Finite Group Databasebeta

← #26137098

Subgroups — #26137098

Order 12032.

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

normal subgroups only

This group has 216 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#20245703C211yesmaximal, characteristic, complemented
2#20245701C211yesmaximal, characteristic, complemented
3#20245636C211yesmaximal, characteristic, complemented
4#20245268C211yesmaximal, characteristic, complemented
5#20241585C211yesmaximal, characteristic, complemented
6#20241577C211yesmaximal, characteristic, complemented
7C47×#1419C211yesmaximal, characteristic, complemented
8#15689555C2211yescharacteristic
9C2×D752C2211yescharacteristic
10C2×#13093965—21no—
11#15689498—21no—
12#15689239—21no—
13#15688962—21no—
14#15688961—21no—
15D1504—21no—
16#15688958—21no—
17#15688957C2211yescharacteristic
18#15688929—21no—
19C16×Dic47C2211yescharacteristic
20C2×D16×C47C2211yescharacteristic
21C47×M64C2211yescharacteristic
22C47×#368C2211yescharacteristic
23#13094046—21no—
24C2×D376—21no—
25C2×#10625334—41no—
26#13094032—41no—
27#13094020—41no—
28Dic376D411yescharacteristic, complemented
29#13093969—21no—
30D752—21no—
31D752—21no—
32D752D411yescharacteristic, complemented
33#13093965—42no—
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—
45C2×C22⋊D47—82no—
46#10625350—41no—
47C2×D188—41no—
48D8×C47—41no—
49D8×C47—41no—
50M16×C47—41no—
51C2×C8×C47C2×D411yescharacteristic
52#10625334—81no—
53#10625334—81no—
54C4×Dic47D811yescharacteristic
55C2×C47⋊C8D811yescharacteristic
56Dic188—21no—
57D376—21no—
58D376—41no—
59D376—41no—
60#10625325—41no—
61#10625324—81no—
62C8×D47—81no—
63C16×C47C2×D411yescharacteristic
64C16×C47#4111yescharacteristic
65C47⋊C16—21no—
66C23×C47—81no—
67C22×D47—81no—
68D4×C47—81no—
69D4×C47—81no—
70C2×C4×C47C2×D811yescharacteristic
71C22⋊D47—81no—
72C22⋊D47—164no—
73C2×Dic47—21no—
74D188—41no—
75D188—81no—
76D188—81no—
77C4×D47—81no—
78Dic94—41no—
79C8×C47—81no—
80C8×C47#12111yescharacteristic
81C8×C47AGL(1,ℤ/8)11yescharacteristic
82C47⋊C8D1611yescharacteristic
83C47⋊C8D1611yescharacteristic
84#13692—471nomaximal, Sylow
85C22×C47—162no—
86C22×C47—161no—
87C22×C47#50911yescharacteristic
88C2×D47—81no—
89C2×D47—162no—
90C2×D47—161no—
91C4×C47#45911yescharacteristic
92C4×C47C2×D1611yescharacteristic
93Dic47—22no—
94Dic47—81no—
95#2263—471no—
96#2263—471no—
97#2246—471no—
98#2178—471no—
99#1422—471no—
100#1419—471no—
101#1419D4711yescharacteristic, complemented
102C2×C47—21no—
103C2×C47—321no—
104C2×C47#220611yescharacteristic
105D47—161no—
106D47—321no—
107#508—471no—
108C2×D16—471no—
109C2×D16—941no—
110C2×D16C2×D4711yescharacteristic
111#493—941no—
112#443—941no—
113SD64—941no—
114SD64—941no—
115D32—941no—
116D32—941no—
117M64—471no—
118M64C2×D4711yescharacteristic
119#368C2×D4711yescharacteristic
120#359—941no—
121C4×C16—471no—
122C47#1369211yescharacteristic, complemented, Sylow
123#135—941no—
124C2×D8—21no—
125C2×D8—941no—
126C2×D8—1881no—
127#131—1881no—
128#127—1881no—
129Q32—471no—
130SD32—941no—
131D16—21no—
132D16—21no—
133D16—471no—
134D16—941no—
135D16—941no—
136D16—1882no—
137C2×C16—471no—
138C2×C16C22×D4711yescharacteristic
139#108—21no—
140#104—1881no—
141C4×C8—471no—
142C32—21no—
143C32—941no—
144#41—1881no—
145C2×D4—41no—
146C2×D4—3762no—
147C2×D4—1881no—
148Q16—941no—
149SD16—1881no—
150D8—41no—
151D8—41no—
152D8—941no—
153D8—3761no—
154D8—3761no—
155D8—1881no—
156D8—1881no—
157M16—41no—
158M16—3761no—
159C2×C8—471no—
160C2×C8—3761no—
161C2×C8D4×D4711yescharacteristic
162C42—471no—
163C16—941no—
164C16#1062535011yescharacteristic
165C16D4×D4711yescharacteristic
166C23—81no—
167C23—3761no—
168Q8—1881no—
169D4—81no—
170D4—81no—
171D4—3761no—
172D4—3761no—
173D4—3761no—
174D4—1881no—
175D4—7524no—
176C2×C4—941no—
177C2×C4—3761no—
178C2×C4D8×D4711yescharacteristic
179C8—81no—
180C8—471no—
181C8—471no—
182C8#1309399711yescharacteristic
183C8#1309405111yescharacteristic
184C22—162no—
185C22—161no—
186C22—3761no—
187C22—7522no—
188C22—7521no—
189C22#1568956011yescharacteristic
190C4—942no—
191C4—3761no—
192C4#1568931711yescharacteristic
193C4D16×D4711yescharacteristic
194C2—21no—
195C2—321no—
196C2—15041no—
197C2—7521no—
198C2#2024542211yescharacteristic
subgroupG/H
centerC2#20245422
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#1419C2
socleC2×C47#2206
hypercenter#1419D47
hypocenterC47#13692
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. #20245703C2semidirect
2. #20245701C2semidirect
3. #20245636C2semidirect
4. #20245268C2semidirect
5. #20241585C2semidirect
6. #20241577C2semidirect
7. C47×#1419C2semidirect
28. Dic376D4semidirect
32. D752D4semidirect
101. #1419D47semidirect
122. C47#13692semidirect

Maximal subgroups

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

subgroupindex
#202457032
#202457012
#202456362
#202452682
#202415852
#202415772
C47×#14192
#1369247