Subgroups — C₂²×#10587529 #14545744

Order 2176.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587529	C₂	1	12	yes	maximal, direct product factor
2	C₂²×#63216	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×D₁₇	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₇	C₄	1	1	yes	characteristic
6	C₂²×#3622	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₁₇	C₄	1	6	yes	—
8	C₂×C₈×D₁₇	C₂²	1	6	yes	—
9	C₂×#63216	C₂²	1	12	yes	complemented
10	#10587529	C₂²	1	16	yes	direct product factor
11	C₂³×D₁₇	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₁₇	C₈	1	1	yes	characteristic
14	C₂×C₄×D₁₇	C₈	1	6	yes	—
15	C₂×C₄×D₁₇	C₂×C₄	1	6	yes	—
16	C₂×C₈×C₁₇	C₂×C₄	1	6	yes	—
17	C₂×#3622	C₂×C₄	1	3	yes	—
18	C₂×#3622	C₂³	1	3	yes	—
19	C₈×D₁₇	C₂×C₄	1	12	yes	—
20	C₈×D₁₇	C₂³	1	4	yes	—
21	#63216	C₂³	1	8	yes	complemented
22	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
23	C₂²×D₁₇	C₁₆	1	8	yes	complemented
24	C₂²×D₁₇	C₂×C₈	1	6	yes	—
25	C₂×C₄×C₁₇	C₂×C₈	1	3	yes	—
26	C₂×C₄×C₁₇	C₂²×C₄	1	3	yes	—
27	C₂×Dic₁₇	C₂×C₈	1	6	yes	—
28	C₄×D₁₇	C₂×C₈	1	12	yes	—
29	C₄×D₁₇	C₂²×C₄	1	4	yes	—
30	C₈×C₁₇	C₂²×C₄	1	4	yes	—
31	#3622	C₂²×C₄	1	3	yes	—
32	#3622	C₂⁴	1	1	yes	characteristic
33	C₂³×C₁₆	—	17	1	no	maximal, Sylow
34	C₂²×C₁₇	C₂×C₁₆	1	4	yes	complemented
35	C₂²×C₁₇	C₂²×C₈	1	3	yes	—
36	C₂×D₁₇	C₂×C₁₆	1	24	yes	complemented
37	C₂×D₁₇	C₂²×C₈	1	4	yes	—
38	C₄×C₁₇	C₂²×C₈	1	3	yes	—
39	C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
40	Dic₁₇	C₂²×C₈	1	4	yes	—
41	C₂³×C₈	—	17	1	no	—
42	C₂²×C₁₆	—	17	2	no	—
43	C₂²×C₁₆	—	17	12	no	—
44	C₂×C₁₇	C₂²×C₁₆	1	6	yes	complemented
45	C₂×C₁₇	C₂³×C₈	1	1	yes	characteristic
46	D₁₇	C₂²×C₁₆	1	8	yes	complemented
47	C₂³×C₄	—	17	1	no	—
48	C₂²×C₈	—	17	1	no	—
49	C₂²×C₈	—	17	6	no	—
50	C₂²×C₈	—	17	6	no	—
51	C₂²×C₈	#595	1	1	yes	characteristic
52	C₂×C₁₆	—	17	16	no	—
53	C₂×C₁₆	—	17	12	no	—
54	C₁₇	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂⁴	—	17	1	no	—
56	C₂²×C₄	—	17	1	no	—
57	C₂²×C₄	—	17	6	no	—
58	C₂²×C₄	—	17	6	no	—
59	C₂²×C₄	C₂×#595	1	1	yes	characteristic
60	C₂×C₈	—	17	3	no	—
61	C₂×C₈	—	17	3	no	—
62	C₂×C₈	—	17	4	no	—
63	C₂×C₈	—	17	12	no	—
64	C₂×C₈	C₂×#595	1	6	yes	—
65	C₁₆	—	17	8	no	—
66	C₂³	—	17	6	no	—
67	C₂³	—	17	8	no	—
68	C₂³	#63242	1	1	yes	characteristic
69	C₂×C₄	—	17	6	no	—
70	C₂×C₄	—	17	12	no	—
71	C₂×C₄	—	17	4	no	—
72	C₂×C₄	#63242	1	3	yes	—
73	C₂×C₄	C₂²×#595	1	3	yes	—
74	C₈	—	17	1	no	—
75	C₈	—	17	3	no	—
76	C₈	C₂²×#595	1	4	yes	—
77	C₂²	—	17	24	no	—
78	C₂²	—	17	4	no	—
79	C₂²	#10587529	1	4	yes	direct product factor
80	C₂²	C₂×#63242	1	3	yes	—
81	C₄	—	17	4	no	—
82	C₄	C₂×#63242	1	3	yes	—
83	C₄	C₂³×#595	1	1	yes	characteristic
84	C₂	—	17	8	no	—
85	C₂	C₂×#10587529	1	6	yes	direct product factor
86	C₂	C₂²×#63242	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	#595
commutator, hypocenter	C₁₇	C₂³×C₁₆
Frattini	C₄	C₂³×#595
Fitting	C₂²×C₈×C₁₇	C₄
socle	C₂³×C₁₇	C₂×C₈
prime radical	C₂³×D₁₇	C₈
cosocle	#3622	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10587529	C₂	direct (N × H)
2. C₂²×#63216	C₂	semidirect
9. C₂×#63216	C₂²	semidirect
10. #10587529	C₂²	direct (N × H)
21. #63216	C₂³	semidirect
23. C₂²×D₁₇	C₁₆	semidirect
34. C₂²×C₁₇	C₂×C₁₆	semidirect
36. C₂×D₁₇	C₂×C₁₆	semidirect
44. C₂×C₁₇	C₂²×C₁₆	semidirect
46. D₁₇	C₂²×C₁₆	semidirect
54. C₁₇	C₂³×C₁₆	semidirect
79. C₂²	#10587529	direct (N × H)
85. C₂	C₂×#10587529	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×#10587529	2
C₂²×#63216	2
C₂²×C₈×D₁₇	2
C₂³×C₁₆	17

Subgroups — C22×#10587529 #14545744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10587529 #14545744