Finite Group Databasebeta

← #20250511

Subgroups — #20250511

Order 6016.

416 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689064C212yesmaximal, complemented
2#15689059C211yesmaximal, characteristic
3#15689042C212yesmaximal, complemented
4#15689020C212yesmaximal, complemented
5#15689011C212yesmaximal
6#15689005C212yesmaximal, complemented
7#15688995C211yesmaximal, characteristic
8#15688981C212yesmaximal
9C47×#393C211yesmaximal, characteristic
10C23×Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2211yescharacteristic
19C2×C4×Dic47C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C22×Q8×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2212yes—
28C2×C22⋊C4×C47C2211yescharacteristic
29#95×C47C2211yescharacteristic
30#95×C47C2212yes—
31C24×C47C2311yescharacteristic
32C2×Q8×C47—42no—
33C2×Q8×C47—41no—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C22×Dic47—24no—
39C22×Dic47—41no—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C22⋊C4×C47—42no—
45C22⋊C4×C47—41no—
46C22⋊Dic47—42no—
47C22⋊Dic47Q814yescomplemented
48C4⋊Dic47—41no—
49Dic47⋊C4—24no—
50Dic47⋊C4—24no—
51Dic47⋊C4—42no—
52Dic47⋊C4—42no—
53Dic47⋊C4—42no—
54C4×Dic47—42no—
55C23×C47—22no—
56C23×C47—22no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47C2×Q812yes—
60C23×C47C2411yescharacteristic
61Q8×C47—44no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—44no—
83C2×Dic47C2×Q814yes—
84C2×Dic47#4114yes—
85C22×C47—22no—
86C22×C47—24no—
87C22×C47—42no—
88C22×C47—41no—
89C22×C47—41no—
90C22×C47C22×Q811yescharacteristic
91C22×C47C2×#4112yes—
92C22×C47H(5,𝔽2)12yes—
93C22×C47H(5,𝔽2)11yescharacteristic
94C22×C472−1+411yescharacteristic
95C4×C47—42no—
96C4×C47—41no—
97C4×C47—41no—
98C4×C47—42no—
99Dic47—24no—
100Dic47—24no—
101Dic47—42no—
102Dic47—42no—
103#2742—471nomaximal, Sylow
104C2×C47—42no—
105C2×C47#54212yes—
106C2×C47#54411yescharacteristic
107C2×C47#55111yescharacteristic
108C2×C47#55412yes—
109C2×C47#56011yescharacteristic
110#400—472no—
111#399—471no—
112#395—472no—
113#393D4711yescharacteristic
114#389—472no—
115#388—472no—
116#387—472no—
117#385—471no—
118#380—472no—
119C47#274211yescharacteristic, complemented, Sylow
120C22×Q8C2×D4711yescharacteristic
121C23×C4—471no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—472no—
127C2×C4⋊C4—471no—
128C2×C22⋊C4—471no—
129C2×C22⋊C4—472no—
130C2×C22⋊C4C2×D4712yes—
131C2×C22⋊C4C2×D4711yescharacteristic
132C2×C42—472no—
133#95—472no—
134#95—472no—
135#95—472no—
136#95—472no—
137#95—472no—
138#95—471no—
139#95C2×D4711yescharacteristic
140#95C2×D4712yes—
141C24C22×D4711yescharacteristic
142C2×Q8—42no—
143C2×Q8—41no—
144C22×C4—472no—
145C22×C4—472no—
146C22×C4—472no—
147C22×C4—472no—
148C22×C4—944no—
149C22×C4—1881no—
150C22×C4C22×D4712yes—
151C22×C4C22×D4712yes—
152C22×C4C22×D4711yescharacteristic
153C22×C4C22×D4711yescharacteristic
154C4⋊C4—944no—
155C4⋊C4—944no—
156C4⋊C4—1882no—
157C4⋊C4—1882no—
158C4⋊C4—1882no—
159C4⋊C4—1881no—
160C22⋊C4—42no—
161C22⋊C4—41no—
162C22⋊C4—474no—
163C22⋊C4—1882no—
164C42—1882no—
165C23—22no—
166C23—22no—
167C23—21no—
168C23—21no—
169C23Q8×D4712yes—
170C23C23×D4711yescharacteristic
171Q8—44no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—474no—
183C2×C4—474no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—1884no—
195C22—22no—
196C22—24no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22C2×Q8×D4711yescharacteristic
201C22#41×D4712yes—
202C22#1309406912yes—
203C22#1309406911yescharacteristic
204C22#1309407111yescharacteristic
205C4—42no—
206C4—41no—
207C4—42no—
208C4—41no—
209C4—944no—
210C4—944no—
211C4—1882no—
212C4—1882no—
213C2—42no—
214C2#1568973712yes—
215C2#1568975211yescharacteristic
216C2#1568980311yescharacteristic
217C2#1568982712yes—
218C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2742
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #15689064C2semidirect
3. #15689042C2semidirect
4. #15689020C2semidirect
6. #15689005C2semidirect
47. C22⋊Dic47Q8semidirect
119. C47#2742semidirect