Finite Group Databasebeta

← #20254540

Subgroups — #20254540

Order 6016.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689678C211yesmaximal, characteristic
2C4⋊Q8×D47C211yesmaximal, characteristic
3#15689526C211yesmaximal, characteristic, complemented
4#15689475C211yesmaximal, characteristic, complemented
5#15689474C211yesmaximal, characteristic, complemented
6#15689460C214yesmaximal
7#15689417C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic
9C47×#500C211yesmaximal, characteristic, complemented
10C2×Q8×D47—21no—
11#13094024C2211yescharacteristic
12#13094024C2211yescharacteristic
13#13094023—21no—
14#13094023C2212yes—
15#13094022—21no—
16#13094015—21no—
17#13094004C2212yes—
18#13094000—21no—
19Q8×Dic47—21no—
20#13093989C2212yes—
21#13093982—21no—
22C4⋊C4×D47—21no—
23C4⋊C4×D47C2212yes—
24C42×D47C2211yescharacteristic
25#13093957C2214yes—
26Dic47⋊C8C2212yes—
27#13093949C2214yes—
28#13093947C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#107×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37Q8×D47—44no—
38C2×C4×D47—22no—
39C2×C4×D47D411yescharacteristic
40C2×C4×D47D411yescharacteristic
41C2×C4×D47C2311yescharacteristic
42C2×Dic94—21no—
43C2×Dic94—22no—
44C2×Dic94C2312yes—
45C2×C8×C47C2312yes—
46C4⋊C4×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47C2312yes—
49C4⋊C4×C47C2312yes—
50C42×C47C2311yescharacteristic
51(C2×D47)⋊C4—22no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4⋊Dic47—22no—
56C4⋊Dic47C2312yes—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60C4×Dic47—22no—
61C4×Dic47D411yescharacteristic
62C4×Dic47D411yescharacteristic
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2312yes—
65C22×D47C2×D411yescharacteristic
66Q8×C47—42no—
67Q8×C47—42no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2411yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47C2×D411yescharacteristic
76C2×Dic47C2×D411yescharacteristic
77C2×Dic47C2×D411yescharacteristic
78C4×D47—22no—
79C4×D47—22no—
80C4×D47—44no—
81C4×D47Q1614yes—
82Dic94—24no—
83Dic94—44no—
84Dic94—42no—
85C8×C47—22no—
86C47⋊C8—22no—
87C22×C47C22×D411yescharacteristic
88C2×D47—21no—
89C2×D47—21no—
90C2×D47C2×Q1612yes—
91C4×C47—42no—
92C4×C47—42no—
93C4×C47C2×Q1612yes—
94C4×C47AGL(1,ℤ/8)12yes—
95C4×C472−1+412yes—
96Dic47—21no—
97Dic47—21no—
98Dic47—42no—
99Dic47—42no—
100Dic47C2×Q1612yes—
101#3230—471nomaximal, Sylow
102C2×C47#53611yescharacteristic
103C2×C47C22×Q1611yescharacteristic
104C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
105D47—22no—
106#533—471no—
107C2×C4⋊Q8—471no—
108#500—471no—
109#500D4711yescharacteristic, complemented
110#487—471no—
111#487—471no—
112#484—474no—
113#477—474no—
114#431—471no—
115C47#323011yescharacteristic, complemented, Sylow
116C22×Q8—941no—
117C4⋊Q8—472no—
118C4⋊Q8—471no—
119C4⋊Q8—471no—
120C4⋊Q8—941no—
121C4⋊Q8—941no—
122C4⋊Q8C2×D4711yescharacteristic
123C4⋊Q8C2×D4711yescharacteristic
124#125—941no—
125C22⋊Q8—472no—
126C22⋊Q8—941no—
127C4×Q8—472no—
128C4×Q8—941no—
129#117—941no—
130C2×C4⋊C4—472no—
131C2×C4⋊C4—941no—
132C2×C42—471no—
133#107—474no—
134#107C2×D4714yes—
135C4⋊C8—472no—
136#103—474no—
137#103—474no—
138C22⋊C8—472no—
139C4×C8—471no—
140C4×C8C2×D4711yescharacteristic
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—472no—
144C2×Q8—942no—
145C2×Q8—941no—
146C2×Q8—1884no—
147C22×C4—471no—
148C22×C4—471no—
149C22×C4—471no—
150C22×C4—942no—
151C2×C8—472no—
152C2×C8C22×D4712yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—472no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4C22×D4712yes—
164C4⋊C4C22×D4712yes—
165C22⋊C4—942no—
166C42—471no—
167C42—471no—
168C42—471no—
169C42—942no—
170C42C22×D4711yescharacteristic
171C23—471no—
172Q8—42no—
173Q8—42no—
174Q8—944no—
175Q8—1884no—
176Q8—1882no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—471no—
180C2×C4—474no—
181C2×C4—471no—
182C2×C4—471no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—1884no—
188C2×C4D4×D4711yescharacteristic
189C2×C4D4×D4711yescharacteristic
190C2×C4C23×D4711yescharacteristic
191C8—22no—
192C8—942no—
193C22—472no—
194C22—941no—
195C22—941no—
196C22C2×D4×D4711yescharacteristic
197C4—42no—
198C4—42no—
199C4—472no—
200C4—941no—
201C4—941no—
202C4—1882no—
203C4—1882no—
204C4Q16×D4712yes—
205C4#1309404812yes—
206C4#1309407212yes—
207C2—942no—
208C2#1568969811yescharacteristic
209C2C2×Q16×D4711yescharacteristic
210C2C2×#1309404811yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#500C2
socleC22×C47C22×D4
hypercenter#500D47
hypocenterC47#3230
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #15689526C2semidirect
4. #15689475C2semidirect
5. #15689474C2semidirect
7. #15689417C2semidirect
9. C47×#500C2semidirect
109. #500D47semidirect
115. C47#3230semidirect