Finite Group Databasebeta

← #20245422

Subgroups — #20245422

Order 6016.

186 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 49 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×D752C211yesmaximal, characteristic, complemented
2C2×#13093965C211yesmaximal, characteristic, complemented
3#15689498C211yesmaximal, characteristic, complemented
4#15689205C211yesmaximal, characteristic, complemented
5Dic47⋊C16C211yesmaximal, characteristic, complemented
6#15688923C211yesmaximal, characteristic, complemented
7C47×#357C211yesmaximal, characteristic, complemented
8C2×D376C2211yescharacteristic
9C2×D376C2211yescharacteristic
10C2×#10625334—21no—
11#13094020—21no—
12#13093986—21no—
13D752—22no—
14#13093965—22no—
15C2×C47⋊C16C2211yescharacteristic
16#13093944—21no—
17C8×Dic47C2211yescharacteristic
18C2×D8×C47C2211yescharacteristic
19C2×C16×C47C2211yescharacteristic
20#107×C47C2211yescharacteristic
21C2×D4×C47—21no—
22C2×C22⋊D47—41no—
23C2×C22⋊D47—41no—
24C2×D188—21no—
25C2×D188—21no—
26C2×C4×D47—41no—
27D8×C47—21no—
28D8×C47—21no—
29C2×C8×C47C2311yescharacteristic
30C4⋊C4×C47—21no—
31#10625334—42no—
32(C2×D47)⋊C4—41no—
33C4×Dic47D411yescharacteristic
34C2×C47⋊C8D411yescharacteristic
35D376—21no—
36D376—21no—
37D376—21no—
38D376D412yescomplemented
39C16×C47—21no—
40C47⋊C16—21no—
41C23×C47—41no—
42C22×D47—41no—
43C22×D47—41no—
44D4×C47—41no—
45D4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47C2×D411yescharacteristic
48C22⋊D47—82no—
49C22⋊D47—82no—
50C2×Dic47D811yescharacteristic
51C2×Dic47D811yescharacteristic
52D188—22no—
53D188—41no—
54D188—41no—
55D188—41no—
56C4×D47—82no—
57C8×C47C2×D411yescharacteristic
58C8×C47#4111yescharacteristic
59C47⋊C8—21no—
60C22×C47—81no—
61C22×C47—81no—
62C22×C47—81no—
63C22×C47C2×D811yescharacteristic
64C2×D47—42no—
65C2×D47—81no—
66C2×D47—81no—
67C2×D47—81no—
68C2×D47—81no—
69C2×D47—81no—
70C4×C47—81no—
71C4×C47#12111yescharacteristic
72C4×C47AGL(1,ℤ/8)11yescharacteristic
73Dic47—21no—
74Dic47D1612yescomplemented
75#2206—471nomaximal, Sylow
76C2×C47—161no—
77C2×C47#45911yescharacteristic
78C2×C47C2×D1611yescharacteristic
79C2×C47#50911yescharacteristic
80D47—82no—
81D47—161no—
82C2×D16—471no—
83C2×D16—471no—
84#493—471no—
85C4×D8—471no—
86C4⋊C16—471no—
87#357—471no—
88#357D4711yescharacteristic, complemented
89C47#220611yescharacteristic, complemented, Sylow
90C2×D8—471no—
91C2×D8—471no—
92C2×D8—941no—
93C2×D8C2×D4711yescharacteristic
94#127—941no—
95C4×D4—941no—
96D16—942no—
97D16—942no—
98C2×C16—471no—
99C2×C16C2×D4711yescharacteristic
100#107C2×D4711yescharacteristic
101#102—941no—
102C4×C8—471no—
103C2×D4—21no—
104C2×D4—941no—
105C2×D4—941no—
106C2×D4—1881no—
107C2×D4—1881no—
108C22×C4—1881no—
109D8—21no—
110D8—21no—
111D8—472no—
112D8—941no—
113D8—941no—
114D8—941no—
115D8—1882no—
116C2×C8—471no—
117C2×C8C22×D4711yescharacteristic
118C4⋊C4—21no—
119C22⋊C4—1881no—
120C42—471no—
121C16—21no—
122C16—941no—
123C23—41no—
124C23—1881no—
125C23—1881no—
126D4—41no—
127D4—41no—
128D4—942no—
129D4—3762no—
130D4—3762no—
131D4—1881no—
132D4—1881no—
133D4—1881no—
134C2×C4—41no—
135C2×C4—471no—
136C2×C4—471no—
137C2×C4—3762no—
138C2×C4D4×D4711yescharacteristic
139C8—941no—
140C8#1062535011yescharacteristic
141C8D4×D4711yescharacteristic
142C22—81no—
143C22—81no—
144C22—81no—
145C22—3761no—
146C22—3761no—
147C22—3761no—
148C22—3761no—
149C22—3761no—
150C22—1882no—
151C22D8×D4711yescharacteristic
152C4—81no—
153C4—472no—
154C4—941no—
155C4#1309399711yescharacteristic
156C4#1309405111yescharacteristic
157C2—161no—
158C2—3762no—
159C2—7521no—
160C2#1568931711yescharacteristic
161C2D16×D4711yescharacteristic
162C2#1568956011yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#357C2
socleC22×C47C2×D8
hypercenter#357D47
hypocenterC47#2206
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. C2×D752C2semidirect
2. C2×#13093965C2semidirect
3. #15689498C2semidirect
4. #15689205C2semidirect
5. Dic47⋊C16C2semidirect
6. #15688923C2semidirect
7. C47×#357C2semidirect
38. D376D4semidirect
74. Dic47D16semidirect
88. #357D47semidirect
89. C47#2206semidirect