Subgroups — C₄×#16862451 #30683036

Order 16884.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16862451	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₇×C₆₇	C₃	1	1	yes	maximal, characteristic
3	#16862451	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₄×C₆₇⋊C₉	—	7	1	no	maximal, Hall
6	C₄×C₇×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₆₇	C₃×C₄	1	1	yes	characteristic
8	C₂×C₆₇⋊C₉	—	7	1	no	—
9	C₂×C₇×C₆₇	C₂×C₉	1	1	yes	characteristic
10	C₃×C₄×C₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₆₇⋊C₉	—	7	1	no	Hall
12	C₇×C₆₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₄×C₆₇	C₇⋊C₉	1	1	yes	characteristic, complemented, Hall
15	C₄×C₇⋊C₉	—	67	1	no	maximal, Hall
16	C₃×C₆₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₂×C₆₇	C₂×C₇⋊C₉	1	1	yes	characteristic
18	C₂×C₇⋊C₉	—	67	1	no	—
19	C₃×C₄×C₇	C₆₇⋊C₃	1	1	yes	characteristic
20	C₆₇	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
21	C₇⋊C₉	—	67	1	no	Hall
22	C₂×C₃×C₇	C₂×C₆₇⋊C₃	1	1	yes	characteristic
23	C₄×C₉	—	469	1	no	Hall
24	C₄×C₇	C₆₇⋊C₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₇	C₄×C₆₇⋊C₃	1	1	yes	characteristic
26	C₂×C₉	—	469	1	no	—
27	C₂×C₇	C₂×C₆₇⋊C₉	1	1	yes	characteristic
28	C₃×C₄	#13064104	1	1	yes	characteristic
29	C₉	—	469	1	no	Sylow
30	C₇	C₄×C₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₂×#13064104	1	1	yes	characteristic
32	C₄	#16862451	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×#13064104	1	1	yes	characteristic
34	C₂	C₂×#16862451	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#13064104
commutator, hypocenter	C₇×C₆₇	C₄×C₉
Frattini	C₂×C₃	C₂×#13064104
Fitting	C₃×C₄×C₇×C₆₇	C₃
socle, prime radical, cosocle	C₂×C₃×C₇×C₆₇	C₂×C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #16862451	C₄	direct (N × H)
6. C₄×C₇×C₆₇	C₉	semidirect
12. C₇×C₆₇	C₄×C₉	semidirect
14. C₄×C₆₇	C₇⋊C₉	semidirect
20. C₆₇	C₄×C₇⋊C₉	semidirect
24. C₄×C₇	C₆₇⋊C₉	semidirect
30. C₇	C₄×C₆₇⋊C₉	semidirect
32. C₄	#16862451	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×#16862451	2
C₃×C₄×C₇×C₆₇	3
C₄×C₆₇⋊C₉	7
C₄×C₇⋊C₉	67

Subgroups — C4×#16862451 #30683036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16862451 #30683036