Subgroups — (C₃⋊(D₁₂₇⋊C₃))⋊D₇ #44544836

Order 32004.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁×C₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊(D₁₂₇⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×(C₁₂₇⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₁⋊D₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	D₇×D₁₂₇⋊C₃	—	3	1	no	maximal
6	C₃×C₇×C₁₂₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	(C₁₂₇⋊C₃)⋊D₇	—	2	1	no	—
8	(C₁₂₇⋊C₃)⋊D₇	D₃	1	1	yes	characteristic, complemented
9	D₇×C₁₂₇⋊C₃	—	3	1	no	—
10	C₇×D₁₂₇⋊C₃	—	3	1	no	—
11	D₂₁×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₇×D₃₈₁	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×D₈₈₉	C₂×C₃	1	1	yes	characteristic, complemented
14	D₃×D₁₂₇⋊C₃	—	7	1	no	maximal, Hall
15	D₇×D₁₂₇	—	3	1	no	Hall
16	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic, complemented
17	C₇×C₁₂₇⋊C₃	—	2	1	no	—
18	C₇×C₁₂₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
19	D₃×C₁₂₇⋊C₃	—	7	1	no	—
20	C₃⋊(D₁₂₇⋊C₃)	D₇	1	1	yes	characteristic, complemented
21	C₃×D₁₂₇⋊C₃	—	7	1	no	—
22	D₈₈₉	C₃×D₃	1	1	yes	characteristic, complemented
23	C₇×D₁₂₇	—	3	1	no	—
24	D₇×C₁₂₇	—	3	1	no	—
25	D₃×D₁₂₇	—	7	1	no	—
26	C₂×D₁₂₇⋊C₃	—	21	1	no	—
27	C₃×C₁₂₇⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
28	C₇×C₁₂₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	D₃₈₁	C₃×D₇	1	1	yes	characteristic, complemented
30	C₃×D₁₂₇	—	7	1	no	—
31	D₃×C₁₂₇	—	7	1	no	—
32	C₂×C₁₂₇⋊C₃	—	21	1	no	—
33	D₁₂₇⋊C₃	—	3	1	no	—
34	D₁₂₇⋊C₃	—	7	1	no	—
35	D₁₂₇⋊C₃	—	14	1	no	—
36	C₂×D₁₂₇	—	21	1	no	Hall
37	C₃×C₁₂₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented
38	C₁₂₇⋊C₃	—	2	1	no	—
39	C₁₂₇⋊C₃	D₃×D₇	1	1	yes	characteristic, complemented
40	C₂×C₁₂₇	—	21	1	no	—
41	D₁₂₇	—	3	1	no	—
42	D₁₂₇	—	7	1	no	—
43	C₃×D₃×D₇	—	127	1	no	maximal, Hall
44	C₁₂₇	C₃×D₃×D₇	1	1	yes	characteristic, complemented, Sylow
45	C₃×D₂₁	—	127	1	no	—
46	C₃×D₃×C₇	—	127	1	no	—
47	C₃²×D₇	—	127	1	no	—
48	C₂×C₃×D₇	—	381	1	no	—
49	D₃×D₇	—	127	1	no	—
50	C₃²×C₇	—	127	1	no	Hall
51	C₂×C₃×C₇	—	381	1	no	—
52	D₂₁	D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
53	C₃×D₇	—	381	1	no	—
54	C₃×D₇	—	127	1	no	—
55	C₃×D₇	—	127	1	no	—
56	C₃×D₇	—	254	1	no	—
57	D₃×C₇	—	127	1	no	—
58	C₂×C₃×D₃	—	889	1	no	Hall
59	C₂×D₇	—	381	1	no	Hall
60	C₃×C₇	—	127	1	no	—
61	C₃×C₇	—	254	1	no	—
62	C₃×C₇	C₂×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
63	C₂×C₃²	—	889	1	no	—
64	C₃×D₃	—	889	1	no	—
65	C₃×D₃	—	127	1	no	—
66	C₂×C₇	—	381	1	no	—
67	D₇	—	3	1	no	—
68	D₇	—	127	1	no	—
69	C₂²×C₃	—	2667	1	no	—
70	C₂×D₃	—	889	1	no	—
71	C₃²	—	127	1	no	Sylow
72	C₇	D₃×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	2667	1	no	—
74	C₂×C₃	—	889	1	no	—
75	C₂×C₃	—	889	1	no	—
76	C₂×C₃	—	381	1	no	—
77	C₂×C₃	—	1778	1	no	—
78	D₃	—	7	1	no	—
79	D₃	—	127	1	no	—
80	C₂²	—	2667	1	no	Sylow
81	C₃	—	127	1	no	—
82	C₃	—	254	1	no	—
83	C₃	D₇×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	21	1	no	—
85	C₂	—	889	1	no	—
86	C₂	—	381	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₂₇	C₂²×C₃
LCS	G ▷ C₃×C₇×C₁₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₁×C₁₂₇⋊C₃	C₂	semidirect
2. C₇×C₃⋊(D₁₂₇⋊C₃)	C₂	semidirect
3. C₃×(C₁₂₇⋊C₃)⋊D₇	C₂	semidirect
4. D₂₁⋊D₁₂₇	C₃	semidirect
6. C₃×C₇×C₁₂₇⋊C₃	C₂²	semidirect
8. (C₁₂₇⋊C₃)⋊D₇	D₃	semidirect
11. D₂₁×C₁₂₇	C₂×C₃	semidirect
12. C₇×D₃₈₁	C₂×C₃	semidirect
13. C₃×D₈₈₉	C₂×C₃	semidirect
16. C₃×C₇×C₁₂₇	C₂²×C₃	semidirect
18. C₇×C₁₂₇⋊C₃	C₂×D₃	semidirect
20. C₃⋊(D₁₂₇⋊C₃)	D₇	semidirect
22. D₈₈₉	C₃×D₃	semidirect
27. C₃×C₁₂₇⋊C₃	C₂×D₇	semidirect
28. C₇×C₁₂₇	C₂×C₃×D₃	semidirect
29. D₃₈₁	C₃×D₇	semidirect
37. C₃×C₁₂₇	C₂×C₃×D₇	semidirect
39. C₁₂₇⋊C₃	D₃×D₇	semidirect
44. C₁₂₇	C₃×D₃×D₇	semidirect
52. D₂₁	D₁₂₇⋊C₃	semidirect
62. C₃×C₇	C₂×D₁₂₇⋊C₃	semidirect
72. C₇	D₃×D₁₂₇⋊C₃	semidirect
83. C₃	D₇×D₁₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₂₁×C₁₂₇⋊C₃	2
C₇×C₃⋊(D₁₂₇⋊C₃)	2
C₃×(C₁₂₇⋊C₃)⋊D₇	2
D₂₁⋊D₁₂₇	3
D₇×D₁₂₇⋊C₃	3
D₃×D₁₂₇⋊C₃	7
C₃×D₃×D₇	127

Subgroups — (C3⋊(D127⋊C3))⋊D7 #44544836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊(D₁₂₇⋊C₃))⋊D₇ #44544836