Subgroups — #30627894⋊C₂ #44535596

Order 31356.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30627902	C₂	1	1	yes	maximal, characteristic, complemented
2	#30627898	C₂	1	1	yes	maximal, characteristic, complemented
3	#30627894	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×D₆₇	C₃	1	1	yes	maximal, characteristic
5	#21463203	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₈₇₁	C₂×C₃	1	1	yes	characteristic
7	C₃×D₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₃×D₆₇	C₂×C₃	1	1	yes	characteristic
9	D₁₃×D₆₇	C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic
11	C₂×D₆₇⋊C₉	—	13	1	no	maximal, Hall
12	D₈₇₁	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₃×D₆₇	C₂×C₉	1	1	yes	characteristic, complemented
14	D₁₃×C₆₇	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×C₆₇⋊C₉	—	13	1	no	—
16	D₆₇⋊C₉	—	13	1	no	—
17	D₆₇⋊C₉	—	13	1	no	—
18	C₁₃×C₆₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×D₆₇	—	13	1	no	—
20	C₆₇⋊C₉	—	13	1	no	Hall
21	C₂×D₁₃⋊C₉	—	67	1	no	maximal, Hall
22	C₂×C₃×C₆₇	—	13	1	no	—
23	C₃×D₆₇	—	13	1	no	—
24	C₃×D₆₇	D₁₃⋊C₃	1	1	yes	characteristic
25	C₂×D₆₇	—	13	1	no	Hall
26	C₂×C₁₃⋊C₉	—	67	1	no	—
27	D₁₃⋊C₉	—	67	1	no	—
28	D₁₃⋊C₉	—	67	1	no	—
29	C₃×C₆₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic
30	C₂×C₃×D₁₃	—	67	1	no	—
31	C₂×C₆₇	—	13	1	no	—
32	D₆₇	—	13	1	no	—
33	D₆₇	D₁₃⋊C₉	1	1	yes	characteristic, complemented
34	C₁₃⋊C₉	—	67	1	no	Hall
35	C₂×C₃×C₁₃	—	67	1	no	—
36	C₃×D₁₃	—	67	1	no	—
37	C₃×D₁₃	D₆₇⋊C₃	1	1	yes	characteristic
38	C₆₇	C₂×D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₃	—	67	1	no	Hall
40	C₃×C₁₃	C₂×D₆₇⋊C₃	1	1	yes	characteristic
41	C₂²×C₉	—	871	1	no	Hall
42	C₂×C₁₃	—	67	1	no	—
43	D₁₃	—	67	1	no	—
44	D₁₃	D₆₇⋊C₉	1	1	yes	characteristic, complemented
45	C₂×C₉	—	871	1	no	—
46	C₂×C₉	—	871	1	no	—
47	C₂×C₉	—	871	1	no	—
48	C₁₃	C₂×D₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	871	1	no	—
50	C₉	—	871	1	no	Sylow
51	C₂×C₃	—	13	1	no	—
52	C₂×C₃	—	67	1	no	—
53	C₂×C₃	—	871	1	no	—
54	C₂²	—	871	1	no	Sylow
55	C₃	#19104944⋊C₂	1	1	yes	characteristic
56	C₂	—	13	1	no	—
57	C₂	—	67	1	no	—
58	C₂	—	871	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#19104944⋊C₂
commutator, hypocenter	C₁₃×C₆₇	C₂²×C₉
Fitting, socle, cosocle	C₃×C₁₃×C₆₇	C₂²×C₃
prime radical	C₃×D₁₃×D₆₇	C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #30627902	C₂	semidirect
2. #30627898	C₂	semidirect
3. #30627894	C₂	semidirect
5. #21463203	C₂²	semidirect
9. D₁₃×D₆₇	C₉	semidirect
12. D₈₇₁	C₂×C₉	semidirect
13. C₁₃×D₆₇	C₂×C₉	semidirect
14. D₁₃×C₆₇	C₂×C₉	semidirect
18. C₁₃×C₆₇	C₂²×C₉	semidirect
33. D₆₇	D₁₃⋊C₉	semidirect
38. C₆₇	C₂×D₁₃⋊C₉	semidirect
44. D₁₃	D₆₇⋊C₉	semidirect
48. C₁₃	C₂×D₆₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
#30627902	2
#30627898	2
#30627894	2
C₃×D₁₃×D₆₇	3
C₂×D₆₇⋊C₉	13
C₂×D₁₃⋊C₉	67

Subgroups — #30627894⋊C2 #44535596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #30627894⋊C₂ #44535596