Finite Group Databasebeta

← #20253519

Subgroups — #20253519

Order 6016.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689680C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic
3#15689454C212yesmaximal
4#15689409C212yesmaximal, complemented
5#15689334C212yesmaximal, complemented
6#15689281C212yesmaximal
7#15689231C214yesmaximal, complemented
8C47×#432C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic
10C2×Dic188C2214yes—
11#13094024C2211yescharacteristic
12#13094024C2211yescharacteristic
13#13094016—21no—
14#13094003—21no—
15#13094003C2212yes—
16C4×Dic94—21no—
17C4×Dic94—21no—
18C4×Dic94—21no—
19C4×Dic94C2212yes—
20C4×Dic94C2212yes—
21C4×Dic94C2212yes—
22#13093983—21no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4—21no—
25C2×C4×Dic47—21no—
26#13093956C2214yes—
27#13093949C2214yes—
28#13093949C2214yes—
29C2×C42×C47C2211yescharacteristic
30C4⋊C8×C47C2212yes—
31C22⋊C8×C47C2212yes—
32#97×C47C2212yes—
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47—21no—
38C2×Dic94—21no—
39C2×Dic94—24no—
40C2×Dic94—21no—
41C2×Dic94C2312yes—
42C2×Dic94C2312yes—
43C2×C8×C47C2314yes—
44C42×C47D411yescharacteristic
45C42×C47D411yescharacteristic
46C42×C47C2311yescharacteristic
47C42×C47C2311yescharacteristic
48C22⋊Dic47—22no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47C2312yes—
54C4⋊Dic47C2312yes—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59C4×Dic47—22no—
60C4×Dic47—22no—
61C4×Dic47—22no—
62Dic188—28no—
63C23×C47C2×D411yescharacteristic
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2411yescharacteristic
73C2×Dic47—24no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—42no—
79Dic94—24no—
80Dic94—22no—
81Dic94—24no—
82Dic94—42no—
83Dic94#4114yes—
84C8×C47—24no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47#13712yes—
88C22×C47C22×D411yescharacteristic
89C4×C47—21no—
90C4×C47—21no—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47#13712yes—
94C4×C47C2×#4112yes—
95Dic47—24no—
96Dic47—42no—
97Dic47—42no—
98Dic47—42no—
99#3113—471nomaximal, Sylow
100C2×C47—22no—
101C2×C47#52511yescharacteristic
102C2×C47C2×#13711yescharacteristic
103C2×C47C2×#13711yescharacteristic
104#533—471no—
105C2×C4×Q8—471no—
106#483—472no—
107#475—472no—
108#462—472no—
109#451—472no—
110#441—474no—
111#432D4711yescharacteristic
112C47#311311yescharacteristic, complemented, Sylow
113C22×Q8—471no—
114C2×Q16—474no—
115C4⋊Q8—471no—
116C4⋊Q8—471no—
117#125—941no—
118C22⋊Q8—472no—
119C22⋊Q8—941no—
120C4×Q8—472no—
121C4×Q8—472no—
122C4×Q8—472no—
123C4×Q8—941no—
124C4×Q8—941no—
125C4×Q8—941no—
126#117—941no—
127C2×C4⋊C4—471no—
128C2×C4⋊C4—941no—
129C2×C42—941no—
130C2×C42C2×D4711yescharacteristic
131#106—474no—
132C4⋊C8C2×D4712yes—
133#103—474no—
134#103—474no—
135C22⋊C8C2×D4712yes—
136#97C2×D4712yes—
137C2×Q8—472no—
138C2×Q8—472no—
139C2×Q8—944no—
140C2×Q8—941no—
141C2×Q8—941no—
142C22×C4—941no—
143C22×C4—941no—
144C22×C4D18811yescharacteristic
145C22×C4D18811yescharacteristic
146C22×C4C22×D4711yescharacteristic
147Q16—948no—
148C2×C8C22×D4714yes—
149C4⋊C4—472no—
150C4⋊C4—472no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4—941no—
156C4⋊C4—941no—
157C4⋊C4—941no—
158C4⋊C4—941no—
159C22⋊C4—942no—
160C42—942no—
161C42—942no—
162C42—942no—
163C42D18811yescharacteristic
164C42D18811yescharacteristic
165C42C22×D4711yescharacteristic
166C42C22×D4711yescharacteristic
167C23C2×D18811yescharacteristic
168Q8—474no—
169Q8—944no—
170Q8—942no—
171Q8—944no—
172Q8—1882no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—944no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—1882no—
182C2×C4C2×D18811yescharacteristic
183C2×C4C2×D18811yescharacteristic
184C2×C4C2×D18811yescharacteristic
185C2×C4C2×D18811yescharacteristic
186C2×C4C2×D18811yescharacteristic
187C2×C4C23×D4711yescharacteristic
188C8—24no—
189C22—21no—
190C22—21no—
191C22#1309405712yes—
192C22C22×D18811yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—944no—
198C4—1882no—
199C4—1882no—
200C4—1882no—
201C4#1309405712yes—
202C4#41×D4712yes—
203C2—22no—
204C2#1568963511yescharacteristic
205C2C2×#1309405711yescharacteristic
206C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3113
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
4. #15689409C2semidirect
5. #15689334C2semidirect
7. #15689231C2semidirect
112. C47#3113semidirect