Finite Group Databasebeta

← #20251719

Subgroups — #20251719

Order 6016.

688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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×#13094007C212yesmaximal, complemented
2C2×#13093998C211yesmaximal, characteristic
3#15689025C212yesmaximal, complemented
4#15689021C212yesmaximal, complemented
5#15689014C214yesmaximal, complemented
6#15689002C212yesmaximal, complemented
7#15688983C211yesmaximal, characteristic, complemented
8C22×C42×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C22⋊D47C2212yes—
11#13094007—28no—
12#13093998—24no—
13C2×C4⋊Dic47C2212yes—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2214yes—
16C2×C22⋊Dic47C2212yes—
17C2×(C2×D47)⋊C4C2214yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2214yes—
20C47⋊#95C2212yes—
21C47⋊#95C2214yes—
22C23×C4×C47C2211yescharacteristic
23C23×C4×C47C2211yescharacteristic
24C23×C4×C47C2211yescharacteristic
25C2×C42×C47—24no—
26C2×C42×C47C2212yes—
27C2×C42×C47C2212yes—
28C24×C47C2311yescharacteristic
29C23×D47C2312yes—
30C22×C4×C47—22no—
31C22×C4×C47—22no—
32C22×C4×C47—22no—
33C22×C4×C47—24no—
34C22×C4×C47—24no—
35C22×C4×C47D414yes—
36C22×C4×C47D414yescomplemented
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—24no—
42C2×C22⋊D47—24no—
43C2×C22⋊D47—24no—
44C22×Dic47C2314yes—
45C22×Dic47C2312yes—
46C2×D188—22no—
47C2×D188—24no—
48C42×C47—24no—
49C42×C47—24no—
50C22⋊Dic47—24no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—28no—
53(C2×D47)⋊C4—28no—
54C4⋊Dic47—22no—
55C4⋊Dic47—24no—
56Dic47⋊C4—28no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47C2×D412yes—
60C23×C47C2×D412yes—
61C23×C47#4112yes—
62C23×C47C2411yescharacteristic
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—24no—
66C22×D47—24no—
67C22×D47—22no—
68C2×C4×C47—28no—
69C2×C4×C47—28no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—28no—
76C2×C4×C47C2×D414yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D412yes—
79C2×C4×C47#4114yes—
80C2×C4×C47#4114yes—
81C22⋊D47—48no—
82C2×Dic47—22no—
83C2×Dic47—24no—
84C2×Dic47—22no—
85C2×Dic47—24no—
86C2×Dic47—24no—
87C2×Dic47—22no—
88D188—44no—
89C22×C47—22no—
90C22×C47—22no—
91C22×C47—24no—
92C22×C47—24no—
93C22×C47#12114yes—
94C22×C47C22×D411yescharacteristic
95C22×C47C22×D411yescharacteristic
96C22×C47C2×#4111yescharacteristic
97C22×C47C2×#4112yes—
98C22×C47C2×#4112yes—
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—44no—
103C2×D47—44no—
104C4×C47—24no—
105C4×C47—22no—
106C4×C47—24no—
107C4×C47#12314yescomplemented
108Dic47—42no—
109Dic47—44no—
110#2854—471nomaximal, Sylow
111C2×C47—24no—
112C2×C47C2×#12111yescharacteristic
113C2×C47C2×#12311yescharacteristic
114C2×C47#52511yescharacteristic
115C2×C47#52912yes—
116C2×C47#53212yes—
117D47—82no—
118C2×#123—472no—
119C2×#121—471no—
120C22×C42D4711yescharacteristic, complemented
121#390—472no—
122#389—472no—
123#388—474no—
124#386—472no—
125#380—471no—
126C47#285411yescharacteristic, complemented, Sylow
127C22×D4—472no—
128C22×D4—471no—
129C23×C4C2×D4711yescharacteristic
130C23×C4C2×D4711yescharacteristic
131C23×C4C2×D4711yescharacteristic
132#123—948no—
133#121—944no—
134C2×C4⋊C4—471no—
135C2×C4⋊C4—474no—
136C2×C4⋊C4—472no—
137C2×C22⋊C4—472no—
138C2×C22⋊C4—472no—
139C2×C22⋊C4—474no—
140C2×C22⋊C4—474no—
141C2×C42—24no—
142C2×C42C2×D4712yes—
143C2×C42C2×D4712yes—
144#95—472no—
145#95—474no—
146C24—472no—
147C24C22×D4711yescharacteristic
148C2×D4—944no—
149C2×D4—944no—
150C2×D4—944no—
151C2×D4—944no—
152C2×D4—942no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—474no—
159C22×C4—472no—
160C22×C4D18814yescomplemented
161C22×C4C22⋊D4714yes—
162C22×C4C22×D4712yes—
163C22×C4C22×D4712yes—
164C22×C4C22×D4711yescharacteristic
165C22×C4C22×D4711yescharacteristic
166C4⋊C4—948no—
167C4⋊C4—944no—
168C4⋊C4—942no—
169C22⋊C4—944no—
170C22⋊C4—948no—
171C22⋊C4—948no—
172C22⋊C4—944no—
173C42—24no—
174C42—24no—
175C23—22no—
176C23—22no—
177C23—942no—
178C23—942no—
179C23—944no—
180C23—942no—
181C23—944no—
182C23C2×D18812yes—
183C23#1062535012yes—
184C23C2×C22⋊D4712yes—
185C23C23×D4711yescharacteristic
186D4—1888no—
187D4—1884no—
188C2×C4—28no—
189C2×C4—28no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—28no—
196C2×C4—942no—
197C2×C4—944no—
198C2×C4—942no—
199C2×C4—944no—
200C2×C4—944no—
201C2×C4—942no—
202C2×C4C2×D18814yes—
203C2×C4#1062535014yes—
204C2×C4#1062535014yes—
205C2×C4C2×C22⋊D4712yes—
206C2×C4C2×C22⋊D4712yes—
207C22—22no—
208C22—22no—
209C22—24no—
210C22—24no—
211C22—1882no—
212C22—1882no—
213C22—1882no—
214C22—1884no—
215C22—1884no—
216C22#1309399814yes—
217C22C22×C22⋊D4711yescharacteristic
218C22C22×D18811yescharacteristic
219C22C2×#1062535011yescharacteristic
220C22C2×#1062535012yes—
221C22C2×#1062535012yes—
222C4—24no—
223C4—22no—
224C4—24no—
225C4—1882no—
226C4—1884no—
227C4#1309400714yescomplemented
228C2—24no—
229C2—3762no—
230C2C2×#1309399811yescharacteristic
231C2C2×#1309400711yescharacteristic
232C2#1568963411yescharacteristic
233C2#1568965712yes—
234C2#1568967312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C42×C47C2
hypercenterC22×C42D47
hypocenterC47#2854
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#13094007C2semidirect
3. #15689025C2semidirect
4. #15689021C2semidirect
5. #15689014C2semidirect
6. #15689002C2semidirect
7. #15688983C2semidirect
8. C22×C42×C47C2semidirect
36. C22×C4×C47D4semidirect
107. C4×C47#123semidirect
120. C22×C42D47semidirect
126. C47#2854semidirect
160. C22×C4D188semidirect
227. C4#13094007semidirect