Finite Group Databasebeta

← #20250419

Subgroups — #20250419

Order 6016.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094023C212yesmaximal
2#15689056C212yesmaximal
3#15689044C212yesmaximal
4#15689043C212yesmaximal
5#15689029C211yesmaximal, characteristic
6#15689021C211yesmaximal, characteristic
7#15689009C212yesmaximal
8#15689006C212yesmaximal
9C47×#389C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11C22×Dic94C2211yescharacteristic
12#13094023—28no—
13C2×C4⋊Dic47C2212yes—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×C4×Dic47C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C4⋊C4×C47C2211yescharacteristic
30C2×C42×C47C2211yescharacteristic
31#95×C47C2212yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×C4×C47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C22×Dic47C2312yes—
41C2×Dic94—24no—
42C2×Dic94—41no—
43C2×Dic94—41no—
44C2×Dic94—42no—
45C2×Dic94—42no—
46C2×Dic94D414yes—
47C4⋊C4×C47—24no—
48C4⋊C4×C47—41no—
49C4⋊C4×C47Q814yescomplemented
50C42×C47—41no—
51C4⋊Dic47—24no—
52C4⋊Dic47—41no—
53C4⋊Dic47—41no—
54C4⋊Dic47Q814yescomplemented
55Dic47⋊C4—24no—
56Dic47⋊C4—24no—
57Dic47⋊C4—42no—
58C4×Dic47—24no—
59C23×C47C2411yescharacteristic
60C2×C4×C47—22no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
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×C47C2×D412yes—
72C2×C4×C47C2×Q812yes—
73C2×C4×C47C2×Q814yes—
74C2×C4×C47C2×Q812yes—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47C2×D414yes—
86C2×Dic47C2×Q814yes—
87Dic94—44no—
88Dic94—48no—
89C22×C47C22×D411yescharacteristic
90C22×C47C22×Q811yescharacteristic
91C22×C47C22×Q811yescharacteristic
92C22×C47H(5,𝔽2)11yescharacteristic
93C22×C47H(5,𝔽2)11yescharacteristic
94C22×C472−1+411yescharacteristic
95C22×C472−1+411yescharacteristic
96C4×C47—22no—
97C4×C47—22no—
98C4×C47—22no—
99C4×C47—24no—
100C4×C47—42no—
101Dic47—24no—
102Dic47—24no—
103Dic47—42no—
104Dic47—42no—
105#2734—471nomaximal, Sylow
106C2×C47#53411yescharacteristic
107C2×C47#54411yescharacteristic
108C2×C47#54411yescharacteristic
109C2×C47D4×Q811yescharacteristic
110C2×C47D4×Q811yescharacteristic
111C2×C47Q8211yescharacteristic
112C2×C47#56311yescharacteristic
113C2×C4⋊Q8—472no—
114#398—472no—
115#395—472no—
116#395—472no—
117#391—471no—
118#389—471no—
119#389D4711yescharacteristic
120#387—472no—
121#387—472no—
122C47#273411yescharacteristic, complemented, Sylow
123C22×Q8—471no—
124C22×Q8—472no—
125C4⋊Q8—948no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4—472no—
128C2×C4⋊C4—472no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—472no—
131C2×C4⋊C4—471no—
132C2×C4⋊C4—471no—
133C2×C4⋊C4C2×D4712yes—
134C2×C4⋊C4C2×D4711yescharacteristic
135C2×C4⋊C4C2×D4711yescharacteristic
136C2×C42—472no—
137C2×C42C2×D4711yescharacteristic
138#95—472no—
139#95—472no—
140#95—472no—
141#95—472no—
142#95—472no—
143#95—472no—
144#95C2×D4712yes—
145C2×Q8—474no—
146C2×Q8—944no—
147C2×Q8—1881no—
148C2×Q8—1881no—
149C2×Q8—1882no—
150C2×Q8—1882no—
151C22×C4—472no—
152C22×C4—472no—
153C22×C4—472no—
154C22×C4—472no—
155C22×C4C22×D4712yes—
156C22×C4C22×D4711yescharacteristic
157C22×C4C22×D4712yes—
158C22×C4C22×D4711yescharacteristic
159C22×C4C22×D4711yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—474no—
163C4⋊C4—944no—
164C4⋊C4—944no—
165C4⋊C4—944no—
166C4⋊C4—1882no—
167C4⋊C4—1881no—
168C4⋊C4—1881no—
169C4⋊C4Dic9414yescomplemented
170C42—41no—
171C42—944no—
172C23C23×D4711yescharacteristic
173Q8—1884no—
174Q8—1888no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—474no—
187C2×C4—474no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4C2×Dic9412yes—
199C2×C4C2×Dic9414yes—
200C2×C4D4×D4712yes—
201C2×C4Q8×D4712yes—
202C22C2×D4×D4711yescharacteristic
203C22C2×Q8×D4711yescharacteristic
204C22C22×Dic9411yescharacteristic
205C22#1309406911yescharacteristic
206C22#1309407011yescharacteristic
207C22#1309407111yescharacteristic
208C22#1309407211yescharacteristic
209C4—22no—
210C4—22no—
211C4—24no—
212C4—22no—
213C4—42no—
214C4—944no—
215C4—944no—
216C4—1882no—
217C4—1882no—
218C2#1568968111yescharacteristic
219C2#1568975211yescharacteristic
220C2#1568975411yescharacteristic
221C2#1568978811yescharacteristic
222C2D4×Dic9411yescharacteristic
223C2Q8×Dic9411yescharacteristic
224C2#1568987711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2734
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
49. C4⋊C4×C47Q8semidirect
54. C4⋊Dic47Q8semidirect
122. C47#2734semidirect
169. C4⋊C4Dic94semidirect