Finite Group Databasebeta

← #20242610

Subgroups — #20242610

Order 6016.

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

normal subgroups only

This group has 200 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#15689853C211yesmaximal, characteristic
2#15689473C211yesmaximal, characteristic
3#15689409C211yesmaximal, characteristic
4#15689334C211yesmaximal, characteristic
5#15688853C211yesmaximal, characteristic
6#15688853C211yesmaximal, characteristic
7C47×#333C211yesmaximal, characteristic
8C2×Dic188—21no—
9#13094024C2211yescharacteristic
10#13094023—21no—
11#13094023—21no—
12#13094022—22no—
13C4×Dic94C2211yescharacteristic
14C4×Dic94C2211yescharacteristic
15#13093989—21no—
16#13093989—21no—
17#13093956—21no—
18#13093949—21no—
19#13093949—21no—
20#13093948—22no—
21C4×C47⋊C8C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47D412yes—
26C2×Dic94—21no—
27C2×Dic94—22no—
28C2×Dic94D411yescharacteristic
29C2×Dic94D411yescharacteristic
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C42×C47C2311yescharacteristic
35C4⋊Dic47—21no—
36C4⋊Dic47—21no—
37C4⋊Dic47D411yescharacteristic
38C4⋊Dic47D411yescharacteristic
39Dic47⋊C4—22no—
40Dic47⋊C4—22no—
41Dic47⋊C4—21no—
42Dic47⋊C4—21no—
43C4×Dic47—22no—
44C4×Dic47—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47Dic188—42no—
48Q8×C47—42no—
49C2×C4×C47—22no—
50C2×C4×C47C2×D411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×Dic47—21no—
54C2×Dic47—21no—
55C2×Dic47—21no—
56C2×Dic47—21no—
57C2×Dic47—41no—
58Dic94—21no—
59Dic94—21no—
60Dic94—41no—
61Dic94—41no—
62Dic94—82no—
63Dic94SD1612yes—
64Dic94Q1612yescomplemented
65C8×C47—41no—
66C8×C47—41no—
67C47⋊C8—41no—
68C22×C47#12011yescharacteristic
69C4×C47—21no—
70C4×C47—42no—
71C4×C47C2×SD1611yescharacteristic
72C4×C47C2×Q1611yescharacteristic
73C4×C47#13711yescharacteristic
74C4×C47#13711yescharacteristic
75Dic47—22no—
76Dic47—22no—
77Dic47—41no—
78Dic47—41no—
79Dic47—81no—
80#1645—471nomaximal, Sylow
81C2×C47#44811yescharacteristic
82C2×C47#45111yescharacteristic
83C2×C47#45511yescharacteristic
84Q82—471no—
85#487—471no—
86#475—471no—
87#462—471no—
88#333D4711yescharacteristic
89Q8⋊C8—471no—
90Q8⋊C8—471no—
91C47#164511yescharacteristic, complemented, Sylow
92C2×Q16—941no—
93C4⋊Q8—471no—
94C4⋊Q8—941no—
95C4⋊Q8—941no—
96C4⋊Q8—942no—
97C4⋊Q8C2×D4711yescharacteristic
98C4×Q8—471no—
99C4×Q8—471no—
100C4×Q8—941no—
101C4×Q8—941no—
102#106—941no—
103C4⋊C8C2×D4711yescharacteristic
104C4⋊C8C2×D4711yescharacteristic
105#103—941no—
106#103—941no—
107#103—942no—
108C4×C8—471no—
109C2×Q8—471no—
110C2×Q8—471no—
111C2×Q8—942no—
112C2×Q8—941no—
113C2×Q8D18812yes—
114Q16—1882no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—941no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—471no—
121C4⋊C4—471no—
122C4⋊C4—942no—
123C4⋊C4—942no—
124C4⋊C4—941no—
125C4⋊C4—941no—
126C4⋊C4—941no—
127C4⋊C4—941no—
128C42—942no—
129C42—941no—
130C42—941no—
131C42C22×D4711yescharacteristic
132Q8—42no—
133Q8—472no—
134Q8—472no—
135Q8—941no—
136Q8—941no—
137Q8—3762no—
138Q8—1881no—
139Q8—1881no—
140C2×C4—22no—
141C2×C4—941no—
142C2×C4—941no—
143C2×C4—941no—
144C2×C4—941no—
145C2×C4—1881no—
146C2×C4C2×D18811yescharacteristic
147C2×C4D4×D4711yescharacteristic
148C2×C4D4×D4711yescharacteristic
149C8—41no—
150C8—41no—
151C8—1881no—
152C22#1309399411yescharacteristic
153C4—21no—
154C4—42no—
155C4—942no—
156C4—942no—
157C4—3761no—
158C4—1881no—
159C4—1881no—
160C4SD16×D4711yescharacteristic
161C4Q16×D4711yescharacteristic
162C4#1309405311yescharacteristic
163C4#1309405611yescharacteristic
164C2#1568926311yescharacteristic
165C2#1568928011yescharacteristic
166C2#1568930311yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#333C2
socleC22×C47#120
hypercenter#333D47
hypocenterC47#1645
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
64. Dic94Q16semidirect
91. C47#1645semidirect