Finite Group Databasebeta

← #26130561

Subgroups — #26130561

Order 12032.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#20245643C211yesmaximal, characteristic
2#20245293C211yesmaximal, characteristic, complemented
3#20242759C211yesmaximal, characteristic, complemented
4#20242745C211yesmaximal, characteristic
5#20241459C211yesmaximal, characteristic, complemented
6#20241438C211yesmaximal, characteristic, complemented
7C47×#1361C211yesmaximal, characteristic
8C2×#13093968—21no—
9C2×#13093968—21no—
10#15689503C2211yescharacteristic
11#15689409—21no—
12#15689320—21no—
13C8×Dic94C2211yescharacteristic
14Dic47⋊C16—21no—
15#15688898—21no—
16C4×C47⋊C16C2211yescharacteristic
17#15688876C2211yescharacteristic
18#15688868—21no—
19#15688867—21no—
20C47×#493C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188—21no—
24C2×Dic188—21no—
25C2×#10625335—41no—
26#13094024—21no—
27C4×Dic94D411yescharacteristic
28#13093968—42no—
29#13093968—42no—
30C2×C47⋊C16D411yescharacteristic
31C2×C47⋊C16D411yescharacteristic
32#13093956—41no—
33C4⋊(C47⋊C8)—21no—
34C4⋊(C47⋊C8)D411yescharacteristic
35Dic47⋊C8—21no—
36#13093949—41no—
37#13093945—41no—
38C8×Dic47—21no—
39C2×D8×C47—21no—
40C2×D8×C47—21no—
41#127×C47—21no—
42C2×C16×C47—21no—
43C4⋊C8×C47—21no—
44C4×C8×C47C2311yescharacteristic
45C2×D4×C47—41no—
46C2×D4×C47—41no—
47C2×D4×C47—41no—
48C2×Dic94—41no—
49C2×Dic94D811yescharacteristic
50D8×C47—41no—
51D8×C47—41no—
52D8×C47—81no—
53C2×C8×C47—41no—
54C2×C8×C47C2×D411yescharacteristic
55C2×C8×C47#4111yescharacteristic
56C42×C47C2×D411yescharacteristic
57#10625335—82no—
58C4⋊Dic47—41no—
59C4⋊Dic47—41no—
60C4⋊Dic47D811yescharacteristic
61Dic47⋊C4—21no—
62C4×Dic47—21no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8—41no—
65Dic188—41no—
66Dic188—41no—
67Dic188—81no—
68C16×C47—41no—
69C47⋊C16—21no—
70C47⋊C16SD1612yescomplemented
71C23×C47—81no—
72D4×C47—81no—
73D4×C47—81no—
74D4×C47—81no—
75D4×C47—81no—
76D4×C47—161no—
77C2×C4×C47#12111yescharacteristic
78C2×C4×C47C2×D811yescharacteristic
79C2×C4×C47#13511yescharacteristic
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—81no—
83Dic94—21no—
84Dic94—21no—
85Dic94—81no—
86Dic94—81no—
87C8×C47—21no—
88C8×C47—81no—
89C8×C47C2×SD1611yescharacteristic
90C8×C47AGL(1,ℤ/8)11yescharacteristic
91C47⋊C8—41no—
92C47⋊C8—81no—
93#12444—471nomaximal, Sylow
94C22×C47—161no—
95C22×C47—161no—
96C22×C47—161no—
97C22×C47#46611yescharacteristic
98C4×C47—21no—
99C4×C47#46011yescharacteristic
100C4×C47#47211yescharacteristic
101C4×C47#50911yescharacteristic
102C4×C47#51011yescharacteristic
103Dic47—41no—
104Dic47—41no—
105Dic47—161no—
106#2248—471no—
107#2183—471no—
108#1670—471no—
109#1668—471no—
110#1371—471no—
111#1362—471no—
112#1361D4711yescharacteristic
113C2×C47—321no—
114C2×C47#166811yescharacteristic
115C2×C47#222011yescharacteristic
116C2×C47#222311yescharacteristic
117C2×SD32—941no—
118C2×SD32—941no—
119#494—471no—
120#493C2×D4711yescharacteristic
121#475—941no—
122#460—941no—
123C8×Q8—471no—
124C4⋊C16—941no—
125C4⋊C16C2×D4711yescharacteristic
126#346—941no—
127C4×C16—471no—
128#335—471no—
129#335C2×D4711yescharacteristic
130#332—941no—
131#331—941no—
132C47#1244411yescharacteristic, complemented, Sylow
133C2×Q16—941no—
134C2×Q16—941no—
135C2×SD16—1881no—
136C2×D8—21no—
137C2×D8—21no—
138C4⋊Q8—941no—
139#127—21no—
140C4×Q8—471no—
141SD32—1882no—
142SD32—1882no—
143C2×C16—21no—
144C2×C16—471no—
145C2×C16—471no—
146#106—1881no—
147C4⋊C8—21no—
148C4⋊C8—471no—
149C4⋊C8—941no—
150C4⋊C8—941no—
151#103—1881no—
152#102—1881no—
153C4×C8—941no—
154C4×C8C22×D4711yescharacteristic
155C2×Q8—471no—
156C2×Q8—1881no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—3761no—
161Q16—1881no—
162Q16—1881no—
163SD16—3762no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—41no—
168C2×C8—941no—
169C2×C8—1881no—
170C2×C8#1062535011yescharacteristic
171C2×C8D4×D4711yescharacteristic
172C4⋊C4—471no—
173C4⋊C4—941no—
174C4⋊C4—1881no—
175C4⋊C4—1881no—
176C42—941no—
177C42D4×D4711yescharacteristic
178C16—41no—
179C16—472no—
180C16—941no—
181C23—81no—
182Q8—941no—
183Q8—941no—
184Q8—3761no—
185Q8—3761no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—3761no—
194C2×C4#1309399711yescharacteristic
195C2×C4D8×D4711yescharacteristic
196C2×C4#1309404511yescharacteristic
197C8—21no—
198C8—81no—
199C8—3761no—
200C8—1881no—
201C8SD16×D4711yescharacteristic
202C8#1309404811yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1568935811yescharacteristic
207C4—21no—
208C4—1881no—
209C4—1881no—
210C4—7521no—
211C4#1568932211yescharacteristic
212C4#1568939211yescharacteristic
213C4#1568955711yescharacteristic
214C4#1568956211yescharacteristic
215C2—321no—
216C2#2024274711yescharacteristic
217C2#2024550011yescharacteristic
218C2#2024551711yescharacteristic
subgroupG/H
centerC22#15689358
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1361C2
socleC22×C47#466
prime radicalC47×#493C22
hypercenter#1361D47
hypocenterC47#12444
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #20245293C2semidirect
3. #20242759C2semidirect
5. #20241459C2semidirect
6. #20241438C2semidirect
70. C47⋊C16SD16semidirect
132. C47#12444semidirect

Maximal subgroups

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

subgroupindex
#202456432
#202452932
#202427592
#202427452
#202414592
#202414382
C47×#13612
#1244447