Finite Group Databasebeta

← #20254548

Subgroups — #20254548

Order 6016.

326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689475C211yesmaximal, characteristic, complemented
5#15689474C211yesmaximal, characteristic, complemented
6#15689466C214yesmaximal
7#15689429C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic
9C47×#500C211yesmaximal, characteristic, complemented
10#13094024C2211yescharacteristic
11#13094024C2211yescharacteristic
12#13094015—21no—
13#13094015C2212yes—
14#13094004—21no—
15#13094004C2212yes—
16#13094000—21no—
17#13094000—21no—
18Q8×Dic47—21no—
19Q8×Dic47—21no—
20#13093989—21no—
21#13093989C2212yes—
22#13093982—21no—
23#13093982C2212yes—
24C42×D47C2211yescharacteristic
25#13093955C2214yes—
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—
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×C47C2312yes—
46C4⋊C4×C47C2312yes—
47C42×C47C2311yescharacteristic
48(C2×D47)⋊C4—22no—
49(C2×D47)⋊C4—22no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47—22no—
54C4⋊Dic47—22no—
55C4⋊Dic47C2312yes—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58C4×Dic47—22no—
59C4×Dic47—22no—
60C4×Dic47D411yescharacteristic
61C4×Dic47D411yescharacteristic
62C4×Dic47C2311yescharacteristic
63C2×C47⋊C8C2312yes—
64C22×D47C2×D411yescharacteristic
65Q8×C47—42no—
66Q8×C47—42no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2411yescharacteristic
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47C2×D411yescharacteristic
75C2×Dic47C2×D411yescharacteristic
76C2×Dic47C2×D411yescharacteristic
77C4×D47—22no—
78C4×D47—22no—
79C4×D47—22no—
80Dic94—24no—
81Dic94—42no—
82C8×C47—22no—
83C47⋊C8—22no—
84C22×C47C22×D411yescharacteristic
85C2×D47—21no—
86C2×D47—21no—
87C2×D47—21no—
88C4×C47—42no—
89C4×C47—42no—
90C4×C47#13512yes—
91C4×C47#13712yes—
92C4×C472−1+412yes—
93Dic47—21no—
94Dic47—21no—
95Dic47—21no—
96Dic47—42no—
97Dic47—42no—
98#3231—471nomaximal, Sylow
99C2×C47#53611yescharacteristic
100C2×C47C2×#13511yescharacteristic
101C2×C47C2×#13711yescharacteristic
102D47—41no—
103#533—471no—
104#533—471no—
105#500D4711yescharacteristic, complemented
106#498—471no—
107#487—471no—
108#487—471no—
109#485—474no—
110#479—474no—
111#431—471no—
112C47#323111yescharacteristic, complemented, Sylow
113C4⋊Q8—471no—
114C4⋊Q8—471no—
115C4⋊Q8C2×D4711yescharacteristic
116C4⋊Q8C2×D4711yescharacteristic
117#125—472no—
118#125—941no—
119C22⋊Q8—472no—
120C22⋊Q8—941no—
121C22⋊Q8—941no—
122C22⋊Q8—941no—
123C4×Q8—472no—
124C4×Q8—941no—
125C4×Q8—941no—
126C4×Q8—941no—
127#117—472no—
128#117—941no—
129C2×C42—471no—
130#107C2×D4714yes—
131#106—474no—
132C4⋊C8—472no—
133#103—474no—
134#103—474no—
135C22⋊C8—472no—
136C4×C8—471no—
137C4×C8C2×D4711yescharacteristic
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—472no—
141C2×Q8—941no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4—471no—
145C2×C8—472no—
146C2×C8C22×D4712yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—472no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—941no—
155C4⋊C4—941no—
156C4⋊C4—941no—
157C4⋊C4C22×D4712yes—
158C4⋊C4C22×D4712yes—
159C22⋊C4—942no—
160C22⋊C4—942no—
161C42—471no—
162C42—471no—
163C42—471no—
164C42—942no—
165C42—942no—
166C42C22×D4711yescharacteristic
167C23—471no—
168Q8—42no—
169Q8—42no—
170Q8—944no—
171Q8—1882no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—471no—
175C2×C4—471no—
176C2×C4—471no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4D4×D4711yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C2×C4C23×D4711yescharacteristic
185C8—22no—
186C8—942no—
187C22—941no—
188C22—941no—
189C22—941no—
190C22C2×D4×D4711yescharacteristic
191C4—42no—
192C4—42no—
193C4—941no—
194C4—941no—
195C4—941no—
196C4—1882no—
197C4—1882no—
198C4#1309404312yes—
199C4#1309405612yes—
200C4#1309407212yes—
201C2—1881no—
202C2#1568969811yescharacteristic
203C2C2×#1309404311yescharacteristic
204C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#500C2
socleC22×C47C22×D4
hypercenter#500D47
hypocenterC47#3231
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. #15689519C2semidirect
4. #15689475C2semidirect
5. #15689474C2semidirect
7. #15689429C2semidirect
9. C47×#500C2semidirect
105. #500D47semidirect
112. C47#3231semidirect