Subgroups — C₄×D₃×#3861 #72245793

Order 3528.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×#3861	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#3861	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃×#3861	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₃×C₇²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×#3861	—	3	1	no	maximal
6	C₂×C₃×#3861	C₂²	1	1	yes	characteristic
7	D₃×#3861	C₄	1	2	yes	direct product factor
8	C₂×D₃×C₇²	C₂×C₃	1	1	yes	characteristic
9	C₂²×#3861	—	3	1	no	—
10	C₃×C₄×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
11	C₇²×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
12	C₄×#3861	—	2	1	no	—
13	C₄×#3861	—	3	1	no	—
14	C₄×#3861	D₃	1	1	yes	characteristic, direct product factor
15	C₄×D₃×ΓL(1,𝔽₈)	—	7	8	no	maximal
16	C₃×#3861	C₂×C₄	1	1	yes	characteristic, complemented, Hall
17	C₂×C₄×C₇²	—	3	1	no	Hall
18	C₂×C₃×C₇²	C₂²×C₃	1	1	yes	characteristic
19	D₃×C₇²	C₃×C₄	1	2	yes	complemented
20	C₂×#3861	—	2	1	no	—
21	C₂×#3861	—	3	2	no	—
22	C₂×#3861	C₂×D₃	1	1	yes	characteristic
23	C₂×D₃×ΓL(1,𝔽₈)	—	7	8	no	—
24	C₃×C₄×ΓL(1,𝔽₈)	—	7	8	no	—
25	Dic₃×ΓL(1,𝔽₈)	—	7	8	no	—
26	C₂²×C₇²	—	3	1	no	—
27	C₄×C₇²	—	3	1	no	—
28	C₄×C₇²	C₃×D₃	1	1	yes	characteristic, complemented
29	C₄×D₃×C₇	ΓL(1,𝔽₈)	1	8	yes	complemented
30	C₂×C₄×ΓL(1,𝔽₈)	—	21	8	no	—
31	C₃×C₇²	C₂×C₃×C₄	1	1	yes	characteristic, complemented
32	#3861	—	2	1	no	—
33	#3861	C₄×D₃	1	1	yes	characteristic, direct product factor
34	C₂×C₃×ΓL(1,𝔽₈)	—	7	8	no	—
35	D₃×ΓL(1,𝔽₈)	—	7	16	no	—
36	C₂×C₇²	—	3	2	no	—
37	C₂×C₇²	C₂×C₃×D₃	1	1	yes	characteristic
38	C₂×D₃×C₇	C₂×ΓL(1,𝔽₈)	1	8	yes	—
39	C₂²×ΓL(1,𝔽₈)	—	21	8	no	—
40	C₃×C₄×C₇	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
41	C₇×Dic₃	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
42	C₄×ΓL(1,𝔽₈)	—	7	8	no	—
43	C₄×ΓL(1,𝔽₈)	—	14	8	no	—
44	C₄×ΓL(1,𝔽₈)	—	21	8	no	—
45	C₃×C₄×D₃	—	49	1	no	Hall
46	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
47	C₂×C₄×C₇	—	3	8	no	—
48	C₇²	C₃×C₄×D₃	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₇	C₂²×ΓL(1,𝔽₈)	1	8	yes	—
50	D₃×C₇	C₄×ΓL(1,𝔽₈)	1	16	yes	complemented
51	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
52	C₂×ΓL(1,𝔽₈)	—	14	8	no	—
53	C₂×ΓL(1,𝔽₈)	—	21	16	no	—
54	C₂×C₃×D₃	—	49	1	no	—
55	C₃²×C₄	—	49	1	no	—
56	C₃×Dic₃	—	49	1	no	—
57	C₂²×C₇	—	3	8	no	—
58	C₄×C₇	—	3	8	no	—
