Finite Group Databasebeta

← #26118570

Subgroups — #26118570

Order 12032.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#20254529C212yesmaximal
2#20244208C211yesmaximal, characteristic
3#20241952C212yesmaximal
4#20241233C211yesmaximal, characteristic
5C47×#3162C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7#15689519—22no—
8#15689473—22no—
9#15689451—24no—
10#15689408—24no—
11#15689176C2212yes—
12C2×#13093949—22no—
13#15688989C2211yescharacteristic
14#15688860—24no—
15C47×#533C2212yes—
16C47×#501—22no—
17C47×#501—22no—
18C47×#427—22no—
19C2×#97×C47C2211yescharacteristic
20C22×Dic94—21no—
21#13094024—22no—
22#13094024—21no—
23#13094024D412yes—
24C2×C4⋊Dic47—22no—
25C2×C4⋊Dic47—21no—
26#13093955—28no—
27C4⋊(C47⋊C8)—22no—
28#13093949—44no—
29#13093948—28no—
30C22⋊(C47⋊C8)D414yes—
31C4×C47⋊C8—22no—
32C47⋊#95—22no—
33C22×C8×C47D412yes—
34C4⋊Q8×C47D412yes—
35C4⋊Q8×C47D412yes—
36#125×C47—22no—
37C22⋊Q8×C47—22no—
38C22⋊Q8×C47—22no—
39C4×Q8×C47—22no—
40C4×Q8×C47—22no—
41#117×C47—22no—
42C2×C42×C47C2311yescharacteristic
43#107×C47—24no—
44#106×C47—22no—
45#106×C47—22no—
46#97×C47—22no—
47C2×Q8×C47—22no—
48C2×Q8×C47—22no—
49C22×C4×C47C2×D412yes—
50C22×C4×C47C2×D411yescharacteristic
51C22×Dic47—41no—
52C22×Dic47—41no—
53C2×Dic94—22no—
54C2×Dic94—42no—
55C2×Dic94—42no—
56C2×Dic94—41no—
57C2×C8×C47—22no—
58C2×C8×C47—22no—
59C2×C8×C47SD1614yes—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—22no—
62C4⋊C4×C47—22no—
63C4⋊C4×C47—22no—
64C4⋊C4×C47—42no—
65C4⋊C4×C47—42no—
66C22⋊C4×C47—42no—
67C42×C47—42no—
68C42×C47C2×D411yescharacteristic
69C42×C47C2×D412yes—
70C42×C47#4111yescharacteristic
71C4⋊Dic47—24no—
72C4⋊Dic47—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—42no—
81C2×C4×C47#12012yes—
82C2×C4×C47#12011yescharacteristic
83C2×C4×C47#12111yescharacteristic
84C2×C4×C47#12112yes—
85C2×C4×C47C2×SD1612yes—
86C2×C4×C47#13712yes—
87C2×Dic47—42no—
88C2×Dic47—81no—
89C2×Dic47—81no—
90C2×Dic47—82no—
91C2×Dic47—81no—
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—82no—
105C4×C47#44812yes—
106C4×C47#46112yes—
107Dic47—82no—
108Dic47—161no—
109#3229—472no—
110#3162D4711yescharacteristic
111#1960—471no—
112#1518—472no—
113#1281—471no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47#200912yes—
117C2×C47#201311yescharacteristic
118#533C2×D4712yes—
119C2×C4⋊Q8—471no—
120#501—22no—
121#501—22no—
122#498—942no—
123#487—942no—
124#483—944no—
125#475—944no—
126#431—472no—
127#427—22no—
128C2×#103—942no—
129C2×#97C2×D4711yescharacteristic
130#382—471no—
131#328—944no—
132C47#1022711yescharacteristic, complemented, Sylow
133C22×Q8—941no—
134C22×C8C22⋊D4712yes—
135C4⋊Q8—472no—
136C4⋊Q8—941no—
137C4⋊Q8—942no—
138C4⋊Q8C22⋊D4712yes—
139C4⋊Q8C22⋊D4712yes—
140#125—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145#117—22no—
146C2×C4⋊C4—942no—
147C2×C4⋊C4—941no—
148C2×C42C22×D4711yescharacteristic
149#107—24no—
150#106—22no—
151#106—22no—
152#106—948no—
153C4⋊C8—942no—
154#103—948no—
155#103—1884no—
156C22⋊C8—474no—
157#97—22no—
158C4×C8—942no—
159#95—942no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—942no—
163C2×Q8—1882no—
164C2×Q8—1882no—
165C2×Q8—1881no—
166C22×C4—1881no—
167C22×C4—1881no—
168C22×C4D4×D4712yes—
169C22×C4C2×C22⋊D4711yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—944no—
173C2×C8#1062533614yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—944no—
181C4⋊C4—1882no—
182C4⋊C4—1882no—
183C22⋊C4—42no—
184C42—42no—
185C42D4×D4711yescharacteristic
186C42#1062535211yescharacteristic
187C42C2×C22⋊D4712yes—
188C23#1309402011yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—3762no—
192Q8—1884no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—3761no—
197C2×C4—3761no—
198C2×C4—3762no—
199C2×C4—3761no—
200C2×C4—1882no—
201C2×C4#1309399212yes—
202C2×C4#1309399311yescharacteristic
203C2×C4#1309399511yescharacteristic
204C2×C4#1309399612yes—
205C2×C4C2×#1062533612yes—
206C2×C4#1309405512yes—
207C8—24no—
208C8—1884no—
209C22—22no—
210C22#1568903111yescharacteristic
211C22#1568949711yescharacteristic
212C22#1568951511yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—3762no—
218C4—7521no—
219C4#1568926212yes—
220C4#1568932512yes—
221C2—21no—
222C2—21no—
223C2#2024444512yes—
224C2#2024447111yescharacteristic
subgroupG/H
centerC22#15689031
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#3162C2
socleC22×C47#392
prime radicalC23×C47#127
hypercenter#3162D47
hypocenterC47#10227
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

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
#202545292
#202442082
#202419522
#202412332
C47×#31622
#1022747