Subgroups — C₂²×#90773 #14271937

Order 1856.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₅₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90773	C₂	1	12	yes	maximal, direct product factor
5	C₂³×D₂₉	—	2	1	no	—
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₉	—	2	1	no	—
8	C₂×D₁₁₆	—	2	3	no	—
9	C₂×D₁₁₆	C₂²	1	6	yes	—
10	C₂×Dic₅₈	—	2	3	no	—
11	C₂×Dic₅₈	C₂²	1	6	yes	complemented
12	C₂×C₈×C₂₉	C₂²	1	6	yes	complemented
13	#90773	C₂²	1	16	yes	direct product factor
14	C₂³×C₂₉	D₄	1	1	yes	characteristic
15	C₂²×D₂₉	—	2	6	no	—
16	C₂²×D₂₉	—	4	4	no	—
17	C₂×C₄×C₂₉	D₄	1	3	yes	—
18	C₂×C₄×C₂₉	C₂³	1	3	yes	—
19	C₂×Dic₂₉	—	2	6	no	—
20	D₁₁₆	—	2	6	no	—
21	D₁₁₆	C₂³	1	4	yes	—
22	Dic₅₈	—	2	6	no	—
23	Dic₅₈	C₂³	1	4	yes	complemented
24	C₈×C₂₉	C₂³	1	4	yes	complemented
25	C₂²×C₂₉	SD₁₆	1	4	yes	complemented
26	C₂²×C₂₉	C₂×D₄	1	3	yes	—
27	C₂×D₂₉	—	2	4	no	—
28	C₂×D₂₉	—	4	12	no	—
29	C₄×C₂₉	C₂×D₄	1	3	yes	—
30	C₄×C₂₉	C₂⁴	1	1	yes	characteristic
31	Dic₂₉	—	2	4	no	—
32	C₂²×SD₁₆	—	29	1	no	maximal, Sylow
33	C₂×C₂₉	C₂×SD₁₆	1	6	yes	complemented
34	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
35	D₂₉	—	4	4	no	—
36	C₂²×Q₈	—	29	1	no	—
37	C₂²×D₄	—	29	1	no	—
38	C₂×SD₁₆	—	29	12	no	—
39	C₂²×C₈	D₂₉	1	1	yes	characteristic, complemented
40	C₂₉	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
41	C₂⁴	—	58	1	no	—
42	C₂×Q₈	—	29	6	no	—
43	C₂×Q₈	—	58	3	no	—
44	C₂×D₄	—	29	6	no	—
45	C₂×D₄	—	58	3	no	—
46	C₂²×C₄	—	58	1	no	—
47	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
48	SD₁₆	—	29	16	no	—
49	C₂×C₈	C₂×D₂₉	1	6	yes	complemented
50	C₂³	—	58	6	no	—
51	C₂³	—	116	4	no	—
52	C₂³	D₁₁₆	1	1	yes	characteristic
53	Q₈	—	29	4	no	—
54	Q₈	—	58	6	no	—
55	D₄	—	29	4	no	—
56	D₄	—	58	6	no	—
57	C₂×C₄	—	58	6	no	—
58	C₂×C₄	D₁₁₆	1	3	yes	—
59	C₂×C₄	C₂²×D₂₉	1	3	yes	—
60	C₈	C₂²×D₂₉	1	4	yes	complemented
61	C₂²	—	58	4	no	—
62	C₂²	—	116	12	no	—
63	C₂²	#90773	1	4	yes	direct product factor
64	C₂²	C₂×D₁₁₆	1	3	yes	—
65	C₄	—	58	4	no	—
66	C₄	C₂×D₁₁₆	1	3	yes	—
67	C₄	C₂³×D₂₉	1	1	yes	characteristic
68	C₂	—	116	4	no	—
69	C₂	C₂×#90773	1	6	yes	direct product factor
70	C₂	C₂²×D₁₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₁₆
commutator, cosocle	C₄×C₂₉	C₂⁴
Frattini	C₄	C₂³×D₂₉
Fitting	C₂²×C₈×C₂₉	C₂
socle	C₂³×C₂₉	D₄
prime radical	C₂²×D₁₁₆	C₂
hypercenter	C₂²×C₈	D₂₉
hypocenter	C₂₉	C₂²×SD₁₆
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₅₈	C₂	semidirect
3. C₂²×C₈×C₂₉	C₂	semidirect
4. C₂×#90773	C₂	direct (N × H)
11. C₂×Dic₅₈	C₂²	semidirect
12. C₂×C₈×C₂₉	C₂²	semidirect
13. #90773	C₂²	direct (N × H)
23. Dic₅₈	C₂³	semidirect
24. C₈×C₂₉	C₂³	semidirect
25. C₂²×C₂₉	SD₁₆	semidirect
33. C₂×C₂₉	C₂×SD₁₆	semidirect
39. C₂²×C₈	D₂₉	semidirect
40. C₂₉	C₂²×SD₁₆	semidirect
49. C₂×C₈	C₂×D₂₉	semidirect
60. C₈	C₂²×D₂₉	semidirect
63. C₂²	#90773	direct (N × H)
69. C₂	C₂×#90773	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₁₆	2
C₂²×Dic₅₈	2
C₂²×C₈×C₂₉	2
C₂×#90773	2
C₂²×SD₁₆	29

Subgroups — C22×#90773 #14271937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#90773 #14271937