Subgroups — C₁₇×#1406 #14524412

Order 2176.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#496	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#355	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×SD₁₆×C₁₇	—	2	1	no	—
5	C₂×D₈×C₁₇	—	2	1	no	—
6	C₁₇×#127	C₄	1	1	yes	characteristic, complemented
7	C₁₇×#124	C₂²	1	1	yes	characteristic
8	C₁₇×#101	—	2	1	no	—
9	C₁₇×#99	—	2	1	no	—
10	C₁₇×#97	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₁₇	D₄	1	1	yes	characteristic
12	C₂×D₄×C₁₇	—	2	1	no	—
13	C₂×D₄×C₁₇	—	4	1	no	—
14	C₂×D₄×C₁₇	D₄	1	1	yes	characteristic
15	SD₁₆×C₁₇	—	4	2	no	—
16	D₈×C₁₇	—	4	2	no	—
17	M₁₆×C₁₇	—	4	1	no	—
18	C₂×C₈×C₁₇	—	2	1	no	—
19	C₂²⋊C₄×C₁₇	—	4	1	no	—
20	C₂²⋊C₄×C₁₇	—	4	1	no	—
21	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₁₇	—	2	1	no	—
23	C₂³×C₁₇	—	4	1	no	—
24	Q₈×C₁₇	—	4	1	no	—
25	D₄×C₁₇	—	4	1	no	—
26	D₄×C₁₇	—	4	1	no	—
27	D₄×C₁₇	—	4	1	no	—
28	D₄×C₁₇	—	8	2	no	—
29	C₂×C₄×C₁₇	—	2	1	no	—
30	C₂×C₄×C₁₇	—	2	1	no	—
31	C₂×C₄×C₁₇	—	8	1	no	—
32	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₁₇	—	2	2	no	—
34	C₈×C₁₇	—	8	1	no	—
35	#1406	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₁₇	—	4	1	no	—
37	C₂²×C₁₇	—	8	1	no	—
38	C₂²×C₁₇	—	8	2	no	—
39	C₂²×C₁₇	—	8	1	no	—
40	C₂²×C₁₇	#99	1	1	yes	characteristic
41	C₄×C₁₇	—	2	1	no	—
42	C₄×C₁₇	—	4	1	no	—
43	C₄×C₁₇	—	4	1	no	—
44	C₄×C₁₇	—	16	1	no	—
45	#496	C₂×C₁₇	1	1	yes	characteristic
46	#355	C₂×C₁₇	1	1	yes	characteristic, complemented
47	#354	C₂×C₁₇	1	1	yes	characteristic, complemented
48	C₂×C₁₇	—	2	1	no	—
49	C₂×C₁₇	—	8	1	no	—
50	C₂×C₁₇	—	16	1	no	—
51	C₂×C₁₇	#353	1	1	yes	characteristic
52	C₂×SD₁₆	—	2	1	no	—
53	C₂×D₈	—	2	1	no	—
54	#127	C₄×C₁₇	1	1	yes	characteristic, complemented
55	#124	C₂²×C₁₇	1	1	yes	characteristic
56	#101	—	2	1	no	—
57	#99	—	2	1	no	—
58	#97	C₄×C₁₇	1	1	yes	characteristic, complemented
59	C₁₇	#1406	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×Q₈	D₄×C₁₇	1	1	yes	characteristic
61	C₂×D₄	—	2	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×D₄	D₄×C₁₇	1	1	yes	characteristic
64	SD₁₆	—	4	2	no	—
65	D₈	—	4	2	no	—
66	M₁₆	—	4	1	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	4	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	4	1	no	—
77	D₄	—	8	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	8	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	8	2	no	—
87	C₂²	—	8	1	no	—
88	C₂²	C₁₇×#99	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	16	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	16	1	no	—
96	C₂	C₁₇×#353	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#353
commutator	C₄²	C₂×C₄×C₁₇
Frattini, cosocle	#124	C₂²×C₁₇
prime radical	C₁₇×#496	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#124 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#355	C₂	semidirect
3. C₁₇×#354	C₂	semidirect
6. C₁₇×#127	C₄	semidirect
10. C₁₇×#97	C₄	semidirect
35. #1406	C₁₇	direct (N × H)
46. #355	C₂×C₁₇	semidirect
47. #354	C₂×C₁₇	semidirect
54. #127	C₄×C₁₇	semidirect
58. #97	C₄×C₁₇	semidirect
59. C₁₇	#1406	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#496	2
C₁₇×#355	2
C₁₇×#354	2
#1406	17

Subgroups — C17×#1406 #14524412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1406 #14524412