Subgroups — C₂×#11763207 #14539283

Order 2176.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587555	C₂	1	2	yes	maximal
2	#11763207	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10587488	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₃₄	—	2	2	no	—
6	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₇	—	2	2	no	—
9	C₂×C₄⋊Dic₁₇	C₂²	1	4	yes	—
10	#10587555	—	2	4	no	—
11	#10587555	C₂²	1	8	yes	—
12	C₄×C₈×C₁₇	C₂²	1	4	yes	—
13	#10587488	C₂²	1	16	yes	—
14	C₂²×C₄×C₁₇	D₄	1	2	yes	—
15	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₇	—	2	4	no	—
17	C₂×Dic₃₄	—	2	8	no	—
18	C₂×Dic₃₄	—	4	8	no	—
19	C₂×C₈×C₁₇	Q₈	1	8	yes	complemented
20	C₂×C₈×C₁₇	C₂³	1	4	yes	—
21	C₄²×C₁₇	D₄	1	2	yes	—
22	C₄²×C₁₇	C₂³	1	2	yes	—
23	C₄⋊Dic₁₇	—	2	4	no	—
24	C₄⋊Dic₁₇	—	2	8	no	—
25	C₄⋊Dic₁₇	C₂³	1	8	yes	—
26	C₂³×C₁₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₁₇	SD₁₆	1	8	yes	—
28	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	—
30	C₂×C₄×C₁₇	C₂×Q₈	1	4	yes	—
31	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
32	C₂×Dic₁₇	—	2	8	no	—
33	C₂×Dic₁₇	—	4	8	no	—
34	Dic₃₄	—	4	16	no	—
35	C₈×C₁₇	C₂×Q₈	1	8	yes	complemented
36	C₂×#498	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	C₄⋊Q₈	1	2	yes	—
38	C₂²×C₁₇	C₂×SD₁₆	1	4	yes	—
39	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
40	C₄×C₁₇	C₄⋊Q₈	1	2	yes	—
41	C₄×C₁₇	C₂×SD₁₆	1	8	yes	—
42	C₄×C₁₇	C₂²×Q₈	1	2	yes	—
43	Dic₁₇	—	4	8	no	—
44	C₂×C₄⋊Q₈	—	17	2	no	—
45	#498	—	17	8	no	—
46	C₂×#106	—	17	4	no	—
47	C₂×C₄×C₈	D₁₇	1	1	yes	characteristic
48	C₂×C₁₇	#498	1	4	yes	complemented
49	C₂×C₁₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₁₇	C₂²×SD₁₆	1	2	yes	—
51	C₂²×Q₈	—	34	2	no	—
52	C₂²×C₈	C₂×D₁₇	1	2	yes	—
53	C₄⋊Q₈	—	17	8	no	—
54	C₄⋊Q₈	—	34	4	no	—
55	C₂×C₄⋊C₄	—	17	4	no	—
56	C₂×C₄⋊C₄	—	34	2	no	—
57	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
58	#106	—	17	16	no	—
59	C₄×C₈	C₂×D₁₇	1	4	yes	—
60	C₁₇	C₂×#498	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₈	—	34	8	no	—
62	C₂×Q₈	—	68	8	no	—
63	C₂²×C₄	—	34	4	no	—
64	C₂²×C₄	D₆₈	1	2	yes	—
65	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
66	C₂×C₈	Dic₃₄	1	8	yes	complemented
67	C₂×C₈	C₂²×D₁₇	1	4	yes	—
68	C₄⋊C₄	—	17	8	no	—
69	C₄⋊C₄	—	34	4	no	—
70	C₄⋊C₄	—	34	8	no	—
71	C₄²	D₆₈	1	2	yes	—
72	C₄²	C₂²×D₁₇	1	2	yes	—
73	C₂³	C₂×D₆₈	1	1	yes	characteristic
74	Q₈	—	68	16	no	—
75	C₂×C₄	—	34	8	no	—
76	C₂×C₄	—	68	8	no	—
77	C₂×C₄	#63219	1	8	yes	—
78	C₂×C₄	C₂×Dic₃₄	1	4	yes	—
79	C₂×C₄	C₂×D₆₈	1	1	yes	characteristic
80	C₂×C₄	C₂×D₆₈	1	4	yes	—
81	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
82	C₈	C₂×Dic₃₄	1	8	yes	complemented
83	C₂²	#10587555	1	2	yes	—
84	C₂²	C₂×#63219	1	4	yes	—
85	C₂²	C₂²×D₆₈	1	1	yes	characteristic
86	C₄	—	68	8	no	—
87	C₄	#10587555	1	2	yes	—
88	C₄	C₂×#63219	1	8	yes	—
89	C₄	C₂²×Dic₃₄	1	2	yes	—
90	C₂	#11763207	1	4	yes	direct product factor
91	C₂	C₂×#10587555	1	1	yes	characteristic
92	C₂	C₂²×#63219	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₆₈
commutator, cosocle	C₂×C₄×C₁₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₇
Fitting	C₂×C₄×C₈×C₁₇	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₁₇
hypocenter	C₁₇	C₂×#498
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #11763207	C₂	direct (N × H)
19. C₂×C₈×C₁₇	Q₈	semidirect
35. C₈×C₁₇	C₂×Q₈	semidirect
48. C₂×C₁₇	#498	semidirect
60. C₁₇	C₂×#498	semidirect
66. C₂×C₈	Dic₃₄	semidirect
82. C₈	C₂×Dic₃₄	semidirect
90. C₂	#11763207	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×#10587555	2
#11763207	2
C₂×#10587488	2
C₂×C₄×C₈×C₁₇	2
C₂×#498	17

Subgroups — C2×#11763207 #14539283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763207 #14539283