Subgroups — C₂³×#63216 #14545743

Order 2176.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#63216	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#3622	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×#3622	C₄	1	7	yes	—
5	C₂²×#3622	C₂²	1	7	yes	—
6	C₂×#63216	C₂²	1	28	yes	direct product factor
7	C₂⁴×C₁₇	C₈	1	1	yes	characteristic
8	C₂²×C₄×C₁₇	C₈	1	7	yes	—
9	C₂²×C₄×C₁₇	C₂×C₄	1	7	yes	—
10	C₂×#3622	C₂×C₄	1	21	yes	—
11	C₂×#3622	C₂³	1	7	yes	—
12	#63216	C₂³	1	8	yes	direct product factor
13	C₂³×C₁₇	C₁₆	1	8	yes	complemented
14	C₂³×C₁₇	C₂×C₈	1	7	yes	—
15	C₂×C₄×C₁₇	C₂×C₈	1	21	yes	—
16	C₂×C₄×C₁₇	C₂²×C₄	1	7	yes	—
17	#3622	C₂²×C₄	1	7	yes	—
18	#3622	C₂⁴	1	1	yes	characteristic
19	C₂³×C₁₆	—	17	1	no	maximal, Sylow
20	C₂²×C₁₇	C₂×C₁₆	1	28	yes	complemented
21	C₂²×C₁₇	C₂²×C₈	1	7	yes	—
22	C₄×C₁₇	C₂²×C₈	1	7	yes	—
23	C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
24	C₂³×C₈	—	17	1	no	—
25	C₂²×C₁₆	—	17	14	no	—
26	C₂×C₁₇	C₂²×C₁₆	1	14	yes	complemented
27	C₂×C₁₇	C₂³×C₈	1	1	yes	characteristic
28	C₂³×C₄	#595	1	1	yes	characteristic
29	C₂²×C₈	—	17	7	no	—
30	C₂²×C₈	—	17	7	no	—
31	C₂×C₁₆	—	17	28	no	—
32	C₁₇	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂⁴	#3624	1	1	yes	characteristic
34	C₂²×C₄	#3624	1	7	yes	—
35	C₂²×C₄	C₂×#595	1	7	yes	—
36	C₂×C₈	—	17	7	no	—
37	C₂×C₈	—	17	21	no	—
38	C₁₆	—	17	8	no	—
39	C₂³	#63216	1	8	yes	direct product factor
40	C₂³	C₂×#3624	1	7	yes	—
41	C₂×C₄	C₂×#3624	1	21	yes	—
42	C₂×C₄	C₂²×#595	1	7	yes	—
43	C₈	—	17	1	no	—
44	C₈	—	17	7	no	—
45	C₂²	C₂×#63216	1	28	yes	direct product factor
46	C₂²	C₂²×#3624	1	7	yes	—
47	C₄	C₂²×#3624	1	7	yes	—
48	C₄	C₂³×#595	1	1	yes	characteristic
49	C₂	C₂²×#63216	1	14	yes	direct product factor
50	C₂	C₂³×#3624	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	#595
commutator, hypocenter	C₁₇	C₂³×C₁₆
Frattini	C₄	C₂³×#595
Fitting	C₂³×C₄×C₁₇	C₄
socle, prime radical	C₂⁴×C₁₇	C₈
cosocle	#3622	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#63216	C₂	direct (N × H)
6. C₂×#63216	C₂²	direct (N × H)
12. #63216	C₂³	direct (N × H)
13. C₂³×C₁₇	C₁₆	semidirect
20. C₂²×C₁₇	C₂×C₁₆	semidirect
26. C₂×C₁₇	C₂²×C₁₆	semidirect
32. C₁₇	C₂³×C₁₆	semidirect
39. C₂³	#63216	direct (N × H)
45. C₂²	C₂×#63216	direct (N × H)
49. C₂	C₂²×#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
C₂²×#63216	2
C₂³×#3622	2
C₂³×C₁₆	17

Subgroups — C23×#63216 #14545743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#63216 #14545743