Subgroups — C₄×C₁₇×#131 #14525880

Order 2176.

572 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#131	C₂	1	2	yes	maximal
2	C₄×#41×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#405	C₂	1	6	yes	maximal, complemented
4	C₄×M₁₆×C₁₇	C₂	1	3	yes	maximal, complemented
5	C₂×C₄×C₈×C₁₇	C₂	1	3	yes	maximal, complemented
6	C₂×#41×C₁₇	C₂²	1	1	yes	characteristic
7	C₁₇×#131	C₄	1	16	yes	direct product factor
8	C₂×M₁₆×C₁₇	C₂²	1	6	yes	—
9	C₂²×C₈×C₁₇	C₂²	1	6	yes	—
10	C₄×Q₈×C₁₇	C₄	1	2	yes	—
11	C₄×D₄×C₁₇	C₄	1	6	yes	—
12	C₁₇×#117	C₂²	1	3	yes	—
13	C₂×C₄²×C₁₇	C₂²	1	3	yes	—
14	C₁₇×#97	C₂²	1	6	yes	—
15	C₄×C₈×C₁₇	C₂²	1	3	yes	—
16	C₄×C₈×C₁₇	C₂²	1	6	yes	—
17	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
18	#41×C₁₇	C₂×C₄	1	8	yes	—
19	C₂×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×D₄×C₁₇	C₂×C₄	1	3	yes	—
21	C₂²×C₄×C₁₇	C₂×C₄	1	6	yes	—
22	C₂²×C₄×C₁₇	C₂³	1	3	yes	—
23	M₁₆×C₁₇	C₂×C₄	1	24	yes	complemented
24	C₂×C₈×C₁₇	C₂×C₄	1	24	yes	complemented
25	C₂×C₈×C₁₇	C₂³	1	2	yes	—
26	C₂×C₈×C₁₇	C₂³	1	6	yes	—
27	C₄⋊C₄×C₁₇	C₂×C₄	1	6	yes	—
28	C₂²⋊C₄×C₁₇	C₂×C₄	1	6	yes	—
29	C₄²×C₁₇	C₂×C₄	1	6	yes	—
30	C₄²×C₁₇	C₂³	1	1	yes	characteristic
31	C₄²×C₁₇	C₂³	1	3	yes	—
32	C₂³×C₁₇	C₂²×C₄	1	3	yes	—
33	Q₈×C₁₇	C₄²	1	4	yes	—
34	D₄×C₁₇	C₄²	1	12	yes	—
35	C₂×C₄×C₁₇	—	2	12	no	—
36	C₂×C₄×C₁₇	C₂²×C₄	1	6	yes	—
37	C₂×C₄×C₁₇	C₂²×C₄	1	3	yes	—
38	C₂×C₄×C₁₇	C₂²×C₄	1	12	yes	—
39	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
40	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
41	C₈×C₁₇	C₂²×C₄	1	4	yes	—
42	C₈×C₁₇	C₂²×C₄	1	12	yes	—
43	C₄×#131	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₁₇	—	2	6	no	—
45	C₂²×C₁₇	C₂×C₄²	1	6	yes	—
46	C₂²×C₁₇	C₂³×C₄	1	1	yes	characteristic
47	C₄×C₁₇	—	2	6	no	—
48	C₄×C₁₇	C₂×C₄²	1	6	yes	—
49	C₄×C₁₇	#131	1	4	yes	direct product factor
50	C₄×C₁₇	C₂³×C₄	1	2	yes	—
51	C₂×#131	C₂×C₁₇	1	2	yes	—
52	C₄×#41	C₂×C₁₇	1	1	yes	characteristic
53	#405	C₂×C₁₇	1	6	yes	complemented
54	C₄×M₁₆	C₂×C₁₇	1	3	yes	complemented
55	C₂×C₄×C₈	C₂×C₁₇	1	3	yes	complemented
56	C₂×C₁₇	—	2	6	no	—
57	C₂×C₁₇	C₂²×C₄²	1	1	yes	characteristic
58	C₂×C₁₇	C₂×#131	1	2	yes	—
59	C₂×#41	C₂²×C₁₇	1	1	yes	characteristic
60	#131	C₄×C₁₇	1	16	yes	direct product factor
61	C₂×M₁₆	C₂²×C₁₇	1	6	yes	—
62	C₂²×C₈	C₂²×C₁₇	1	6	yes	—
63	C₄×Q₈	C₄×C₁₇	1	2	yes	—
64	C₄×D₄	C₄×C₁₇	1	6	yes	—
65	#117	C₂²×C₁₇	1	3	yes	—
66	C₂×C₄²	C₂²×C₁₇	1	3	yes	—
67	#97	C₂²×C₁₇	1	6	yes	—
68	C₄×C₈	C₂²×C₁₇	1	3	yes	—
69	C₄×C₈	C₂²×C₁₇	1	6	yes	—
70	C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
71	C₁₇	C₄×#131	1	1	yes	characteristic, direct product factor, Sylow
72	#41	C₂×C₄×C₁₇	1	8	yes	—
73	C₂×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
74	C₂×D₄	C₂×C₄×C₁₇	1	3	yes	—
75	C₂²×C₄	C₂×C₄×C₁₇	1	6	yes	—
76	C₂²×C₄	C₂³×C₁₇	1	3	yes	—
77	M₁₆	C₂×C₄×C₁₇	1	24	yes	complemented
78	C₂×C₈	C₂×C₄×C₁₇	1	24	yes	complemented
79	C₂×C₈	C₂³×C₁₇	1	2	yes	—
80	C₂×C₈	C₂³×C₁₇	1	6	yes	—
81	C₄⋊C₄	C₂×C₄×C₁₇	1	6	yes	—
82	C₂²⋊C₄	C₂×C₄×C₁₇	1	6	yes	—
83	C₄²	C₂×C₄×C₁₇	1	6	yes	—
84	C₄²	C₂³×C₁₇	1	1	yes	characteristic
85	C₄²	C₂³×C₁₇	1	3	yes	—
86	C₂³	C₂²×C₄×C₁₇	1	3	yes	—
87	Q₈	C₄²×C₁₇	1	4	yes	—
88	D₄	C₄²×C₁₇	1	12	yes	—
89	C₂×C₄	—	2	12	no	—
90	C₂×C₄	C₂²×C₄×C₁₇	1	6	yes	—
91	C₂×C₄	C₂²×C₄×C₁₇	1	2	yes	—
92	C₂×C₄	C₂²×C₄×C₁₇	1	12	yes	—
93	C₂×C₄	C₂²×C₄×C₁₇	1	3	yes	—
94	C₂×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
95	C₈	C₂²×C₄×C₁₇	1	4	yes	—
96	C₈	C₂²×C₄×C₁₇	1	12	yes	—
97	C₂²	—	2	6	no	—
98	C₂²	C₂×C₄²×C₁₇	1	6	yes	—
99	C₂²	C₂³×C₄×C₁₇	1	1	yes	characteristic
100	C₄	—	2	6	no	—
101	C₄	C₂×C₄²×C₁₇	1	6	yes	—
102	C₄	C₁₇×#131	1	4	yes	direct product factor
103	C₄	C₂³×C₄×C₁₇	1	2	yes	—
104	C₂	—	2	6	no	—
105	C₂	C₂²×C₄²×C₁₇	1	1	yes	characteristic
106	C₂	C₂×C₁₇×#131	1	2	yes	—

