Finite Group Databasebeta

← #19143989

Subgroups — #19143989

Order 5504.

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

normal subgroups only

This group has 766 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
1#14583735C211yesmaximal, characteristic, complemented
2#14583411C212yesmaximal, complemented
3#14583406C211yesmaximal, characteristic, complemented
4#14583090C214yesmaximal, complemented
5#14583087C214yesmaximal, complemented
6#14582872C212yesmaximal, complemented
7C43×#410C211yesmaximal, characteristic, complemented
8#13063373—21no—
9#13063372—22no—
10#13063371—22no—
11#13063370—21no—
12#13063370C2214yes—
13C2×#10621898—22no—
14C2×#10621898C2212yes—
15#41×D43—24no—
16C22×C4×D43C2211yescharacteristic, complemented
17#13063309C2214yescomplemented
18#13063306C2212yescomplemented
19#13063305—22no—
20#13063301—21no—
21#13063300—22no—
22#13063296—21no—
23#13063295C2214yescomplemented
24#13063293C2212yescomplemented
25C4×D172—24no—
26C4×C22⋊D43—22no—
27#13063284C2211yescharacteristic, complemented
28#13063239C2218yescomplemented
29C2×#41×C43C2211yescharacteristic
30#117×C43C2212yescomplemented
31#99×C43C2214yescomplemented
32C23×D43C2311yescharacteristic
33#41×C43—22no—
34#41×C43—22no—
35C2×Q8×C43D411yescharacteristic, complemented
36C2×D4×C43D411yescharacteristic, complemented
37C2×D4×C43C2312yes—
38C22×C4×C43D412yescomplemented
39C22×C4×C43C2311yescharacteristic
40C2×C22⋊D43—24no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43C2314yes—
43C22×Dic43C2311yescharacteristic
44#10621902—24no—
45Q8×D43—24no—
46#10621900—24no—
47#10621900—28no—
48D4×D43—24no—
49D4×D43—28no—
50#10621898—24no—
51#10621898—24no—
52#10621898—22no—
53#10621898—22no—
54#10621898—24no—
55#10621898—22no—
56#10621898—22no—
57C2×D172—22no—
58C2×D172—24no—
59C2×D172D412yescomplemented
60C2×C4×D43—24no—
61C2×C4×D43—21no—
62C2×C4×D43—22no—
63C2×C4×D43—21no—
64C2×C4×D43—22no—
65C2×C4×D43D414yescomplemented
66C2×Dic86—22no—
67C2×Dic86D412yescomplemented
68C4⋊C4×C43—22no—
69C22⋊C4×C43C2314yes—
70C42×C43—22no—
71C22⋊Dic43—22no—
72C22⋊Dic43C2312yes—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—24no—
75(C2×D43)⋊C4—24no—
76C4⋊Dic43—21no—
77C4⋊Dic43—24no—
78Dic43⋊C4—22no—
79C4×Dic43—21no—
80C23×C43C2×D412yes—
81C23×C43C2411yescharacteristic
82C22×D43—22no—
83C22×D43—21no—
84C22×D43—24no—
85C22×D43—42no—
86C22×D43C2×D414yes—
87Q8×C43—22no—
88D4×C43—24no—
89D4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—22no—
92C2×C4×C43—24no—
93C2×C4×C43C2×D412yes—
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2×D412yes—
98C22⋊D43—28no—
99C22⋊D43—24no—
100C22⋊D43—24no—
101C22⋊D43—44no—
102C2×Dic43—24no—
103C2×Dic43—22no—
104C2×Dic43—21no—
105C2×Dic43—22no—
106C2×Dic43C2×D414yes—
107D172—24no—
108D172—22no—
109D172—22no—
110D172—48no—
111C4×D43—28no—
112C4×D43—24no—
113C4×D43—24no—
114C4×D43—41no—
115C4×D43—42no—
116C4×D43—41no—
117Dic86—24no—
118Dic86—22no—
119Dic86—22no—
120C22×C43—22no—
121C22×C43—41no—
122C22×C43—42no—
123C22×C43C22×D412yes—
124C22×C43C22×D411yescharacteristic
125C2×D43—24no—
126C2×D43—22no—
127C2×D43—24no—
128C2×D43—41no—
129C2×D43—42no—
130C2×D43—41no—
131C2×D43—44no—
132C2×D43—84no—
133C4×C43—22no—
134C4×C43—44no—
135C4×C43#12011yescharacteristic
136C4×C43#12012yes—
137C4×C43#12011yescharacteristic
138Dic43—24no—
139Dic43—42no—
140Dic43—41no—
141#3025—431nomaximal, Sylow
142C2×C43—21no—
143C2×C43—22no—
144C2×C43—42no—
145C2×C43C2×#12011yescharacteristic
146D43—42no—
147D43—44no—
148#585—431no—
149#525—431no—
