Finite Group Databasebeta

← #26136895

Subgroups — #26136895

Order 12032.

182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 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
2#20245273C211yesmaximal, characteristic
3#20245258C211yesmaximal, characteristic, complemented
4#20241580C211yesmaximal, characteristic, complemented
5#20241574C211yesmaximal, characteristic
6#20241523C211yesmaximal, characteristic, complemented
7C47×#1426C211yesmaximal, characteristic, complemented
8#15689555C2211yescharacteristic
9C2×Dic376C2211yescharacteristic
10#15689239—21no—
11#15689217—21no—
12Dic752C412yescomplemented
13#15688962C412yescomplemented
14#15688957C2211yescharacteristic
15#15688929—21no—
16#15688926—21no—
17#15688898C2211yescharacteristic
18C47×M64C2211yescharacteristic
19C47×#368C2211yescharacteristic
20C47×#367C2211yescharacteristic
21#13094046—21no—
22C2×Dic188—21no—
23#13094032—41no—
24#13093989—41no—
25Dic376—21no—
26Dic376C2×C412yes—
27Dic376C2×C411yescharacteristic
28#13093969—21no—
29D752C2×C411yescharacteristic
30C2×C47⋊C16D411yescharacteristic
31#13093950—41no—
32#13093947—41no—
33C8×Dic47D411yescharacteristic
34C47⋊C32—21no—
35C2×C16×C47C2311yescharacteristic
36#108×C47—21no—
37#107×C47—21no—
38C32×C47C2×C412yes—
39#10625350—41no—
40C2×Dic94—41no—
41M16×C47—41no—
42C2×C8×C47C2×D411yescharacteristic
43C4⋊C4×C47—41no—
44Dic47⋊C4—81no—
45C4×Dic47—81no—
46C4×Dic47D811yescharacteristic
47C2×C47⋊C8D811yescharacteristic
48Dic188—21no—
49Dic188—22no—
50Dic188—41no—
51D376—21no—
52#10625325—41no—
53#10625324—81no—
54C8×D47—81no—
55C16×C47C22×C411yescharacteristic
56C16×C47#4111yescharacteristic
57C47⋊C16—21no—
58C2×C4×C47—81no—
59C2×C4×C47C2×D811yescharacteristic
60C22⋊D47—81no—
61C2×Dic47—21no—
62C2×Dic47—81no—
63D188—41no—
64C4×D47—81no—
65Dic94—41no—
66Dic94—42no—
67Dic94—81no—
68C8×C47—81no—
69C8×C47C4×D411yescharacteristic
70C8×C47#13511yescharacteristic
71C47⋊C8—21no—
72#13657—471nomaximal, Sylow
73C22×C47#50911yescharacteristic
74C2×D47—81no—
75C4×C47—161no—
76C4×C47C4×D811yescharacteristic
77C4×C47#50911yescharacteristic
78Dic47—41no—
79Dic47—82no—
80Dic47—81no—
81#2264—471no—
82#2179—471no—
83#2176—471no—
84#1426D4711yescharacteristic, complemented
85#1420—471no—
86#1418—471no—
87#1398—471no—
88C2×C47—21no—
89C2×C47#217711yescharacteristic
90D47—161no—
91#508—471no—
92C2×Q32—471no—
93#443—941no—
94C4×Q16—941no—
95Q64—472no—
96SD64—472no—
97M64—471no—
98M64C2×D4711yescharacteristic
99#368C2×D4711yescharacteristic
100#367C2×D4711yescharacteristic
101#359—941no—
102#358—941no—
103#346—471no—
104C47#1365711yescharacteristic, complemented, Sylow
105#135—941no—
106C2×Q16—941no—
107#131—1881no—
108C4×Q8—1881no—
109Q32—472no—
110Q32—471no—
111Q32—941no—
112SD32—941no—
113D16—471no—
114C2×C16—471no—
115C2×C16C22×D4711yescharacteristic
116#108—21no—
117#107—21no—
118#104—1881no—
119#103—1881no—
120C4×C8—471no—
121C32—941no—
122C32C4×D4712yes—
123#41—1881no—
124C2×Q8—1881no—
125Q16—941no—
126Q16—942no—
127Q16—1881no—
128SD16—1881no—
129D8—941no—
130M16—41no—
131M16—3761no—
132C2×C8—471no—
133C2×C8—3761no—
134C2×C8D4×D4711yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—3761no—
137C42—471no—
138C42—3761no—
139C16—941no—
140C16C2×C4×D4711yescharacteristic
141C16#1062535411yescharacteristic
142Q8—3761no—
143Q8—1881no—
144Q8—1882no—
145D4—3761no—
146D4—1881no—
147C2×C4—81no—
148C2×C4—941no—
149C2×C4—3761no—
150C2×C4—3761no—
151C2×C4D8×D4711yescharacteristic
152C8—81no—
153C8—941no—
154C8#1309398611yescharacteristic
155C8#1309404711yescharacteristic
156C22—3761no—
157C22#1568956011yescharacteristic
158C4—161no—
159C4—3761no—
160C4—3762no—
161C4—1881no—
162C4#1568920511yescharacteristic
163C4#1568956011yescharacteristic
164C2—21no—
165C2—7521no—
166C2#2024526311yescharacteristic
subgroupG/H
centerC2#20245263
commutatorC16×C47C22×C4
FrattiniC2×C16C22×D47
FittingC47×#1426C2
socleC2×C47#2177
prime radical#15689555C22
cosocleC2×C16×C47C23
hypercenter#1426D47
hypocenterC47#13657
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

Complements

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

NH ≅ G/Ntype
3. #20245258C2semidirect
4. #20241580C2semidirect
6. #20241523C2semidirect
7. C47×#1426C2semidirect
12. Dic752C4semidirect
13. #15688962C4semidirect
84. #1426D47semidirect
104. C47#13657semidirect

Maximal subgroups

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

subgroupindex
#202457082
#202452732
#202452582
#202415802
#202415742
#202415232
C47×#14262
#1365747