Subgroups — #11763708

Order 1088.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587593	C₂	1	1	yes	maximal, characteristic
2	#10587538	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63216	C₂	1	1	yes	maximal, characteristic, complemented
4	#63252	C₄	1	1	yes	characteristic
5	M₁₆×C₁₇	C₄	1	1	yes	characteristic
6	C₂×#3622	C₂²	1	1	yes	characteristic
7	#63218	—	2	1	no	—
8	C₈×D₁₇	—	2	1	no	—
9	#63216	—	2	1	no	—
10	#63216	—	2	1	no	—
11	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₁₇	—	2	1	no	—
13	D₆₈	C₈	1	1	yes	characteristic
14	C₄×D₁₇	—	2	1	no	—
15	Dic₃₄	C₈	1	1	yes	characteristic
16	C₈×C₁₇	—	2	1	no	—
17	#3622	D₄	1	1	yes	characteristic
18	#3622	D₄	1	1	yes	characteristic
19	C₂²×C₁₇	M₁₆	1	1	yes	characteristic
20	C₂×D₁₇	—	2	1	no	—
21	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
23	Dic₁₇	—	2	1	no	—
24	#350	—	17	1	no	maximal, Sylow
25	C₂×C₁₇	—	2	1	no	—
26	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
27	D₁₇	—	4	1	no	—
28	#131	—	17	1	no	—
29	M₃₂	—	17	1	no	—
30	C₂×C₁₆	—	17	1	no	—
31	C₁₇	#350	1	1	yes	characteristic, complemented, Sylow
32	#41	—	17	1	no	—
33	M₁₆	—	34	1	no	—
34	M₁₆	#595	1	1	yes	characteristic
35	C₂×C₈	—	17	1	no	—
36	C₂×C₈	—	34	1	no	—
37	C₁₆	—	34	1	no	—
38	C₁₆	—	34	1	no	—
39	Q₈	—	17	1	no	—
40	D₄	—	17	1	no	—
41	D₄	—	34	1	no	—
42	C₂×C₄	—	34	1	no	—
43	C₂×C₄	C₂×#595	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	17	1	no	—
46	C₈	—	17	1	no	—
47	C₂²	—	34	1	no	—
48	C₂²	#63243	1	1	yes	characteristic
49	C₄	—	34	1	no	—
50	C₄	#63242	1	1	yes	characteristic
51	C₄	C₂²⋊#595	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	68	1	no	—
54	C₂	#10587543	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₈
Frattini	C₂×C₄	C₂×#595
Fitting	M₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₂²⋊C₈
prime radical	#63252	C₄
cosocle	C₂×#3622	C₂²
hypercenter	M₁₆	#595
hypocenter	C₁₇	#350
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. #10587538	C₂	semidirect
3. C₂×#63216	C₂	semidirect
31. C₁₇	#350	semidirect

Maximal subgroups

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

subgroup	index
#10587593	2
#10587538	2
C₂×#63216	2
#350	17