Subgroups — C₂×#10588029 #11765629

Order 1134.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10588029	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₉×ΓL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇⋊C₂₇	C₃	1	2	yes	maximal, complemented
5	C₉×ΓL(1,𝔽₈)	C₂×C₃	1	1	yes	characteristic
6	C₇×C₂₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇⋊C₂₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₂₇⋊C₃	—	7	1	no	maximal, Hall
9	C₂×C₃×ΓL(1,𝔽₈)	C₉	1	1	yes	characteristic
10	C₂×C₇×C₉	C₃²	1	1	yes	characteristic
11	C₂×C₇⋊C₉	C₉	1	2	yes	—
12	C₂₇⋊C₃	—	7	1	no	Sylow
13	C₃×ΓL(1,𝔽₈)	C₂×C₉	1	1	yes	characteristic
14	C₇×C₉	C₂×C₃²	1	1	yes	characteristic
15	C₇⋊C₉	C₂×C₉	1	2	yes	—
16	C₂×C₃×C₉	—	7	1	no	—
17	C₂×C₂₇	—	7	2	no	—
18	C₂×C₂₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₂×C₃×C₇	C₃×C₉	1	1	yes	characteristic
20	C₂×ΓL(1,𝔽₈)	—	3	1	no	—
21	C₃×C₉	—	7	1	no	—
22	C₂₇	—	7	2	no	—
23	C₂₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
24	C₃×C₇	C₂×C₃×C₉	1	1	yes	characteristic
25	ΓL(1,𝔽₈)	—	3	1	no	—
26	C₂×C₃²	—	7	1	no	—
27	C₂×C₉	—	7	2	no	—
28	C₂×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₂×C₇	C₂₇⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₃²	—	7	1	no	—
31	C₉	—	7	2	no	—
32	C₉	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₇	C₂×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	—	21	1	no	—
35	C₂×C₃	C₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
36	C₃	—	21	1	no	—
37	C₃	C₂×C₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
38	C₂	#10588029	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	C₂×C₉	C₃×ΓL(1,𝔽₈)
commutator	C₃×C₇	C₂×C₃×C₉
Frattini	C₉	C₂×C₃×ΓL(1,𝔽₈)
Fitting	C₂×C₇×C₂₇	C₃
socle	C₂×C₃×C₇	C₃×C₉
prime radical	C₂×C₃×ΓL(1,𝔽₈)	C₉
cosocle	C₇×C₉	C₂×C₃²
hypercenter	C₂×C₂₇	ΓL(1,𝔽₈)
hypocenter	C₇	C₂×C₂₇⋊C₃
LCS	G ▷ C₃×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₂₇

Complements

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

N	H ≅ G/N	type
1. #10588029	C₂	direct (N × H)
3. C₂×C₇×C₂₇	C₃	semidirect
4. C₂×C₇⋊C₂₇	C₃	semidirect
6. C₇×C₂₇	C₂×C₃	semidirect
7. C₇⋊C₂₇	C₂×C₃	semidirect
18. C₂×C₂₇	ΓL(1,𝔽₈)	semidirect
23. C₂₇	C₂×ΓL(1,𝔽₈)	semidirect
29. C₂×C₇	C₂₇⋊C₃	semidirect
33. C₇	C₂×C₂₇⋊C₃	semidirect
38. C₂	#10588029	direct (N × H)

Maximal subgroups

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

subgroup	index
#10588029	2
C₂×C₉×ΓL(1,𝔽₈)	3
C₂×C₇×C₂₇	3
C₂×C₇⋊C₂₇	3
C₂×C₂₇⋊C₃	7

Subgroups — C2×#10588029 #11765629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588029 #11765629