59	C₄×C₇	D₃×ΓL(1,𝔽₈)	1	8	yes	complemented
60	C₂×C₃×C₄	—	147	1	no	—
61	C₄×D₃	#3861	1	1	yes	characteristic, direct product factor
62	C₃×C₇	C₂×C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
63	ΓL(1,𝔽₈)	—	7	8	no	—
64	ΓL(1,𝔽₈)	—	14	8	no	—
65	C₂×C₃²	—	49	1	no	—
66	C₃×D₃	—	49	2	no	—
67	C₂×C₇	—	3	16	no	—
68	C₂×C₇	C₂×D₃×ΓL(1,𝔽₈)	1	8	yes	—
69	C₂²×C₃	—	147	1	no	—
70	C₂×D₃	C₂×#3861	1	1	yes	characteristic
71	C₃×C₄	—	49	1	no	—
72	C₃×C₄	—	98	1	no	—
73	C₃×C₄	—	147	1	no	—
74	C₃×C₄	C₂×#3861	1	1	yes	characteristic, complemented
75	Dic₃	C₂×#3861	1	1	yes	characteristic, complemented
76	C₃²	—	49	1	no	Sylow
77	C₂×C₄	—	3	1	no	Sylow
78	C₇	C₄×D₃×ΓL(1,𝔽₈)	1	8	yes	complemented
79	C₂×C₃	—	49	1	no	—
80	C₂×C₃	—	98	1	no	—
81	C₂×C₃	—	147	2	no	—
82	C₂×C₃	C₂²×#3861	1	1	yes	characteristic
83	D₃	C₄×#3861	1	2	yes	direct product factor
84	C₂²	—	3	1	no	—
85	C₄	—	3	1	no	—
86	C₄	D₃×#3861	1	1	yes	characteristic, direct product factor
87	C₃	—	49	1	no	—
88	C₃	—	98	1	no	—
89	C₃	C₂×C₄×#3861	1	1	yes	characteristic, complemented
90	C₂	—	3	2	no	—
91	C₂	C₂×D₃×#3861	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₃×#3861
commutator, hypocenter	C₃×C₇²	C₂×C₃×C₄
Frattini	C₂	C₂×D₃×#3861
Fitting	C₃×C₄×C₇²	C₂×C₃
socle, cosocle	C₂×C₃×C₇²	C₂²×C₃
prime radical	C₂×D₃×#3861	C₂
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#3861	C₂	semidirect
3. Dic₃×#3861	C₂	semidirect
4. C₄×D₃×C₇²	C₃	semidirect
7. D₃×#3861	C₄	direct (N × H)
10. C₃×C₄×C₇²	C₂×C₃	semidirect
11. C₇²×Dic₃	C₂×C₃	semidirect
14. C₄×#3861	D₃	direct (N × H)
16. C₃×#3861	C₂×C₄	semidirect
19. D₃×C₇²	C₃×C₄	semidirect
28. C₄×C₇²	C₃×D₃	semidirect
29. C₄×D₃×C₇	ΓL(1,𝔽₈)	semidirect
31. C₃×C₇²	C₂×C₃×C₄	semidirect
33. #3861	C₄×D₃	direct (N × H)
40. C₃×C₄×C₇	C₂×ΓL(1,𝔽₈)	semidirect
41. C₇×Dic₃	C₂×ΓL(1,𝔽₈)	semidirect
48. C₇²	C₃×C₄×D₃	semidirect
50. D₃×C₇	C₄×ΓL(1,𝔽₈)	semidirect
59. C₄×C₇	D₃×ΓL(1,𝔽₈)	semidirect
61. C₄×D₃	#3861	direct (N × H)
62. C₃×C₇	C₂×C₄×ΓL(1,𝔽₈)	semidirect
74. C₃×C₄	C₂×#3861	semidirect
75. Dic₃	C₂×#3861	semidirect
78. C₇	C₄×D₃×ΓL(1,𝔽₈)	semidirect
83. D₃	C₄×#3861	direct (N × H)
86. C₄	D₃×#3861	direct (N × H)
89. C₃	C₂×C₄×#3861	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×#3861	2
C₃×C₄×#3861	2
Dic₃×#3861	2
C₄×D₃×C₇²	3
C₂×C₄×#3861	3
C₄×D₃×ΓL(1,𝔽₈)	7

Subgroups — C4×D3×#3861 #72245793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃×#3861 #72245793