Finite Group Databasebeta

← #26113795

Subgroups — #26113795

Order 12032.

488 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 99 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#20253848C211yesmaximal, characteristic
2#20242106C212yesmaximal, complemented
3#20242023C211yesmaximal, characteristic
4#20241259C212yesmaximal, complemented
5C47×#2980C211yesmaximal, characteristic
6C2×#13094054—22no—
7C2×#13094024C2211yescharacteristic
8#15689518—22no—
9#15689502C412yes—
10#15689495C412yes—
11#15689180C2212yes—
12C4×#10625329C2211yescharacteristic
13#15688870—24no—
14#15688863—22no—
15C47×#532C2211yescharacteristic
16C47×#435—24no—
17C47×#432C2212yes—
18C47×#408—22no—
19C22×Dic94—21no—
20#13094054—44no—
21#13094054—44no—
22C2×#10625337—24no—
23C2×#10625335—24no—
24C2×#10625329—21no—
25#13094024—22no—
26#13094024—21no—
27#13094024C2×C412yes—
28C2×C4⋊Dic47—22no—
29C4⋊(C47⋊C8)—22no—
30C22⋊(C47⋊C8)—22no—
31#13093935—21no—
32#13093935—22no—
33C4×C47⋊C8C2×C412yes—
34C2×#41×C47D412yes—
35C2×M16×C47—22no—
36C22×C8×C47—22no—
37C4⋊Q8×C47C2×C411yescharacteristic
38#127×C47C2×C411yescharacteristic
39#124×C47D412yes—
40#121×C47—22no—
41C4×D4×C47—22no—
42C2×C42×C47C2311yescharacteristic
43C4⋊C8×C47D414yes—
44C22⋊C8×C47—24no—
45C22⋊C8×C47—22no—
46#97×C47—22no—
47#41×C47—42no—
48#41×C47—42no—
49C2×Q8×C47C22⋊C412yes—
50C2×D4×C47—22no—
51C2×D4×C47—22no—
52C2×D4×C47C22⋊C412yes—
53C22×C4×C47—22no—
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47#4112yes—
56C22×Dic47—41no—
57C2×Dic94—22no—
58C2×Dic94—42no—
59C2×Dic94—42no—
60C2×Dic94—41no—
61M16×C47—82no—
62C2×C8×C47—24no—
63C2×C8×C47—82no—
64C4⋊C4×C47—22no—
65C22⋊C4×C47—24no—
66C42×C47C22×C411yescharacteristic
67C42×C47C2×D411yescharacteristic
68C42×C47C2×D412yes—
69#10625337—48no—
70#10625335—48no—
71C4⋊Dic47—24no—
72C4⋊Dic47—42no—
73#10625329—24no—
74C2×C47⋊C8—22no—
75C2×C47⋊C8—42no—
76C23×C47—22no—
77C23×C47#12311yescharacteristic
78Q8×C47—42no—
79D4×C47—42no—
80D4×C47—82no—
81D4×C47—82no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—42no—
85C2×C4×C47—42no—
86C2×C4×C47—42no—
87C2×C4×C47C2×C22⋊C411yescharacteristic
88C2×C4×C47C4×D412yes—
89C2×C4×C47#12011yescharacteristic
90C2×C4×C47#12112yes—
91C2×Dic47—42no—
92C2×Dic47—81no—
93C2×Dic47—81no—
94Dic94—44no—
95Dic94—82no—
96C8×C47—44no—
97C47⋊C8—24no—
98C47⋊C8—82no—
99#9421—471nomaximal, Sylow
100C22×C47—21no—
101C22×C47—22no—
102C22×C47—42no—
103C22×C47—44no—
104C22×C47#38611yescharacteristic
105C4×C47—21no—
106C4×C47—22no—
107C4×C47—22no—
108C4×C47—42no—
109C4×C47#45312yes—
110Dic47—82no—
111#3152—471no—
112#2980D4711yescharacteristic
113#1556—472no—
114#1536—471no—
115#1291—472no—
