Finite Group Databasebeta

← #20256423

Subgroups — #20256423

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#15689848C211yesmaximal, characteristic, complemented
2#15689843C211yesmaximal, characteristic
3#15689514C212yesmaximal
4#15689502C211yesmaximal, characteristic, complemented
5#15689343C212yesmaximal
6#15689334C211yesmaximal, characteristic, complemented
7#15689332C212yesmaximal, complemented
8#15689250C211yesmaximal, characteristic, complemented
9#15689227C212yesmaximal, complemented
10C4×#10625335C211yesmaximal, characteristic
11C47×#461C211yesmaximal, characteristic
12C2×Dic188C2212yes—
13C2×#10625337C2212yes—
14C2×#10625337C2212yes—
15C2×#10625335C2211yescharacteristic
16#13094024C2211yescharacteristic
17#13094022C2212yes—
18#13094017—22no—
19#13094015—21no—
20#13094014—22no—
21#13094011C2212yes—
22#13094003—21no—
23Q8×Dic47C2212yes—
24C4×Dic94C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093989—21no—
27#13093989C2212yes—
28#13093983—21no—
29#13093955C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2212yes—
32#13093947C2211yescharacteristic
33#13093945C2211yescharacteristic
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C2×SD16×C47C2212yes—
37C4⋊Q8×C47C2211yescharacteristic
38C4×D4×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47C2312yes—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C2×Dic94D411yescharacteristic
45C2×Dic94C2311yescharacteristic
46C2×Dic94C2312yes—
47SD16×C47—42no—
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47C2311yescharacteristic
52C22⋊C4×C47—21no—
53C42×C47C2311yescharacteristic
54C22⋊Dic47—22no—
55C22⋊Dic47—22no—
56#10625337—24no—
57#10625337—42no—
58#10625335—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2311yescharacteristic
64Dic47⋊C4—21no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—21no—
70C4×Dic47—22no—
71C4×Dic47—22no—
72C4×Dic47C2312yes—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75Dic188—42no—
76C23×C47—21no—
77Q8×C47—22no—
78Q8×C47—22no—
79D4×C47—21no—
80D4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—42no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2411yescharacteristic
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47C2×D412yes—
91C2×Dic47C2×D412yes—
92Dic94—22no—
93Dic94—21no—
94Dic94—22no—
95Dic94—21no—
96Dic94—22no—
97C8×C47—22no—
98C47⋊C8—21no—
99C47⋊C8#4112yes—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47C22×D411yescharacteristic
104C4×C47—21no—
105C4×C47—42no—
106C4×C47—41no—
107C4×C47#13712yes—
108C4×C47C2×#4111yescharacteristic
109C4×C47H(5,𝔽2)11yescharacteristic
110Dic47—22no—
111Dic47—22no—
112Dic47—41no—
113Dic47—42no—
114Dic47—41no—
115#3398—471nomaximal, Sylow
116C2×C47—81no—
117C2×C47#55011yescharacteristic
118C2×C47C2×#13711yescharacteristic
119C2×C47#57811yescharacteristic
120#557—471no—
121#556—471no—
122#497—472no—
123#494—471no—
124#464—472no—
125#462—471no—
126#462—472no—
127#461D4711yescharacteristic
128#446—471no—
129#441—472no—
130C4×SD16—471no—
131C47#339811yescharacteristic, complemented, Sylow
132C2×Q16—472no—
133C2×Q16—472no—
134C2×Q16—472no—
135C2×SD16—471no—
136C2×SD16C2×D4712yes—
137C4⋊Q8—472no—
138C4⋊Q8—471no—
139C4⋊Q8C2×D4711yescharacteristic
140#126—942no—
141#125—942no—
142#125—941no—
143#124—472no—
144C22⋊Q8—941no—
145C4×Q8—471no—
146C4×Q8—472no—
147C4×Q8—472no—
148C4×Q8—471no—
149C4×Q8—941no—
150C4×D4C2×D4711yescharacteristic
151#117—941no—
152#106—471no—
153C4⋊C8—472no—
154C4⋊C8C2×D4711yescharacteristic
155#103—472no—
156#103—471no—
157#103C2×D4712yes—
158#102—471no—
159#97—472no—
160C4×C8—471no—
161C2×Q8—471no—
162C2×Q8—472no—
163C2×Q8—471no—
164C2×Q8C22×D4712yes—
165C2×D4C22×D4711yescharacteristic
166C22×C4—21no—
167Q16—944no—
168Q16—1882no—
169Q16—1882no—
170SD16—42no—
171SD16—942no—
172C2×C8—471no—
173C2×C8—471no—
174C2×C8C22×D4712yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—472no—
178C4⋊C4—471no—
179C4⋊C4—471no—
180C4⋊C4—942no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C4⋊C4C22×D4711yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C42—472no—
192C42—942no—
193C42—942no—
194C42—941no—
195C42C22×D4711yescharacteristic
196C23—21no—
197Q8—22no—
198Q8—22no—
199Q8—942no—
200Q8—941no—
201Q8—942no—
202Q8—941no—
203Q8—942no—
204D4—21no—
205D4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—472no—
210C2×C4—472no—
211C2×C4—941no—
212C2×C4—942no—
213C2×C4—941no—
214C2×C4D4×D4711yescharacteristic
215C2×C4D4×D4711yescharacteristic
216C2×C4C23×D4711yescharacteristic
217C8—22no—
218C8—472no—
219C8—941no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22C2×D4×D4711yescharacteristic
224C4—21no—
225C4—42no—
226C4—41no—
227C4—942no—
228C4—942no—
229C4—1882no—
230C4—1881no—
231C4—1881no—
232C4#1309405312yes—
233C4#41×D4711yescharacteristic
234C4#1309406911yescharacteristic
235C2—81no—
236C2#1568979111yescharacteristic
237C2C2×#1309405311yescharacteristic
238C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3398
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689848C2semidirect
4. #15689502C2semidirect
6. #15689334C2semidirect
7. #15689332C2semidirect
8. #15689250C2semidirect
9. #15689227C2semidirect
131. C47#3398semidirect