Subgroups — C₃×#534 #5864

Order 192.

346 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₃×#123	C₂	1	4	yes	maximal, complemented
3	C₃×#121	C₂	1	4	yes	maximal, complemented
4	C₃×#120	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#534	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂⁴×C₃	C₂²	1	1	yes	characteristic
8	C₂⁴×C₃	C₂²	1	2	yes	complemented
9	C₂×C₃×D₄	—	2	8	no	—
10	C₂×C₃×D₄	C₂²	1	4	yes	—
11	C₂×C₃×D₄	C₂²	1	4	yes	complemented
12	C₂×C₃×D₄	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₄	C₂²	1	2	yes	complemented
14	C₂²×C₃×C₄	C₂²	1	2	yes	complemented
15	C₃×C₄⋊C₄	C₂²	1	4	yes	complemented
16	C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
18	C₂²×D₄	C₂×C₃	1	2	yes	complemented
19	#123	C₂×C₃	1	4	yes	complemented
20	#121	C₂×C₃	1	4	yes	complemented
21	#120	C₂×C₃	1	4	yes	complemented
22	C₂×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂³×C₃	—	2	4	no	—
24	C₂³×C₃	—	4	2	no	—
25	C₂³×C₃	—	4	4	no	—
26	C₂³×C₃	D₄	1	4	yes	complemented
27	C₂³×C₃	C₂³	1	4	yes	—
28	C₂³×C₃	C₂³	1	2	yes	—
29	C₂³×C₃	C₂³	1	1	yes	characteristic
30	C₃×D₄	—	2	8	no	—
31	C₃×D₄	—	2	8	no	—
32	C₃×D₄	—	4	4	no	—
33	C₂×C₃×C₄	—	2	4	no	—
34	C₂×C₃×C₄	—	4	2	no	—
35	C₂×C₃×C₄	C₂³	1	4	yes	—
36	C₂×C₃×C₄	C₂³	1	4	yes	—
37	C₂⁴	C₂²×C₃	1	1	yes	characteristic
38	C₂⁴	C₂²×C₃	1	2	yes	complemented
39	C₂×D₄	—	2	8	no	—
40	C₂×D₄	C₂²×C₃	1	4	yes	—
41	C₂×D₄	C₂²×C₃	1	4	yes	complemented
42	C₂×D₄	C₂²×C₃	1	4	yes	complemented
43	C₂²×C₄	C₂²×C₃	1	2	yes	complemented
44	C₂²×C₄	C₂²×C₃	1	2	yes	complemented
45	C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
46	C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
47	C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
48	C₂²×C₃	—	2	2	no	—
49	C₂²×C₃	—	2	4	no	—
50	C₂²×C₃	—	2	4	no	—
51	C₂²×C₃	—	2	8	no	—
52	C₂²×C₃	—	4	4	no	—
53	C₂²×C₃	—	4	8	no	—
54	C₂²×C₃	C₂×D₄	1	4	yes	—
55	C₂²×C₃	C₂×D₄	1	2	yes	—
56	C₂²×C₃	C₂⁴	1	1	yes	characteristic
57	C₃×C₄	—	2	4	no	—
58	C₃×C₄	—	2	4	no	—
59	C₂³	—	2	4	no	—
60	C₂³	—	4	2	no	—
61	C₂³	—	4	4	no	—
62	C₂³	C₃×D₄	1	4	yes	complemented
63	C₂³	C₂³×C₃	1	4	yes	—
64	C₂³	C₂³×C₃	1	2	yes	—
65	C₂³	C₂³×C₃	1	1	yes	characteristic
66	D₄	—	2	8	no	—
67	D₄	—	2	8	no	—
68	D₄	—	4	4	no	—
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₂³×C₃	1	4	yes	—
72	C₂×C₄	C₂³×C₃	1	4	yes	—
73	C₂×C₃	—	2	4	no	—
74	C₂×C₃	—	2	2	no	—
75	C₂×C₃	—	4	4	no	—
76	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
77	C₂×C₃	H(5,𝔽₂)	1	2	yes	—
78	C₂²	—	2	2	no	—
79	C₂²	—	2	4	no	—
80	C₂²	—	2	4	no	—
81	C₂²	—	2	8	no	—
82	C₂²	—	4	4	no	—
83	C₂²	—	4	8	no	—
84	C₂²	C₂×C₃×D₄	1	4	yes	—
85	C₂²	C₂×C₃×D₄	1	2	yes	—
86	C₂²	C₂⁴×C₃	1	1	yes	characteristic
87	C₄	—	2	4	no	—
88	C₄	—	2	4	no	—
89	C₃	#534	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	—	2	4	no	—
91	C₂	—	2	2	no	—
92	C₂	—	4	4	no	—
93	C₂	C₂²×C₃×D₄	1	1	yes	characteristic
94	C₂	C₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄	C₂	semidirect
2. C₃×#123	C₂	semidirect
3. C₃×#121	C₂	semidirect
4. C₃×#120	C₂	semidirect
5. C₂×C₃×C₂²⋊C₄	C₂	semidirect
6. #534	C₃	direct (N × H)
8. C₂⁴×C₃	C₂²	semidirect
11. C₂×C₃×D₄	C₂²	semidirect
12. C₂×C₃×D₄	C₂²	semidirect
13. C₂²×C₃×C₄	C₂²	semidirect
14. C₂²×C₃×C₄	C₂²	semidirect
15. C₃×C₄⋊C₄	C₂²	semidirect
16. C₃×C₂²⋊C₄	C₂²	semidirect
17. C₃×C₂²⋊C₄	C₂²	semidirect
18. C₂²×D₄	C₂×C₃	semidirect
19. #123	C₂×C₃	semidirect
20. #121	C₂×C₃	semidirect
21. #120	C₂×C₃	semidirect
22. C₂×C₂²⋊C₄	C₂×C₃	semidirect
26. C₂³×C₃	D₄	semidirect
38. C₂⁴	C₂²×C₃	semidirect
41. C₂×D₄	C₂²×C₃	semidirect
42. C₂×D₄	C₂²×C₃	semidirect
43. C₂²×C₄	C₂²×C₃	semidirect
44. C₂²×C₄	C₂²×C₃	semidirect
45. C₄⋊C₄	C₂²×C₃	semidirect
46. C₂²⋊C₄	C₂²×C₃	semidirect
47. C₂²⋊C₄	C₂²×C₃	semidirect
62. C₂³	C₃×D₄	semidirect
89. C₃	#534	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₄	2
C₃×#123	2
C₃×#121	2
C₃×#120	2
C₂×C₃×C₂²⋊C₄	2
#534	3

Subgroups — C3×#534 #5864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#534 #5864