Subgroups — C₂×#11762635 #14530561

Order 2176.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587489	C₂	1	2	yes	maximal
2	#11762635	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊Dic₁₇	—	2	2	no	—
6	C₂×C₁₆×C₁₇	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₁₇	C₂²	1	2	yes	—
8	#10587489	—	2	2	no	—
9	#10587489	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₇	D₄	1	1	yes	characteristic
11	C₂²×Dic₁₇	—	4	2	no	—
12	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₇	Q₈	1	2	yes	—
15	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₁₇	—	2	4	no	—
17	C₄⋊Dic₁₇	—	4	2	no	—
18	C₁₆×C₁₇	C₂×C₄	1	4	yes	complemented
19	C₂³×C₁₇	D₈	1	1	yes	characteristic
20	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₇	Q₁₆	1	2	yes	—
23	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₁₇	—	4	4	no	—
25	C₂×Dic₁₇	—	8	4	no	—
26	C₈×C₁₇	C₄⋊C₄	1	2	yes	—
27	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
29	C₂×#366	—	17	1	no	maximal, Sylow
30	C₂²×C₁₇	#107	1	2	yes	—
31	C₂²×C₁₇	D₁₆	1	2	yes	—
32	C₂²×C₁₇	Q₃₂	1	2	yes	—
33	C₂²×C₁₇	C₂×D₈	1	1	yes	characteristic
34	C₄×C₁₇	#107	1	2	yes	—
35	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₄×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₁₇	—	8	4	no	—
38	C₂²×C₁₆	D₁₇	1	1	yes	characteristic
39	C₂×#107	—	17	2	no	—
40	#366	—	17	4	no	—
41	C₂×C₁₇	#366	1	4	yes	complemented
42	C₂×C₁₇	C₂×#107	1	1	yes	characteristic
43	C₂×C₁₇	C₂×D₁₆	1	1	yes	characteristic
44	C₂×C₁₇	C₂×Q₃₂	1	1	yes	characteristic
45	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	34	2	no	—
47	C₂×C₁₆	Dic₁₇	1	4	yes	complemented
48	C₂×C₁₆	C₂×D₁₇	1	2	yes	—
49	#107	—	17	4	no	—
50	#107	—	34	2	no	—
51	C₁₇	C₂×#366	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₄	—	68	2	no	—
53	C₂²×C₄	D₆₈	1	1	yes	characteristic
54	C₂×C₈	Dic₃₄	1	2	yes	—
55	C₂×C₈	D₆₈	1	1	yes	characteristic
56	C₂×C₈	C₂×Dic₁₇	1	2	yes	—
57	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
58	C₄⋊C₄	—	34	4	no	—
59	C₄⋊C₄	—	68	2	no	—
60	C₁₆	C₂×Dic₁₇	1	4	yes	complemented
61	C₂³	D₁₃₆	1	1	yes	characteristic
62	C₂×C₄	—	68	4	no	—
63	C₂×C₄	—	136	4	no	—
64	C₂×C₄	D₁₃₆	1	1	yes	characteristic
65	C₂×C₄	Dic₆₈	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₁₇	1	2	yes	—
67	C₂×C₄	C₂×D₆₈	1	1	yes	characteristic
68	C₈	C₄⋊Dic₁₇	1	2	yes	—
69	C₈	C₂×Dic₃₄	1	1	yes	characteristic
70	C₈	C₂²×Dic₁₇	1	1	yes	characteristic
71	C₂²	D₂₇₂	1	2	yes	—
72	C₂²	Dic₁₃₆	1	2	yes	—
73	C₂²	#10587489	1	2	yes	—
74	C₂²	C₂×D₁₃₆	1	1	yes	characteristic
75	C₄	—	136	4	no	—
76	C₄	#10587489	1	2	yes	—
77	C₄	C₂×Dic₆₈	1	1	yes	characteristic
78	C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
79	C₂	#11762635	1	4	yes	direct product factor
80	C₂	C₂×#10587489	1	1	yes	characteristic
81	C₂	C₂×D₂₇₂	1	1	yes	characteristic
82	C₂	C₂×Dic₁₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₃₆
commutator	C₈×C₁₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₇
Fitting	C₂²×C₁₆×C₁₇	C₂
socle, prime radical	C₂³×C₁₇	D₈
cosocle	C₂×C₈×C₁₇	C₂³
hypercenter	C₂²×C₁₆	D₁₇
hypocenter	C₁₇	C₂×#366
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #11762635	C₂	direct (N × H)
6. C₂×C₁₆×C₁₇	C₄	semidirect
18. C₁₆×C₁₇	C₂×C₄	semidirect
41. C₂×C₁₇	#366	semidirect
47. C₂×C₁₆	Dic₁₇	semidirect
51. C₁₇	C₂×#366	semidirect
60. C₁₆	C₂×Dic₁₇	semidirect
79. C₂	#11762635	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×#10587489	2
#11762635	2
C₂²×C₁₆×C₁₇	2
C₂×#366	17

Subgroups — C2×#11762635 #14530561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11762635 #14530561