Finite Group Databasebeta

← #20251450

Subgroups — #20251450

Order 6016.

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

normal subgroups only

This group has 430 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×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094017C211yesmaximal, characteristic
3#15689065C212yesmaximal, complemented
4#15689059C212yesmaximal
5#15689057C212yesmaximal, complemented
6#15689051C212yesmaximal
7#15689044C211yesmaximal, characteristic, complemented
8#15689042C211yesmaximal, characteristic, complemented
9#15689035C211yesmaximal, characteristic
10#15688990C211yesmaximal, characteristic, complemented
11C47×#393C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13#13094022—24no—
14#13094017—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2212yes—
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C2×Q8×C47—22no—
39C2×Q8×C47—42no—
40C22×C4×C47C2312yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2312yes—
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×Dic94—22no—
51C2×Dic94—42no—
52C22⋊C4×C47—22no—
53C22⋊C4×C47—42no—
54C22⋊Dic47—22no—
55C22⋊Dic47—22no—
56C22⋊Dic47—42no—
57C4⋊Dic47—22no—
58C4⋊Dic47—42no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—24no—
62Dic47⋊C4—24no—
63Dic47⋊C4—42no—
64C4×Dic47D414yes—
65C23×C47—21no—
66C23×C47—22no—
67C23×C47—21no—
68C23×C47—22no—
69C23×C47—21no—
70C23×C47C2411yescharacteristic
71Q8×C47—44no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47C2×D412yes—
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—22no—
96C2×Dic47C2×D412yes—
97C2×Dic47C2×D412yes—
98Dic94—44no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47—42no—
103C22×C47—42no—
104C22×C47C22×D411yescharacteristic
105C22×C47H(5,𝔽2)12yes—
106C22×C472−1+411yescharacteristic
107C22×C472−1+412yes—
108C22×C472−1+411yescharacteristic
109C4×C47—22no—
110C4×C47—42no—
111C4×C47—41no—
112C4×C47—42no—
113Dic47—22no—
114Dic47—22no—
115Dic47—42no—
116Dic47—41no—
117Dic47—41no—
118Dic47—42no—
119#2821—471nomaximal, Sylow
120C2×C47—81no—
121C2×C47#53511yescharacteristic
122C2×C47#53611yescharacteristic
123C2×C47#53611yescharacteristic
124C2×C47#56312yes—
125C2×C47#56312yes—
126C2×C4⋊Q8—471no—
127C2×#126—471no—
128#400—472no—
129#399—472no—
130#398—472no—
131#397—472no—
132#395—471no—
133#395—471no—
134#393—471no—
135#393D4711yescharacteristic
136#383—471no—
137C47#282111yescharacteristic, complemented, Sylow
138C22×Q8—471no—
139C22×Q8C2×D4711yescharacteristic
140C4⋊Q8—944no—
141#126—944no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—471no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—472no—
149C2×C22⋊C4—471no—
150C2×C22⋊C4—471no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4C2×D4711yescharacteristic
153C2×C22⋊C4C2×D4712yes—
154C2×C42—471no—
155#95—471no—
156#95—472no—
157#95—472no—
158#95—472no—
159#95—472no—
160#95—472no—
161#95C2×D4711yescharacteristic
162#95C2×D4712yes—
163C24C22×D4711yescharacteristic
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—942no—
167C2×Q8—1882no—
168C22×C4—471no—
169C22×C4—471no—
170C22×C4—472no—
171C22×C4—471no—
172C22×C4—472no—
173C22×C4—471no—
174C22×C4C22×D4712yes—
175C22×C4C22×D4711yescharacteristic
176C22×C4C22×D4712yes—
177C22×C4C22×D4711yescharacteristic
178C4⋊C4—942no—
179C4⋊C4—944no—
180C4⋊C4—944no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—1882no—
184C4⋊C4—1882no—
185C22⋊C4—22no—
186C22⋊C4—42no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C22⋊C4—1882no—
190C42—474no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23C23×D4711yescharacteristic
197Q8—44no—
198Q8—1884no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—472no—
209C2×C4—472no—
210C2×C4—942no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—941no—
224C2×C4D4×D4712yes—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22C2×D4×D4711yescharacteristic
231C22#1309406912yes—
232C22#1309407111yescharacteristic
233C22#1309407112yes—
234C22#1309407211yescharacteristic
235C4—22no—
236C4—42no—
237C4—42no—
238C4—41no—
239C4—942no—
240C4—942no—
241C4—1882no—
242C4—1882no—
243C4—1881no—
244C4—1881no—
245C2—81no—
246C2#1568968811yescharacteristic
247C2#1568969311yescharacteristic
248C2#1568969611yescharacteristic
249C2#1568987312yes—
250C2#1568987412yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2821
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
3. #15689065C2semidirect
5. #15689057C2semidirect
7. #15689044C2semidirect
8. #15689042C2semidirect
10. #15688990C2semidirect
137. C47#2821semidirect