Finite Group Databasebeta

← #20241885

Subgroups — #20241885

Order 6016.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#15689675C211yesmaximal, characteristic
2#15689173C211yesmaximal, characteristic
3#15688974C211yesmaximal, characteristic
4#15688861C211yesmaximal, characteristic
5#15688860C211yesmaximal, characteristic
6#15688859C211yesmaximal, characteristic
7C47×#328C211yesmaximal, characteristic
8#13094023C411yescharacteristic, complemented
9#13094022C411yescharacteristic, complemented
10#13094014—21no—
11#13094003C2211yescharacteristic
12#13094001—21no—
13Q8×Dic47C411yescharacteristic, complemented
14#13093989—21no—
15#13093989C411yescharacteristic, complemented
16#13093980—21no—
17C2×Dic47⋊C4—21no—
18C2×C4×Dic47—21no—
19C2×C4×Dic47C2211yescharacteristic
20Dic47⋊C8—21no—
21C22⋊(C47⋊C8)C2211yescharacteristic
22C8×Dic47—21no—
23C47⋊#95C2211yescharacteristic
24C22⋊Q8×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C2×Q8×C47C2×C411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47D411yescharacteristic
32C22×Dic47D411yescharacteristic
33C2×Dic94—21no—
34C2×Dic94C2×C411yescharacteristic
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47C2×C411yescharacteristic
38C22⋊C4×C47—21no—
39C22⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47C2×C411yescharacteristic
42Dic47⋊C4—24no—
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C4×Dic47—42no—
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47C2×C411yescharacteristic
53C4×Dic47D411yescharacteristic
54C4×Dic47D411yescharacteristic
55C2×C47⋊C8—21no—
56C23×C47C2×D411yescharacteristic
57Q8×C47—41no—
58C2×C4×C47—22no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—41no—
71C2×Dic47—41no—
72C2×Dic47C22⋊C411yescharacteristic
73C2×Dic47C22⋊C411yescharacteristic
74C2×Dic47C22⋊C411yescharacteristic
75C2×Dic47C22⋊C411yescharacteristic
76C2×Dic47SD1612yes—
77C2×Dic47Q1612yes—
78Dic94—42no—
79Dic94—41no—
80C8×C47—41no—
81C47⋊C8—41no—
82C22×C47—21no—
83C22×C47—21no—
84C22×C47C2×C22⋊C411yescharacteristic
85C22×C47C2×SD1611yescharacteristic
86C22×C47C2×Q1611yescharacteristic
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—42no—
90C4×C47—41no—
91C4×C47—41no—
92Dic47—21no—
93Dic47—42no—
94Dic47—41no—
95Dic47—41no—
96Dic47#10312yes—
97Dic47#10312yes—
98Dic47#10412yes—
99#1503—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47#41011yescharacteristic
103C2×C47C2×#10311yescharacteristic
104C2×C47C2×#10411yescharacteristic
105#533—471no—
106#431—471no—
107C4×C4⋊C4—471no—
108#328—471no—
109#328—471no—
110#328—471no—
111#328D4711yescharacteristic
112C47#150311yescharacteristic, complemented, Sylow
113C4⋊Q8—471no—
114C4⋊Q8—471no—
115#125—941no—
116C22⋊Q8—471no—
117C22⋊Q8—941no—
118C22⋊Q8C2×D4711yescharacteristic
119C4×Q8—471no—
120C4×Q8—471no—
121C4×Q8—941no—
122#117—941no—
123C2×C4⋊C4—941no—
124C2×C42—471no—
125C2×C42—941no—
126C4⋊C8—941no—
127C22⋊C8—471no—
128C22⋊C8C2×D4711yescharacteristic
129C4×C8—941no—
130#95—471no—
131#95C2×D4711yescharacteristic
132C2×Q8—471no—
133C2×Q8—941no—
134C2×Q8C4×D4711yescharacteristic
135C22×C4—21no—
136C22×C4—471no—
137C22×C4—471no—
138C22×C4—941no—
139C22×C4C22×D4711yescharacteristic
140C2×C8—21no—
141C2×C8—941no—
142C4⋊C4—21no—
143C4⋊C4—471no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—944no—
150C4⋊C4—941no—
151C4⋊C4C4×D4711yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—941no—
154C42—471no—
155C42—471no—
156C42—471no—
157C42—471no—
158C42—941no—
159C42—941no—
160C42—1882no—
161C23D4×D4711yescharacteristic
162Q8—41no—
163Q8—1881no—
164Q8—1882no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—471no—
172C2×C4—471no—
173C2×C4—471no—
174C2×C4—472no—
175C2×C4—472no—
176C2×C4—471no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—1881no—
182C2×C4—1881no—
183C2×C4C2×C4×D4711yescharacteristic
184C2×C4D4×D4711yescharacteristic
185C8—41no—
186C8—1881no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D4711yescharacteristic
190C22SD16×D4711yescharacteristic
191C22Q16×D4711yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—472no—
198C4—472no—
199C4—472no—
200C4—941no—
201C4—1882no—
202C4—1881no—
203C4—1881no—
204C2—21no—
205C2—21no—
206C2#1568909511yescharacteristic
207C2#103×D4711yescharacteristic
208C2#104×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#328C2
socleC22×C47C2×C22⋊C4
hypercenter#328D47
hypocenterC47#1503
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #13094023C4semidirect
9. #13094022C4semidirect
13. Q8×Dic47C4semidirect
15. #13093989C4semidirect
112. C47#1503semidirect