Subgroups — #1366×C₁₅₁ #34064698

Order 19328.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#499×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#364×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	#364×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#125×C₁₅₁	C₄	1	2	yes	—
5	M₃₂×C₁₅₁	—	2	1	no	—
6	M₃₂×C₁₅₁	—	2	1	no	—
7	#107×C₁₅₁	—	2	1	no	—
8	#106×C₁₅₁	—	2	1	no	—
9	C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₅₁	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₅₁	D₄	1	1	yes	characteristic
12	C₄⋊C₄×C₁₅₁	—	2	2	no	—
13	C₄⋊C₄×C₁₅₁	—	4	2	no	—
14	C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₁₅₁	—	4	1	no	—
16	C₁₆×C₁₅₁	—	4	1	no	—
17	C₂×C₄×C₁₅₁	—	2	1	no	—
18	C₂×C₄×C₁₅₁	—	4	2	no	—
19	C₂×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₁₅₁	SD₁₆	1	1	yes	characteristic
21	C₈×C₁₅₁	SD₁₆	1	1	yes	characteristic
22	C₈×C₁₅₁	Q₁₆	1	1	yes	characteristic
23	C₈×C₁₅₁	Q₁₆	1	1	yes	characteristic
24	C₂²×C₁₅₁	#100	1	1	yes	characteristic
25	C₄×C₁₅₁	—	4	1	no	—
26	C₄×C₁₅₁	—	8	2	no	—
27	C₄×C₁₅₁	#103	1	1	yes	characteristic
28	C₄×C₁₅₁	#103	1	1	yes	characteristic
29	C₂×C₁₅₁	—	2	1	no	—
30	C₂×C₁₅₁	#333	1	1	yes	characteristic
31	C₁₅₁	#1366	1	1	yes	characteristic, direct product factor, Sylow
32	#1366	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	#499	C₂×C₁₅₁	1	1	yes	characteristic
34	#364	C₂×C₁₅₁	1	1	yes	characteristic
35	#364	C₂×C₁₅₁	1	1	yes	characteristic
36	#125	C₄×C₁₅₁	1	2	yes	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	2	1	no	—
39	#107	—	2	1	no	—
40	#106	—	2	1	no	—
41	C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
42	C₂×C₈	D₄×C₁₅₁	1	1	yes	characteristic
43	C₂×C₈	D₄×C₁₅₁	1	1	yes	characteristic
44	C₄⋊C₄	—	2	2	no	—
45	C₄⋊C₄	—	4	2	no	—
46	C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	4	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	4	2	no	—
51	C₂×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
52	C₈	SD₁₆×C₁₅₁	1	1	yes	characteristic
53	C₈	SD₁₆×C₁₅₁	1	1	yes	characteristic
54	C₈	Q₁₆×C₁₅₁	1	1	yes	characteristic
55	C₈	Q₁₆×C₁₅₁	1	1	yes	characteristic
56	C₂²	#100×C₁₅₁	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	2	no	—
59	C₄	#103×C₁₅₁	1	1	yes	characteristic
60	C₄	#103×C₁₅₁	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#333×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₅₁	#333
commutator	C₄²	C₂×C₄×C₁₅₁
Frattini, cosocle	C₄×C₈	C₂²×C₁₅₁
prime radical	C₂²×C₁₅₁	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₅₁ ◁ C₂×C₄×C₁₅₁ ◁ C₄×C₈×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
31. C₁₅₁	#1366	direct (N × H)
32. #1366	C₁₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
#499×C₁₅₁	2
#364×C₁₅₁	2
#1366	151

Subgroups — #1366×C151 #34064698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1366×C₁₅₁ #34064698