Finite Group Databasebeta

← #19146434

Subgroups — #19146434

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583591C211yesmaximal, characteristic, complemented
2#14583543C211yesmaximal, characteristic
3#14583252C211yesmaximal, characteristic, complemented
4#14583230C211yesmaximal, characteristic, complemented
5#14583222C211yesmaximal, characteristic, complemented
6#14583201C211yesmaximal, characteristic, complemented
7#14583138C211yesmaximal, characteristic, complemented
8#14583125C211yesmaximal, characteristic, complemented
9#14583119C211yesmaximal, characteristic, complemented
10#14583058C211yesmaximal, characteristic, complemented
11SD16×Dic43C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
13#14582892C211yesmaximal, characteristic, complemented
14C2×#13063246C211yesmaximal, characteristic, complemented
15C43×#450C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621885C2211yescharacteristic, complemented
18C22×C43⋊C8C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic, complemented
20#13063320—21no—
21#13063316—21no—
22#13063316C2211yescharacteristic, complemented
23#13063312C2211yescharacteristic
24#13063309—21no—
25#13063306—21no—
26#13063304C2211yescharacteristic
27#13063301C2211yescharacteristic, complemented
28#13063297—21no—
29#13063296C2211yescharacteristic
30#13063294—21no—
31Q8×Dic43C2211yescharacteristic, complemented
32D4×Dic43C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34#13063283C2211yescharacteristic, complemented
35#13063281—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37C2×C22⋊Dic43—21no—
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063249C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43—22no—
63C2×D4×C43—41no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73#10621900—22no—
74#10621900—41no—
75C2×C4×D43C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77SD16×C43—22no—
78SD16×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621885—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—81no—
116C23×C43C2×D411yescharacteristic
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—42no—
124D4×C43#4112yes—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—22no—
132C22⋊D43—42no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—81no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144C4×D43—21no—
145C4×D43—21no—
146Dic86—21no—
147Dic86—21no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—22no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—84no—
161C22×C43#13512yes—
162C22×C43C22×D411yescharacteristic
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—21no—
172Dic43—21no—
173Dic43—21no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3296—431nomaximal, Sylow
179C2×C43—22no—
180C2×C43—42no—
181C2×C43—81no—
182C2×C43#54611yescharacteristic
183C2×C43C2×#13511yescharacteristic
184C2×C43#57711yescharacteristic
185D43—41no—
186#552—431no—
187#546—431no—
188#488—431no—
189#483—431no—
190#482—431no—
191#478—431no—
192#467—431no—
193#465—431no—
194#464—431no—
195#452—431no—
196#450D4311yescharacteristic, complemented
197C4×SD16—431no—
198C8×D4—431no—
199#416—431no—
200C2×#102—431no—
201C43#329611yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4C2×D4311yescharacteristic
204C2×Q16—431no—
205C2×SD16C2×D4311yescharacteristic
206C2×SD16C2×D4311yescharacteristic
207C22×C8—431no—
208C22×C8—431no—
209#126—861no—
210#125—431no—
211#125—861no—
212#124—431no—
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8C2×D4311yescharacteristic
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—431no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227C2×C22⋊C4—861no—
228#107—431no—
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102C2×D4311yescharacteristic
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8C2×D4311yescharacteristic
244C4×C8—431no—
245C24—21no—
246#41—862no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—431no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4C22×D4311yescharacteristic
257C2×D4C22×D4311yescharacteristic
258C22×C4—431no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263Q16—1721no—
264SD16—22no—
265SD16—41no—
266C2×C8—431no—
267C2×C8—431no—
268C2×C8—1721no—
269C2×C8—1721no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—431no—
286C22⋊C4—431no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—431no—
295C42—861no—
296C42—861no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—431no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—861no—
307Q8—861no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—862no—
313D4—3441no—
314D4—1722no—
315D4#1062190012yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—3441no—
330C2×C4—1722no—
331C2×C4—1722no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22#1306334612yes—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—861no—
356C4—861no—
357C4—861no—
358C4—1721no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4C2×#1062190011yescharacteristic
363C4#1306337011yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—1721no—
368C2#1458353611yescharacteristic
369C2C2×#1306334611yescharacteristic
370C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3296
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14583591C2semidirect
3. #14583252C2semidirect
4. #14583230C2semidirect
5. #14583222C2semidirect
6. #14583201C2semidirect
7. #14583138C2semidirect
8. #14583125C2semidirect
9. #14583119C2semidirect
10. #14583058C2semidirect
11. SD16×Dic43C2semidirect
12. (C22⋊D43)⋊C8C2semidirect
13. #14582892C2semidirect
14. C2×#13063246C2semidirect
15. C43×#450C2semidirect
17. C2×#10621885C22semidirect
19. C2×C8×D43C22semidirect
22. #13063316C22semidirect
27. #13063301C22semidirect
31. Q8×Dic43C22semidirect
34. #13063283C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063257C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063250C22semidirect
43. #13063250C22semidirect
44. #13063249C22semidirect
45. #13063248C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
196. #450D43semidirect
201. C43#3296semidirect