Subgroups — #11763690

Order 1088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63247	C₂	1	1	yes	maximal, characteristic
2	C₂×#63247	C₂	1	1	yes	maximal, characteristic
3	#10587563	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
5	#63247	—	2	1	no	—
6	#63247	—	2	1	no	—
7	#63247	—	2	1	no	—
8	#63247	C₄	1	2	yes	complemented
9	C₂×#3624	—	2	1	no	—
10	C₂×#3624	C₄	1	2	yes	complemented
11	C₂²⋊C₄×C₁₇	C₄	1	1	yes	characteristic
12	C₂²⋊Dic₁₇	C₄	1	1	yes	characteristic
13	#63225	—	2	1	no	—
14	C₄×Dic₁₇	—	2	1	no	—
15	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×Dic₁₇	—	2	1	no	—
18	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₇	D₄	1	1	yes	characteristic
21	C₂×Dic₁₇	D₄	1	1	yes	characteristic
22	C₂×Dic₁₇	D₄	1	1	yes	characteristic
23	C₂×Dic₁₇	Q₈	1	1	yes	characteristic
24	#3624	—	2	2	no	—
25	#3624	—	2	2	no	—
26	C₂²×C₁₇	—	4	1	no	—
27	C₂²×C₁₇	C₄²	1	1	yes	characteristic
28	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₁₇	—	4	1	no	—
31	Dic₁₇	—	4	1	no	—
32	Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
33	Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
35	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
36	#344	—	17	1	no	maximal, Sylow
37	C₂×C₁₇	—	2	1	no	—
38	C₂×C₁₇	—	2	1	no	—
39	C₂×C₁₇	—	2	1	no	—
40	C₂×C₁₇	#95	1	1	yes	characteristic
41	C₂×M₁₆	—	17	1	no	—
42	C₂×M₁₆	—	17	1	no	—
43	#117	—	17	1	no	—
44	C₁₇	#344	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₄	—	17	1	no	—
46	M₁₆	—	17	2	no	—
47	M₁₆	—	34	1	no	—
48	M₁₆	—	34	1	no	—
49	M₁₆	—	34	1	no	—
50	C₂×C₈	—	17	2	no	—
51	C₂×C₈	—	34	1	no	—
52	C₄⋊C₄	—	34	1	no	—
53	C₂²⋊C₄	—	17	1	no	—
54	C₂²⋊C₄	#595	1	1	yes	characteristic
55	C₄²	—	34	1	no	—
56	C₂³	C₂×#595	1	1	yes	characteristic
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₂×C₄	—	17	1	no	—
63	C₂×C₄	—	17	1	no	—
64	C₂×C₄	—	34	1	no	—
65	C₈	—	34	2	no	—
66	C₈	—	34	2	no	—
67	C₂²	—	4	1	no	—
68	C₂²	C₄×#595	1	1	yes	characteristic
69	C₂²	C₄⋊#595	1	1	yes	characteristic
70	C₂²	C₂²⋊#595	1	1	yes	characteristic
71	C₄	—	4	1	no	—
72	C₄	—	17	1	no	—
73	C₄	—	17	1	no	—
74	C₄	—	17	1	no	—
75	C₄	—	17	1	no	—
76	C₄	—	68	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	—	2	1	no	—
80	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#595)⋊C₄
commutator	C₂²×C₁₇	C₄²
Frattini	C₂³	C₂×#595
Fitting	C₂²⋊C₄×C₁₇	C₄
socle	C₂×C₁₇	#95
prime radical	C₂³×C₁₇	C₂×C₄
cosocle	C₂²×Dic₁₇	C₂²
hypercenter	C₂²⋊C₄	#595
hypocenter	C₁₇	#344
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
8. #63247	C₄	semidirect
10. C₂×#3624	C₄	semidirect
44. C₁₇	#344	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63247	2
#10587563	2
#344	17