Subgroups — C₂×#11763650 #14543977

Order 2176.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#3624	C₂	1	2	yes	maximal
2	#11763650	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#3624	C₄	1	4	yes	—
5	C₂²×C₈×C₁₇	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
7	C₂²×#3622	C₄	1	1	yes	characteristic
8	C₄×#3624	C₄	1	4	yes	—
9	C₄×#3624	C₂²	1	4	yes	—
10	C₈×Dic₁₇	C₄	1	2	yes	—
11	C₈×Dic₁₇	C₂²	1	2	yes	—
12	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₁₇	C₂×C₄	1	2	yes	—
14	C₂×#3624	—	2	8	no	—
15	C₂×#3624	C₂×C₄	1	8	yes	—
16	C₂×C₈×C₁₇	C₈	1	4	yes	complemented
17	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
18	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
20	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
21	C₂×#3622	C₈	1	4	yes	complemented
22	C₂×#3622	C₂×C₄	1	2	yes	—
23	C₂³×C₁₇	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₁₇	C₄²	1	2	yes	—
29	C₂×Dic₁₇	M₁₆	1	8	yes	—
30	C₂×Dic₁₇	C₂²×C₄	1	2	yes	—
31	#3624	—	2	8	no	—
32	C₈×C₁₇	C₂×C₈	1	4	yes	complemented
33	#3622	C₂×C₈	1	4	yes	complemented
34	C₂×#322	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	C₄×C₈	1	2	yes	—
36	C₂²×C₁₇	#97	1	4	yes	—
37	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
38	C₄×C₁₇	C₄×C₈	1	2	yes	—
39	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
41	Dic₁₇	#97	1	4	yes	—
42	Dic₁₇	C₂×M₁₆	1	4	yes	—
43	C₂×C₄×C₈	—	17	2	no	—
44	C₂×C₄×C₈	—	17	1	no	—
45	#322	—	17	4	no	—
46	C₂×C₁₇	#322	1	4	yes	complemented
47	C₂×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
48	C₂×C₁₇	C₂×#97	1	2	yes	—
49	C₂²×C₈	—	17	1	no	—
50	C₂²×C₈	—	17	4	no	—
51	C₂²×C₈	#595	1	1	yes	characteristic
52	C₂×C₄²	—	17	1	no	—
53	C₄×C₈	—	17	4	no	—
54	C₄×C₈	—	17	4	no	—
55	C₄×C₈	—	17	2	no	—
56	C₄×C₈	—	17	2	no	—
57	C₁₇	C₂×#322	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	17	2	no	—
59	C₂²×C₄	C₂×#595	1	1	yes	characteristic
60	C₂×C₈	—	17	4	no	—
61	C₂×C₈	—	17	2	no	—
62	C₂×C₈	—	17	8	no	—
63	C₂×C₈	—	34	8	no	—
64	C₂×C₈	#3624	1	4	yes	complemented
65	C₂×C₈	C₂×#595	1	2	yes	—
66	C₄²	—	17	2	no	—
67	C₄²	—	17	1	no	—
68	C₄²	—	17	1	no	—
69	C₂³	C₄×#595	1	1	yes	characteristic
70	C₂×C₄	—	17	2	no	—
71	C₂×C₄	—	17	2	no	—
72	C₂×C₄	—	17	8	no	—
73	C₂×C₄	#63242	1	2	yes	—
74	C₂×C₄	C₄×#595	1	1	yes	characteristic
75	C₂×C₄	C₂×#3624	1	2	yes	—
76	C₂×C₄	C₂²×#595	1	1	yes	characteristic
77	C₈	—	17	4	no	—
78	C₈	—	34	8	no	—
79	C₈	C₂×#3624	1	4	yes	complemented
80	C₂²	#10587532	1	4	yes	—
81	C₂²	C₄×#3624	1	2	yes	—
82	C₂²	C₂×C₄×#595	1	1	yes	characteristic
83	C₄	—	17	4	no	—
84	C₄	—	17	4	no	—
85	C₄	C₄×#3624	1	2	yes	—
86	C₄	C₂×#63242	1	1	yes	characteristic
87	C₄	C₂²×#3624	1	1	yes	characteristic
88	C₂	#11763650	1	4	yes	direct product factor
89	C₂	C₂×C₄×#3624	1	1	yes	characteristic
90	C₂	C₂×#10587532	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×#595
commutator	C₂×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#595
Fitting	C₂²×C₈×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₄²
cosocle	C₄×Dic₁₇	C₂³
hypercenter	C₂²×C₈	#595
hypocenter	C₁₇	C₂×#322
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #11763650	C₂	direct (N × H)
16. C₂×C₈×C₁₇	C₈	semidirect
21. C₂×#3622	C₈	semidirect
32. C₈×C₁₇	C₂×C₈	semidirect
33. #3622	C₂×C₈	semidirect
46. C₂×C₁₇	#322	semidirect
57. C₁₇	C₂×#322	semidirect
64. C₂×C₈	#3624	semidirect
79. C₈	C₂×#3624	semidirect
88. C₂	#11763650	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×C₄×#3624	2
#11763650	2
C₂×C₈×Dic₁₇	2
C₂×#322	17

Subgroups — C2×#11763650 #14543977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763650 #14543977