Subgroups — C₂×#31775461 #46853643

Order 34916.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31775461	C₂	1	2	yes	maximal, direct product factor
2	C₂×#22576609	C₂	1	1	yes	maximal, characteristic, complemented
3	#22576609	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₂₄₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₂₉×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented
6	D₁₂₄₇	C₂×C₇	1	2	yes	complemented
7	C₂₉×C₄₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂×D₄₃⋊C₇	—	29	1	no	maximal, Hall
9	C₂×D₂₉⋊C₇	—	43	1	no	maximal, Hall
10	C₂×C₄₃⋊C₇	—	29	1	no	—
11	D₄₃⋊C₇	—	29	2	no	—
12	C₂×C₂₉⋊C₇	—	43	1	no	—
13	D₂₉⋊C₇	—	43	2	no	—
14	C₄₃⋊C₇	—	29	1	no	Hall
15	C₂₉⋊C₇	—	43	1	no	Hall
16	C₂×D₄₃	—	29	1	no	Hall
17	C₂×D₂₉	—	43	1	no	Hall
18	C₂×C₄₃	D₂₉⋊C₇	1	1	yes	characteristic, complemented
19	D₄₃	—	29	2	no	—
20	C₂×C₂₉	D₄₃⋊C₇	1	1	yes	characteristic, complemented
21	D₂₉	—	43	2	no	—
22	C₄₃	C₂×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
23	C₂₉	C₂×D₄₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₇	—	1247	1	no	Hall
25	C₂×C₇	—	1247	2	no	—
26	C₂×C₇	—	1247	1	no	—
27	C₇	—	1247	1	no	Sylow
28	C₂²	—	1247	1	no	Sylow
29	C₂	—	1247	2	no	—
30	C₂	#31775461	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#31775461
commutator, cosocle, hypocenter	C₂₉×C₄₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₂₉×C₄₃	C₂×C₇
LCS	G ▷ C₂₉×C₄₃
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.