Finite Group Databasebeta

← #26121306

Subgroups — #26121306

Order 12032.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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#20244369C211yesmaximal, characteristic
2#20242162C211yesmaximal, characteristic
3#20242158C211yesmaximal, characteristic
4#20241790C211yesmaximal, characteristic
5#20241790C211yesmaximal, characteristic
6#20241217C211yesmaximal, characteristic
7C47×#1832C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689176C2211yescharacteristic
10#15689176C2211yescharacteristic
11#15689147C2211yescharacteristic
12#15688883—22no—
13#15688875—22no—
14#15688873—22no—
15#15688853—22no—
16#15688853—22no—
17C2×C4⋊C8×C47C2211yescharacteristic
18C2×C4⋊C8×C47C2211yescharacteristic
19C47×#376C2211yescharacteristic
20C47×#336—22no—
21C2×#10625329—21no—
22#13094024Q811yescharacteristic
23#13094024Q811yescharacteristic
24#13094016—21no—
25#13094003—21no—
26#13094003—21no—
27C4×Dic94—21no—
28C4×Dic94—21no—
29#13093983—21no—
30C4⋊(C47⋊C8)—21no—
31C4⋊(C47⋊C8)—21no—
32C4⋊(C47⋊C8)—21no—
33C4⋊(C47⋊C8)—21no—
34C22⋊(C47⋊C8)—21no—
35C22⋊(C47⋊C8)—21no—
36C4×C47⋊C8D412yes—
37C4×C47⋊C8D412yes—
38C22×C8×C47—21no—
39C22×C8×C47—21no—
40C2×C42×C47D412yes—
41C2×C42×C47C2311yescharacteristic
42C4⋊C8×C47—21no—
43C4⋊C8×C47—21no—
44C4⋊C8×C47—21no—
45C4⋊C8×C47—21no—
46#95×C47—21no—
47#95×C47—21no—
48C22×C4×C47—22no—
49C22×C4×C47C2×D411yescharacteristic
50C22×C4×C47#4111yescharacteristic
51C22×C4×C47#4111yescharacteristic
52C2×Dic94—21no—
53C2×Dic94—21no—
54C2×C8×C47—41no—
55C2×C8×C47—41no—
56C2×C8×C47—42no—
57C2×C8×C47—42no—
58C42×C47—22no—
59C42×C47—22no—
60C42×C47C2×D411yescharacteristic
61C42×C47C2×D411yescharacteristic
62C42×C47C2×Q811yescharacteristic
63C42×C47#4111yescharacteristic
64C22⋊Dic47—41no—
65C4⋊Dic47—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47—21no—
68C4⋊Dic47—21no—
69Dic47⋊C4—41no—
70Dic47⋊C4—41no—
71C4×Dic47—41no—
72#10625329—42no—
73C2×C47⋊C8—22no—
74C2×C47⋊C8—22no—
75C2×C47⋊C8—41no—
76C23×C47#12311yescharacteristic
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—42no—
80C2×C4×C47—42no—
81C2×C4×C47—42no—
82C2×C4×C47C22⋊Q811yescharacteristic
83C2×C4×C47C22⋊Q811yescharacteristic
84C2×C4×C47C22⋊Q811yescharacteristic
85C2×C4×C47#12311yescharacteristic
86C2×C4×C47#12311yescharacteristic
87C2×C4×C47#12711yescharacteristic
88C2×C4×C47#13512yes—
89C2×C4×C47#13712yes—
90C2×Dic47—41no—
91C2×Dic47—41no—
92Dic94—42no—
93Dic94—42no—
94C8×C47—81no—
95C8×C47—81no—
96C47⋊C8—42no—
97C47⋊C8—42no—
98C47⋊C8—81no—
99#10669—471nomaximal, Sylow
100C22×C47—21no—
101C22×C47—21no—
102C22×C47#39911yescharacteristic
103C22×C47#48512yes—
104C4×C47—21no—
105C4×C47—21no—
106C4×C47—21no—
107C4×C47—21no—
108C4×C47—82no—
109C4×C47#47912yes—
110C4×C47#49511yescharacteristic
111C4×C47#49711yescharacteristic
112Dic47—81no—
113Dic47—81no—
