Subgroups — C₂×#19134210 #25084288

Order 11008.

1342 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583276	C₂	1	6	yes	maximal, complemented
2	#19134210	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₃₄₄	—	2	12	no	—
5	C₂×#13063322	C₂²	1	4	yes	—
6	#14583276	—	2	12	no	—
7	#14583276	C₂²	1	24	yes	complemented
8	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	—
9	C₈²×C₄₃	C₂²	1	4	yes	complemented
10	C₂²×D₁₇₂	—	2	12	no	—
11	C₂×D₃₄₄	—	2	48	no	—
12	C₂×D₃₄₄	—	4	48	no	—
13	#13063322	—	2	12	no	—
14	#13063322	C₂³	1	8	yes	—
15	C₂²×C₈×C₄₃	D₄	1	6	yes	—
16	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
17	C₄×C₈×C₄₃	D₄	1	6	yes	—
18	C₄×C₈×C₄₃	C₂³	1	6	yes	—
19	C₂³×D₄₃	—	4	4	no	—
20	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
21	C₂×D₁₇₂	—	2	24	no	—
22	C₂×D₁₇₂	—	4	12	no	—
23	C₂×D₁₇₂	—	4	48	no	—
24	C₂×C₈×C₄₃	D₈	1	24	yes	complemented
25	C₂×C₈×C₄₃	C₂×D₄	1	12	yes	—
26	C₄²×C₄₃	C₂×D₄	1	3	yes	—
27	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
28	D₃₄₄	—	4	96	no	—
29	C₂³×C₄₃	#127	1	1	yes	characteristic
30	C₂²×D₄₃	—	4	8	no	—
31	C₂²×D₄₃	—	8	24	no	—
32	C₂×C₄×C₄₃	#127	1	3	yes	—
33	C₂×C₄×C₄₃	C₂×D₈	1	12	yes	—
34	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
35	D₁₇₂	—	4	48	no	—
36	D₁₇₂	—	8	24	no	—
37	C₈×C₄₃	C₂×D₈	1	24	yes	complemented
38	C₂×#1712	—	43	1	no	maximal, Sylow
39	C₂²×C₄₃	#493	1	6	yes	—
40	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
41	C₂×D₄₃	—	8	24	no	—
42	C₂×D₄₃	—	16	16	no	—
43	C₄×C₄₃	#493	1	6	yes	—
44	C₄×C₄₃	C₂²×D₈	1	6	yes	—
45	C₂×#493	—	43	6	no	—
46	#1712	—	43	8	no	—
47	C₂×C₈²	D₄₃	1	1	yes	characteristic, complemented
48	C₂×C₄₃	#1712	1	4	yes	complemented
49	C₂×C₄₃	C₂×#493	1	3	yes	—
50	D₄₃	—	16	8	no	—
51	C₂²×D₈	—	86	12	no	—
52	C₂×#127	—	43	4	no	—
53	#493	—	43	24	no	—
54	#493	—	86	12	no	—
55	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	—
56	C₈²	C₂×D₄₃	1	4	yes	complemented
57	C₄₃	C₂×#1712	1	1	yes	characteristic, complemented, Sylow
58	C₂²×D₄	—	86	12	no	—
59	C₂×D₈	—	86	48	no	—
60	C₂×D₈	—	172	48	no	—
61	C₂²×C₈	D₁₇₂	1	6	yes	—
62	#127	—	43	8	no	—
63	#127	—	86	12	no	—
64	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
65	C₄×C₈	D₁₇₂	1	6	yes	—
66	C₄×C₈	C₂²×D₄₃	1	6	yes	—
67	C₂⁴	—	172	4	no	—
68	C₂×D₄	—	86	24	no	—
69	C₂×D₄	—	172	12	no	—
70	C₂×D₄	—	172	48	no	—
71	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
72	D₈	—	172	96	no	—
73	C₂×C₈	D₃₄₄	1	24	yes	complemented
74	C₂×C₈	C₂×D₁₇₂	1	12	yes	—
75	C₄²	C₂×D₁₇₂	1	3	yes	—
76	C₄²	C₂³×D₄₃	1	1	yes	characteristic
77	C₂³	—	344	24	no	—
78	C₂³	—	172	8	no	—
79	C₂³	#13063322	1	1	yes	characteristic
80	D₄	—	344	24	no	—
81	D₄	—	172	48	no	—
82	C₂×C₄	#13063322	1	3	yes	—
83	C₂×C₄	C₂×D₃₄₄	1	12	yes	—
84	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
85	C₈	C₂×D₃₄₄	1	24	yes	complemented
86	C₂²	—	344	24	no	—
87	C₂²	—	688	16	no	—
88	C₂²	#14583276	1	6	yes	—
89	C₂²	C₂×#13063322	1	1	yes	characteristic
90	C₄	#14583276	1	6	yes	—
91	C₄	C₂²×D₃₄₄	1	6	yes	—
92	C₂	—	688	8	no	—
93	C₂	#19134210	1	4	yes	direct product factor
94	C₂	C₂×#14583276	1	3	yes	—

	subgroup	G/H
center	C₂³	#13063322
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₈²×C₄₃	C₂
socle	C₂³×C₄₃	#127
hypercenter	C₂×C₈²	D₄₃
hypocenter	C₄₃	C₂×#1712
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
1. C₂×#14583276	C₂	semidirect
2. #19134210	C₂	direct (N × H)
3. C₂×C₈²×C₄₃	C₂	semidirect
7. #14583276	C₂²	semidirect
9. C₈²×C₄₃	C₂²	semidirect
24. C₂×C₈×C₄₃	D₈	semidirect
37. C₈×C₄₃	C₂×D₈	semidirect
47. C₂×C₈²	D₄₃	semidirect
48. C₂×C₄₃	#1712	semidirect
56. C₈²	C₂×D₄₃	semidirect
57. C₄₃	C₂×#1712	semidirect
73. C₂×C₈	D₃₄₄	semidirect
85. C₈	C₂×D₃₄₄	semidirect
93. C₂	#19134210	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×#14583276	2
#19134210	2
C₂×C₈²×C₄₃	2
C₂×#1712	43

Subgroups — C2×#19134210 #25084288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19134210 #25084288