Subgroups — #49097190

Order 35968.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823895	C₂	1	1	yes	maximal, characteristic
2	#31823581	C₂	1	2	yes	maximal, complemented
3	#31823293	C₂	1	1	yes	maximal, characteristic, complemented
4	#31823271	C₂	1	2	yes	maximal, complemented
5	#346×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#22582901	C₂²	1	2	yes	—
7	#22582885	—	2	2	no	—
8	Dic₂₂₄₈	C₄	1	1	yes	characteristic, complemented
9	#22582824	C₄	1	2	yes	complemented
10	D₄₄₉₆	C₄	1	1	yes	characteristic, complemented
11	#22582815	C₂²	1	2	yes	—
12	#22582807	—	2	2	no	—
13	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
16	#17985138	—	2	2	no	—
17	Dic₁₁₂₄	C₂×C₄	1	2	yes	—
18	#17985127	—	2	2	no	—
19	D₂₂₄₈	C₂×C₄	1	2	yes	—
20	#17985122	—	2	2	no	—
21	#17985121	—	4	2	no	—
22	C₈×D₂₈₁	—	4	2	no	—
23	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
24	C₂×C₈×C₂₈₁	C₂³	1	1	yes	characteristic
25	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
26	C₁₆×C₂₈₁	—	2	1	no	—
27	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
29	Dic₅₆₂	—	2	2	no	—
30	D₁₁₂₄	—	2	2	no	—
31	C₂²⋊D₂₈₁	—	4	2	no	—
32	C₄×D₂₈₁	—	4	2	no	—
33	#14555886	—	4	2	no	—
34	C₂×C₄×C₂₈₁	—	2	1	no	—
35	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
36	C₈×C₂₈₁	D₈	1	2	yes	—
37	C₈×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₂₈₁	#41	1	1	yes	characteristic
39	C₂²×C₂₈₁	#135	1	1	yes	characteristic
40	C₂×D₂₈₁	—	4	2	no	—
41	C₄×C₂₈₁	—	4	1	no	—
42	C₄×C₂₈₁	C₄×D₄	1	1	yes	characteristic
43	C₄×C₂₈₁	C₂×D₈	1	1	yes	characteristic
44	Dic₂₈₁	—	4	2	no	—
45	C₂×C₂₈₁	—	2	1	no	—
46	C₂×C₂₈₁	C₄×D₈	1	1	yes	characteristic
47	D₂₈₁	—	8	2	no	—
48	C₂₈₁	#2179	1	1	yes	characteristic, complemented, Sylow
49	#2179	—	281	1	no	maximal, Sylow
50	#508	—	281	1	no	—
51	#443	—	281	2	no	—
52	#368	—	281	1	no	—
53	#359	—	281	2	no	—
54	#346	D₂₈₁	1	1	yes	characteristic, complemented
55	#135	—	281	2	no	—
56	#131	—	562	2	no	—
57	Q₃₂	—	281	1	no	—
58	SD₃₂	—	281	2	no	—
59	D₁₆	—	281	1	no	—
60	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
61	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
62	#108	—	281	2	no	—
63	#104	—	562	2	no	—
64	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
65	#41	—	562	2	no	—
66	Q₁₆	—	281	2	no	—
67	SD₁₆	—	562	2	no	—
68	D₈	—	281	2	no	—
69	M₁₆	—	562	2	no	—
70	M₁₆	—	1124	2	no	—
71	C₂×C₈	—	1124	2	no	—
72	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
74	C₄²	D₁₁₂₄	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₂₈₁	1	1	yes	characteristic
77	C₁₆	C₄×D₂₈₁	1	1	yes	characteristic
78	Q₈	—	562	2	no	—
79	D₄	—	562	2	no	—
80	D₄	—	1124	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	1124	2	no	—
83	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
84	C₈	—	1124	2	no	—
85	C₈	D₂₂₄₈	1	2	yes	—
86	C₈	C₂×C₄×D₂₈₁	1	1	yes	characteristic
87	C₈	#17985138	1	1	yes	characteristic
88	C₂²	—	1124	2	no	—
89	C₂²	#22582901	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	1124	2	no	—
92	C₄	C₄×D₁₁₂₄	1	1	yes	characteristic
93	C₄	C₂×D₂₂₄₈	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	2248	2	no	—
96	C₂	C₄×D₂₂₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₂₂₄₈
commutator	C₈×C₂₈₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₈₁
Fitting	#346×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₄×D₈
prime radical	#31823895	C₂
cosocle	C₂×C₈×C₂₈₁	C₂³
hypercenter	#346	D₂₈₁
hypocenter	C₂₈₁	#2179
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #31823581	C₂	semidirect
3. #31823293	C₂	semidirect
4. #31823271	C₂	semidirect
5. #346×C₂₈₁	C₂	semidirect
8. Dic₂₂₄₈	C₄	semidirect
9. #22582824	C₄	semidirect
10. D₄₄₉₆	C₄	semidirect
48. C₂₈₁	#2179	semidirect
54. #346	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823895	2
#31823581	2
#31823293	2
#31823271	2
#346×C₂₈₁	2
#2179	281