Finite Group Databasebeta

← #26137147

Subgroups — #26137147

Order 12032.

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

normal subgroups only

This group has 180 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
1C2×#15688963C211yesmaximal, characteristic, complemented
2#20245683C211yesmaximal, characteristic
3#20245514C211yesmaximal, characteristic
4#20245510C211yesmaximal, characteristic
5#20241591C211yesmaximal, characteristic, complemented
6#20241582C211yesmaximal, characteristic, complemented
7C47×#1420C211yesmaximal, characteristic, complemented
8C2×Dic376C2211yescharacteristic
9#15689539C2211yescharacteristic
10#15689399—21no—
11#15689395—21no—
12#15688963—21no—
13#15688963—21no—
14#15688956—21no—
15C2×C47⋊C32C2211yescharacteristic
16C32×D47—21no—
17#15688953C2211yescharacteristic
18#15688939—21no—
19#15688938—21no—
20C2×Q32×C47C2211yescharacteristic
21C47×M64C2211yescharacteristic
22C47×#368C2211yescharacteristic
23#13094057—41no—
24#13094055—41no—
25C2×Dic188—21no—
26#13094030D411yescharacteristic
27Dic376—21no—
28Dic376—21no—
29#13093964D411yescharacteristic
30#13093963—21no—
31C16×D47—21no—
32#13093960—21no—
33#13093943—41no—
34#13093942—41no—
35C47⋊C32D411yescharacteristic
36C47⋊C32D411yescharacteristic
37C2×Q16×C47—21no—
38Q32×C47—21no—
39Q32×C47—21no—
40C2×C16×C47C2311yescharacteristic
41#108×C47—21no—
42C32×C47—21no—
43C2×Q8×C47—41no—
44#10625350D811yescharacteristic
45C2×Dic94—41no—
46Q16×C47—41no—
47Q16×C47—41no—
48M16×C47—41no—
49C2×C8×C47C2×D411yescharacteristic
50#10625337—81no—
51#10625336—81no—
52#10625329—41no—
53#10625329D811yescharacteristic
54Dic188—41no—
55Dic188—41no—
56Dic188—81no—
57#10625325—81no—
58#10625324—21no—
59C8×D47—21no—
60C16×C47C2×D411yescharacteristic
61C16×C47#4111yescharacteristic
62C47⋊C16—21no—
63Q8×C47—81no—
64Q8×C47—81no—
65C2×C4×C47—81no—
66C2×C4×C47C2×D811yescharacteristic
67C22⋊D47—21no—
68C2×Dic47—81no—
69D188D1611yescharacteristic
70C4×D47—21no—
71Dic94—81no—
72Dic94—81no—
73Dic94D1611yescharacteristic
74C8×C47—81no—
75C8×C47#12111yescharacteristic
76C8×C47#13511yescharacteristic
77C47⋊C8—21no—
78C47⋊C8—81no—
79#13701—471nomaximal, Sylow
80C22×C47#50811yescharacteristic
81C2×D47—21no—
82C4×C47—161no—
83C4×C47#46611yescharacteristic
84C4×C47C2×D1611yescharacteristic
85Dic47—21no—
86Dic47—161no—
87C2×Q64—471no—
88#2258—471no—
89#2222—471no—
90#2222—471no—
91#1425—471no—
92#1420—471no—
93#1420D4711yescharacteristic, complemented
94C2×C47—21no—
95C2×C47#221511yescharacteristic
96D47—41no—
97C2×Q32—471no—
98C2×Q32C2×D4711yescharacteristic
99#504—471no—
100#473—941no—
101#473—941no—
102Q64—941no—
103Q64—941no—
104M64—941no—
105M64C2×D4711yescharacteristic
106C2×C32—471no—
107C2×C32—941no—
108#368—471no—
109#368C2×D4711yescharacteristic
110#362—941no—
111#362—941no—
112C47#1370111yescharacteristic, complemented, Sylow
113#137—1881no—
114#137—1881no—
115C2×Q16—21no—
116C2×Q16—941no—
117#131—471no—
118Q32—21no—
119Q32—21no—
120Q32—941no—
121Q32—941no—
122M32—471no—
123M32—941no—
124C2×C16—941no—
125C2×C16C22×D4711yescharacteristic
126#108—21no—
127#108—941no—
128#101—1881no—
129#101—1881no—
130C32—21no—
131C32—471no—
132C32—471no—
133#41—471no—
134C2×Q8—41no—
135C2×Q8—1881no—
136Q16—41no—
137Q16—41no—
138Q16—3761no—
139Q16—3761no—
140Q16—1881no—
141Q16—1881no—
142SD16—3761no—
143SD16—3761no—
144M16—41no—
145M16—471no—
146M16—941no—
147M16—1881no—
148C2×C8—941no—
149C2×C8D4×D4711yescharacteristic
150C16—941no—
151C16#1062535011yescharacteristic
152C16D4×D4711yescharacteristic
153Q8—81no—
154Q8—81no—
155Q8—471no—
156Q8—3761no—
157Q8—3761no—
158D4—471no—
159D4—941no—
160C2×C4—81no—
161C2×C4—941no—
162C2×C4—3761no—
163C2×C4D8×D4711yescharacteristic
164C8—81no—
165C8—941no—
166C8—3761no—
167C8#1309399711yescharacteristic
168C8#1309404511yescharacteristic
169C22—941no—
170C22#1568955411yescharacteristic
171C4—161no—
172C4—941no—
173C4—7521no—
174C4#1568935811yescharacteristic
175C4D16×D4711yescharacteristic
176C2—21no—
177C2—1881no—
178C2#2024547311yescharacteristic
subgroupG/H
centerC2#20245473
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#1420C2
socleC2×C47#2215
prime radical#10625350D8
hypercenter#1420D47
hypocenterC47#13701
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. C2×#15688963C2semidirect
5. #20241591C2semidirect
6. #20241582C2semidirect
7. C47×#1420C2semidirect
93. #1420D47semidirect
112. C47#13701semidirect

Maximal subgroups

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

subgroupindex
C2×#156889632
#202456832
#202455142
#202455102
#202415912
#202415822
C47×#14202
#1370147