Subgroups — C₂×Q₈×#595 #11763874

Order 1088.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic
2	Q₈×#595	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊#595	C₂	1	3	yes	maximal
4	C₂×C₄×#595	C₂	1	3	yes	maximal
5	C₂²×#595	C₂²	1	3	yes	—
6	C₂²×#595	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₁₇	C₄	1	1	yes	characteristic, complemented
8	Q₈×D₁₇	C₄	1	4	yes	complemented
9	Q₈×D₁₇	C₂²	1	4	yes	—
10	C₂×C₄×D₁₇	C₂²	1	3	yes	—
11	C₂×Dic₃₄	C₄	1	3	yes	complemented
12	C₄⋊#595	C₂²	1	12	yes	—
13	C₄×#595	C₂²	1	12	yes	—
14	C₂²×D₁₇	C₂³	1	1	yes	characteristic
15	C₂×#595	—	2	6	no	—
16	C₂×#595	Q₈	1	4	yes	direct product factor
17	C₂×#595	C₂³	1	6	yes	—
18	C₂×#595	C₂³	1	2	yes	—
19	Q₈×C₁₇	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₁₇	C₂×C₄	1	3	yes	—
21	C₂×Dic₁₇	C₂×C₄	1	3	yes	—
22	C₄×D₁₇	C₂×C₄	1	6	yes	—
23	C₄×D₁₇	C₂³	1	6	yes	—
24	Dic₃₄	C₂×C₄	1	12	yes	complemented
25	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₁₇	C₂×Q₈	1	2	yes	—
28	C₂×D₁₇	#41	1	2	yes	—
29	C₂×D₁₇	C₂⁴	1	1	yes	characteristic
30	#595	—	2	6	no	—
31	#595	C₂×Q₈	1	4	yes	direct product factor
32	C₄×C₁₇	C₂²×C₄	1	6	yes	—
33	Dic₁₇	C₂²×C₄	1	6	yes	—
34	C₂×C₄×Q₈	—	17	1	no	maximal, Sylow
35	C₂×C₁₇	C₄×Q₈	1	2	yes	complemented
36	C₂×C₁₇	C₂³×C₄	1	1	yes	characteristic
37	D₁₇	C₄×Q₈	1	2	yes	complemented
38	D₁₇	C₂²×Q₈	1	1	yes	characteristic
39	D₁₇	C₂×#41	1	1	yes	characteristic
40	C₂²×Q₈	—	17	1	no	—
41	C₄×Q₈	—	17	8	no	—
42	C₂×C₄⋊C₄	—	17	3	no	—
43	C₂×C₄²	—	17	3	no	—
44	C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	17	4	no	—
46	C₂×Q₈	—	17	4	no	—
47	C₂×Q₈	—	17	3	no	—
48	C₂×Q₈	#595	1	1	yes	characteristic, direct product factor
49	C₂²×C₄	—	17	1	no	—
50	C₂²×C₄	—	17	3	no	—
51	C₂²×C₄	—	17	3	no	—
52	C₄⋊C₄	—	17	12	no	—
53	C₄²	—	17	12	no	—
54	C₂³	—	17	1	no	—
55	Q₈	—	17	12	no	—
56	Q₈	C₂×#595	1	4	yes	direct product factor
57	C₂×C₄	—	17	2	no	—
58	C₂×C₄	—	17	4	no	—
59	C₂×C₄	—	17	3	no	—
60	C₂×C₄	—	17	6	no	—
61	C₂×C₄	—	17	6	no	—
62	C₂×C₄	—	17	6	no	—
63	C₂×C₄	—	34	6	no	—
64	C₂×C₄	C₂×#595	1	3	yes	—
65	C₂²	—	17	2	no	—
66	C₂²	—	17	2	no	—
67	C₂²	—	17	1	no	—
68	C₂²	—	17	1	no	—
69	C₂²	C₂²×#595	1	1	yes	characteristic
70	C₄	—	17	4	no	—
71	C₄	—	17	6	no	—
72	C₄	—	34	6	no	—
73	C₄	C₂²×#595	1	6	yes	—
74	C₂	—	17	1	no	—
75	C₂	—	17	1	no	—
76	C₂	—	17	2	no	—
77	C₂	Q₈×#595	1	2	yes	direct product factor
78	C₂	C₂³×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#595
commutator	C₂×C₁₇	C₂³×C₄
Frattini	C₂	C₂³×#595
Fitting	C₂×Q₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂²×C₄
prime radical	C₂²×D₁₇	C₂³
cosocle	C₂×D₁₇	C₂⁴
hypercenter	C₂×Q₈	#595
hypocenter	C₁₇	C₂×C₄×Q₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#595	C₂	direct (N × H)
7. C₂×Q₈×C₁₇	C₄	semidirect
8. Q₈×D₁₇	C₄	semidirect
11. C₂×Dic₃₄	C₄	semidirect
16. C₂×#595	Q₈	direct (N × H)
19. Q₈×C₁₇	C₂×C₄	semidirect
24. Dic₃₄	C₂×C₄	semidirect
31. #595	C₂×Q₈	direct (N × H)
35. C₂×C₁₇	C₄×Q₈	semidirect
37. D₁₇	C₄×Q₈	semidirect
44. C₁₇	C₂×C₄×Q₈	semidirect
48. C₂×Q₈	#595	direct (N × H)
56. Q₈	C₂×#595	direct (N × H)
77. C₂	Q₈×#595	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₁₇	2
Q₈×#595	2
C₂×C₄⋊#595	2
C₂×C₄×#595	2
C₂×C₄×Q₈	17

Subgroups — C2×Q8×#595 #11763874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×#595 #11763874