Subgroups — C₂×#27132061 #37567780

Order 24444.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27132061	C₂	1	2	yes	maximal, direct product factor
2	C₂×#20259170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₇×C₉₇	C₃	1	1	yes	maximal, characteristic
4	#20259170	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₇×C₉₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₉₇	C₂×C₃	1	1	yes	characteristic
7	C₂²×C₉₇⋊C₉	—	7	1	no	maximal, Hall
8	C₂×D₇×C₉₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₉₇	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉₇⋊C₉	—	7	2	no	—
11	C₂×C₉₇⋊C₉	—	7	1	no	—
12	C₂×C₇×C₉₇	C₂×C₉	1	1	yes	characteristic, complemented
13	D₇×C₉₇	C₂×C₉	1	2	yes	complemented
14	C₂²×C₃×C₉₇	—	21	1	no	—
15	C₉₇⋊C₉	—	7	1	no	Hall
16	C₇×C₉₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₉₇	—	21	2	no	—
18	C₂×C₃×C₉₇	AGL(1,𝔽₇)	1	1	yes	characteristic
19	C₂²×C₉₇	—	21	1	no	Hall
20	C₃×C₉₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
21	C₂×D₇⋊C₉	—	97	1	no	maximal, Hall
22	C₂×C₉₇	—	21	2	no	—
23	C₂×C₉₇	D₇⋊C₉	1	1	yes	characteristic, complemented
24	C₂×C₇⋊C₉	—	97	1	no	—
25	D₇⋊C₉	—	97	2	no	—
26	C₉₇	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃×D₇	C₉₇⋊C₃	1	1	yes	characteristic
28	C₇⋊C₉	—	97	1	no	Hall
29	C₂×C₃×C₇	C₂×C₉₇⋊C₃	1	1	yes	characteristic
30	C₃×D₇	C₂×C₉₇⋊C₃	1	2	yes	—
31	C₂²×C₉	—	679	1	no	Hall
32	C₂×D₇	C₉₇⋊C₉	1	1	yes	characteristic, complemented, Hall
33	C₃×C₇	C₂²×C₉₇⋊C₃	1	1	yes	characteristic
34	C₂×C₉	—	679	2	no	—
35	C₂×C₉	—	679	1	no	—
36	C₂×C₇	C₂×C₉₇⋊C₉	1	1	yes	characteristic, complemented
37	D₇	C₂×C₉₇⋊C₉	1	2	yes	complemented
38	C₂²×C₃	—	21	1	no	—
39	C₉	—	679	1	no	Sylow
40	C₇	C₂²×C₉₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	21	2	no	—
42	C₂×C₃	#16861354	1	1	yes	characteristic
43	C₂²	—	21	1	no	Sylow
44	C₃	C₂×#16861354	1	1	yes	characteristic
45	C₂	—	21	2	no	—
46	C₂	#27132061	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#16861354
commutator, hypocenter	C₇×C₉₇	C₂²×C₉
Frattini	C₃	C₂×#16861354
Fitting, socle	C₂×C₃×C₇×C₉₇	C₂×C₃
prime radical	C₂×C₃×D₇×C₉₇	C₃
cosocle	C₃×C₇×C₉₇	C₂²×C₃
LCS	G ▷ C₇×C₉₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. #27132061	C₂	direct (N × H)
2. C₂×#20259170	C₂	semidirect
4. #20259170	C₂²	semidirect
8. C₂×D₇×C₉₇	C₉	semidirect
12. C₂×C₇×C₉₇	C₂×C₉	semidirect
13. D₇×C₉₇	C₂×C₉	semidirect
16. C₇×C₉₇	C₂²×C₉	semidirect
23. C₂×C₉₇	D₇⋊C₉	semidirect
26. C₉₇	C₂×D₇⋊C₉	semidirect
32. C₂×D₇	C₉₇⋊C₉	semidirect
36. C₂×C₇	C₂×C₉₇⋊C₉	semidirect
37. D₇	C₂×C₉₇⋊C₉	semidirect
40. C₇	C₂²×C₉₇⋊C₉	semidirect
46. C₂	#27132061	direct (N × H)

Maximal subgroups

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

subgroup	index
#27132061	2
C₂×#20259170	2
C₂×C₃×D₇×C₉₇	3
C₂²×C₉₇⋊C₉	7
C₂×D₇⋊C₉	97

Subgroups — C2×#27132061 #37567780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27132061 #37567780