Finite Group Databasebeta

← #20252262

Subgroups — #20252262

Order 6016.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×#13094046C211yesmaximal, characteristic
2#15689604C212yesmaximal, complemented
3#15689222C214yesmaximal, complemented
4#15689217C212yesmaximal, complemented
5#15689205C212yesmaximal, complemented
6#15689122C212yesmaximal, complemented
7#15689078C211yesmaximal, characteristic, complemented
8C2×#107×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2212yes—
10#13094046C418yescomplemented
11C2×Dic188C2211yescharacteristic
12C2×#10625325C2212yes—
13C2×D376C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13093989C2214yes—
16#13093986C2214yes—
17C4×C22⋊D47—24no—
18#13093983C2211yescharacteristic
19#13093982—22no—
20C4⋊C4×D47—22no—
21#13093947C2214yes—
22#13093944C2214yes—
23#13093934C2212yes—
24C8×Dic47C2212yes—
25C22×C8×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2212yes—
27#107×C47C2212yes—
28#107×C47C2212yes—
29C22×C4×C47—22no—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—22no—
32#10625350—24no—
33#10625350C2×C418yescomplemented
34C2×D188C2312yes—
35C2×C4×D47—22no—
36C2×C4×D47—24no—
37C2×Dic94C2312yes—
38C2×C8×C47C2×C414yescomplemented
39C2×C8×C47C2311yescharacteristic
40C2×C8×C47C2311yescharacteristic
41C4⋊C4×C47—22no—
42C4⋊C4×C47C2314yes—
43C22⋊Dic47D412yes—
44(C2×D47)⋊C4—24no—
45C4⋊Dic47D411yescharacteristic
46C4⋊Dic47D411yescharacteristic
47Dic47⋊C4—24no—
48C4×Dic47—24no—
49C4×Dic47C2312yes—
50#10625329—22no—
51C2×C47⋊C8C2312yes—
52Dic188C2×C414yescomplemented
53D376C2×C414yescomplemented
54#10625325C2×C418yescomplemented
55C23×C47C2×D411yescharacteristic
56C22×D47—22no—
57C2×C4×C47—24no—
58C2×C4×C47—82no—
59C2×C4×C47C22×C412yes—
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47#4112yes—
62C2×C4×C47C2411yescharacteristic
63C22⋊D47—28no—
64C2×Dic47—22no—
65C2×Dic47C2×D412yes—
66C2×Dic47C2×D412yes—
67D188—22no—
68D188C22×C414yes—
69C4×D47—28no—
70C4×D47—84no—
71Dic94—22no—
72Dic94C22×C414yes—
73C8×C47C22×C412yes—
74C8×C47C22×C412yes—
75C47⋊C8—22no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47C4×D412yes—
79C22×C47C22×D411yescharacteristic
80C2×D47—24no—
81C2×D47—42no—
82C2×D47—42no—
83C4×C47—44no—
84C4×C47C4×D412yes—
85C4×C47C23×C411yescharacteristic
86C4×C47C2×#4111yescharacteristic
87Dic47—24no—
88Dic47—22no—
89Dic47—22no—
90#2951—471nomaximal, Sylow
91C2×C47—22no—
92C2×C47C2×C4×D411yescharacteristic
93C2×C47#57611yescharacteristic
94C2×C47#57811yescharacteristic
95D47—44no—
96C2×#135—471no—
97#520—472no—
98#440—474no—
99C4×Q16—472no—
100C4×D8—472no—
101C2×#107D4711yescharacteristic, complemented
102#417—472no—
103#405—471no—
104C47#295111yescharacteristic, complemented, Sylow
105C2×#41—472no—
106#135—478no—
107C2×Q16—471no—
108C2×SD16—472no—
109C2×D8—471no—
110C2×M16—471no—
111C22×C8C2×D4711yescharacteristic
112C4×Q8—474no—
113C4×D4—474no—
114C4×D4—944no—
115#117—471no—
116#117—942no—
117C2×C4⋊C4—942no—
118C2×C4⋊C4C2×D4712yes—
119#107C2×D4712yes—
120#107C2×D4712yes—
121#103—474no—
122#102—474no—
123#97—472no—
124C4×C8—472no—
125#41—478no—
126#41—944no—
127C2×Q8—472no—
128C2×D4—472no—
129C2×D4—942no—
130C22×C4—22no—
131C22×C4—944no—
132C22×C4—942no—
133C22×C4C22×D4711yescharacteristic
134Q16—474no—
135SD16—478no—
136D8—474no—
137M16—942no—
138C2×C8—472no—
139C2×C8C4×D4714yescomplemented
140C2×C8C22×D4711yescharacteristic
141C2×C8C22×D4711yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—471no—
144C4⋊C4—471no—
145C4⋊C4—944no—
146C4⋊C4C22×D4714yes—
147C22⋊C4—472no—
148C22⋊C4—944no—
149C42—472no—
150C42—944no—
151C23—942no—
152C23D4×D4711yescharacteristic
153Q8—474no—
154Q8—942no—
155D4—474no—
156D4—948no—
157D4—942no—
158C2×C4—24no—
159C2×C4—82no—
160C2×C4—472no—
161C2×C4—472no—
162C2×C4—942no—
163C2×C4—948no—
164C2×C4—3764no—
165C2×C4C2×C4×D4712yes—
166C2×C4D4×D4711yescharacteristic
167C2×C4#1062535412yes—
168C2×C4C23×D4711yescharacteristic
169C8—942no—
170C8C2×C4×D4712yes—
171C8C2×C4×D4712yes—
172C22—21no—
173C22—21no—
174C22—944no—
175C22—1882no—
176C22—1882no—
177C22#1309398612yes—
178C22C2×D4×D4711yescharacteristic
179C4—44no—
180C4—944no—
181C4—942no—
182C4—942no—
183C4#1309398612yes—
184C4C22×C4×D4711yescharacteristic
185C4C2×#1062535411yescharacteristic
186C2—22no—
187C2—1884no—
188C2C2×#1309398611yescharacteristic
189C2#1568992411yescharacteristic
190C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC2×#107×C47C2
socleC22×C47C22×D4
hypercenterC2×#107D47
hypocenterC47#2951
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #15689604C2semidirect
3. #15689222C2semidirect
4. #15689217C2semidirect
5. #15689205C2semidirect
6. #15689122C2semidirect
7. #15689078C2semidirect
8. C2×#107×C47C2semidirect
10. #13094046C4semidirect
33. #10625350C2×C4semidirect
38. C2×C8×C47C2×C4semidirect
52. Dic188C2×C4semidirect
53. D376C2×C4semidirect
54. #10625325C2×C4semidirect
101. C2×#107D47semidirect
104. C47#2951semidirect
139. C2×C8C4×D47semidirect