Subgroups — #37524068

Order 22932.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153186	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₆₃₇	C₃	1	1	yes	maximal, characteristic
3	#19153186	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic
5	#15692572	—	7	1	no	maximal
6	Dic₆₃₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₃×C₄₉	C₃×C₄	1	1	yes	characteristic
8	Dic₄₉⋊C₉	—	13	1	no	maximal, Hall
9	C₂×#11717942	—	7	1	no	—
10	C₂×C₁₃×C₄₉	C₂×C₉	1	1	yes	characteristic
11	C₃×Dic₉₁	—	21	1	no	—
12	C₂×C₄₉⋊C₉	—	13	1	no	—
13	#11717942	—	7	1	no	—
14	C₁₃×C₄₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₄₉	—	39	1	no	—
16	C₂×C₃×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic
17	Dic₁₃⋊C₉	—	49	1	no	Hall
18	C₄₉⋊C₉	—	13	1	no	Hall
19	Dic₉₁	—	21	1	no	—
20	C₂×C₃×C₄₉	D₁₃⋊C₃	1	1	yes	characteristic
21	C₃×C₇×C₁₃	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
22	Dic₇⋊C₉	—	91	1	no	—
23	C₂×C₁₃⋊C₉	—	49	1	no	—
24	Dic₄₉	—	39	1	no	Hall
25	C₂×C₇×C₁₃	D₇⋊C₉	1	1	yes	characteristic
26	C₃×Dic₁₃	—	147	1	no	—
27	C₃×C₄₉	Dic₁₃⋊C₃	1	1	yes	characteristic
28	C₂×C₇⋊C₉	—	91	1	no	—
29	C₁₃⋊C₉	—	49	1	no	Hall
30	C₂×C₄₉	D₁₃⋊C₉	1	1	yes	characteristic
31	C₇×C₁₃	Dic₇⋊C₉	1	1	yes	characteristic
32	C₃×Dic₇	—	273	1	no	—
33	C₂×C₃×C₁₃	D₄₉⋊C₃	1	1	yes	characteristic
34	C₇⋊C₉	—	91	1	no	—
35	Dic₁₃	—	147	1	no	Hall
36	C₄₉	Dic₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃×C₇	#10587723	1	1	yes	characteristic
38	C₃×C₁₃	(C₄₉⋊C₃)⋊C₄	1	1	yes	characteristic
39	C₄×C₉	—	637	1	no	Hall
40	Dic₇	—	273	1	no	—
41	C₂×C₁₃	D₄₉⋊C₉	1	1	yes	characteristic
42	C₃×C₇	#11763964	1	1	yes	characteristic
43	C₂×C₉	—	637	1	no	—
44	C₂×C₇	#13109903	1	1	yes	characteristic
45	C₁₃	Dic₄₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₄	—	1911	1	no	—
47	C₉	—	637	1	no	Sylow
48	C₇	#15692572	1	1	yes	characteristic
49	C₂×C₃	#16838420	1	1	yes	characteristic
50	C₄	—	1911	1	no	Sylow
51	C₃	#21439444	1	1	yes	characteristic
52	C₂	#26039370	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#16838420
commutator, hypocenter	C₁₃×C₄₉	C₄×C₉
Frattini	C₂×C₃×C₇	#10587723
Fitting, cosocle	C₂×C₃×C₁₃×C₄₉	C₂×C₃
socle, prime radical	C₂×C₃×C₇×C₁₃	AGL(1,𝔽₇)
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. #19153186	C₄	semidirect
6. Dic₆₃₇	C₉	semidirect
14. C₁₃×C₄₉	C₄×C₉	semidirect
36. C₄₉	Dic₁₃⋊C₉	semidirect
45. C₁₃	Dic₄₉⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19153186	2
C₃×Dic₆₃₇	3
#15692572	7
Dic₄₉⋊C₉	13