Finite Group Databasebeta

← #20242488

Subgroups — #20242488

Order 6016.

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

normal subgroups only

This group has 250 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#15689788C211yesmaximal, characteristic, complemented
2#15689320C211yesmaximal, characteristic, complemented
3#15689315C211yesmaximal, characteristic
4#15688869C211yesmaximal, characteristic, complemented
5#15688855C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic, complemented
7C47×#486C211yesmaximal, characteristic, complemented
8C2×Q8×D47—21no—
9C2×#10625335—21no—
10C2×#10625334—21no—
11#13094023—21no—
12#13094002—22no—
13#13094000—21no—
14C4×Dic94C2211yescharacteristic
15C4×D188C2211yescharacteristic
16#13093986—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093945—21no—
20#13093945—21no—
21C4⋊Q8×C47C2211yescharacteristic
22#127×C47C2211yescharacteristic
23#102×C47—22no—
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29Q8×D47—42no—
30Q8×D47—42no—
31C2×D188D411yescharacteristic
32C2×C4×D47—22no—
33C2×C4×D47—21no—
34C2×Dic94—22no—
35C2×Dic94D411yescharacteristic
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47D412yes—
39C42×C47C2311yescharacteristic
40#10625335—42no—
41#10625334—42no—
42(C2×D47)⋊C4—22no—
43(C2×D47)⋊C4—21no—
44C4⋊Dic47D411yescharacteristic
45C4⋊Dic47D411yescharacteristic
46Dic47⋊C4—22no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C23×C47—41no—
52C22×D47—21no—
53Q8×C47—41no—
54Q8×C47—41no—
55D4×C47—42no—
56D4×C47—41no—
57D4×C47—41no—
58D4×C47—41no—
59D4×C47—41no—
60C2×C4×C47—22no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×Dic47—21no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67D188—21no—
68D188SD1612yescomplemented
69C4×D47—44no—
70C4×D47—41no—
71C4×D47—41no—
72Dic94—21no—
73Dic94—44no—
74Dic94D812yescomplemented
75C8×C47—41no—
76C47⋊C8—41no—
77C47⋊C8—41no—
78C22×C47—81no—
79C22×C47—81no—
80C22×C47—81no—
81C22×C47#12011yescharacteristic
82C2×D47—22no—
83C2×D47—41no—
84C2×D47—41no—
85C4×C47—21no—
86C4×C47—42no—
87C4×C47C2×D811yescharacteristic
88C4×C47C2×SD1611yescharacteristic
89C4×C47AGL(1,ℤ/8)11yescharacteristic
90C4×C47#13711yescharacteristic
91Dic47—22no—
92Dic47—41no—
93Dic47—41no—
94#1627—471nomaximal, Sylow
95C2×C47—161no—
96C2×C47#44711yescharacteristic
97C2×C47#44811yescharacteristic
98C2×C47#45411yescharacteristic
99D47—42no—
100D4×Q8—471no—
101#486D4711yescharacteristic, complemented
102#460—471no—
103#459—471no—
104#332—471no—
105Q8⋊C8—471no—
106D4⋊C8—471no—
107C47#162711yescharacteristic, complemented, Sylow
108C22×Q8—941no—
109C2×SD16—941no—
110C2×D8—941no—
111C4⋊Q8—941no—
112C4⋊Q8C2×D4711yescharacteristic
113#127C2×D4711yescharacteristic
114C22⋊Q8—941no—
115C22⋊Q8—942no—
116C4×Q8—471no—
117C4×D4—471no—
118C4×D4—941no—
119C4⋊C8—471no—
120C4⋊C8—471no—
121#102—22no—
122#102—941no—
123#102—941no—
124C4×C8C2×D4711yescharacteristic
125C2×Q8—21no—
126C2×Q8—471no—
127C2×Q8—942no—
128C2×Q8—1882no—
129C2×Q8—1882no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—471no—
134C22×C4—942no—
135C22×C4—941no—
136SD16—1882no—
137D8—1882no—
138C2×C8—21no—
139C2×C8—941no—
140C2×C8—941no—
141C4⋊C4—21no—
142C4⋊C4—471no—
143C4⋊C4—471no—
144C4⋊C4—942no—
145C4⋊C4—941no—
146C4⋊C4C22⋊D4712yes—
147C22⋊C4—942no—
148C22⋊C4—941no—
149C42—941no—
150C42C22×D4711yescharacteristic
151C23—41no—
152C23—941no—
153Q8—41no—
154Q8—41no—
155Q8—472no—
156Q8—941no—
157Q8—1884no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—472no—
164D4—941no—
165C2×C4—22no—
166C2×C4—941no—
167C2×C4—941no—
168C2×C4—941no—
169C2×C4—1884no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4D4×D4711yescharacteristic
173C2×C4D4×D4711yescharacteristic
174C2×C4C2×C22⋊D4711yescharacteristic
175C8—41no—
176C8—1881no—
177C8—1881no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—942no—
182C22—1881no—
183C22—1881no—
184C22#1309399211yescharacteristic
185C4—21no—
186C4—42no—
187C4—942no—
188C4—1881no—
189C4—1881no—
190C4D8×D4711yescharacteristic
191C4SD16×D4711yescharacteristic
192C4#1309404811yescharacteristic
193C4#1309405311yescharacteristic
194C2—161no—
195C2—1882no—
196C2#1568925511yescharacteristic
197C2#1568926011yescharacteristic
198C2#1568929511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#486C2
socleC22×C47#120
hypercenter#486D47
hypocenterC47#1627
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689788C2semidirect
2. #15689320C2semidirect
4. #15688869C2semidirect
5. #15688855C2semidirect
6. #15688852C2semidirect
7. C47×#486C2semidirect
68. D188SD16semidirect
74. Dic94D8semidirect
101. #486D47semidirect
107. C47#1627semidirect