Finite Group Databasebeta

← #19142655

Subgroups — #19142655

Order 5504.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13063320C211yesmaximal, characteristic
3#14582841C212yesmaximal, complemented
4#14582834C212yesmaximal
5#14582829C211yesmaximal, characteristic, complemented
6#14582826C211yesmaximal, characteristic
7#14582825C211yesmaximal, characteristic
8#14582819C212yesmaximal, complemented
9#14582812C212yesmaximal
10#14582766C211yesmaximal, characteristic, complemented
11C43×#398C211yesmaximal, characteristic, complemented
12C22×Dic86C2212yes—
13#13063324—24no—
14#13063320—24no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2211yescharacteristic
21C2×(C2×D43)⋊C4C2211yescharacteristic
22C2×(C2×D43)⋊C4C2211yescharacteristic
23C2×(C2×D43)⋊C4C2212yes—
24C2×(C2×D43)⋊C4C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C23×D43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×Dic43C2312yes—
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×Dic86—24no—
49C2×Dic86—42no—
50C2×Dic86—42no—
51C4⋊C4×C43—22no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43—42no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—42no—
58(C2×D43)⋊C4—42no—
59C4⋊Dic43—22no—
60C4⋊Dic43—22no—
61Dic43⋊C4—22no—
62Dic43⋊C4—24no—
63Dic43⋊C4—42no—
64C4×Dic43D414yes—
65C23×C43C2411yescharacteristic
66C22×D43—21no—
67C22×D43—21no—
68C22×D43—21no—
69C22×D43—22no—
70C22×D43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
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×C43C2×D412yes—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—22no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43C2×D412yes—
96C2×Dic43C2×D412yes—
97Dic86—48no—
98C22×C43C22×D411yescharacteristic
99C22×C43H(5,𝔽2)11yescharacteristic
100C22×C43H(5,𝔽2)11yescharacteristic
101C22×C432−1+412yes—
102C22×C432−1+412yes—
103C2×D43—41no—
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—42no—
107C2×D43—42no—
108C4×C43—22no—
109C4×C43—42no—
110C4×C43—41no—
111C4×C43—41no—
112C4×C43—42no—
113Dic43—22no—
114Dic43—22no—
115Dic43—42no—
116Dic43—41no—
117Dic43—42no—
118#2821—431nomaximal, Sylow
119C2×C43#53511yescharacteristic
120C2×C43#53611yescharacteristic
121C2×C43#53611yescharacteristic
122C2×C43#56312yes—
123C2×C43#56312yes—
124D43—81no—
125C2×C4⋊Q8—431no—
126C2×#126—431no—
127#400—432no—
128#399—432no—
129#398—431no—
130#398D4311yescharacteristic, complemented
131#397—431no—
132#397—431no—
133#395—432no—
134#393—432no—
135#383—431no—
136C43#282111yescharacteristic, complemented, Sylow
137C22×Q8—432no—
138C4⋊Q8—864no—
139#126—864no—
140C2×C4⋊C4—431no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4—431no—
144C2×C4⋊C4—432no—
145C2×C4⋊C4C2×D4311yescharacteristic
146C2×C4⋊C4C2×D4311yescharacteristic
147C2×C4⋊C4C2×D4312yes—
148C2×C22⋊C4—431no—
149C2×C22⋊C4—431no—
150C2×C22⋊C4—431no—
151C2×C22⋊C4—432no—
152C2×C22⋊C4—432no—
153C2×C42—431no—
154#95—432no—
155#95—431no—
156#95—432no—
157#95—432no—
158#95—432no—
159#95—432no—
160#95C2×D4311yescharacteristic
161#95C2×D4312yes—
162C24—431no—
163C2×Q8—864no—
164C2×Q8—1722no—
165C2×Q8—1722no—
166C22×C4—431no—
167C22×C4—431no—
168C22×C4—432no—
169C22×C4—431no—
170C22×C4—432no—
171C22×C4C22×D4312yes—
172C22×C4C22×D4311yescharacteristic
173C22×C4C22×D4312yes—
174C22×C4C22×D4311yescharacteristic
175C22×C4C22×D4311yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—864no—
182C4⋊C4—862no—
183C4⋊C4—1722no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C22⋊C4—862no—
187C22⋊C4—1722no—
188C22⋊C4—1722no—
189C42—434no—
190C23—861no—
191C23—861no—
192C23—861no—
193C23—862no—
194C23—862no—
195C23C23×D4311yescharacteristic
196Q8—1728no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—432no—
210C2×C4—432no—
211C2×C4—861no—
212C2×C4—861no—
213C2×C4—862no—
214C2×C4—861no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4D4×D4312yes—
223C22—1722no—
224C22—1722no—
225C22—1721no—
226C22—1721no—
227C22—1721no—
228C22C2×D4×D4311yescharacteristic
229C22#1306337011yescharacteristic
230C22#1306337111yescharacteristic
231C22#1306337212yes—
232C22#1306337312yes—
233C4—22no—
234C4—42no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—862no—
239C4—862no—
240C4—1722no—
241C4—1722no—
242C4—1721no—
243C2—3441no—
244C2#1458346511yescharacteristic
245C2#1458347111yescharacteristic
246C2#1458347411yescharacteristic
247C2#1458365012yes—
248C2#1458365312yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2821
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13063324C2semidirect
3. #14582841C2semidirect
5. #14582829C2semidirect
8. #14582819C2semidirect
10. #14582766C2semidirect
11. C43×#398C2semidirect
130. #398D43semidirect
136. C43#2821semidirect