Finite Group Databasebeta

← #20241961

Subgroups — #20241961

Order 6016.

288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13094003C211yesmaximal, characteristic
2#15688983C211yesmaximal, characteristic
3#15688861C214yesmaximal, complemented
4C2×C22⋊C8×C47C211yesmaximal, characteristic
5C22×Dic94C411yescharacteristic, complemented
6#13094003—21no—
7#13094003—21no—
8#13094003C412yescomplemented
9#13094003C2212yes—
10C2×C4⋊Dic47—21no—
11C2×C4⋊Dic47C411yescharacteristic, complemented
12C2×Dic47⋊C4—21no—
13C2×C22⋊Dic47—21no—
14C2×C22⋊Dic47—21no—
15C47⋊#95C2212yes—
16C23×C4×C47C2211yescharacteristic
17C22×C8×C47—21no—
18C22⋊C8×C47—21no—
19C22⋊C8×C47C2212yes—
20C24×C47D411yescharacteristic
21C22×C4×C47—42no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—21no—
29C22×Dic47—21no—
30C22×Dic47—22no—
31C2×Dic94—21no—
32C2×Dic94—42no—
33C2×Dic94C2×C412yes—
34C2×C8×C47—22no—
35C2×C8×C47—42no—
36C22⋊Dic47—22no—
37C22⋊Dic47—22no—
38C22⋊Dic47—42no—
39C4⋊Dic47—21no—
40C4⋊Dic47—42no—
41C4⋊Dic47C2×C412yes—
42Dic47⋊C4—22no—
43Dic47⋊C4—22no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47C22⋊C411yescharacteristic
47C23×C47C22⋊C411yescharacteristic
48C23×C47SD1612yes—
49C23×C47Q1612yes—
50C23×C47C2×D411yescharacteristic
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—22no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C22×C411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×Dic47—22no—
62C2×Dic47—22no—
63C2×Dic47—42no—
64C2×Dic47—42no—
65C2×Dic47—42no—
66C2×Dic47—42no—
67C2×Dic47—42no—
68Dic94—42no—
69Dic94—42no—
70C8×C47—42no—
71C22×C47—21no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—42no—
78C22×C47—42no—
79C22×C47#10312yes—
80C22×C47#10312yes—
81C22×C47C2×C22⋊C411yescharacteristic
82C22×C47C2×SD1611yescharacteristic
83C22×C47C2×Q1611yescharacteristic
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47#9912yes—
88Dic47—42no—
89Dic47—42no—
90Dic47—82no—
91#1520—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—22no—
94C2×C47—22no—
95C2×C47—21no—
96C2×C47C2×#9911yescharacteristic
97C2×C47C2×#10311yescharacteristic
98C2×C47#42111yescharacteristic
99C2×C22⋊Q8—471no—
100C2×C22⋊C8D4711yescharacteristic
101#380—471no—
102#328—474no—
103C47#152011yescharacteristic, complemented, Sylow
104C22×Q8—471no—
105C23×C4C2×D4711yescharacteristic
106C22×C8—21no—
107C22⋊Q8—472no—
108C22⋊Q8—472no—
109C22⋊Q8—941no—
110C22⋊Q8—941no—
111C2×C4⋊C4—471no—
112C2×C4⋊C4—941no—
113C2×C4⋊C4—941no—
114C2×C22⋊C4—941no—
115C2×C22⋊C4—941no—
116C22⋊C8—21no—
117C22⋊C8C2×D4712yes—
118#95—472no—
119C24D18811yescharacteristic
120C2×Q8—472no—
121C2×Q8—941no—
122C2×Q8—1882no—
123C22×C4—42no—
124C22×C4—941no—
125C22×C4—941no—
126C22×C4—942no—
127C22×C4C4×D4711yescharacteristic
128C22×C4C4×D4711yescharacteristic
129C22×C4D18811yescharacteristic
130C22×C4C22⋊D4711yescharacteristic
131C22×C4C22⋊D4711yescharacteristic
132C22×C4C22×D4711yescharacteristic
133C2×C8—22no—
134C2×C8—42no—
135C4⋊C4—472no—
136C4⋊C4—942no—
137C4⋊C4—941no—
138C4⋊C4—942no—
139C4⋊C4—1882no—
140C22⋊C4—942no—
141C22⋊C4—942no—
142C22⋊C4—1882no—
143C23—41no—
144C23—41no—
145C23#1062532512yes—
146C23Dic18812yes—
147C23(C2×D47)⋊C411yescharacteristic
148C23(C2×D47)⋊C411yescharacteristic
149C23C2×D18811yescharacteristic
150Q8—1882no—
151Q8—1882no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—942no—
159C2×C4—942no—
160C2×C4—1882no—
161C2×C4—1882no—
162C2×C4—1882no—
163C2×C4—1882no—
164C2×C4—1882no—
165C2×C4(C2×D47)⋊C411yescharacteristic
166C2×C4(C2×D47)⋊C411yescharacteristic
167C2×C4C2×C4×D4711yescharacteristic
168C2×C4C2×C22⋊D4711yescharacteristic
169C8—42no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22#1309394912yes—
179C22#1309394912yes—
180C22C2×(C2×D47)⋊C411yescharacteristic
181C22C2×#1062532511yescharacteristic
182C22C2×Dic18811yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—3762no—
187C4—1882no—
188C4—1882no—
189C4#1309393812yes—
190C2—21no—
191C2—22no—
192C2—22no—
193C2—21no—
194C2C2×#1309393811yescharacteristic
195C2C2×#1309394911yescharacteristic
196C2#1568913911yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×C22⋊C8D47
hypocenterC47#1520
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #15688861C2semidirect
5. C22×Dic94C4semidirect
8. #13094003C4semidirect
11. C2×C4⋊Dic47C4semidirect
103. C47#1520semidirect