Finite Group Databasebeta

← #20254569

Subgroups — #20254569

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#15689680C211yesmaximal, characteristic, complemented
2#15689657C211yesmaximal, characteristic
3#15689525C212yesmaximal, complemented
4#15689478C212yesmaximal, complemented
5#15689465C212yesmaximal, complemented
6#15689448C212yesmaximal
7#15689419C211yesmaximal, characteristic, complemented
8#15689414C211yesmaximal, characteristic, complemented
9#15689409C211yesmaximal, characteristic, complemented
10#15689404C211yesmaximal, characteristic, complemented
11C47×#431C211yesmaximal, characteristic, complemented
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094018—21no—
15#13094016C2212yes—
16#13094016C2211yescharacteristic
17#13094012C2211yescharacteristic
18#13094007—21no—
19#13094003—21no—
20#13094003—21no—
21#13094003C2211yescharacteristic
22#13093998C2211yescharacteristic
23C4×Dic94—21no—
24C4×Dic94—21no—
25C4×Dic94C2211yescharacteristic
26C4×D188C2211yescharacteristic
27C4×C22⋊D47—21no—
28#13093983C2212yes—
29#13093981—21no—
30#13093958C2212yes—
31#13093958C2212yes—
32#13093956C2212yes—
33#13093956C2212yes—
34#13093949C2212yes—
35#13093949C2212yes—
36#13093946C2212yes—
37#13093946C2212yes—
38C2×C42×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40C4⋊C8×C47C2211yescharacteristic
41C22⋊C8×C47C2212yes—
42C4×C8×C47C2212yes—
43C22×C4×C47D411yescharacteristic
44C22×C4×C47D411yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C2×D188C2311yescharacteristic
48C2×C4×D47—21no—
49C2×Dic94—21no—
50C2×Dic94—21no—
51C2×Dic94C2311yescharacteristic
52C2×C8×C47C2312yes—
53C2×C8×C47C2312yes—
54C42×C47D411yescharacteristic
55C42×C47D411yescharacteristic
56C42×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58C22⋊Dic47—22no—
59C22⋊Dic47—21no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—21no—
63(C2×D47)⋊C4—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47C2312yes—
67C4⋊Dic47C2312yes—
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73Dic47⋊C4—22no—
74Dic47⋊C4—22no—
75Dic47⋊C4—21no—
76C4×Dic47—21no—
77C4×Dic47—22no—
78C23×C47C2×D411yescharacteristic
79C22×D47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—41no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2411yescharacteristic
90C22⋊D47—42no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96D188—21no—
97D188—21no—
98C4×D47—42no—
99Dic94—21no—
100Dic94—21no—
101Dic94—42no—
102Dic94—42no—
103C8×C47—22no—
104C8×C47—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#13512yes—
117C4×C472−1+411yescharacteristic
118C4×C472−1+411yescharacteristic
119Dic47—41no—
120Dic47—42no—
121Dic47—41no—
122Dic47—42no—
123Dic47—41no—
124#3233—471nomaximal, Sylow
125C2×C47—41no—
126C2×C47#53611yescharacteristic
127C2×C47C2×#13511yescharacteristic
128C2×C47#57511yescharacteristic
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#475—471no—
139#474—471no—
140#431D4711yescharacteristic, complemented
141C47#323311yescharacteristic, complemented, Sylow
142C4⋊Q8—471no—
143C4⋊Q8—471no—
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—471no—
154C4×Q8—941no—
155C4×Q8—941no—
156C4×D4—471no—
157C4×D4—941no—
158#117—472no—
159#117—941no—
160C2×C42C2×D4711yescharacteristic
161#107—472no—
162#107—472no—
163#106—472no—
164#106—472no—
165C4⋊C8C2×D4711yescharacteristic
166C4⋊C8C2×D4711yescharacteristic
167#103—472no—
168#103—472no—
169#102—472no—
170#102—472no—
171C22⋊C8C2×D4712yes—
172C4×C8C2×D4712yes—
173C2×Q8—471no—
174C2×Q8—941no—
175C2×Q8—941no—
176C2×D4—471no—
177C2×D4—941no—
178C22×C4—941no—
179C22×C4D18811yescharacteristic
180C22×C4D18811yescharacteristic
181C22×C4C22×D4711yescharacteristic
182C2×C8C22×D4712yes—
183C2×C8C22×D4712yes—
184C4⋊C4—472no—
185C4⋊C4—472no—
186C4⋊C4—471no—
187C4⋊C4—471no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4—942no—
193C4⋊C4—942no—
194C4⋊C4—941no—
195C4⋊C4—941no—
196C22⋊C4—942no—
197C22⋊C4—941no—
198C22⋊C4—941no—
199C22⋊C4—941no—
200C22⋊C4—941no—
201C22⋊C4—941no—
202C42—942no—
203C42—941no—
204C42D18811yescharacteristic
205C42D18811yescharacteristic
206C42C22×D4711yescharacteristic
207C42C22×D4711yescharacteristic
208C23—941no—
209C23C2×D18811yescharacteristic
210Q8—941no—
211Q8—941no—
212Q8—1882no—
213Q8—1882no—
214D4—941no—
215D4—941no—
216D4—1882no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—941no—
226C2×C4—1882no—
227C2×C4C2×D18811yescharacteristic
228C2×C4C2×D18811yescharacteristic
229C2×C4C2×D18811yescharacteristic
230C2×C4C2×D18811yescharacteristic
231C2×C4C2×D18811yescharacteristic
232C2×C4C23×D4711yescharacteristic
233C8—22no—
234C8—22no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—1881no—
239C22—1881no—
240C22—1881no—
241C22C22×D18811yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—1881no—
247C4—1882no—
248C4—1881no—
249C4—1882no—
250C4—1881no—
251C4#1309404612yes—
252C4#1309407111yescharacteristic
253C4#1309407111yescharacteristic
254C2—41no—
255C2—3761no—
256C2#1568969911yescharacteristic
257C2C2×#1309404611yescharacteristic
258C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#431C2
socleC22×C47C22×D4
hypercenter#431D47
hypocenterC47#3233
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
3. #15689525C2semidirect
4. #15689478C2semidirect
5. #15689465C2semidirect
7. #15689419C2semidirect
8. #15689414C2semidirect
9. #15689409C2semidirect
10. #15689404C2semidirect
11. C47×#431C2semidirect
140. #431D47semidirect
141. C47#3233semidirect