Subgroups — C₁₇×#1322 #14524328

Order 2176.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₂²⋊C₁₆	C₂	1	2	yes	maximal
3	C₂²×C₈×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₁₇	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₁₇	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₇	—	2	2	no	—
7	C₁₇×C₄⋊C₈	—	2	2	no	—
8	C₂²×C₄×C₁₇	C₈	1	1	yes	characteristic
9	C₂²×C₄×C₁₇	C₈	1	1	yes	characteristic
10	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₁₇	—	2	1	no	—
12	C₂×C₈×C₁₇	—	4	1	no	—
13	C₂×C₈×C₁₇	—	4	1	no	—
14	C₂×C₈×C₁₇	D₄	1	2	yes	—
15	C₄²×C₁₇	—	2	1	no	—
16	C₄²×C₁₇	—	2	1	no	—
17	C₁₆×C₁₇	—	4	2	no	—
18	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₁₇	—	2	1	no	—
20	C₂×C₄×C₁₇	—	2	1	no	—
21	C₂×C₄×C₁₇	—	2	1	no	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	—	2	1	no	—
24	C₂×C₄×C₁₇	—	4	1	no	—
25	C₂×C₄×C₁₇	C₁₆	1	2	yes	complemented
26	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
28	C₈×C₁₇	—	2	2	no	—
29	C₈×C₁₇	—	4	1	no	—
30	#1322	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂²×C₁₇	—	2	1	no	—
32	C₂²×C₁₇	—	2	1	no	—
33	C₂²×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
35	C₂²×C₁₇	M₃₂	1	1	yes	characteristic
36	C₄×C₁₇	—	2	1	no	—
37	C₄×C₁₇	—	2	2	no	—
38	C₄×C₁₇	—	4	1	no	—
39	C₄×C₁₇	#99	1	1	yes	characteristic
40	C₄×C₁₇	#101	1	1	yes	characteristic
41	C₂×C₄⋊C₈	C₂×C₁₇	1	1	yes	characteristic
42	C₂²⋊C₁₆	C₂×C₁₇	1	2	yes	—
43	C₂×C₁₇	—	2	1	no	—
44	C₂×C₁₇	—	2	1	no	—
45	C₂×C₁₇	#324	1	1	yes	characteristic
46	C₂×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
47	C₂×C₁₇	#349	1	1	yes	characteristic
48	C₂²×C₈	C₄×C₁₇	1	1	yes	characteristic
49	C₂²×C₈	C₂²×C₁₇	1	1	yes	characteristic
50	C₂×C₄²	C₄×C₁₇	1	1	yes	characteristic
51	C₂×C₁₆	—	2	2	no	—
52	C₄⋊C₈	—	2	2	no	—
53	C₁₇	#1322	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₄	C₈×C₁₇	1	1	yes	characteristic
55	C₂²×C₄	C₈×C₁₇	1	1	yes	characteristic
56	C₂²×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	—	4	1	no	—
59	C₂×C₈	—	4	1	no	—
60	C₂×C₈	D₄×C₁₇	1	2	yes	—
61	C₄²	—	2	1	no	—
62	C₄²	—	2	1	no	—
63	C₁₆	—	4	2	no	—
64	C₂³	C₂×C₈×C₁₇	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	4	1	no	—
71	C₂×C₄	C₁₆×C₁₇	1	2	yes	complemented
72	C₂×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
73	C₂×C₄	M₁₆×C₁₇	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₈	—	4	1	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	C₁₇×C₂²⋊C₈	1	1	yes	characteristic
79	C₂²	C₂×C₁₆×C₁₇	1	1	yes	characteristic
80	C₂²	C₁₇×M₃₂	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	2	2	no	—
83	C₄	—	4	1	no	—
84	C₄	C₁₇×#99	1	1	yes	characteristic
85	C₄	C₁₇×#101	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	C₁₇×#324	1	1	yes	characteristic
89	C₂	C₁₇×C₂²⋊C₁₆	1	1	yes	characteristic
90	C₂	C₁₇×#349	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²⋊C₄
commutator	C₂²	C₂×C₁₆×C₁₇
Frattini, cosocle	C₂²×C₈	C₂²×C₁₇
socle	C₂²×C₁₇	C₂²⋊C₈
prime radical	C₂³×C₁₇	C₂×C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
25. C₂×C₄×C₁₇	C₁₆	semidirect
30. #1322	C₁₇	direct (N × H)
53. C₁₇	#1322	direct (N × H)
71. C₂×C₄	C₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₇×C₄⋊C₈	2
C₁₇×C₂²⋊C₁₆	2
#1322	17

Subgroups — C17×#1322 #14524328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1322 #14524328