Finite Group Databasebeta

← #20254567

Subgroups — #20254567

Order 6016.

332 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689657C211yesmaximal, characteristic
2#15689522C212yesmaximal, complemented
3#15689480C212yesmaximal, complemented
4#15689464C212yesmaximal, complemented
5#15689447C212yesmaximal
6#15689415C211yesmaximal, characteristic, complemented
7#15689410C211yesmaximal, characteristic, complemented
8#15689405C211yesmaximal, characteristic, complemented
9#15689400C211yesmaximal, characteristic, complemented
10#15689176C211yesmaximal, characteristic, complemented
11C47×#533C211yesmaximal, characteristic, complemented
12#13094018—21no—
13#13094016C2211yescharacteristic
14#13094012C2211yescharacteristic
15#13094007—21no—
16#13094003C2211yescharacteristic
17#13093998C2211yescharacteristic
18C4×Dic94C2211yescharacteristic
19C4×D188C2211yescharacteristic
20C4×C22⋊D47—21no—
21#13093981—21no—
22#13093957C2212yes—
23#13093957C2212yes—
24#13093955C2212yes—
25#13093955C2212yes—
26C4⋊(C47⋊C8)C2211yescharacteristic
27C4⋊(C47⋊C8)C2211yescharacteristic
28#13093947C2212yes—
29#13093947C2212yes—
30#13093944C2212yes—
31#13093944C2212yes—
32C22⋊(C47⋊C8)C2212yes—
33C4×C47⋊C8C2212yes—
34C4⋊Q8×C47C2211yescharacteristic
35C4⋊Q8×C47C2211yescharacteristic
36#125×C47C2212yes—
37C22⋊Q8×C47—21no—
38C22⋊Q8×C47—21no—
39C4×Q8×C47—21no—
40C4×Q8×C47—21no—
41#117×C47C2212yes—
42C2×C42×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×Q8×C47—21no—
45C22×C4×C47D411yescharacteristic
46C22×C4×C47D411yescharacteristic
47C22×C4×C47C2311yescharacteristic
48C2×C22⋊D47—21no—
49C2×D188C2311yescharacteristic
50C2×C4×D47—21no—
51C2×Dic94C2311yescharacteristic
52C4⋊C4×C47—22no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C4⋊C4×C47C2312yes—
57C4⋊C4×C47C2312yes—
58C22⋊C4×C47—22no—
59C42×C47—22no—
60C42×C47D411yescharacteristic
61C42×C47D411yescharacteristic
62C42×C47C2311yescharacteristic
63C42×C47C2311yescharacteristic
64C22⋊Dic47—21no—
65(C2×D47)⋊C4—21no—
66(C2×D47)⋊C4—21no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—21no—
69C4⋊Dic47C2311yescharacteristic
70C4⋊Dic47C2311yescharacteristic
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75C4×Dic47—21no—
76C2×C47⋊C8C2312yes—
77C2×C47⋊C8C2312yes—
78C23×C47C2×D411yescharacteristic
79C22×D47—21no—
80Q8×C47—42no—
81Q8×C47—42no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—41no—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2411yescharacteristic
94C22⋊D47—42no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98D188—21no—
99D188—21no—
100C4×D47—42no—
101Dic94—21no—
102Dic94—21no—
103C47⋊C8—22no—
104C47⋊C8—22no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—21no—
108C22×C47C22×D411yescharacteristic
109C2×D47—41no—
110C2×D47—41no—
111C2×D47—41no—
112C4×C47—21no—
113C4×C47—21no—
114C4×C47—21no—
115C4×C47—21no—
116C4×C47—42no—
117C4×C47—42no—
118C4×C47#13512yes—
119C4×C472−1+411yescharacteristic
120C4×C472−1+411yescharacteristic
121Dic47—41no—
122Dic47—41no—
123Dic47—41no—
124#3233—471nomaximal, Sylow
125C2×C47—41no—
126C2×C47#53611yescharacteristic
127C2×C47C2×#13511yescharacteristic
128C2×C47#57511yescharacteristic
129D47—81no—
130#533D4711yescharacteristic, complemented
131#529—471no—
132#499—472no—
133#488—472no—
134#485—472no—
135#482—472no—
136#477—471no—
137#476—471no—
138#475—471no—
139#474—471no—
140#431—471no—
141C47#323311yescharacteristic, complemented, Sylow
142C4⋊Q8C2×D4711yescharacteristic
143C4⋊Q8C2×D4711yescharacteristic
144#126—941no—
145#125—471no—
146#125C2×D4712yes—
147#124—471no—
148#123—941no—
149C22⋊Q8—21no—
150C22⋊Q8—21no—
151C22⋊Q8—471no—
152#121—471no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—471no—
156C4×D4—471no—
157C4×D4—941no—
158#117—941no—
159#117C2×D4712yes—
160C2×C42C2×D4711yescharacteristic
161#107—472no—
162#107—472no—
163#106—472no—
164#106—472no—
165C4⋊C8—471no—
166C4⋊C8—471no—
167#103—472no—
168#103—472no—
169#102—472no—
170#102—472no—
171C22⋊C8—472no—
172C4×C8—472no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—471no—
176C2×D4—471no—
177C2×D4—941no—
178C22×C4—941no—
179C22×C4C22⋊D4711yescharacteristic
180C22×C4C22⋊D4711yescharacteristic
181C22×C4C22×D4711yescharacteristic
182C2×C8—472no—
183C2×C8—472no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4C22×D4712yes—
195C4⋊C4C22×D4712yes—
196C22⋊C4—22no—
197C22⋊C4—941no—
198C22⋊C4—941no—
199C22⋊C4—941no—
200C22⋊C4—941no—
201C22⋊C4—941no—
202C42—22no—
203C42—941no—
204C42C22⋊D4711yescharacteristic
205C42C22⋊D4711yescharacteristic
206C42C22×D4711yescharacteristic
207C42C22×D4711yescharacteristic
208C23—941no—
209C23C2×C22⋊D4711yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—941no—
213Q8—941no—
214D4—941no—
215D4—941no—
216D4—1882no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—941no—
224C2×C4—941no—
225C2×C4—941no—
226C2×C4—1882no—
227C2×C4C2×C22⋊D4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C2×C4C2×C22⋊D4711yescharacteristic
231C2×C4C2×C22⋊D4711yescharacteristic
232C2×C4C23×D4711yescharacteristic
233C8—942no—
234C8—942no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—1881no—
239C22—1881no—
240C22—1881no—
241C22C22×C22⋊D4711yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—1881no—
249C4—1881no—
250C4—1881no—
251C4#1309404412yes—
252C4#1309407211yescharacteristic
253C4#1309407211yescharacteristic
254C2—41no—
255C2—3761no—
256C2#1568969711yescharacteristic
257C2C2×#1309404411yescharacteristic
258C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#533C2
socleC22×C47C22×D4
hypercenter#533D47
hypocenterC47#3233
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #15689522C2semidirect
3. #15689480C2semidirect
4. #15689464C2semidirect
6. #15689415C2semidirect
7. #15689410C2semidirect
8. #15689405C2semidirect
9. #15689400C2semidirect
10. #15689176C2semidirect
11. C47×#533C2semidirect
130. #533D47semidirect
141. C47#3233semidirect