Finite Group Databasebeta

← #20244919

Subgroups — #20244919

Order 6016.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#13093956C211yesmaximal, characteristic, complemented
2C2×#13093955C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic
4#15689026C211yesmaximal, characteristic
5#15688992C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—22no—
12C2×C22⋊Dic47—22no—
13C2×C4×Dic47C2211yescharacteristic
14#13093956—22no—
15#13093955—22no—
16#13093945—22no—
17C22×D4×C47C2211yescharacteristic
18C22×C8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20#102×C47—22no—
21C24×C47—21no—
22C2×D4×C47—21no—
23C2×D4×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47Q812yes—
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47D412yes—
33C2×C8×C47—21no—
34C2×C8×C47—21no—
35C2×C8×C47D412yes—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C22⋊Dic47—44no—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43Dic47⋊C4—44no—
44C4×Dic47—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8D412yes—
49C23×C47—22no—
50C23×C47—41no—
51C23×C47—41no—
52C23×C47—42no—
53C23×C47—42no—
54C23×C47C2×D411yescharacteristic
55D4×C47—22no—
56D4×C47—22no—
57D4×C47—41no—
58D4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—42no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×Q811yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47—42no—
72C2×Dic47—42no—
73C2×Dic47SD1614yes—
74C8×C47—22no—
75C47⋊C8—22no—
76C22×C47—42no—
77C22×C47—44no—
78C22×C47—82no—
79C22×C47—81no—
80C22×C47—81no—
81C22×C47C22⋊Q811yescharacteristic
82C22×C47#12311yescharacteristic
83C22×C47#12711yescharacteristic
84C22×C47C2×SD1612yes—
85C22×C47AGL(1,ℤ/8)12yes—
86C4×C47—81no—
87C4×C47C22⋊Q811yescharacteristic
88C4×C47C22⋊Q811yescharacteristic
89C4×C47#12311yescharacteristic
90C4×C47#12311yescharacteristic
91Dic47—24no—
92Dic47—81no—
93Dic47—81no—
94#2094—471nomaximal, Sylow
95C2×C47—82no—
96C2×C47#39911yescharacteristic
97C2×C47#47612yes—
98C2×C47#48112yes—
99C2×C47#49211yescharacteristic
100C2×C47#49611yescharacteristic
101C2×#106—471no—
102C2×#106—471no—
103C2×#102—471no—
104C2×#102D4711yescharacteristic
105#390—471no—
106#384—471no—
107#336—471no—
108C47#209411yescharacteristic, complemented, Sylow
109C22×D4C2×D4711yescharacteristic
110C22×C8—471no—
111C22×C8C2×D4711yescharacteristic
112C2×C4⋊C4—471no—
113C2×C4⋊C4—471no—
114C2×C4⋊C4—942no—
115C2×C4⋊C4C2×D4711yescharacteristic
116C2×C22⋊C4—942no—
117C2×C42—471no—
118#106—942no—
119#106—942no—
120#102—22no—
121#102—942no—
122C24—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4Dic9412yes—
129C22×C4—21no—
130C22×C4—472no—
131C22×C4—941no—
132C22×C4—941no—
133C22×C4C22×D4711yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—472no—
137C2×C8—941no—
138C2×C8—941no—
139C2×C8C22⋊D4712yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—941no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C4⋊C4—1884no—
147C22⋊C4—1884no—
148C42—941no—
149C42—941no—
150C23—22no—
151C23—41no—
152C23—41no—
153C23—42no—
154C23—42no—
155C23D4×D4711yescharacteristic
156D4—22no—
157D4—22no—
158D4—41no—
159D4—41no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—474no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—1881no—
166C2×C4—1881no—
167C2×C4—1882no—
168C2×C4—1882no—
169C2×C4C2×Dic9411yescharacteristic
170C2×C4#1062535011yescharacteristic
171C2×C4D4×D4711yescharacteristic
172C2×C4#1062535211yescharacteristic
173C2×C4#1062535211yescharacteristic
174C2×C4C2×C22⋊D4711yescharacteristic
175C8—22no—
176C8—942no—
177C22—42no—
178C22—44no—
179C22—81no—
180C22—81no—
181C22—82no—
182C22#1309400111yescharacteristic
183C22#1309400611yescharacteristic
184C22#1309402011yescharacteristic
185C22SD16×D4712yes—
186C22#1309404812yes—
187C4—81no—
188C4—944no—
189C4—3761no—
190C4—3761no—
191C4#1309400111yescharacteristic
192C4#1309400311yescharacteristic
193C4#1309400511yescharacteristic
194C4#1309400611yescharacteristic
195C2—82no—
196C2#1568905911yescharacteristic
197C2#1568941112yes—
198C2#1568944012yes—
199C2#1568949411yescharacteristic
200C2#1568951111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2094
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#13093956C2semidirect
2. C2×#13093955C2semidirect
5. #15688992C2semidirect
6. #15688877C2semidirect
108. C47#2094semidirect