Finite Group Databasebeta

← #20254571

Subgroups — #20254571

Order 6016.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689678C211yesmaximal, characteristic, complemented
2#15689660C211yesmaximal, characteristic
3#15689523C212yesmaximal, complemented
4#15689479C212yesmaximal, complemented
5#15689462C212yesmaximal, complemented
6#15689449C212yesmaximal
7#15689418C211yesmaximal, characteristic, complemented
8#15689414C211yesmaximal, characteristic, complemented
9#15689400C211yesmaximal, characteristic, complemented
10#15689175C211yesmaximal, characteristic, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12#13094024C2211yescharacteristic
13#13094019—21no—
14#13094015C2212yes—
15#13094015C2211yescharacteristic
16#13094013C2211yescharacteristic
17#13094009—21no—
18#13094004—21no—
19#13094000—21no—
20#13094000C2211yescharacteristic
21#13093999C2211yescharacteristic
22Q8×Dic47—21no—
23#13093989—21no—
24C4×D188—21no—
25C4×D188C2211yescharacteristic
26#13093982C2212yes—
27#13093981—21no—
28C42×D47C2211yescharacteristic
29#13093957C2212yes—
30#13093957C2212yes—
31#13093956C2212yes—
32C4⋊(C47⋊C8)C2211yescharacteristic
33#13093948C2212yes—
34#13093946C2212yes—
35#13093944C2212yes—
36(C2×D47)⋊C8C2212yes—
37C8×Dic47C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39C4×Q8×C47C2211yescharacteristic
40#106×C47C2212yes—
41C4⋊C8×C47C2211yescharacteristic
42#103×C47C2212yes—
43C2×Q8×C47—21no—
44C2×Q8×C47C2311yescharacteristic
45C2×D188—21no—
46C2×D188C2311yescharacteristic
47C2×C4×D47—21no—
48C2×C4×D47D411yescharacteristic
49C2×C4×D47D411yescharacteristic
50C2×C4×D47C2311yescharacteristic
51C2×Dic94—21no—
52C2×C8×C47C2312yes—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2312yes—
56C4⋊C4×C47C2311yescharacteristic
57C42×C47—21no—
58C42×C47C2311yescharacteristic
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—21no—
63(C2×D47)⋊C4—21no—
64(C2×D47)⋊C4—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47—22no—
68C4⋊Dic47C2312yes—
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—22no—
73C4×Dic47—22no—
74C4×Dic47D411yescharacteristic
75C4×Dic47D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78C22×D47—21no—
79C22×D47C2×D411yescharacteristic
80Q8×C47—21no—
81Q8×C47—21no—
82Q8×C47—42no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2411yescharacteristic
89C2×Dic47—22no—
90C2×Dic47—21no—
91C2×Dic47C2×D411yescharacteristic
92C2×Dic47C2×D411yescharacteristic
93C2×Dic47C2×D411yescharacteristic
94D188—21no—
95D188—21no—
96D188—42no—
97C4×D47—22no—
98C4×D47—21no—
99C4×D47—21no—
100C4×D47—41no—
101C4×D47—42no—
102Dic94—42no—
103C8×C47—22no—
104C47⋊C8—22no—
105C22×C47C22×D411yescharacteristic
106C2×D47—21no—
107C2×D47—21no—
108C2×D47—21no—
109C2×D47—41no—
110C2×D47—41no—
111C2×D47—41no—
112C4×C47—21no—
113C4×C47—41no—
114C4×C47—42no—
115C4×C47—41no—
116C4×C47#13512yes—
117C4×C472−1+411yescharacteristic
118C4×C472−1+411yescharacteristic
119Dic47—21no—
120Dic47—21no—
121Dic47—21no—
122Dic47—41no—
123Dic47—42no—
124#3233—471nomaximal, Sylow
125C2×C47#53611yescharacteristic
126C2×C47C2×#13511yescharacteristic
127C2×C47#57511yescharacteristic
128D47—41no—
129D47—81no—
130#533—471no—
131#529—471no—
132#499—472no—
133#488—472no—
134#485—472no—
135#482—472no—
136#477—471no—
137#476—471no—
138#475D4711yescharacteristic, complemented
139#474—471no—
140#431—471no—
141C47#323311yescharacteristic, complemented, Sylow
142C4⋊Q8—471no—
143C4⋊Q8C2×D4711yescharacteristic
144#126—941no—
145#125—471no—
146#125—472no—
147#124—471no—
148#123—941no—
149C22⋊Q8—471no—
150C22⋊Q8—941no—
151C22⋊Q8—941no—
152#121—471no—
153C4×Q8—941no—
154C4×Q8—941no—
155C4×Q8C2×D4711yescharacteristic
156C4×D4—471no—
157C4×D4—941no—
158#117—472no—
159#117—941no—
160C2×C42—471no—
161#107—472no—
162#107—472no—
163#106—472no—
164#106C2×D4712yes—
165C4⋊C8—471no—
166C4⋊C8C2×D4711yescharacteristic
167#103—472no—
168#103C2×D4712yes—
169#102—472no—
170#102—472no—
171C22⋊C8—472no—
172C4×C8—472no—
173C2×Q8—21no—
174C2×Q8—941no—
175C2×Q8C22×D4711yescharacteristic
176C2×D4—471no—
177C2×D4—941no—
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—471no—
181C22×C4—941no—
182C2×C8—472no—
183C2×C8C22×D4712yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—472no—
187C4⋊C4—471no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C4⋊C4—942no—
191C4⋊C4—941no—
192C4⋊C4—942no—
193C4⋊C4—941no—
194C4⋊C4C22×D4712yes—
195C4⋊C4C22×D4711yescharacteristic
196C22⋊C4—941no—
197C22⋊C4—941no—
198C22⋊C4—941no—
199C22⋊C4—942no—
200C22⋊C4—941no—
201C22⋊C4—941no—
202C42—21no—
203C42—471no—
204C42—471no—
205C42—471no—
206C42—942no—
207C42C22×D4711yescharacteristic
208C23—471no—
209C23—941no—
210Q8—21no—
211Q8—21no—
212Q8—42no—
213Q8—1882no—
214D4—941no—
215D4—941no—
216D4—1882no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—471no—
221C2×C4—471no—
222C2×C4—471no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—941no—
226C2×C4—942no—
227C2×C4—941no—
228C2×C4—1881no—
229C2×C4—1882no—
230C2×C4D4×D4711yescharacteristic
231C2×C4D4×D4711yescharacteristic
232C2×C4C23×D4711yescharacteristic
233C8—22no—
234C8—942no—
235C22—941no—
236C22—941no—
237C22—941no—
238C22—1881no—
239C22—1881no—
240C22—1881no—
241C22C2×D4×D4711yescharacteristic
242C4—21no—
243C4—42no—
244C4—41no—
245C4—41no—
246C4—941no—
247C4—941no—
248C4—941no—
249C4—1881no—
250C4—1882no—
251C4#1309404512yes—
252C4#1309407111yescharacteristic
253C4#1309407211yescharacteristic
254C2—3761no—
255C2—1881no—
256C2#1568969611yescharacteristic
257C2C2×#1309404511yescharacteristic
258C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3233
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689523C2semidirect
4. #15689479C2semidirect
5. #15689462C2semidirect
7. #15689418C2semidirect
8. #15689414C2semidirect
9. #15689400C2semidirect
10. #15689175C2semidirect
11. C47×#475C2semidirect
138. #475D47semidirect
141. C47#3233semidirect