Subgroups — C₂×D₈₅₃₃ #46802438

Order 34132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₅₃₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₂₁₉	—	7	1	no	maximal, Hall
5	C₂×C₂₃×C₅₃	D₇	1	1	yes	characteristic, complemented
6	D₁₂₁₉	—	7	2	no	—
7	C₂×D₃₇₁	—	23	1	no	maximal, Hall
8	C₂₃×C₅₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₅₃	D₂₃	1	1	yes	characteristic, complemented
10	D₃₇₁	—	23	2	no	—
11	C₂×D₁₆₁	—	53	1	no	maximal, Hall
12	C₇×C₅₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₂₃	D₅₃	1	1	yes	characteristic, complemented
14	D₁₆₁	—	53	2	no	—
15	C₂×D₅₃	—	161	1	no	Hall
16	C₇×C₂₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅₃	D₁₆₁	1	1	yes	characteristic, complemented
18	D₅₃	—	161	2	no	—
19	C₂×D₂₃	—	371	1	no	Hall
20	C₅₃	C₂×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₂₃	D₃₇₁	1	1	yes	characteristic, complemented
22	D₂₃	—	371	2	no	—
23	C₂×D₇	—	1219	1	no	Hall
24	C₂₃	C₂×D₃₇₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	D₁₂₁₉	1	1	yes	characteristic, complemented
26	D₇	—	1219	2	no	—
27	C₇	C₂×D₁₂₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	8533	1	no	Sylow
29	C₂	—	8533	2	no	—
30	C₂	D₈₅₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₅₃₃
commutator, cosocle, hypocenter	C₇×C₂₃×C₅₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₃×C₅₃	C₂
LCS	G ▷ C₇×C₂₃×C₅₃
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.