Subgroups — (C₁₂₇⋊C₃)⋊(C₂₇⋊C₃) #44525202

Order 30861.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23779872	C₃	1	3	yes	maximal, complemented
2	#23779871	C₃	1	3	yes	maximal, complemented
3	#23779870	C₃	1	3	yes	maximal, complemented
4	(C₁₂₇⋊C₃)⋊C₂₇	C₃	1	3	yes	maximal, complemented
5	C₃×C₉×C₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
6	#16812186	C₃²	1	9	yes	complemented
7	C₃²×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
8	C₃×#11765917	C₉	1	1	yes	characteristic
9	C₃×#11765917	C₃²	1	1	yes	characteristic
10	C₉×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
11	C₉×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
12	C₉×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
13	C₉×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
14	C₉×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
15	C₉×C₁₂₇⋊C₃	C₉	1	1	yes	characteristic
16	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
17	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
18	C₉×C₁₂₇⋊C₃	C₃²	1	1	yes	characteristic
19	C₃×C₉×C₁₂₇	C₉	1	1	yes	characteristic
20	C₃²×C₁₂₇	C₃×C₉	1	1	yes	characteristic
21	C₃×C₁₂₇⋊C₃	—	3	3	no	—
22	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
23	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
24	C₃×C₁₂₇⋊C₃	C₃×C₉	1	1	yes	characteristic
25	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
26	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
27	C₉×C₁₂₇	C₃×C₉	1	1	yes	characteristic
28	#11765917	C₃×C₉	1	1	yes	characteristic
29	#11765917	C₃×C₉	1	1	yes	characteristic
30	#11765917	C₃×C₉	1	1	yes	characteristic
31	#11765917	C₃×C₉	1	1	yes	characteristic
32	#11765917	C₃×C₉	1	1	yes	characteristic
33	#11765917	C₃³	1	1	yes	characteristic
34	C₃×C₁₂₇	—	3	1	no	—
35	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
36	C₁₂₇⋊C₃	—	3	1	no	—
37	C₁₂₇⋊C₃	—	3	1	no	—
38	C₁₂₇⋊C₃	C₂₇⋊C₃	1	3	yes	complemented
39	C₃×C₂₇⋊C₃	—	127	1	no	maximal, Sylow
40	C₁₂₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₃²×C₉	—	127	1	no	—
42	C₂₇⋊C₃	—	127	3	no	—
43	C₂₇⋊C₃	—	127	3	no	—
44	C₂₇⋊C₃	—	127	3	no	—
45	C₃×C₂₇	—	127	3	no	—
46	C₃³	—	127	1	no	—
47	C₃×C₉	—	127	1	no	—
48	C₃×C₉	—	127	1	no	—
49	C₃×C₉	—	127	1	no	—
50	C₃×C₉	—	127	1	no	—
51	C₃×C₉	—	127	1	no	—
52	C₃×C₉	—	127	1	no	—
53	C₃×C₉	—	127	1	no	—
54	C₃×C₉	—	127	1	no	—
55	C₃×C₉	—	127	1	no	—
56	C₃×C₉	—	127	1	no	—
57	C₃×C₉	—	127	1	no	—
58	C₃×C₉	#11765919	1	1	yes	characteristic
59	C₂₇	—	127	9	no	—
60	C₃²	—	381	3	no	—
61	C₃²	—	127	1	no	—
62	C₃²	—	127	1	no	—
63	C₃²	—	127	1	no	—
64	C₃²	C₃×#11765919	1	1	yes	characteristic
65	C₉	—	127	1	no	—
66	C₉	—	127	1	no	—
67	C₉	—	127	1	no	—
68	C₉	—	127	1	no	—
69	C₉	—	127	1	no	—
70	C₉	—	127	1	no	—
71	C₉	C₃×#11765919	1	1	yes	characteristic
72	C₉	C₃×#11765919	1	1	yes	characteristic
73	C₉	C₃×#11765919	1	1	yes	characteristic
74	C₃	—	3	1	no	—
75	C₃	—	381	1	no	—
76	C₃	—	381	1	no	—
77	C₃	—	127	3	no	—
78	C₃	C₃²×#11765919	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃×#11765919
commutator, socle	C₃×C₁₂₇	C₃²×C₉
Frattini	C₃	C₃²×#11765919
Fitting	C₃×C₉×C₁₂₇	C₉
prime radical	C₃²×C₁₂₇⋊C₃	C₉
cosocle	#11765917	C₃³
hypercenter	C₃×C₉	#11765919
hypocenter	C₁₂₇	C₃×C₂₇⋊C₃
LCS	G ▷ C₃×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₉ ◁ C₃×C₉

Complements

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

N	H ≅ G/N	type
1. #23779872	C₃	semidirect
2. #23779871	C₃	semidirect
3. #23779870	C₃	semidirect
4. (C₁₂₇⋊C₃)⋊C₂₇	C₃	semidirect
6. #16812186	C₃²	semidirect
38. C₁₂₇⋊C₃	C₂₇⋊C₃	semidirect
40. C₁₂₇	C₃×C₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#23779872	3
#23779871	3
#23779870	3
(C₁₂₇⋊C₃)⋊C₂₇	3
C₃×C₉×C₁₂₇⋊C₃	3
C₃×C₂₇⋊C₃	127

Subgroups — (C127⋊C3)⋊(C27⋊C3) #44525202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₁₂₇⋊C₃)⋊(C₂₇⋊C₃) #44525202