114#1995—471no—
115#1832D4711yescharacteristic
116#1571—471no—
117#1570—471no—
118#1481—471no—
119#1481—471no—
120#1274—471no—
121C2×C47—22no—
122C2×C47#209711yescharacteristic
123C2×C47#209811yescharacteristic
124C2×C47#209811yescharacteristic
125#533—471no—
126#431—471no—
127#431—471no—
128#423—471no—
129C2×C4⋊C8C2×D4711yescharacteristic
130C2×C4⋊C8C2×D4711yescharacteristic
131#376C2×D4711yescharacteristic
132#339—942no—
133#336—22no—
134#335—942no—
135#334—942no—
136Q8⋊C8—942no—
137Q8⋊C8—942no—
138C47#1066911yescharacteristic, complemented, Sylow
139C2×M16—941no—
140C22×C8—21no—
141C22×C8—21no—
142C4⋊Q8—471no—
143C4⋊Q8—471no—
144#125—941no—
145C22⋊Q8—941no—
146C22⋊Q8—941no—
147C4×Q8—941no—
148C4×Q8—941no—
149#117—941no—
150C2×C42C22⋊D4712yes—
151C2×C42C22×D4711yescharacteristic
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—941no—
157C4⋊C8—941no—
158C4⋊C8—941no—
159C4⋊C8—941no—
160C22⋊C8—941no—
161C22⋊C8—941no—
162C4×C8—472no—
163C4×C8—472no—
164#95—21no—
165#95—21no—
166C2×Q8—941no—
167C2×Q8—941no—
168C22×C4—22no—
169C22×C4#1062535011yescharacteristic
170C22×C4#1062535011yescharacteristic
171C22×C4C2×C22⋊D4711yescharacteristic
172M16—1882no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—942no—
178C2×C8—942no—
179C2×C8—1881no—
180C4⋊C4—941no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4—1881no—
185C4⋊C4—1881no—
186C22⋊C4—1881no—
187C42—22no—
188C42—22no—
189C42—1881no—
190C42D4×D4711yescharacteristic
191C42D4×D4711yescharacteristic
192C42Q8×D4711yescharacteristic
193C42#1062535411yescharacteristic
194C23#1309400711yescharacteristic
195Q8—1882no—
196Q8—1882no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—1881no—
203C2×C4—1881no—
204C2×C4#1309400011yescharacteristic
205C2×C4#1309400211yescharacteristic
206C2×C4#1309400211yescharacteristic
207C2×C4#1309400911yescharacteristic
208C2×C4#1309400911yescharacteristic
209C2×C4#1309402011yescharacteristic
210C2×C4#1309404412yes—
211C2×C4#1309405412yes—
212C8—81no—
213C8—81no—
214C8—3761no—
215C8—1882no—
216C8—1882no—
217C22—21no—
218C22—21no—
219C22#1568905811yescharacteristic
220C22#1568946412yes—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—82no—
226C4—3761no—
227C4—3761no—
228C4#1568942712yes—
229C4#1568950511yescharacteristic
230C4#1568951811yescharacteristic
231C2—22no—
232C2#2024493911yescharacteristic
233C2#2024494411yescharacteristic
234C2#2024494411yescharacteristic
subgroupG/H
centerC2×C4#13094020
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1832C2
socleC22×C47#399
prime radicalC23×C47#123
hypercenter#1832D47
hypocenterC47#10669
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
138. C47#10669semidirect

Maximal subgroups

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

subgroupindex
#202443692
#202421622
#202421582
#202417902
#202412172
C47×#18322
#1066947