Finite Group Databasebeta

← #26130680

Subgroups — #26130680

Order 12032.

196 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 53 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#20245629C211yesmaximal, characteristic, complemented
2#20245565C211yesmaximal, characteristic, complemented
3#20245461C211yesmaximal, characteristic
4#20245229C211yesmaximal, characteristic, complemented
5#20241455C211yesmaximal, characteristic, complemented
6#20241450C211yesmaximal, characteristic, complemented
7C47×#1357C211yesmaximal, characteristic, complemented
8#15689559—21no—
9#15689541—21no—
10#15689525C2211yescharacteristic
11#15689241C2211yescharacteristic
12#15688946—21no—
13#15688944C2211yescharacteristic
14#15688936—21no—
15#15688934—21no—
16#15688924—21no—
17#15688924—21no—
18#15688908—21no—
19#15688899C2211yescharacteristic
20C47×#493C2211yescharacteristic
21C47×#364C2211yescharacteristic
22C47×#364C2211yescharacteristic
23#13094046D411yescharacteristic
24#13094030—21no—
25#13094016—21no—
26#13093968—41no—
27#13093965—41no—
28#13093964—21no—
29#13093963—41no—
30C2×C47⋊C16D411yescharacteristic
31C2×C47⋊C16D411yescharacteristic
32C16×D47—41no—
33#13093960D411yescharacteristic
34#13093958—21no—
35#13093956—21no—
36#13093952—21no—
37C2×D8×C47—21no—
38C2×D8×C47—21no—
39#127×C47—21no—
40M32×C47—21no—
41M32×C47—21no—
42C4×C8×C47C2311yescharacteristic
43C2×D4×C47—41no—
44C2×D4×C47—81no—
45#10625350—21no—
46D8×C47—41no—
47D8×C47—41no—
48D8×C47—41no—
49D8×C47—41no—
50C2×C8×C47C2×D411yescharacteristic
51C2×C8×C47C2×D411yescharacteristic
52C42×C47#4111yescharacteristic
53C4⋊Dic47—41no—
54Dic47⋊C4—81no—
55#10625329—21no—
56Dic188SD1611yescharacteristic
57D376SD1611yescharacteristic
58#10625325—21no—
59#10625324—41no—
60C8×D47—41no—
61C16×C47—41no—
62C16×C47—41no—
63C47⋊C16—21no—
64C47⋊C16—21no—
65C47⋊C16—41no—
66C23×C47—81no—
67D4×C47—81no—
68D4×C47—81no—
69D4×C47—162no—
70C2×C4×C47—21no—
71C2×C4×C47#12111yescharacteristic
72C22⋊D47—41no—
73C2×Dic47—81no—
74D188—21no—
75C4×D47—41no—
76Dic94—21no—
77C8×C47C2×SD1611yescharacteristic
78C8×C47#13511yescharacteristic
79C8×C47#13511yescharacteristic
80C8×C47AGL(1,ℤ/8)11yescharacteristic
81C47⋊C8—41no—
82#12465—471nomaximal, Sylow
83C22×C47—162no—
84C22×C47—161no—
85C22×C47#47211yescharacteristic
86C2×D47—41no—
87C4×C47—41no—
88C4×C47#46311yescharacteristic
89C4×C47#46511yescharacteristic
90Dic47—41no—
91Dic47—161no—
92#2244—471no—
93#2231—471no—
94#2213—471no—
95#2171—471no—
96#1369—471no—
97#1366—471no—
98#1357D4711yescharacteristic, complemented
99C2×C47—21no—
100C2×C47—321no—
101C2×C47#167711yescharacteristic
102D47—81no—
103#509—941no—
104#504—941no—
105#499—471no—
106#493C2×D4711yescharacteristic
107#443—471no—
108#365—941no—
109#364—471no—
110#364C2×D4711yescharacteristic
111#364C2×D4711yescharacteristic
112#361—941no—
113#360—941no—
114#357—941no—
115#357—941no—
116#350—941no—
117#346—471no—
118C47#1246511yescharacteristic, complemented, Sylow
119#135—471no—
120C2×D8—21no—
121C2×D8—21no—
122#131—941no—
123#127—21no—
124#125—941no—
125SD32—1881no—
126D16—1881no—
127M32—21no—
128M32—21no—
129M32—941no—
130M32—1881no—
131C2×C16—471no—
132C2×C16—471no—
133C2×C16—1881no—
134#108—471no—
135#107—941no—
136#106—941no—
137#104—941no—
138C4×C8C22×D4711yescharacteristic
139#41—941no—
140C2×D4—41no—
141C2×D4—81no—
142Q16—471no—
143SD16—941no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—41no—
148D8—471no—
149M16—941no—
150M16—1881no—
151C2×C8—1881no—
152C2×C8D4×D4711yescharacteristic
153C2×C8D4×D4711yescharacteristic
154C4⋊C4—3761no—
155C4⋊C4—1881no—
156C42#1062535011yescharacteristic
157C16—41no—
158C16—41no—
159C16—941no—
160C16—941no—
161C16—1881no—
162C23—81no—
163Q8—941no—
164D4—81no—
165D4—81no—
166D4—162no—
167D4—941no—
168D4—1881no—
169C2×C4—21no—
170C2×C4—3761no—
171C2×C4—1881no—
172C2×C4#1309399711yescharacteristic
173C8—1881no—
174C8SD16×D4711yescharacteristic
175C8#1309404311yescharacteristic
176C8#1309404511yescharacteristic
177C8#1309404811yescharacteristic
178C22—162no—
179C22—161no—
180C22—1881no—
181C22#1568939211yescharacteristic
182C4—41no—
183C4—1881no—
184C4—7521no—
185C4#1568933711yescharacteristic
186C4#1568935111yescharacteristic
187C2—21no—
188C2—321no—
189C2—3761no—
190C2#2024279611yescharacteristic
subgroupG/H
centerC2#20242796
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1357C2
socleC2×C47#1677
prime radical#20245461C2
hypercenter#1357D47
hypocenterC47#12465
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
1. #20245629C2semidirect
2. #20245565C2semidirect
4. #20245229C2semidirect
5. #20241455C2semidirect
6. #20241450C2semidirect
7. C47×#1357C2semidirect
98. #1357D47semidirect
118. C47#12465semidirect

Maximal subgroups

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

subgroupindex
#202456292
#202455652
#202454612
#202452292
#202414552
#202414502
C47×#13572
#1246547