Subgroups — #11763692

Order 1088.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587677	C₂	1	1	yes	maximal, characteristic
2	C₂×#63243	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₁₇	C₂²	1	1	yes	characteristic
5	C₂²⋊#595	C₄	1	2	yes	—
6	C₂×#3624	C₄	1	2	yes	complemented
7	C₄⋊#595	—	2	1	no	—
8	C₄×#595	—	2	1	no	—
9	#63243	—	2	1	no	—
10	#63243	—	2	1	no	—
11	M₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
12	#63223	C₄	1	1	yes	characteristic, complemented
13	#63218	—	2	1	no	—
14	C₈×D₁₇	—	2	1	no	—
15	C₂²×D₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×#595	—	2	2	no	—
17	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₇	D₄	1	1	yes	characteristic
20	C₄×D₁₇	D₄	1	1	yes	characteristic
21	C₄×D₁₇	D₄	1	1	yes	characteristic
22	C₄×D₁₇	Q₈	1	1	yes	characteristic
23	#3624	—	2	2	no	—
24	C₈×C₁₇	—	2	1	no	—
25	#3622	—	2	1	no	—
26	C₂²×C₁₇	C₄²	1	1	yes	characteristic
27	C₂×D₁₇	—	4	1	no	—
28	C₂×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₁₇	C₄⋊C₄	1	1	yes	characteristic
30	#595	—	4	2	no	—
31	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
33	Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
34	Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
35	#344	—	17	1	no	maximal, Sylow
36	C₂×C₁₇	—	2	1	no	—
37	C₂×C₁₇	#95	1	1	yes	characteristic
38	D₁₇	—	2	1	no	—
39	D₁₇	—	2	1	no	—
40	C₂×M₁₆	—	17	1	no	—
41	C₂×M₁₆	—	17	1	no	—
42	#117	—	17	1	no	—
43	C₁₇	#344	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	17	1	no	—
45	M₁₆	—	17	1	no	—
46	M₁₆	—	34	1	no	—
47	M₁₆	—	34	1	no	—
48	M₁₆	—	34	1	no	—
49	M₁₆	#595	1	1	yes	characteristic, complemented
50	C₂×C₈	—	17	2	no	—
51	C₂×C₈	—	34	1	no	—
52	C₄⋊C₄	—	34	1	no	—
53	C₂²⋊C₄	—	17	2	no	—
54	C₄²	—	34	1	no	—
55	C₂³	—	17	1	no	—
56	C₂×C₄	—	17	1	no	—
57	C₂×C₄	—	17	1	no	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	34	2	no	—
62	C₂×C₄	C₂×#595	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	34	2	no	—
65	C₈	—	34	1	no	—
66	C₂²	—	17	1	no	—
67	C₂²	—	17	1	no	—
68	C₂²	—	68	1	no	—
69	C₂²	C₄×#595	1	1	yes	characteristic
70	C₄	—	17	1	no	—
71	C₄	—	17	1	no	—
72	C₄	—	68	2	no	—
73	C₄	C₄⋊#595	1	1	yes	characteristic
74	C₄	C₂²⋊#595	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	34	1	no	—
77	C₂	—	34	1	no	—
78	C₂	(C₂×#595)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×#595)⋊C₄
commutator	C₂²×C₁₇	C₄²
Frattini	C₂×C₄	C₂×#595
Fitting	M₁₆×C₁₇	C₄
socle	C₂×C₁₇	#95
prime radical	C₂²×D₁₇	C₂×C₄
cosocle	C₂×C₄×D₁₇	C₂²
hypercenter	M₁₆	#595
hypocenter	C₁₇	#344
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#3624	C₄	semidirect
11. M₁₆×C₁₇	C₄	semidirect
12. #63223	C₄	semidirect
43. C₁₇	#344	semidirect
49. M₁₆	#595	semidirect

Maximal subgroups

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

subgroup	index
#10587677	2
C₂×#63243	2
M₁₆×D₁₇	2
#344	17