Subgroups — C₂₇⋊C₃×C₁₂₇⋊C₃ #44525082

Order 30861.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#23779840	C₃	1	2	yes	maximal, complemented
3	#23779839	C₃	1	3	yes	maximal, complemented
4	#23779838	C₃	1	3	yes	maximal, complemented
5	C₂₇×C₁₂₇⋊C₃	C₃	1	3	yes	maximal, complemented
6	C₂₇⋊C₃×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
8	C₃×#11765917	C₉	1	2	yes	—
9	C₉×C₁₂₇⋊C₃	C₉	1	2	yes	—
10	C₉×C₁₂₇⋊C₃	C₉	1	2	yes	—
11	C₉×C₁₂₇⋊C₃	C₉	1	2	yes	—
12	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
13	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
14	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
15	#16812178	C₃²	1	6	yes	complemented
16	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
17	C₂₇×C₁₂₇	C₃²	1	3	yes	complemented
18	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
19	C₃×C₁₂₇⋊C₃	—	3	3	no	—
20	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
21	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
23	C₉×C₁₂₇	C₃×C₉	1	2	yes	—
24	C₉×C₁₂₇	C₃³	1	1	yes	characteristic
25	#11765917	C₃×C₉	1	2	yes	—
26	#11765917	C₃×C₉	1	2	yes	—
27	#11765917	C₃×C₉	1	2	yes	—
28	C₃×C₁₂₇	—	3	1	no	—
29	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
30	C₁₂₇⋊C₃	—	3	1	no	—
31	C₁₂₇⋊C₃	—	3	1	no	—
32	C₁₂₇⋊C₃	C₂₇⋊C₃	1	3	yes	direct product factor
33	C₃×C₂₇⋊C₃	—	127	1	no	maximal, Sylow
34	C₁₂₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₃²×C₉	—	127	1	no	—
36	C₂₇⋊C₃	—	127	2	no	—
37	C₂₇⋊C₃	—	127	3	no	—
38	C₂₇⋊C₃	—	127	3	no	—
39	C₂₇⋊C₃	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃×C₂₇	—	127	3	no	—
41	C₃³	—	127	1	no	—
42	C₃×C₉	—	127	2	no	—
43	C₃×C₉	—	127	2	no	—
44	C₃×C₉	—	127	2	no	—
45	C₃×C₉	—	127	2	no	—
46	C₃×C₉	—	127	1	no	—
47	C₃×C₉	—	127	1	no	—
48	C₃×C₉	—	127	1	no	—
49	C₃×C₉	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
50	C₂₇	—	127	6	no	—
51	C₂₇	C₃×C₁₂₇⋊C₃	1	3	yes	complemented
52	C₃²	—	381	3	no	—
53	C₃²	—	127	1	no	—
54	C₃²	—	127	1	no	—
55	C₃²	—	127	1	no	—
56	C₃²	C₉×C₁₂₇⋊C₃	1	1	yes	characteristic
57	C₉	—	127	2	no	—
58	C₉	—	127	2	no	—
59	C₉	—	127	2	no	—
60	C₉	C₉×C₁₂₇⋊C₃	1	2	yes	—
61	C₉	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
62	C₃	—	3	1	no	—
63	C₃	—	381	1	no	—
64	C₃	—	381	1	no	—
65	C₃	—	127	3	no	—
66	C₃	C₃×C₉×C₁₂₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉	C₃²×C₁₂₇⋊C₃
commutator, socle	C₃×C₁₂₇	C₃²×C₉
Fitting	C₂₇⋊C₃×C₁₂₇	C₃
prime radical	C₃²×C₁₂₇⋊C₃	C₉
cosocle	C₉×C₁₂₇	C₃³
hypercenter	C₂₇⋊C₃	C₁₂₇⋊C₃
hypocenter	C₁₂₇	C₃×C₂₇⋊C₃
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #23779840	C₃	semidirect
3. #23779839	C₃	semidirect
4. #23779838	C₃	semidirect
5. C₂₇×C₁₂₇⋊C₃	C₃	semidirect
6. C₂₇⋊C₃×C₁₂₇	C₃	semidirect
15. #16812178	C₃²	semidirect
17. C₂₇×C₁₂₇	C₃²	semidirect
32. C₁₂₇⋊C₃	C₂₇⋊C₃	direct (N × H)
34. C₁₂₇	C₃×C₂₇⋊C₃	semidirect
39. C₂₇⋊C₃	C₁₂₇⋊C₃	direct (N × H)
51. C₂₇	C₃×C₁₂₇⋊C₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₉×C₁₂₇⋊C₃	3
#23779840	3
#23779839	3
#23779838	3
C₂₇×C₁₂₇⋊C₃	3
C₂₇⋊C₃×C₁₂₇	3
C₃×C₂₇⋊C₃	127

Subgroups — C27⋊C3×C127⋊C3 #44525082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₇⋊C₃×C₁₂₇⋊C₃ #44525082