Finite Group Databasebeta

← #20256383

Subgroups — #20256383

Order 6016.

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

normal subgroups only

This group has 372 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#15689847C211yesmaximal, characteristic, complemented
3#15689508C212yesmaximal, complemented
4#15689497C211yesmaximal, characteristic, complemented
5#15689347C212yesmaximal, complemented
6#15689341C212yesmaximal, complemented
7#15689319C211yesmaximal, characteristic
8#15689247C211yesmaximal, characteristic, complemented
9C4×#10625336C211yesmaximal, characteristic, complemented
10#15689208C212yesmaximal, complemented
11C47×#462C211yesmaximal, characteristic, complemented
12C2×#10625336C2212yes—
13C2×#10625336C2211yescharacteristic
14C2×#10625336C2212yes—
15C2×D376C2212yes—
16#13094021C2211yescharacteristic
17#13094019—22no—
18#13094013C2212yes—
19#13094013C2212yes—
20#13094012—21no—
21#13094009—22no—
22#13094004—21no—
23Q8×Dic47C2212yes—
24C4×Dic94C2211yescharacteristic
25C4×D188—21no—
26C4×D188C2211yescharacteristic
27#13093986C2212yes—
28#13093982—21no—
29#13093955C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093948C2211yescharacteristic
32#13093946C2212yes—
33#13093944C2211yescharacteristic
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
36C2×Q16×C47C2212yes—
37C4⋊Q8×C47C2211yescharacteristic
38C4×Q8×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47C2312yes—
42C2×Q8×C47C2311yescharacteristic
43C2×D188—21no—
44C2×D188—21no—
45C2×D188C2311yescharacteristic
46C2×D188C2312yes—
47C2×C4×D47—21no—
48C2×C4×D47—22no—
49C2×Dic94D411yescharacteristic
50Q16×C47—42no—
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2311yescharacteristic
56C42×C47—21no—
57C42×C47C2311yescharacteristic
58#10625336—24no—
59#10625336—22no—
60#10625336—42no—
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—
66(C2×D47)⋊C4—22no—
67C4⋊Dic47—22no—
68C4⋊Dic47D411yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4D412yes—
71C4×Dic47—22no—
72C4×Dic47C2312yes—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75D376—42no—
76C22×D47—21no—
77C22×D47—22no—
78Q8×C47—22no—
79Q8×C47—21no—
80Q8×C47—22no—
81Q8×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—21no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91D188—21no—
92D188—22no—
93D188—21no—
94D188—22no—
95D188—42no—
96D188—81no—
97C4×D47—42no—
98C4×D47—82no—
99Dic94—22no—
100C8×C47—22no—
101C47⋊C8—21no—
102C47⋊C8#4112yes—
103C22×C47C22×D411yescharacteristic
104C2×D47—41no—
105C2×D47—42no—
106C2×D47—41no—
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—41no—
110C4×C47—21no—
111C4×C47—42no—
112C4×C47—41no—
113C4×C47—41no—
114C4×C47#13512yes—
115C4×C47C2×#4111yescharacteristic
116C4×C47H(5,𝔽2)11yescharacteristic
117Dic47—22no—
118Dic47—22no—
119Dic47—41no—
120#3394—471nomaximal, Sylow
121C2×C47#55011yescharacteristic
122C2×C47C2×#13511yescharacteristic
123C2×C47#57711yescharacteristic
124D47—81no—
125D47—82no—
126#559—471no—
127#556—471no—
128#495—472no—
129#492—471no—
130#464—472no—
131#463—472no—
132#462D4711yescharacteristic, complemented
133#459—471no—
134C8×Q8—471no—
135C4×SD16—471no—
136C4×SD16—472no—
137C47#339411yescharacteristic, complemented, Sylow
138C2×Q16C2×D4712yes—
139C2×SD16—472no—
140C2×SD16—471no—
141C2×SD16—472no—
142C2×D8—472no—
143C4⋊Q8C2×D4711yescharacteristic
144#127—471no—
145#126—942no—
146#124—472no—
147#124—472no—
148#124—941no—
149#123—942no—
150C22⋊Q8—941no—
151C4×Q8—471no—
152C4×Q8—472no—
153C4×Q8C2×D4711yescharacteristic
154C4×D4—472no—
155C4×D4—471no—
156C4×D4—941no—
157#117—941no—
158#106—471no—
159C4⋊C8—472no—
160C4⋊C8C2×D4711yescharacteristic
161#103—471no—
162#103C2×D4712yes—
163#102—472no—
164#102—471no—
165C4×C8—472no—
166C4×C8—471no—
167C2×Q8—471no—
168C2×Q8C22×D4711yescharacteristic
169C2×Q8C22×D4712yes—
170C2×D4—471no—
171C2×D4—472no—
172C2×D4—941no—
173C2×D4—941no—
174C22×C4—942no—
175C22×C4—941no—
176Q16—42no—
177SD16—944no—
178SD16—942no—
179SD16—1882no—
180D8—1882no—
181C2×C8—471no—
182C2×C8—471no—
183C2×C8C22×D4712yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—472no—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—942no—
191C4⋊C4C22×D4711yescharacteristic
192C22⋊C4—942no—
193C22⋊C4—942no—
194C22⋊C4—942no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C22⋊C4—941no—
198C42—21no—
199C42—472no—
200C42—942no—
201C42C22×D4711yescharacteristic
202C23—941no—
203C23—942no—
204Q8—21no—
205Q8—22no—
206Q8—22no—
207Q8—21no—
208Q8—942no—
209D4—941no—
210D4—942no—
211D4—941no—
212D4—942no—
213D4—3761no—
214D4—1882no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—472no—
219C2×C4—472no—
220C2×C4—941no—
221C2×C4—3762no—
222C2×C4—1882no—
223C2×C4D4×D4711yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4C23×D4711yescharacteristic
226C8—22no—
227C8—472no—
228C8—941no—
229C22—1881no—
230C22—1882no—
231C22—1881no—
232C22—1882no—
233C22—1882no—
234C22—1881no—
235C22C2×D4×D4711yescharacteristic
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—942no—
241C4—942no—
242C4—1881no—
243C4#1309404712yes—
244C4#41×D4711yescharacteristic
245C4#1309406911yescharacteristic
246C2—3761no—
247C2—3762no—
248C2#1568979111yescharacteristic
249C2C2×#1309404711yescharacteristic
250C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#462C2
socleC22×C47C22×D4
hypercenter#462D47
hypocenterC47#3394
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
2. #15689847C2semidirect
3. #15689508C2semidirect
4. #15689497C2semidirect
5. #15689347C2semidirect
6. #15689341C2semidirect
8. #15689247C2semidirect
9. C4×#10625336C2semidirect
10. #15689208C2semidirect
11. C47×#462C2semidirect
132. #462D47semidirect
137. C47#3394semidirect