Finite Group Databasebeta

← #19145357

Subgroups — #19145357

Order 5504.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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, complemented
2C2×#13063296C211yesmaximal, characteristic, complemented
3#14583235C211yesmaximal, characteristic, complemented
4#14583221C212yesmaximal, complemented
5#14583215C211yesmaximal, characteristic, complemented
6#14583132C212yesmaximal, complemented
7#14583127C212yesmaximal, complemented
8#14583050C211yesmaximal, characteristic, complemented
9#14583041C212yesmaximal, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#447C211yesmaximal, characteristic, complemented
12C2×#10621900C2211yescharacteristic, complemented
13C22×C22⋊D43—21no—
14C22×C4×D43C2211yescharacteristic
15C2×#10621883C2212yescomplemented
16C2×C8×D43C2212yescomplemented
17#13063307—21no—
18#13063305C2211yescharacteristic, complemented
19#13063304C2211yescharacteristic
20#13063296—21no—
21#13063296—21no—
22#13063296C2212yes—
23#13063296C2212yes—
24#13063296C2211yescharacteristic, complemented
25#13063293—21no—
26D4×Dic43—21no—
27(C22⋊D43)⋊C4—21no—
28#13063283C2211yescharacteristic, complemented
29C2×C4⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43—21no—
31#13063259C2212yescomplemented
32#13063256C2212yescomplemented
33#13063250C2212yescomplemented
34#13063246C2212yescomplemented
35#13063246C2212yescomplemented
36C22⋊(C43⋊C8)C2211yescharacteristic
37(C2×D43)⋊C8C2212yescomplemented
38C22×D4×C43C2211yescharacteristic
39C2×D8×C43C2212yescomplemented
40#121×C43C2211yescharacteristic
41#102×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C24×C43—21no—
44C23×D43D411yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43—42no—
48C2×D4×C43C2312yes—
49C2×D4×C43C2311yescharacteristic
50C22×C4×C43C2311yescharacteristic
51C2×C22⋊D43—21no—
52C2×C22⋊D43—21no—
53C2×C22⋊D43—22no—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—44no—
56C22×Dic43—21no—
57C22×Dic43—21no—
58C22×Dic43D411yescharacteristic
59#10621900—42no—
60C2×C4×D43—42no—
61C2×C4×D43D411yescharacteristic
62C2×C4×D43D411yescharacteristic
63C2×C4×D43C2311yescharacteristic
64C2×C4×D43C2311yescharacteristic
65C2×Dic86C2311yescharacteristic
66D8×C43—42no—
67C2×C8×C43C2312yes—
68C4⋊C4×C43C2311yescharacteristic
69C22⋊C4×C43—21no—
70C22⋊Dic43—22no—
71C22⋊Dic43—22no—
72C22⋊Dic43—21no—
73C22⋊Dic43—21no—
74#10621883—42no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77C4⋊Dic43—21no—
78C4⋊Dic43—21no—
79C4⋊Dic43C2311yescharacteristic
80C4⋊Dic43C2312yes—
81Dic43⋊C4—21no—
82C4×Dic43—21no—
83C2×C43⋊C8C2312yes—
84C8×D43—42no—
85C23×C43—22no—
86C23×C43—21no—
87C23×C43—42no—
88C23×C43—42no—
89C23×C43—42no—
90C23×C43C2×D411yescharacteristic
91C22×D43—22no—
92C22×D43—22no—
93C22×D43—41no—
94C22×D43C2×D411yescharacteristic
95C22×D43C2×D411yescharacteristic
96D4×C43—22no—
97D4×C43—22no—
98D4×C43—22no—
99D4×C43—42no—
100D4×C43—42no—
101C2×C4×C43—22no—
102C2×C4×C43—21no—
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43C2411yescharacteristic
105C22⋊D43—42no—
106C22⋊D43—44no—
107C22⋊D43—42no—
108C22⋊D43—44no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111C2×Dic43—22no—
112C2×Dic43—41no—
113C2×Dic43—42no—
114C2×Dic43—42no—
115C2×Dic43C2×D411yescharacteristic
116C2×Dic43C2×D411yescharacteristic
117C4×D43—22no—
118C4×D43—22no—
119C4×D43—41no—
120C4×D43—41no—
121Dic86—22no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43—42no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—41no—
130C22×C43—42no—
131C22×C43—41no—
132C22×C43—84no—
133C22×C43#13512yes—
134C22×C43C22×D411yescharacteristic
135C2×D43—21no—
136C2×D43—21no—
137C2×D43—21no—
138C2×D43—21no—
139C2×D43—21no—
140C2×D43—44no—
141C2×D43AGL(1,ℤ/8)12yes—
142C4×C43—21no—
143C4×C43—41no—
144C4×C43H(5,𝔽2)12yes—
145Dic43—21no—
146Dic43—21no—
147Dic43—41no—
148Dic43—42no—
149Dic43—41no—
