Finite Group Databasebeta

← #20251422

Subgroups — #20251422

Order 6016.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#13094002C211yesmaximal, characteristic
2C2×#13094000C211yesmaximal, characteristic
3#15689064C212yesmaximal, complemented
4#15689063C211yesmaximal, characteristic, complemented
5#15689062C211yesmaximal, characteristic, complemented
6#15689052C212yesmaximal
7#15689049C212yesmaximal
8#15689043C212yesmaximal, complemented
9#15689042C211yesmaximal, characteristic, complemented
10#15688985C211yesmaximal, characteristic
11C47×#395C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14#13094002—24no—
15#13094000—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2211yescharacteristic
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2211yescharacteristic
24C2×(C2×D47)⋊C4C2212yes—
25C47⋊#95C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C23×D47C2311yescharacteristic
38C2×Q8×C47—22no—
39C2×Q8×C47—42no—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×C4×D47—42no—
51C2×C4×D47D414yes—
52C2×Dic94—22no—
53C2×Dic94—42no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—42no—
56(C2×D47)⋊C4—24no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—42no—
60C4⋊Dic47—22no—
61Dic47⋊C4—22no—
62Dic47⋊C4—24no—
63Dic47⋊C4—22no—
64Dic47⋊C4—42no—
65C23×C47C2411yescharacteristic
66C22×D47—22no—
67C22×D47—21no—
68C22×D47—21no—
69C22×D47—22no—
70C22×D47C2×D412yes—
71Q8×C47—44no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47C2×D412yes—
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47—22no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—24no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47C2×D412yes—
97C4×D47—44no—
98Dic94—44no—
99C22×C47C22×D411yescharacteristic
100C22×C47H(5,𝔽2)12yes—
101C22×C472−1+411yescharacteristic
102C22×C472−1+411yescharacteristic
103C22×C472−1+412yes—
104C2×D47—22no—
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—42no—
108C2×D47—42no—
109C4×C47—22no—
110C4×C47—41no—
111C4×C47—42no—
112C4×C47—41no—
113C4×C47—42no—
114Dic47—22no—
115Dic47—41no—
116Dic47—41no—
117Dic47—42no—
118Dic47—42no—
119#2817—471nomaximal, Sylow
120C2×C47#53411yescharacteristic
121C2×C47#53611yescharacteristic
122C2×C47#53611yescharacteristic
123C2×C47#56312yes—
124C2×C47#56312yes—
125D47—42no—
126C2×C22⋊Q8—471no—
127C2×C22⋊Q8—471no—
128#400—471no—
129#400—471no—
130#400—472no—
131#397—472no—
132#397—472no—
133#395—471no—
134#395—472no—
135#395D4711yescharacteristic, complemented
136#381—471no—
137C47#281711yescharacteristic, complemented, Sylow
138C22×Q8—471no—
139C22×Q8C2×D4711yescharacteristic
140C23×C4—471no—
141C22⋊Q8—944no—
142C22⋊Q8—944no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—471no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4C2×D4711yescharacteristic
149C2×C4⋊C4C2×D4712yes—
150C2×C22⋊C4—471no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—471no—
153C2×C22⋊C4—472no—
154#95—472no—
155#95—471no—
156#95—472no—
157#95—472no—
158#95—472no—
159#95—472no—
160#95—472no—
161#95C2×D4711yescharacteristic
162#95C2×D4712yes—
163C24—471no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—942no—
167C2×Q8—1882no—
168C22×C4—471no—
169C22×C4—474no—
170C22×C4—472no—
171C22×C4—471no—
172C22×C4—472no—
173C22×C4—471no—
174C22×C4—1882no—
175C22×C4C22×D4712yes—
176C22×C4C22×D4711yescharacteristic
177C22×C4C22×D4711yescharacteristic
178C22×C4C22×D4712yes—
179C22×C4C22×D4711yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4—942no—
183C4⋊C4—944no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4—1882no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C22⋊C4—944no—
190C22⋊C4—1882no—
191C23—472no—
192C23—942no—
193C23—941no—
194C23—941no—
195C23—942no—
196C23C23×D4711yescharacteristic
197Q8—44no—
198Q8—1884no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—472no—
212C2×C4—942no—
213C2×C4—941no—
214C2×C4—942no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—941no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—941no—
222C2×C4—944no—
223C2×C4—1884no—
224C2×C4D4×D4712yes—
225C22—942no—
226C22—942no—
227C22—942no—
228C22—1882no—
229C22—1882no—
230C22C2×D4×D4711yescharacteristic
231C22#1309406912yes—
232C22#1309407111yescharacteristic
233C22#1309407211yescharacteristic
234C22#1309407212yes—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—41no—
240C4—942no—
241C4—1882no—
242C4—1881no—
243C4—1881no—
244C4—1882no—
245C2—1882no—
246C2#1568968311yescharacteristic
247C2#1568969611yescharacteristic
248C2#1568969811yescharacteristic
249C2#1568987212yes—
250C2#1568987412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2817
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #15689064C2semidirect
4. #15689063C2semidirect
5. #15689062C2semidirect
8. #15689043C2semidirect
9. #15689042C2semidirect
11. C47×#395C2semidirect
135. #395D47semidirect
137. C47#2817semidirect