Finite Group Databasebeta

← #20254132

Subgroups — #20254132

Order 6016.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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
2#15689678C211yesmaximal, characteristic
3#15689519C211yesmaximal, characteristic, complemented
4#15689502C211yesmaximal, characteristic, complemented
5#15689474C211yesmaximal, characteristic, complemented
6#15689380C214yesmaximal
7#15689227C214yesmaximal, complemented
8C4×#10625324C211yesmaximal, characteristic
9C47×#487C211yesmaximal, characteristic, complemented
10C2×#10625337C2214yes—
11C2×#10625324C2212yes—
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094015—21no—
15#13094015—21no—
16#13094004—21no—
17#13094004C2212yes—
18#13094000—21no—
19#13094000C2212yes—
20Q8×Dic47—21no—
21Q8×Dic47C2212yes—
22#13093989—21no—
23#13093989C2212yes—
24#13093982—21no—
25#13093982—21no—
26C42×D47C2211yescharacteristic
27#13093955C2214yes—
28#13093949C2214yes—
29#13093934C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#103×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47C2312yes—
37C2×C4×D47D411yescharacteristic
38C2×C4×D47D411yescharacteristic
39C2×C4×D47C2311yescharacteristic
40C2×Dic94—21no—
41C2×Dic94C2312yes—
42C2×C8×C47C2312yes—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47C2312yes—
47C42×C47C2311yescharacteristic
48#10625337—28no—
49(C2×D47)⋊C4—22no—
50(C2×D47)⋊C4—22no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47—22no—
55C4⋊Dic47—22no—
56C4⋊Dic47C2312yes—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59C4×Dic47—22no—
60C4×Dic47—22no—
61C4×Dic47D411yescharacteristic
62C4×Dic47D411yescharacteristic
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2312yes—
65#10625324—24no—
66C22×D47C2×D411yescharacteristic
67Q8×C47—24no—
68Q8×C47—42no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2411yescharacteristic
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47C2×D411yescharacteristic
77C2×Dic47C2×D411yescharacteristic
78C2×Dic47C2×D411yescharacteristic
79C4×D47—22no—
80C4×D47—22no—
81C4×D47—22no—
82Dic94—24no—
83Dic94—42no—
84C8×C47—22no—
85C47⋊C8#4114yes—
86C22×C47C22×D411yescharacteristic
87C2×D47—21no—
88C2×D47—21no—
89C2×D47—21no—
90C4×C47—42no—
91C4×C47—42no—
92C4×C47#13712yes—
93C4×C47#13712yes—
94C4×C47C2×#4112yes—
95Dic47—21no—
96Dic47—21no—
97Dic47—21no—
98Dic47—42no—
99Dic47—42no—
100#3185—471nomaximal, Sylow
101C2×C47#53211yescharacteristic
102C2×C47C2×#13711yescharacteristic
103C2×C47C2×#13711yescharacteristic
104D47—41no—
105#533—471no—
106#533—471no—
107#498—471no—
108#494—471no—
109#487—471no—
110#487D4711yescharacteristic, complemented
111#470—474no—
112#441—474no—
113C4×M16—471no—
114C47#318511yescharacteristic, complemented, Sylow
115C2×Q16—474no—
116C2×M16—472no—
117C4⋊Q8—471no—
118C4⋊Q8—471no—
119C4⋊Q8C2×D4711yescharacteristic
120C4⋊Q8C2×D4711yescharacteristic
121#125—941no—
122#125—941no—
123C22⋊Q8—472no—
124C22⋊Q8—472no—
125C22⋊Q8—941no—
126C22⋊Q8—941no—
127C4×Q8—472no—
128C4×Q8—472no—
129C4×Q8—941no—
130C4×Q8—941no—
131#117—941no—
132#117—941no—
133C2×C42—471no—
134#106—474no—
135#103—474no—
136#103C2×D4714yes—
137#97—472no—
138C4×C8—471no—
139C4×C8C2×D4711yescharacteristic
140C2×Q8—21no—
141C2×Q8—472no—
142C2×Q8—941no—
143C2×Q8C22×D4712yes—
144C22×C4—471no—
145C22×C4—471no—
146C22×C4—471no—
147Q16—948no—
148M16—944no—
149C2×C8—472no—
150C2×C8C22×D4712yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—472no—
155C4⋊C4—942no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4—941no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4C22×D4712yes—
163C22⋊C4—942no—
164C22⋊C4—942no—
165C42—471no—
166C42—471no—
167C42—471no—
168C42—942no—
169C42—942no—
170C42C22×D4711yescharacteristic
171C23—471no—
172Q8—24no—
173Q8—42no—
174Q8—944no—
175Q8—1882no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—471no—
179C2×C4—471no—
180C2×C4—471no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4D4×D4711yescharacteristic
187C2×C4D4×D4711yescharacteristic
188C2×C4C23×D4711yescharacteristic
189C8—22no—
190C8—474no—
191C22—941no—
192C22—941no—
193C22—941no—
194C22C2×D4×D4711yescharacteristic
195C4—42no—
196C4—42no—
197C4—941no—
198C4—941no—
199C4—941no—
200C4—1882no—
201C4—1882no—
202C4#1309405312yes—
203C4#1309405612yes—
204C4#41×D4712yes—
205C2—1881no—
206C2#1568967211yescharacteristic
207C2C2×#1309405311yescharacteristic
208C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#487C2
socleC22×C47C22×D4
hypercenter#487D47
hypocenterC47#3185
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #15689519C2semidirect
4. #15689502C2semidirect
5. #15689474C2semidirect
7. #15689227C2semidirect
9. C47×#487C2semidirect
110. #487D47semidirect
114. C47#3185semidirect