Subgroups — C₂×#30630664 #44544671

Order 32004.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30630664	C₂	1	2	yes	maximal, direct product factor
2	C₂×#22547877	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₇×D₁₂₇	C₃	1	1	yes	maximal, characteristic
4	#22547877	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₁₂₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic
7	C₂×#11765917⋊C₂	—	7	1	no	maximal, Hall
8	C₂×C₇×D₁₂₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic
10	C₂×#11765917	—	7	1	no	—
11	#11765917⋊C₂	—	7	2	no	—
12	C₂×C₇×C₁₂₇	C₂×C₉	1	1	yes	characteristic, complemented
13	C₇×D₁₂₇	C₂×C₉	1	2	yes	complemented
14	C₂×C₃×D₁₂₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	#11765917	—	7	1	no	Hall
16	C₇×C₁₂₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₂₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₃×D₁₂₇	C₂×ΓL(1,𝔽₈)	1	2	yes	—
19	C₂×D₁₂₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₂₇	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₂×C₁₂₇	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
22	D₁₂₇	C₂×C₇⋊C₉	1	2	yes	complemented
23	C₂²×C₇⋊C₉	—	127	1	no	maximal, Hall
24	C₁₂₇	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇⋊C₉	—	127	2	no	—
26	C₂×C₇⋊C₉	—	127	1	no	—
27	C₂²×C₃×C₇	—	127	1	no	—
28	C₇⋊C₉	—	127	1	no	Hall
29	C₂×C₃×C₇	—	127	2	no	—
30	C₂×C₃×C₇	D₁₂₇⋊C₃	1	1	yes	characteristic
31	C₂²×C₉	—	889	1	no	Hall
32	C₂²×C₇	—	127	1	no	Hall
33	C₃×C₇	C₂×D₁₂₇⋊C₃	1	1	yes	characteristic
34	C₂×C₉	—	889	2	no	—
35	C₂×C₉	—	889	1	no	—
36	C₂×C₇	—	127	2	no	—
37	C₂×C₇	#11765917⋊C₂	1	1	yes	characteristic, complemented
38	C₂²×C₃	—	127	1	no	—
39	C₉	—	889	1	no	Sylow
40	C₇	C₂×#11765917⋊C₂	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	127	2	no	—
42	C₂×C₃	#19128625	1	1	yes	characteristic
43	C₂²	—	127	1	no	Sylow
44	C₃	C₂×#19128625	1	1	yes	characteristic
45	C₂	—	127	2	no	—
46	C₂	#30630664	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#19128625
commutator, hypocenter	C₇×C₁₂₇	C₂²×C₉
Frattini	C₃	C₂×#19128625
Fitting, socle	C₂×C₃×C₇×C₁₂₇	C₂×C₃
prime radical	C₂×C₃×C₇×D₁₂₇	C₃
cosocle	C₃×C₇×C₁₂₇	C₂²×C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. #30630664	C₂	direct (N × H)
2. C₂×#22547877	C₂	semidirect
4. #22547877	C₂²	semidirect
8. C₂×C₇×D₁₂₇	C₉	semidirect
12. C₂×C₇×C₁₂₇	C₂×C₉	semidirect
13. C₇×D₁₂₇	C₂×C₉	semidirect
16. C₇×C₁₂₇	C₂²×C₉	semidirect
19. C₂×D₁₂₇	C₇⋊C₉	semidirect
21. C₂×C₁₂₇	C₂×C₇⋊C₉	semidirect
22. D₁₂₇	C₂×C₇⋊C₉	semidirect
24. C₁₂₇	C₂²×C₇⋊C₉	semidirect
37. C₂×C₇	#11765917⋊C₂	semidirect
40. C₇	C₂×#11765917⋊C₂	semidirect
46. C₂	#30630664	direct (N × H)

Maximal subgroups

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

subgroup	index
#30630664	2
C₂×#22547877	2
C₂×C₃×C₇×D₁₂₇	3
C₂×#11765917⋊C₂	7
C₂²×C₇⋊C₉	127

Subgroups — C2×#30630664 #44544671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30630664 #44544671