Finite Group Databasebeta

← #20242475

Subgroups — #20242475

Order 6016.

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

normal subgroups only

This group has 256 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#15689777C211yesmaximal, characteristic, complemented
2#15689469C211yesmaximal, characteristic, complemented
3#15689315C211yesmaximal, characteristic, complemented
4#15688870C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#459C211yesmaximal, characteristic, complemented
8C2×#10625352—21no—
9C2×#10625334—21no—
10#13094024C2211yescharacteristic
11#13094008—22no—
12#13094004—21no—
13#13093998—21no—
14C4×D188C2211yescharacteristic
15C2×C4⋊Dic47—21no—
16C4⋊(C47⋊C8)C2211yescharacteristic
17#13093945—21no—
18#13093945—22no—
19C4×C47⋊C8C2211yescharacteristic
20C2×D8×C47—21no—
21#127×C47C2211yescharacteristic
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24#102×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47D411yescharacteristic
29C22×C4×C47—21no—
30C2×C22⋊D47—22no—
31C22×Dic47—22no—
32#10625352—42no—
33#10625352—42no—
34C2×D188D411yescharacteristic
35C2×C4×D47—21no—
36C2×Dic94—21no—
37D8×C47—42no—
38C2×C8×C47—21no—
39C4⋊C4×C47D411yescharacteristic
40C22⋊C4×C47—21no—
41C42×C47C2311yescharacteristic
42#10625334—42no—
43(C2×D47)⋊C4—22no—
44(C2×D47)⋊C4—21no—
45C4⋊Dic47—22no—
46C4⋊Dic47—21no—
47C4⋊Dic47D411yescharacteristic
48C4⋊Dic47D412yes—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C23×C47—21no—
52C23×C47—41no—
53C22×D47—21no—
54D4×C47—21no—
55D4×C47—42no—
56D4×C47—41no—
57D4×C47—41no—
58D4×C47—41no—
59D4×C47—41no—
60D4×C47D812yescomplemented
61C2×C4×C47—21no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C22⋊D47—44no—
68C2×Dic47—22no—
69C2×Dic47—21no—
70C2×Dic47—44no—
71D188—21no—
72D188—21no—
73C4×D47—41no—
74C4×D47—41no—
75Dic94—41no—
76Dic94—41no—
77C8×C47—41no—
78C47⋊C8—41no—
79C47⋊C8—41no—
80C22×C47—22no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47—81no—
84C22×C47—81no—
85C22×C47—81no—
86C22×C47#12011yescharacteristic
87C2×D47—41no—
88C2×D47—41no—
89C2×D47—41no—
90C4×C47—21no—
91C4×C47—41no—
92C4×C47C2×D811yescharacteristic
93C4×C47#13511yescharacteristic
94C4×C47AGL(1,ℤ/8)11yescharacteristic
95C4×C47AGL(1,ℤ/8)11yescharacteristic
96Dic47—42no—
97Dic47—41no—
98#1625—471nomaximal, Sylow
99C2×C47—42no—
100C2×C47—161no—
101C2×C47#44711yescharacteristic
102C2×C47#44911yescharacteristic
103C2×C47#45411yescharacteristic
104D47—81no—
105#547—471no—
106#486—471no—
107#459—471no—
108#459D4711yescharacteristic, complemented
109#332—471no—
110D4⋊C8—471no—
111D4⋊C8—471no—
112C47#162511yescharacteristic, complemented, Sylow
113C2×#41—941no—
114C2×D8—21no—
115C2×D8—941no—
116C4⋊Q8—471no—
117#127C2×D4711yescharacteristic
118#123—942no—
119C22⋊Q8—941no—
120#121—941no—
121C4×D4—471no—
122C4×D4C2×D4711yescharacteristic
123C2×C4⋊C4—941no—
124C4⋊C8—471no—
125C4⋊C8C2×D4711yescharacteristic
126#102—21no—
127#102—941no—
128#102—942no—
129C4×C8—471no—
130#41—1882no—
131#41—1882no—
132C2×Q8—941no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—471no—
137C2×D4—942no—
138C2×D4C22⋊D4711yescharacteristic
139C22×C4—21no—
140C22×C4—942no—
141C22×C4—941no—
142D8—42no—
143D8—1882no—
144C2×C8—21no—
145C2×C8—941no—
146C2×C8—941no—
147C4⋊C4—471no—
148C4⋊C4—472no—
149C4⋊C4—942no—
150C4⋊C4—941no—
151C4⋊C4C22⋊D4711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—942no—
154C22⋊C4—941no—
155C42C22×D4711yescharacteristic
156C23—21no—
157C23—41no—
158C23—941no—
159Q8—1881no—
160Q8—1881no—
161D4—21no—
162D4—42no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—941no—
168D4—941no—
169D4—1884no—
170D4#1062533412yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—941no—
175C2×C4—942no—
176C2×C4—1884no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4D4×D4711yescharacteristic
180C2×C4D4×D4711yescharacteristic
181C2×C4C2×C22⋊D4711yescharacteristic
182C8—41no—
183C8—1881no—
184C8—1881no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—1881no—
192C22—1881no—
193C22—1881no—
194C22#1309399211yescharacteristic
195C4—21no—
196C4—41no—
197C4—1881no—
198C4—1882no—
199C4C2×#1062533411yescharacteristic
200C4#1309404311yescharacteristic
201C4#1309404811yescharacteristic
202C4#1309404911yescharacteristic
203C2—42no—
204C2—161no—
205C2—3761no—
206C2#1568925611yescharacteristic
207C2#1568926511yescharacteristic
208C2#1568929411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#459C2
socleC22×C47#120
hypercenter#459D47
hypocenterC47#1625
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689777C2semidirect
2. #15689469C2semidirect
3. #15689315C2semidirect
4. #15688870C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×#459C2semidirect
60. D4×C47D8semidirect
108. #459D47semidirect
112. C47#1625semidirect
170. D4#10625334semidirect