Subgroups — C₂³×#63214 #14541877

Order 2176.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#63214	C₂	1	14	yes	maximal, direct product factor
2	C₂³×C₈×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₁₇	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₁₇	C₄	1	7	yes	—
5	C₂²×C₈×C₁₇	C₂²	1	7	yes	—
6	C₂×#63214	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×C₈×C₁₇	C₂×C₄	1	21	yes	—
11	C₂×C₈×C₁₇	C₂³	1	7	yes	—
12	#63214	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	C₈×C₁₇	C₂²×C₄	1	7	yes	—
18	C₈×C₁₇	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	D₁₇	1	1	yes	characteristic
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	Dic₁₇	1	1	yes	characteristic
29	C₂²×C₈	Dic₁₇	1	7	yes	—
30	C₂²×C₈	C₂×D₁₇	1	7	yes	—
31	C₂×C₁₆	—	17	28	no	—
32	C₁₇	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂⁴	#3622	1	1	yes	characteristic
34	C₂²×C₄	#3622	1	7	yes	—
35	C₂²×C₄	C₂×Dic₁₇	1	7	yes	—
36	C₂×C₈	C₂×Dic₁₇	1	21	yes	—
37	C₂×C₈	C₂²×D₁₇	1	7	yes	—
38	C₁₆	—	17	8	no	—
39	C₂³	#63214	1	8	yes	direct product factor
40	C₂³	C₂×#3622	1	7	yes	—
41	C₂×C₄	C₂×#3622	1	21	yes	—
42	C₂×C₄	C₂²×Dic₁₇	1	7	yes	—
43	C₈	C₂²×Dic₁₇	1	7	yes	—
44	C₈	C₂³×D₁₇	1	1	yes	characteristic
45	C₂²	C₂×#63214	1	28	yes	direct product factor
46	C₂²	C₂²×#3622	1	7	yes	—
47	C₄	C₂²×#3622	1	7	yes	—
48	C₄	C₂³×Dic₁₇	1	1	yes	characteristic
49	C₂	C₂²×#63214	1	14	yes	direct product factor
50	C₂	C₂³×#3622	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₈	D₁₇
commutator, hypocenter	C₁₇	C₂³×C₁₆
Frattini	C₈	C₂³×D₁₇
Fitting	C₂³×C₈×C₁₇	C₂
socle, prime radical	C₂⁴×C₁₇	C₈
cosocle	C₈×C₁₇	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#63214	C₂	direct (N × H)
6. C₂×#63214	C₂²	direct (N × H)
12. #63214	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	#63214	direct (N × H)
45. C₂²	C₂×#63214	direct (N × H)
49. C₂	C₂²×#63214	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×#63214	2
C₂³×C₈×C₁₇	2
C₂³×C₁₆	17

Subgroups — C23×#63214 #14541877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#63214 #14541877