Finite Group Databasebeta

← #26130679

Subgroups — #26130679

Order 12032.

196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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#20245564C211yesmaximal, characteristic, complemented
3#20245230C211yesmaximal, characteristic, complemented
4#20241455C211yesmaximal, characteristic, complemented
5#20241448C211yesmaximal, characteristic, complemented
6#20241425C211yesmaximal, characteristic, complemented
7C47×#2213C211yesmaximal, characteristic
8#15689540—21no—
9#15689525C2211yescharacteristic
10#15688947—21no—
11#15688944C2211yescharacteristic
12#15688944C2211yescharacteristic
13#15688933—21no—
14#15688924—21no—
15#15688924—21no—
16#15688907—21no—
17#15688899C2211yescharacteristic
18C47×#509—21no—
19C47×#493C2211yescharacteristic
20C47×#443C2211yescharacteristic
21C47×#364C2211yescharacteristic
22C47×#361—21no—
23#13094016—21no—
24#13093964—21no—
25#13093964—21no—
26#13093964—41no—
27C2×C47⋊C16—41no—
28C2×C47⋊C16D411yescharacteristic
29C2×C47⋊C16D411yescharacteristic
30#13093958—21no—
31#13093956—21no—
32#135×C47D411yescharacteristic
33C2×D8×C47—21no—
34C2×D8×C47—21no—
35#131×C47—21no—
36#127×C47—21no—
37SD32×C47—41no—
38D16×C47—41no—
39M32×C47—21no—
40#108×C47D411yescharacteristic
41#104×C47—21no—
42C4×C8×C47C2311yescharacteristic
43#41×C47—21no—
44C2×D4×C47—41no—
45C2×D4×C47—81no—
46Q16×C47SD1611yescharacteristic
47SD16×C47—21no—
48D8×C47—41no—
49D8×C47—41no—
50D8×C47—41no—
51D8×C47—41no—
52D8×C47SD1611yescharacteristic
53M16×C47—21no—
54M16×C47—41no—
55C2×C8×C47—41no—
56C2×C8×C47C2×D411yescharacteristic
57C2×C8×C47C2×D411yescharacteristic
58C42×C47#4111yescharacteristic
59C4⋊Dic47—41no—
60Dic47⋊C4—81no—
61C16×C47—41no—
62C47⋊C16—21no—
63C47⋊C16—21no—
64C47⋊C16—41no—
65C47⋊C16—41no—
66C23×C47—81no—
67Q8×C47—21no—
68D4×C47—21no—
69D4×C47—41no—
70D4×C47—81no—
71D4×C47—81no—
72D4×C47—162no—
73C2×C4×C47—21no—
74C2×C4×C47—41no—
75C2×C4×C47#12111yescharacteristic
76C2×Dic47—81no—
77C8×C47—41no—
78C8×C47C2×SD1611yescharacteristic
79C8×C47#13511yescharacteristic
80C8×C47#13511yescharacteristic
81C8×C47AGL(1,ℤ/8)11yescharacteristic
82#12465—471nomaximal, Sylow
83C22×C47—41no—
84C22×C47—162no—
85C22×C47—161no—
86C22×C47#47211yescharacteristic
87C4×C47—41no—
88C4×C47—41no—
89C4×C47#46311yescharacteristic
90C4×C47#46511yescharacteristic
91Dic47—161no—
92#2244—471no—
93#2231—471no—
94#2213D4711yescharacteristic
95#2171—471no—
96#1369—471no—
97#1366—471no—
98#1357—471no—
99C2×C47—21no—
100C2×C47—81no—
101C2×C47—321no—
102C2×C47#167711yescharacteristic
103#509—21no—
104#504—941no—
105#499—471no—
106#493C2×D4711yescharacteristic
107#443C2×D4711yescharacteristic
108#365—941no—
109#364—471no—
110#364—471no—
111#364C2×D4711yescharacteristic
112#361—21no—
113#360—941no—
114#357—941no—
115#357—941no—
116#350—941no—
117#346—471no—
118C47#1246511yescharacteristic, complemented, Sylow
119#135C22⋊D4711yescharacteristic
120C2×D8—21no—
121C2×D8—21no—
122#131—21no—
123#127—21no—
124#125—941no—
125SD32—41no—
126D16—41no—
127M32—21no—
128M32—941no—
129M32—941no—
130M32—1881no—
131C2×C16—471no—
132C2×C16—471no—
133C2×C16—1881no—
134#108C22⋊D4711yescharacteristic
135#107—941no—
136#106—941no—
137#104—21no—
138C4×C8C22×D4711yescharacteristic
139#41—21no—
140C2×D4—41no—
141C2×D4—81no—
142Q16#1062533511yescharacteristic
143SD16—21no—
144D8—41no—
145D8—41no—
146D8—41no—
147D8—41no—
148D8#1062533511yescharacteristic
149M16—21no—
150M16—41no—
151C2×C8—41no—
152C2×C8D4×D4711yescharacteristic
153C2×C8C2×C22⋊D4711yescharacteristic
154C4⋊C4—3761no—
155C4⋊C4—1881no—
156C42#1062535211yescharacteristic
157C16—41no—
158C16—941no—
159C16—941no—
160C16—1881no—
161C16—1881no—
162C23—81no—
163Q8—21no—
164D4—21no—
165D4—41no—
166D4—81no—
167D4—81no—
168D4—162no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—3761no—
172C2×C4#1309399611yescharacteristic
173C8—41no—
174C8C2×#1062533511yescharacteristic
175C8#1309404311yescharacteristic
176C8#1309404411yescharacteristic
177C8#1309404811yescharacteristic
178C22—41no—
179C22—162no—
180C22—161no—
181C22#1568939111yescharacteristic
182C4—41no—
183C4—41no—
184C4—7521no—
185C4#1568933611yescharacteristic
186C4#1568935011yescharacteristic
187C2—21no—
188C2—81no—
189C2—321no—
190C2#2024279511yescharacteristic
subgroupG/H
centerC2#20242795
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
Fitting, prime radicalC47×#2213C2
socleC2×C47#1677
hypercenter#2213D47
hypocenterC47#12465
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #20245629C2semidirect
2. #20245564C2semidirect
3. #20245230C2semidirect
4. #20241455C2semidirect
5. #20241448C2semidirect
6. #20241425C2semidirect
118. C47#12465semidirect

Maximal subgroups

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

subgroupindex
#202456292
#202455642
#202452302
#202414552
#202414482
#202414252
C47×#22132
#1246547