Subgroups — C₂×#14543599 #17949626

Order 4352.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543599	C₂	1	2	yes	maximal, direct product factor
2	C₂×#11762528	C₂	1	1	yes	maximal, characteristic
3	#11762528	C₄	1	1	yes	characteristic
4	#11762528	C₂²	1	1	yes	characteristic
5	C₂×C₁₇×C₃₂	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
7	C₁₇×C₃₂	C₈	1	1	yes	characteristic
8	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
10	C₁₆×C₁₇	C₁₆	1	1	yes	characteristic
11	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₁₂₈	—	17	1	no	maximal, Sylow
13	C₂×C₄×C₁₇	C₃₂	1	1	yes	characteristic
14	C₈×C₁₇	C₃₂	1	1	yes	characteristic
15	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
16	C₂×C₆₄	—	17	1	no	—
17	C₁₂₈	—	17	2	no	—
18	C₂²×C₁₇	C₆₄	1	1	yes	characteristic
19	C₄×C₁₇	C₆₄	1	1	yes	characteristic
20	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
21	C₂×C₃₂	#595	1	1	yes	characteristic
22	C₆₄	—	17	1	no	—
23	C₆₄	—	17	1	no	—
24	C₂×C₁₇	C₁₂₈	1	2	yes	complemented
25	C₂×C₁₇	C₂×C₆₄	1	1	yes	characteristic
26	C₂×C₁₆	#3624	1	1	yes	characteristic
27	C₃₂	#3624	1	1	yes	characteristic
28	C₃₂	C₂×#595	1	1	yes	characteristic
29	C₁₇	C₂×C₁₂₈	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₈	#63216	1	1	yes	characteristic
31	C₁₆	#63216	1	1	yes	characteristic
32	C₁₆	C₂×#3624	1	1	yes	characteristic
33	C₂×C₄	#10587467	1	1	yes	characteristic
34	C₈	#10587467	1	1	yes	characteristic
35	C₈	C₂×#63216	1	1	yes	characteristic
36	C₂²	#11763648	1	1	yes	characteristic
37	C₄	#11763648	1	1	yes	characteristic
38	C₄	C₂×#10587467	1	1	yes	characteristic
39	C₂	#14543599	1	2	yes	direct product factor
40	C₂	C₂×#11763648	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	#595
commutator, hypocenter	C₁₇	C₂×C₁₂₈
Frattini	C₃₂	C₂×#595
Fitting	C₂×C₁₇×C₃₂	C₄
socle, prime radical	C₂²×C₁₇	C₆₄
cosocle	#11762528	C₂²
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #14543599	C₂	direct (N × H)
24. C₂×C₁₇	C₁₂₈	semidirect
29. C₁₇	C₂×C₁₂₈	semidirect
39. C₂	#14543599	direct (N × H)

Maximal subgroups

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

subgroup	index
#14543599	2
C₂×#11762528	2
C₂×C₁₂₈	17

Subgroups — C2×#14543599 #17949626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14543599 #17949626