Finite Group Databasebeta

← #26137091

Subgroups — #26137091

Order 12032.

200 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 51 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#20245708C211yesmaximal, characteristic, complemented
2#20245701C211yesmaximal, characteristic
3#20245646C211yesmaximal, characteristic, complemented
4#20245268C211yesmaximal, characteristic, complemented
5#20241585C211yesmaximal, characteristic, complemented
6#20241580C211yesmaximal, characteristic, complemented
7C47×#1419C211yesmaximal, characteristic, complemented
8#15689555C2211yescharacteristic
9C2×Dic376C2211yescharacteristic
10C2×#13093968—21no—
11#15689506—21no—
12#15689239—21no—
13Dic752—21no—
14#15688962—21no—
15#15688961—21no—
16#15688958—21no—
17#15688957C2211yescharacteristic
18#15688929—21no—
19C16×Dic47C2211yescharacteristic
20C2×D16×C47C2211yescharacteristic
21C47×M64C2211yescharacteristic
22C47×#368C2211yescharacteristic
23#13094046—21no—
24C2×Dic188—21no—
25C2×#10625335—41no—
26#13094032—41no—
27#13094011—41no—
28Dic376—21no—
29Dic376—21no—
30Dic376D411yescharacteristic
31#13093969—21no—
32#13093968—42no—
33D752D411yescharacteristic
34C2×C47⋊C16D411yescharacteristic
35#13093950—41no—
36C8×Dic47D411yescharacteristic
37C47⋊C32—21no—
38C2×D8×C47—21no—
39D16×C47—21no—
40D16×C47—21no—
41C2×C16×C47C2311yescharacteristic
42#108×C47—21no—
43C32×C47—21no—
44C2×D4×C47—41no—
45#10625350—41no—
46C2×Dic94—41no—
47D8×C47—41no—
48D8×C47—41no—
49M16×C47—41no—
50C2×C8×C47C2×D411yescharacteristic
51C22⋊Dic47—82no—
52#10625335—81no—
53#10625335—81no—
54C4×Dic47D811yescharacteristic
55C2×C47⋊C8D811yescharacteristic
56Dic188—21no—
57Dic188—41no—
58Dic188—41no—
59D376—21no—
60#10625325—41no—
61#10625324—81no—
62C8×D47—81no—
63C16×C47C2×D411yescharacteristic
64C16×C47#4111yescharacteristic
65C47⋊C16—21no—
66C23×C47—81no—
67D4×C47—81no—
68D4×C47—81no—
69C2×C4×C47C2×D811yescharacteristic
70C22⋊D47—81no—
71C2×Dic47—21no—
72C2×Dic47—81no—
73D188—41no—
74C4×D47—81no—
75Dic94—41no—
76Dic94—81no—
77Dic94—81no—
78C8×C47—81no—
79C8×C47#12111yescharacteristic
80C8×C47AGL(1,ℤ/8)11yescharacteristic
81C47⋊C8D1611yescharacteristic
82C47⋊C8D1611yescharacteristic
83#13691—471nomaximal, Sylow
84C22×C47—162no—
85C22×C47—161no—
86C22×C47#50911yescharacteristic
87C2×D47—81no—
88C4×C47#45911yescharacteristic
89C4×C47C2×D1611yescharacteristic
90Dic47—41no—
91Dic47—81no—
92Dic47—161no—
93#2264—471no—
94#2263—471no—
95#2249—471no—
96#2178—471no—
97#1422—471no—
98#1420—471no—
99#1419D4711yescharacteristic, complemented
100C2×C47—21no—
101C2×C47—321no—
102C2×C47#220611yescharacteristic
103D47—161no—
104#508—471no—
105C2×Q32—471no—
106C2×SD32—941no—
107C2×D16C2×D4711yescharacteristic
108#495—941no—
109#443—941no—
110Q64—941no—
111SD64—941no—
112SD64—941no—
113D32—941no—
114M64—471no—
115M64C2×D4711yescharacteristic
116#368C2×D4711yescharacteristic
117#359—941no—
118C4×C16—471no—
119C47#1369111yescharacteristic, complemented, Sylow
120#135—941no—
121C2×Q16—941no—
122C2×SD16—1881no—
123C2×D8—21no—
124#131—1881no—
125#124—1881no—
126Q32—471no—
127Q32—941no—
128Q32—941no—
129SD32—941no—
130SD32—1882no—
131D16—21no—
132D16—21no—
133D16—471no—
134C2×C16—471no—
135C2×C16C22×D4711yescharacteristic
136#108—21no—
137#104—1881no—
138C4×C8—471no—
139C32—21no—
140C32—941no—
141#41—1881no—
142C2×Q8—1881no—
143C2×D4—41no—
144Q16—941no—
145Q16—1881no—
146Q16—1881no—
147SD16—3761no—
148SD16—3761no—
149SD16—1881no—
150D8—41no—
151D8—41no—
152D8—941no—
153M16—41no—
154M16—3761no—
155C2×C8—471no—
156C2×C8—3761no—
157C2×C8D4×D4711yescharacteristic
158C22⋊C4—3762no—
159C42—471no—
160C16—941no—
161C16#1062535011yescharacteristic
162C16D4×D4711yescharacteristic
163C23—81no—
164Q8—3761no—
165Q8—3761no—
166Q8—1881no—
167D4—81no—
168D4—81no—
169D4—3761no—
170D4—1881no—
171C2×C4—941no—
172C2×C4—3761no—
173C2×C4—3761no—
174C2×C4D8×D4711yescharacteristic
175C8—81no—
176C8—471no—
177C8—471no—
178C8#1309399711yescharacteristic
179C8#1309405111yescharacteristic
180C22—162no—
181C22—161no—
182C22—3761no—
183C22#1568956011yescharacteristic
184C4—3761no—
185C4—1881no—
186C4—7521no—
187C4#1568931711yescharacteristic
188C4D16×D4711yescharacteristic
189C2—21no—
190C2—321no—
191C2—7521no—
192C2#2024542211yescharacteristic
subgroupG/H
centerC2#20245422
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#1419C2
socleC2×C47#2206
prime radical#20245701C2
hypercenter#1419D47
hypocenterC47#13691
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #20245708C2semidirect
3. #20245646C2semidirect
4. #20245268C2semidirect
5. #20241585C2semidirect
6. #20241580C2semidirect
7. C47×#1419C2semidirect
99. #1419D47semidirect
119. C47#13691semidirect

Maximal subgroups

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

subgroupindex
#202457082
#202457012
#202456462
#202452682
#202415852
#202415802
C47×#14192
#1369147