Subgroups — #46799285

Order 33852.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22554956	C₂	1	1	yes	maximal, characteristic
2	C₁₃×Dic₇×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#22554956	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₄×#11925881	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	#14579600	—	13	1	no	maximal, Hall
8	C₂×#11925881	—	7	1	no	—
9	C₄×C₁₃×C₃₁	—	7	1	no	Hall
10	C₂×#10620253	—	13	1	no	—
11	#11925881	—	7	1	no	Hall
12	#11763962	—	31	1	no	maximal, Hall
13	Dic₇×C₃₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₃₁	AGL(1,𝔽₇)	1	1	yes	characteristic
15	#10620253	—	13	1	no	Hall
16	C₂×#63271	—	31	1	no	—
17	C₂×C₇×C₃₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₁₃×C₃₁	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Hall
19	C₄×C₃₁⋊C₃	—	91	1	no	Hall
20	C₁₃×Dic₇	C₃₁⋊C₃	1	1	yes	characteristic, complemented, 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	C₂×C₃₁⋊C₃	1	1	yes	characteristic
25	C₄×C₁₃⋊C₃	—	217	1	no	Hall
26	C₄×C₃₁	—	7	1	no	Hall
27	C₃₁⋊C₃	—	91	1	no	Hall
28	C₇×C₁₃	C₄×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
29	ΓL(1,𝔽₈)⋊C₄	—	403	1	no	Hall
30	C₂×C₁₃⋊C₃	—	217	1	no	—
31	C₂×C₃₁	#10587721	1	1	yes	characteristic
32	C₄×C₁₃	—	7	1	no	Hall
33	C₂×ΓL(1,𝔽₈)	—	403	1	no	—
34	C₁₃⋊C₃	—	217	1	no	Hall
35	C₃₁	#11763962	1	1	yes	characteristic, complemented, Sylow
36	Dic₇	#11925881	1	1	yes	characteristic, complemented, Hall
37	C₂×C₁₃	#13049959	1	1	yes	characteristic
38	ΓL(1,𝔽₈)	—	403	1	no	Hall
39	C₂×C₇	C₂×#11925881	1	1	yes	characteristic
40	C₁₃	#14579600	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	2821	1	no	Hall
42	C₇	C₄×#11925881	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	2821	1	no	—
44	C₄	—	7	1	no	Sylow
45	C₃	—	2821	1	no	Sylow
46	C₂	#30683654	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#30683654
commutator, hypocenter	C₇×C₁₃×C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₁₃×C₃₁	C₂×C₃
prime radical	C₂×#22554956	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. C₁₃×Dic₇×C₃₁	C₃	semidirect
3. #22554956	C₄	semidirect
6. C₇×C₁₃×C₃₁	C₃×C₄	semidirect
13. Dic₇×C₃₁	C₁₃⋊C₃	semidirect
18. C₁₃×C₃₁	ΓL(1,𝔽₈)⋊C₄	semidirect
20. C₁₃×Dic₇	C₃₁⋊C₃	semidirect
22. C₇×C₃₁	C₄×C₁₃⋊C₃	semidirect
28. C₇×C₁₃	C₄×C₃₁⋊C₃	semidirect
35. C₃₁	#11763962	semidirect
36. Dic₇	#11925881	semidirect
40. C₁₃	#14579600	semidirect
42. C₇	C₄×#11925881	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22554956	2
C₁₃×Dic₇×C₃₁	3
C₄×#11925881	7
#14579600	13
#11763962	31