Subgroups — #49095443

Order 35968.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823487	C₂	1	1	yes	maximal, characteristic
2	C₂×#22582790	C₂	1	1	yes	maximal, characteristic
3	#31823227	C₂	1	4	yes	maximal
4	#423×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#17985122	C₂²	1	2	yes	—
6	C₂²×#14555886	C₂²	1	2	yes	—
7	C₄⋊#14555886	—	2	2	no	—
8	#22582790	C₄	1	4	yes	—
9	C₂×M₁₆×C₂₈₁	C₂²	1	2	yes	—
10	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₂₈₁	—	2	2	no	—
12	#17985122	—	2	4	no	—
13	C₂×#14555886	—	2	2	no	—
14	C₂×#14555886	—	2	2	no	—
15	C₂×#14555886	—	2	2	no	—
16	C₂×#14555886	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₂₈₁	Q₈	1	2	yes	—
18	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
19	M₁₆×C₂₈₁	—	2	4	no	—
20	C₂×C₈×C₂₈₁	—	2	2	no	—
21	C₄²×C₂₈₁	C₂×C₄	1	2	yes	—
22	C₄²×C₂₈₁	D₄	1	2	yes	—
23	#14555886	—	2	4	no	—
24	#14555886	—	4	2	no	—
25	C₂³×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₂₈₁	—	4	2	no	—
27	C₂×C₄×C₂₈₁	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₈₁	#41	1	2	yes	—
31	C₂×C₄×C₂₈₁	#41	1	2	yes	—
32	C₈×C₂₈₁	—	4	2	no	—
33	C₂²×C₂₈₁	—	2	2	no	—
34	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₂₈₁	#125	1	2	yes	—
36	C₄×C₂₈₁	—	2	4	no	—
37	C₄×C₂₈₁	#117	1	2	yes	—
38	C₄×C₂₈₁	#124	1	1	yes	characteristic
39	C₄×C₂₈₁	#124	1	1	yes	characteristic
40	C₂×C₂₈₁	—	2	2	no	—
41	C₂×C₂₈₁	#382	1	1	yes	characteristic
42	C₂×C₂₈₁	#430	1	2	yes	—
43	C₂₈₁	#1838	1	1	yes	characteristic, complemented, Sylow
44	#1838	—	281	1	no	maximal, Sylow
45	#423	—	281	1	no	—
46	#423	D₂₈₁	1	1	yes	characteristic
47	C₂×#97	—	281	1	no	—
48	#341	—	281	4	no	—
49	C₂×M₁₆	—	281	2	no	—
50	C₂×M₁₆	C₂×D₂₈₁	1	2	yes	—
51	C₂²×C₈	—	281	2	no	—
52	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
53	C₄⋊C₈	—	2	2	no	—
54	C₄⋊C₈	—	562	2	no	—
55	#97	—	281	4	no	—
56	C₂²×C₄	Dic₅₆₂	1	2	yes	—
57	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
58	M₁₆	—	2	4	no	—
59	M₁₆	—	562	4	no	—
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	—	281	4	no	—
62	C₂×C₈	—	562	2	no	—
63	C₂×C₈	—	562	2	no	—
64	C₂×C₈	—	562	2	no	—
65	C₄²	C₄×D₂₈₁	1	2	yes	—
66	C₄²	C₂²⋊D₂₈₁	1	2	yes	—
67	C₂³	C₂×Dic₅₆₂	1	1	yes	characteristic
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	#17985117	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
71	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
72	C₂×C₄	#17985137	1	2	yes	—
73	C₂×C₄	#17985139	1	2	yes	—
74	C₈	—	4	2	no	—
75	C₈	—	562	4	no	—
76	C₈	—	1124	2	no	—
77	C₂²	—	2	2	no	—
78	C₂²	C₂×#17985117	1	1	yes	characteristic
79	C₂²	#22582870	1	2	yes	—
80	C₄	—	2	4	no	—
81	C₄	#22582837	1	2	yes	—
82	C₄	#22582866	1	1	yes	characteristic
83	C₄	#22582868	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#31823328	1	1	yes	characteristic
86	C₂	#31823511	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₂₈₁
commutator	C₂×C₄×C₂₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₈₁
Fitting	#423×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×C₄⋊C₄
prime radical	C₂³×C₂₈₁	C₂×Q₈
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	#423	D₂₈₁
hypocenter	C₂₈₁	#1838
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
43. C₂₈₁	#1838	semidirect

Maximal subgroups

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

subgroup	index
#31823487	2
C₂×#22582790	2
#31823227	2
#423×C₂₈₁	2
#1838	281