Finite Group Databasebeta

← #20251445

Subgroups — #20251445

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×#13094023C211yesmaximal, characteristic, complemented
2C2×#13094017C211yesmaximal, characteristic
3#15689064C212yesmaximal, complemented
4#15689059C212yesmaximal
5#15689055C211yesmaximal, characteristic, complemented
6#15689054C211yesmaximal, characteristic, complemented
7#15689048C211yesmaximal, characteristic
8#15689044C212yesmaximal, complemented
9#15689035C212yesmaximal
10#15688990C211yesmaximal, characteristic, complemented
11C47×#397C211yesmaximal, characteristic
12C22×Dic94C2212yes—
13#13094023—24no—
14#13094017—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2212yes—
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C22⋊Dic47C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C47⋊#95C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C24×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×Dic94—24no—
49C2×Dic94—42no—
50C2×Dic94—42no—
51C4⋊C4×C47—22no—
52C22⋊C4×C47—22no—
53C22⋊C4×C47—42no—
54C22⋊Dic47—22no—
55C22⋊Dic47—22no—
56C22⋊Dic47—42no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—42no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62Dic47⋊C4—24no—
63Dic47⋊C4—42no—
64C4×Dic47D414yes—
65C23×C47—21no—
66C23×C47—21no—
67C23×C47—21no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47C2411yescharacteristic
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D412yes—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47C2×D412yes—
96C2×Dic47C2×D412yes—
97Dic94—48no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47C22×D411yescharacteristic
104C22×C47H(5,𝔽2)11yescharacteristic
105C22×C47H(5,𝔽2)11yescharacteristic
106C22×C472−1+412yes—
107C22×C472−1+412yes—
108C4×C47—22no—
109C4×C47—42no—
110C4×C47—41no—
111C4×C47—42no—
112Dic47—22no—
113Dic47—22no—
114Dic47—42no—
115Dic47—41no—
116Dic47—41no—
117Dic47—42no—
118#2821—471nomaximal, Sylow
119C2×C47—81no—
120C2×C47#53511yescharacteristic
121C2×C47#53611yescharacteristic
122C2×C47#53611yescharacteristic
123C2×C47#56312yes—
124C2×C47#56312yes—
125C2×C4⋊Q8—471no—
126C2×#126—471no—
127#400—472no—
128#399—472no—
129#398—471no—
130#398—471no—
131#397—471no—
132#397D4711yescharacteristic
133#395—472no—
134#393—472no—
135#383—471no—
136C47#282111yescharacteristic, complemented, Sylow
137C22×Q8—472no—
138C4⋊Q8—944no—
139#126—944no—
140C2×C4⋊C4—471no—
141C2×C4⋊C4—471no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C22⋊C4—471no—
149C2×C22⋊C4—471no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4C2×D4711yescharacteristic
152C2×C22⋊C4C2×D4712yes—
153C2×C42—471no—
154#95—472no—
155#95—471no—
156#95—472no—
157#95—472no—
158#95—472no—
159#95—472no—
160#95C2×D4711yescharacteristic
161#95C2×D4712yes—
162C24C22×D4711yescharacteristic
163C2×Q8—944no—
164C2×Q8—1882no—
165C2×Q8—1882no—
166C22×C4—471no—
167C22×C4—471no—
168C22×C4—472no—
169C22×C4—471no—
170C22×C4—472no—
171C22×C4—471no—
172C22×C4C22×D4712yes—
173C22×C4C22×D4711yescharacteristic
174C22×C4C22×D4712yes—
175C22×C4C22×D4711yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—942no—
178C4⋊C4—944no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—942no—
182C4⋊C4—1882no—
183C4⋊C4—1882no—
184C22⋊C4—22no—
185C22⋊C4—42no—
186C22⋊C4—942no—
187C22⋊C4—942no—
188C22⋊C4—1882no—
189C42—474no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—22no—
194C23—22no—
195C23C23×D4711yescharacteristic
196Q8—1888no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—472no—
207C2×C4—472no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—942no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—942no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—941no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4D4×D4712yes—
223C22—42no—
224C22—42no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22C2×D4×D4711yescharacteristic
229C22#1309406911yescharacteristic
230C22#1309407011yescharacteristic
231C22#1309407112yes—
232C22#1309407112yes—
233C4—22no—
234C4—42no—
235C4—42no—
236C4—41no—
237C4—942no—
238C4—942no—
239C4—1882no—
240C4—1882no—
241C4—1881no—
242C4—1881no—
243C2—81no—
244C2#1568968911yescharacteristic
245C2#1568969311yescharacteristic
246C2#1568969511yescharacteristic
247C2#1568987512yes—
248C2#1568987612yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2821
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13094023C2semidirect
3. #15689064C2semidirect
5. #15689055C2semidirect
6. #15689054C2semidirect
8. #15689044C2semidirect
10. #15688990C2semidirect
136. C47#2821semidirect