Subgroups — #49097188

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	#31823579	C₂	1	2	yes	maximal, complemented
3	#31823269	C₂	1	2	yes	maximal, complemented
4	#31823238	C₂	1	1	yes	maximal, characteristic, complemented
5	#368×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#22582901	C₂²	1	2	yes	—
7	#22582887	—	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	C₂×#17985113	C₂²	1	1	yes	characteristic
12	#22582805	—	2	2	no	—
13	C₈×Dic₂₈₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
15	#108×C₂₈₁	C₂²	1	2	yes	—
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	#17985121	—	4	2	no	—
21	C₂×#14555886	D₄	1	1	yes	characteristic
22	C₈×D₂₈₁	—	4	2	no	—
23	C₄×Dic₂₈₁	D₄	1	1	yes	characteristic
24	#17985113	—	2	1	no	—
25	M₁₆×C₂₈₁	—	2	2	no	—
26	C₂×C₈×C₂₈₁	C₂³	1	1	yes	characteristic
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	C₂×Dic₂₈₁	—	2	1	no	—
33	C₄×D₂₈₁	—	4	2	no	—
34	#14555886	D₈	1	2	yes	—
35	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
36	C₈×C₂₈₁	—	4	2	no	—
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	C₄×D₄	1	1	yes	characteristic
42	C₄×C₂₈₁	C₂×D₈	1	1	yes	characteristic
43	Dic₂₈₁	—	4	1	no	—
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	D₂₈₁	1	1	yes	characteristic, complemented
53	#359	—	281	2	no	—
54	#346	—	281	1	no	—
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	—	281	1	no	—
61	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
62	#108	C₂×D₂₈₁	1	2	yes	—
63	#104	—	562	2	no	—
64	C₄×C₈	—	281	1	no	—
65	#41	—	562	2	no	—
66	Q₁₆	—	281	2	no	—
67	SD₁₆	—	562	2	no	—
68	D₈	—	281	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	1124	2	no	—
71	C₂×C₈	—	281	1	no	—
72	C₂×C₈	—	1124	2	no	—
73	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
74	C₄²	—	281	1	no	—
75	C₁₆	—	562	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	—	562	1	no	—
82	C₂×C₄	—	1124	2	no	—
83	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
84	C₈	—	4	2	no	—
85	C₈	—	281	2	no	—
86	C₈	C₂×C₄×D₂₈₁	1	1	yes	characteristic
87	C₈	#17985139	1	1	yes	characteristic
88	C₂²	—	1124	2	no	—
89	C₂²	#22582902	1	1	yes	characteristic
90	C₄	—	1124	1	no	—
91	C₄	—	1124	2	no	—
92	C₄	#22582841	1	1	yes	characteristic
93	C₄	D₈×D₂₈₁	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	2248	2	no	—
96	C₂	#31823545	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₂₈₁
commutator	C₈×C₂₈₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₈₁
Fitting	#368×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₄×D₈
prime radical	#31823895	C₂
cosocle	C₂×C₈×C₂₈₁	C₂³
hypercenter	#368	D₂₈₁
hypocenter	C₂₈₁	#2179
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #31823579	C₂	semidirect
3. #31823269	C₂	semidirect
4. #31823238	C₂	semidirect
5. #368×C₂₈₁	C₂	semidirect
8. Dic₂₂₄₈	C₄	semidirect
9. #22582824	C₄	semidirect
10. D₄₄₉₆	C₄	semidirect
48. C₂₈₁	#2179	semidirect
52. #368	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
#31823579	2
#31823269	2
#31823238	2
#368×C₂₈₁	2
#2179	281