Subgroups — C₂×#31772255 #46828992

Order 34572.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31772255	C₂	1	2	yes	maximal, direct product factor
2	C₂×#22575687	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₇×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#22575687	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₆₇×D₄₃	C₂×C₃	1	2	yes	complemented
7	C₄₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₆₇⋊C₃	—	43	1	no	maximal, Hall
9	C₂×D₄₃⋊C₃	—	67	1	no	maximal, Hall
10	C₂×C₆₇⋊C₃	—	43	2	no	—
11	C₂×C₆₇⋊C₃	—	43	1	no	—
12	C₂²×C₆₇	—	43	1	no	Hall
13	C₂×C₄₃⋊C₃	—	67	1	no	—
14	D₄₃⋊C₃	—	67	2	no	—
15	C₆₇⋊C₃	—	43	1	no	Hall
16	C₂×D₄₃	C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₆₇	—	43	2	no	—
18	C₂×C₆₇	D₄₃⋊C₃	1	1	yes	characteristic, complemented
19	C₄₃⋊C₃	—	67	1	no	Hall
20	C₂×C₄₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented
21	D₄₃	C₂×C₆₇⋊C₃	1	2	yes	complemented
22	C₆₇	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₄₃	C₂²×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2881	1	no	Hall
25	C₂×C₃	—	2881	2	no	—
26	C₂×C₃	—	2881	1	no	—
27	C₂²	—	43	1	no	Sylow
28	C₃	—	2881	1	no	Sylow
29	C₂	—	43	2	no	—
30	C₂	#31772255	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#31772255
commutator, cosocle, hypocenter	C₄₃×C₆₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₄₃×C₆₇	C₂×C₃
LCS	G ▷ C₄₃×C₆₇
UCS	C₁ ◁ C₂

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

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