Subgroups — C₂×#11763754 #14545230

Order 2176.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763754	C₂	1	8	yes	maximal, direct product factor
2	C₂×(C₂×#595)⋊C₄	C₂	1	6	yes	maximal
3	C₂×C₄²×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂³×#595	C₂²	1	4	yes	—
5	C₂²×C₄×D₁₇	C₂²	1	3	yes	—
6	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×Dic₁₇	C₄	1	3	yes	complemented
8	C₄²×D₁₇	C₄	1	4	yes	complemented
9	C₄²×D₁₇	C₂²	1	4	yes	—
10	(C₂×#595)⋊C₄	C₂²	1	24	yes	—
11	C₂³×D₁₇	C₂³	1	1	yes	characteristic
12	C₂²×#595	—	2	24	no	—
13	C₂²×#595	C₂³	1	8	yes	—
14	C₂²×C₄×C₁₇	C₂×C₄	1	3	yes	—
15	C₂²×Dic₁₇	C₂×C₄	1	3	yes	—
16	C₂×C₄×D₁₇	—	2	12	no	—
17	C₂×C₄×D₁₇	C₂×C₄	1	6	yes	—
18	C₂×C₄×D₁₇	C₂³	1	6	yes	—
19	C₄²×C₁₇	C₂×C₄	1	4	yes	complemented
20	C₄×Dic₁₇	C₂×C₄	1	12	yes	complemented
21	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
22	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
23	C₂²×D₁₇	#41	1	12	yes	—
24	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
25	C₂×#595	—	2	24	no	—
26	C₂×#595	—	4	16	no	—
27	C₂×C₄×C₁₇	—	2	6	no	—
28	C₂×C₄×C₁₇	C₂²×C₄	1	6	yes	—
29	C₂×Dic₁₇	—	2	6	no	—
30	C₂×Dic₁₇	C₂²×C₄	1	6	yes	—
31	C₄×D₁₇	—	2	12	no	—
32	C₄×D₁₇	—	2	12	no	—
33	C₂×#383	—	17	1	no	maximal, Sylow
34	C₂²×C₁₇	#117	1	6	yes	—
35	C₂²×C₁₇	C₂³×C₄	1	1	yes	characteristic
36	C₂×D₁₇	#117	1	6	yes	—
37	C₂×D₁₇	#126	1	16	yes	—
38	C₂×D₁₇	C₂×#41	1	6	yes	—
39	#595	—	4	8	no	—
40	C₄×C₁₇	—	2	6	no	—
41	Dic₁₇	—	2	6	no	—
42	C₂²×C₄²	—	17	1	no	—
43	#383	—	17	8	no	—
44	C₂×#95	—	17	6	no	—
45	C₂×C₁₇	#383	1	4	yes	complemented
46	C₂×C₁₇	C₂×#117	1	3	yes	—
47	D₁₇	#383	1	4	yes	complemented
48	D₁₇	C₂×#126	1	4	yes	—
49	C₂³×C₄	—	17	3	no	—
50	C₂³×C₄	—	17	4	no	—
51	C₂×C₄²	—	17	3	no	—
52	C₂×C₄²	—	17	4	no	—
53	C₂×C₄²	—	17	4	no	—
54	C₂×C₄²	#595	1	1	yes	characteristic, complemented
55	#95	—	17	24	no	—
56	C₁₇	C₂×#383	1	1	yes	characteristic, complemented, Sylow
57	C₂⁴	—	17	1	no	—
58	C₂²×C₄	—	17	3	no	—
59	C₂²×C₄	—	17	6	no	—
60	C₂²×C₄	—	17	6	no	—
61	C₂²×C₄	—	17	8	no	—
62	C₂²×C₄	—	34	12	no	—
63	C₂²×C₄	—	34	24	no	—
64	C₂²×C₄	C₂×#595	1	3	yes	—
65	C₄²	—	17	12	no	—
66	C₄²	C₂×#595	1	4	yes	complemented
67	C₂³	—	17	12	no	—
68	C₂³	—	17	1	no	—
69	C₂³	—	17	1	no	—
70	C₂³	C₂²×#595	1	1	yes	characteristic
71	C₂×C₄	—	2	6	no	—
72	C₂×C₄	—	17	6	no	—
73	C₂×C₄	—	34	12	no	—
74	C₂×C₄	—	34	12	no	—
75	C₂×C₄	—	34	6	no	—
76	C₂×C₄	—	34	24	no	—
77	C₂×C₄	—	68	16	no	—
78	C₂×C₄	C₂²×#595	1	6	yes	—
79	C₂²	—	17	16	no	—
80	C₂²	—	17	6	no	—
81	C₂²	—	17	6	no	—
82	C₂²	#10587677	1	6	yes	—
83	C₂²	C₂³×#595	1	1	yes	characteristic
84	C₄	—	2	6	no	—
85	C₄	—	34	6	no	—
86	C₄	—	68	8	no	—
87	C₂	—	17	4	no	—
88	C₂	—	17	4	no	—
89	C₂	#11763754	1	4	yes	direct product factor
90	C₂	C₂×#10587677	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×#595
commutator	C₂²×C₁₇	C₂³×C₄
Frattini	C₂²	C₂³×#595
Fitting	C₂×C₄²×C₁₇	C₄
socle	C₂³×C₁₇	C₂²×C₄
prime radical	C₂³×D₁₇	C₂³
cosocle	C₂²×D₁₇	C₂⁴
hypercenter	C₂×C₄²	#595
hypocenter	C₁₇	C₂×#383
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #11763754	C₂	direct (N × H)
6. C₂×C₄²×C₁₇	C₄	semidirect
7. C₂×C₄×Dic₁₇	C₄	semidirect
8. C₄²×D₁₇	C₄	semidirect
19. C₄²×C₁₇	C₂×C₄	semidirect
20. C₄×Dic₁₇	C₂×C₄	semidirect
45. C₂×C₁₇	#383	semidirect
47. D₁₇	#383	semidirect
54. C₂×C₄²	#595	semidirect
56. C₁₇	C₂×#383	semidirect
66. C₄²	C₂×#595	semidirect
89. C₂	#11763754	direct (N × H)

Maximal subgroups

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

subgroup	index
#11763754	2
C₂×(C₂×#595)⋊C₄	2
C₂×C₄²×D₁₇	2
C₂×#383	17

Subgroups — C2×#11763754 #14545230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763754 #14545230