Finite Group Databasebeta

← #20251089

Subgroups — #20251089

Order 6016.

472 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 137 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#15689062C211yesmaximal, characteristic, complemented
2#15689046C212yesmaximal, complemented
3#15689043C211yesmaximal, characteristic, complemented
4#15689035C212yesmaximal, complemented
5#15689007C212yesmaximal, complemented
6#15689003C212yesmaximal
7#15688995C212yesmaximal, complemented
8#15688981C212yesmaximal, complemented
9C47×#390C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C23×Dic47C2212yes—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2212yes—
19C47⋊#95C2211yescharacteristic
20C47⋊#95C2212yes—
21C47⋊#95C2211yescharacteristic
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C22×D4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2212yes—
29C2×C22⋊C4×C47C2212yes—
30C2×C42×C47C2211yescharacteristic
31C24×C47C2312yes—
32C2×D4×C47—41no—
33C2×D4×C47—41no—
34C2×D4×C47Q814yescomplemented
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—24no—
40C22×Dic47—42no—
41C22×Dic47—42no—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C2×Dic94—42no—
47C2×Dic94—41no—
48C4⋊C4×C47—41no—
49C22⋊C4×C47—42no—
50C22⋊C4×C47—42no—
51C42×C47—41no—
52C22⋊Dic47—24no—
53C22⋊Dic47—42no—
54C22⋊Dic47—42no—
55C4⋊Dic47—41no—
56Dic47⋊C4—24no—
57Dic47⋊C4—42no—
58Dic47⋊C4—42no—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47—22no—
64C23×C47—22no—
65C23×C47C2×Q814yes—
66C23×C47C2411yescharacteristic
67D4×C47—44no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47C2×Q812yes—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—48no—
90C2×Dic47#4114yes—
91Dic94—44no—
92C22×C47—24no—
93C22×C47—24no—
94C22×C47—24no—
95C22×C47—42no—
96C22×C47—42no—
97C22×C47—42no—
98C22×C47—42no—
99C22×C47C22×Q811yescharacteristic
100C22×C47C2×#4112yes—
101C22×C47H(5,𝔽2)11yescharacteristic
102C22×C47H(5,𝔽2)12yes—
103C22×C47H(5,𝔽2)11yescharacteristic
104C4×C47—22no—
105C4×C47—42no—
106C4×C47—41no—
107C4×C47—41no—
108Dic47—24no—
109Dic47—42no—
110Dic47—42no—
111Dic47—42no—
112#2784—471nomaximal, Sylow
113C2×C47—44no—
114C2×C47#53812yes—
115C2×C47#54311yescharacteristic
116C2×C47#55412yes—
117C2×C47#55511yescharacteristic
118C2×C47#56011yescharacteristic
119#400—471no—
120#396—472no—
121#395—471no—
122#393—472no—
123#390D4711yescharacteristic
124#387—472no—
125#386—472no—
126#385—472no—
127#380—472no—
128C47#278411yescharacteristic, complemented, Sylow
129C22×Q8—471no—
130C22×D4C2×D4711yescharacteristic
131C23×C4—472no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—472no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4C2×D4711yescharacteristic
137C2×C22⋊C4—472no—
138C2×C22⋊C4—472no—
139C2×C22⋊C4—472no—
140C2×C22⋊C4C2×D4712yes—
141C2×C22⋊C4C2×D4712yes—
142C2×C42C2×D4711yescharacteristic
143#95—471no—
144#95—472no—
145#95—471no—
146#95—472no—
147#95—472no—
148#95—472no—
149#95—472no—
150C24C22×D4712yes—
151C2×Q8—1882no—
152C2×Q8—1881no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4Dic9414yescomplemented
156C22×C4—472no—
157C22×C4—472no—
158C22×C4—472no—
159C22×C4—472no—
160C22×C4—944no—
161C22×C4—1882no—
162C22×C4—1882no—
163C22×C4C22×D4711yescharacteristic
164C22×C4C22×D4712yes—
165C22×C4C22×D4711yescharacteristic
166C22×C4C22×D4711yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—944no—
169C4⋊C4—1882no—
170C4⋊C4—1882no—
171C4⋊C4—1881no—
172C22⋊C4—42no—
173C22⋊C4—42no—
174C22⋊C4—944no—
175C22⋊C4—1882no—
176C22⋊C4—1882no—
177C42—41no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23C2×Dic9414yes—
185C23C23×D4711yescharacteristic
186Q8—1884no—
187D4—44no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—474no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—1888no—
210C2×C4C2×Dic9412yes—
211C22—24no—
212C22—24no—
213C22—24no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—42no—
218C22C22×Dic9411yescharacteristic
219C22#41×D4712yes—
220C22#1309406911yescharacteristic
221C22#1309406911yescharacteristic
222C22#1309406912yes—
223C4—22no—
224C4—41no—
225C4—41no—
226C4—42no—
227C4—944no—
228C4—1882no—
229C4—1882no—
230C4—1882no—
231C2—44no—
232C2#1568970512yes—
233C2#1568974911yescharacteristic
234C2#1568983212yes—
235C2#1568983511yescharacteristic
236C2#1568986011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2784
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #15689062C2semidirect
2. #15689046C2semidirect
3. #15689043C2semidirect
4. #15689035C2semidirect
5. #15689007C2semidirect
7. #15688995C2semidirect
8. #15688981C2semidirect
34. C2×D4×C47Q8semidirect
128. C47#2784semidirect
155. C2×D4Dic94semidirect