Finite Group Databasebeta

← #19145459

Subgroups — #19145459

Order 5504.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583468C211yesmaximal, characteristic, complemented
2#14583465C211yesmaximal, characteristic, complemented
3#14583226C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583223C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic, complemented
8#14583136C211yesmaximal, characteristic, complemented
9#14583134C211yesmaximal, characteristic, complemented
10#14583035C211yesmaximal, characteristic, complemented
11#14583034C211yesmaximal, characteristic, complemented
12#14583034C211yesmaximal, characteristic, complemented
13#14583032C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic, complemented
18C2×D4×D43C2211yescharacteristic, complemented
19C2×D344C2211yescharacteristic
20C2×D344C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621872C2211yescharacteristic, complemented
24C2×C8×D43C2211yescharacteristic, complemented
25#13063322—21no—
26#13063321—21no—
27#13063313—21no—
28#13063311—21no—
29#13063300C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic, complemented
32#13063300C2211yescharacteristic, complemented
33#13063300C2211yescharacteristic, complemented
34#13063299C2211yescharacteristic
35#13063296C2211yescharacteristic, complemented
36#13063295—21no—
37#13063295—21no—
38#13063295—21no—
39#13063293—21no—
40#13063283C2211yescharacteristic, complemented
41#13063258C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063245C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43D411yescharacteristic
68C2×C22⋊D43D411yescharacteristic
69D4×D43—41no—
70D4×D43—41no—
71#10621898—41no—
72#10621898—41no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172D411yescharacteristic
82C2×D172C2311yescharacteristic
83C2×D172C2311yescharacteristic
84C2×D172C2311yescharacteristic
85C2×C4×D43C2311yescharacteristic
86C2×C4×D43C2311yescharacteristic
87C2×Dic86D411yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C2×C8×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C42×C43—21no—
96C22⋊Dic43—21no—
97#10621882—41no—
98#10621882—41no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106C4⋊Dic43C2311yescharacteristic
107C4×Dic43—21no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110D344—41no—
111D344—41no—
112#10621872—41no—
113C8×D43—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43C2×D411yescharacteristic
126C22×D43C2×D411yescharacteristic
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—81no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—41no—
138C22⋊D43—41no—
139C22⋊D43—42no—
140C22⋊D43—81no—
141C22⋊D43—81no—
142C2×Dic43—21no—
143C2×Dic43C2×D411yescharacteristic
144C2×Dic43C2×D411yescharacteristic
145D172—21no—
146D172—21no—
147D172—21no—
148D172—21no—
149D172—21no—
150D172—21no—
151D172—41no—
152D172—42no—
153D172—81no—
154D172—81no—
155D172—81no—
156D172—81no—
157D172—81no—
158C4×D43—21no—
159C4×D43—21no—
160C4×D43—21no—
161C4×D43—21no—
162Dic86—41no—
163C8×C43—21no—
164C8×C43—21no—
165C43⋊C8—21no—
166C43⋊C8—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43C22×D411yescharacteristic
174C2×D43—21no—
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—21no—
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—84no—
190C2×D43—84no—
191C4×C43—21no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43—41no—
195C4×C43H(5,𝔽2)11yescharacteristic
196C4×C43H(5,𝔽2)11yescharacteristic
197Dic43—21no—
198Dic43—21no—
199Dic43—41no—
200#3199—431nomaximal, Sylow
201C2×C43—41no—
202C2×C43—81no—
203C2×C43#53411yescharacteristic
204C2×C43#57611yescharacteristic
205C2×C43#57611yescharacteristic
206D43—41no—
207D43—41no—
208D43—81no—
209D43—81no—
210D43—81no—
211#535—431no—
212#535—431no—
213#482—431no—
214#482—431no—
215#482—431no—
216#482D4311yescharacteristic, complemented
217#469—431no—
218#469—431no—
219#466—431no—
220#466—431no—
221#447—431no—
222#447—431no—
223#447—431no—
224#447—431no—
225#408—431no—
226C43#319911yescharacteristic, complemented, Sylow
227C2×#41—431no—
228C22×D4—431no—
229C22×D4—431no—
230C2×D8—431no—
231C2×D8—431no—
232C2×D8—431no—
233C2×D8—431no—
234C2×M16—431no—
235C22×C8—431no—
236#127—861no—
237#127—861no—
238#124—861no—
