Finite Group Databasebeta

← #20251536

Subgroups — #20251536

Order 6016.

408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689053C211yesmaximal, characteristic, complemented
2#15689052C212yesmaximal, complemented
3#15689049C212yesmaximal, complemented
4#15689045C212yesmaximal, complemented
5#15689041C212yesmaximal
6#15689034C212yesmaximal, complemented
7#15689024C211yesmaximal, characteristic
8#15689005C212yesmaximal, complemented
9C47×#395C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×(C2×D47)⋊C4C2212yes—
15C2×(C2×D47)⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×C4×Dic47C2211yescharacteristic
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2211yescharacteristic
26C22×Q8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2212yes—
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31C23×D47C2312yes—
32C2×Q8×C47—41no—
33C2×Q8×C47—42no—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2312yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C2×D188—22no—
43C2×D188—41no—
44C2×D188—41no—
45C4⋊C4×C47—41no—
46C4⋊C4×C47—42no—
47(C2×D47)⋊C4—42no—
48(C2×D47)⋊C4—42no—
49(C2×D47)⋊C4—42no—
50(C2×D47)⋊C4—42no—
51(C2×D47)⋊C4—42no—
52(C2×D47)⋊C4—42no—
53C4⋊Dic47—41no—
54Dic47⋊C4—24no—
55Dic47⋊C4—42no—
56C4×Dic47—41no—
57C23×C47C2411yescharacteristic
58C22×D47—22no—
59C22×D47—22no—
60C22×D47—22no—
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—22no—
65Q8×C47—44no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47#4112yes—
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—
88D188—44no—
89C22×C47C2×#4111yescharacteristic
90C22×C47H(5,𝔽2)11yescharacteristic
91C22×C47H(5,𝔽2)12yes—
92C22×C47H(5,𝔽2)11yescharacteristic
93C22×C472−1+412yes—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—42no—
100C2×D47—42no—
101C4×C47—22no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47—42no—
106Dic47—42no—
107Dic47—42no—
108Dic47—42no—
109#2830—471nomaximal, Sylow
110C2×C47#53811yescharacteristic
111C2×C47#54212yes—
112C2×C47#56011yescharacteristic
113C2×C47#56212yes—
114C2×C47#56311yescharacteristic
115D47—82no—
116#398—471no—
117#397—472no—
118#397—472no—
119#396—472no—
120#395D4711yescharacteristic, complemented
121#394—472no—
122#393—472no—
123#390—471no—
124#387—472no—
125C47#283011yescharacteristic, complemented, Sylow
126C22×Q8C2×D4711yescharacteristic
127C22×D4—471no—
128C2×C4⋊C4—472no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C4⋊C4C2×D4712yes—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C22⋊C4—472no—
136C2×C22⋊C4—472no—
137C2×C22⋊C4—472no—
138C2×C22⋊C4—472no—
139C2×C42—471no—
140#95—472no—
141#95—472no—
142#95—472no—
143#95—472no—
144#95—471no—
145#95C2×D4712yes—
146#95C2×D4711yescharacteristic
147C24—472no—
148C2×Q8—42no—
149C2×Q8—41no—
150C2×D4—942no—
151C2×D4—1881no—
152C2×D4—1881no—
153C22×C4—472no—
154C22×C4—472no—
155C22×C4—472no—
156C22×C4C22×D4712yes—
157C22×C4C22×D4711yescharacteristic
158C22×C4C22×D4712yes—
159C22×C4C22×D4711yescharacteristic
160C22×C4C22×D4711yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—42no—
163C4⋊C4—944no—
164C4⋊C4—1882no—
165C4⋊C4—1881no—
166C22⋊C4—1882no—
167C22⋊C4—1882no—
168C22⋊C4—1882no—
169C22⋊C4—1882no—
170C22⋊C4—1882no—
171C22⋊C4—1882no—
172C42—1881no—
173C23—942no—
174C23—942no—
175C23—942no—
176C23—942no—
177C23—942no—
178C23—942no—
179C23—942no—
180C23C23×D4711yescharacteristic
181Q8—44no—
182D4—1884no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4#1062535412yes—
205C22—1882no—
206C22—1882no—
207C22—1882no—
208C22—1882no—
209C22—1882no—
210C22—1882no—
211C22—1882no—
212C22C2×#1062535411yescharacteristic
213C22#1309406912yes—
214C22#1309406911yescharacteristic
215C22#1309407011yescharacteristic
216C22#1309407212yes—
217C4—22no—
218C4—41no—
219C4—42no—
220C4—41no—
221C4—42no—
222C4—1882no—
223C4—1882no—
224C4—1882no—
225C2—3762no—
226C2#1568971311yescharacteristic
227C2#1568974712yes—
228C2#1568986211yescharacteristic
229C2#1568986912yes—
230C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2830
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #15689053C2semidirect
2. #15689052C2semidirect
3. #15689049C2semidirect
4. #15689045C2semidirect
6. #15689034C2semidirect
8. #15689005C2semidirect
9. C47×#395C2semidirect
120. #395D47semidirect
125. C47#2830semidirect