Subgroups — #14544723

Order 2176.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587535	C₂	1	4	yes	maximal
2	#11763813	C₂	1	2	yes	maximal
3	C₄×C₈×D₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#63243	C₂²	1	4	yes	—
5	C₂×C₈×D₁₇	C₂²	1	2	yes	—
6	C₄²×D₁₇	C₂²	1	1	yes	characteristic
7	C₄⋊#3624	—	2	4	no	—
8	#10587535	—	2	8	no	—
9	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
10	C₈×Dic₁₇	C₄	1	2	yes	—
11	C₄×#3622	C₄	1	1	yes	characteristic
12	C₂×C₄×D₁₇	Q₈	1	2	yes	—
13	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
14	C₂×#3624	—	2	4	no	—
15	#63243	—	2	8	no	—
16	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
17	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₁₇	D₄	1	2	yes	—
20	C₂×#3622	C₂×C₄	1	2	yes	—
21	C₈×D₁₇	D₄	1	4	yes	—
22	C₈×D₁₇	Q₈	1	4	yes	—
23	C₂²×D₁₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
27	C₂×Dic₁₇	C₂×D₄	1	1	yes	characteristic
28	C₄×D₁₇	—	2	4	no	—
29	C₄×D₁₇	C₂×D₄	1	2	yes	—
30	C₄×D₁₇	C₂×Q₈	1	2	yes	—
31	#3624	—	4	4	no	—
32	C₈×C₁₇	C₄⋊C₄	1	4	yes	—
33	#3622	C₄⋊C₄	1	4	yes	—
34	#1848	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×D₁₇	—	2	2	no	—
37	C₂×D₁₇	C₄⋊Q₈	1	2	yes	—
38	C₄×C₁₇	#108	1	4	yes	complemented
39	C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
40	Dic₁₇	—	2	2	no	—
41	Dic₁₇	#127	1	1	yes	characteristic
42	Dic₁₇	C₄⋊Q₈	1	1	yes	characteristic
43	C₂×#108	—	17	4	no	—
44	#423	—	17	2	no	—
45	C₂×C₄×C₈	—	17	1	no	—
46	C₂×C₁₇	#384	1	1	yes	characteristic
47	C₂×C₁₇	C₂×#108	1	2	yes	—
48	D₁₇	—	2	2	no	—
49	C₂×M₁₆	—	17	4	no	—
50	C₂²×C₈	—	17	2	no	—
51	C₂×C₄²	—	17	1	no	—
52	#108	—	34	8	no	—
53	C₄⋊C₈	—	34	4	no	—
54	C₄×C₈	—	17	2	no	—
55	C₄×C₈	—	17	1	no	—
56	C₄×C₈	#595	1	1	yes	characteristic
57	C₁₇	#1848	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	17	1	no	—
59	C₂²×C₄	—	17	2	no	—
60	M₁₆	—	34	8	no	—
61	C₂×C₈	—	17	2	no	—
62	C₂×C₈	—	17	4	no	—
63	C₂×C₈	—	17	4	no	—
64	C₂×C₈	—	34	4	no	—
65	C₂×C₈	C₂×#595	1	2	yes	—
66	C₄²	—	17	2	no	—
67	C₄²	—	17	1	no	—
68	C₄²	C₂×#595	1	1	yes	characteristic
69	C₂³	—	17	1	no	—
70	C₂×C₄	—	17	1	no	—
71	C₂×C₄	—	17	2	no	—
72	C₂×C₄	—	17	2	no	—
73	C₂×C₄	—	17	2	no	—
74	C₂×C₄	—	34	4	no	—
75	C₂×C₄	C₄⋊#595	1	2	yes	—
76	C₂×C₄	C₂²×#595	1	1	yes	characteristic
77	C₈	—	17	4	no	—
78	C₈	—	68	4	no	—
79	C₈	C₄⋊#595	1	4	yes	—
80	C₂²	—	17	2	no	—
81	C₂²	—	34	2	no	—
82	C₂²	C₂×C₄⋊#595	1	1	yes	characteristic
83	C₄	—	17	1	no	—
84	C₄	—	17	1	no	—
85	C₄	—	34	2	no	—
86	C₄	#10587535	1	4	yes	complemented
87	C₄	C₂×C₄⋊#595	1	2	yes	—
88	C₂	—	34	2	no	—
89	C₂	#11763755	1	1	yes	characteristic
90	C₂	C₂×#10587535	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#595
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₄×C₈×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇	C₂×Q₈
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	C₄×C₈	#595
hypocenter	C₁₇	#1848
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
38. C₄×C₁₇	#108	semidirect
57. C₁₇	#1848	semidirect
86. C₄	#10587535	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587535	2
#11763813	2
C₄×C₈×D₁₇	2
#1848	17