Finite Group Databasebeta

← #20248749

Subgroups — #20248749

Order 6016.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×Q8×Dic47C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689063C211yesmaximal, characteristic
4#15689062C211yesmaximal, characteristic
5#15689042C211yesmaximal, characteristic
6#15689027C212yesmaximal
7#15689018C212yesmaximal
8#15689010C212yesmaximal
9#15689009C212yesmaximal
10#15688987C211yesmaximal, characteristic
11C47×#395C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13Q8×Dic47—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×Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2211yescharacteristic
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C4⋊C4×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C2×Q8×C47—22no—
38C2×Q8×C47—24no—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×Dic94—22no—
51C2×Dic94—22no—
52C2×Dic94Q814yescomplemented
53C4⋊C4×C47—22no—
54C4⋊C4×C47—24no—
55C4⋊Dic47—22no—
56C4⋊Dic47—24no—
57Dic47⋊C4—22no—
58Dic47⋊C4—24no—
59Dic47⋊C4—22no—
60Dic47⋊C4—24no—
61C4×Dic47—22no—
62C4×Dic47—22no—
63C4×Dic47—24no—
64C4×Dic47D414yes—
65C23×C47C2411yescharacteristic
66Q8×C47—28no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×Q812yes—
79C2×C4×C47#4114yes—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—24no—
89C2×Dic47—22no—
90C2×Dic47C2×D412yes—
91C2×Dic47C2×D412yes—
92C2×Dic47C2×Q812yes—
93C2×Dic47C2×Q812yes—
94C2×Dic47#4112yes—
95Dic94—28no—
96C22×C47C22×D411yescharacteristic
97C22×C47C22×Q811yescharacteristic
98C22×C47C2×#4111yescharacteristic
99C22×C47C2×#4112yes—
100C22×C472−1+412yes—
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—24no—
104C4×C47—41no—
105C4×C47—42no—
106Dic47—22no—
107Dic47—22no—
108Dic47—41no—
109Dic47—42no—
110Dic47—42no—
111Dic47C22⋊Q814yes—
112#2581—471nomaximal, Sylow
113C2×C47C2×C22⋊Q811yescharacteristic
114C2×C47#52511yescharacteristic
115C2×C47#53611yescharacteristic
116C2×C47#55612yes—
117C2×C47#55712yes—
118C2×C4×Q8—471no—
119C2×C4×Q8—471no—
120#400—471no—
121#400—471no—
122#395—471no—
123#395D4711yescharacteristic
124#391—472no—
125#389—472no—
126#387—472no—
127#387—472no—
128#382—471no—
129C47#258111yescharacteristic, complemented, Sylow
130C22×Q8—471no—
131C22×Q8C2×D4711yescharacteristic
132C4×Q8—944no—
133C4×Q8—944no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—472no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4C2×D4711yescharacteristic
141C2×C4⋊C4C2×D4712yes—
142C2×C42—471no—
143C2×C42—471no—
144C2×C42—471no—
145C2×C42—472no—
146#95—472no—
147#95—471no—
148#95—472no—
149#95—472no—
150#95—472no—
151#95—472no—
152#95—472no—
153#95C2×D4711yescharacteristic
154#95C2×D4712yes—
155C2×Q8—22no—
156C2×Q8—24no—
157C2×Q8—474no—
158C2×Q8—942no—
159C2×Q8—942no—
160C22×C4—471no—
161C22×C4—471no—
162C22×C4—471no—
163C22×C4—472no—
164C22×C4—472no—
165C22×C4—471no—
166C22×C4C22×D4712yes—
167C22×C4C22×D4711yescharacteristic
168C22×C4C22×D4711yescharacteristic
169C22×C4C22×D4712yes—
170C22×C4C22×D4711yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—24no—
173C4⋊C4—944no—
174C4⋊C4—942no—
175C4⋊C4—944no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—944no—
179C42—474no—
180C42—942no—
181C42—944no—
182C42—942no—
183C23C23×D4711yescharacteristic
184Q8—28no—
185Q8—948no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—472no—
197C2×C4—472no—
198C2×C4—472no—
199C2×C4—472no—
200C2×C4—472no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—942no—
204C2×C4—941no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—944no—
211C2×C4D4×D4712yes—
212C2×C4#1062535214yes—
213C2×C4Q8×D4712yes—
214C22C2×D4×D4711yescharacteristic
215C22C2×Q8×D4711yescharacteristic
216C22#41×D4711yescharacteristic
217C22C2×#1062535212yes—
218C22#1309407212yes—
219C4—22no—
220C4—22no—
221C4—24no—
222C4—42no—
223C4—41no—
224C4—474no—
225C4—942no—
226C4—942no—
227C4—1882no—
228C4—1881no—
229C4—1882no—
230C2C22⋊Q8×D4711yescharacteristic
231C2#1568962911yescharacteristic
232C2#1568969811yescharacteristic
233C2#1568984412yes—
234C2#1568984812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2581
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
52. C2×Dic94Q8semidirect
129. C47#2581semidirect