Finite Group Databasebeta

← #26118939

Subgroups — #26118939

Order 12032.

542 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 111 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#20254513C212yesmaximal
2#20251766C211yesmaximal, characteristic, complemented
3#20242074C212yesmaximal, complemented
4#20241221C211yesmaximal, characteristic, complemented
5C47×#1962C211yesmaximal, characteristic
6C2×#13094024C2212yes—
7#15689519—22no—
8#15689469—22no—
9#15689439—24no—
10#15689413—24no—
11#15689176C2212yes—
12#15689029—24no—
13#15688989—22no—
14#15688868—24no—
15C47×#532C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C2×#104×C47—22no—
18C43×C47C2211yescharacteristic
19C22×Dic94—22no—
20#13094024—22no—
21#13094024—22no—
22#13094024—22no—
23#13094024—22no—
24C2×C4⋊Dic47—22no—
25C2×C4⋊Dic47D414yes—
26#13093955—28no—
27C4⋊(C47⋊C8)D414yes—
28#13093945—28no—
29C22⋊(C47⋊C8)—22no—
30C4×C47⋊C8—22no—
31C47⋊#95—28no—
32C2×#41×C47—21no—
33C2×M16×C47—21no—
34C4⋊Q8×C47D411yescharacteristic
35#127×C47D411yescharacteristic
36#124×C47—21no—
37#121×C47—22no—
38C4×D4×C47—22no—
39C2×C42×C47—22no—
40C2×C42×C47D412yes—
41C2×C42×C47C2311yescharacteristic
42C4⋊C8×C47—22no—
43#104×C47—44no—
44#41×C47—42no—
45#41×C47—42no—
46C2×Q8×C47—21no—
47C2×D4×C47—22no—
48C2×D4×C47—21no—
49C2×D4×C47—41no—
50C22×C4×C47—22no—
51C22×C4×C47—41no—
52C22×C4×C47C2×D412yes—
53C22×C4×C47C2×D411yescharacteristic
54C22×Dic47—24no—
55C2×Dic94—48no—
56C2×Dic94—42no—
57C2×Dic94—42no—
58M16×C47—42no—
59C2×C8×C47—41no—
60C4⋊C4×C47—22no—
61C22⋊C4×C47—42no—
62C42×C47—22no—
63C42×C47—44no—
64C42×C47SD1614yes—
65C42×C47C2×D411yescharacteristic
66C42×C47C2×D412yes—
67C42×C47#4111yescharacteristic
68C4⋊Dic47—24no—
69C4⋊Dic47—24no—
70C4⋊Dic47—42no—
71C4⋊Dic47—42no—
72C2×C47⋊C8—24no—
73C23×C47—41no—
74C23×C47#12011yescharacteristic
75Q8×C47—42no—
76D4×C47—44no—
77D4×C47—42no—
78D4×C47—82no—
79C2×C4×C47—24no—
80C2×C4×C47—24no—
81C2×C4×C47—44no—
82C2×C4×C47—41no—
83C2×C4×C47—81no—
84C2×C4×C47—81no—
85C2×C4×C47#12012yes—
86C2×C4×C47#12112yes—
87C2×C4×C47#12111yescharacteristic
88C2×C4×C47#12711yescharacteristic
89C2×C4×C47C2×SD1612yes—
90C2×C4×C47#13712yes—
91C2×Dic47—48no—
92C2×Dic47—44no—
93Dic94—84no—
94Dic94—84no—
95C8×C47—81no—
96C47⋊C8—44no—
97#10285—471nomaximal, Sylow
98C22×C47—22no—
99C22×C47—82no—
100C22×C47—81no—
101C22×C47#39211yescharacteristic
102C22×C47#44812yes—
103C4×C47—22no—
104C4×C47—44no—
105C4×C47—81no—
106C4×C47#45414yes—
107C4×C47#46112yes—
108C4×C47#49211yescharacteristic
109C4×C47#49711yescharacteristic
110Dic47—84no—
111#3227—472no—
112#2862—471no—
113#1962D4711yescharacteristic
114#1549—472no—
115#1276—471no—
