Finite Group Databasebeta

← #19144516

Subgroups — #19144516

Order 5504.

458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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#14583406C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14583233C212yesmaximal, complemented
4#14583228C212yesmaximal, complemented
5#14583216C212yesmaximal, complemented
6#14583211C212yesmaximal, complemented
7#14582941C211yesmaximal, characteristic, complemented
8#14582939C211yesmaximal, characteristic, complemented
9#14582900C211yesmaximal, characteristic, complemented
10#14582862C211yesmaximal, characteristic, complemented
11C43×#417C211yesmaximal, characteristic, complemented
12C22×C4×D43—21no—
13C22×C4×D43C2211yescharacteristic
14C2×#10621877C2211yescharacteristic
15#13063306—21no—
16#13063301C2211yescharacteristic
17#13063301C2211yescharacteristic
18#13063296C2211yescharacteristic
19#13063296C2211yescharacteristic
20#13063293—21no—
21C4×C22⋊D43—21no—
22C4×C22⋊D43—21no—
23#13063284C2211yescharacteristic
24C2×C4⋊Dic43C2211yescharacteristic
25C2×Dic43⋊C4—21no—
26C4⋊C4×D43—21no—
27C4⋊C4×D43—21no—
28C4⋊C4×D43C2212yes—
29C4⋊C4×D43C2212yes—
30#13063259C2212yescomplemented
31#13063258C2212yescomplemented
32#13063257C2212yescomplemented
33#13063256C2212yescomplemented
34#13063249C2212yescomplemented
35#13063246C2212yescomplemented
36(C2×D43)⋊C8C2212yes—
37(C2×D43)⋊C8C2212yes—
38C2×#41×C43C2211yescharacteristic
39C2×M16×C43C2211yescharacteristic
40C2×C4⋊C4×C43C2211yescharacteristic
41#103×C43C2212yescomplemented
42#102×C43C2212yescomplemented
43C23×D43D411yescharacteristic
44#41×C43—22no—
45#41×C43—22no—
46C2×Q8×C43C2311yescharacteristic
47C2×D4×C43—21no—
48C2×D4×C43C2311yescharacteristic
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—21no—
53C2×C22⋊D43—21no—
54C22×Dic43—21no—
55C22×Dic43D411yescharacteristic
56C2×C4×D43—22no—
57C2×C4×D43—22no—
58C2×C4×D43—22no—
59C2×C4×D43—22no—
60C2×C4×D43—44no—
61C2×C4×D43D411yescharacteristic
62C2×C4×D43D411yescharacteristic
63C2×C4×D43C2311yescharacteristic
64C2×C4×D43C2311yescharacteristic
65M16×C43—22no—
66C2×C8×C43C2312yes—
67C4⋊C4×C43—21no—
68C4⋊C4×C43C2312yes—
69C22⋊Dic43—21no—
70C22⋊Dic43—21no—
71C22⋊Dic43—21no—
72(C2×D43)⋊C4—21no—
73(C2×D43)⋊C4—21no—
74C4⋊Dic43—21no—
75C4⋊Dic43C2312yes—
76C4⋊Dic43C2311yescharacteristic
77C4⋊Dic43C2311yescharacteristic
78Dic43⋊C4—22no—
79Dic43⋊C4—22no—
80Dic43⋊C4—21no—
81Dic43⋊C4—21no—
82C4×Dic43—21no—
83#10621877—22no—
84C2×C43⋊C8C2312yes—
85C23×C43—21no—
86C23×C43C2×D411yescharacteristic
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—22no—
90C22×D43C2×D411yescharacteristic
91C22×D43C2×D411yescharacteristic
92Q8×C43—21no—
93Q8×C43—21no—
94D4×C43—21no—
95D4×C43—21no—
96D4×C43—42no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—42no—
100C2×C4×C43—42no—
101C2×C4×C43C2×D411yescharacteristic
102C2×C4×C43#4112yes—
103C2×C4×C43#4112yes—
104C2×C4×C43C2411yescharacteristic
105C22⋊D43—42no—
106C22⋊D43—42no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—22no—
111C2×Dic43—42no—
112C2×Dic43C2×D411yescharacteristic
113C2×Dic43C2×D411yescharacteristic
114C4×D43—22no—
115C4×D43—22no—
116C4×D43—21no—
117C4×D43—21no—
118C4×D43—21no—
119C4×D43—21no—
120C4×D43—44no—
121C4×D43—44no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—41no—
127C22×C43—41no—
128C22×C43—41no—
129C22×C43#12312yes—
130C22×C43C22×D411yescharacteristic
131C2×D43—28no—
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—21no—
135C2×D43—21no—
136C2×D43AGL(1,ℤ/8)12yes—
137C2×D43#13712yes—
138C4×C43—41no—
139C4×C43—42no—
140C4×C43#12312yes—
141C4×C43C2×#4111yescharacteristic
142C4×C43C2×#4111yescharacteristic
143Dic43—21no—
144Dic43—21no—
145Dic43—42no—
146Dic43—41no—
