Finite Group Databasebeta

← #19140363

Subgroups — #19140363

Order 5504.

528 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13063324C211yesmaximal, characteristic, complemented
2C2×#13063303C212yesmaximal
3C2×#13063283C211yesmaximal, characteristic
4#14582832C212yesmaximal, complemented
5#14582829C211yesmaximal, characteristic, complemented
6#14582828C212yesmaximal
7#14582826C211yesmaximal, characteristic
8#14582825C211yesmaximal, characteristic
9#14582803C212yesmaximal, complemented
10#14582763C211yesmaximal, characteristic, complemented
11C43×#398C211yesmaximal, characteristic, complemented
12C22×Dic86C2212yes—
13C22×C4×D43C2211yescharacteristic
14#13063324—24no—
15#13063303—28no—
16#13063283—24no—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×C4⋊Dic43C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×C4×Dic43C2211yescharacteristic
27C2×C4×Dic43C2211yescharacteristic
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2211yescharacteristic
32C43⋊#95C2212yes—
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2211yescharacteristic
35C2×C4⋊C4×C43C2212yes—
36#95×C43C2212yes—
37#95×C43C2211yescharacteristic
38C23×D43C2311yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2311yescharacteristic
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C22×Dic43C2311yescharacteristic
49C2×C4×D43—22no—
50C2×C4×D43—22no—
51C2×C4×D43D414yes—
52C2×Dic86—24no—
53C2×Dic86—24no—
54C2×Dic86—24no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—24no—
57C4⋊C4×C43—22no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—24no—
61(C2×D43)⋊C4—24no—
62C4⋊Dic43—22no—
63C4⋊Dic43—22no—
64Dic43⋊C4—24no—
65Dic43⋊C4—24no—
66Dic43⋊C4—24no—
67C4×Dic43—22no—
68C4×Dic43D414yes—
69C23×C43C2411yescharacteristic
70C22×D43—21no—
71C22×D43—21no—
72C22×D43—22no—
73C22×D43—22no—
74C22×D43C2×D412yes—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—22no—
85C2×C4×C43—22no—
86C2×C4×C43C2×D412yes—
87C2×C4×C43C2×D412yes—
88C2×Dic43—22no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43C2×D412yes—
98C2×Dic43C2×D412yes—
99C2×Dic43C2×D412yes—
100C2×Dic43#4112yes—
101C4×D43—28no—
102Dic86—48no—
103C22×C43C22×D411yescharacteristic
104C22×C43C22×D411yescharacteristic
105C22×C43C2×#4111yescharacteristic
106C22×C432−1+412yes—
107C22×C432−1+412yes—
108C2×D43—22no—
109C2×D43—24no—
110C2×D43—41no—
111C2×D43—41no—
112C2×D43—42no—
113C4×C43—22no—
114C4×C43—22no—
115C4×C43—42no—
116C4×C43—41no—
117C4×C43—42no—
118Dic43—22no—
119Dic43—42no—
120Dic43—42no—
121Dic43—41no—
122Dic43#12114yes—
123#2621—431nomaximal, Sylow
124C2×C43C2×#12111yescharacteristic
125C2×C43#53611yescharacteristic
126C2×C43#53612yes—
127C2×C43#53611yescharacteristic
128C2×C43#54112yes—
129D43—42no—
130C2×C4⋊Q8—431no—
131C2×C22⋊Q8—432no—
132C2×#117—431no—
133#398—431no—
134#398—432no—
135#398D4311yescharacteristic, complemented
136#397—431no—
137#397—431no—
138#397—432no—
139#391—432no—
140#382—431no—
141C43#262111yescharacteristic, complemented, Sylow
142C22×Q8—432no—
143C23×C4—431no—
144C4⋊Q8—864no—
145C22⋊Q8—868no—
146#117—864no—
147C2×C4⋊C4—431no—
148C2×C4⋊C4—432no—
149C2×C4⋊C4—432no—
150C2×C4⋊C4—432no—
151C2×C4⋊C4—431no—
152C2×C4⋊C4C2×D4311yescharacteristic
153C2×C4⋊C4C2×D4312yes—
154C2×C4⋊C4C2×D4311yescharacteristic
155C2×C22⋊C4—431no—
156C2×C22⋊C4—431no—
157C2×C22⋊C4—432no—
158C2×C22⋊C4—432no—
159C2×C42—431no—
160C2×C42—431no—
161#95—432no—
162#95—431no—
163#95—432no—
164#95—432no—
165#95—432no—
166#95C2×D4311yescharacteristic
167#95C2×D4312yes—
168C24—431no—
169C2×Q8—864no—
170C2×Q8—864no—
171C2×Q8—864no—
172C22×C4—431no—
173C22×C4—431no—
174C22×C4—434no—
175C22×C4—431no—
176C22×C4—432no—
177C22×C4—432no—
178C22×C4—862no—
179C22×C4—862no—
180C22×C4C22×D4311yescharacteristic
181C22×C4C22×D4312yes—
182C22×C4C22×D4312yes—
183C22×C4C22×D4311yescharacteristic
184C22×C4C22×D4311yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—24no—
187C4⋊C4—22no—
188C4⋊C4—862no—
189C4⋊C4—864no—
190C4⋊C4—864no—
191C4⋊C4—864no—
192C4⋊C4—862no—
193C22⋊C4—862no—
194C22⋊C4—864no—
195C22⋊C4—864no—
196C22⋊C4—862no—
197C42—434no—
198C42—862no—
199C23—432no—
200C23—861no—
201C23—861no—
202C23—862no—
203C23—862no—
204C23C23×D4311yescharacteristic
205Q8—1728no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—432no—
218C2×C4—432no—
219C2×C4—432no—
220C2×C4—432no—
221C2×C4—868no—
222C2×C4—862no—
223C2×C4—861no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—862no—
230C2×C4—862no—
231C2×C4D4×D4312yes—
232C2×C4D4×D4312yes—
233C22—862no—
234C22—864no—
235C22—1721no—
236C22—1721no—
237C22—1722no—
238C22C2×D4×D4311yescharacteristic
239C22C2×D4×D4311yescharacteristic
240C22#41×D4311yescharacteristic
241C22#1306337212yes—
242C22#1306337312yes—
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—42no—
248C4—434no—
249C4—862no—
250C4—1722no—
251C4—1722no—
252C4—1721no—
253C2—1722no—
254C2#121×D4311yescharacteristic
255C2#1458347111yescharacteristic
256C2#1458347212yes—
257C2#1458347411yescharacteristic
258C2#1458350812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2621
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13063324C2semidirect
4. #14582832C2semidirect
5. #14582829C2semidirect
9. #14582803C2semidirect
10. #14582763C2semidirect
11. C43×#398C2semidirect
135. #398D43semidirect
141. C43#2621semidirect