Finite Group Databasebeta

← #20256122

Subgroups — #20256122

Order 6016.

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

normal subgroups only

This group has 382 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#15689793C211yesmaximal, characteristic
3#15689486C212yesmaximal, complemented
4#15689425C212yesmaximal, complemented
5#15689400C211yesmaximal, characteristic, complemented
6#15689322C212yesmaximal, complemented
7#15689320C211yesmaximal, characteristic, complemented
8#15689253C211yesmaximal, characteristic, complemented
9#15689220C212yesmaximal, complemented
10C4×#10625325C211yesmaximal, characteristic, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×#10625352—21no—
13C2×#10625325C2211yescharacteristic
14C2×#10625335C2212yes—
15#13094022—21no—
16#13094020C2212yes—
17#13094015C2212yes—
18#13094014—22no—
19#13093996—22no—
20#13093995—21no—
21Q8×Dic47—21no—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24#13093989C2212yes—
25C4×D188C2211yescharacteristic
26D4×Dic47C2212yes—
27#13093957C2212yes—
28#13093956C2211yescharacteristic
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093946C2211yescharacteristic
33#13093945C2212yes—
34#13093944C2212yes—
35#13093934C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37#127×C47C2211yescharacteristic
38#102×C47C2212yes—
39#102×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2312yes—
45C2×C22⋊D47—22no—
46C2×C22⋊D47—22no—
47C22×Dic47—22no—
48#10625352—44no—
49C2×D188C2311yescharacteristic
50C2×C4×D47—21no—
51C2×Dic94D411yescharacteristic
52C2×Dic94C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C2×C8×C47C2311yescharacteristic
55C4⋊C4×C47—21no—
56C4⋊C4×C47C2312yes—
57C42×C47C2311yescharacteristic
58C22⋊Dic47—22no—
59#10625335—24no—
60(C2×D47)⋊C4—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—21no—
70C4×Dic47—22no—
71C4×Dic47C2312yes—
72C2×C47⋊C8C2312yes—
73#10625325—22no—
74C23×C47—22no—
75C22×D47—21no—
76Q8×C47—42no—
77D4×C47—22no—
78D4×C47—22no—
79D4×C47—42no—
80D4×C47—81no—
81C2×C4×C47—22no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C22⋊D47—44no—
86C22⋊D47—82no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—44no—
91C2×Dic47C2×D412yes—
92C2×Dic47C2×D412yes—
93D188—21no—
94D188—21no—
95C4×D47—42no—
96Dic94—22no—
97Dic94—21no—
98Dic94#4112yescomplemented
99C8×C47—21no—
100C8×C47—21no—
101C47⋊C8—22no—
102C22×C47—42no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47C22×D411yescharacteristic
106C2×D47—41no—
107C2×D47—41no—
108C2×D47—41no—
109C4×C47—21no—
110C4×C47—42no—
111C4×C47AGL(1,ℤ/8)12yes—
112C4×C47C2×#4111yescharacteristic
113C4×C472−1+411yescharacteristic
114Dic47—22no—
115Dic47—22no—
116Dic47—22no—
117Dic47—41no—
118Dic47—41no—
119#3368—471nomaximal, Sylow
120C2×C47—82no—
121C2×C47#54811yescharacteristic
122C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C47#57711yescharacteristic
124D47—81no—
125#557—471no—
126#550—471no—
127#490—472no—
128#486D4711yescharacteristic, complemented
129#478—472no—
130#474—471no—
131#460—471no—
132#460—472no—
133#446—471no—
134#440—472no—
135C4×SD16—471no—
136C47#336811yescharacteristic, complemented, Sylow
137C2×#41—941no—
138C2×SD16—472no—
139C2×SD16—471no—
140C4⋊Q8—941no—
141C4⋊Q8C2×D4711yescharacteristic
142#127—472no—
143#127C2×D4711yescharacteristic
144#125—472no—
145#125—942no—
146#121—941no—
147#121—942no—
148C4×Q8—471no—
149C4×Q8—472no—
150C4×Q8—471no—
151C4×Q8—941no—
152C4×D4—472no—
153C4×D4—471no—
154#107—472no—
155#106—471no—
156C4⋊C8—472no—
157C4⋊C8—471no—
158#103—471no—
159#102—472no—
160#102—471no—
161#102—472no—
162#102C2×D4712yes—
163#102C2×D4712yes—
164#97—472no—
165C4×C8C2×D4711yescharacteristic
166#41—1884no—
167C2×Q8—21no—
168C2×Q8—471no—
169C2×Q8—471no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—471no—
173C2×D4—942no—
174C2×D4—942no—
175C2×D4C22×D4712yes—
176C22×C4—942no—
177C22×C4—941no—
178SD16—942no—
179SD16—944no—
180C2×C8—472no—
181C2×C8C22×D4711yescharacteristic
182C2×C8C22×D4711yescharacteristic
183C4⋊C4—21no—
184C4⋊C4—472no—
185C4⋊C4—471no—
186C4⋊C4—471no—
187C4⋊C4—471no—
188C4⋊C4—942no—
189C4⋊C4—942no—
190C4⋊C4—942no—
191C4⋊C4—941no—
192C4⋊C4C22×D4712yes—
193C22⋊C4—942no—
194C22⋊C4—941no—
195C42—472no—
196C42—942no—
197C42—941no—
198C42C22×D4711yescharacteristic
199C23—22no—
200C23—941no—
201Q8—42no—
202Q8—472no—
203Q8—942no—
204Q8—941no—
205D4—22no—
206D4—22no—
207D4—42no—
208D4—81no—
209D4—941no—
210D4—941no—
211D4—3762no—
212D4—1884no—
213C2×C4—22no—
214C2×C4—472no—
215C2×C4—472no—
216C2×C4—941no—
217C2×C4—941no—
218C2×C4—941no—
219C2×C4—1884no—
220C2×C4—1882no—
221C2×C4D4×D4711yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4C23×D4711yescharacteristic
224C8—21no—
225C8—21no—
226C8—942no—
227C22—42no—
228C22—42no—
229C22—42no—
230C22—1881no—
231C22—1881no—
232C22—1881no—
233C22C2×D4×D4711yescharacteristic
234C4—21no—
235C4—42no—
236C4—942no—
237C4—942no—
238C4—942no—
239C4—1881no—
240C4—1881no—
241C4#1309404812yes—
242C4#41×D4711yescharacteristic
243C4#1309407111yescharacteristic
244C2—82no—
245C2—3761no—
246C2#1568978111yescharacteristic
247C2C2×#1309404811yescharacteristic
248C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3368
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689848C2semidirect
3. #15689486C2semidirect
4. #15689425C2semidirect
5. #15689400C2semidirect
6. #15689322C2semidirect
7. #15689320C2semidirect
8. #15689253C2semidirect
9. #15689220C2semidirect
10. C4×#10625325C2semidirect
11. C47×#486C2semidirect
98. Dic94#41semidirect
128. #486D47semidirect
136. C47#3368semidirect