Finite Group Databasebeta

← #26121182

Subgroups — #26121182

Order 12032.

236 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 67 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#20242160C211yesmaximal, characteristic
2#20242116C211yesmaximal, characteristic
3#20242089C211yesmaximal, characteristic
4#20241860C211yesmaximal, characteristic
5#20241257C211yesmaximal, characteristic
6#20241249C211yesmaximal, characteristic
7C47×#1307C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689180C2211yescharacteristic
10#15689176C2211yescharacteristic
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12#15688873—22no—
13#15688871—21no—
14#15688870—21no—
15#15688870—21no—
16#15688868—21no—
17#15688853—22no—
18C47×#432C2211yescharacteristic
19C47×#432C2211yescharacteristic
20C47×#423C2211yescharacteristic
21C22×C47⋊C8—21no—
22#13094024D411yescharacteristic
23#13094024D411yescharacteristic
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—
36#13093935—21no—
37C4×C47⋊C8D412yes—
38C2×M16×C47—21no—
39C2×C42×C47C2311yescharacteristic
40C4⋊C8×C47—21no—
41C4⋊C8×C47—21no—
42C4⋊C8×C47—21no—
43C4⋊C8×C47—21no—
44C22⋊C8×C47—21no—
45C22⋊C8×C47—21no—
46#97×C47—21no—
47#97×C47—21no—
48C22×C4×C47#4111yescharacteristic
49C22×C4×C47#4111yescharacteristic
50C22×C4×C47#4111yescharacteristic
51C2×Dic94—21no—
52C2×Dic94—21no—
53M16×C47—81no—
54C2×C8×C47—41no—
55C2×C8×C47—41no—
56C2×C8×C47—41no—
57C42×C47C2×D411yescharacteristic
58C42×C47C2×D411yescharacteristic
59C42×C47#4111yescharacteristic
60C42×C47#4111yescharacteristic
61C22⋊Dic47—41no—
62C4⋊Dic47—21no—
63C4⋊Dic47—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—21no—
66Dic47⋊C4—41no—
67Dic47⋊C4—41no—
68C4×Dic47—41no—
69C2×C47⋊C8—22no—
70C2×C47⋊C8—41no—
71C2×C47⋊C8—41no—
72C2×C47⋊C8—81no—
73C23×C47#12611yescharacteristic
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47#12111yescharacteristic
79C2×C4×C47#12311yescharacteristic
80C2×C4×C47#12311yescharacteristic
81C2×C4×C47#12311yescharacteristic
82C2×C4×C47#12411yescharacteristic
83C2×C4×C47#12611yescharacteristic
84C2×Dic47—41no—
85C2×Dic47—41no—
86Dic94—41no—
87Dic94—41no—
88Dic94—81no—
89C8×C47—81no—
90C8×C47—81no—
91C8×C47—81no—
92C47⋊C8—42no—
93C47⋊C8—81no—
94C47⋊C8—81no—
95#10648—471nomaximal, Sylow
96C22×C47—21no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47#39711yescharacteristic
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—21no—
104C4×C47—21no—
105C4×C47#47111yescharacteristic
106C4×C47#47111yescharacteristic
107Dic47—81no—
108Dic47—81no—
109#1570—471no—
110#1559—471no—
111#1552—471no—
112#1497—471no—
113#1307D4711yescharacteristic
114#1290—471no—
115#1287—471no—
116C2×C47—41no—
117C2×C47#207911yescharacteristic
118C2×C47#208011yescharacteristic
119C2×C47#208211yescharacteristic
120#533—471no—
121#432—471no—
122#432C2×D4711yescharacteristic
123#432C2×D4711yescharacteristic
124#431—471no—
125#423C2×D4711yescharacteristic
126C2×C4⋊C8—471no—
127#334—942no—
128#333—941no—
129#332—941no—
130#332—941no—
131#332—941no—
132Q8⋊C8—942no—
133C47#1064811yescharacteristic, complemented, Sylow
134C2×M16—21no—
135C22×C8—941no—
136C4⋊Q8—471no—
137C4⋊Q8—471no—
138#125—941no—
139C22⋊Q8—941no—
140C22⋊Q8—941no—
141C4×Q8—941no—
142C4×Q8—941no—
143#117—941no—
144C2×C42C22×D4711yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—941no—
150C4⋊C8—941no—
151C4⋊C8—941no—
152C4⋊C8—941no—
153C22⋊C8—21no—
154C22⋊C8—21no—
155C22⋊C8—941no—
156C22⋊C8—941no—
157#97—21no—
158#97—21no—
159#97—941no—
160C4×C8—472no—
161C2×Q8—941no—
162C2×Q8—941no—
163C22×C4#1062535011yescharacteristic
164C22×C4#1062535011yescharacteristic
165C22×C4#1062535011yescharacteristic
166M16—81no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—942no—
171C2×C8—3761no—
172C2×C8—1881no—
173C2×C8—1881no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C4⋊C4—941no—
178C4⋊C4—1881no—
179C4⋊C4—1881no—
180C22⋊C4—1881no—
181C42—1881no—
182C42D4×D4711yescharacteristic
183C42D4×D4711yescharacteristic
184C42#1062535211yescharacteristic
185C42#1062535411yescharacteristic
186C23#1309401811yescharacteristic
187Q8—3761no—
188Q8—1881no—
189Q8—1881no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1881no—
195C2×C4—1881no—
196C2×C4#1309399711yescharacteristic
197C2×C4#1309400611yescharacteristic
198C2×C4#1309400911yescharacteristic
199C2×C4#1309400911yescharacteristic
200C2×C4#1309401011yescharacteristic
201C2×C4#1309401911yescharacteristic
202C8—81no—
203C8—81no—
204C8—81no—
205C8—3761no—
206C8—3761no—
207C8—1882no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1568905211yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—3761no—
218C4—3761no—
219C4#1568938511yescharacteristic
220C4#1568938911yescharacteristic
221C2—41no—
222C2#2024483711yescharacteristic
223C2#2024484311yescharacteristic
224C2#2024485811yescharacteristic
subgroupG/H
centerC22#15689052
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1307C2
socleC22×C47#397
prime radicalC23×C47#126
hypercenter#1307D47
hypocenterC47#10648
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
133. C47#10648semidirect

Maximal subgroups

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

subgroupindex
#202421602
#202421162
#202420892
#202418602
#202412572
#202412492
C47×#13072
#1064847