Subgroups — #34069264

Order 19328.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₁₅₁⋊C₈)	C₂	1	6	yes	maximal
2	#376×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₅₁⋊C₈	C₂²	1	4	yes	—
4	C₄⋊(C₁₅₁⋊C₈)	—	2	12	no	—
5	C₂×C₄²×C₁₅₁	C₂²	1	3	yes	—
6	#95×C₁₅₁	C₄	1	4	yes	—
7	C₂×C₁₅₁⋊C₈	—	2	12	no	—
8	C₂²×C₄×C₁₅₁	C₂×C₄	1	6	yes	—
9	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
10	C₄²×C₁₅₁	D₄	1	6	yes	—
11	C₄²×C₁₅₁	Q₈	1	6	yes	—
12	C₁₅₁⋊C₈	—	4	4	no	—
13	C₂³×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₅₁	—	2	12	no	—
15	C₂×C₄×C₁₅₁	C₄⋊C₄	1	12	yes	—
16	C₂×C₄×C₁₅₁	C₂×D₄	1	3	yes	—
17	C₂×C₄×C₁₅₁	C₂×Q₈	1	3	yes	—
18	C₂²×C₁₅₁	C₂×C₄⋊C₄	1	3	yes	—
19	C₂²×C₁₅₁	#131	1	4	yes	—
20	C₄×C₁₅₁	—	2	12	no	—
21	C₄×C₁₅₁	#127	1	1	yes	characteristic
22	C₄×C₁₅₁	C₄⋊Q₈	1	3	yes	—
23	C₂×C₁₅₁	#384	1	1	yes	characteristic
24	C₂×C₁₅₁	#424	1	6	yes	—
25	C₁₅₁	#1843	1	1	yes	characteristic, complemented, Sylow
26	#1843	—	151	1	no	maximal, Sylow
27	C₂×C₄⋊C₈	—	151	6	no	—
28	#376	D₁₅₁	1	1	yes	characteristic
29	C₂²×C₈	—	151	4	no	—
30	C₂×C₄²	C₂×D₁₅₁	1	3	yes	—
31	C₄⋊C₈	—	302	12	no	—
32	#95	Dic₁₅₁	1	4	yes	—
33	C₂²×C₄	C₂×Dic₁₅₁	1	6	yes	—
34	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
35	C₂×C₈	—	302	12	no	—
36	C₄²	D₆₀₄	1	6	yes	—
37	C₄²	Dic₃₀₂	1	6	yes	—
38	C₂³	C₂²×Dic₁₅₁	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₁₅₁	1	12	yes	—
41	C₂×C₄	C₂×D₆₀₄	1	3	yes	—
42	C₂×C₄	C₂×Dic₃₀₂	1	3	yes	—
43	C₈	—	604	4	no	—
44	C₂²	C₂×C₄⋊Dic₁₅₁	1	3	yes	—
45	C₂²	#18012746	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#18012736	1	1	yes	characteristic
48	C₄	#18012739	1	3	yes	—
49	C₂	#23752082	1	1	yes	characteristic
50	C₂	#23752239	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₅₁
commutator, socle, prime radical	C₂³×C₁₅₁	C₂²×C₄
Fitting	#376×C₁₅₁	C₂
cosocle	C₂²×C₄×C₁₅₁	C₂³
hypercenter	#376	D₁₅₁
hypocenter	C₁₅₁	#1843
LCS	G ▷ C₂³×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
25. C₁₅₁	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₁₅₁⋊C₈)	2
#376×C₁₅₁	2
#1843	151