Finite Group Databasebeta

← #19143959

Subgroups — #19143959

Order 5504.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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
1#14583697C212yesmaximal, complemented
2#14583473C211yesmaximal, characteristic, complemented
3#14583082C214yesmaximal, complemented
4#14583072C214yesmaximal, complemented
5#14582916C212yesmaximal, complemented
6C2×#13063244C211yesmaximal, characteristic, complemented
7C2×2−1+4×C43C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063356—22no—
10#13063355C2214yescomplemented
11#13063351—22no—
12#13063350C2214yescomplemented
13#13063345—24no—
14C2×#10621877C2212yes—
15#13063323C2212yescomplemented
16#13063314C2212yescomplemented
17#13063308—22no—
18#13063301—22no—
19#13063284C2211yescharacteristic
20#13063252C2218yescomplemented
21#13063244C2214yescomplemented
222−1+4×C43—24no—
232−1+4×C43—22no—
242−1+4×C43C2214yes—
25C2×#41×C43—22no—
26C2×#41×C43—22no—
27C2×#41×C43C2212yes—
28C22×Q8×C43—22no—
29C22×Q8×C43C2211yescharacteristic
30#41×C43—28no—
31#41×C43—28no—
32#41×C43—28no—
33#41×C43—28no—
34#41×C43—22no—
35#41×C43—22no—
36#41×C43D414yes—
37#41×C43C2314yes—
38C2×Q8×C43—22no—
39C2×Q8×C43—28no—
40C2×Q8×C43—28no—
41C2×Q8×C43—22no—
42C2×Q8×C43—22no—
43C2×Q8×C43D412yes—
44C2×Q8×C43D412yes—
45C2×Q8×C43C2312yes—
46C2×D4×C43—22no—
47C2×D4×C43—22no—
48C2×D4×C43D412yes—
49C22×C4×C43—24no—
50C22×C4×C43—22no—
51C22×C4×C43D412yes—
52C22×C4×C43C2311yescharacteristic
53C2×C22⋊D43—21no—
54#10621898—22no—
55#10621898—22no—
56C2×D172C2311yescharacteristic
57C2×C4×D43—21no—
58C2×Dic86C2311yescharacteristic
59C22⋊Dic43—21no—
60#10621885—24no—
61#10621884—24no—
62#10621883—24no—
63#10621882—24no—
64(C2×D43)⋊C4—24no—
65C4⋊Dic43—21no—
66Dic43⋊C4—24no—
67C4×Dic43C2312yes—
68#10621877—22no—
69#10621877C2314yes—
70C2×C43⋊C8—22no—
71C23×C43—22no—
72C23×C43C2×D411yescharacteristic
73C22×D43—21no—
74Q8×C43—28no—
75Q8×C43—22no—
76Q8×C43—24no—
77Q8×C43—24no—
78Q8×C43C2×D414yes—
79D4×C43—28no—
80D4×C43—24no—
81D4×C43—24no—
82D4×C43—22no—
83D4×C43C2×D414yes—
84C2×C4×C43—216no—
85C2×C4×C43—22no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—24no—
89C2×C4×C43—24no—
90C2×C4×C43C2×D414yes—
91C2×C4×C43C2×D411yescharacteristic
92C2×C4×C43C2×D412yes—
93C2×C4×C43C2×D412yes—
94C2×C4×C43C2411yescharacteristic
95C22⋊D43—41no—
96C22⋊D43—41no—
97C2×Dic43—22no—
98C2×Dic43—21no—
99D172—22no—
100C4×D43—42no—
101Dic86—22no—
102C43⋊C8—24no—
103C22×C43—24no—
104C22×C43—41no—
105C22×C43—44no—
106C22×C43#12011yescharacteristic
107C22×C43#12011yescharacteristic
108C22×C43C22×D411yescharacteristic
109C2×D43—42no—
110C2×D43—41no—
111C4×C43—24no—
112C4×C43—24no—
113C4×C43#12012yes—
114C4×C43C22×D412yes—
115Dic43—42no—
116Dic43—41no—
117#3020—431nomaximal, Sylow
118C2×C43—21no—
119C2×C43—21no—
120C2×C43—21no—
121C2×C43—44no—
122C2×C43C2×#12011yescharacteristic
123D43—81no—
124C2×2−1+4D4311yescharacteristic, complemented
125#575—432no—
126#536—431no—
127#456—434no—
128#454—434no—
129#421—432no—
130C2×#101—431no—
131C43#302011yescharacteristic, complemented, Sylow
1322−1+4—24no—
1332−1+4—22no—
1342−1+4C2×D4314yes—
135C2×#41—22no—
136C2×#41—22no—
137C2×#41—431no—
138C2×#41C2×D4312yes—
139C22×Q8—22no—
140C22×Q8C2×D4311yescharacteristic
141#137—434no—
142#137—862no—
143AGL(1,ℤ/8)—434no—
144AGL(1,ℤ/8)—862no—
145#135—864no—
146C2×M16—432no—
147C4⋊Q8—432no—
148#124—432no—
149#123—862no—
150C22⋊Q8—862no—
151#117—431no—
152#104—438no—
153#101—434no—
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—862no—
161#41—862no—
162#41C22⋊D4314yes—
163#41C22×D4314yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—431no—
170C2×Q8C22⋊D4312yes—
171C2×Q8C22⋊D4312yes—
172C2×Q8C22×D4312yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—431no—
176C2×D4—861no—
177C2×D4C22⋊D4312yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—861no—
181C22×C4C22⋊D4312yes—
182C22×C4C22×D4311yescharacteristic
183Q16—864no—
184SD16—864no—
185SD16—864no—
186D8—864no—
187M16—434no—
188M16—862no—
189C2×C8—862no—
190C4⋊C4—861no—
191C4⋊C4—864no—
192C22⋊C4—861no—
193C22⋊C4—864no—
194C42—432no—
195C23—22no—
196C23—861no—
197C23C2×C22⋊D4311yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—862no—
203Q8C2×C22⋊D4314yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—862no—
209D4—1721no—
210D4—1721no—
211D4C2×C22⋊D4314yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—862no—
219C2×C4—861no—
220C2×C4—1722no—
221C2×C4C2×C22⋊D4314yes—
222C2×C4C2×C22⋊D4311yescharacteristic
223C2×C4C2×C22⋊D4312yes—
224C2×C4C2×C22⋊D4312yes—
225C2×C4C23×D4311yescharacteristic
226C8—864no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—1722no—
231C22—1721no—
232C22#1306329411yescharacteristic
233C22#1306329411yescharacteristic
234C22C22×C22⋊D4311yescharacteristic
235C4—24no—
236C4—24no—
237C4—1722no—
238C4—1721no—
239C4#1306329412yes—
240C4C22×C22⋊D4312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—3441no—
246C2C2×#1306329411yescharacteristic
subgroupG/H
centerC2C2×#13063294
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×2−1+4×C43C2
socleC2×C43C2×#120
hypercenterC2×2−1+4D43
hypocenterC43#3020
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. #14583473C2semidirect
3. #14583082C2semidirect
4. #14583072C2semidirect
5. #14582916C2semidirect
6. C2×#13063244C2semidirect
7. C2×2−1+4×C43C2semidirect
10. #13063355C22semidirect
12. #13063350C22semidirect
15. #13063323C22semidirect
16. #13063314C22semidirect
20. #13063252C22semidirect
21. #13063244C22semidirect
124. C2×2−1+4D43semidirect
131. C43#3020semidirect