Finite Group Databasebeta

← #26118572

Subgroups — #26118572

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#20254534C212yesmaximal
2#20253912C211yesmaximal, characteristic
3#20244208C211yesmaximal, characteristic
4#20241953C212yesmaximal
5C47×#1281C211yesmaximal, characteristic
6#15689680C2212yes—
7C2×#13094024C2211yescharacteristic
8#15689532—22no—
9#15689532—22no—
10#15689521—22no—
11#15689474—22no—
12#15689454—24no—
13#15689409—24no—
14#15689161—22no—
15C2×#13093949—22no—
16#15688989C2211yescharacteristic
17#15688861—24no—
18C47×#431C2212yes—
19C2×#97×C47C2211yescharacteristic
20C22×Dic94—21no—
21#13094024—22no—
22#13094024—21no—
23#13094024D412yes—
24#13094024D412yes—
25#13094024D412yes—
26#13094016—22no—
27#13094003—22no—
28#13094003—22no—
29C4×Dic94—22no—
30C4×Dic94—22no—
31#13093983—22no—
32C2×C4⋊Dic47—22no—
33C2×C4⋊Dic47—21no—
34#13093958—24no—
35#13093956—28no—
36#13093956—22no—
37#13093956—22no—
38#13093949—28no—
39#13093949—44no—
40C47⋊#95—22no—
41C22×C8×C47D412yes—
42C2×C42×C47C2311yescharacteristic
43C4⋊C8×C47—22no—
44C22⋊C8×C47D414yes—
45#97×C47—22no—
46C4×C8×C47—22no—
47C22×C4×C47C2×D412yes—
48C22×C4×C47C2×D411yescharacteristic
49C22×Dic47—41no—
50C22×Dic47—41no—
51C2×Dic94—22no—
52C2×Dic94—22no—
53C2×Dic94—22no—
54C2×Dic94—42no—
55C2×Dic94—42no—
56C2×Dic94—41no—
57C2×C8×C47—22no—
58C2×C8×C47—22no—
59C2×C8×C47—24no—
60C2×C8×C47SD1614yes—
61C42×C47C2×D411yescharacteristic
62C42×C47C2×D412yes—
63C42×C47#4111yescharacteristic
64C22⋊Dic47—42no—
65C4⋊Dic47—24no—
66C4⋊Dic47—22no—
67C4⋊Dic47—22no—
68C4⋊Dic47—22no—
69C4⋊Dic47—22no—
70C4⋊Dic47—42no—
71C4⋊Dic47—42no—
72Dic47⋊C4—42no—
73Dic47⋊C4—42no—
74C4×Dic47—42no—
75C23×C47#12711yescharacteristic
76C2×C4×C47—42no—
77C2×C4×C47#12012yes—
78C2×C4×C47#12011yescharacteristic
79C2×C4×C47#12112yes—
80C2×C4×C47#12111yescharacteristic
81C2×C4×C47C2×SD1612yes—
82C2×C4×C47#13712yes—
83C2×Dic47—42no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C2×Dic47—81no—
87C2×Dic47—81no—
88C2×Dic47—82no—
89C2×Dic47—81no—
90Dic94—44no—
91Dic94—44no—
92Dic94—82no—
93Dic94—82no—
94C8×C47—24no—
95C8×C47—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#44812yes—
104C4×C47#46112yes—
105Dic47—82no—
106Dic47—82no—
107Dic47—82no—
108Dic47—161no—
109#3229—472no—
110#3162—471no—
111#1960—471no—
112#1518—472no—
113#1281D4711yescharacteristic
114C2×C47—21no—
115C2×C47—21no—
116C2×C47#200912yes—
117C2×C47#201311yescharacteristic
118#533—472no—
119C2×C4⋊Q8—471no—
120#501—942no—
121#501—942no—
122#498—942no—
123#487—942no—
124#483—944no—
125#475—944no—
126#431C2×D4712yes—
127#427—942no—
128C2×#103—942no—
129C2×#97C2×D4711yescharacteristic
130#382—471no—
131#328—944no—
132C47#1022711yescharacteristic, complemented, Sylow
133C22×Q8—941no—
134C22×C8D18812yes—
135C4⋊Q8—472no—
136C4⋊Q8—472no—
137C4⋊Q8—472no—
138C4⋊Q8—942no—
139C4⋊Q8—941no—
140#125—942no—
141C22⋊Q8—942no—
142C22⋊Q8—942no—
143C4×Q8—942no—
144C4×Q8—942no—
145#117—942no—
146C2×C4⋊C4—942no—
147C2×C4⋊C4—941no—
148C2×C42C22×D4711yescharacteristic
149#107—944no—
150#106—942no—
151#106—942no—
152#106—948no—
153C4⋊C8—22no—
154#103—948no—
155#103—1884no—
156C22⋊C8D18814yes—
157#97—22no—
158C4×C8—22no—
159#95—942no—
160C2×Q8—942no—
161C2×Q8—942no—
162C2×Q8—942no—
163C2×Q8—1882no—
164C2×Q8—1882no—
165C2×Q8—1881no—
166C22×C4—1881no—
167C22×C4—1881no—
168C22×C4C2×D18812yes—
169C22×C4C2×D18811yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—24no—
173C2×C8#1062532514yes—
174C4⋊C4—944no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—1882no—
180C4⋊C4—1882no—
181C4⋊C4—1882no—
182C4⋊C4—1882no—
183C22⋊C4—1882no—
184C42—1882no—
185C42D4×D4712yes—
186C42D4×D4711yescharacteristic
187C42#1062535411yescharacteristic
188C23#1309402111yescharacteristic
189Q8—3762no—
190Q8—3762no—
191Q8—1884no—
192Q8—1884no—
193C2×C4—42no—
194C2×C4—3761no—
195C2×C4—3761no—
196C2×C4—3762no—
197C2×C4—3761no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4#1309399412yes—
202C2×C4#1309399411yescharacteristic
203C2×C4#1309399912yes—
204C2×C4#1309399911yescharacteristic
205C2×C4C2×#1062532512yes—
206C2×C4#1309405712yes—
207C8—24no—
208C8—44no—
209C22—22no—
210C22#1568903311yescharacteristic
211C22#1568949611yescharacteristic
212C22#1568951711yescharacteristic
213C4—22no—
214C4—22no—
215C4—3762no—
216C4—3762no—
217C4—3762no—
218C4—7521no—
219C4#1568926412yes—
220C4#1568932912yes—
221C2—21no—
222C2—21no—
223C2#2024445112yes—
224C2#2024447311yescharacteristic
subgroupG/H
centerC22#15689033
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1281C2
socleC22×C47#392
prime radicalC23×C47#127
hypercenter#1281D47
hypocenterC47#10227
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

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
#202545342
#202539122
#202442082
#202419532
C47×#12812
#1022747