Subgroups — C₂²×#90796 #14272237

Order 1856.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6599	C₂	1	2	yes	maximal, complemented
3	C₂×#90796	C₂	1	12	yes	maximal, direct product factor
4	C₂³×D₂₉	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₂₉	C₄	1	1	yes	characteristic
6	C₂²×Dic₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₂₉	C₄	1	6	yes	—
8	C₂×C₄×D₂₉	C₂²	1	6	yes	—
9	C₂×#6599	C₂²	1	12	yes	complemented
10	#90796	C₂²	1	16	yes	direct product factor
11	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×D₂₉	—	2	4	no	—
13	C₂²×D₂₉	C₂×C₄	1	6	yes	—
14	C₂×C₄×C₂₉	C₂×C₄	1	6	yes	—
15	C₂×Dic₂₉	C₂×C₄	1	3	yes	—
16	C₂×Dic₂₉	C₂³	1	3	yes	—
17	C₄×D₂₉	C₂×C₄	1	12	yes	—
18	C₄×D₂₉	C₂³	1	4	yes	—
19	#6599	C₂³	1	8	yes	complemented
20	C₂²×C₂₉	M₁₆	1	4	yes	complemented
21	C₂²×C₂₉	C₂²×C₄	1	3	yes	—
22	C₂×D₂₉	—	2	12	no	—
23	C₂×D₂₉	C₂²×C₄	1	4	yes	—
24	C₄×C₂₉	C₂²×C₄	1	4	yes	—
25	Dic₂₉	C₂²×C₄	1	3	yes	—
26	Dic₂₉	C₂⁴	1	1	yes	characteristic
27	C₂²×M₁₆	—	29	1	no	maximal, Sylow
28	C₂×C₂₉	C₂×M₁₆	1	6	yes	complemented
29	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
30	D₂₉	—	2	4	no	—
31	C₂³×C₄	—	29	1	no	—
32	C₂×M₁₆	—	29	12	no	—
33	C₂²×C₈	—	29	2	no	—
34	C₂₉	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂⁴	—	29	1	no	—
36	C₂²×C₄	—	29	1	no	—
37	C₂²×C₄	—	29	6	no	—
38	C₂²×C₄	—	29	6	no	—
39	C₂²×C₄	#1181	1	1	yes	characteristic
40	M₁₆	—	29	16	no	—
41	C₂×C₈	—	29	12	no	—
42	C₂³	—	29	6	no	—
43	C₂³	—	58	4	no	—
44	C₂³	C₂×#1181	1	1	yes	characteristic
45	C₂×C₄	—	29	3	no	—
46	C₂×C₄	—	29	3	no	—
47	C₂×C₄	—	29	4	no	—
48	C₂×C₄	—	29	12	no	—
49	C₂×C₄	C₂×#1181	1	6	yes	—
50	C₈	—	29	8	no	—
51	C₂²	—	29	4	no	—
52	C₂²	—	58	12	no	—
53	C₂²	#90796	1	4	yes	direct product factor
54	C₂²	C₂²×#1181	1	3	yes	—
55	C₄	—	29	1	no	—
56	C₄	—	29	3	no	—
57	C₄	C₂²×#1181	1	4	yes	—
58	C₂	—	58	4	no	—
59	C₂	C₂×#90796	1	6	yes	direct product factor
60	C₂	C₂³×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1181
commutator	C₂×C₂₉	C₂³×C₄
Frattini	C₂	C₂³×#1181
Fitting	C₂²×C₄×C₂₉	C₄
socle	C₂³×C₂₉	C₂×C₄
prime radical	C₂³×D₂₉	C₄
cosocle	Dic₂₉	C₂⁴
hypercenter	C₂²×C₄	#1181
hypocenter	C₂₉	C₂²×M₁₆
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#6599	C₂	semidirect
3. C₂×#90796	C₂	direct (N × H)
9. C₂×#6599	C₂²	semidirect
10. #90796	C₂²	direct (N × H)
19. #6599	C₂³	semidirect
20. C₂²×C₂₉	M₁₆	semidirect
28. C₂×C₂₉	C₂×M₁₆	semidirect
34. C₂₉	C₂²×M₁₆	semidirect
53. C₂²	#90796	direct (N × H)
59. C₂	C₂×#90796	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×C₄×D₂₉	2
C₂²×#6599	2
C₂×#90796	2
C₂²×M₁₆	29

Subgroups — C22×#90796 #14272237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#90796 #14272237