Finite Group Databasebeta

← #19144522

Subgroups — #19144522

Order 5504.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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#14583412C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14583232C211yesmaximal, characteristic, complemented
4#14583228C212yesmaximal, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583217C211yesmaximal, characteristic, complemented
7#14583214C212yesmaximal, complemented
8#14582940C212yesmaximal, complemented
9#14582899C212yesmaximal, complemented
10#14582861C211yesmaximal, characteristic, complemented
11C43×#484C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C22×C4×D43—21no—
14C22×C4×D43C2211yescharacteristic
15C2×#10621872C2212yes—
16#13063310—21no—
17#13063301C2211yescharacteristic
18#13063300C2211yescharacteristic
19#13063299C2211yescharacteristic
20#13063295—21no—
21#13063287—21no—
22(C22⋊D43)⋊C4—21no—
23#13063283C2211yescharacteristic
24C2×C4⋊Dic43C2211yescharacteristic
25C2×Dic43⋊C4—21no—
26C4⋊C4×D43—21no—
27C4⋊C4×D43—21no—
28C4⋊C4×D43C2212yes—
29C4⋊C4×D43C2212yes—
30#13063258C2212yescomplemented
31#13063257C2212yescomplemented
32#13063256C2212yescomplemented
33#13063249C2212yescomplemented
34#13063247C2212yescomplemented
35#13063245C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37(C2×D43)⋊C8C2212yes—
38C22⋊Q8×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic
40#107×C43C2212yescomplemented
41#103×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C23×D43D411yescharacteristic
44C2×Q8×C43C2311yescharacteristic
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C2×C22⋊D43—21no—
48C22×Dic43—21no—
49C22×Dic43D411yescharacteristic
50#10621902—24no—
51C2×D172—21no—
52C2×D172—21no—
53C2×D172C2311yescharacteristic
54C2×C4×D43—24no—
55C2×C4×D43—21no—
56C2×C4×D43—22no—
57C2×C4×D43—22no—
58C2×C4×D43—44no—
59C2×C4×D43D411yescharacteristic
60C2×C4×D43D411yescharacteristic
61C2×C4×D43C2311yescharacteristic
62C2×C4×D43C2311yescharacteristic
63C2×C8×C43C2312yes—
64C4⋊C4×C43—21no—
65C4⋊C4×C43—21no—
66C4⋊C4×C43C2312yes—
67C4⋊C4×C43C2311yescharacteristic
68C22⋊C4×C43—21no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—21no—
72(C2×D43)⋊C4—21no—
73C4⋊Dic43—21no—
74C4⋊Dic43C2312yes—
75C4⋊Dic43C2311yescharacteristic
76Dic43⋊C4—22no—
77Dic43⋊C4—22no—
78Dic43⋊C4—21no—
79C4×Dic43—21no—
80C2×C43⋊C8C2312yes—
81#10621872—24no—
82C23×C43C2×D411yescharacteristic
83C22×D43—22no—
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—21no—
87C22×D43C2×D411yescharacteristic
88C22×D43C2×D411yescharacteristic
89Q8×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—42no—
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2411yescharacteristic
97C22⋊D43—42no—
98C2×Dic43—22no—
99C2×Dic43—21no—
100C2×Dic43—22no—
101C2×Dic43—42no—
102C2×Dic43C2×D411yescharacteristic
103C2×Dic43C2×D411yescharacteristic
104D172—22no—
105D172—42no—
106D172—42no—
107C4×D43—22no—
108C4×D43—22no—
109C4×D43—22no—
110C4×D43—44no—
111C4×D43—44no—
112C4×D43—42no—
113C4×D43#4114yes—
114C8×C43—22no—
115C43⋊C8—22no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43#13712yes—
119C22×C43C22×D411yescharacteristic
120C2×D43—28no—
121C2×D43—21no—
122C2×D43—21no—
123C2×D43—21no—
124C2×D43—21no—
125C2×D43—41no—
126C2×D43—41no—
127C2×D43—41no—
128C2×D43#12312yes—
129C2×D43AGL(1,ℤ/8)12yes—
130C4×C43—21no—
131C4×C43—41no—
132C4×C43—42no—
133C4×C43—41no—
134C4×C43C2×#4112yes—
135Dic43—21no—
136Dic43—42no—
137Dic43—41no—
138Dic43#12312yes—
