Finite Group Databasebeta

← #20256418

Subgroups — #20256418

Order 6016.

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

normal subgroups only

This group has 350 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#15689851C211yesmaximal, characteristic, complemented
2#15689847C211yesmaximal, characteristic
3#15689516C212yesmaximal
4#15689502C211yesmaximal, characteristic, complemented
5#15689348C212yesmaximal
6#15689331C212yesmaximal, complemented
7#15689329C211yesmaximal, characteristic
8#15689250C211yesmaximal, characteristic, complemented
9#15689227C212yesmaximal, complemented
10C4×#10625336C211yesmaximal, characteristic
11C47×#462C211yesmaximal, characteristic, complemented
12C2×#10625337C2212yes—
13C2×#10625337C2212yes—
14C2×#10625325C2212yes—
15C2×#10625336C2211yescharacteristic
16#13094024C2211yescharacteristic
17#13094022C2212yes—
18#13094019—22no—
19#13094016—21no—
20#13094014—22no—
21#13094013C2212yes—
22#13094004—21no—
23Q8×Dic47C2212yes—
24C4×Dic94—21no—
25C4×Dic94C2211yescharacteristic
26#13093989C2212yes—
27C4×D188C2211yescharacteristic
28#13093982—21no—
29#13093955C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2212yes—
32#13093948C2211yescharacteristic
33#13093944C2211yescharacteristic
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C2×Q16×C47C2212yes—
37C4⋊Q8×C47C2211yescharacteristic
38C4×Q8×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47C2312yes—
42C2×Q8×C47C2311yescharacteristic
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×Dic94D411yescharacteristic
46C2×Dic94C2312yes—
47Q16×C47—42no—
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2311yescharacteristic
53C42×C47—21no—
54C42×C47C2311yescharacteristic
55#10625337—24no—
56#10625337—42no—
57#10625336—22no—
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47D411yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4D412yes—
70C4×Dic47—22no—
71C4×Dic47—22no—
72C4×Dic47C2312yes—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75#10625325—42no—
76C22×D47—21no—
77Q8×C47—21no—
78Q8×C47—22no—
79Q8×C47—22no—
80Q8×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91D188—21no—
92D188—21no—
93C4×D47—42no—
94Dic94—22no—
95Dic94—22no—
96Dic94—22no—
97C8×C47—22no—
98C47⋊C8—21no—
99C47⋊C8#4112yes—
100C22×C47C22×D411yescharacteristic
101C2×D47—41no—
102C2×D47—41no—
103C2×D47—41no—
104C4×C47—21no—
105C4×C47—42no—
106C4×C47—41no—
107C4×C47—41no—
108C4×C47#13712yes—
109C4×C47C2×#4111yescharacteristic
110C4×C47H(5,𝔽2)11yescharacteristic
111Dic47—22no—
112Dic47—22no—
113Dic47—42no—
114Dic47—41no—
115#3398—471nomaximal, Sylow
116C2×C47#55011yescharacteristic
117C2×C47C2×#13711yescharacteristic
118C2×C47#57811yescharacteristic
119D47—81no—
120#557—471no—
121#556—471no—
122#497—472no—
123#494—471no—
124#464—472no—
125#462—472no—
126#462D4711yescharacteristic, complemented
127#461—471no—
128#446—471no—
129#441—472no—
130C4×SD16—471no—
131C47#339811yescharacteristic, complemented, Sylow
132C2×Q16—472no—
133C2×Q16—472no—
134C2×Q16C2×D4712yes—
135C2×SD16—471no—
136C2×SD16—472no—
137C4⋊Q8—472no—
138C4⋊Q8—471no—
139C4⋊Q8C2×D4711yescharacteristic
140#126—942no—
141#125—941no—
142#125—942no—
143#124—472no—
144C22⋊Q8—941no—
145C4×Q8—471no—
146C4×Q8—472no—
147C4×Q8—472no—
148C4×Q8—941no—
149C4×Q8C2×D4711yescharacteristic
150C4×D4—471no—
151#117—941no—
152#106—471no—
153C4⋊C8—472no—
154C4⋊C8C2×D4711yescharacteristic
155#103—471no—
156#103—472no—
157#103C2×D4712yes—
158#102—471no—
159#97—472no—
160C4×C8—471no—
161C2×Q8—471no—
162C2×Q8—472no—
163C2×Q8C22×D4711yescharacteristic
164C2×Q8C22×D4712yes—
165C2×D4—471no—
166C22×C4—941no—
167Q16—42no—
168Q16—944no—
169Q16—1882no—
170SD16—942no—
171SD16—1882no—
172C2×C8—471no—
173C2×C8—471no—
174C2×C8C22×D4712yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—472no—
179C4⋊C4—471no—
180C4⋊C4—471no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C4⋊C4C22×D4711yescharacteristic
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—941no—
191C42—21no—
192C42—472no—
193C42—942no—
194C42—942no—
195C42C22×D4711yescharacteristic
196C23—941no—
197Q8—21no—
198Q8—22no—
199Q8—21no—
200Q8—22no—
201Q8—942no—
202Q8—942no—
203Q8—942no—
204D4—941no—
205D4—941no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—472no—
210C2×C4—472no—
211C2×C4—941no—
212C2×C4—942no—
213C2×C4—1882no—
214C2×C4D4×D4711yescharacteristic
215C2×C4D4×D4711yescharacteristic
216C2×C4C23×D4711yescharacteristic
217C8—22no—
218C8—472no—
219C8—941no—
220C22—1881no—
221C22—1881no—
222C22—1881no—
223C22C2×D4×D4711yescharacteristic
224C4—21no—
225C4—41no—
226C4—42no—
227C4—41no—
228C4—942no—
229C4—942no—
230C4—1882no—
231C4—1881no—
232C4#1309405612yes—
233C4#41×D4711yescharacteristic
234C4#1309406911yescharacteristic
235C2—3761no—
236C2#1568979111yescharacteristic
237C2C2×#1309405611yescharacteristic
238C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#462C2
socleC22×C47C22×D4
hypercenter#462D47
hypocenterC47#3398
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. #15689851C2semidirect
4. #15689502C2semidirect
6. #15689331C2semidirect
8. #15689250C2semidirect
9. #15689227C2semidirect
11. C47×#462C2semidirect
126. #462D47semidirect
131. C47#3398semidirect