Subgroups — C₂×C₃×#63214 #13108754

Order 1632.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃×#63214	C₂	1	2	yes	maximal, direct product factor
3	C₂×#63214	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₁₇	C₄	1	1	yes	characteristic
5	C₃×C₈×C₁₇	C₄	1	1	yes	characteristic
6	C₃×C₈×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₇	C₂×C₃	1	1	yes	characteristic
8	#63214	C₂×C₃	1	2	yes	direct product factor
9	C₂²×C₃×C₁₇	C₈	1	1	yes	characteristic
10	C₃×C₄×C₁₇	C₈	1	1	yes	characteristic
11	C₃×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₇	C₃×C₄	1	1	yes	characteristic
13	C₈×C₁₇	C₃×C₄	1	1	yes	characteristic
14	C₈×C₁₇	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₁₇	C₁₆	1	2	yes	complemented
16	C₂×C₃×C₁₇	C₂×C₈	1	1	yes	characteristic
17	C₂×C₃×C₁₆	—	17	1	no	maximal, Hall
18	C₂²×C₁₇	C₃×C₈	1	1	yes	characteristic
19	C₄×C₁₇	C₃×C₈	1	1	yes	characteristic
20	C₄×C₁₇	C₂×C₃×C₄	1	1	yes	characteristic
21	C₃×C₁₇	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₈	D₁₇	1	1	yes	characteristic
23	C₃×C₁₆	—	17	2	no	—
24	C₂×C₁₇	C₃×C₁₆	1	2	yes	complemented
25	C₂×C₁₇	C₂×C₃×C₈	1	1	yes	characteristic
26	C₂×C₁₆	—	17	1	no	Sylow
27	C₂×C₃×C₄	Dic₁₇	1	1	yes	characteristic
28	C₃×C₈	Dic₁₇	1	1	yes	characteristic
29	C₃×C₈	C₂×D₁₇	1	1	yes	characteristic
30	C₁₇	C₂×C₃×C₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	C₃×D₁₇	1	1	yes	characteristic
32	C₁₆	—	17	2	no	—
33	C₂²×C₃	#3622	1	1	yes	characteristic
34	C₃×C₄	#3622	1	1	yes	characteristic
35	C₃×C₄	C₂×Dic₁₇	1	1	yes	characteristic
36	C₂×C₄	C₃×Dic₁₇	1	1	yes	characteristic
37	C₈	C₃×Dic₁₇	1	1	yes	characteristic
38	C₈	C₂×C₃×D₁₇	1	1	yes	characteristic
39	C₂×C₃	#63214	1	2	yes	direct product factor
40	C₂×C₃	C₂×#3622	1	1	yes	characteristic
41	C₂²	C₃×#3622	1	1	yes	characteristic
42	C₄	C₃×#3622	1	1	yes	characteristic
43	C₄	C₂×C₃×Dic₁₇	1	1	yes	characteristic
44	C₃	C₂×#63214	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×#63214	1	2	yes	direct product factor
46	C₂	C₂×C₃×#3622	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₈	D₁₇
commutator, hypocenter	C₁₇	C₂×C₃×C₁₆
Frattini	C₈	C₂×C₃×D₁₇
Fitting	C₂×C₃×C₈×C₁₇	C₂
socle, prime radical	C₂²×C₃×C₁₇	C₈
cosocle	C₈×C₁₇	C₂²×C₃
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×#63214	C₂	direct (N × H)
3. C₂×#63214	C₃	direct (N × H)
8. #63214	C₂×C₃	direct (N × H)
15. C₂×C₃×C₁₇	C₁₆	semidirect
21. C₃×C₁₇	C₂×C₁₆	semidirect
24. C₂×C₁₇	C₃×C₁₆	semidirect
30. C₁₇	C₂×C₃×C₁₆	semidirect
39. C₂×C₃	#63214	direct (N × H)
44. C₃	C₂×#63214	direct (N × H)
45. C₂	C₃×#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
C₂×C₃×C₈×C₁₇	2
C₃×#63214	2
C₂×#63214	3
C₂×C₃×C₁₆	17

Subgroups — C2×C3×#63214 #13108754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63214 #13108754