Subgroups — C₂×#11762642 #14531075

Order 2176.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
2	#11762642	C₂	1	4	yes	maximal, direct product factor
3	C₂×#10587465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×#63214	C₄	1	1	yes	characteristic
8	C₁₆×D₁₇	C₄	1	2	yes	—
9	C₁₆×D₁₇	C₂²	1	2	yes	—
10	C₁₇×C₃₂	C₂²	1	2	yes	complemented
11	#10587465	C₂²	1	2	yes	complemented
12	C₂×C₄×D₁₇	C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×#3622	C₈	1	1	yes	characteristic
15	C₈×D₁₇	C₈	1	2	yes	—
16	C₈×D₁₇	C₂×C₄	1	2	yes	—
17	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₁₇	C₂³	1	1	yes	characteristic
19	#63214	C₂×C₄	1	2	yes	—
20	C₂²×D₁₇	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₁₇	C₁₆	1	1	yes	characteristic
23	C₄×D₁₇	C₁₆	1	2	yes	—
24	C₄×D₁₇	C₂×C₈	1	2	yes	—
25	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
27	#3622	C₂×C₈	1	2	yes	—
28	C₂×M₆₄	—	17	1	no	maximal, Sylow
29	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
30	C₂×D₁₇	—	2	2	no	—
31	C₂×D₁₇	C₂×C₁₆	1	2	yes	—
32	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
34	Dic₁₇	C₂×C₁₆	1	2	yes	—
35	C₂²×C₁₆	—	17	1	no	—
36	M₆₄	—	17	4	no	—
37	C₂×C₃₂	—	17	1	no	—
38	C₂×C₃₂	D₁₇	1	1	yes	characteristic, complemented
39	C₂×C₁₇	M₆₄	1	2	yes	complemented
40	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
41	D₁₇	—	2	2	no	—
42	C₂²×C₈	—	17	1	no	—
43	C₂×C₁₆	—	17	1	no	—
44	C₂×C₁₆	—	17	2	no	—
45	C₂×C₁₆	—	17	2	no	—
46	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
47	C₃₂	—	17	2	no	—
48	C₃₂	C₂×D₁₇	1	2	yes	complemented
49	C₁₇	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	17	1	no	—
51	C₂×C₈	—	17	1	no	—
52	C₂×C₈	—	17	2	no	—
53	C₂×C₈	—	17	2	no	—
54	C₂×C₈	C₄×D₁₇	1	1	yes	characteristic
55	C₁₆	—	17	2	no	—
56	C₁₆	C₄×D₁₇	1	1	yes	characteristic
57	C₁₆	C₂²×D₁₇	1	1	yes	characteristic
58	C₂³	—	17	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	2	no	—
61	C₂×C₄	—	17	2	no	—
62	C₂×C₄	C₈×D₁₇	1	1	yes	characteristic
63	C₈	—	17	2	no	—
64	C₈	C₈×D₁₇	1	1	yes	characteristic
65	C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
66	C₂²	—	17	2	no	—
67	C₂²	—	34	2	no	—
68	C₂²	C₁₆×D₁₇	1	1	yes	characteristic
69	C₄	—	17	2	no	—
70	C₄	C₁₆×D₁₇	1	1	yes	characteristic
71	C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
72	C₂	—	34	2	no	—
73	C₂	#11762642	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₁₇
commutator	C₂×C₁₇	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₇
Fitting	C₂×C₁₇×C₃₂	C₂
socle	C₂²×C₁₇	C₂×C₁₆
prime radical	C₂²×D₁₇	C₁₆
cosocle	C₁₆×C₁₇	C₂³
hypercenter	C₂×C₃₂	D₁₇
hypocenter	C₁₇	C₂×M₆₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #11762642	C₂	direct (N × H)
3. C₂×#10587465	C₂	semidirect
4. C₂×C₁₇×C₃₂	C₂	semidirect
10. C₁₇×C₃₂	C₂²	semidirect
11. #10587465	C₂²	semidirect
38. C₂×C₃₂	D₁₇	semidirect
39. C₂×C₁₇	M₆₄	semidirect
48. C₃₂	C₂×D₁₇	semidirect
49. C₁₇	C₂×M₆₄	semidirect
73. C₂	#11762642	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×C₁₆×D₁₇	2
#11762642	2
C₂×#10587465	2
C₂×C₁₇×C₃₂	2
C₂×M₆₄	17

Subgroups — C2×#11762642 #14531075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11762642 #14531075