Subgroups — #49094972

Order 35968.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823866	C₂	1	2	yes	maximal, complemented
2	#31823843	C₂	1	1	yes	maximal, characteristic, complemented
3	#31823809	C₂	1	2	yes	maximal
4	#31823184	C₂	1	1	yes	maximal, characteristic, complemented
5	#492×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₂₄	—	2	2	no	—
7	#22582879	C₂²	1	2	yes	—
8	#22582812	—	2	4	no	—
9	#22582800	—	2	4	no	—
10	C₄×#14555886	C₂²	1	2	yes	—
11	C₂×SD₁₆×C₂₈₁	—	2	2	no	—
12	C₄⋊Q₈×C₂₈₁	C₂²	1	1	yes	characteristic
13	#127×C₂₈₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
15	C₂×Dic₅₆₂	—	2	2	no	—
16	Dic₁₁₂₄	—	4	4	no	—
17	C₂×#14555886	D₄	1	4	yes	—
18	C₄⋊Dic₂₈₁	—	2	2	no	—
19	C₄⋊Dic₂₈₁	—	2	2	no	—
20	C₂×Q₈×C₂₈₁	—	2	1	no	—
21	C₂×D₄×C₂₈₁	—	2	2	no	—
22	C₂×D₄×C₂₈₁	—	2	1	no	—
23	SD₁₆×C₂₈₁	—	4	4	no	—
24	C₂×C₈×C₂₈₁	D₄	1	2	yes	—
25	C₄⋊C₄×C₂₈₁	—	2	2	no	—
26	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
27	Dic₅₆₂	—	4	4	no	—
28	C₂×Dic₂₈₁	—	4	2	no	—
29	#14555886	—	2	4	no	—
30	C₂³×C₂₈₁	—	4	1	no	—
31	Q₈×C₂₈₁	—	4	2	no	—
32	D₄×C₂₈₁	—	4	2	no	—
33	D₄×C₂₈₁	—	4	4	no	—
34	C₂×C₄×C₂₈₁	—	4	1	no	—
35	C₂×C₄×C₂₈₁	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
37	C₈×C₂₈₁	D₈	1	4	yes	—
38	C₂²×C₂₈₁	—	8	1	no	—
39	C₂²×C₂₈₁	—	8	2	no	—
40	C₂²×C₂₈₁	#127	1	1	yes	characteristic
41	C₄×C₂₈₁	—	8	1	no	—
42	C₄×C₂₈₁	C₂×D₈	1	2	yes	—
43	C₄×C₂₈₁	#137	1	4	yes	—
44	Dic₂₈₁	—	8	2	no	—
45	C₂×C₂₈₁	—	16	1	no	—
46	C₂×C₂₈₁	#493	1	1	yes	characteristic
47	C₂×C₂₈₁	#497	1	2	yes	—
48	C₂₈₁	#1722	1	1	yes	characteristic, complemented, Sylow
49	#1722	—	281	1	no	maximal, Sylow
50	#500	—	281	2	no	—
51	#494	—	281	1	no	—
52	#492	D₂₈₁	1	1	yes	characteristic
53	#486	—	281	2	no	—
54	#322	—	281	1	no	—
55	C₂×Q₁₆	—	562	2	no	—
56	C₂×SD₁₆	—	2	2	no	—
57	C₄⋊Q₈	—	281	2	no	—
58	C₄⋊Q₈	C₂×D₂₈₁	1	1	yes	characteristic
59	#127	C₂×D₂₈₁	1	1	yes	characteristic
60	#107	—	562	4	no	—
61	#102	—	562	4	no	—
62	C₄×C₈	—	281	2	no	—
63	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
64	C₂×Q₈	—	2	1	no	—
65	C₂×Q₈	—	562	2	no	—
66	C₂×D₄	—	2	2	no	—
67	C₂×D₄	—	2	1	no	—
68	Q₁₆	—	1124	4	no	—
69	SD₁₆	—	4	4	no	—
70	C₂×C₈	—	281	4	no	—
71	C₂×C₈	C₂²⋊D₂₈₁	1	2	yes	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	562	2	no	—
74	C₄⋊C₄	—	562	2	no	—
75	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
76	C₂³	—	4	1	no	—
77	Q₈	—	4	2	no	—
78	Q₈	—	1124	4	no	—
79	D₄	—	4	2	no	—
80	D₄	—	4	4	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	—	1124	2	no	—
83	C₂×C₄	D₄×D₂₈₁	1	2	yes	—
84	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
85	C₈	—	562	4	no	—
86	C₈	#17985123	1	4	yes	—
87	C₂²	—	8	1	no	—
88	C₂²	—	8	2	no	—
89	C₂²	#22582875	1	1	yes	characteristic
90	C₄	—	8	1	no	—
91	C₄	—	2248	2	no	—
92	C₄	C₂×#17985123	1	2	yes	—
93	C₄	#22582908	1	4	yes	—
94	C₂	—	16	1	no	—
95	C₂	#31823839	1	1	yes	characteristic
96	C₂	#31823854	1	2	yes	—

	subgroup	G/H
center	C₂²	#22582875
commutator, cosocle	C₄²×C₂₈₁	C₂³
Frattini	C₄²	C₂²×D₂₈₁
Fitting	#492×C₂₈₁	C₂
socle	C₂²×C₂₈₁	#127
prime radical	#127×C₂₈₁	C₂²
hypercenter	#492	D₂₈₁
hypocenter	C₂₈₁	#1722
LCS	G ▷ C₄²×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

Complements

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

N	H ≅ G/N	type
1. #31823866	C₂	semidirect
2. #31823843	C₂	semidirect
4. #31823184	C₂	semidirect
48. C₂₈₁	#1722	semidirect

Maximal subgroups

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

subgroup	index
#31823866	2
#31823843	2
#31823809	2
#31823184	2
#492×C₂₈₁	2
#1722	281