Finite Group Databasebeta

← #20256375

Subgroups — #20256375

Order 6016.

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

normal subgroups only

This group has 360 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#15689847C211yesmaximal, characteristic, complemented
2#15689843C211yesmaximal, characteristic, complemented
3#15689504C212yesmaximal
4#15689502C211yesmaximal, characteristic, complemented
5#15689348C212yesmaximal, complemented
6#15689343C212yesmaximal, complemented
7#15689329C211yesmaximal, characteristic, complemented
8#15689247C211yesmaximal, characteristic, complemented
9#15689215C212yesmaximal, complemented
10C4×#10625334C211yesmaximal, characteristic
11C47×#461C211yesmaximal, characteristic, complemented
12C2×#10625337C2212yes—
13C2×#10625337C2212yes—
14C2×#10625325C2212yes—
15C2×#10625334C2211yescharacteristic
16#13094024C2211yescharacteristic
17#13094019—22no—
18#13094017—22no—
19#13094013C2212yes—
20#13094011C2212yes—
21#13094004—21no—
22#13094003—21no—
23Q8×Dic47C2212yes—
24C4×Dic94C2211yescharacteristic
25#13093989C2212yes—
26C4×D188C2211yescharacteristic
27#13093983—21no—
28#13093982—21no—
29#13093957C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2212yes—
32#13093945C2211yescharacteristic
33#13093944C2211yescharacteristic
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
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×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×Dic94D411yescharacteristic
47C2×Dic94C2312yes—
48SD16×C47—42no—
49C2×C8×C47C2312yes—
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2311yescharacteristic
53C22⋊C4×C47—21no—
54C42×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56C22⋊Dic47—22no—
57#10625337—24no—
58#10625337—42no—
59#10625334—22no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63C4⋊Dic47—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47—22no—
66C4⋊Dic47D411yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68Dic47⋊C4—22no—
69Dic47⋊C4D412yes—
70C4×Dic47—22no—
71C4×Dic47—22no—
72C4×Dic47C2312yes—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75#10625325—42no—
76C23×C47—21no—
77C22×D47—21no—
78Q8×C47—22no—
79Q8×C47—22no—
80D4×C47—21no—
81D4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—42no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47C2×D412yes—
91C2×Dic47C2×D412yes—
92D188—21no—
93D188—21no—
94C4×D47—42no—
95Dic94—22no—
96Dic94—22no—
97Dic94—22no—
98C8×C47—22no—
99C47⋊C8—21no—
100C47⋊C8#4112yes—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47C22×D411yescharacteristic
105C2×D47—41no—
106C2×D47—41no—
107C2×D47—41no—
108C4×C47—21no—
109C4×C47—42no—
110C4×C47—41no—
111C4×C47#13512yes—
112C4×C47C2×#4111yescharacteristic
113C4×C47H(5,𝔽2)11yescharacteristic
114Dic47—22no—
115Dic47—22no—
116Dic47—42no—
117Dic47—41no—
118#3393—471nomaximal, Sylow
119C2×C47—81no—
120C2×C47#55011yescharacteristic
121C2×C47C2×#13511yescharacteristic
122C2×C47#57811yescharacteristic
123D47—81no—
124#556—471no—
125#556—471no—
126#495—472no—
127#494—471no—
128#464—472no—
129#464—472no—
130#461—471no—
131#461D4711yescharacteristic, complemented
132C8×Q8—471no—
133C4×Q16—472no—
134C4×D8—471no—
135C47#339311yescharacteristic, complemented, Sylow
136C2×Q16—472no—
137C2×Q16—472no—
138C2×SD16—472no—
139C2×SD16C2×D4712yes—
140C2×D8—471no—
141C4⋊Q8—471no—
142C4⋊Q8C2×D4711yescharacteristic
143#126—942no—
144#126—942no—
145#124—472no—
146#124—472no—
147C22⋊Q8—941no—
148C22⋊Q8—941no—
149C4×Q8—471no—
150C4×Q8—472no—
151C4×Q8—472no—
152C4×D4—471no—
153C4×D4C2×D4711yescharacteristic
154#117—941no—
155#117—941no—
156#107—471no—
157C4⋊C8—472no—
158C4⋊C8C2×D4711yescharacteristic
159#103—472no—
160#103C2×D4712yes—
161#102—471no—
162#102—471no—
163C4×C8—472no—
164C4×C8—471no—
165C2×Q8—471no—
166C2×Q8—472no—
167C2×Q8C22×D4712yes—
168C2×D4—471no—
169C2×D4C22×D4711yescharacteristic
170C22×C4—21no—
171C22×C4—941no—
172Q16—944no—
173Q16—1882no—
174SD16—42no—
175SD16—1882no—
176D8—942no—
177C2×C8—471no—
178C2×C8—471no—
179C2×C8C22×D4712yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—472no—
183C4⋊C4—471no—
184C4⋊C4—471no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4C22×D4711yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—942no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C22⋊C4—942no—
195C22⋊C4—941no—
196C42—472no—
197C42—942no—
198C42—942no—
199C42C22×D4711yescharacteristic
200C23—21no—
201C23—941no—
202Q8—22no—
203Q8—22no—
204Q8—942no—
205Q8—942no—
206Q8—942no—
207D4—21no—
208D4—21no—
209D4—941no—
210D4—941no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—472no—
215C2×C4—472no—
216C2×C4—941no—
217C2×C4—942no—
218C2×C4—1882no—
219C2×C4D4×D4711yescharacteristic
220C2×C4D4×D4711yescharacteristic
221C2×C4C23×D4711yescharacteristic
222C8—22no—
223C8—472no—
224C8—941no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—1881no—
229C22—1881no—
230C22—1881no—
231C22C2×D4×D4711yescharacteristic
232C4—21no—
233C4—42no—
234C4—41no—
235C4—942no—
236C4—942no—
237C4—1882no—
238C4—1881no—
239C4#1309404512yes—
240C4#41×D4711yescharacteristic
241C4#1309406911yescharacteristic
242C2—81no—
243C2—3761no—
244C2#1568979111yescharacteristic
245C2C2×#1309404511yescharacteristic
246C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3393
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. #15689847C2semidirect
2. #15689843C2semidirect
4. #15689502C2semidirect
5. #15689348C2semidirect
6. #15689343C2semidirect
7. #15689329C2semidirect
8. #15689247C2semidirect
9. #15689215C2semidirect
11. C47×#461C2semidirect
131. #461D47semidirect
135. C47#3393semidirect