Subgroups — C₄×#21463204 #44535568

Order 31356.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21463204	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic
3	#21463204	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₃×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic
7	C₄×C₆₇⋊C₉	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₆₇	C₂×C₉	1	1	yes	characteristic
9	C₂×C₆₇⋊C₉	—	13	1	no	—
10	C₁₃×C₆₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₆₇	C₁₃⋊C₃	1	1	yes	characteristic
12	C₆₇⋊C₉	—	13	1	no	Hall
13	C₄×C₁₃⋊C₉	—	67	1	no	maximal, Hall
14	C₂×C₃×C₆₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
15	C₄×C₆₇	C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃⋊C₉	—	67	1	no	—
17	C₃×C₆₇	C₄×C₁₃⋊C₃	1	1	yes	characteristic
18	C₃×C₄×C₁₃	C₆₇⋊C₃	1	1	yes	characteristic
19	C₂×C₆₇	C₂×C₁₃⋊C₉	1	1	yes	characteristic
20	C₁₃⋊C₉	—	67	1	no	Hall
21	C₂×C₃×C₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic
22	C₆₇	C₄×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
23	C₄×C₁₃	C₆₇⋊C₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₁₃	C₄×C₆₇⋊C₃	1	1	yes	characteristic
25	C₄×C₉	—	871	1	no	Hall
26	C₂×C₁₃	C₂×C₆₇⋊C₉	1	1	yes	characteristic
27	C₂×C₉	—	871	1	no	—
28	C₁₃	C₄×C₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₄	#14579732	1	1	yes	characteristic
30	C₉	—	871	1	no	Sylow
31	C₂×C₃	C₂×#14579732	1	1	yes	characteristic
32	C₄	#21463204	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×#14579732	1	1	yes	characteristic
34	C₂	C₂×#21463204	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#14579732
commutator, hypocenter	C₁₃×C₆₇	C₄×C₉
Frattini	C₂×C₃	C₂×#14579732
Fitting	C₃×C₄×C₁₃×C₆₇	C₃
socle, prime radical, cosocle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #21463204	C₄	direct (N × H)
5. C₄×C₁₃×C₆₇	C₉	semidirect
10. C₁₃×C₆₇	C₄×C₉	semidirect
15. C₄×C₆₇	C₁₃⋊C₉	semidirect
22. C₆₇	C₄×C₁₃⋊C₉	semidirect
23. C₄×C₁₃	C₆₇⋊C₉	semidirect
28. C₁₃	C₄×C₆₇⋊C₉	semidirect
32. C₄	#21463204	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#21463204	2
C₃×C₄×C₁₃×C₆₇	3
C₄×C₆₇⋊C₉	13
C₄×C₁₃⋊C₉	67

Subgroups — C4×#21463204 #44535568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#21463204 #44535568