Subgroups — #44397935

Order 29056.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₂₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#28408858	C₂	1	1	yes	maximal, characteristic
3	#366×C₂₂₇	C₂	1	1	yes	maximal, characteristic
4	#20300222	—	2	1	no	—
5	C₂₂₇⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₂₂₇	C₂²	1	1	yes	characteristic
7	#107×C₂₂₇	—	2	1	no	—
8	C₄⋊Dic₂₂₇	—	4	1	no	—
9	C₂×C₈×C₂₂₇	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₂₂₇	—	4	1	no	—
11	C₁₆×C₂₂₇	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₂₇	Q₈	1	1	yes	characteristic
13	C₂×Dic₂₂₇	—	8	1	no	—
14	C₂×C₄×C₂₂₇	—	8	1	no	—
15	C₂×C₄×C₂₂₇	D₈	1	1	yes	characteristic
16	C₈×C₂₂₇	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₂₇	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₂₇	D₁₆	1	1	yes	characteristic
19	C₄×C₂₂₇	—	16	1	no	—
20	C₄×C₂₂₇	#107	1	1	yes	characteristic
21	C₄×C₂₂₇	Q₃₂	1	1	yes	characteristic
22	Dic₂₂₇	—	16	1	no	—
23	C₂×C₂₂₇	#366	1	1	yes	characteristic
24	C₂×C₂₂₇	SD₆₄	1	1	yes	characteristic
25	C₂×C₂₂₇	SD₆₄	1	1	yes	characteristic
26	C₂₂₇	#1424	1	1	yes	characteristic, complemented, Sylow
27	#1424	—	227	1	no	maximal, Sylow
28	C₂×C₃₂	—	227	1	no	—
29	#366	—	227	1	no	—
30	#366	D₂₂₇	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₂₂₇	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	454	1	no	—
34	C₃₂	—	227	2	no	—
35	C₂×C₈	C₂²⋊D₂₂₇	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	908	1	no	—
38	C₁₆	C₄×D₂₂₇	1	1	yes	characteristic
39	C₁₆	Dic₄₅₄	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	1816	1	no	—
42	C₂×C₄	#16813869	1	1	yes	characteristic
43	C₈	Dic₂₂₇⋊C₄	1	1	yes	characteristic
44	C₈	#16813874	1	1	yes	characteristic
45	C₂²	#20300229	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	3632	1	no	—
48	C₄	#20300221	1	1	yes	characteristic
49	C₄	#20300234	1	1	yes	characteristic
50	C₂	#28408857	1	1	yes	characteristic
51	C₂	#28408869	1	1	yes	characteristic
52	C₂	#28408870	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#20300229
commutator	C₁₆×C₂₂₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₂₇
Fitting	#366×C₂₂₇	C₂
socle, prime radical	C₂²×C₂₂₇	D₁₆
cosocle	C₂×C₁₆×C₂₂₇	C₂²
hypercenter	#366	D₂₂₇
hypocenter	C₂₂₇	#1424
LCS	G ▷ C₁₆×C₂₂₇ ▷ C₈×C₂₂₇ ▷ C₄×C₂₂₇ ▷ C₂×C₂₂₇ ▷ C₂₂₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₂₂₇⋊C₃₂	C₄	semidirect
26. C₂₂₇	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₂₇⋊C₃₂	2
#28408858	2
#366×C₂₂₇	2
#1424	227