Finite Group Databasebeta

← #20241950

Subgroups — #20241950

Order 6016.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#15688987C211yesmaximal, 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×Dic47C2211yescharacteristic
19Dic47⋊C8—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C8×Dic47—21no—
22C47⋊#95—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—21no—
43Dic47⋊C4—21no—
44Dic47⋊C4—21no—
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47Dic47⋊C4—42no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C4×Dic47C2×C411yescharacteristic
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47D411yescharacteristic
53C4×Dic47D411yescharacteristic
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56Q8×C47—41no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×Dic47—21no—
66C2×Dic47—21no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47C22⋊C411yescharacteristic
72C2×Dic47C22⋊C411yescharacteristic
73C2×Dic47C22⋊C411yescharacteristic
74C2×Dic47C22⋊C411yescharacteristic
75C2×Dic47SD1612yes—
76C2×Dic47Q1612yes—
77Dic94—42no—
78Dic94—41no—
79C8×C47—41no—
80C47⋊C8—41no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47C2×C22⋊C411yescharacteristic
84C22×C47C2×SD1611yescharacteristic
85C22×C47C2×Q1611yescharacteristic
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—41no—
89C4×C47—41no—
90C4×C47—81no—
91Dic47—21no—
92Dic47—21no—
93Dic47—41no—
94Dic47—41no—
95Dic47—81no—
96Dic47#10312yes—
97Dic47#10312yes—
98#1518—471nomaximal, Sylow
99C2×C47—21no—
100C2×C47—21no—
101C2×C47#41011yescharacteristic
102C2×C47C2×#10311yescharacteristic
103C2×C47#42111yescharacteristic
104#533—471no—
105#431—471no—
106#382—471no—
107#328—471no—
108#328—471no—
109#328—471no—
110#328D4711yescharacteristic
111C47#151811yescharacteristic, complemented, Sylow
112C4⋊Q8—471no—
113C4⋊Q8—471no—
114#125—941no—
115C22⋊Q8—471no—
116C22⋊Q8—941no—
117C22⋊Q8C2×D4711yescharacteristic
118C4×Q8—471no—
119C4×Q8—471no—
120C4×Q8—941no—
121#117—941no—
122C2×C4⋊C4—941no—
123C2×C42—471no—
124C4⋊C8—941no—
125C22⋊C8—471no—
126C22⋊C8C2×D4711yescharacteristic
127C4×C8—941no—
128#95—471no—
129#95—941no—
130#95C2×D4711yescharacteristic
131C2×Q8—471no—
132C2×Q8—941no—
133C2×Q8C4×D4711yescharacteristic
134C22×C4—21no—
135C22×C4—471no—
136C22×C4—471no—
137C22×C4—941no—
138C22×C4C22×D4711yescharacteristic
139C2×C8—21no—
140C2×C8—941no—
141C4⋊C4—21no—
142C4⋊C4—471no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—1882no—
150C4⋊C4C4×D4711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—941no—
153C42—471no—
154C42—471no—
155C42—471no—
156C42—471no—
157C42—941no—
158C42—941no—
159C23D4×D4711yescharacteristic
160Q8—41no—
161Q8—1881no—
162Q8—1882no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—471no—
170C2×C4—471no—
171C2×C4—472no—
172C2×C4—472no—
173C2×C4—471no—
174C2×C4—471no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4—1881no—
180C2×C4—1881no—
181C2×C4C2×C4×D4711yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C8—41no—
184C8—1881no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D4711yescharacteristic
188C22SD16×D4711yescharacteristic
189C22Q16×D4711yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—472no—
196C4—472no—
197C4—941no—
198C4—941no—
199C4—3761no—
200C4—1881no—
201C4—1881no—
202C2—21no—
203C2—21no—
204C2#1568909511yescharacteristic
205C2#103×D4711yescharacteristic
206C2#1568913811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#328C2
socleC22×C47C2×C22⋊C4
hypercenter#328D47
hypocenterC47#1518
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
111. C47#1518semidirect