Finite Group Databasebeta

← #20246141

Subgroups — #20246141

Order 6016.

484 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 177 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×#13094003C211yesmaximal, characteristic
2#15689027C212yesmaximal, complemented
3#15689017C212yesmaximal
4#15689011C212yesmaximal
5#15689006C212yesmaximal, complemented
6#15689005C212yesmaximal, complemented
7#15688974C212yesmaximal, complemented
8C4×C22⋊Dic47C211yesmaximal, characteristic
9C47×#381C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11#13094003C418yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2212yes—
18C2×C4×Dic47C2212yes—
19C2×C4×Dic47C2211yescharacteristic
20C2×C4×Dic47C2211yescharacteristic
21C2×C4×Dic47C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C23×C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2211yescharacteristic
30#95×C47C2212yes—
31#95×C47C2212yes—
32C24×C47C2311yescharacteristic
33C22×C4×C47—41no—
34C22×C4×C47—41no—
35C22×C4×C47C2×C414yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C2×Dic94—41no—
45C2×Dic94—41no—
46C2×Dic94C2×C414yes—
47C22⋊C4×C47—41no—
48C22⋊C4×C47—41no—
49C22⋊Dic47—24no—
50C22⋊Dic47C2×C418yes—
51C4⋊Dic47C2×C414yes—
52Dic47⋊C4—24no—
53Dic47⋊C4—42no—
54Dic47⋊C4C2×C418yes—
55C4×Dic47—24no—
56C4×Dic47—41no—
57C4×Dic47—42no—
58C4×Dic47—41no—
59C23×C47—22no—
60C23×C47—21no—
61C23×C47—21no—
62C23×C47—22no—
63C23×C47C22×C412yes—
64C23×C47C2411yescharacteristic
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—44no—
76C2×C4×C47C22×C412yes—
77C2×C4×C47C22×C412yes—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47C22×C414yes—
88C2×Dic47C22×C414yes—
89C2×Dic47#4114yes—
90Dic94—44no—
91C22×C47—22no—
92C22×C47—22no—
93C22×C47—22no—
94C22×C47—42no—
95C22×C47—42no—
96C22×C47C23×C411yescharacteristic
97C22×C47C2×#4112yes—
98C22×C47H(5,𝔽2)11yescharacteristic
99C22×C47H(5,𝔽2)11yescharacteristic
100C22×C472−1+412yes—
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—42no—
104C4×C47—42no—
105Dic47—24no—
106Dic47—24no—
107Dic47—24no—
108Dic47—42no—
109#2332—471nomaximal, Sylow
110C2×C47—42no—
111C2×C47C4×#4111yescharacteristic
112C2×C47#51811yescharacteristic
113C2×C47#51911yescharacteristic
114C2×C47#53912yes—
115C2×C47#54212yes—
116C2×C22⋊Q8—471no—
117#391—472no—
118#388—472no—
119#388—472no—
120#387—472no—
121#387—472no—
122#381D4711yescharacteristic
123C4×C4⋊C4—472no—
124C4×C22⋊C4—471no—
125C47#233211yescharacteristic, complemented, Sylow
126C22×Q8—471no—
127C23×C4C2×D4711yescharacteristic
128C22⋊Q8—478no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4—472no—
132C2×C4⋊C4—472no—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C22⋊C4C2×D4711yescharacteristic
136C2×C22⋊C4C2×D4711yescharacteristic
137C2×C42—472no—
138C2×C42—471no—
139C2×C42—471no—
140C2×C42—472no—
141#95—472no—
142#95—472no—
143#95—472no—
144#95—472no—
145#95—472no—
146#95C2×D4712yes—
147#95C2×D4712yes—
148C24C22×D4711yescharacteristic
149C2×Q8—474no—
150C2×Q8—1881no—
151C2×Q8—1881no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—472no—
155C22×C4—472no—
156C22×C4—472no—
157C22×C4—472no—
158C22×C4C4×D4714yes—
159C22×C4C22×D4712yes—
160C22×C4C22×D4712yes—
161C22×C4C22×D4711yescharacteristic
162C22×C4C22×D4711yescharacteristic
163C4⋊C4—478no—
164C4⋊C4—474no—
165C4⋊C4—944no—
166C4⋊C4—1882no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—478no—
170C22⋊C4—944no—
171C42—944no—
172C42—1881no—
173C42—1881no—
174C42—1882no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D4712yes—
180C23C23×D4711yescharacteristic
181Q8—1884no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—44no—
193C2×C4—474no—
194C2×C4—474no—
195C2×C4—474no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4C2×C4×D4712yes—
206C2×C4C2×C4×D4712yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D4711yescharacteristic
213C22#41×D4712yes—
214C22#1309406911yescharacteristic
215C22#1309406911yescharacteristic
216C22#1309407112yes—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—42no—
221C4—944no—
222C4—944no—
223C4—944no—
224C4—1882no—
225C2—42no—
226C2#1568959111yescharacteristic
227C2#1568959611yescharacteristic
228C2#1568960011yescharacteristic
229C2#1568971612yes—
230C2#1568974112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#381C2
socleC23×C47C24
hypercenter#381D47
hypocenterC47#2332
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #15689027C2semidirect
5. #15689006C2semidirect
6. #15689005C2semidirect
7. #15688974C2semidirect
11. #13094003C4semidirect
125. C47#2332semidirect