Subgroups — #49093262

Order 35968.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823542	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#17985113	C₂	1	1	yes	maximal, characteristic, complemented
3	#346×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#17985121	—	2	1	no	—
5	C₄×D₁₁₂₄	C₄	1	1	yes	characteristic
6	C₂×#17985113	—	2	1	no	—
7	C₄⋊#14555886	C₄	1	1	yes	characteristic
8	#22582791	—	2	1	no	—
9	C₂×C₁₆×C₂₈₁	—	2	1	no	—
10	C₄×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₂×D₁₁₂₄	C₈	1	1	yes	characteristic
12	C₂×C₄×D₂₈₁	—	2	1	no	—
13	#17985121	—	4	1	no	—
14	#17985121	—	4	1	no	—
15	C₂×#14555886	—	2	1	no	—
16	C₄⋊Dic₂₈₁	C₈	1	1	yes	characteristic
17	#17985115	—	2	1	no	—
18	#17985113	—	4	1	no	—
19	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
21	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
22	C₁₆×C₂₈₁	—	2	2	no	—
23	C₂²×D₂₈₁	—	2	1	no	—
24	D₁₁₂₄	—	4	1	no	—
25	C₂×Dic₂₈₁	—	2	1	no	—
26	C₄×D₂₈₁	—	4	1	no	—
27	C₄×D₂₈₁	—	4	1	no	—
28	#14555886	—	4	1	no	—
29	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₂₈₁	M₁₆	1	1	yes	characteristic
32	C₈×C₂₈₁	—	2	1	no	—
33	C₈×C₂₈₁	D₈	1	1	yes	characteristic
34	C₈×C₂₈₁	SD₁₆	1	1	yes	characteristic
35	C₂²×C₂₈₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₂₈₁	—	4	1	no	—
37	C₂×D₂₈₁	—	4	1	no	—
38	C₂×D₂₈₁	—	4	1	no	—
39	C₄×C₂₈₁	—	2	1	no	—
40	C₄×C₂₈₁	—	2	1	no	—
41	C₄×C₂₈₁	#102	1	1	yes	characteristic
42	C₄×C₂₈₁	#104	1	1	yes	characteristic
43	Dic₂₈₁	—	4	1	no	—
44	C₂×C₂₈₁	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₂₈₁	#349	1	1	yes	characteristic
46	C₂×C₂₈₁	#350	1	1	yes	characteristic
47	D₂₈₁	—	8	1	no	—
48	C₂₈₁	#1330	1	1	yes	characteristic, complemented, Sylow
49	#1330	—	281	1	no	maximal, Sylow
50	#436	—	281	1	no	—
51	C₄⋊C₁₆	—	281	1	no	—
52	#346	D₂₈₁	1	1	yes	characteristic, complemented
53	C₂×M₁₆	—	562	1	no	—
54	C₄×D₄	—	281	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₂×C₁₆	—	562	1	no	—
57	C₄⋊C₈	—	281	1	no	—
58	C₂²⋊C₈	—	562	1	no	—
59	C₄×C₈	C₂×D₂₈₁	1	1	yes	characteristic
60	C₂×D₄	—	281	1	no	—
61	C₂²×C₄	—	562	1	no	—
62	M₁₆	—	1124	1	no	—
63	M₁₆	—	1124	1	no	—
64	C₂×C₈	—	562	1	no	—
65	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
66	C₂×C₈	D₁₁₂₄	1	1	yes	characteristic
67	C₄⋊C₄	—	281	1	no	—
68	C₂²⋊C₄	—	562	1	no	—
69	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
70	C₁₆	—	2	2	no	—
71	C₁₆	—	1124	1	no	—
72	C₂³	—	562	1	no	—
73	D₄	—	1124	1	no	—
74	C₂×C₄	—	562	1	no	—
75	C₂×C₄	—	1124	1	no	—
76	C₂×C₄	—	1124	1	no	—
77	C₂×C₄	#17985115	1	1	yes	characteristic
78	C₂×C₄	C₈×D₂₈₁	1	1	yes	characteristic
79	C₂×C₄	#17985121	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	1124	1	no	—
82	C₈	D₂₂₄₈	1	1	yes	characteristic
83	C₈	#17985127	1	1	yes	characteristic
84	C₂²	—	1124	1	no	—
85	C₂²	—	1124	1	no	—
86	C₂²	—	1124	1	no	—
87	C₂²	#22582791	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	1124	1	no	—
91	C₄	#22582801	1	1	yes	characteristic
92	C₄	#22582807	1	1	yes	characteristic
93	C₂	—	2248	1	no	—
94	C₂	#31823192	1	1	yes	characteristic
95	C₂	#31823244	1	1	yes	characteristic
96	C₂	#31823248	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#17985115
commutator	C₂×C₄×C₂₈₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₈₁
Fitting	#346×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂²⋊C₈
prime radical	C₂×D₁₁₂₄	C₈
cosocle	C₄×C₈×C₂₈₁	C₂²
hypercenter	#346	D₂₈₁
hypocenter	C₂₈₁	#1330
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. C₄⋊#17985113	C₂	semidirect
3. #346×C₂₈₁	C₂	semidirect
48. C₂₈₁	#1330	semidirect
52. #346	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823542	2
C₄⋊#17985113	2
#346×C₂₈₁	2
#1330	281