Subgroups — #14528690

Order 2176.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587490	C₂	1	2	yes	maximal
2	C₄×#63223	C₂	1	2	yes	maximal
3	#11762574	C₂	1	2	yes	maximal
4	C₂×C₁₇×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×#63223	C₂²	1	4	yes	—
9	C₁₇×#97	C₄	1	4	yes	—
10	#10587490	C₄	1	8	yes	complemented
11	#10587474	—	2	2	no	—
12	C₄×#3622	—	2	2	no	—
13	C₂²×C₄×C₁₇	Q₈	1	2	yes	—
14	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₁₇	—	2	2	no	—
16	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
19	C₄²×C₁₇	C₂×C₄	1	2	yes	—
20	C₄²×C₁₇	D₄	1	2	yes	—
21	#63223	—	2	4	no	—
22	#63223	C₂×C₄	1	8	yes	—
23	C₂×#3622	—	2	4	no	—
24	C₂³×C₁₇	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₁₇	—	4	2	no	—
26	C₂×C₄×C₁₇	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₁₇	#41	1	2	yes	—
31	C₈×C₁₇	—	2	2	no	—
32	C₈×C₁₇	C₄²	1	4	yes	—
33	#3622	—	2	8	no	—
34	#1778	—	17	1	no	maximal, Sylow
35	C₂²×C₁₇	—	2	2	no	—
36	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₁₇	C₄×Q₈	1	2	yes	—
38	C₄×C₁₇	—	2	4	no	—
39	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₁₇	#117	1	1	yes	characteristic
41	C₄×C₁₇	C₄×D₄	1	2	yes	—
42	C₂×#108	—	17	2	no	—
43	C₄×M₁₆	—	17	2	no	—
44	C₂×#97	D₁₇	1	1	yes	characteristic
45	#341	—	17	2	no	—
46	C₂×C₁₇	—	2	2	no	—
47	C₂×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₁₇	#430	1	2	yes	—
49	C₂×M₁₆	—	17	4	no	—
50	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic
51	C₂²×C₈	C₂×D₁₇	1	1	yes	characteristic
52	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
53	#108	—	17	8	no	—
54	#97	—	34	2	no	—
55	#97	Dic₁₇	1	4	yes	—
56	C₄×C₈	—	34	2	no	—
57	C₁₇	#1778	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	Dic₃₄	1	2	yes	—
59	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
60	M₁₆	—	17	8	no	—
61	M₁₆	—	34	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	34	4	no	—
64	C₂×C₈	C₄×D₁₇	1	4	yes	—
65	C₂×C₈	C₂×Dic₁₇	1	2	yes	—
66	C₂×C₈	C₂×Dic₁₇	1	2	yes	—
67	C₄²	D₆₈	1	2	yes	—
68	C₄²	C₂×Dic₁₇	1	2	yes	—
69	C₂³	C₂×Dic₃₄	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₄⋊Dic₁₇	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₁₇	1	2	yes	—
73	C₂×C₄	C₂×D₆₈	1	1	yes	characteristic
74	C₂×C₄	#63252	1	2	yes	—
75	C₂×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
76	C₈	—	2	2	no	—
77	C₈	—	34	8	no	—
78	C₈	C₄×Dic₁₇	1	4	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	C₄×Dic₃₄	1	2	yes	—
81	C₂²	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	C₄×D₆₈	1	2	yes	—
84	C₄	C₂×C₄×Dic₁₇	1	1	yes	characteristic
85	C₄	#10587612	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	C₄×C₄⋊Dic₁₇	1	1	yes	characteristic
88	C₂	#11762858	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₆₈
commutator	C₄×C₁₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₇
Fitting	C₂×C₁₇×#97	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₄
prime radical	C₂³×C₁₇	C₂×Q₈
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×#97	D₁₇
hypocenter	C₁₇	#1778
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
10. #10587490	C₄	semidirect
57. C₁₇	#1778	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587490	2
C₄×#63223	2
#11762574	2
C₂×C₁₇×#97	2
#1778	17