Subgroups — C₁₇×#1413 #14524419

Order 2176.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#491	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#356	C₂	1	2	yes	maximal
3	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
4	C₁₇×#125	C₄	1	1	yes	characteristic
5	C₁₇×#103	—	2	2	no	—
6	C₁₇×#101	—	2	2	no	—
7	C₁₇×#97	C₄	1	1	yes	characteristic
8	C₂×Q₈×C₁₇	D₄	1	2	yes	—
9	M₁₆×C₁₇	—	4	2	no	—
10	C₂×C₈×C₁₇	—	2	1	no	—
11	C₄⋊C₄×C₁₇	—	2	1	no	—
12	C₄⋊C₄×C₁₇	—	4	1	no	—
13	C₄⋊C₄×C₁₇	—	4	1	no	—
14	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
15	Q₈×C₁₇	—	4	2	no	—
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×C₄×C₁₇	—	2	2	no	—
18	C₂×C₄×C₁₇	—	4	1	no	—
19	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₁₇	—	4	1	no	—
21	C₈×C₁₇	—	8	2	no	—
22	#1413	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂²×C₁₇	#99	1	1	yes	characteristic
24	C₄×C₁₇	—	2	1	no	—
25	C₄×C₁₇	—	4	1	no	—
26	C₄×C₁₇	—	4	2	no	—
27	C₄×C₁₇	—	8	1	no	—
28	#491	C₂×C₁₇	1	1	yes	characteristic
29	#356	C₂×C₁₇	1	2	yes	—
30	C₂×C₁₇	—	2	1	no	—
31	C₂×C₁₇	#354	1	1	yes	characteristic
32	C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
33	#125	C₄×C₁₇	1	1	yes	characteristic
34	#103	—	2	2	no	—
35	#101	—	2	2	no	—
36	#97	C₄×C₁₇	1	1	yes	characteristic
37	C₁₇	#1413	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×Q₈	D₄×C₁₇	1	2	yes	—
39	M₁₆	—	4	2	no	—
40	C₂×C₈	—	2	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	—	4	1	no	—
43	C₄⋊C₄	—	4	1	no	—
44	C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
45	Q₈	—	4	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	4	1	no	—
49	C₂×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	8	2	no	—
52	C₂²	C₁₇×#99	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	4	2	no	—
56	C₄	—	8	1	no	—
57	C₂	—	2	1	no	—
58	C₂	C₁₇×#354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#354
commutator	C₄²	C₂×C₄×C₁₇
Frattini, cosocle	C₄⋊Q₈	C₂²×C₁₇
prime radical	C₂²×C₁₇	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₁₇×C₄⋊Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
22. #1413	C₁₇	direct (N × H)
37. C₁₇	#1413	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×#491	2
C₁₇×#356	2
#1413	17

Subgroups — C17×#1413 #14524419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1413 #14524419