Finite Group Databasebeta

← #20245495

Subgroups — #20245495

Order 6016.

150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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×#13093970C211yesmaximal, characteristic, complemented
2C2×#13093963C211yesmaximal, characteristic
3#15689365C211yesmaximal, characteristic
4#15689361C211yesmaximal, characteristic
5#15688950C211yesmaximal, characteristic, complemented
6#15688928C211yesmaximal, characteristic, complemented
7C47×#358C211yesmaximal, characteristic, complemented
8C2×Dic188C2211yescharacteristic
9C2×C8×D47C2211yescharacteristic
10#13094004—21no—
11#13094000—21no—
12#13093970—22no—
13#13093963—22no—
14C2×C47⋊C16C2211yescharacteristic
15#13093958C2211yescharacteristic
16#13093948—21no—
17#13093947—21no—
18C2×Q16×C47C2211yescharacteristic
19C2×C16×C47C2211yescharacteristic
20#107×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×C4×D47D411yescharacteristic
23C2×Dic94—21no—
24Q16×C47—21no—
25Q16×C47—21no—
26C2×C8×C47C2311yescharacteristic
27C4⋊C4×C47—21no—
28(C2×D47)⋊C4—41no—
29(C2×D47)⋊C4—41no—
30C4⋊Dic47—21no—
31C4⋊Dic47—41no—
32Dic47⋊C4—41no—
33C2×C47⋊C8D411yescharacteristic
34Dic188—21no—
35Dic188—21no—
36C8×D47—21no—
37C8×D47—21no—
38C16×C47—21no—
39C47⋊C16D412yes—
40C22×D47D811yescharacteristic
41Q8×C47—41no—
42Q8×C47—41no—
43C2×C4×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47C2×D411yescharacteristic
46C2×Dic47—41no—
47C2×Dic47—41no—
48C2×Dic47D811yescharacteristic
49C4×D47—21no—
50C4×D47—21no—
51Dic94—41no—
52Dic94—41no—
53C8×C47C2×D411yescharacteristic
54C8×C47#4111yescharacteristic
55C47⋊C8—21no—
56C22×C47C2×D811yescharacteristic
57C2×D47—21no—
58C2×D47—21no—
59C2×D47—21no—
60C4×C47—81no—
61C4×C47—81no—
62C4×C47#12111yescharacteristic
63C4×C47#13511yescharacteristic
64Dic47—21no—
65Dic47—81no—
66Dic47—81no—
67#2219—471nomaximal, Sylow
68C2×C47#46611yescharacteristic
69C2×C47#51011yescharacteristic
70C2×C47#51011yescharacteristic
71D47—41no—
72C2×Q32—471no—
73C2×M32—471no—
74#467—471no—
75#467—471no—
76#367—471no—
77#358—471no—
78#358D4711yescharacteristic, complemented
79C47#221911yescharacteristic, complemented, Sylow
80C2×Q16—471no—
81C2×Q16C2×D4711yescharacteristic
82C22×C8—471no—
83C22⋊Q8—941no—
84C22⋊Q8—941no—
85Q32—942no—
86M32—942no—
87C2×C16—471no—
88C2×C16C2×D4711yescharacteristic
89#107—471no—
90#107C2×D4711yescharacteristic
91#103—941no—
92#103—941no—
93C2×Q8—21no—
94C2×Q8—941no—
95C22×C4—471no—
96Q16—21no—
97Q16—21no—
98Q16—941no—
99Q16—941no—
100C2×C8—471no—
101C2×C8—941no—
102C2×C8—941no—
103C2×C8C22×D4711yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—941no—
106C4⋊C4—1881no—
107C4⋊C4—1881no—
108C22⋊C4—1881no—
109C22⋊C4—1881no—
110C16—21no—
111C16—472no—
112C23—471no—
113Q8—41no—
114Q8—41no—
115Q8—1881no—
116Q8—1881no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—471no—
120C2×C4—941no—
121C2×C4—941no—
122C2×C4—1881no—
123C2×C4—1881no—
124C2×C4D4×D4711yescharacteristic
125C8—941no—
126C8#1062535011yescharacteristic
127C8D4×D4711yescharacteristic
128C22—941no—
129C22—941no—
130C22—941no—
131C22D8×D4711yescharacteristic
132C4—81no—
133C4—81no—
134C4—941no—
135C4—3761no—
136C4—3761no—
137C4#1309399711yescharacteristic
138C4#1309404511yescharacteristic
139C2—1881no—
140C2#1568935811yescharacteristic
141C2#1568956211yescharacteristic
142C2#1568956511yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#358C2
socleC22×C47C2×D8
hypercenter#358D47
hypocenterC47#2219
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
1. C2×#13093970C2semidirect
5. #15688950C2semidirect
6. #15688928C2semidirect
7. C47×#358C2semidirect
78. #358D47semidirect
79. C47#2219semidirect