Finite Group Databasebeta

← #20249170

Subgroups — #20249170

Order 6016.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×C4⋊Dic47C211yesmaximal, characteristic, complemented
2#15689062C212yesmaximal, complemented
3#15689059C212yesmaximal, complemented
4#15689053C212yesmaximal, complemented
5#15689048C212yesmaximal, complemented
6#15689003C212yesmaximal
7#15688995C212yesmaximal, complemented
8#15688986C211yesmaximal, characteristic, complemented
9C2×#123×C47C211yesmaximal, characteristic
10C23×Dic47C2212yes—
11C2×C4⋊Dic47—24no—
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2212yes—
14C2×Dic47⋊C4C2214yes—
15C2×C22⋊Dic47C2212yes—
16C2×C22⋊Dic47C2214yes—
17C47⋊#95C2212yes—
18C47⋊#95C2212yes—
19C47⋊#95C2214yes—
20C47⋊#95C2214yes—
21C22×D4×C47C2211yescharacteristic
22C23×C4×C47C2211yescharacteristic
23#123×C47—24no—
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2211yescharacteristic
29C24×C47C2311yescharacteristic
30C24×C47C2311yescharacteristic
31C2×D4×C47—22no—
32C2×D4×C47—24no—
33C22×C4×C47—24no—
34C22×C4×C47D414yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×Dic47—24no—
41C22×Dic47—44no—
42C22×Dic47C2314yes—
43C22×Dic47C2314yes—
44C4⋊C4×C47—22no—
45C4⋊C4×C47—22no—
46C22⋊C4×C47—22no—
47C22⋊C4×C47—22no—
48C22⋊C4×C47—22no—
49C22⋊Dic47—24no—
50C22⋊Dic47—44no—
51C4⋊Dic47—24no—
52C4⋊Dic47—24no—
53Dic47⋊C4—44no—
54C23×C47—22no—
55C23×C47—22no—
56C23×C47—21no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47—22no—
60C23×C47C2×D412yes—
61C23×C47#4114yes—
62C23×C47C2411yescharacteristic
63D4×C47—44no—
64C2×C4×C47—28no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D412yes—
75C2×Dic47—24no—
76C2×Dic47—24no—
77C2×Dic47—24no—
78C2×Dic47—24no—
79C2×Dic47—24no—
80C2×Dic47—24no—
81C2×Dic47—48no—
82C22×C47—22no—
83C22×C47—22no—
84C22×C47—28no—
85C22×C47—41no—
86C22×C47—41no—
87C22×C47—41no—
88C22×C47—44no—
89C22×C47#12314yes—
90C22×C47C22×D411yescharacteristic
91C22×C47C2×#4112yes—
92C22×C47H(5,𝔽2)12yes—
93C22×C472−1+412yes—
94C4×C47—22no—
95C4×C47—22no—
96C4×C47—41no—
97C4×C47—41no—
98C4×C47—41no—
99Dic47—44no—
100Dic47—44no—
101#2623—471nomaximal, Sylow
102C2×C47—24no—
103C2×C47—81no—
104C2×C47C2×#12311yescharacteristic
105C2×C47#53511yescharacteristic
106C2×C47#53611yescharacteristic
107C2×C47#53914yes—
108C2×#123D4711yescharacteristic
109C22×C4⋊C4—471no—
110#400—472no—
111#399—472no—
112#398—472no—
113#397—472no—
114#386—472no—
115#385—472no—
116#381—471no—
117C47#262311yescharacteristic, complemented, Sylow
118C22×D4C2×D4711yescharacteristic
119C23×C4—472no—
120C23×C4C2×D4711yescharacteristic
121#123—24no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—474no—
125C2×C4⋊C4—944no—
126C2×C4⋊C4C2×D4711yescharacteristic
127C2×C4⋊C4C2×D4711yescharacteristic
128C2×C22⋊C4—472no—
129C2×C22⋊C4—474no—
130C2×C22⋊C4C2×D4711yescharacteristic
131C2×C22⋊C4C2×D4711yescharacteristic
132C2×C22⋊C4C2×D4711yescharacteristic
133#95—472no—
134#95—472no—
135#95—474no—
136#95—474no—
137C24C22×D4711yescharacteristic
138C24C22×D4711yescharacteristic
139C2×D4—24no—
140C2×D4—22no—
141C22×C4—24no—
142C22×C4—474no—
143C22×C4—474no—
144C22×C4—944no—
145C22×C4—1884no—
146C22×C4C22⋊D4714yes—
147C22×C4C22×D4711yescharacteristic
148C22×C4C22×D4711yescharacteristic
149C22×C4C22×D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—944no—
155C4⋊C4—944no—
156C4⋊C4—1884no—
157C22⋊C4—22no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—944no—
161C22⋊C4—1884no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23—22no—
166C23—22no—
167C23—22no—
168C23#1062535214yes—
169C23C2×C22⋊D4712yes—
170C23C23×D4711yescharacteristic
171D4—44no—
172C2×C4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—944no—
182C2×C4—944no—
183C2×C4—944no—
184C2×C4—944no—
185C2×C4—944no—
186C2×C4—944no—
187C2×C4—1888no—
188C2×C4C2×C22⋊D4712yes—
189C2×C4C2×C22⋊D4712yes—
190C22—22no—
191C22—22no—
192C22—28no—
193C22—41no—
194C22—41no—
195C22—41no—
196C22—44no—
197C22#1309400514yes—
198C22C22×C22⋊D4711yescharacteristic
199C22C2×#1062535212yes—
200C22#1309407012yes—
201C22#1309407112yes—
202C4—22no—
203C4—22no—
204C4—41no—
205C4—41no—
206C4—41no—
207C4—1884no—
208C4—1884no—
209C2—24no—
210C2—81no—
211C2C2×#1309400511yescharacteristic
212C2#1568968711yescharacteristic
213C2#1568969411yescharacteristic
214C2#1568971714yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#123×C47C2
hypercenterC2×#123D47
hypocenterC47#2623
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊Dic47C2semidirect
2. #15689062C2semidirect
3. #15689059C2semidirect
4. #15689053C2semidirect
5. #15689048C2semidirect
7. #15688995C2semidirect
8. #15688986C2semidirect
117. C47#2623semidirect