239#124—861no—
240#121—431no—
241#121—431no—
242#121—431no—
243#121—431no—
244#121—431no—
245#121—431no—
246#121—431no—
247#121C2×D4311yescharacteristic
248#120—861no—
249#120—861no—
250#120—861no—
251#120—861no—
252#117—431no—
253#117C2×D4311yescharacteristic, complemented
254#107—431no—
255#107C2×D4311yescharacteristic, complemented
256#106—431no—
257#106C2×D4311yescharacteristic, complemented
258#102—431no—
259#102—431no—
260#102—431no—
261#102—431no—
262#102—431no—
263#102—431no—
264#102C2×D4311yescharacteristic, complemented
265#102C2×D4311yescharacteristic, complemented
266C22⋊C8—431no—
267C22⋊C8—431no—
268C22⋊C8—431no—
269C22⋊C8C2×D4311yescharacteristic, complemented
270C24—861no—
271C24—861no—
272#41—1721no—
273#41—1721no—
274C2×Q8—431no—
275C2×D4—21no—
276C2×D4—431no—
277C2×D4—431no—
278C2×D4—431no—
279C2×D4—431no—
280C2×D4—431no—
281C2×D4—431no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—861no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—1721no—
292C2×D4—1721no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4C22×D4311yescharacteristic
296C22×C4—431no—
297C22×C4—431no—
298C22×C4C22×D4311yescharacteristic
299D8—1721no—
300D8—1721no—
301D8—1721no—
302D8—1721no—
303M16—1721no—
304C2×C8—431no—
305C2×C8—431no—
306C2×C8—1721no—
307C2×C8C22×D4311yescharacteristic
308C2×C8C22×D4311yescharacteristic
309C4⋊C4—431no—
310C4⋊C4C22×D4311yescharacteristic
311C4⋊C4C22×D4311yescharacteristic
312C4⋊C4C22×D4311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C22⋊C4—861no—
322C22⋊C4—861no—
323C42—21no—
324C42—861no—
325C23—21no—
326C23—431no—
327C23—431no—
328C23—861no—
329C23—861no—
330C23—861no—
331C23—3441no—
332C23—3441no—
333C23—3441no—
334C23—3441no—
335C23—1722no—
336C23—1722no—
337C23D4×D4311yescharacteristic
338Q8—1721no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—861no—
343D4—861no—
344D4—861no—
345D4—861no—
346D4—861no—
347D4—861no—
348D4—3441no—
349D4—3441no—
350D4—3441no—
351D4—3441no—
352D4—3441no—
353D4—3441no—
354D4—3441no—
355D4—1721no—
356D4—1722no—
357D4—1721no—
358D4—1721no—
359D4—1722no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—431no—
366C2×C4—431no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4D4×D4311yescharacteristic
373C2×C4C23×D4311yescharacteristic
374C8—21no—
375C8—21no—
376C8—861no—
377C8—861no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—861no—
385C22—861no—
386C22—861no—
387C22—861no—
388C22—861no—
389C22—861no—
390C22—3444no—
391C22—3444no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22—1721no—
396C22—1721no—
397C22—1721no—
398C22—1721no—
399C22—1721no—
400C22—1721no—
401C22C2×D4×D4311yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—861no—
407C4—861no—
408C4—1721no—
409C4#1306337111yescharacteristic
410C4#1306337111yescharacteristic
411C2—41no—
412C2—81no—
413C2—3441no—
414C2—3441no—
415C2—3441no—
416C2—1721no—
417C2—1721no—
418C2#1458346011yescharacteristic
419C2#1458370111yescharacteristic
420C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3199
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14583468C2semidirect
2. #14583465C2semidirect
3. #14583226C2semidirect
4. #14583225C2semidirect
5. #14583223C2semidirect
6. #14583153C2semidirect
7. #14583151C2semidirect
8. #14583136C2semidirect
9. #14583134C2semidirect
10. #14583035C2semidirect
11. #14583034C2semidirect
12. #14583034C2semidirect
13. #14583032C2semidirect
14. #14582864C2semidirect
15. C43×#482C2semidirect
17. C22×D172C22semidirect
18. C2×D4×D43C22semidirect
23. C2×#10621872C22semidirect
24. C2×C8×D43C22semidirect
31. #13063300C22semidirect
32. #13063300C22semidirect
33. #13063300C22semidirect
35. #13063296C22semidirect
40. #13063283C22semidirect
41. #13063258C22semidirect
42. #13063256C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
45. #13063245C22semidirect
46. #13063245C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
53. #117×C43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
58. C22⋊C8×C43C22semidirect
216. #482D43semidirect
226. C43#3199semidirect
253. #117C2×D43semidirect
255. #107C2×D43semidirect
257. #106C2×D43semidirect
264. #102C2×D43semidirect
265. #102C2×D43semidirect
269. C22⋊C8C2×D43semidirect