Finite Group Databasebeta

← #20253781

Subgroups — #20253781

Order 6016.

424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094024C211yesmaximal, characteristic, complemented
2#15689482C214yesmaximal, complemented
3#15689473C212yesmaximal, complemented
4#15689469C212yesmaximal, complemented
5#15689124C214yesmaximal, complemented
6C4×#10625329C211yesmaximal, characteristic, complemented
7C47×#532C211yesmaximal, characteristic
8C22×Dic94—21no—
9C2×#10625329C2212yes—
10#13094024—21no—
11#13094024—21no—
12#13094024C2212yes—
13#13094024C2212yes—
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47C2212yes—
16#13093948C2218yes—
17#13093945C2218yes—
18#13093935C2212yes—
19C4×C47⋊C8C2212yes—
20C2×#41×C47C2212yes—
21C4⋊Q8×C47C2211yescharacteristic
22#127×C47C2211yescharacteristic
23#124×C47C2212yes—
24#121×C47—21no—
25#121×C47—21no—
26C4×D4×C47—21no—
27C4×D4×C47—21no—
28C2×C42×C47C2211yescharacteristic
29#41×C47—28no—
30C2×Q8×C47C2312yes—
31C2×D4×C47—22no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47C2312yes—
35C22×C4×C47—22no—
36C22×C4×C47D411yescharacteristic
37C22×C4×C47D411yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—22no—
40C2×Dic94—22no—
41C2×Dic94—22no—
42C2×Dic94—44no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C22⋊C4×C47—22no—
46C22⋊C4×C47—22no—
47C42×C47D411yescharacteristic
48C42×C47D411yescharacteristic
49C42×C47C2311yescharacteristic
50C42×C47C2311yescharacteristic
51C4⋊Dic47—22no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47C2314yes—
55#10625329—24no—
56C2×C47⋊C8C2314yes—
57C23×C47—22no—
58C23×C47C2×D411yescharacteristic
59Q8×C47—24no—
60D4×C47—24no—
61D4×C47—44no—
62D4×C47—42no—
63D4×C47—42no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—44no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47#4114yes—
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—24no—
76C2×Dic47—44no—
77Dic94—44no—
78Dic94—44no—
79C47⋊C8—24no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—42no—
83C22×C47—42no—
84C22×C47—42no—
85C22×C47#12412yes—
86C22×C47C22×D411yescharacteristic
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—42no—
90C4×C47#12412yes—
91C4×C47AGL(1,ℤ/8)12yes—
92C4×C47#13712yes—
93C4×C47C2×#4112yes—
94Dic47—44no—
95#3141—471nomaximal, Sylow
96C2×C47—22no—
97C2×C47—82no—
98C2×C47C2×#12411yescharacteristic
99C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
100C2×C47C2×#13711yescharacteristic
101#532D4711yescharacteristic
102C2×C4⋊Q8—471no—
103#489—474no—
104#487—472no—
105#486—472no—
106#417—474no—
107C4×M16—471no—
108C47#314111yescharacteristic, complemented, Sylow
109C2×#41C2×D4712yes—
110C22×Q8—941no—
111C2×M16—472no—
112C4⋊Q8—472no—
113C4⋊Q8—472no—
114C4⋊Q8—941no—
115C4⋊Q8—941no—
116C4⋊Q8C2×D4711yescharacteristic
117#127C2×D4711yescharacteristic
118#124C2×D4712yes—
119#121—21no—
120#121—21no—
121C4×D4—21no—
122C4×D4—21no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—941no—
125C2×C42C2×D4711yescharacteristic
126#103—478no—
127#102—478no—
128#97—472no—
129C4×C8—472no—
130#41—28no—
131C2×Q8—942no—
132C2×Q8—942no—
133C2×Q8—1884no—
134C2×Q8C22×D4712yes—
135C2×D4—22no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4C22×D4712yes—
139C22×C4—22no—
140C22×C4—942no—
141C22×C4C22⋊D4711yescharacteristic
142C22×C4C22⋊D4711yescharacteristic
143C22×C4C22×D4711yescharacteristic
144M16—944no—
145C2×C8—474no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—474no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C22⋊C4—22no—
153C22⋊C4—22no—
154C42C22⋊D4711yescharacteristic
155C42C22⋊D4711yescharacteristic
156C42C22×D4711yescharacteristic
157C42C22×D4711yescharacteristic
158C23—22no—
159C23C2×C22⋊D4711yescharacteristic
160Q8—24no—
161Q8—1884no—
162Q8—1884no—
163D4—24no—
164D4—44no—
165D4—42no—
166D4—42no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—44no—
171C2×C4—944no—
172C2×C4—1884no—
173C2×C4#1062535214yes—
174C2×C4C2×C22⋊D4711yescharacteristic
175C2×C4C2×C22⋊D4711yescharacteristic
176C2×C4C2×C22⋊D4711yescharacteristic
177C2×C4C2×C22⋊D4711yescharacteristic
178C2×C4C2×C22⋊D4711yescharacteristic
179C2×C4C23×D4711yescharacteristic
180C8—944no—
181C22—21no—
182C22—21no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22#1309401112yes—
187C22C22×C22⋊D4711yescharacteristic
188C4—21no—
189C4—21no—
190C4—42no—
191C4—1884no—
192C4#1309401112yes—
193C4#1309404912yes—
194C4#1309405412yes—
195C4C2×#1062535212yes—
196C2—22no—
197C2—82no—
198C2C2×#1309401111yescharacteristic
199C2C2×#1309404911yescharacteristic
200C2C2×#1309405411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#532C2
socleC22×C47C22×D4
hypercenter#532D47
hypocenterC47#3141
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#13094024C2semidirect
2. #15689482C2semidirect
3. #15689473C2semidirect
4. #15689469C2semidirect
5. #15689124C2semidirect
6. C4×#10625329C2semidirect
108. C47#3141semidirect