Finite Group Databasebeta

← #20245927

Subgroups — #20245927

Order 6016.

652 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 209 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×#13094012C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic, complemented
3C2×#13093986C211yesmaximal, characteristic
4#15689028C211yesmaximal, characteristic, complemented
5#15689024C211yesmaximal, characteristic
6#15689012C214yesmaximal, complemented
7#15688970C214yesmaximal, complemented
8C42×Dic47C211yesmaximal, characteristic, complemented
9C47×#382C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13#13094012C418yescomplemented
14#13093989—24no—
15#13093986—24no—
16C2×Dic47⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2214yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2214yes—
20C2×C4×Dic47C2212yes—
21C2×C4×Dic47C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C2×C4×Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2214yes—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C42×C47C2211yescharacteristic
29#95×C47C2214yes—
30C23×D47C2312yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47C2312yes—
36C22×Dic47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2311yescharacteristic
39C2×D188—22no—
40C2×D188—22no—
41C2×D188C2×C414yes—
42C2×C4×D47—24no—
43C2×C4×D47—28no—
44C2×Dic94—22no—
45C2×Dic94—22no—
46C2×Dic94C2×C414yescomplemented
47C4⋊C4×C47—22no—
48C4⋊C4×C47—22no—
49C42×C47C2×C414yescomplemented
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—28no—
52(C2×D47)⋊C4C2×C4116yescomplemented
53Dic47⋊C4—24no—
54C4×Dic47—22no—
55C4×Dic47—24no—
56C4×Dic47—24no—
57C4×Dic47—24no—
58C4×Dic47D414yes—
59C23×C47C2411yescharacteristic
60C22×D47—22no—
61C22×D47—24no—
62C22×D47—24no—
63C22×D47—22no—
64C22×D47C22×C414yes—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—24no—
70C2×C4×C47—24no—
71C2×C4×C47C22×C414yes—
72C2×C4×C47C22×C412yes—
73C2×C4×C47C2×D412yes—
74C2×C4×C47#4112yes—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47C22×C414yes—
81C2×Dic47C2×D412yes—
82C2×Dic47C2×D412yes—
83C2×Dic47#4114yes—
84C2×Dic47#4114yes—
85D188—28no—
86C4×D47—48no—
87Dic94—28no—
88C22×C47C23×C411yescharacteristic
89C22×C47C22×D411yescharacteristic
90C22×C47C2×#4112yes—
91C22×C47C2×#4112yes—
92C22×C47C2×#4111yescharacteristic
93C2×D47—24no—
94C2×D47—28no—
95C2×D47—42no—
96C2×D47—44no—
97C2×D47—42no—
98C4×C47—24no—
99C4×C47—42no—
100C4×C47—42no—
101C4×C47C4×D414yes—
102Dic47—24no—
103Dic47—24no—
104Dic47—22no—
105Dic47#12414yescomplemented
106C4×#124—471nomaximal, Sylow
107C2×C47C2×C4×D411yescharacteristic
108C2×C47C4×#4112yes—
109C2×C47C2×#12411yescharacteristic
110C2×C47#52912yes—
111C2×C47#53211yescharacteristic
112D47—44no—
113C2×#124—471no—
114C2×C4×Q8—471no—
115C2×C4×D4—471no—
116#391—471no—
117#390—471no—
118#388—474no—
119#382D4711yescharacteristic, complemented
120C4×C22⋊C4—474no—
121C43—471no—
122C47C4×#12411yescharacteristic, complemented, Sylow
123C22×Q8—471no—
124C22×D4—471no—
125C23×C4—472no—
126#124—478no—
127C4×Q8—944no—
128C4×D4—944no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C22⋊C4—474no—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—474no—
135C2×C42—471no—
136C2×C42—472no—
137C2×C42—472no—
138C2×C42—472no—
139C2×C42—471no—
140C2×C42C2×D4711yescharacteristic
141#95—474no—
142#95C2×D4714yes—
143C24—472no—
144C2×Q8—474no—
145C2×Q8—942no—
146C2×Q8—942no—
147C2×D4—474no—
148C2×D4—942no—
149C2×D4—942no—
150C22×C4—471no—
151C22×C4—472no—
152C22×C4—472no—
153C22×C4—471no—
154C22×C4—944no—
155C22×C4—948no—
156C22×C4C22×D4712yes—
157C22×C4C22×D4712yes—
158C22×C4C22×D4712yes—
159C22×C4C22×D4711yescharacteristic
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—944no—
163C22⋊C4—4716no—
164C22⋊C4—948no—
165C22⋊C4—944no—
166C42—474no—
167C42—944no—
168C42—944no—
169C42—944no—
170C42—942no—
171C42C4×D4714yescomplemented
172C23—474no—
173C23—942no—
174C23—944no—
175C23—944no—
176C23—942no—
177C23C23×D4711yescharacteristic
178Q8—948no—
179D4—948no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—472no—
187C2×C4—474no—
188C2×C4—474no—
189C2×C4—472no—
190C2×C4—474no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—1888no—
197C2×C4C2×C4×D4714yes—
198C2×C4C2×C4×D4712yes—
199C2×C4D4×D4712yes—
200C2×C4#1062535412yes—
201C22—944no—
202C22—948no—
203C22—1882no—
204C22—1884no—
205C22—1882no—
206C22C22×C4×D4711yescharacteristic
207C22C2×D4×D4711yescharacteristic
208C22#41×D4712yes—
209C22#41×D4712yes—
210C22C2×#1062535411yescharacteristic
211C4—24no—
212C4—42no—
213C4—42no—
214C4—474no—
215C4—944no—
216C4—944no—
217C4—942no—
218C4#1309398614yes—
219C2—1884no—
220C2C2×#1309398611yescharacteristic
221C2#1568959112yes—
222C2#124×D4711yescharacteristic
223C2#1568965812yes—
224C2#1568967211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#382C2
socleC23×C47C24
hypercenter#382D47
hypocenterC47C4×#124
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#13093989C2semidirect
4. #15689028C2semidirect
6. #15689012C2semidirect
7. #15688970C2semidirect
8. C42×Dic47C2semidirect
9. C47×#382C2semidirect
13. #13094012C4semidirect
46. C2×Dic94C2×C4semidirect
49. C42×C47C2×C4semidirect
52. (C2×D47)⋊C4C2×C4semidirect
105. Dic47#124semidirect
119. #382D47semidirect
122. C47C4×#124semidirect
171. C42C4×D47semidirect