116C2×C47—22no—
117C2×C47—161no—
118C2×C47#200312yes—
119C2×C47#201311yescharacteristic
120#532C2×D4711yescharacteristic
121C2×C4⋊Q8—472no—
122#498—942no—
123#486—942no—
124#481—944no—
125#476—944no—
126#431—472no—
127#423C2×D4711yescharacteristic
128C2×#104—22no—
129#391—944no—
130#382—942no—
131C43C2×D4711yescharacteristic
132#332—944no—
133C47#1028511yescharacteristic, complemented, Sylow
134C2×#41—21no—
135C22×Q8—942no—
136C2×M16—21no—
137C4⋊Q8—942no—
138C4⋊Q8—942no—
139C4⋊Q8—942no—
140C4⋊Q8—942no—
141C4⋊Q8D18811yescharacteristic
142#127D18811yescharacteristic
143#124—21no—
144#121—22no—
145C4×D4—22no—
146C2×C4⋊C4—474no—
147C2×C4⋊C4—942no—
148C2×C42—22no—
149C2×C42C22⋊D4712yes—
150C2×C42C22×D4711yescharacteristic
151#106—948no—
152C4⋊C8—22no—
153C4⋊C8—474no—
154#104—44no—
155#102—948no—
156C22⋊C8—942no—
157C4×C8—942no—
158#95—948no—
159#41—42no—
160#41—42no—
161C2×Q8—21no—
162C2×Q8—1888no—
163C2×Q8—1882no—
164C2×Q8—1882no—
165C2×D4—22no—
166C2×D4—21no—
167C2×D4—41no—
168C22×C4—22no—
169C22×C4—41no—
170C22×C4—944no—
171C22×C4D4×D4712yes—
172C22×C4C2×C22⋊D4711yescharacteristic
173M16—42no—
174C2×C8—41no—
175C2×C8—944no—
176C4⋊C4—22no—
177C4⋊C4—944no—
178C4⋊C4—944no—
179C4⋊C4—1882no—
180C4⋊C4—1882no—
181C22⋊C4—42no—
182C42—22no—
183C42—44no—
184C42#1062533514yes—
185C42C2×D18811yescharacteristic
186C42#1062535011yescharacteristic
187C42D4×D4712yes—
188C23—41no—
189C23#1309399211yescharacteristic
190Q8—42no—
191Q8—3764no—
192Q8—3764no—
193D4—44no—
194D4—42no—
195D4—82no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—41no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—1888no—
203C2×C4—1884no—
204C2×C4#1309399412yes—
205C2×C4#1309399712yes—
206C2×C4#1309399811yescharacteristic
207C2×C4#1309402011yescharacteristic
208C2×C4C2×#1062533512yes—
209C2×C4#1309405412yes—
210C8—81no—
211C8—1884no—
212C22—22no—
213C22—82no—
214C22—81no—
215C22#1568903211yescharacteristic
216C22#1568926112yes—
217C4—22no—
218C4—44no—
219C4—81no—
220C4—3764no—
221C4#1568929714yes—
222C4#1568932812yes—
223C4#1568949511yescharacteristic
224C4#1568951811yescharacteristic
225C2—22no—
226C2—161no—
227C2#2024440912yes—
228C2#2024447011yescharacteristic
subgroupG/H
centerC22#15689032
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1962C2
socleC22×C47#392
prime radicalC47×#532C22
hypercenter#1962D47
hypocenterC47#10285
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #20251766C2semidirect
3. #20242074C2semidirect
4. #20241221C2semidirect
133. C47#10285semidirect

Maximal subgroups

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

subgroupindex
#202545132
#202517662
#202420742
#202412212
C47×#19622
#1028547