Subgroups — #34067309

Order 19328.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₅₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#23752038	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#18012673	—	2	1	no	—
5	C₁₅₁⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
7	#107×C₁₅₁	—	2	1	no	—
8	C₄⋊Dic₁₅₁	—	4	1	no	—
9	C₂×C₈×C₁₅₁	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₅₁	—	4	1	no	—
11	C₁₆×C₁₅₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₅₁	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₅₁	—	8	1	no	—
14	C₂×C₄×C₁₅₁	—	8	1	no	—
15	C₂×C₄×C₁₅₁	D₈	1	1	yes	characteristic
16	C₈×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₅₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₅₁	D₁₆	1	1	yes	characteristic
19	C₄×C₁₅₁	—	16	1	no	—
20	C₄×C₁₅₁	#107	1	1	yes	characteristic
21	C₄×C₁₅₁	Q₃₂	1	1	yes	characteristic
22	Dic₁₅₁	—	16	1	no	—
23	C₂×C₁₅₁	#366	1	1	yes	characteristic
24	C₂×C₁₅₁	D₃₂	1	1	yes	characteristic
25	C₂×C₁₅₁	Q₆₄	1	1	yes	characteristic
26	C₁₅₁	#1423	1	1	yes	characteristic, complemented, Sylow
27	#1423	—	151	1	no	maximal, Sylow
28	C₂×C₃₂	—	151	1	no	—
29	#366	—	151	1	no	—
30	#366	D₁₅₁	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₅₁	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	302	1	no	—
34	C₃₂	—	151	2	no	—
35	C₂×C₈	C₂²⋊D₁₅₁	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	604	1	no	—
38	C₁₆	C₄×D₁₅₁	1	1	yes	characteristic
39	C₁₆	Dic₃₀₂	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	1208	1	no	—
42	C₂×C₄	#14558989	1	1	yes	characteristic
43	C₈	Dic₁₅₁⋊C₄	1	1	yes	characteristic
44	C₈	#14558994	1	1	yes	characteristic
45	C₂²	#18012680	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	2416	1	no	—
48	C₄	#18012672	1	1	yes	characteristic
49	C₄	#18012685	1	1	yes	characteristic
50	C₂	#23752037	1	1	yes	characteristic
51	C₂	#23752047	1	1	yes	characteristic
52	C₂	#23752052	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#18012680
commutator	C₁₆×C₁₅₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₅₁
Fitting	#366×C₁₅₁	C₂
socle, prime radical	C₂²×C₁₅₁	D₁₆
cosocle	C₂×C₁₆×C₁₅₁	C₂²
hypercenter	#366	D₁₅₁
hypocenter	C₁₅₁	#1423
LCS	G ▷ C₁₆×C₁₅₁ ▷ C₈×C₁₅₁ ▷ C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
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. C₁₅₁⋊C₃₂	C₄	semidirect
26. C₁₅₁	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₅₁⋊C₃₂	2
#23752038	2
#366×C₁₅₁	2
#1423	151