Subgroups — #30630682⋊C₂ #44544779

Order 32004.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30630688	C₂	1	1	yes	maximal, characteristic, complemented
2	#30630684	C₂	1	1	yes	maximal, characteristic, complemented
3	#30630682	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
5	#22547883	C₂²	1	1	yes	characteristic, complemented, Hall
6	(C₁₂₇⋊C₃)⋊D₇	C₂×C₃	1	1	yes	characteristic
7	D₇×C₁₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
8	C₇×D₁₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
9	C₂×#11765919⋊C₂	—	7	1	no	maximal, Hall
10	D₇×D₁₂₇	C₉	1	1	yes	characteristic, complemented, Hall
11	C₇×C₁₂₇⋊C₃	C₂²×C₃	1	1	yes	characteristic
12	C₂×#11765919	—	7	1	no	—
13	#11765919⋊C₂	—	7	1	no	—
14	#11765919⋊C₂	—	7	1	no	—
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×D₁₂₇⋊C₃	—	7	1	no	—
19	#11765919	—	7	1	no	Hall
20	C₇×C₁₂₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₂₇⋊C₃	—	7	1	no	—
22	D₁₂₇⋊C₃	—	7	1	no	—
23	D₁₂₇⋊C₃	AGL(1,𝔽₇)	1	1	yes	characteristic
24	C₂×D₁₂₇	—	7	1	no	Hall
25	C₁₂₇⋊C₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
26	C₂×C₁₂₇	—	7	1	no	—
27	D₁₂₇	—	7	1	no	—
28	D₁₂₇	D₇⋊C₉	1	1	yes	characteristic, complemented
29	C₂×D₇⋊C₉	—	127	1	no	maximal, Hall
30	C₁₂₇	C₂×D₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇⋊C₉	—	127	1	no	—
32	D₇⋊C₉	—	127	1	no	—
33	D₇⋊C₉	—	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	—	127	1	no	—
39	C₂²×C₉	—	889	1	no	Hall
40	C₂×D₇	—	127	1	no	Hall
41	C₃×C₇	—	127	1	no	—
42	C₂×C₉	—	889	1	no	—
43	C₂×C₉	—	889	1	no	—
44	C₂×C₉	—	889	1	no	—
45	C₂×C₇	—	127	1	no	—
46	D₇	—	127	1	no	—
47	D₇	#11765919⋊C₂	1	1	yes	characteristic, complemented
48	C₂²×C₃	—	889	1	no	—
49	C₉	—	889	1	no	Sylow
50	C₇	C₂×#11765919⋊C₂	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	889	1	no	—
52	C₂×C₃	—	889	1	no	—
53	C₂×C₃	—	127	1	no	—
54	C₂²	—	889	1	no	Sylow
55	C₃	—	127	1	no	—
56	C₂	—	7	1	no	—
57	C₂	—	889	1	no	—
58	C₂	—	127	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. #30630688	C₂	semidirect
2. #30630684	C₂	semidirect
3. #30630682	C₂	semidirect
5. #22547883	C₂²	semidirect
10. D₇×D₁₂₇	C₉	semidirect
15. D₈₈₉	C₂×C₉	semidirect
16. C₇×D₁₂₇	C₂×C₉	semidirect
17. D₇×C₁₂₇	C₂×C₉	semidirect
20. C₇×C₁₂₇	C₂²×C₉	semidirect
28. D₁₂₇	D₇⋊C₉	semidirect
30. C₁₂₇	C₂×D₇⋊C₉	semidirect
47. D₇	#11765919⋊C₂	semidirect
50. C₇	C₂×#11765919⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#30630688	2
#30630684	2
#30630682	2
D₇×D₁₂₇⋊C₃	3
C₂×#11765919⋊C₂	7
C₂×D₇⋊C₉	127

Subgroups — #30630682⋊C2 #44544779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #30630682⋊C₂ #44544779