Finite Group Databasebeta

← #26130559

Subgroups — #26130559

Order 12032.

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

normal subgroups only

This group has 228 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#20245296C211yesmaximal, characteristic, complemented
2#20242755C211yesmaximal, characteristic, complemented
3#20242745C211yesmaximal, characteristic
4#20241460C211yesmaximal, characteristic, complemented
5#20241437C211yesmaximal, characteristic, complemented
6#20241434C211yesmaximal, characteristic
7C47×#2248C211yesmaximal, characteristic
8#15689405—21no—
9#15689320—21no—
10C8×Dic94C2211yescharacteristic
11C4⋊(C47⋊C16)C2211yescharacteristic
12Dic47⋊C16—21no—
13#15688898—21no—
14#15688876C2211yescharacteristic
15#15688876C2211yescharacteristic
16#15688869—21no—
17#15688867—21no—
18C2×SD32×C47—21no—
19C2×SD32×C47—21no—
20C47×#494C2211yescharacteristic
21C47×#493C2211yescharacteristic
22C4×C16×C47C2211yescharacteristic
23C2×#10625335—41no—
24C4×Dic94D411yescharacteristic
25C2×C47⋊C16—21no—
26#13093955—41no—
27C4⋊(C47⋊C8)—21no—
28C4⋊(C47⋊C8)—21no—
29C4⋊(C47⋊C8)D411yescharacteristic
30Dic47⋊C8—21no—
31#13093947—41no—
32#13093945—41no—
33C8×Dic47—21no—
34C2×Q16×C47—21no—
35C2×Q16×C47—21no—
36C2×D8×C47—21no—
37C2×D8×C47—21no—
38C4⋊Q8×C47—21no—
39#127×C47—21no—
40SD32×C47—42no—
41SD32×C47—42no—
42C2×C16×C47D411yescharacteristic
43C2×C16×C47D411yescharacteristic
44C4×C8×C47C2311yescharacteristic
45C2×Q8×C47—41no—
46C2×D4×C47—41no—
47C2×D4×C47—41no—
48C2×D4×C47—41no—
49C2×Dic94D811yescharacteristic
50Q16×C47—41no—
51Q16×C47—41no—
52Q16×C47—81no—
53D8×C47—41no—
54D8×C47—41no—
55D8×C47—81no—
56C2×C8×C47C2×D411yescharacteristic
57C2×C8×C47#4111yescharacteristic
58C4⋊C4×C47—41no—
59C4⋊C4×C47—41no—
60C42×C47C2×D411yescharacteristic
61#10625335—82no—
62C4⋊Dic47D811yescharacteristic
63Dic47⋊C4—21no—
64C4×Dic47—21no—
65C2×C47⋊C8—21no—
66C2×C47⋊C8—41no—
67C2×C47⋊C8—41no—
68C16×C47—21no—
69C16×C47SD1612yescomplemented
70C47⋊C16—41no—
71C23×C47—81no—
72Q8×C47—81no—
73Q8×C47—81no—
74D4×C47—81no—
75D4×C47—81no—
76D4×C47—81no—
77D4×C47—81no—
78D4×C47—161no—
79C2×C4×C47—81no—
80C2×C4×C47#12111yescharacteristic
81C2×C4×C47C2×D811yescharacteristic
82C2×C4×C47#13511yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85Dic94—21no—
86Dic94—21no—
87C8×C47—21no—
88C8×C47C2×SD1611yescharacteristic
89C8×C47AGL(1,ℤ/8)11yescharacteristic
90C47⋊C8—41no—
91C47⋊C8—81no—
92C47⋊C8—81no—
93#12444—471nomaximal, Sylow
94C22×C47—161no—
95C22×C47—161no—
96C22×C47—161no—
97C22×C47#46611yescharacteristic
98C4×C47—21no—
99C4×C47—161no—
100C4×C47#46011yescharacteristic
101C4×C47#47211yescharacteristic
102C4×C47#50911yescharacteristic
103C4×C47#51011yescharacteristic
104Dic47—41no—
105Dic47—41no—
106#2248D4711yescharacteristic
107#2183—471no—
108#1670—471no—
109#1668—471no—
110#1371—471no—
111#1362—471no—
112#1361—471no—
113C2×C47—321no—
114C2×C47#166811yescharacteristic
115C2×C47#222011yescharacteristic
116C2×C47#222311yescharacteristic
117C2×SD32—21no—
118C2×SD32—21no—
119#494C2×D4711yescharacteristic
120#493C2×D4711yescharacteristic
121#475—941no—
122#460—941no—
123C8×Q8—471no—
124C4⋊C16—471no—
125C4⋊C16—941no—
126#346—941no—
127C4×C16C2×D4711yescharacteristic
128#335—471no—
129#335—471no—
130#332—941no—
131#331—941no—
132C47#1244411yescharacteristic, complemented, Sylow
133C2×Q16—21no—
134C2×Q16—21no—
135C2×SD16—1881no—
136C2×D8—21no—
137C2×D8—21no—
138C4⋊Q8—21no—
139#127—21no—
140C4×Q8—471no—
141SD32—42no—
142SD32—42no—
143C2×C16—941no—
144C2×C16C22⋊D4711yescharacteristic
145C2×C16C22⋊D4711yescharacteristic
146#106—1881no—
147C4⋊C8—471no—
148C4⋊C8—941no—
149C4⋊C8—941no—
150C4⋊C8—941no—
151#103—1881no—
152#102—1881no—
153C4×C8—941no—
154C4×C8C22×D4711yescharacteristic
155C2×Q8—41no—
156C2×Q8—471no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—41no—
161Q16—41no—
162Q16—81no—
163SD16—3762no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—941no—
168C2×C8—1881no—
169C2×C8—1881no—
170C2×C8#1062535211yescharacteristic
171C2×C8C2×C22⋊D4711yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—471no—
175C4⋊C4—941no—
176C42—941no—
177C42D4×D4711yescharacteristic
178C16—21no—
179C16—1881no—
180C16#1062533512yescomplemented
181C23—81no—
182Q8—81no—
183Q8—81no—
184Q8—941no—
185Q8—941no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—81no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4#1309399511yescharacteristic
195C2×C4D8×D4711yescharacteristic
196C2×C4#1309404311yescharacteristic
197C8—21no—
198C8—3761no—
199C8—3761no—
200C8—1881no—
201C8C2×#1062533511yescharacteristic
202C8#1309405011yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1568935611yescharacteristic
207C4—21no—
208C4—161no—
209C4—1881no—
210C4—1881no—
211C4#1568932011yescharacteristic
212C4#1568939011yescharacteristic
213C4#1568956011yescharacteristic
214C4#1568956211yescharacteristic
215C2—321no—
216C2#2024274511yescharacteristic
217C2#2024549811yescharacteristic
218C2#2024551511yescharacteristic
subgroupG/H
centerC22#15689356
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#2248C2
socleC22×C47#466
prime radicalC47×#493C22
hypercenter#2248D47
hypocenterC47#12444
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #20245296C2semidirect
2. #20242755C2semidirect
4. #20241460C2semidirect
5. #20241437C2semidirect
69. C16×C47SD16semidirect
132. C47#12444semidirect
180. C16#10625335semidirect

Maximal subgroups

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

subgroupindex
#202452962
#202427552
#202427452
#202414602
#202414372
#202414342
C47×#22482
#1244447