150#525—432no—
151#458—434no—
152B(4,𝔽2)—434no—
153#410—432no—
154#410D4311yescharacteristic, complemented
155C43#302511yescharacteristic, complemented, Sylow
1562−1+4—862no—
1572−1+4—861no—
158H(5,𝔽2)—434no—
159H(5,𝔽2)—862no—
160H(5,𝔽2)—861no—
161C2×#41—432no—
162C2×#41—864no—
163C2×#41—862no—
164C2×#41C2×D4311yescharacteristic
165C23×C4—431no—
166#123—432no—
167#123—434no—
168C22⋊Q8—862no—
169C22⋊Q8—861no—
170#121—862no—
171#121—861no—
172#120—432no—
173#120—434no—
174C4×D4—864no—
175C4×D4—862no—
176#117—431no—
177#117C2×D4312yescomplemented
178#99—438no—
179#99C2×D4314yescomplemented
180C24—431no—
181#41—22no—
182#41—22no—
183#41—864no—
184#41—864no—
185#41—868no—
186#41—864no—
187#41—864no—
188#41—862no—
189#41—862no—
190#41—864no—
191#41—862no—
192#41—862no—
193C2×Q8—432no—
194C2×Q8—862no—
195C2×Q8—864no—
196C2×Q8D17211yescharacteristic, complemented
197C2×D4—434no—
198C2×D4—432no—
199C2×D4—862no—
200C2×D4—864no—
201C2×D4—868no—
202C2×D4—864no—
203C2×D4—864no—
204C2×D4—862no—
205C2×D4D17211yescharacteristic, complemented
206C2×D4C22×D4312yes—
207C22×C4—434no—
208C22×C4—431no—
209C22×C4—864no—
210C22×C4—861no—
211C22×C4—861no—
212C22×C4—862no—
213C22×C4—862no—
214C22×C4D17212yescomplemented
215C22×C4C22×D4311yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—864no—
218C4⋊C4—861no—
219C4⋊C4—862no—
220C22⋊C4—432no—
221C22⋊C4—864no—
222C22⋊C4—864no—
223C22⋊C4—862no—
224C22⋊C4—862no—
225C22⋊C4C22×D4314yes—
226C42—22no—
227C42—861no—
228C23—434no—
229C23—864no—
230C23—862no—
231C23—861no—
232C23—1722no—
233C23C2×D17212yes—
234C23C23×D4311yescharacteristic
235Q8—22no—
236Q8—864no—
237Q8—862no—
238Q8—862no—
239D4—24no—
240D4—22no—
241D4—864no—
242D4—868no—
243D4—864no—
244D4—864no—
245D4—862no—
246D4—862no—
247D4—1728no—
248D4—1724no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—434no—
253C2×C4—868no—
254C2×C4—864no—
255C2×C4—864no—
256C2×C4—864no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—861no—
260C2×C4—1721no—
261C2×C4—1722no—
262C2×C4—1721no—
263C2×C4C2×D17212yes—
264C2×C4C2×D17211yescharacteristic
265C2×C4C2×D17211yescharacteristic
266C2×C4D4×D4312yes—
267C2×C4D4×D4312yes—
268C22—22no—
269C22—41no—
270C22—42no—
271C22—864no—
272C22—862no—
273C22—864no—
274C22—3444no—
275C22—1724no—
276C22—1722no—
277C22—1721no—
278C22—1721no—
279C22C2×D4×D4312yes—
280C22C22×D17211yescharacteristic
281C4—22no—
282C4—44no—
283C4—864no—
284C4—1722no—
285C4—1721no—
286C4#1306329511yescharacteristic
287C4#1306329512yes—
288C4#1306329511yescharacteristic
289C2—22no—
290C2—21no—
291C2—42no—
292C2—1722no—
293C2—1724no—
294C2C2×#1306329511yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC43×#410C2
socleC2×C43C2×#120
hypercenter#410D43
hypocenterC43#3025
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14583735C2semidirect
2. #14583411C2semidirect
3. #14583406C2semidirect
4. #14583090C2semidirect
5. #14583087C2semidirect
6. #14582872C2semidirect
7. C43×#410C2semidirect
16. C22×C4×D43C22semidirect
17. #13063309C22semidirect
18. #13063306C22semidirect
23. #13063295C22semidirect
24. #13063293C22semidirect
27. #13063284C22semidirect
28. #13063239C22semidirect
30. #117×C43C22semidirect
31. #99×C43C22semidirect
35. C2×Q8×C43D4semidirect
36. C2×D4×C43D4semidirect
38. C22×C4×C43D4semidirect
59. C2×D172D4semidirect
65. C2×C4×D43D4semidirect
67. C2×Dic86D4semidirect
154. #410D43semidirect
155. C43#3025semidirect
177. #117C2×D43semidirect
179. #99C2×D43semidirect
196. C2×Q8D172semidirect
205. C2×D4D172semidirect
214. C22×C4D172semidirect