Finite Group Databasebeta

← #20246655

Subgroups — #20246655

Order 6016.

528 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 155 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, complemented
2C2×#13093980C211yesmaximal, characteristic
3#15689063C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic
5#15689057C212yesmaximal, complemented
6#15689046C212yesmaximal
7#15689042C211yesmaximal, characteristic, complemented
8#15688974C211yesmaximal, characteristic, complemented
9#15688974C212yesmaximal, complemented
10C22⋊C4×Dic47C212yesmaximal
11C47×#393C211yesmaximal, characteristic
12C23×Dic47C2211yescharacteristic
13Q8×Dic47—24no—
14#13093980—24no—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C4×Dic47C2212yes—
25C2×C4×Dic47C2212yes—
26C2×C4×Dic47C2211yescharacteristic
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2211yescharacteristic
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2212yes—
34C2×C22⋊C4×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C2×Q8×C47—22no—
39C2×Q8×C47—24no—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×Dic47—22no—
45C22×Dic47—22no—
46C22×Dic47Q814yescomplemented
47C22×Dic47C2311yescharacteristic
48C22×Dic47C2312yes—
49C22×Dic47C2311yescharacteristic
50C22×Dic47C2311yescharacteristic
51C22×Dic47C2312yes—
52C22×Dic47C2311yescharacteristic
53C22⋊C4×C47—22no—
54C22⋊C4×C47—24no—
55C22⋊Dic47—22no—
56C22⋊Dic47—24no—
57C4⋊Dic47—22no—
58C4⋊Dic47—24no—
59Dic47⋊C4—22no—
60Dic47⋊C4—24no—
61Dic47⋊C4—22no—
62Dic47⋊C4—24no—
63Dic47⋊C4—24no—
64C4×Dic47—22no—
65C4×Dic47—24no—
66C4×Dic47—24no—
67C4×Dic47D414yes—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47C2×Q812yes—
73C23×C47C2411yescharacteristic
74Q8×C47—28no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D412yes—
84C2×C4×C47#4114yes—
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—28no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47C2×D412yes—
97C2×Dic47C2×D412yes—
98C2×Dic47C2×Q812yes—
99C2×Dic47C2×Q812yes—
100C2×Dic47#4114yes—
101C2×Dic47#4112yes—
102C22×C47—22no—
103C22×C47—24no—
104C22×C47—41no—
105C22×C47—42no—
106C22×C47—41no—
107C22×C47C22×D411yescharacteristic
108C22×C47C22×Q811yescharacteristic
109C22×C47C2×#4111yescharacteristic
110C22×C47C2×#4112yes—
111C22×C47C2×#4112yes—
112C4×C47—22no—
113C4×C47—24no—
114C4×C47—42no—
115C4×C47—41no—
116Dic47—22no—
117Dic47—24no—
118Dic47—22no—
119Dic47—41no—
120Dic47—42no—
121Dic47C22⋊Q814yes—
122#2396—471nomaximal, Sylow
123C2×C47—42no—
124C2×C47C2×C22⋊Q811yescharacteristic
125C2×C47#52511yescharacteristic
126C2×C47#52912yes—
127C2×C47#53211yescharacteristic
128C2×C47#53312yes—
129C2×C4×Q8—471no—
130C2×#117—471no—
131#400—471no—
132#399—471no—
133#398—472no—
134#396—472no—
135#395—471no—
136#393D4711yescharacteristic
137C4×C4⋊C4—471no—
138C4×C4⋊C4—472no—
139C4×C22⋊C4—472no—
140C47#239611yescharacteristic, complemented, Sylow
141C22×Q8C2×D4711yescharacteristic
142C23×C4—471no—
143C4×Q8—944no—
144#117—944no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4—471no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—472no—
150C2×C4⋊C4—472no—
151C2×C4⋊C4—472no—
152C2×C22⋊C4—471no—
153C2×C22⋊C4—472no—
154C2×C22⋊C4C2×D4711yescharacteristic
155C2×C22⋊C4C2×D4712yes—
156C2×C42—471no—
157C2×C42—471no—
158C2×C42—472no—
159C2×C42—472no—
160#95—472no—
161#95—472no—
162#95—471no—
163#95—472no—
164#95C2×D4712yes—
165#95C2×D4711yescharacteristic
166C24C22×D4711yescharacteristic
167C2×Q8—22no—
168C2×Q8—24no—
169C22×C4—471no—
170C22×C4—474no—
171C22×C4—471no—
172C22×C4—472no—
173C22×C4—471no—
174C22×C4—471no—
175C22×C4—472no—
176C22×C4—942no—
177C22×C4—942no—
178C22×C4C22×D4712yes—
179C22×C4C22×D4711yescharacteristic
180C22×C4C22×D4711yescharacteristic
181C22×C4C22×D4712yes—
182C4⋊C4—944no—
183C4⋊C4—944no—
184C4⋊C4—942no—
185C4⋊C4—944no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C4⋊C4—944no—
189C22⋊C4—22no—
190C22⋊C4—24no—
191C22⋊C4—944no—
192C22⋊C4—942no—
193C42—474no—
194C42—944no—
195C42—942no—
196C42—944no—
197C23—21no—
198C23—22no—
199C23—21no—
200C23—22no—
201C23Q8×D4712yes—
202C23C23×D4711yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—472no—
213C2×C4—472no—
214C2×C4—472no—
215C2×C4—472no—
216C2×C4—472no—
217C2×C4—474no—
218C2×C4—948no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—941no—
223C2×C4—942no—
224C2×C4—941no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4D4×D4712yes—
230C2×C4#1062535214yes—
231C22—22no—
232C22—24no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22C2×D4×D4711yescharacteristic
237C22C2×Q8×D4711yescharacteristic
238C22#41×D4711yescharacteristic
239C22#41×D4712yes—
240C22C2×#1062535212yes—
241C4—22no—
242C4—24no—
243C4—42no—
244C4—41no—
245C4—474no—
246C4—942no—
247C4—944no—
248C4—942no—
249C4—1881no—
250C4—1882no—
251C2—42no—
252C2C22⋊Q8×D4711yescharacteristic
253C2#1568962911yescharacteristic
254C2#1568965212yes—
255C2#1568967211yescharacteristic
256C2#1568967512yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2396
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic47C2semidirect
3. #15689063C2semidirect
5. #15689057C2semidirect
7. #15689042C2semidirect
8. #15688974C2semidirect
9. #15688974C2semidirect
46. C22×Dic47Q8semidirect
140. C47#2396semidirect