Finite Group Databasebeta

← #19140462

Subgroups — #19140462

Order 5504.

512 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063315C211yesmaximal, characteristic, complemented
2C2×D4×Dic43C211yesmaximal, characteristic
3#14582835C212yesmaximal, complemented
4#14582831C211yesmaximal, characteristic, complemented
5#14582829C211yesmaximal, characteristic, complemented
6#14582827C212yesmaximal, complemented
7#14582813C211yesmaximal, characteristic
8#14582774C212yesmaximal, complemented
9#14582771C212yesmaximal, complemented
10#14582766C211yesmaximal, characteristic, complemented
11C43×#394C211yesmaximal, characteristic
12C23×Dic43C2212yes—
13#13063315—24no—
14D4×Dic43—24no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2212yes—
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×C22⋊Dic43C2212yes—
25C2×C22⋊Dic43C2212yes—
26C2×C4×Dic43C2211yescharacteristic
27C43⋊#95C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×D4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C22⋊C4×C43C2212yes—
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2312yes—
38C2×D4×C43—22no—
39C2×D4×C43—24no—
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×Dic43—24no—
45C22×Dic43—42no—
46C22×Dic43—42no—
47C22×Dic43C2312yes—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2312yes—
50C22×Dic43C2311yescharacteristic
51C22×Dic43C2311yescharacteristic
52C22×Dic43C2311yescharacteristic
53C4⋊C4×C43—22no—
54C22⋊C4×C43—24no—
55C22⋊C4×C43—42no—
56C22⋊Dic43—24no—
57C22⋊Dic43—24no—
58C22⋊Dic43—42no—
59C4⋊Dic43—22no—
60C4⋊Dic43—22no—
61C4⋊Dic43—42no—
62Dic43⋊C4—22no—
63Dic43⋊C4—22no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—42no—
67C4×Dic43D414yes—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—22no—
71C23×C43—22no—
72C23×C43—22no—
73C23×C43—22no—
74C23×C43#4114yes—
75C23×C43C2411yescharacteristic
76D4×C43—28no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—21no—
83C2×C4×C43—22no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43C2×D412yes—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43—21no—
91C2×Dic43—21no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—22no—
101C2×Dic43—48no—
102C2×Dic43C2×D412yes—
103C2×Dic43C2×D412yes—
104C22×C43—24no—
105C22×C43—24no—
106C22×C43—24no—
107C22×C43—42no—
108C22×C43—42no—
109C22×C43—42no—
110C22×C43—42no—
111C22×C43C22×D411yescharacteristic
112C22×C43C2×#4112yes—
113C22×C43H(5,𝔽2)11yescharacteristic
114C22×C43H(5,𝔽2)11yescharacteristic
115C22×C432−1+412yes—
116C4×C43—22no—
117C4×C43—41no—
118C4×C43—41no—
119C4×C43—42no—
120Dic43—22no—
121Dic43—22no—
122Dic43—41no—
123Dic43—41no—
124Dic43—42no—
125Dic43—42no—
126#2633—431nomaximal, Sylow
127C2×C43—44no—
128C2×C43#52511yescharacteristic
129C2×C43#53511yescharacteristic
130C2×C43#53611yescharacteristic
131C2×C43#53912yes—
132C2×C43#53912yes—
133C2×#125—431no—
134C2×C4×D4—431no—
135#399—432no—
136#398—431no—
137#398—431no—
138#397—432no—
139#394—431no—
140#394D4311yescharacteristic
141#385—432no—
142#385—432no—
143#383—431no—
144C43#263311yescharacteristic, complemented, Sylow
145C22×D4C2×D4311yescharacteristic
146C23×C4—432no—
147#125—864no—
148C4×D4—864no—
149C2×C4⋊C4—431no—
150C2×C4⋊C4—431no—
151C2×C4⋊C4—431no—
152C2×C4⋊C4—431no—
153C2×C4⋊C4—431no—
154C2×C4⋊C4—431no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4C2×D4311yescharacteristic
158C2×C22⋊C4—432no—
159C2×C22⋊C4—432no—
160C2×C22⋊C4—432no—
161C2×C22⋊C4C2×D4312yes—
162C2×C22⋊C4C2×D4312yes—
163C2×C42—431no—
164#95—432no—
165#95—431no—
166#95—432no—
167#95—432no—
168#95—432no—
169#95C2×D4311yescharacteristic
170C24C22×D4312yes—
171C2×D4—24no—
172C2×D4—22no—
173C22×C4—431no—
174C22×C4—431no—
175C22×C4—432no—
176C22×C4—431no—
177C22×C4—432no—
178C22×C4—431no—
179C22×C4—864no—
180C22×C4—1722no—
181C22×C4—1722no—
182C22×C4C22×D4312yes—
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4311yescharacteristic
185C22×C4C22×D4311yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—862no—
188C4⋊C4—862no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—864no—
198C22⋊C4—864no—
199C22⋊C4—1722no—
200C42—434no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23#1062190014yes—
208C23C23×D4311yescharacteristic
209D4—28no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—432no—
220C2×C4—432no—
221C2×C4—861no—
222C2×C4—861no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—861no—
226C2×C4—861no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—861no—
230C2×C4—862no—
231C2×C4—861no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—862no—
235C2×C4—1728no—
236C2×C4D4×D4312yes—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D4311yescharacteristic
245C22C2×#1062190012yes—
246C22#1306337011yescharacteristic
247C22#1306337111yescharacteristic
248C22#1306337212yes—
249C4—22no—
250C4—41no—
251C4—41no—
252C4—42no—
253C4—862no—
254C4—862no—
255C4—1721no—
256C4—1722no—
257C4—1721no—
258C4—1722no—
259C2—44no—
260C2#1458340511yescharacteristic
261C2#1458346511yescharacteristic
262C2#1458346911yescharacteristic
263C2#1458349312yes—
264C2#1458349412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2633
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063315C2semidirect
3. #14582835C2semidirect
4. #14582831C2semidirect
5. #14582829C2semidirect
6. #14582827C2semidirect
8. #14582774C2semidirect
9. #14582771C2semidirect
10. #14582766C2semidirect
144. C43#2633semidirect