	subgroup	G/H
center	C₄×C₈×C₁₇	C₂²
commutator	C₂	C₂²×C₄²×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂³×C₄
prime radical	C₂×#41×C₁₇	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₇×#405	C₂	semidirect
4. C₄×M₁₆×C₁₇	C₂	semidirect
5. C₂×C₄×C₈×C₁₇	C₂	semidirect
7. C₁₇×#131	C₄	direct (N × H)
23. M₁₆×C₁₇	C₂×C₄	semidirect
24. C₂×C₈×C₁₇	C₂×C₄	semidirect
43. C₄×#131	C₁₇	direct (N × H)
49. C₄×C₁₇	#131	direct (N × H)
53. #405	C₂×C₁₇	semidirect
54. C₄×M₁₆	C₂×C₁₇	semidirect
55. C₂×C₄×C₈	C₂×C₁₇	semidirect
60. #131	C₄×C₁₇	direct (N × H)
71. C₁₇	C₄×#131	direct (N × H)
77. M₁₆	C₂×C₄×C₁₇	semidirect
78. C₂×C₈	C₂×C₄×C₁₇	semidirect
102. C₄	C₁₇×#131	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×C₁₇×#131	2
C₄×#41×C₁₇	2
C₁₇×#405	2
C₄×M₁₆×C₁₇	2
C₂×C₄×C₈×C₁₇	2
C₄×#131	17

Subgroups — C4×C17×#131 #14525880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₇×#131 #14525880