Finite Group Databasebeta

← #20242719

Subgroups — #20242719

Order 6016.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#15689877C211yesmaximal, characteristic
2#15689529C211yesmaximal, characteristic, complemented
3#15689485C211yesmaximal, characteristic
4#15688865C211yesmaximal, characteristic, complemented
5#15688864C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic
7C47×#491C211yesmaximal, characteristic, complemented
8#13094023—21no—
9#13094019—21no—
10#13094019—21no—
11#13094016C2211yescharacteristic
12#13094012C2211yescharacteristic
13#13094009—21no—
14#13094004—21no—
15#13094002—21no—
16#13093957—21no—
17#13093955—21no—
18#13093947—21no—
19#13093944—21no—
20#13093935C2211yescharacteristic
21#13093935C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#125×C47C2211yescharacteristic
24#103×C47—21no—
25#103×C47—21no—
26#97×C47C2211yescharacteristic
27C2×Q8×C47—21no—
28C2×D188D411yescharacteristic
29C2×C4×D47—21no—
30C2×Dic94—21no—
31C2×Dic94D411yescharacteristic
32C2×C8×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C4⋊C4×C47D411yescharacteristic
39C42×C47C2311yescharacteristic
40(C2×D47)⋊C4—21no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47D411yescharacteristic
47C4⋊Dic47D411yescharacteristic
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51C4×Dic47—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C22×D47—21no—
55Q8×C47—42no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×Dic47—21no—
63C2×Dic47—21no—
64C2×Dic47—21no—
65D188—41no—
66C4×D47—81no—
67Dic94—41no—
68Dic94—81no—
69C8×C47—41no—
70C47⋊C8—22no—
71C47⋊C8—41no—
72C22×C47#12011yescharacteristic
73C2×D47—41no—
74C2×D47—41no—
75C2×D47—41no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—21no—
79C4×C47—41no—
80C4×C47—41no—
81C4×C47—81no—
82Dic47—41no—
83Dic47—41no—
84Dic47—41no—
85#1664—471nomaximal, Sylow
86C2×C47#45411yescharacteristic
87C2×C47#45511yescharacteristic
88C2×C47#45611yescharacteristic
89D47—81no—
90#563—471no—
91#501—471no—
92#491D4711yescharacteristic, complemented
93#489—471no—
94#330—471no—
95#330—471no—
96#329—471no—
97C47#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—941no—
99C4⋊Q8C2×D4711yescharacteristic
100#126—941no—
101#126—941no—
102#125—471no—
103#125C2×D4711yescharacteristic
104#124—471no—
105#123—941no—
106C22⋊Q8—941no—
107C22⋊Q8—941no—
108#107—941no—
109#106—941no—
110#103—21no—
111#103—21no—
112#103—941no—
113#102—941no—
114#97—471no—
115#97—471no—
116#97C2×D4711yescharacteristic
117C2×Q8—21no—
118C2×Q8—471no—
119C2×Q8—941no—
120C2×D4—471no—
121C22×C4—941no—
122C2×C8—21no—
123C2×C8—941no—
124C2×C8—941no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—471no—
130C4⋊C4—471no—
131C4⋊C4—941no—
132C4⋊C4—941no—
133C4⋊C4—941no—
134C4⋊C4—941no—
135C4⋊C4C22⋊D4711yescharacteristic
136C4⋊C4C22⋊D4711yescharacteristic
137C22⋊C4—941no—
138C22⋊C4—941no—
139C22⋊C4—941no—
140C22⋊C4—941no—
141C22⋊C4—941no—
142C42—941no—
143C42C22×D4711yescharacteristic
144C23—941no—
145Q8—42no—
146Q8—3761no—
147Q8—1881no—
148D4—1881no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—941no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—3761no—
156C2×C4D4×D4711yescharacteristic
157C2×C4D4×D4711yescharacteristic
158C2×C4C2×C22⋊D4711yescharacteristic
159C8—41no—
160C8—942no—
161C8—1881no—
162C22—1881no—
163C22—1881no—
164C22—1881no—
165C22#1309399211yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—1881no—
173C4—1881no—
174C4—1881no—
175C2—3761no—
176C2#1568929511yescharacteristic
177C2#1568929911yescharacteristic
178C2#1568930411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#491C2
socleC22×C47#120
hypercenter#491D47
hypocenterC47#1664
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #15689529C2semidirect
4. #15688865C2semidirect
5. #15688864C2semidirect
7. C47×#491C2semidirect
92. #491D47semidirect
97. C47#1664semidirect