Subgroups — C₂×#11762646 #14531084

Order 2176.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₇₂	C₂	1	1	yes	maximal, characteristic
2	#11762646	C₂	1	4	yes	maximal, direct product factor
3	C₂×#10587465	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₁₇	—	2	1	no	—
6	C₂×D₁₃₆	—	2	1	no	—
7	C₁₇×Q₃₂	—	2	1	no	—
8	C₁₇×Q₃₂	C₂²	1	2	yes	complemented
9	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
10	D₂₇₂	—	2	1	no	—
11	D₂₇₂	C₂²	1	2	yes	—
12	#10587465	C₂²	1	2	yes	complemented
13	C₂×Q₈×C₁₇	—	4	1	no	—
14	C₂×D₆₈	—	4	1	no	—
15	Q₁₆×C₁₇	—	2	2	no	—
16	Q₁₆×C₁₇	—	4	1	no	—
17	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
18	D₁₃₆	—	2	2	no	—
19	D₁₃₆	—	4	1	no	—
20	C₁₆×C₁₇	D₄	1	1	yes	characteristic
21	C₁₆×C₁₇	C₂³	1	1	yes	characteristic
22	C₂²×D₁₇	—	8	1	no	—
23	Q₈×C₁₇	—	4	2	no	—
24	Q₈×C₁₇	—	8	1	no	—
25	C₂×C₄×C₁₇	—	8	1	no	—
26	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
27	D₆₈	—	4	2	no	—
28	D₆₈	—	8	1	no	—
29	C₈×C₁₇	D₈	1	1	yes	characteristic
30	C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
31	C₂×SD₆₄	—	17	1	no	maximal, Sylow
32	C₂²×C₁₇	D₁₆	1	1	yes	characteristic
33	C₂×D₁₇	—	8	2	no	—
34	C₂×D₁₇	—	16	2	no	—
35	C₄×C₁₇	—	8	2	no	—
36	C₄×C₁₇	D₁₆	1	1	yes	characteristic
37	C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
38	C₂×Q₃₂	D₁₇	1	1	yes	characteristic, complemented
39	C₂×D₁₆	—	17	1	no	—
40	SD₆₄	—	17	4	no	—
41	C₂×C₃₂	—	17	1	no	—
42	C₂×C₁₇	SD₆₄	1	2	yes	complemented
43	C₂×C₁₇	C₂×D₁₆	1	1	yes	characteristic
44	D₁₇	—	16	2	no	—
45	C₂×Q₁₆	—	2	1	no	—
46	C₂×D₈	—	34	1	no	—
47	Q₃₂	—	2	1	no	—
48	Q₃₂	C₂×D₁₇	1	2	yes	complemented
49	D₁₆	—	17	2	no	—
50	D₁₆	—	34	1	no	—
51	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
52	C₃₂	—	17	2	no	—
53	C₁₇	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	4	1	no	—
55	C₂×D₄	—	68	1	no	—
56	Q₁₆	—	2	2	no	—
57	Q₁₆	—	4	1	no	—
58	D₈	—	34	2	no	—
59	D₈	—	68	1	no	—
60	C₂×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
62	C₁₆	C₂²×D₁₇	1	1	yes	characteristic
63	C₂³	—	136	1	no	—
64	Q₈	—	4	2	no	—
65	Q₈	—	8	1	no	—
66	D₄	—	68	2	no	—
67	D₄	—	136	1	no	—
68	C₂×C₄	—	8	1	no	—
69	C₂×C₄	#63228	1	1	yes	characteristic
70	C₈	#63228	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
72	C₂²	—	272	2	no	—
73	C₂²	—	136	2	no	—
74	C₂²	#10587497	1	1	yes	characteristic
75	C₄	—	8	2	no	—
76	C₄	#10587497	1	1	yes	characteristic
77	C₄	C₂×#63228	1	1	yes	characteristic
78	C₂	—	272	2	no	—
79	C₂	#11762646	1	2	yes	direct product factor
80	C₂	C₂×#10587497	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10587497
commutator, cosocle	C₁₆×C₁₇	C₂³
Frattini	C₁₆	C₂²×D₁₇
Fitting	C₂×C₁₇×Q₃₂	C₂
socle	C₂²×C₁₇	D₁₆
prime radical	C₂×D₂₇₂	C₂
hypercenter	C₂×Q₃₂	D₁₇
hypocenter	C₁₇	C₂×SD₆₄
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #11762646	C₂	direct (N × H)
3. C₂×#10587465	C₂	semidirect
4. C₂×C₁₇×Q₃₂	C₂	semidirect
8. C₁₇×Q₃₂	C₂²	semidirect
12. #10587465	C₂²	semidirect
38. C₂×Q₃₂	D₁₇	semidirect
42. C₂×C₁₇	SD₆₄	semidirect
48. Q₃₂	C₂×D₁₇	semidirect
53. C₁₇	C₂×SD₆₄	semidirect
79. C₂	#11762646	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×D₂₇₂	2
#11762646	2
C₂×#10587465	2
C₂×C₁₇×Q₃₂	2
C₂×SD₆₄	17

Subgroups — C2×#11762646 #14531084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11762646 #14531084