Subgroups — C₂×#1010 #5963

Order 192.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#1010	C₂	1	16	yes	maximal, direct product factor
3	C₂×D₃×Q₈	C₂	1	2	yes	maximal, complemented
4	C₂×#237	C₂	1	6	yes	maximal, complemented
5	C₂×#235	C₂	1	3	yes	maximal, complemented
6	C₂²×Dic₆	C₂	1	3	yes	maximal, complemented
7	C₂×2₋¹⁺⁴	—	3	1	no	maximal, Sylow
8	C₃×#41	C₂²	1	8	yes	complemented
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₄	C₂²	1	3	yes	—
11	C₂²×C₃×C₄	C₂²	1	3	yes	—
12	C₂×#67	C₂²	1	6	yes	—
13	C₂²×Dic₃	C₂²	1	6	yes	—
14	D₃×Q₈	C₂²	1	16	yes	complemented
15	#237	C₂²	1	48	yes	complemented
16	#235	C₂²	1	24	yes	complemented
17	C₂×D₁₂	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃	C₂²	1	6	yes	—
19	C₂×Dic₆	C₂²	1	3	yes	—
20	C₂×Dic₆	C₂²	1	6	yes	—
21	C₂×Dic₆	C₂²	1	24	yes	complemented
22	2₋¹⁺⁴	—	3	16	no	—
23	C₂×#41	—	3	6	no	—
24	C₂×#41	—	3	3	no	—
25	C₂×#41	D₃	1	1	yes	characteristic, complemented
26	C₂²×Q₈	—	3	2	no	—
27	C₂²×Q₈	—	3	3	no	—
28	C₂³×C₃	C₂³	1	3	yes	—
29	C₂²×D₃	C₂³	1	2	yes	—
30	C₃×Q₈	C₂³	1	4	yes	—
31	C₃×D₄	C₂³	1	12	yes	—
32	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂³	1	3	yes	—
34	C₂×C₃×C₄	C₂³	1	12	yes	—
35	#67	C₂³	1	24	yes	—
36	C₂×Dic₃	C₂³	1	6	yes	—
37	C₂×Dic₃	C₂³	1	24	yes	—
38	D₁₂	C₂³	1	4	yes	—
39	C₄×D₃	C₂³	1	24	yes	—
40	Dic₆	C₂³	1	12	yes	—
41	Dic₆	C₂³	1	24	yes	—
42	#41	—	3	48	no	—
43	#41	—	3	24	no	—
44	#41	C₂×D₃	1	8	yes	complemented
45	C₂×Q₈	—	3	16	no	—
46	C₂×Q₈	—	3	6	no	—
47	C₂×Q₈	—	3	3	no	—
48	C₂×Q₈	—	3	24	no	—
49	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
50	C₂×D₄	—	3	6	no	—
51	C₂×D₄	—	3	1	no	—
52	C₂×D₄	C₂×D₃	1	3	yes	—
53	C₂²×C₄	—	3	6	no	—
54	C₂²×C₄	—	3	6	no	—
55	C₂²×C₄	C₂×D₃	1	3	yes	—
56	C₂²×C₃	—	2	6	no	—
57	C₂²×C₃	C₂⁴	1	6	yes	—
58	C₂²×C₃	C₂⁴	1	1	yes	characteristic
59	C₂×D₃	—	2	4	no	—
60	C₂×D₃	C₂⁴	1	4	yes	—
61	C₃×C₄	C₂⁴	1	2	yes	—
62	C₃×C₄	C₂⁴	1	6	yes	—
63	Dic₃	C₂⁴	1	12	yes	—
64	C₂³	—	3	2	no	—
65	C₂³	C₂²×D₃	1	3	yes	—
66	Q₈	—	3	24	no	—
67	Q₈	—	3	12	no	—
68	Q₈	C₂²×D₃	1	4	yes	—
69	D₄	—	3	24	no	—
70	D₄	—	3	4	no	—
71	D₄	C₂²×D₃	1	12	yes	—
72	C₂×C₄	—	3	24	no	—
73	C₂×C₄	—	3	6	no	—
74	C₂×C₄	—	3	24	no	—
75	C₂×C₄	C₂²×D₃	1	12	yes	—
76	C₂×C₄	C₂²×D₃	1	3	yes	—
77	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
78	C₂×C₃	—	2	6	no	—
79	C₂×C₃	2₋¹⁺⁴	1	2	yes	complemented
80	C₂×C₃	C₂⁵	1	1	yes	characteristic
81	D₃	—	2	4	no	—
82	C₂²	—	2	6	no	—
83	C₂²	—	3	4	no	—
84	C₂²	—	6	4	no	—
85	C₂²	C₂³×D₃	1	6	yes	—
86	C₂²	C₂³×D₃	1	1	yes	characteristic
87	C₄	—	3	12	no	—
88	C₄	C₂³×D₃	1	6	yes	—
89	C₄	C₂³×D₃	1	2	yes	—
90	C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	2	6	no	—
92	C₂	—	6	4	no	—
93	C₂	#1010	1	2	yes	direct product factor
94	C₂	C₂⁴×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₃
commutator, cosocle	C₂×C₃	C₂⁵
Frattini	C₂	C₂⁴×D₃
Fitting	C₂×C₃×#41	C₂
socle	C₂²×C₃	C₂⁴
hypercenter	C₂×#41	D₃
hypocenter	C₃	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#41	C₂	semidirect
2. #1010	C₂	direct (N × H)
3. C₂×D₃×Q₈	C₂	semidirect
4. C₂×#237	C₂	semidirect
5. C₂×#235	C₂	semidirect
6. C₂²×Dic₆	C₂	semidirect
8. C₃×#41	C₂²	semidirect
14. D₃×Q₈	C₂²	semidirect
15. #237	C₂²	semidirect
16. #235	C₂²	semidirect
21. C₂×Dic₆	C₂²	semidirect
25. C₂×#41	D₃	semidirect
44. #41	C₂×D₃	semidirect
79. C₂×C₃	2₋¹⁺⁴	semidirect
90. C₃	C₂×2₋¹⁺⁴	semidirect
93. C₂	#1010	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#41	2
#1010	2
C₂×D₃×Q₈	2
C₂×#237	2
C₂×#235	2
C₂²×Dic₆	2
C₂×2₋¹⁺⁴	3

Subgroups — C2×#1010 #5963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1010 #5963