Finite Group Databasebeta

← #20254539

Subgroups — #20254539

Order 6016.

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

normal subgroups only

This group has 360 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
1#15689680C211yesmaximal, characteristic
2#15689526C212yesmaximal, complemented
3#15689475C212yesmaximal, complemented
4#15689458C214yesmaximal
5#15689415C214yesmaximal, complemented
6#15689176C211yesmaximal, characteristic
7C2×C4⋊Q8×C47C211yesmaximal, characteristic
8#13094024C2211yescharacteristic
9#13094024C2211yescharacteristic
10#13094016—21no—
11#13094003—21no—
12#13094003C2212yes—
13C4×Dic94—21no—
14C4×Dic94C2212yes—
15#13093983—21no—
16#13093957C2218yes—
17C4⋊(C47⋊C8)C2212yes—
18#13093947C2218yes—
19C22⋊(C47⋊C8)C2212yes—
20C4×C47⋊C8C2212yes—
21C22×Q8×C47—21no—
22C4⋊Q8×C47—21no—
23C4⋊Q8×C47—21no—
24C4⋊Q8×C47C2212yes—
25C4⋊Q8×C47C2212yes—
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47C2212yes—
28C2×C42×C47C2211yescharacteristic
29C2×Q8×C47—22no—
30C2×Q8×C47—22no—
31C2×Q8×C47—44no—
32C22×C4×C47—22no—
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C2×Dic94—21no—
37C2×Dic94C2312yes—
38C4⋊C4×C47—22no—
39C4⋊C4×C47—22no—
40C4⋊C4×C47—22no—
41C4⋊C4×C47C2314yes—
42C42×C47D411yescharacteristic
43C42×C47D411yescharacteristic
44C42×C47C2311yescharacteristic
45C42×C47C2311yescharacteristic
46C22⋊Dic47—22no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47C2312yes—
51Dic47⋊C4—22no—
52Dic47⋊C4—22no—
53C4×Dic47—22no—
54C2×C47⋊C8C2314yes—
55C23×C47C2×D411yescharacteristic
56Q8×C47—44no—
57Q8×C47—44no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—24no—
61C2×C4×C47—44no—
62C2×C4×C47Q1614yes—
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2411yescharacteristic
69C2×Dic47—22no—
70C2×Dic47—22no—
71Dic94—24no—
72Dic94—42no—
73C47⋊C8—24no—
74C22×C47—21no—
75C22×C47—21no—
76C22×C47C2×Q1612yes—
77C22×C47C22×D411yescharacteristic
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—44no—
81C4×C47C2×Q1612yes—
82C4×C47C2×Q1612yes—
83C4×C47AGL(1,ℤ/8)12yes—
84C4×C472−1+412yes—
85Dic47—42no—
86Dic47—42no—
87#3230—471nomaximal, Sylow
88C2×C47—22no—
89C2×C47#53611yescharacteristic
90C2×C47C22×Q1611yescharacteristic
91C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
92#533—471no—
93C2×C4⋊Q8D4711yescharacteristic
94#500—472no—
95#487—472no—
96#484—474no—
97#477—474no—
98#431—471no—
99C47#323011yescharacteristic, complemented, Sylow
100C22×Q8—21no—
101C4⋊Q8—21no—
102C4⋊Q8—21no—
103C4⋊Q8—471no—
104C4⋊Q8—471no—
105C4⋊Q8C2×D4712yes—
106C4⋊Q8C2×D4712yes—
107#125—941no—
108C22⋊Q8—472no—
109C22⋊Q8—941no—
110C4×Q8—472no—
111C4×Q8—941no—
112#117—941no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4C2×D4712yes—
115C2×C42C2×D4711yescharacteristic
116#107—478no—
117C4⋊C8—472no—
118#103—478no—
119C22⋊C8—472no—
120C4×C8—472no—
121C2×Q8—22no—
122C2×Q8—22no—
123C2×Q8—44no—
124C2×Q8—472no—
125C2×Q8—941no—
126C22×C4—22no—
127C22×C4C22⋊D4711yescharacteristic
128C22×C4C22⋊D4711yescharacteristic
129C22×C4C22×D4711yescharacteristic
130C2×C8—474no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4—22no—
134C4⋊C4—472no—
135C4⋊C4—942no—
136C4⋊C4—942no—
137C4⋊C4—941no—
138C4⋊C4—941no—
139C4⋊C4—941no—
140C4⋊C4C22×D4714yes—
141C22⋊C4—942no—
142C42—942no—
143C42C22⋊D4711yescharacteristic
144C42C22⋊D4711yescharacteristic
145C42C22×D4711yescharacteristic
146C42C22×D4711yescharacteristic
147C23C2×C22⋊D4711yescharacteristic
148Q8—44no—
149Q8—44no—
150Q8—944no—
151Q8—1882no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—44no—
156C2×C4—942no—
157C2×C4—942no—
158C2×C4#1062533714yes—
159C2×C4C2×C22⋊D4711yescharacteristic
160C2×C4C2×C22⋊D4711yescharacteristic
161C2×C4C2×C22⋊D4711yescharacteristic
162C2×C4C2×C22⋊D4711yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C2×C4C23×D4711yescharacteristic
165C8—944no—
166C22—21no—
167C22—21no—
168C22C2×#1062533712yes—
169C22C22×C22⋊D4711yescharacteristic
170C4—21no—
171C4—21no—
172C4—44no—
173C4—1882no—
174C4—1882no—
175C4C2×#1062533712yes—
176C4C2×#1062533712yes—
177C4#1309405012yes—
178C4#1309407212yes—
179C2—22no—
180C2#1568969711yescharacteristic
181C2C22×#1062533711yescharacteristic
182C2C2×#1309405011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4⋊Q8×C47C2
socleC22×C47C22×D4
hypercenterC2×C4⋊Q8D47
hypocenterC47#3230
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689526C2semidirect
3. #15689475C2semidirect
5. #15689415C2semidirect
99. C47#3230semidirect