Finite Group Databasebeta

← #19143951

Subgroups — #19143951

Order 5504.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13063370C211yesmaximal, characteristic, complemented
2#14583697C212yesmaximal, complemented
3#14583076C214yesmaximal, complemented
4#14583066C214yesmaximal, complemented
5#14582917C212yesmaximal, complemented
6C2×#13063242C211yesmaximal, characteristic, complemented
7C43×#535C211yesmaximal, characteristic, complemented
8#13063370—22no—
9#13063370—24no—
10#13063370C2214yes—
11C2×#10621898C2212yes—
12C2×#10621900—22no—
13C22×C22⋊D43—22no—
14C2×D4×D43—22no—
15#13063356C2214yescomplemented
16#13063355—22no—
17#13063351C2214yescomplemented
18#13063350—22no—
19#13063345—24no—
20C2×#10621877C2212yescomplemented
21#13063253C2218yescomplemented
22#13063242C2214yescomplemented
23C2×#41×C43C2211yescharacteristic, complemented
24C22×D4×C43C2211yescharacteristic
25#127×C43C2212yescomplemented
26#124×C43C2212yescomplemented
27#121×C43—22no—
28#120×C43—22no—
29#117×C43C2211yescharacteristic, complemented
30C24×C43D412yes—
31C23×D43—22no—
32#41×C43—22no—
33#41×C43—22no—
34C2×Q8×C43C2311yescharacteristic, complemented
35C2×D4×C43—22no—
36C2×D4×C43—22no—
37C2×D4×C43—21no—
38C2×D4×C43—24no—
39C2×D4×C43D412yes—
40C2×D4×C43C2312yes—
41C2×D4×C43C2311yescharacteristic, complemented
42C22×C4×C43—21no—
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—24no—
45C2×C22⋊D43—28no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—28no—
48C22×Dic43—22no—
49#10621900—28no—
50#10621900—28no—
51D4×D43—28no—
52D4×D43—28no—
53#10621898—22no—
54#10621898—22no—
55#10621898D414yescomplemented
56#10621898C2314yes—
57C2×D172D412yescomplemented
58C2×C4×D43—22no—
59C2×Dic86D412yescomplemented
60C4⋊C4×C43—21no—
61C22⋊C4×C43—21no—
62C22⋊C4×C43—24no—
63C42×C43C2312yescomplemented
64#10621885—24no—
65#10621884—24no—
66#10621883—24no—
67#10621882—24no—
68#10621877—22no—
69#10621877C2314yescomplemented
70C2×C43⋊C8—22no—
71C23×C43—22no—
72C23×C43—22no—
73C23×C43—21no—
74C23×C43—82no—
75C23×C43C2×D414yes—
76C23×C43C2×D411yescharacteristic
77C22×D43—22no—
78C22×D43—28no—
79C22×D43—84no—
80Q8×C43—22no—
81D4×C43—24no—
82D4×C43—24no—
83D4×C43—22no—
84D4×C43—41no—
85D4×C43—41no—
86D4×C43—84no—
87C2×C4×C43—22no—
88C2×C4×C43—21no—
89C2×C4×C43—42no—
90C2×C4×C43C2×D412yes—
91C2×C4×C43C2×D412yes—
92C2×C4×C43C2×D411yescharacteristic
93C2×C4×C43C2411yescharacteristic
94C22⋊D43—216no—
95C22⋊D43—24no—
96C22⋊D43—24no—
97C2×Dic43—28no—
98C2×Dic43—22no—
99D172—22no—
100D172C2×D414yes—
101C4×D43—24no—
102C4×D43—24no—
103Dic86—22no—
104Dic86C2×D414yes—
105C43⋊C8—24no—
106C22×C43—24no—
107C22×C43—41no—
108C22×C43—44no—
109C22×C43—44no—
110C22×C43—42no—
111C22×C43—41no—
112C22×C43—82no—
113C22×C43#12011yescharacteristic
114C22×C43#12011yescharacteristic
115C22×C43C22×D411yescharacteristic
116C2×D43—24no—
117C2×D43—44no—
118C2×D43—88no—
119C4×C43—42no—
120C4×C43—41no—
121C4×C43#12012yes—
122C4×C43C22×D412yes—
123Dic43—24no—
124#3019—431nomaximal, Sylow
125C2×C43—21no—
126C2×C43—21no—
127C2×C43—21no—
128C2×C43—44no—
129C2×C43—81no—
130C2×C43C2×#12011yescharacteristic
131D43—44no—
132C2×H(5,𝔽2)—431no—
133#575—432no—
134#535D4311yescharacteristic, complemented
135#455—434no—
136#453—434no—
137#421—432no—
138C2×#100—431no—
