Finite Group Databasebeta

← #19144517

Subgroups — #19144517

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#14583409C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14583235C211yesmaximal, characteristic, complemented
4#14583234C211yesmaximal, characteristic, complemented
5#14583231C212yesmaximal, complemented
6#14583215C211yesmaximal, characteristic, complemented
7#14583211C212yesmaximal, complemented
8#14582938C212yesmaximal, complemented
9#14582897C212yesmaximal, complemented
10#14582861C211yesmaximal, characteristic, complemented
11C43×#481C211yesmaximal, characteristic, complemented
12C2×#10621900C2211yescharacteristic
13C22×C4×D43—21no—
14C22×C4×D43C2211yescharacteristic
15C2×#10621872C2212yes—
16#13063307—21no—
17#13063305C2211yescharacteristic
18#13063304C2211yescharacteristic
19#13063296C2211yescharacteristic
20#13063293—21no—
21D4×Dic43—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#13063259C2212yescomplemented
31#13063258C2212yescomplemented
32#13063256C2212yescomplemented
33#13063250C2212yescomplemented
34#13063248C2212yescomplemented
35#13063246C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37(C2×D43)⋊C8C2212yes—
38#121×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic
40#106×C43C2212yescomplemented
41#102×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C23×D43D411yescharacteristic
44C2×D4×C43—21no—
45C2×D4×C43C2311yescharacteristic
46C22×C4×C43—21no—
47C22×C4×C43C2311yescharacteristic
48C2×C22⋊D43—21no—
49C2×C22⋊D43—21no—
50C22×Dic43—21no—
51C22×Dic43—21no—
52C22×Dic43D411yescharacteristic
53#10621900—24no—
54C2×C4×D43—24no—
55C2×C4×D43—22no—
56C2×C4×D43—22no—
57C2×C4×D43—44no—
58C2×C4×D43D411yescharacteristic
59C2×C4×D43D411yescharacteristic
60C2×C4×D43C2311yescharacteristic
61C2×C4×D43C2311yescharacteristic
62C2×Dic86C2311yescharacteristic
63C2×C8×C43C2312yes—
64C4⋊C4×C43—21no—
65C4⋊C4×C43C2312yes—
66C4⋊C4×C43C2311yescharacteristic
67C22⋊C4×C43—21no—
68C22⋊Dic43—21no—
69C22⋊Dic43—21no—
70(C2×D43)⋊C4—21no—
71(C2×D43)⋊C4—21no—
72C4⋊Dic43—21no—
73C4⋊Dic43—21no—
74C4⋊Dic43C2312yes—
75C4⋊Dic43C2311yescharacteristic
76Dic43⋊C4—21no—
77Dic43⋊C4—22no—
78Dic43⋊C4—22no—
79C4×Dic43—21no—
80C2×C43⋊C8C2312yes—
81#10621872—24no—
82C23×C43—21no—
83C23×C43C2×D411yescharacteristic
84C22×D43—22no—
85C22×D43—22no—
86C22×D43—22no—
87C22×D43C2×D411yescharacteristic
88C22×D43C2×D411yescharacteristic
89D4×C43—22no—
90D4×C43—42no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—22no—
94C2×C4×C43—42no—
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2411yescharacteristic
97C22⋊D43—42no—
98C22⋊D43—42no—
99C2×Dic43—22no—
100C2×Dic43—21no—
101C2×Dic43—22no—
102C2×Dic43—21no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43C2×D411yescharacteristic
106C2×Dic43C2×D411yescharacteristic
107C4×D43—22no—
108C4×D43—22no—
109C4×D43—22no—
110C4×D43—44no—
111C4×D43—44no—
112C4×D43#4114yes—
113Dic86—22no—
114C8×C43—22no—
115C43⋊C8—22no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—41no—
119C22×C43—41no—
120C22×C43—41no—
121C22×C43#13712yes—
122C22×C43C22×D411yescharacteristic
123C2×D43—28no—
124C2×D43—21no—
125C2×D43—21no—
126C2×D43—21no—
127C2×D43—21no—
128C2×D43#12312yes—
