Finite Group Databasebeta

← #20256179

Subgroups — #20256179

Order 6016.

384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689858C211yesmaximal, characteristic, complemented
2#15689788C211yesmaximal, characteristic, complemented
3#15689484C212yesmaximal, complemented
4#15689471C211yesmaximal, characteristic, complemented
5#15689412C212yesmaximal, complemented
6#15689341C212yesmaximal, complemented
7#15689319C211yesmaximal, characteristic
8#15689250C211yesmaximal, characteristic, complemented
9#15689234C212yesmaximal, complemented
10C4×#10625336C211yesmaximal, characteristic, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13C2×#10625336C2211yescharacteristic
14C2×D376C2212yes—
15#13094023C2212yes—
16#13094021C2211yescharacteristic
17#13094013C2212yes—
18#13094012—21no—
19#13094009—22no—
20#13094002—22no—
21#13094000—21no—
22C4×Dic94C2211yescharacteristic
23C4×D188—21no—
24C4×D188C2211yescharacteristic
25#13093986C2212yes—
26#13093986C2212yes—
27#13093955C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093948C2211yescharacteristic
30#13093946C2212yes—
31#13093944C2212yes—
32#13093944C2211yescharacteristic
33#13093944C2212yes—
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43Q8×D47—44no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188C2312yes—
47C2×D188C2311yescharacteristic
48C2×C4×D47—21no—
49C2×C4×D47—22no—
50C2×C4×D47—22no—
51C2×Dic94—22no—
52C2×Dic94D411yescharacteristic
53C2×C8×C47C2312yes—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C4⋊C4×C47C2312yes—
57C4⋊C4×C47C2311yescharacteristic
58C42×C47—21no—
59C42×C47C2311yescharacteristic
60#10625336—22no—
61(C2×D47)⋊C4—21no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—22no—
66C4⋊Dic47D411yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68Dic47⋊C4—22no—
69Dic47⋊C4D412yes—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73D376—24no—
74C22×D47—21no—
75C22×D47—22no—
76Q8×C47—21no—
77Q8×C47—21no—
78Q8×C47—42no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C2×Dic47—21no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88D188—22no—
89D188—21no—
90D188—22no—
91D188—42no—
92D188—81no—
93D188#4112yes—
94C4×D47—44no—
95C4×D47—42no—
96C4×D47—82no—
97Dic94—22no—
98Dic94—44no—
99C8×C47—22no—
100C47⋊C8—21no—
101C47⋊C8—21no—
102C22×C47C22×D411yescharacteristic
103C2×D47—22no—
104C2×D47—41no—
105C2×D47—41no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—42no—
109C4×C47—21no—
110C4×C47—41no—
111C4×C47—42no—
112C4×C47—41no—
113C4×C47AGL(1,ℤ/8)12yes—
114C4×C47C2×#4111yescharacteristic
115C4×C472−1+411yescharacteristic
116Dic47—22no—
117Dic47—22no—
118Dic47—41no—
119#3373—471nomaximal, Sylow
120C2×C47#54811yescharacteristic
121C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
122C2×C47#57711yescharacteristic
123D47—42no—
124D47—82no—
125#559—471no—
126D4×Q8—471no—
127#489—472no—
128#486—471no—
129#476—472no—
130#475D4711yescharacteristic, complemented
131#463—472no—
132#459—471no—
133#446—471no—
134#442—472no—
135C4×SD16—471no—
136C47#337311yescharacteristic, complemented, Sylow
137C22×Q8—941no—
138C2×SD16—471no—
139C2×D8—472no—
140C4⋊Q8—472no—
141C4⋊Q8C2×D4711yescharacteristic
142#127—471no—
143#124—472no—
144#124—941no—
145#123—942no—
146C22⋊Q8—942no—
147C22⋊Q8—941no—
148C4×Q8—471no—
149C4×Q8C2×D4711yescharacteristic
150C4×D4—472no—
151C4×D4—472no—
152C4×D4—471no—
153C4×D4—941no—
154#106—471no—
155#106C2×D4712yes—
156C4⋊C8—472no—
157C4⋊C8C2×D4711yescharacteristic
158#103—471no—
159#103C2×D4712yes—
160#102—472no—
161#102—471no—
162#102—472no—
163#102—472no—
164#97—472no—
165C4×C8—471no—
166C2×Q8—21no—
167C2×Q8—471no—
168C2×Q8—942no—
169C2×Q8—1884no—
170C2×Q8C22×D4711yescharacteristic
171C2×D4—471no—
172C2×D4—472no—
173C2×D4—941no—
174C2×D4—941no—
175C22×C4—942no—
176C22×C4—942no—
177C22×C4—941no—
178SD16—942no—
179D8—944no—
180C2×C8—471no—
181C2×C8—471no—
182C2×C8C22×D4712yes—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—472no—
186C4⋊C4—471no—
187C4⋊C4—471no—
188C4⋊C4—942no—
189C4⋊C4C22×D4712yes—
190C4⋊C4C22×D4711yescharacteristic
191C22⋊C4—942no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C22⋊C4—942no—
195C22⋊C4—941no—
196C42—21no—
197C42—472no—
198C42C22×D4711yescharacteristic
199C23—941no—
200C23—942no—
201Q8—21no—
202Q8—21no—
203Q8—42no—
204Q8—942no—
205Q8—1884no—
206D4—472no—
207D4—942no—
208D4—941no—
209D4—942no—
210D4—3761no—
211D4—1882no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—472no—
216C2×C4—472no—
217C2×C4—941no—
218C2×C4—3762no—
219C2×C4—1884no—
220C2×C4—1882no—
221C2×C4D4×D4711yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4C23×D4711yescharacteristic
224C8—22no—
225C8—941no—
226C8—941no—
227C22—942no—
228C22—1882no—
229C22—1882no—
230C22—1882no—
231C22—1881no—
232C22—1881no—
233C22C2×D4×D4711yescharacteristic
234C4—21no—
235C4—41no—
236C4—42no—
237C4—41no—
238C4—942no—
239C4—942no—
240C4—1881no—
241C4#1309405112yes—
242C4#41×D4711yescharacteristic
243C4#1309407211yescharacteristic
244C2—3762no—
245C2—1882no—
246C2#1568978311yescharacteristic
247C2C2×#1309405111yescharacteristic
248C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3373
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. #15689858C2semidirect
2. #15689788C2semidirect
3. #15689484C2semidirect
4. #15689471C2semidirect
5. #15689412C2semidirect
6. #15689341C2semidirect
8. #15689250C2semidirect
9. #15689234C2semidirect
10. C4×#10625336C2semidirect
11. C47×#475C2semidirect
130. #475D47semidirect
136. C47#3373semidirect