150#3188—431nomaximal, Sylow
151C2×C43—22no—
152C2×C43—81no—
153C2×C43—82no—
154C2×C43#53411yescharacteristic
155C2×C43C2×#13511yescharacteristic
156C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
157D43—22no—
158D43—41no—
159#525—431no—
160C2×#121—431no—
161#484—431no—
162#482—432no—
163#481—431no—
164#466—432no—
165#465—432no—
166#450—431no—
167#449—432no—
168#447D4311yescharacteristic, complemented
169C2×C22⋊C8—431no—
170C43#318811yescharacteristic, complemented, Sylow
171C2×#41—431no—
172C22×D4—861no—
173C22×D4C2×D4311yescharacteristic
174C23×C4—431no—
175C2×SD16—432no—
176C2×D8C2×D4312yescomplemented
177C22×C8—432no—
178#123—861no—
179C22⋊Q8—431no—
180C22⋊Q8—431no—
181#121—432no—
182#121—432no—
183#121—431no—
184#121—861no—
185#121—861no—
186#121C2×D4311yescharacteristic
187#120—861no—
188C4×D4—861no—
189C4×D4—861no—
190#117—431no—
191C2×C4⋊C4—431no—
192C2×C22⋊C4—861no—
193#107—432no—
194#106—432no—
195#103—432no—
196#102—432no—
197#102—432no—
198#102C2×D4312yescomplemented
199C22⋊C8—431no—
200C22⋊C8—432no—
201C22⋊C8C2×D4311yescharacteristic
202C24—21no—
203C24—431no—
204#41—1722no—
205C2×Q8—431no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—861no—
210C2×D4—861no—
211C2×D4—862no—
212C2×D4—862no—
213C2×D4—1724no—
214C2×D4C22×D4311yescharacteristic
215C2×D4C22×D4312yes—
216C22×C4—431no—
217C22×C4—431no—
218C22×C4—431no—
219C22×C4—431no—
220C22×C4—431no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4—1722no—
224C22×C4C22×D4311yescharacteristic
225SD16—1722no—
226D8—42no—
227C2×C8—432no—
228C2×C8—1722no—
229C2×C8C22×D4312yes—
230C4⋊C4—431no—
231C4⋊C4—432no—
232C4⋊C4—861no—
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4C22×D4311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—862no—
240C22⋊C4—862no—
241C22⋊C4—861no—
242C22⋊C4—861no—
243C42—861no—
244C23—21no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—431no—
250C23—431no—
251C23—862no—
252C23—862no—
253C23—1721no—
254C23D4×D4311yescharacteristic
255Q8—862no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—1724no—
262D4—1722no—
263D4—1724no—
264D4—1722no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—431no—
268C2×C4—431no—
269C2×C4—862no—
270C2×C4—862no—
271C2×C4—861no—
272C2×C4—862no—
273C2×C4—861no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1722no—
278C2×C4—1722no—
279C2×C4D4×D4311yescharacteristic
280C2×C4C23×D4311yescharacteristic
281C8—22no—
282C8—862no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—84no—
292C22—432no—
293C22—861no—
294C22—861no—
295C22—861no—
296C22—861no—
297C22—861no—
298C22—1724no—
299C22#1306334412yes—
300C22C2×D4×D4311yescharacteristic
301C4—21no—
302C4—41no—
303C4—861no—
304C4—861no—
305C4—1722no—
306C4—1721no—
307C4—1721no—
308C4#1306337012yes—
309C2—22no—
310C2—82no—
311C2—81no—
312C2—862no—
313C2—1721no—
314C2#1458345911yescharacteristic
315C2C2×#1306334411yescharacteristic
316C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#447C2
socleC22×C43C22×D4
hypercenter#447D43
hypocenterC43#3188
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14583409C2semidirect
2. C2×#13063296C2semidirect
3. #14583235C2semidirect
4. #14583221C2semidirect
5. #14583215C2semidirect
6. #14583132C2semidirect
7. #14583127C2semidirect
8. #14583050C2semidirect
9. #14583041C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#447C2semidirect
12. C2×#10621900C22semidirect
15. C2×#10621883C22semidirect
16. C2×C8×D43C22semidirect
18. #13063305C22semidirect
24. #13063296C22semidirect
28. #13063283C22semidirect
31. #13063259C22semidirect
32. #13063256C22semidirect
33. #13063250C22semidirect
34. #13063246C22semidirect
35. #13063246C22semidirect
37. (C2×D43)⋊C8C22semidirect
39. C2×D8×C43C22semidirect
41. #102×C43C22semidirect
168. #447D43semidirect
170. C43#3188semidirect
176. C2×D8C2×D43semidirect
198. #102C2×D43semidirect