Finite Group Databasebeta

← #20249582

Subgroups — #20249582

Order 6016.

408 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 141 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#15689059C212yesmaximal
2#15689057C212yesmaximal, complemented
3#15689055C212yesmaximal, complemented
4#15689046C212yesmaximal
5#15689021C212yesmaximal, complemented
6#15689007C212yesmaximal, complemented
7#15688986C211yesmaximal, characteristic
8#15688983C211yesmaximal, characteristic
9C4×C22⋊C4×C47C211yesmaximal, characteristic
10C2×C4⋊Dic47C2212yes—
11C2×C4⋊Dic47C2212yes—
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×C22⋊Dic47C2211yescharacteristic
18C2×C22⋊Dic47C2211yescharacteristic
19C2×C22⋊Dic47C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2211yescharacteristic
22C47⋊#95C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C23×C4×C47C2211yescharacteristic
27C2×C22⋊C4×C47C2212yes—
28C2×C42×C47C2212yes—
29#95×C47C2211yescharacteristic
30#95×C47C2211yescharacteristic
31C24×C47C2311yescharacteristic
32C22×C4×C47—42no—
33C22×C4×C47Q814yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22⋊C4×C47—24no—
43C42×C47—42no—
44C22⋊Dic47—41no—
45C22⋊Dic47—41no—
46C22⋊Dic47—42no—
47C4⋊Dic47—24no—
48C4⋊Dic47—42no—
49C4⋊Dic47—42no—
50Dic47⋊C4—24no—
51Dic47⋊C4—42no—
52Dic47⋊C4—42no—
53Dic47⋊C4—42no—
54C23×C47—22no—
55C23×C47—21no—
56C23×C47—22no—
57C23×C47—21no—
58C23×C47C2×Q812yes—
59C23×C47C2411yescharacteristic
60C2×C4×C47—22no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—44no—
68C2×C4×C47C2×Q812yes—
69C2×C4×C47C2×Q812yes—
70C2×C4×C47#4114yes—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C22×C47—22no—
84C22×C47—22no—
85C22×C47—22no—
86C22×C47—42no—
87C22×C47—42no—
88C22×C47C22×Q811yescharacteristic
89C22×C47C2×#4112yes—
90C22×C47H(5,𝔽2)12yes—
91C22×C47H(5,𝔽2)11yescharacteristic
92C22×C472−1+411yescharacteristic
93C4×C47—24no—
94C4×C47—22no—
95C4×C47—22no—
96C4×C47—42no—
97Dic47—42no—
98Dic47—42no—
99Dic47—42no—
100Dic47—42no—
101#2667—471nomaximal, Sylow
102C2×C47—42no—
103C2×C47#53311yescharacteristic
104C2×C47#53912yes—
105C2×C47#54012yes—
106C2×C47#54311yescharacteristic
107C2×C47#54411yescharacteristic
108#399—472no—
109#398—472no—
110#398—472no—
111#396—472no—
112#389—472no—
113#387—472no—
114#381—471no—
115#380—471no—
116C4×C22⋊C4D4711yescharacteristic
117C47#266711yescharacteristic, complemented, Sylow
118C23×C4C2×D4711yescharacteristic
119C2×C4⋊C4—472no—
120C2×C4⋊C4—472no—
121C2×C4⋊C4—472no—
122C2×C4⋊C4—472no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C22⋊C4—471no—
127C2×C22⋊C4—471no—
128C2×C22⋊C4—472no—
129C2×C22⋊C4C2×D4712yes—
130C2×C42C2×D4712yes—
131#95—472no—
132#95—471no—
133#95—471no—
134#95—472no—
135#95—472no—
136#95—472no—
137#95C2×D4711yescharacteristic
138#95C2×D4711yescharacteristic
139C24C22×D4711yescharacteristic
140C22×C4—42no—
141C22×C4—472no—
142C22×C4—472no—
143C22×C4—472no—
144C22×C4—472no—
145C22×C4Dic9414yes—
146C22×C4C22×D4712yes—
147C22×C4C22×D4711yescharacteristic
148C22×C4C22×D4711yescharacteristic
149C22×C4C22×D4712yes—
150C4⋊C4—944no—
151C4⋊C4—944no—
152C4⋊C4—1882no—
153C4⋊C4—1882no—
154C4⋊C4—1882no—
155C4⋊C4—1882no—
156C4⋊C4—1882no—
157C22⋊C4—24no—
158C22⋊C4—1882no—
159C22⋊C4—1881no—
160C22⋊C4—1881no—
161C42—42no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23C2×Dic9412yes—
167C23C23×D4711yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—44no—
176C2×C4—942no—
177C2×C4—942no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4C2×Dic9412yes—
189C2×C4C2×Dic9412yes—
190C2×C4#1062535014yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22C22×Dic9411yescharacteristic
197C22C2×#1062535012yes—
198C22#1309406912yes—
199C22#1309407011yescharacteristic
200C22#1309407111yescharacteristic
201C4—22no—
202C4—22no—
203C4—24no—
204C4—42no—
205C4—1882no—
206C4—1882no—
207C4—1882no—
208C4—1882no—
209C2—42no—
210C2#1568968011yescharacteristic
211C2#1568971512yes—
212C2#1568972412yes—
213C2#1568974911yescharacteristic
214C2#1568975111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C22⋊C4×C47C2
hypercenterC4×C22⋊C4D47
hypocenterC47#2667
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #15689057C2semidirect
3. #15689055C2semidirect
5. #15689021C2semidirect
6. #15689007C2semidirect
117. C47#2667semidirect