116C2×C47—41no—
117C2×C47—82no—
118C2×C47#188711yescharacteristic
119C2×C47#190212yes—
120C2×#137—942no—
121#532C2×D4711yescharacteristic
122C2×C4⋊Q8—471no—
123#497—942no—
124#494—472no—
125#492—472no—
126#435—24no—
127#432—472no—
128#432C2×D4712yes—
129#408—22no—
130C4×M16—471no—
131#332—944no—
132#329—942no—
133C47#942111yescharacteristic, complemented, Sylow
134C2×#41C22⋊D4712yes—
135C22×Q8—941no—
136#137—1884no—
137#137—1884no—
138C2×Q16—944no—
139C2×SD16—944no—
140C2×M16—22no—
141C2×M16—941no—
142C22×C8—22no—
143C4⋊Q8—472no—
144C4⋊Q8—941no—
145C4⋊Q8—942no—
146C4⋊Q8C4×D4711yescharacteristic
147#127C4×D4711yescharacteristic
148#124D18812yes—
149#121—22no—
150C4×D4—22no—
151C2×C4⋊C4—942no—
152C2×C42C22×D4711yescharacteristic
153C4⋊C8—942no—
154C4⋊C8C22⋊D4714yes—
155C22⋊C8—24no—
156C22⋊C8—22no—
157C22⋊C8—942no—
158#97—22no—
159#97—941no—
160#97—942no—
161C4×C8—472no—
162#41—42no—
163#41—42no—
164C2×Q8—942no—
165C2×Q8—1882no—
166C2×Q8—1882no—
167C2×Q8—1881no—
168C2×Q8(C2×D47)⋊C412yes—
169C2×D4—22no—
170C2×D4—22no—
171C2×D4(C2×D47)⋊C412yes—
172C22×C4—22no—
173C22×C4—1881no—
174C22×C4#1062535012yes—
175C22×C4C2×C22⋊D4711yescharacteristic
176Q16—1888no—
177SD16—1888no—
178M16—82no—
179M16—944no—
180C2×C8—24no—
181C2×C8—82no—
182C2×C8—942no—
183C2×C8—1882no—
184C4⋊C4—22no—
185C4⋊C4—944no—
186C4⋊C4—1882no—
187C22⋊C4—24no—
188C42C2×C4×D4711yescharacteristic
189C42C2×D18811yescharacteristic
190C42C2×C22⋊D4712yes—
191C23—22no—
192C23#1309400711yescharacteristic
193Q8—42no—
194Q8—3762no—
195Q8—1884no—
196D4—42no—
197D4—82no—
198D4—82no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—3761no—
205C2×C4—3761no—
206C2×C4—1882no—
207C2×C4C2×(C2×D47)⋊C411yescharacteristic
208C2×C4C4×C22⋊D4712yes—
209C2×C4#1309399311yescharacteristic
210C2×C4#1309399812yes—
211C8—44no—
212C8—944no—
213C8—3762no—
214C22—21no—
215C22—22no—
216C22—42no—
217C22—44no—
218C22#1568900211yescharacteristic
219C4—21no—
220C4—22no—
221C4—22no—
222C4—42no—
223C4—3762no—
224C4#1568929112yes—
225C2—41no—
226C2—82no—
227C2#2024378611yescharacteristic
228C2#2024386112yes—
subgroupG/H
centerC22#15689002
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2980C2
socleC22×C47#386
prime radicalC47×#532C22
cosocleC2×C42×C47C23
hypercenter#2980D47
hypocenterC47#9421
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2980

Complements

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

NH ≅ G/Ntype
2. #20242106C2semidirect
4. #20241259C2semidirect
133. C47#9421semidirect

Maximal subgroups

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

subgroupindex
#202538482
#202421062
#202420232
#202412592
C47×#29802
#942147