Finite Group Databasebeta

← #20256424

Subgroups — #20256424

Order 6016.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689847C211yesmaximal, characteristic
3#15689516C212yesmaximal
4#15689347C212yesmaximal
5#15689331C212yesmaximal, complemented
6#15689330C211yesmaximal, characteristic, complemented
7#15689325C211yesmaximal, characteristic
8#15689253C211yesmaximal, characteristic, complemented
9#15689230C212yesmaximal, complemented
10C4×#10625325C211yesmaximal, characteristic
11C47×#494C211yesmaximal, characteristic, complemented
12C2×#10625337C2212yes—
13C2×#10625325C2211yescharacteristic
14C2×#10625336C2212yes—
15#13094022C2212yes—
16#13094019—22no—
17#13094015—21no—
18#13094014—22no—
19#13094013C2212yes—
20#13094004—21no—
21Q8×Dic47C2212yes—
22Q8×Dic47C2212yes—
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25#13093989—21no—
26C4×D188C2211yescharacteristic
27#13093982—21no—
28#13093956C2211yescharacteristic
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093948C2212yes—
33#13093948C2212yes—
34#13093946C2211yescharacteristic
35#13093934C2212yes—
36C2×Q16×C47C2212yes—
37C2×Q16×C47C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39C4⋊Q8×C47C2211yescharacteristic
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47C2312yes—
42C2×Q8×C47C2312yes—
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×Dic94D411yescharacteristic
46C2×Dic94C2311yescharacteristic
47Q16×C47—24no—
48Q16×C47—42no—
49C2×C8×C47C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C42×C47C2311yescharacteristic
56#10625337—42no—
57#10625336—42no—
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47D411yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66Dic47⋊C4—21no—
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4D412yes—
70C4×Dic47—21no—
71C4×Dic47—22no—
72C4×Dic47—22no—
73C4×Dic47C2312yes—
74C2×C47⋊C8C2312yes—
75#10625325—22no—
76C22×D47—21no—
77Q8×C47—22no—
78Q8×C47—22no—
79Q8×C47—22no—
80Q8×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91D188—21no—
92D188—21no—
93C4×D47—42no—
94Dic94—22no—
95Dic94—21no—
96Dic94—21no—
97C8×C47—21no—
98C8×C47#4112yes—
99C47⋊C8—22no—
100C22×C47C22×D411yescharacteristic
101C2×D47—41no—
102C2×D47—41no—
103C2×D47—41no—
104C4×C47—21no—
105C4×C47—42no—
106C4×C47—42no—
107C4×C47#13712yes—
108C4×C47C2×#4111yescharacteristic
109C4×C47H(5,𝔽2)11yescharacteristic
110Dic47—22no—
111Dic47—22no—
112Dic47—41no—
113Dic47—41no—
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#494D4711yescharacteristic, complemented
124#464—472no—
125#462—472no—
126#462—471no—
127#461—471no—
128#446—471no—
129#441—472no—
130C4×SD16—471no—
131C47#339811yescharacteristic, complemented, Sylow
132C2×Q16—472no—
133C2×Q16C2×D4712yes—
134C2×Q16C2×D4712yes—
135C2×SD16—472no—
136C2×SD16—471no—
137C4⋊Q8—472no—
138C4⋊Q8C2×D4711yescharacteristic
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×D4—471no—
151#117—941no—
152#106—471no—
153C4⋊C8—472no—
154C4⋊C8—471no—
155#103—472no—
156#103—472no—
157#103—471no—
158#102—471no—
159#97—472no—
160C4×C8C2×D4711yescharacteristic
161C2×Q8—471no—
162C2×Q8—471no—
163C2×Q8C22×D4712yes—
164C2×Q8C22×D4712yes—
165C2×D4—471no—
166C22×C4—941no—
167Q16—24no—
168Q16—42no—
169Q16—1882no—
170SD16—942no—
171SD16—1882no—
172C2×C8—472no—
173C2×C8C22×D4711yescharacteristic
174C2×C8C22×D4711yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—21no—
179C4⋊C4—472no—
180C4⋊C4—471no—
181C4⋊C4—471no—
182C4⋊C4—471no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4—941no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—941no—
191C42—472no—
192C42—942no—
193C42—942no—
194C42—941no—
195C42C22×D4711yescharacteristic
196C23—941no—
197Q8—22no—
198Q8—22no—
199Q8—22no—
200Q8—22no—
201Q8—942no—
202Q8—941no—
203Q8—941no—
204D4—941no—
205D4—941no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—472no—
209C2×C4—472no—
210C2×C4—941no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—1882no—
214C2×C4D4×D4711yescharacteristic
215C2×C4D4×D4711yescharacteristic
216C2×C4C23×D4711yescharacteristic
217C8—21no—
218C8—942no—
219C8#1062535212yes—
220C22—1881no—
221C22—1881no—
222C22—1881no—
223C22C2×D4×D4711yescharacteristic
224C4—21no—
225C4—42no—
226C4—42no—
227C4—942no—
228C4—942no—
229C4—1881no—
230C4—1881no—
231C4—1881no—
232C4#1309405612yes—
233C4C2×#1062535211yescharacteristic
234C4#1309406911yescharacteristic
235C2—3761no—
236C2#1568979311yescharacteristic
237C2C2×#1309405611yescharacteristic
238C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#494C2
socleC22×C47C22×D4
hypercenter#494D47
hypocenterC47#3398
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #15689848C2semidirect
5. #15689331C2semidirect
6. #15689330C2semidirect
8. #15689253C2semidirect
9. #15689230C2semidirect
11. C47×#494C2semidirect
123. #494D47semidirect
131. C47#3398semidirect