129C2×D43AGL(1,ℤ/8)12yes—
130C4×C43—21no—
131C4×C43—42no—
132C4×C43—41no—
133C4×C43C2×#4112yes—
134Dic43—21no—
135Dic43—41no—
136Dic43—42no—
137Dic43—41no—
138Dic43#12312yes—
139#3092—431nomaximal, Sylow
140C2×C43—22no—
141C2×C43—81no—
142C2×C43C2×#12311yescharacteristic
143C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C43C2×#13711yescharacteristic
145D43—22no—
146D43—22no—
147#525—431no—
148C22×C4⋊C4—431no—
149#484—431no—
150#484—431no—
151#483—432no—
152#481—431no—
153#481D4311yescharacteristic, complemented
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⋊Q8—431no—
166#121—431no—
167#121C2×D4311yescharacteristic
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#107—432no—
181#106—432no—
182#106C2×D4312yescomplemented
183#103—432no—
184#103—432no—
185#102—432no—
186#102C2×D4312yescomplemented
187C22⋊C8—431no—
188C22⋊C8—432no—
189C22⋊C8C2×D4311yescharacteristic
190C24—431no—
191#41—864no—
192C2×Q8—431no—
193C2×D4—21no—
194C2×D4—861no—
195C2×D4—861no—
196C2×D4C22×D4311yescharacteristic
197C22×C4—21no—
198C22×C4—431no—
199C22×C4—431no—
200C22×C4—431no—
201C22×C4—431no—
202C22×C4—431no—
203C22×C4—864no—
204C22×C4—862no—
205C22×C4—862no—
206C22×C4—861no—
207C22×C4—861no—
208C22×C4—1724no—
209C22×C4C22×D4311yescharacteristic
210M16—864no—
211C2×C8—432no—
212C2×C8C22×D4312yes—
213C4⋊C4—21no—
214C4⋊C4—432no—
215C4⋊C4—431no—
216C4⋊C4—862no—
217C4⋊C4—862no—
218C4⋊C4—861no—
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—21no—
230C23—431no—
231C23—431no—
232C23—862no—
233C23—862no—
234C23—862no—
235C23D4×D4311yescharacteristic
236Q8—862no—
237D4—22no—
238D4—42no—
239D4—1722no—
240D4—1722no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—431no—
246C2×C4—434no—
247C2×C4—431no—
248C2×C4—862no—
249C2×C4—862no—
250C2×C4—862no—
251C2×C4—862no—
252C2×C4—861no—
253C2×C4—861no—
254C2×C4—862no—
255C2×C4—1724no—
256C2×C4—1724no—
257C2×C4—1722no—
258C2×C4—1722no—
259C2×C4D4×D4311yescharacteristic
260C2×C4C23×D4311yescharacteristic
261C8—22no—
262C8—862no—
263C22—21no—
264C22—21no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—432no—
269C22—432no—
270C22—868no—
271C22—861no—
272C22—861no—
273C22—861no—
274C22—861no—
275C22#1306335412yes—
276C22C2×D4×D4311yescharacteristic
277C4—21no—
278C4—42no—
279C4—41no—
280C4—432no—
281C4—861no—
282C4—1721no—
283C4—1722no—
284C4—1721no—
285C4#41×D4312yes—
286C2—22no—
287C2—81no—
288C2—862no—
289C2—862no—
290C2#123×D4311yescharacteristic
291C2AGL(1,ℤ/8)×D4311yescharacteristic
292C2C2×#1306335411yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#481C2
socleC22×C43C22×D4
hypercenter#481D43
hypocenterC43#3092
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14583235C2semidirect
4. #14583234C2semidirect
5. #14583231C2semidirect
6. #14583215C2semidirect
7. #14583211C2semidirect
8. #14582938C2semidirect
9. #14582897C2semidirect
10. #14582861C2semidirect
11. C43×#481C2semidirect
30. #13063259C22semidirect
31. #13063258C22semidirect
32. #13063256C22semidirect
33. #13063250C22semidirect
34. #13063248C22semidirect
35. #13063246C22semidirect
40. #106×C43C22semidirect
41. #102×C43C22semidirect
153. #481D43semidirect
158. C43#3092semidirect
182. #106C2×D43semidirect
186. #102C2×D43semidirect