Finite Group Databasebeta

← #20255969

Subgroups — #20255969

Order 6016.

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

normal subgroups only

This group has 374 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#15689778C211yesmaximal, characteristic
3#15689526C211yesmaximal, characteristic, complemented
4#15689460C212yesmaximal, complemented
5#15689446C212yesmaximal, complemented
6#15689409C211yesmaximal, characteristic, complemented
7#15689368C212yesmaximal, complemented
8C4×#10625335C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic, complemented
10#15689164C212yesmaximal, complemented
11C47×#474C211yesmaximal, characteristic, complemented
12C2×#10625350—21no—
13C2×#10625335C2211yescharacteristic
14C2×#10625324C2212yes—
15#13094024C2211yescharacteristic
16#13094019—22no—
17#13094013—21no—
18#13094006—22no—
19#13094004C2212yes—
20#13094003—21no—
21#13093995C2212yes—
22Q8×Dic47—21no—
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25#13093982C2212yes—
26C4⋊C4×D47C2212yes—
27#13093957C2212yes—
28#13093957C2212yes—
29#13093956C2212yes—
30#13093955C2211yescharacteristic
31#13093949C2212yes—
32#13093947C2211yescharacteristic
33#13093945C2211yescharacteristic
34(C2×D47)⋊C8C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×D4×C47C2211yescharacteristic
38#107×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#102×C47C2212yes—
41C2×Q8×C47—21no—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C2×C22⋊D47—22no—
45#10625350—44no—
46C2×D188D411yescharacteristic
47C2×C4×D47—22no—
48C2×C4×D47C2312yes—
49C2×Dic94—21no—
50C2×Dic94C2311yescharacteristic
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2311yescharacteristic
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—21no—
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58#10625335—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4D412yes—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47D411yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66C4⋊Dic47C2312yes—
67Dic47⋊C4—21no—
68Dic47⋊C4—22no—
69C4×Dic47—21no—
70C4×Dic47—22no—
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73#10625324—24no—
74C23×C47—21no—
75C22×D47C2×D412yes—
76Q8×C47—42no—
77D4×C47—21no—
78D4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—42no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C22⋊D47—44no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47C2×D412yes—
90D188—22no—
91C4×D47—22no—
92C4×D47—22no—
93C4×D47—44no—
94Dic94—21no—
95Dic94—21no—
96Dic94—42no—
97C8×C47—22no—
98C47⋊C8—21no—
99C47⋊C8#4112yescomplemented
100C22×C47—41no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47C22×D411yescharacteristic
104C2×D47—22no—
105C2×D47—22no—
106C2×D47—22no—
107C4×C47—21no—
108C4×C47—41no—
109C4×C47—42no—
110C4×C47AGL(1,ℤ/8)12yes—
111C4×C47C2×#4111yescharacteristic
112C4×C472−1+411yescharacteristic
113Dic47—22no—
114Dic47—41no—
115Dic47—42no—
116Dic47—41no—
117#3353—471nomaximal, Sylow
118C2×C47—81no—
119C2×C47#54711yescharacteristic
120C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C47#57811yescharacteristic
122D47—42no—
123#556—471no—
124#547—471no—
125#500—471no—
126#484—472no—
127#482—472no—
128#475—471no—
129#474D4711yescharacteristic, complemented
130#468—472no—
131C4×SD16—471no—
132#436—471no—
133#428—472no—
134C47#335311yescharacteristic, complemented, Sylow
135C2×#41—941no—
136C2×SD16—471no—
137C2×M16—472no—
138C4⋊Q8—471no—
139C4⋊Q8C2×D4711yescharacteristic
140#126—942no—
141#124—941no—
142#123—942no—
143C22⋊Q8—472no—
144C22⋊Q8—941no—
145#121—472no—
146C4×Q8—471no—
147C4×Q8—941no—
148C4×D4—471no—
149C4×D4C2×D4711yescharacteristic
150#117—472no—
151C2×C4⋊C4—472no—
152#107—472no—
153#107—472no—
154#107C2×D4712yes—
155#106—472no—
156#106—471no—
157C4⋊C8C2×D4711yescharacteristic
158#103—472no—
159#103—471no—
160#102—471no—
161#102C2×D4712yes—
162C22⋊C8—472no—
163C4×C8—471no—
164#41—1884no—
165C2×Q8—21no—
166C2×Q8—471no—
167C2×Q8—941no—
168C2×D4—471no—
169C2×D4—942no—
170C2×D4C22×D4711yescharacteristic
171C22×C4—21no—
172C22×C4—472no—
173C22×C4—942no—
174SD16—942no—
175M16—944no—
176C2×C8—471no—
177C2×C8—471no—
178C2×C8C22×D4712yes—
179C4⋊C4—21no—
180C4⋊C4—471no—
181C4⋊C4—471no—
182C4⋊C4—472no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—941no—
186C4⋊C4—941no—
187C4⋊C4C22×D4712yes—
188C4⋊C4C22×D4711yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—472no—
191C22⋊C4—942no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C42—942no—
195C42—941no—
196C42C22×D4711yescharacteristic
197C23—21no—
198C23—472no—
199Q8—42no—
200Q8—941no—
201Q8—941no—
202Q8—1882no—
203D4—21no—
204D4—21no—
205D4—942no—
206D4—1884no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—472no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—1884no—
217C2×C4D4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C2×C4C23×D4711yescharacteristic
220C8—22no—
221C8—472no—
222C8—941no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—942no—
227C22—942no—
228C22—942no—
229C22C2×D4×D4711yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—942no—
234C4—1881no—
235C4—1882no—
236C4—1881no—
237C4#1309404812yes—
238C4#41×D4711yescharacteristic
239C4#1309407211yescharacteristic
240C2—81no—
241C2—1882no—
242C2#1568977511yescharacteristic
243C2C2×#1309404811yescharacteristic
244C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3353
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689847C2semidirect
3. #15689526C2semidirect
4. #15689460C2semidirect
5. #15689446C2semidirect
6. #15689409C2semidirect
7. #15689368C2semidirect
8. C4×#10625335C2semidirect
9. #15689200C2semidirect
10. #15689164C2semidirect
11. C47×#474C2semidirect
99. C47⋊C8#41semidirect
129. #474D47semidirect
134. C47#3353semidirect