Finite Group Databasebeta

← #20255110

Subgroups — #20255110

Order 6016.

484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094046C212yesmaximal, complemented
2#15689778C212yesmaximal, complemented
3#15689503C211yesmaximal, characteristic, complemented
4#15689364C212yesmaximal, complemented
5#15689329C212yesmaximal, complemented
6#15689287C214yesmaximal, complemented
7C4×D376C211yesmaximal, characteristic, complemented
8C8×D4×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2214yes—
10#13094046—28no—
11C2×Dic188C2212yes—
12C2×Dic188C2212yes—
13C2×#10625325C2214yes—
14C2×D376C2211yescharacteristic
15#13094024C2212yes—
16#13094006—24no—
17#13094003C2214yes—
18#13093995—22no—
19C4×D188C2212yes—
20C4⋊C4×D47—22no—
21#13093958C2211yescharacteristic
22#13093949C2214yes—
23#13093946C2212yes—
24C22×C8×C47C2212yes—
25C4×D4×C47C2211yescharacteristic
26C4⋊C8×C47C2211yescharacteristic
27C22⋊C8×C47C2212yes—
28C4×C8×C47C2211yescharacteristic
29C2×D4×C47D411yescharacteristic
30C22×C4×C47C2312yes—
31C2×C22⋊D47—24no—
32#10625350—28no—
33#10625350—44no—
34C2×D188C2312yes—
35C2×C4×D47—22no—
36C2×C4×D47—24no—
37C2×Dic94C2314yes—
38C2×C8×C47—24no—
39C2×C8×C47C2312yes—
40C2×C8×C47C2311yescharacteristic
41C2×C8×C47C2311yescharacteristic
42C4⋊C4×C47D411yescharacteristic
43C22⋊C4×C47D412yes—
44C42×C47C2311yescharacteristic
45C22⋊Dic47—24no—
46(C2×D47)⋊C4—22no—
47C4⋊Dic47—22no—
48C4⋊Dic47—22no—
49C4⋊Dic47C2312yes—
50Dic47⋊C4—24no—
51Dic188—24no—
52Dic188—42no—
53D376D414yescomplemented
54#10625325—28no—
55C23×C47C2×D412yes—
56C22×D47—22no—
57D4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47C2×D412yes—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2411yescharacteristic
64C22⋊D47—48no—
65C2×Dic47—22no—
66C2×Dic47—24no—
67D188—22no—
68D188C2×D414yes—
69C4×D47—48no—
70C4×D47—44no—
71Dic94—24no—
72Dic94—24no—
73C8×C47—22no—
74C8×C47—21no—
75C8×C47C2×D412yes—
76C22×C47—22no—
77C22×C47—22no—
78C22×C47—22no—
79C22×C47C22×D411yescharacteristic
80C2×D47—24no—
81C2×D47—42no—
82C2×D47—42no—
83C4×C47—22no—
84C4×C47—21no—
85C4×C47#13512yescomplemented
86C4×C47C22×D411yescharacteristic
87C4×C47H(5,𝔽2)11yescharacteristic
88Dic47—44no—
89Dic47—42no—
90#3283—471nomaximal, Sylow
91C2×C47—42no—
92C2×C47D4211yescharacteristic
93C2×C47C2×#13511yescharacteristic
94C2×C47#57811yescharacteristic
95D47—44no—
96C2×#135—472no—
97#547—472no—
98#494—471no—
99#467—472no—
100#461—472no—
101#452—474no—
102C4×D8—471no—
103C8×D4D4711yescharacteristic, complemented
104C47#328311yescharacteristic, complemented, Sylow
105C2×#41—474no—
106#135—948no—
107C2×Q16—472no—
108C2×Q16—472no—
109C2×SD16—474no—
110C2×D8—471no—
111C22×C8C2×D4712yes—
112C4⋊Q8—472no—
113#123—944no—
114C22⋊Q8—474no—
115#121—942no—
116C4×D4—472no—
117C4×D4C2×D4711yescharacteristic
118C2×C4⋊C4—942no—
119#107—471no—
120C4⋊C8C2×D4711yescharacteristic
121#103—474no—
122#102—472no—
123C22⋊C8C2×D4712yes—
124C4×C8C2×D4711yescharacteristic
125#41—948no—
126#41—1884no—
127C2×Q8—474no—
128C2×D4—472no—
129C2×D4—944no—
130C2×D4D18811yescharacteristic
131C22×C4—942no—
132C22×C4—944no—
133C22×C4C22×D4712yes—
134Q16—944no—
135Q16—1882no—
136SD16—948no—
137D8—474no—
138C2×C8—24no—
139C2×C8C22×D4711yescharacteristic
140C2×C8C22×D4712yes—
141C2×C8C22×D4711yescharacteristic
142C4⋊C4—472no—
143C4⋊C4—944no—
144C4⋊C4—942no—
145C4⋊C4—942no—
146C4⋊C4D18811yescharacteristic
147C22⋊C4—944no—
148C22⋊C4—942no—
149C22⋊C4D18812yes—
150C42C22×D4711yescharacteristic
151C23—942no—
152C23C2×D18812yes—
153Q8—944no—
154Q8—944no—
155D4—22no—
156D4—474no—
157D4—942no—
158D4—1888no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—942no—
162C2×C4—944no—
163C2×C4—1888no—
164C2×C4—1884no—
165C2×C4C2×D18811yescharacteristic
166C2×C4C2×D18812yes—
167C2×C4C2×D18811yescharacteristic
168C2×C4C23×D4711yescharacteristic
169C8—22no—
170C8—21no—
171C8D4×D4712yes—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—944no—
176C22—1882no—
177C22—1882no—
178C22C22×D18811yescharacteristic
179C4—22no—
180C4—21no—
181C4—1884no—
182C4—1882no—
183C4#1309404612yescomplemented
184C4C2×D4×D4711yescharacteristic
185C4#1309407011yescharacteristic
186C2—42no—
187C2—1884no—
188C2D4×D18811yescharacteristic
189C2C2×#1309404611yescharacteristic
190C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC8×D4×C47C2
socleC22×C47C22×D4
hypercenterC8×D4D47
hypocenterC47#3283
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13094046C2semidirect
2. #15689778C2semidirect
3. #15689503C2semidirect
4. #15689364C2semidirect
5. #15689329C2semidirect
6. #15689287C2semidirect
7. C4×D376C2semidirect
8. C8×D4×C47C2semidirect
53. D376D4semidirect
85. C4×C47#135semidirect
103. C8×D4D47semidirect
104. C47#3283semidirect
183. C4#13094046semidirect