Finite Group Databasebeta

← #20254310

Subgroups — #20254310

Order 6016.

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

normal subgroups only

This group has 428 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#15689495C212yesmaximal, complemented
3#15689475C212yesmaximal, complemented
4#15689328C214yesmaximal, complemented
5#15689261C214yesmaximal, complemented
6#15689176C211yesmaximal, characteristic, complemented
7C47×#532C211yesmaximal, characteristic
8C22×Dic94C2212yes—
9C2×#10625335C2218yes—
10#13094024—21no—
11#13094024—21no—
12#13094024C2212yes—
13#13094024C2212yes—
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47—21no—
16C4⋊(C47⋊C8)C2212yes—
17#13093947C2218yes—
18C22⋊(C47⋊C8)C2212yes—
19C4×C47⋊C8C2212yes—
20C2×#41×C47—21no—
21C4⋊Q8×C47C2211yescharacteristic
22#127×C47C2211yescharacteristic
23#124×C47—21no—
24#121×C47—21no—
25#121×C47C2212yes—
26C4×D4×C47—21no—
27C4×D4×C47C2212yes—
28C2×C42×C47C2211yescharacteristic
29#41×C47—44no—
30C2×Q8×C47—21no—
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—44no—
42C2×Dic94C2314yes—
43C4⋊C4×C47—21no—
44C4⋊C4×C47C2312yes—
45C22⋊C4×C47—22no—
46C22⋊C4×C47—22no—
47C42×C47D411yescharacteristic
48C42×C47D411yescharacteristic
49C42×C47C2311yescharacteristic
50C42×C47C2311yescharacteristic
51#10625335—48no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56C2×C47⋊C8C2314yes—
57C23×C47—22no—
58C23×C47C2×D411yescharacteristic
59Q8×C47—42no—
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×C47SD1614yescomplemented
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—24no—
76C2×Dic47—44no—
77Dic94—28no—
78Dic94—44no—
79C47⋊C8—24no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—42no—
83C22×C47—42no—
84C22×C47—42no—
85C22×C47C2×SD1612yes—
86C22×C47C22×D411yescharacteristic
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—42no—
90C4×C47C2×SD1612yes—
91C4×C47C2×SD1612yes—
92C4×C47#13712yes—
93C4×C47H(5,𝔽2)12yes—
94Dic47—44no—
95#3206—471nomaximal, Sylow
96C2×C47—22no—
97C2×C47—82no—
98C2×C47#53511yescharacteristic
99C2×C47C22×SD1611yescharacteristic
100C2×C47C2×#13711yescharacteristic
101#532D4711yescharacteristic
102C2×C4⋊Q8—471no—
103#492—472no—
104#487—472no—
105#461—474no—
106#448—474no—
107#431—471no—
108C47#320611yescharacteristic, complemented, Sylow
109C2×#41—21no—
110C22×Q8—472no—
111C2×SD16—478no—
112C4⋊Q8—472no—
113C4⋊Q8—472no—
114C4⋊Q8—941no—
115C4⋊Q8—941no—
116C4⋊Q8C2×D4711yescharacteristic
117#127C2×D4711yescharacteristic
118#124—21no—
119#121—21no—
120#121C2×D4712yes—
121C4×D4—21no—
122C4×D4C2×D4712yes—
123C2×C4⋊C4—941no—
124C2×C4⋊C4—941no—
125C2×C42C2×D4711yescharacteristic
126C4⋊C8—472no—
127#103—478no—
128C22⋊C8—472no—
129C4×C8—472no—
130#41—44no—
131C2×Q8—21no—
132C2×Q8—474no—
133C2×Q8—942no—
134C2×Q8—1884no—
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
144SD16—1888no—
145C2×C8—474no—
146C4⋊C4—21no—
147C4⋊C4—942no—
148C4⋊C4—942no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4C22×D4712yes—
152C22⋊C4—22no—
153C22⋊C4—22no—
154C42C22⋊D4711yescharacteristic
155C42C22⋊D4711yescharacteristic
156C42C22×D4711yescharacteristic
157C42C22×D4711yescharacteristic
158C23—22no—
159C23C2×C22⋊D4711yescharacteristic
160Q8—42no—
161Q8—948no—
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#1062533514yescomplemented
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—
186C22C2×#1062533512yes—
187C22C22×C22⋊D4711yescharacteristic
188C4—21no—
189C4—21no—
190C4—42no—
191C4—1884no—
192C4C2×#1062533512yes—
193C4C2×#1062533512yes—
194C4#1309405412yes—
195C4#1309407012yes—
196C2—22no—
197C2—82no—
198C2#1568968711yescharacteristic
199C2C22×#1062533511yescharacteristic
200C2C2×#1309405411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#532C2
socleC22×C47C22×D4
hypercenter#532D47
hypocenterC47#3206
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. #15689495C2semidirect
3. #15689475C2semidirect
4. #15689328C2semidirect
5. #15689261C2semidirect
6. #15689176C2semidirect
68. C2×C4×C47SD16semidirect
108. C47#3206semidirect
173. C2×C4#10625335semidirect