Subgroups — #46799247

Order 33852.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22554957	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₃×Dic₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#22554957	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
5	#18012811	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	#14579595	—	13	1	no	maximal, Hall
8	C₂×#11925882	—	7	1	no	—
9	C₁₃×Dic₃₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₂×#10620252	—	13	1	no	—
11	#11925882	—	7	1	no	Hall
12	C₄×#63271	—	31	1	no	maximal, Hall
13	C₇×Dic₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₃₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	#10620252	—	13	1	no	Hall
16	C₂×#63271	—	31	1	no	—
17	C₂×C₇×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₁₃×C₃₁	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
19	(C₃₁⋊C₃)⋊C₄	—	91	1	no	Hall
20	C₄×C₇×C₁₃	—	31	1	no	Hall
21	#63271	—	31	1	no	Hall
22	C₇×C₃₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃₁⋊C₃	—	91	1	no	—
24	C₂×C₇×C₁₃	D₃₁⋊C₃	1	1	yes	characteristic
25	C₄×C₁₃⋊C₃	—	217	1	no	Hall
26	Dic₃₁	#63271	1	1	yes	characteristic, complemented, Hall
27	C₃₁⋊C₃	—	91	1	no	Hall
28	C₇×C₁₃	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Hall
29	C₄×ΓL(1,𝔽₈)	—	403	1	no	Hall
30	C₂×C₁₃⋊C₃	—	217	1	no	—
31	C₂×C₃₁	C₂×#63271	1	1	yes	characteristic
32	C₄×C₁₃	—	31	1	no	Hall
33	C₂×ΓL(1,𝔽₈)	—	403	1	no	—
34	C₁₃⋊C₃	—	217	1	no	Hall
35	C₃₁	C₄×#63271	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	31	1	no	Hall
37	C₂×C₁₃	#13049954	1	1	yes	characteristic
38	ΓL(1,𝔽₈)	—	403	1	no	Hall
39	C₂×C₇	#14559022	1	1	yes	characteristic
40	C₁₃	#14579595	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	2821	1	no	Hall
42	C₇	#18012811	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	2821	1	no	—
44	C₄	—	31	1	no	Sylow
45	C₃	—	2821	1	no	Sylow
46	C₂	#30683616	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#30683616
commutator, hypocenter	C₇×C₁₃×C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×#22554957	C₂
LCS	G ▷ C₇×C₁₃×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₃×Dic₃₁	C₃	semidirect
3. #22554957	C₄	semidirect
6. C₇×C₁₃×C₃₁	C₃×C₄	semidirect
9. C₁₃×Dic₃₁	ΓL(1,𝔽₈)	semidirect
13. C₇×Dic₃₁	C₁₃⋊C₃	semidirect
18. C₁₃×C₃₁	C₄×ΓL(1,𝔽₈)	semidirect
22. C₇×C₃₁	C₄×C₁₃⋊C₃	semidirect
26. Dic₃₁	#63271	semidirect
28. C₇×C₁₃	(C₃₁⋊C₃)⋊C₄	semidirect
35. C₃₁	C₄×#63271	semidirect
40. C₁₃	#14579595	semidirect
42. C₇	#18012811	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22554957	2
C₇×C₁₃×Dic₃₁	3
#18012811	7
#14579595	13
C₄×#63271	31