Subgroups — C₁₆×#63216 #17948317

Order 4352.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#63216	C₂	1	2	yes	maximal
2	C₁₆×#3622	C₂	1	1	yes	maximal, characteristic
3	C₄×#63216	C₄	1	4	yes	—
4	C₄×#63214	C₄	1	1	yes	characteristic
5	C₈×#3622	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×#63216	C₈	1	8	yes	—
8	C₂×C₁₆×C₁₇	C₈	1	2	yes	—
9	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₂×#63214	C₈	1	2	yes	—
11	C₄×#3622	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₁₇	C₄²	1	1	yes	characteristic
15	C₂×#3622	C₂×C₈	1	4	yes	—
16	#63216	C₁₆	1	16	yes	direct product factor
17	C₁₆×C₁₇	C₁₆	1	4	yes	complemented
18	#63214	C₁₆	1	4	yes	complemented
19	C₁₆²	—	17	1	no	maximal, Sylow
20	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
21	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
22	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
23	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
24	#3622	C₂×C₁₆	1	8	yes	—
25	C₈×C₁₆	—	17	2	no	—
26	C₈×C₁₆	—	17	1	no	—
27	C₂²×C₁₇	C₈²	1	1	yes	characteristic
28	C₄×C₁₇	C₄×C₁₆	1	4	yes	—
29	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
30	C₄×C₁₇	C₄×C₁₆	1	1	yes	characteristic
31	C₄×C₁₆	—	17	4	no	—
32	C₄×C₁₆	—	17	1	no	—
33	C₄×C₁₆	#595	1	1	yes	characteristic
34	C₈²	—	17	1	no	—
35	C₂×C₁₇	C₈×C₁₆	1	2	yes	—
36	C₂×C₁₇	C₈×C₁₆	1	1	yes	characteristic
37	C₂×C₁₆	—	17	8	no	—
38	C₂×C₁₆	—	17	2	no	—
39	C₂×C₁₆	#3624	1	2	yes	—
40	C₄×C₈	—	17	2	no	—
41	C₄×C₈	C₂×#595	1	1	yes	characteristic
42	C₁₇	C₁₆²	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₈	—	17	4	no	—
44	C₂×C₈	#63242	1	1	yes	characteristic
45	C₂×C₈	C₂×#3624	1	1	yes	characteristic
46	C₄²	C₄×#595	1	1	yes	characteristic
47	C₁₆	—	17	16	no	—
48	C₁₆	—	17	4	no	—
49	C₁₆	#63216	1	4	yes	direct product factor
50	C₂×C₄	C₈×#595	1	2	yes	—
51	C₂×C₄	C₄×#3624	1	1	yes	characteristic
52	C₈	—	17	8	no	—
53	C₈	#10587529	1	2	yes	—
54	C₈	C₂×#63216	1	2	yes	—
55	C₂²	C₈×#3624	1	1	yes	characteristic
56	C₄	C₁₆×#595	1	4	yes	—
57	C₄	C₄×#63216	1	1	yes	characteristic
58	C₄	#11763695	1	1	yes	characteristic
59	C₂	C₁₆×#3624	1	2	yes	—
60	C₂	C₈×#63216	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₆	#595
commutator, hypocenter	C₁₇	C₁₆²
Frattini	C₄×C₈	C₂×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	C₈²
cosocle	C₈×#3622	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
16. #63216	C₁₆	direct (N × H)
17. C₁₆×C₁₇	C₁₆	semidirect
18. #63214	C₁₆	semidirect
42. C₁₇	C₁₆²	semidirect
49. C₁₆	#63216	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#63216	2
C₁₆×#3622	2
C₁₆²	17

Subgroups — C16×#63216 #17948317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#63216 #17948317