Subgroups — D₇×#11765917⋊C₂ #44544661

Order 32004.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11765917⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×#11765917	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#11765917⋊C₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₁₂₇	C₃	1	1	yes	maximal, characteristic
5	C₇×#11765917	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₈₈₉	C₂×C₃	1	1	yes	characteristic
7	C₃×D₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₇×D₁₂₇	C₂×C₃	1	1	yes	characteristic
9	C₂×#11765917⋊C₂	—	7	1	no	maximal, Hall
10	D₇×D₁₂₇	C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₂₇	C₂²×C₃	1	1	yes	characteristic
12	C₂×#11765917	—	7	1	no	—
13	#11765917⋊C₂	—	7	1	no	—
14	#11765917⋊C₂	D₇	1	1	yes	characteristic, direct product factor
15	D₈₈₉	C₂×C₉	1	1	yes	characteristic, complemented
16	C₇×D₁₂₇	C₂×C₉	1	1	yes	characteristic, complemented
17	D₇×C₁₂₇	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₃×D₁₂₇	—	7	1	no	—
19	#11765917	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	C₇×C₁₂₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₂₇	—	7	1	no	—
22	C₃×D₁₂₇	—	7	1	no	—
23	C₃×D₁₂₇	C₃×D₇	1	1	yes	characteristic
24	C₂×D₁₂₇	—	7	1	no	Hall
25	C₃×C₁₂₇	C₂×C₃×D₇	1	1	yes	characteristic
26	C₂×C₁₂₇	—	7	1	no	—
27	D₁₂₇	—	7	1	no	—
28	D₁₂₇	C₉×D₇	1	1	yes	characteristic, complemented
29	C₂×C₉×D₇	—	127	1	no	maximal, Hall
30	C₁₂₇	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇×C₉	—	127	1	no	—
32	C₉×D₇	—	127	1	no	—
33	C₉×D₇	—	127	1	no	—
34	C₂×C₃×D₇	—	127	1	no	—
35	C₇×C₉	—	127	1	no	Hall
36	C₂×C₃×C₇	—	127	1	no	—
37	C₃×D₇	—	127	1	no	—
38	C₃×D₇	D₁₂₇⋊C₃	1	1	yes	characteristic
39	C₂²×C₉	—	889	1	no	Hall
40	C₂×D₇	—	127	1	no	Hall
41	C₃×C₇	C₂×D₁₂₇⋊C₃	1	1	yes	characteristic
42	C₂×C₉	—	889	1	no	—
43	C₂×C₉	—	889	1	no	—
44	C₂×C₉	—	127	1	no	—
45	C₂×C₇	—	127	1	no	—
46	D₇	—	127	1	no	—
47	D₇	#11765917⋊C₂	1	1	yes	characteristic, direct product factor
48	C₂²×C₃	—	889	1	no	—
49	C₉	—	127	1	no	Sylow
50	C₇	C₂×#11765917⋊C₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	7	1	no	—
52	C₂×C₃	—	889	1	no	—
53	C₂×C₃	—	127	1	no	—
54	C₂²	—	889	1	no	Sylow
55	C₃	D₇×D₁₂₇⋊C₃	1	1	yes	characteristic
56	C₂	—	7	1	no	—
57	C₂	—	889	1	no	—
58	C₂	—	127	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₇×D₁₂₇⋊C₃
commutator, hypocenter	C₇×C₁₂₇	C₂²×C₉
Fitting, socle, cosocle	C₃×C₇×C₁₂₇	C₂²×C₃
prime radical	C₃×D₇×D₁₂₇	C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #11765917⋊D₇	C₂	semidirect
2. D₇×#11765917	C₂	semidirect
3. C₇×#11765917⋊C₂	C₂	semidirect
5. C₇×#11765917	C₂²	semidirect
10. D₇×D₁₂₇	C₉	semidirect
14. #11765917⋊C₂	D₇	direct (N × H)
15. D₈₈₉	C₂×C₉	semidirect
16. C₇×D₁₂₇	C₂×C₉	semidirect
17. D₇×C₁₂₇	C₂×C₉	semidirect
19. #11765917	C₂×D₇	semidirect
20. C₇×C₁₂₇	C₂²×C₉	semidirect
28. D₁₂₇	C₉×D₇	semidirect
30. C₁₂₇	C₂×C₉×D₇	semidirect
47. D₇	#11765917⋊C₂	direct (N × H)
50. C₇	C₂×#11765917⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#11765917⋊D₇	2
D₇×#11765917	2
C₇×#11765917⋊C₂	2
C₃×D₇×D₁₂₇	3
C₂×#11765917⋊C₂	7
C₂×C₉×D₇	127

Subgroups — D7×#11765917⋊C2 #44544661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#11765917⋊C₂ #44544661