147Dic43—41no—
148#3092—431nomaximal, Sylow
149C2×C43—22no—
150C2×C43—81no—
151C2×C43C2×#12311yescharacteristic
152C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C43C2×#13711yescharacteristic
154D43—22no—
155D43—22no—
156#525—431no—
157C22×C4⋊C4—431no—
158#484—432no—
159#483—432no—
160#481—432no—
161#480—432no—
162#428—431no—
163#428—431no—
164#417—431no—
165#417D4311yescharacteristic, complemented
166#407—431no—
167C43#309211yescharacteristic, complemented, Sylow
168C2×#41C2×D4311yescharacteristic
169C23×C4—431no—
170C23×C4—861no—
171C2×M16—431no—
172C2×M16C2×D4311yescharacteristic
173#123—861no—
174C22⋊Q8—431no—
175C22⋊Q8—431no—
176#121—431no—
177#121—431no—
178#120—861no—
179C4×D4—861no—
180C4×D4—861no—
181#117—431no—
182C2×C4⋊C4—431no—
183C2×C4⋊C4—432no—
184C2×C4⋊C4—432no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4—861no—
187C2×C4⋊C4—861no—
188C2×C4⋊C4C2×D4311yescharacteristic
189#107—432no—
190#107—432no—
191#106—432no—
192#106—432no—
193#103—432no—
194#103C2×D4312yescomplemented
195#102—432no—
196#102C2×D4312yescomplemented
197C22⋊C8—432no—
198C22⋊C8—432no—
199C24—431no—
200#41—22no—
201#41—22no—
202C2×Q8C22×D4311yescharacteristic
203C2×D4—21no—
204C2×D4—861no—
205C2×D4—861no—
206C2×D4C22×D4311yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—431no—
210C22×C4—431no—
211C22×C4—431no—
212C22×C4—431no—
213C22×C4—431no—
214C22×C4—862no—
215C22×C4—862no—
216C22×C4—862no—
217C22×C4—862no—
218C22×C4—861no—
219C22×C4—1724no—
220C22×C4C22×D4311yescharacteristic
221M16—22no—
222M16—862no—
223C2×C8—432no—
224C2×C8C22×D4312yes—
225C4⋊C4—21no—
226C4⋊C4—432no—
227C4⋊C4—431no—
228C4⋊C4—431no—
229C4⋊C4—862no—
230C4⋊C4—862no—
231C4⋊C4—861no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C4⋊C4C22×D4312yes—
235C22⋊C4—861no—
236C22⋊C4—861no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—861no—
240C42—861no—
241C23—21no—
242C23—431no—
243C23—431no—
244C23—862no—
245C23—862no—
246C23—862no—
247C23D4×D4311yescharacteristic
248Q8—21no—
249Q8—21no—
250D4—21no—
251D4—21no—
252D4—42no—
253D4—1722no—
254D4—1722no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—431no—
260C2×C4—431no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—861no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—861no—
270C2×C4—862no—
271C2×C4—1724no—
272C2×C4—1724no—
273C2×C4—1722no—
274C2×C4#1062189812yes—
275C2×C4D4×D4311yescharacteristic
276C2×C4#1062190012yes—
277C2×C4C23×D4311yescharacteristic
278C8—22no—
279C8—862no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—432no—
286C22—432no—
287C22—868no—
288C22—861no—
289C22—861no—
290C22—861no—
291C22—861no—
292C22#1306330712yes—
293C22C2×D4×D4311yescharacteristic
294C4—41no—
295C4—42no—
296C4—861no—
297C4—861no—
298C4—1722no—
299C4—1721no—
300C4—1721no—
301C4#1306330712yes—
302C4C2×#1062190011yescharacteristic
303C4C2×#1062189811yescharacteristic
304C2—22no—
305C2—81no—
306C2—862no—
307C2—862no—
308C2C2×#1306330711yescharacteristic
309C2AGL(1,ℤ/8)×D4311yescharacteristic
310C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#417C2
socleC22×C43C22×D4
hypercenter#417D43
hypocenterC43#3092
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14583233C2semidirect
4. #14583228C2semidirect
5. #14583216C2semidirect
6. #14583211C2semidirect
7. #14582941C2semidirect
8. #14582939C2semidirect
9. #14582900C2semidirect
10. #14582862C2semidirect
11. C43×#417C2semidirect
30. #13063259C22semidirect
31. #13063258C22semidirect
32. #13063257C22semidirect
33. #13063256C22semidirect
34. #13063249C22semidirect
35. #13063246C22semidirect
41. #103×C43C22semidirect
42. #102×C43C22semidirect
165. #417D43semidirect
167. C43#3092semidirect
194. #103C2×D43semidirect
196. #102C2×D43semidirect