Subgroups — #13108965

Order 1632.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₆₈	C₂	1	1	yes	maximal, characteristic
2	#11717850	C₂	1	2	yes	maximal, complemented
3	#10587539	—	3	1	no	maximal, Hall
4	C₂²×C₃×D₁₇	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₃×D₁₇	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊#595	—	2	2	no	—
7	C₂×C₃×C₄×C₁₇	C₄	1	1	yes	characteristic, complemented
8	C₃×D₆₈	—	2	2	no	—
9	C₂×D₆₈	D₃	1	1	yes	characteristic
10	C₂²⋊#595	—	3	2	no	—
11	C₂²×C₃×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×D₁₇	—	2	1	no	—
13	C₂×C₃×D₁₇	—	4	1	no	—
14	C₂×C₃×D₁₇	—	4	1	no	—
15	C₂×C₃×D₁₇	D₄	1	2	yes	—
16	C₃⋊#595	—	4	2	no	—
17	C₃×C₄×C₁₇	—	2	1	no	—
18	C₂²×D₁₇	Dic₃	1	1	yes	characteristic, complemented
19	C₂²×D₁₇	C₂×D₃	1	1	yes	characteristic
20	C₂×#595	—	6	2	no	—
21	C₂×C₄×C₁₇	Dic₃	1	1	yes	characteristic, complemented
22	D₆₈	—	2	2	no	—
23	C₂×C₃×C₁₇	—	2	1	no	—
24	C₂×C₃×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₃×D₁₇	—	2	2	no	—
26	C₃×D₁₇	—	4	1	no	—
27	#834	—	17	1	no	maximal, Hall
28	C₂²×C₁₇	C₂×Dic₃	1	1	yes	characteristic
29	C₂×D₁₇	—	2	1	no	—
30	C₂×D₁₇	—	4	1	no	—
31	C₂×D₁₇	—	4	1	no	—
32	C₂×D₁₇	#67	1	2	yes	—
33	#595	—	12	2	no	—
34	C₄×C₁₇	—	2	1	no	—
35	C₃×C₁₇	#99	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×D₄	—	17	1	no	—
37	#217	—	17	2	no	—
38	C₂×C₁₇	—	2	1	no	—
39	C₂×C₁₇	#217	1	1	yes	characteristic
40	D₁₇	—	2	2	no	—
41	D₁₇	—	4	1	no	—
42	#99	—	51	1	no	Sylow
43	C₂³×C₃	—	17	1	no	—
44	C₂³×C₃	—	17	1	no	—
45	C₃×D₄	—	34	2	no	—
46	C₂×C₃×C₄	#595	1	1	yes	characteristic, complemented
47	C₂×Dic₃	—	34	2	no	—
48	C₁₇	#834	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	17	1	no	—
50	C₂²⋊C₄	—	51	2	no	—
51	C₂²×C₃	—	17	2	no	—
52	C₂²×C₃	—	34	1	no	—
53	C₂²×C₃	—	68	1	no	—
54	C₂²×C₃	—	68	1	no	—
55	C₂²×C₃	C₂×#595	1	1	yes	characteristic
56	C₃×C₄	—	2	1	no	—
57	Dic₃	—	68	2	no	—
58	C₂³	—	17	1	no	—
59	C₂³	—	17	1	no	—
60	D₄	—	34	2	no	—
61	C₂×C₄	—	102	2	no	—
62	C₂×C₄	C₃⋊#595	1	1	yes	characteristic, complemented
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	—	34	2	no	—
65	C₂×C₃	—	68	1	no	—
66	C₂×C₃	C₂²⋊#595	1	1	yes	characteristic
67	C₂²	—	17	2	no	—
68	C₂²	—	34	1	no	—
69	C₂²	—	68	1	no	—
70	C₂²	—	68	1	no	—
71	C₂²	C₂×C₃⋊#595	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	—	204	2	no	—
74	C₃	#10587539	1	1	yes	characteristic, complemented, Sylow
75	C₂	—	2	1	no	—
76	C₂	—	34	2	no	—
77	C₂	—	68	1	no	—
78	C₂	#11717850	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11717850
commutator	C₂²×C₃×C₁₇	C₂×C₄
Frattini	C₂²	C₂×C₃⋊#595
Fitting	C₂×C₃×C₄×C₁₇	C₄
socle	C₂×C₃×C₁₇	C₂²⋊C₄
prime radical	C₂×C₃×D₆₈	C₂
cosocle	C₂²×C₃×D₁₇	C₂²
hypercenter	C₂×C₄	C₃⋊#595
hypocenter	C₃×C₁₇	#99
LCS	G ▷ C₂²×C₃×C₁₇ ▷ C₂×C₃×C₁₇ ▷ C₃×C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #11717850	C₂	semidirect
4. C₂²×C₃×D₁₇	C₄	semidirect
7. C₂×C₃×C₄×C₁₇	C₄	semidirect
18. C₂²×D₁₇	Dic₃	semidirect
21. C₂×C₄×C₁₇	Dic₃	semidirect
35. C₃×C₁₇	#99	semidirect
46. C₂×C₃×C₄	#595	semidirect
48. C₁₇	#834	semidirect
62. C₂×C₄	C₃⋊#595	semidirect
74. C₃	#10587539	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₆₈	2
#11717850	2
#10587539	3
#834	17