Subgroups — C₄×#22582815 #49095205

Order 35968.

228 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22582815	C₂	1	2	yes	maximal
2	C₄×#17985122	C₂	1	2	yes	maximal
3	#31823228	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#17985122	C₂²	1	4	yes	—
6	#22582815	C₄	1	8	yes	direct product factor
7	#22582790	—	2	2	no	—
8	C₄×#14555886	—	2	2	no	—
9	C₂²×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₂₈₁	C₄	1	4	yes	—
13	#17985122	—	2	4	no	—
14	#17985122	C₂×C₄	1	8	yes	—
15	C₂×#14555886	—	2	4	no	—
16	C₂²×C₄×C₂₈₁	Q₈	1	2	yes	—
17	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
18	C₂×C₈×C₂₈₁	—	2	2	no	—
19	C₂×C₈×C₂₈₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₂₈₁	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₂₈₁	C₂×C₄	1	2	yes	—
22	C₄²×C₂₈₁	C₂×C₄	1	2	yes	—
23	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
24	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
25	#14555886	—	2	8	no	—
26	C₂³×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₂₈₁	—	2	4	no	—
28	C₂×C₄×C₂₈₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₂₈₁	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₂₈₁	C₂²×C₄	1	2	yes	—
31	C₂×C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₂₈₁	#41	1	2	yes	—
34	C₈×C₂₈₁	—	2	2	no	—
35	C₈×C₂₈₁	C₄²	1	4	yes	—
36	C₂²×C₂₈₁	—	2	2	no	—
37	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₂₈₁	C₄×Q₈	1	2	yes	—
39	C₄×C₂₈₁	—	2	2	no	—
40	C₄×C₂₈₁	#108	1	4	yes	complemented
41	C₄×C₂₈₁	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₂₈₁	#117	1	1	yes	characteristic
43	C₄×C₂₈₁	C₄×D₄	1	2	yes	—
44	C₂×C₂₈₁	—	2	2	no	—
45	C₂×C₂₈₁	C₄×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₂₈₁	C₂×#108	1	2	yes	—
47	C₂₈₁	C₄×#108	1	1	yes	characteristic, complemented, Sylow
48	C₄×#108	—	281	1	no	maximal, Sylow
49	C₂×#108	—	281	2	no	—
50	C₄×M₁₆	—	281	2	no	—
51	C₂×C₄×C₈	D₂₈₁	1	1	yes	characteristic
52	#341	—	281	2	no	—
53	C₂×M₁₆	—	281	4	no	—
54	C₂²×C₈	C₂×D₂₈₁	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₂₈₁	1	1	yes	characteristic
56	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
57	#108	—	281	8	no	—
58	#97	—	562	2	no	—
59	C₄×C₈	—	562	2	no	—
60	C₄×C₈	Dic₂₈₁	1	4	yes	—
61	C₂²×C₄	Dic₅₆₂	1	2	yes	—
62	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
63	M₁₆	—	281	8	no	—
64	M₁₆	—	562	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	562	4	no	—
67	C₂×C₈	C₄×D₂₈₁	1	4	yes	—
68	C₂×C₈	C₂×Dic₂₈₁	1	2	yes	—
69	C₂×C₈	C₂×Dic₂₈₁	1	2	yes	—
70	C₄²	C₂×Dic₂₈₁	1	2	yes	—
71	C₄²	D₁₁₂₄	1	1	yes	characteristic
72	C₄²	D₁₁₂₄	1	1	yes	characteristic
73	C₂³	C₂×Dic₅₆₂	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄⋊Dic₂₈₁	1	2	yes	—
76	C₂×C₄	C₄⋊Dic₂₈₁	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₂₈₁	1	2	yes	—
78	C₂×C₄	C₂²×Dic₂₈₁	1	1	yes	characteristic
79	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
80	C₂×C₄	#17985138	1	2	yes	—
81	C₈	—	2	2	no	—
82	C₈	—	562	8	no	—
83	C₈	C₄×Dic₂₈₁	1	4	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄⋊Dic₂₈₁	1	1	yes	characteristic
86	C₂²	C₄×Dic₅₆₂	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#22582815	1	4	yes	direct product factor
89	C₄	C₂×C₄×Dic₂₈₁	1	1	yes	characteristic
90	C₄	#22582838	1	1	yes	characteristic
91	C₄	C₄×D₁₁₂₄	1	2	yes	—
92	C₂	—	2	2	no	—
93	C₂	C₄×C₄⋊Dic₂₈₁	1	1	yes	characteristic
94	C₂	C₂×#22582815	1	2	yes	—

	subgroup	G/H
center	C₄²	D₁₁₂₄
commutator	C₄×C₂₈₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₈₁
Fitting	C₂×C₄×C₈×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×C₄⋊C₄
prime radical	C₂³×C₂₈₁	C₂×Q₈
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	C₂×C₄×C₈	D₂₈₁
hypocenter	C₂₈₁	C₄×#108
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #22582815	C₄	direct (N × H)
40. C₄×C₂₈₁	#108	semidirect
47. C₂₈₁	C₄×#108	semidirect
88. C₄	#22582815	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#22582815	2
C₄×#17985122	2
#31823228	2
C₂×C₄×C₈×C₂₈₁	2
C₄×#108	281

Subgroups — C4×#22582815 #49095205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#22582815 #49095205