139#3092—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43C2×#12311yescharacteristic
142C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
143C2×C43C2×#13711yescharacteristic
144D43—22no—
145D43—22no—
146D43—81no—
147#525—431no—
148C22×C4⋊C4—431no—
149#484—431no—
150#484D4311yescharacteristic, complemented
151#483—432no—
152#481—431no—
153#481—431no—
154#480—432no—
155#428—432no—
156#417—432no—
157#407—431no—
158C43#309211yescharacteristic, complemented, Sylow
159C2×#41—431no—
160C23×C4—431no—
161C23×C4—861no—
162C2×M16—432no—
163#123—861no—
164C22⋊Q8—431no—
165C22⋊Q8C2×D4311yescharacteristic
166#121—431no—
167#121—431no—
168#120—861no—
169C4×D4—861no—
170C4×D4—861no—
171#117—431no—
172C2×C4⋊C4—431no—
173C2×C4⋊C4—432no—
174C2×C4⋊C4—432no—
175C2×C4⋊C4—861no—
176C2×C4⋊C4—861no—
177C2×C4⋊C4—861no—
178C2×C4⋊C4C2×D4311yescharacteristic
179#107—432no—
180#107C2×D4312yescomplemented
181#106—432no—
182#106—432no—
183#103—432no—
184#103C2×D4312yescomplemented
185#102—432no—
186#102—432no—
187C22⋊C8—431no—
188C22⋊C8—432no—
189C22⋊C8C2×D4311yescharacteristic
190C24—431no—
191#41—864no—
192C2×Q8C22×D4311yescharacteristic
193C2×D4—431no—
194C2×D4—861no—
195C2×D4—861no—
196C2×D4—861no—
197C22×C4—21no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—431no—
201C22×C4—431no—
202C22×C4—431no—
203C22×C4—864no—
204C22×C4—861no—
205C22×C4—862no—
206C22×C4—862no—
207C22×C4—861no—
208C22×C4—1724no—
209C22×C4C22×D4311yescharacteristic
210M16—864no—
211C2×C8—432no—
212C2×C8C22×D4312yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—432no—
216C4⋊C4—431no—
217C4⋊C4—862no—
218C4⋊C4—862no—
219C4⋊C4—861no—
220C4⋊C4—861no—
221C4⋊C4C22×D4312yes—
222C4⋊C4C22×D4311yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—861no—
225C22⋊C4—861no—
226C22⋊C4—861no—
227C22⋊C4—861no—
228C42—861no—
229C23—431no—
230C23—431no—
231C23—862no—
232C23—862no—
233C23—862no—
234C23—861no—
235C23D4×D4311yescharacteristic
236Q8—22no—
237D4—862no—
238D4—1722no—
239D4—1722no—
240D4—1722no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—431no—
247C2×C4—434no—
248C2×C4—431no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—862no—
253C2×C4—861no—
254C2×C4—862no—
255C2×C4—1722no—
256C2×C4—1724no—
257C2×C4—1724no—
258C2×C4—1722no—
259C2×C4D4×D4311yescharacteristic
260C2×C4C23×D4311yescharacteristic
261C8—22no—
262C8—862no—
263C22—21no—
264C22—21no—
265C22—432no—
266C22—432no—
267C22—868no—
268C22—861no—
269C22—861no—
270C22—861no—
271C22—861no—
272C22—1721no—
273C22—1721no—
274C22—1721no—
275C22#1306335712yes—
276C22C2×D4×D4311yescharacteristic
277C4—21no—
278C4—41no—
279C4—42no—
280C4—41no—
281C4—432no—
282C4—861no—
283C4—1722no—
284C4—1721no—
285C4#41×D4312yes—
286C2—22no—
287C2—862no—
288C2—862no—
289C2—3441no—
290C2#123×D4311yescharacteristic
291C2AGL(1,ℤ/8)×D4311yescharacteristic
292C2C2×#1306335711yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#484C2
socleC22×C43C22×D4
hypercenter#484D43
hypocenterC43#3092
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14583232C2semidirect
4. #14583228C2semidirect
5. #14583218C2semidirect
6. #14583217C2semidirect
7. #14583214C2semidirect
8. #14582940C2semidirect
9. #14582899C2semidirect
10. #14582861C2semidirect
11. C43×#484C2semidirect
30. #13063258C22semidirect
31. #13063257C22semidirect
32. #13063256C22semidirect
33. #13063249C22semidirect
34. #13063247C22semidirect
35. #13063245C22semidirect
40. #107×C43C22semidirect
41. #103×C43C22semidirect
150. #484D43semidirect
158. C43#3092semidirect
180. #107C2×D43semidirect
184. #103C2×D43semidirect