Finite Group Databasebeta

← #20249269

Subgroups — #20249269

Order 6016.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#13094015C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689064C212yesmaximal
4#15689063C211yesmaximal, characteristic
5#15689062C211yesmaximal, characteristic
6#15689054C211yesmaximal, characteristic
7#15689043C212yesmaximal
8#15689010C212yesmaximal
9#15689009C212yesmaximal
10#15688990C211yesmaximal, characteristic
11C47×#398C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13#13094015—24no—
14#13093989—24no—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C2×C4×Dic47C2211yescharacteristic
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2212yes—
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C22×C4×C47C2312yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×Dic94—22no—
49C2×Dic94—22no—
50C2×Dic94—22no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—24no—
54C4⋊Dic47—22no—
55C4⋊Dic47—24no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—24no—
59Dic47⋊C4—24no—
60C4×Dic47—22no—
61C4×Dic47—22no—
62C4×Dic47D414yes—
63C23×C47C2411yescharacteristic
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
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×C47C2×D412yes—
76C2×C4×C47#4112yes—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—24no—
88C2×Dic47—22no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91C2×Dic47#4112yes—
92Dic94—28no—
93C22×C47C22×D411yescharacteristic
94C22×C47C2×#4111yescharacteristic
95C22×C47C2×#4111yescharacteristic
96C22×C472−1+412yes—
97C22×C472−1+412yes—
98C4×C47—22no—
99C4×C47—22no—
100C4×C47—42no—
101C4×C47—41no—
102C4×C47—42no—
103Dic47—22no—
104Dic47—22no—
105Dic47—22no—
106Dic47—41no—
107Dic47—42no—
108Dic47—42no—
109#2634—471nomaximal, Sylow
110C2×C47#52511yescharacteristic
111C2×C47#53611yescharacteristic
112C2×C47#53611yescharacteristic
113C2×C47#54112yes—
114C2×C47#54112yes—
115C2×#125—471no—
116C2×C4×Q8—471no—
117#400—471no—
118#400—471no—
119#400—472no—
120#398—471no—
121#398D4711yescharacteristic
122#395—472no—
123#387—472no—
124#387—472no—
125#383—471no—
126C47#263411yescharacteristic, complemented, Sylow
127C22×Q8—471no—
128#125—944no—
129C4×Q8—944no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4—471no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4—472no—
136C2×C4⋊C4C2×D4711yescharacteristic
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C4⋊C4C2×D4712yes—
139C2×C42—471no—
140C2×C42—471no—
141C2×C42—471no—
142#95—472no—
143#95—472no—
144#95—471no—
145#95—472no—
146#95—472no—
147#95—472no—
148#95—472no—
149#95—472no—
150#95C2×D4711yescharacteristic
151#95C2×D4712yes—
152C2×Q8—942no—
153C2×Q8—942no—
154C2×Q8—942no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—472no—
159C22×C4—471no—
160C22×C4—472no—
161C22×C4C22×D4712yes—
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4712yes—
164C22×C4C22×D4711yescharacteristic
165C22×C4C22×D4711yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—24no—
169C4⋊C4—944no—
170C4⋊C4—942no—
171C4⋊C4—944no—
172C4⋊C4—944no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C42—474no—
176C42—942no—
177C42—942no—
178C23C23×D4711yescharacteristic
179Q8—948no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—472no—
192C2×C4—472no—
193C2×C4—472no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—942no—
199C2×C4—941no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—944no—
206C2×C4D4×D4712yes—
207C2×C4#1062535212yes—
208C22C2×D4×D4711yescharacteristic
209C22#41×D4711yescharacteristic
210C22C2×#1062535211yescharacteristic
211C22#1309407112yes—
212C22#1309407212yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—42no—
217C4—41no—
218C4—942no—
219C4—942no—
220C4—942no—
221C4—1882no—
222C4—1881no—
223C4—1882no—
224C2#1568963311yescharacteristic
225C2#1568969511yescharacteristic
226C2#1568969811yescharacteristic
227C2#1568973212yes—
228C2#1568973312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#398C2
hypercenter#398D47
hypocenterC47#2634
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
126. C47#2634semidirect