Subgroups — C₂×#19151433 #26022549

Order 11392.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#19151433	C₂	1	4	yes	maximal, direct product factor
3	C₂×#15667918	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₇₁₂	—	2	1	no	—
6	D₁₄₂₄	—	2	1	no	—
7	D₁₄₂₄	C₂²	1	2	yes	complemented
8	#15667918	C₂²	1	2	yes	complemented
9	C₂×D₈×C₈₉	—	2	1	no	—
10	D₁₆×C₈₉	—	2	1	no	—
11	D₁₆×C₈₉	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×D₃₅₆	—	4	1	no	—
14	D₇₁₂	—	2	2	no	—
15	D₇₁₂	—	4	1	no	—
16	C₂×D₄×C₈₉	—	4	1	no	—
17	D₈×C₈₉	—	2	2	no	—
18	D₈×C₈₉	—	4	1	no	—
19	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
20	C₁₆×C₈₉	D₄	1	1	yes	characteristic
21	C₁₆×C₈₉	C₂³	1	1	yes	characteristic
22	C₂³×C₈₉	—	8	1	no	—
23	C₂²×D₈₉	—	8	1	no	—
24	D₄×C₈₉	—	4	2	no	—
25	D₄×C₈₉	—	8	1	no	—
26	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
27	D₃₅₆	—	4	2	no	—
28	D₃₅₆	—	8	1	no	—
29	C₈×C₈₉	D₈	1	1	yes	characteristic
30	C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₈₉	—	8	2	no	—
32	C₂²×C₈₉	—	16	2	no	—
33	C₂²×C₈₉	D₁₆	1	1	yes	characteristic
34	C₂×D₈₉	—	8	2	no	—
35	C₂×D₈₉	—	16	2	no	—
36	C₄×C₈₉	D₁₆	1	1	yes	characteristic
37	C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
38	C₂×C₈₉	—	16	2	no	—
39	C₂×C₈₉	D₃₂	1	2	yes	complemented
40	C₂×C₈₉	C₂×D₁₆	1	1	yes	characteristic
41	D₈₉	—	16	2	no	—
42	C₂×D₃₂	—	89	1	no	maximal, Sylow
43	C₈₉	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₁₆	—	89	1	no	—
45	C₂×D₁₆	D₈₉	1	1	yes	characteristic, complemented
46	D₃₂	—	89	4	no	—
47	C₂×C₃₂	—	89	1	no	—
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	—	178	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	—	89	2	no	—
52	D₁₆	—	178	1	no	—
53	D₁₆	C₂×D₈₉	1	2	yes	complemented
54	C₂×C₁₆	C₂×D₈₉	1	1	yes	characteristic
55	C₃₂	—	89	2	no	—
56	C₂×D₄	—	4	1	no	—
57	C₂×D₄	—	356	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	D₈	—	356	1	no	—
61	D₈	—	178	2	no	—
62	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
63	C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
64	C₁₆	C₂²×D₈₉	1	1	yes	characteristic
65	C₂³	—	8	1	no	—
66	C₂³	—	712	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	356	2	no	—
70	D₄	—	712	1	no	—
71	C₂×C₄	#13083559	1	1	yes	characteristic
72	C₈	#13083559	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	1424	2	no	—
77	C₂²	—	712	2	no	—
78	C₂²	#15667953	1	1	yes	characteristic
79	C₄	#15667953	1	1	yes	characteristic
80	C₄	C₂×#13083559	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	1424	2	no	—
83	C₂	#19151433	1	2	yes	direct product factor
84	C₂	C₂×#15667953	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15667953
commutator, cosocle	C₁₆×C₈₉	C₂³
Frattini	C₁₆	C₂²×D₈₉
Fitting	C₂×D₁₆×C₈₉	C₂
socle	C₂²×C₈₉	D₁₆
hypercenter	C₂×D₁₆	D₈₉
hypocenter	C₈₉	C₂×D₃₂
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₄₂₄	C₂	semidirect
2. #19151433	C₂	direct (N × H)
3. C₂×#15667918	C₂	semidirect
4. C₂×D₁₆×C₈₉	C₂	semidirect
7. D₁₄₂₄	C₂²	semidirect
8. #15667918	C₂²	semidirect
11. D₁₆×C₈₉	C₂²	semidirect
39. C₂×C₈₉	D₃₂	semidirect
43. C₈₉	C₂×D₃₂	semidirect
45. C₂×D₁₆	D₈₉	semidirect
53. D₁₆	C₂×D₈₉	semidirect
83. C₂	#19151433	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×D₁₄₂₄	2
#19151433	2
C₂×#15667918	2
C₂×D₁₆×C₈₉	2
C₂×D₃₂	89

Subgroups — C2×#19151433 #26022549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19151433 #26022549