Subgroups — #11763889

Order 1088.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63256	C₂	1	1	yes	maximal, characteristic
2	#10587680	C₂	1	8	yes	maximal, complemented
3	D₁₇⋊M₁₆	C₂	1	6	yes	maximal, complemented
4	C₂×Q₈×C₁₇	C₄	1	1	yes	characteristic
5	#63256	C₄	1	4	yes	—
6	#63256	C₂²	1	4	yes	—
7	C₂×D₆₈	C₄	1	3	yes	—
8	C₂×C₄×D₁₇	C₂²	1	3	yes	—
9	#63247	C₂²	1	4	yes	—
10	#63243	C₂²	1	12	yes	complemented
11	#63242	C₂²	1	12	yes	complemented
12	C₂²×D₁₇	C₂×C₄	1	3	yes	—
13	Q₈×C₁₇	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₁₇	C₂×C₄	1	3	yes	—
15	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
16	D₆₈	C₂×C₄	1	12	yes	—
17	C₄×D₁₇	C₂×C₄	1	6	yes	—
18	C₄×D₁₇	C₂³	1	6	yes	—
19	#3624	C₂³	1	8	yes	—
20	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₁₇	—	4	3	no	—
22	C₂×D₁₇	C₂²×C₄	1	6	yes	—
23	C₄×C₁₇	C₂²×C₄	1	6	yes	—
24	Dic₁₇	C₂²×C₄	1	1	yes	characteristic
25	Dic₁₇	C₂⁴	1	1	yes	characteristic
26	#568	—	17	1	no	maximal, Sylow
27	C₂×C₁₇	—	2	1	no	—
28	C₂×C₁₇	C₂³×C₄	1	1	yes	characteristic
29	D₁₇	—	2	6	no	—
30	C₂×#41	—	17	1	no	—
31	#131	—	17	8	no	—
32	C₂×M₁₆	—	17	6	no	—
33	C₁₇	#568	1	1	yes	characteristic, complemented, Sylow
34	#41	—	17	4	no	—
35	#41	—	17	4	no	—
36	C₂×Q₈	#595	1	1	yes	characteristic
37	C₂×D₄	—	17	3	no	—
38	C₂²×C₄	—	17	3	no	—
39	M₁₆	—	17	12	no	—
40	M₁₆	—	17	4	no	—
41	C₂×C₈	—	17	12	no	—
42	C₂³	—	17	3	no	—
43	Q₈	C₂×#595	1	4	yes	—
44	D₄	—	17	12	no	—
45	C₂×C₄	—	17	1	no	—
46	C₂×C₄	—	17	6	no	—
47	C₂×C₄	—	17	6	no	—
48	C₂×C₄	C₂×#595	1	3	yes	—
49	C₈	—	17	8	no	—
50	C₂²	—	17	6	no	—
51	C₂²	—	68	3	no	—
52	C₂²	C₂²×#595	1	1	yes	characteristic
53	C₄	—	17	1	no	—
54	C₄	—	17	1	no	—
55	C₄	C₂²×#595	1	6	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	34	6	no	—
58	C₂	C₂³×#595	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#595
commutator, socle	C₂×C₁₇	C₂³×C₄
Fitting	C₂×Q₈×C₁₇	C₄
prime radical	C₂×#63256	C₂
cosocle	Dic₁₇	C₂⁴
hypercenter	C₂×Q₈	#595
hypocenter	C₁₇	#568
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #10587680	C₂	semidirect
3. D₁₇⋊M₁₆	C₂	semidirect
10. #63243	C₂²	semidirect
11. #63242	C₂²	semidirect
33. C₁₇	#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63256	2
#10587680	2
D₁₇⋊M₁₆	2
#568	17