Finite Group Databasebeta

← #20242685

Subgroups — #20242685

Order 6016.

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

normal subgroups only

This group has 206 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, complemented
2#15689510C211yesmaximal, characteristic
3#15689487C211yesmaximal, characteristic, complemented
4#15688865C211yesmaximal, characteristic, complemented
5#15688864C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic, complemented
7C47×#490C211yesmaximal, characteristic, complemented
8C2×#10625335—21no—
9C2×#10625334—21no—
10#13094023—21no—
11#13094019—21no—
12#13094019—21no—
13#13094016C2211yescharacteristic
14#13094012C2211yescharacteristic
15#13094009—21no—
16#13094004—21no—
17#13094002—21no—
18#13093945—21no—
19#13093945—21no—
20#13093935C2211yescharacteristic
21#13093935C2211yescharacteristic
22#127×C47C2211yescharacteristic
23#125×C47C2211yescharacteristic
24#102×C47—21no—
25#102×C47—21no—
26#97×C47C2211yescharacteristic
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D188D411yescharacteristic
31C2×C4×D47—21no—
32C2×Dic94—21no—
33C2×Dic94D411yescharacteristic
34C2×C8×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47D411yescharacteristic
38C4⋊C4×C47D411yescharacteristic
39C42×C47C2311yescharacteristic
40#10625335—42no—
41#10625334—42no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47D411yescharacteristic
49C4⋊Dic47D411yescharacteristic
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53C4×Dic47—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C23×C47—41no—
57C22×D47—21no—
58D4×C47—41no—
59D4×C47—41no—
60D4×C47—42no—
61D4×C47—42no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70D188—41no—
71C4×D47—81no—
72Dic94—41no—
73Dic94—81no—
74C8×C47—41no—
75C47⋊C8—22no—
76C47⋊C8—41no—
77C22×C47—81no—
78C22×C47—81no—
79C22×C47—81no—
80C22×C47#12011yescharacteristic
81C2×D47—41no—
82C2×D47—41no—
83C2×D47—41no—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—41no—
88C4×C47—41no—
89Dic47—41no—
90Dic47—41no—
91Dic47—41no—
92#1657—471nomaximal, Sylow
93C2×C47—161no—
94C2×C47#45311yescharacteristic
95C2×C47#45411yescharacteristic
96C2×C47#45411yescharacteristic
97D47—81no—
98#563—471no—
99#496—471no—
100#490—471no—
101#490D4711yescharacteristic, complemented
102#330—471no—
103#330—471no—
104#329—471no—
105C47#165711yescharacteristic, complemented, Sylow
106C2×SD16—941no—
107C2×D8—941no—
108C4⋊Q8—941no—
109#127C2×D4711yescharacteristic
110#126—941no—
111#126—941no—
112#125—471no—
113#125C2×D4711yescharacteristic
114#124—471no—
115#123—941no—
116C22⋊Q8—941no—
117C22⋊Q8—941no—
118#102—21no—
119#102—21no—
120#102—941no—
121#102—941no—
122#97—471no—
123#97—471no—
124#97C2×D4711yescharacteristic
125C2×Q8—471no—
126C2×Q8—941no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—471no—
131C22×C4—941no—
132SD16—1882no—
133D8—1882no—
134C2×C8—21no—
135C2×C8—941no—
136C2×C8—941no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—471no—
140C4⋊C4—471no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4C22⋊D4711yescharacteristic
146C4⋊C4C22⋊D4711yescharacteristic
147C22⋊C4—941no—
148C22⋊C4—941no—
149C22⋊C4—941no—
150C22⋊C4—941no—
151C22⋊C4—941no—
152C42—941no—
153C42C22×D4711yescharacteristic
154C23—41no—
155C23—941no—
156Q8—3761no—
157Q8—1881no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—1881no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—941no—
166C2×C4—941no—
167C2×C4—941no—
168C2×C4—3761no—
169C2×C4D4×D4711yescharacteristic
170C2×C4D4×D4711yescharacteristic
171C2×C4C2×C22⋊D4711yescharacteristic
172C8—41no—
173C8—942no—
174C8—1881no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—1881no—
179C22—1881no—
180C22—1881no—
181C22#1309399211yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—1881no—
188C4—1881no—
189C4—1881no—
190C2—161no—
191C2—3761no—
192C2#1568928911yescharacteristic
193C2#1568929411yescharacteristic
194C2#1568929511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#490C2
socleC22×C47#120
hypercenter#490D47
hypocenterC47#1657
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #15689877C2semidirect
3. #15689487C2semidirect
4. #15688865C2semidirect
5. #15688864C2semidirect
6. #15688862C2semidirect
7. C47×#490C2semidirect
101. #490D47semidirect
105. C47#1657semidirect