Finite Group Databasebeta

← #20242485

Subgroups — #20242485

Order 6016.

210 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689848C211yesmaximal, characteristic, complemented
2#15689471C211yesmaximal, characteristic
3#15689324C211yesmaximal, characteristic
4#15689324C211yesmaximal, characteristic
5#15688853C211yesmaximal, characteristic, complemented
6#15688853C211yesmaximal, characteristic, complemented
7C47×#332C211yesmaximal, characteristic, complemented
8C2×#10625325—21no—
9C2×#10625325—21no—
10#13094022—21no—
11#13094021C2211yescharacteristic
12#13094015—21no—
13#13094014—22no—
14Q8×Dic47—21no—
15C4×Dic94C2211yescharacteristic
16C4×Dic94C2211yescharacteristic
17#13093989—21no—
18#13093946—21no—
19#13093946—21no—
20#13093944—22no—
21C4×C47⋊C8C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×D188—21no—
27C2×D188—21no—
28C2×D188—21no—
29C2×Dic94D411yescharacteristic
30C2×Dic94D411yescharacteristic
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47D412yes—
35C42×C47C2311yescharacteristic
36C4⋊Dic47—22no—
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—
47#10625325—42no—
48#10625325—42no—
49C22×D47—41no—
50Q8×C47—41no—
51Q8×C47—41no—
52C2×C4×C47—22no—
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×Dic47—21no—
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—21no—
60D188—42no—
61D188—41no—
62D188—41no—
63D188—41no—
64D188—41no—
65Dic94—21no—
66Dic94—21no—
67Dic94—21no—
68Dic94SD1612yescomplemented
69C8×C47—41no—
70C8×C47—41no—
71C47⋊C8—41no—
72C22×C47#12011yescharacteristic
73C2×D47—81no—
74C2×D47—81no—
75C2×D47—81no—
76C4×C47—21no—
77C4×C47—42no—
78C4×C47C2×SD1611yescharacteristic
79C4×C47#13511yescharacteristic
80C4×C47AGL(1,ℤ/8)11yescharacteristic
81C4×C47#13711yescharacteristic
82Dic47—22no—
83Dic47—41no—
84Dic47—41no—
85Dic47—41no—
86#1626—471nomaximal, Sylow
87C2×C47#44811yescharacteristic
88C2×C47#44911yescharacteristic
89C2×C47#45411yescharacteristic
90D47—161no—
91#557—471no—
92#486—471no—
93#460—471no—
94#460—471no—
95#332D4711yescharacteristic, complemented
96Q8⋊C8—471no—
97Q8⋊C8—471no—
98C47#162611yescharacteristic, complemented, Sylow
99C2×SD16—941no—
100C2×SD16—941no—
101C4⋊Q8—941no—
102C4⋊Q8C2×D4711yescharacteristic
103#127—471no—
104#125—941no—
105#125—942no—
106C4×Q8—471no—
107C4×Q8—471no—
108C4×Q8—941no—
109C4×Q8—941no—
110C4⋊C8C2×D4711yescharacteristic
111C4⋊C8C2×D4711yescharacteristic
112#102—941no—
113#102—941no—
114#102—942no—
115C4×C8—471no—
116C2×Q8—21no—
117C2×Q8—471no—
118C2×Q8—471no—
119C2×D4—941no—
120C2×D4—941no—
121C2×D4—941no—
122SD16—1882no—
123SD16—1882no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—941no—
127C4⋊C4—21no—
128C4⋊C4—471no—
129C4⋊C4—471no—
130C4⋊C4—942no—
131C4⋊C4—942no—
132C4⋊C4—942no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4D18812yes—
136C42—942no—
137C42—941no—
138C42—941no—
139C42C22×D4711yescharacteristic
140C23—1881no—
141Q8—41no—
142Q8—41no—
143Q8—472no—
144Q8—941no—
145Q8—941no—
146Q8—941no—
147D4—1882no—
148D4—1881no—
149D4—1881no—
150D4—1881no—
151D4—1881no—
152C2×C4—22no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—941no—
156C2×C4—941no—
157C2×C4C2×D18811yescharacteristic
158C2×C4D4×D4711yescharacteristic
159C2×C4D4×D4711yescharacteristic
160C8—41no—
161C8—41no—
162C8—1881no—
163C22—3761no—
164C22—3761no—
165C22—3761no—
166C22#1309399411yescharacteristic
167C4—21no—
168C4—42no—
169C4—942no—
170C4—1881no—
171C4—1881no—
172C4—1881no—
173C4SD16×D4711yescharacteristic
174C4#1309404511yescharacteristic
175C4#1309404811yescharacteristic
176C4#1309405611yescharacteristic
177C2—7521no—
178C2#1568926311yescharacteristic
179C2#1568926911yescharacteristic
180C2#1568929811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#332C2
socleC22×C47#120
hypercenter#332D47
hypocenterC47#1626
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #15689848C2semidirect
5. #15688853C2semidirect
6. #15688853C2semidirect
7. C47×#332C2semidirect
68. Dic94SD16semidirect
95. #332D47semidirect
98. C47#1626semidirect