139C43#301911yescharacteristic, complemented, Sylow
140H(5,𝔽2)—434no—
141H(5,𝔽2)—864no—
142H(5,𝔽2)—862no—
143C2×#41—432no—
144C2×#41—862no—
145C2×#41C2×D4311yescharacteristic, complemented
146C22×D4—862no—
147C22×D4—862no—
148C22×D4C2×D4311yescharacteristic
149#137—434no—
150#137—862no—
151AGL(1,ℤ/8)—434no—
152AGL(1,ℤ/8)—862no—
153#135—864no—
154C2×M16—432no—
155#127C2×D4312yescomplemented
156#124C2×D4312yescomplemented
157#121—22no—
158#120—22no—
159#117C2×D4311yescharacteristic, complemented
160#104—438no—
161#100—434no—
162C24—862no—
163C24C22⋊D4312yes—
164#41—22no—
165#41—22no—
166#41—434no—
167#41—434no—
168#41—868no—
169#41—868no—
170#41—862no—
171#41—862no—
172C2×Q8—432no—
173C2×Q8C22×D4311yescharacteristic, complemented
174C2×D4—21no—
175C2×D4—24no—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—432no—
179C2×D4—868no—
180C2×D4—868no—
181C2×D4—864no—
182C2×D4—868no—
183C2×D4—862no—
184C2×D4—868no—
185C2×D4C22⋊D4312yes—
186C2×D4C22×D4312yes—
187C2×D4C22×D4311yescharacteristic, complemented
188C22×C4—21no—
189C22×C4—862no—
190C22×C4—862no—
191C22×C4C22×D4311yescharacteristic
192Q16—864no—
193SD16—864no—
194SD16—864no—
195D8—864no—
196M16—434no—
197M16—862no—
198C2×C8—862no—
199C4⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—24no—
202C42C22×D4312yescomplemented
203C23—22no—
204C23—22no—
205C23—21no—
206C23—82no—
207C23—868no—
208C23—862no—
209C23—3444no—
210C23C2×C22⋊D4314yes—
211C23C2×C22⋊D4311yescharacteristic
212Q8—22no—
213Q8—434no—
214Q8—862no—
215D4—24no—
216D4—24no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—84no—
221D4—434no—
222D4—8616no—
223D4—864no—
224D4—864no—
225D4—862no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—868no—
230C2×C4—862no—
231C2×C4—864no—
232C2×C4—864no—
233C2×C4D4×D4312yes—
234C2×C4D4×D4312yes—
235C2×C4C2×C22⋊D4311yescharacteristic
236C2×C4C23×D4311yescharacteristic
237C8—864no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—42no—
243C22—41no—
244C22—82no—
245C22—864no—
246C22—3448no—
247C22—1724no—
248C22#1306329311yescharacteristic
249C22#1306329311yescharacteristic
250C22C22×C22⋊D4311yescharacteristic
251C4—42no—
252C4—41no—
253C4—864no—
254C4#1306329312yes—
255C4C2×D4×D4312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—81no—
261C2—1724no—
262C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#535C2
socleC2×C43C2×#120
hypercenter#535D43
hypocenterC43#3019
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#13063370C2semidirect
2. #14583697C2semidirect
3. #14583076C2semidirect
4. #14583066C2semidirect
5. #14582917C2semidirect
6. C2×#13063242C2semidirect
7. C43×#535C2semidirect
15. #13063356C22semidirect
17. #13063351C22semidirect
20. C2×#10621877C22semidirect
21. #13063253C22semidirect
22. #13063242C22semidirect
23. C2×#41×C43C22semidirect
25. #127×C43C22semidirect
26. #124×C43C22semidirect
29. #117×C43C22semidirect
34. C2×Q8×C43C23semidirect
41. C2×D4×C43C23semidirect
55. #10621898D4semidirect
57. C2×D172D4semidirect
59. C2×Dic86D4semidirect
63. C42×C43C23semidirect
69. #10621877C23semidirect
134. #535D43semidirect
139. C43#3019semidirect
145. C2×#41C2×D43semidirect
155. #127C2×D43semidirect
156. #124C2×D43semidirect
159. #117C2×D43semidirect
173. C2×Q8C22×D43semidirect
187. C2×D4C22×D43semidirect
202. C42C22×D43semidirect