C22×C47#49711yescharacteristic
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—82no—
104C4×C47—161no—
105C4×C47#44812yes—
106C4×C47#46112yes—
107Dic47—82no—
108Dic47—82no—
109#3229—472no—
110#3162—471no—
111#1960D4711yescharacteristic
112#1518—472no—
113#1281—471no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47#200912yes—
117C2×C47#201311yescharacteristic
118#533—472no—
119C2×C4⋊Q8C2×D4711yescharacteristic
120#501—942no—
121#501—942no—
122#498—942no—
123#487—942no—
124#483—944no—
125#475—944no—
126#431—472no—
127#427—942no—
128C2×#103—22no—
129C2×#97C2×D4711yescharacteristic
130#382C2×D4711yescharacteristic
131#328—944no—
132C47#1022711yescharacteristic, complemented, Sylow
133C22×Q8—21no—
134C22×C8C22⋊D4712yes—
135C4⋊Q8—21no—
136C4⋊Q8—22no—
137C4⋊Q8—472no—
138C4⋊Q8—472no—
139C4⋊Q8D18812yes—
140#125—942no—
141C22⋊Q8—942no—
142C22⋊Q8—942no—
143C4×Q8—942no—
144C4×Q8—942no—
145#117—942no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C42C22×D4711yescharacteristic
149#107—944no—
150#106—948no—
151#106—942no—
152#106—942no—
153C4⋊C8—942no—
154#103—44no—
155#103—948no—
156C22⋊C8—474no—
157#97—22no—
158C4×C8—942no—
159#95—22no—
160C2×Q8—22no—
161C2×Q8—41no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—942no—
165C2×Q8—942no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4D4×D4712yes—
169C22×C4C2×C22⋊D4711yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—944no—
173C2×C8#1062533514yes—
174C4⋊C4—24no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—1882no—
182C4⋊C4—1882no—
183C22⋊C4—1882no—
184C42—1882no—
185C42C2×D18811yescharacteristic
186C42#1062535011yescharacteristic
187C42D4×D4712yes—
188C23#1309402011yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—3762no—
192Q8—1884no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—81no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4#1309399211yescharacteristic
202C2×C4#1309399412yes—
203C2×C4#1309399712yes—
204C2×C4#1309399811yescharacteristic
205C2×C4C2×#1062533512yes—
206C2×C4#1309405412yes—
207C8—24no—
208C8—1884no—
209C22—22no—
210C22#1568903211yescharacteristic
211C22#1568949511yescharacteristic
212C22#1568951811yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—161no—
217C4—3762no—
218C4—3762no—
219C4#1568926112yes—
220C4#1568932812yes—
221C2—21no—
222C2—21no—
223C2#2024445012yes—
224C2#2024447011yescharacteristic
subgroupG/H
centerC22#15689032
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1960C2
socleC22×C47#392
prime radicalC23×C47#127
hypercenter#1960D47
hypocenterC47#10227
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
132. C47#10227semidirect

Maximal subgroups

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

subgroupindex
#202545322
#202539122
#202419512
#202412332
C47×#19602
#1022747