Finite Group Databasebeta

← #19146549

Subgroups — #19146549

Order 5504.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583549C211yesmaximal, characteristic, complemented
2#14583537C211yesmaximal, characteristic, complemented
3#14583260C211yesmaximal, characteristic, complemented
4#14583228C211yesmaximal, characteristic, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583187C211yesmaximal, characteristic, complemented
7#14583150C211yesmaximal, characteristic, complemented
8#14583125C211yesmaximal, characteristic, complemented
9#14583116C211yesmaximal, characteristic, complemented
10#14583031C211yesmaximal, characteristic, complemented
11#14583011C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic, complemented
16C2×#10621900—21no—
17C2×D4×D43C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621877C2211yescharacteristic, complemented
20C2×C8×D43C2211yescharacteristic
21#13063324C2211yescharacteristic, complemented
22#13063314C2211yescharacteristic
23#13063308—21no—
24#13063307—21no—
25#13063306—21no—
26#13063302—21no—
27#13063301C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063297—21no—
30#13063296C2211yescharacteristic
31#13063293—21no—
32D4×Dic43C2211yescharacteristic
33D4×Dic43C2211yescharacteristic, complemented
34C4×C22⋊D43C2211yescharacteristic
35C2×C4⋊Dic43C2211yescharacteristic, complemented
36C4⋊C4×D43C2211yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38#13063257C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic, complemented
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic, complemented
52C2×#41×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic, complemented
54C2×D8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76#10621900—44no—
77D4×D43—22no—
78D4×D43—41no—
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×Dic86—21no—
83SD16×C43—41no—
84D8×C43—22no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43D411yescharacteristic
93#10621882—41no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4D411yescharacteristic
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4D411yescharacteristic
107C4×Dic43C2311yescharacteristic
108#10621877—41no—
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C8×D43—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—81no—
119C22×D43C2×D411yescharacteristic
120Q8×C43—21no—
121Q8×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—42no—
126D4×C43—42no—
127D4×C43#4112yescomplemented
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—42no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—22no—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C22⋊D43—81no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—81no—
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147C2×Dic43C2×D411yescharacteristic
148D172—21no—
149D172—21no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—42no—
153Dic86—42no—
154C8×C43—21no—
155C8×C43—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—22no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43C22×D411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—84no—
174C2×D43AGL(1,ℤ/8)12yes—
175C4×C43—21no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43C2×#4111yescharacteristic
179C4×C43H(5,𝔽2)11yescharacteristic
180Dic43—21no—
181Dic43—21no—
182Dic43—21no—
183Dic43—41no—
184Dic43—41no—
185Dic43—41no—
186#3306—431nomaximal, Sylow
187C2×C43—42no—
188C2×C43—41no—
189C2×C43—81no—
190C2×C43#54611yescharacteristic
191C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C43#57711yescharacteristic
193D43—22no—
194D43—81no—
195#547—431no—
196#546—431no—
197#489—431no—
198#483—431no—
199#481—431no—
200#476—431no—
201#469—431no—
202#465—431no—
203#463—431no—
204#449D4311yescharacteristic, complemented
205#447—431no—
206#442—431no—
207#435—431no—
208#417—431no—
209C2×#102—431no—
210C43#330611yescharacteristic, complemented, Sylow
211C2×#41—861no—
212C2×#41C2×D4311yescharacteristic
213C22×D4—431no—
214C2×SD16C2×D4311yescharacteristic, complemented
215C2×D8—431no—
216C2×D8C2×D4311yescharacteristic
217C2×M16—431no—
218C22×C8—431no—
219C4⋊Q8—431no—
220#124—431no—
221#123—861no—
222#123—861no—
223#123—861no—
224C22⋊Q8—431no—
225C22⋊Q8—861no—
226#121—431no—
227#121—431no—
228#121—861no—
229#121C2×D4311yescharacteristic, complemented
230#120—861no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C22⋊C4—861no—
237#106—431no—
238#106—431no—
239#106—431no—
240C4⋊C8—431no—
241#103—431no—
242#103—431no—
243#103C2×D4311yescharacteristic, complemented
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102C2×D4311yescharacteristic
251C22⋊C8—431no—
252C22⋊C8C2×D4311yescharacteristic, complemented
253#97—431no—
254C24—861no—
255#41—22no—
256#41—41no—
257#41—1724no—
258C2×Q8—861no—
259C2×Q8C22×D4311yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—861no—
265C2×D4—862no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—1721no—
269C2×D4C22×D4311yescharacteristic
270C2×D4C22×D4311yescharacteristic
271C22×C4—21no—
272C22×C4—431no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4C22×D4311yescharacteristic
278SD16—41no—
279D8—22no—
280D8—1721no—
281M16—1721no—
282C2×C8—431no—
283C2×C8—431no—
284C2×C8—1721no—
285C2×C8C22×D4311yescharacteristic
286C2×C8C22×D4311yescharacteristic
287C4⋊C4—431no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4C22×D4311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—431no—
298C22⋊C4—431no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C42—431no—
307C23—21no—
308C23—21no—
309C23—431no—
310C23—861no—
311C23—3441no—
312C23—1722no—
313C23—1722no—
314C23D4×D4311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1722no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—862no—
324D4—861no—
325D4—861no—
326D4—3441no—
327D4—1722no—
328D4—1722no—
329D4#1062190012yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—431no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—3441no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4D4×D4311yescharacteristic
348C2×C4C23×D4311yescharacteristic
349C8—21no—
350C8—21no—
351C8—861no—
352C8—861no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—432no—
363C22—861no—
364C22—861no—
365C22—3444no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22C2×D4×D4311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—861no—
374C4—861no—
375C4—861no—
376C4—1721no—
377C4—1721no—
378C4—1721no—
379C4C2×#1062190011yescharacteristic
380C4#1306337011yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—862no—
385C2—3441no—
386C2#1458353611yescharacteristic
387C2AGL(1,ℤ/8)×D4311yescharacteristic
388C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3306
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14583549C2semidirect
2. #14583537C2semidirect
3. #14583260C2semidirect
4. #14583228C2semidirect
5. #14583218C2semidirect
6. #14583187C2semidirect
7. #14583150C2semidirect
8. #14583125C2semidirect
9. #14583116C2semidirect
10. #14583031C2semidirect
11. #14583011C2semidirect
12. #14582973C2semidirect
13. #14582900C2semidirect
14. #102×D43C2semidirect
15. C43×#449C2semidirect
19. C2×#10621877C22semidirect
21. #13063324C22semidirect
33. D4×Dic43C22semidirect
35. C2×C4⋊Dic43C22semidirect
38. #13063257C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063249C22semidirect
43. #13063249C22semidirect
48. #13063246C22semidirect
51. #13063235C22semidirect
53. C2×SD16×C43C22semidirect
55. #121×C43C22semidirect
56. #103×C43C22semidirect
58. C22⋊C8×C43C22semidirect
127. D4×C43#41semidirect
204. #449D43semidirect
210. C43#3306semidirect
214. C2×SD16C2×D43semidirect
229. #121C2×D43semidirect
243. #103C2×D43semidirect
252. C22⋊C8C2×D43semidirect
329. D4#10621900semidirect