Subgroups — C₄×#90777 #14271116

Order 1856.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#90777	C₂	1	2	yes	maximal
3	#11745151	C₂	1	2	yes	maximal, complemented
4	C₄×#6597	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₂₉	C₄	1	2	yes	—
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₄²×C₂₉	C₄	1	2	yes	—
8	C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	#90777	C₄	1	8	yes	direct product factor
11	C₂×#6597	C₂²	1	4	yes	—
12	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₉	—	2	4	no	—
14	C₂×C₄×C₂₉	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	#6597	C₂×C₄	1	8	yes	complemented
20	C₂²×C₂₉	—	2	2	no	—
21	C₂²×C₂₉	C₄²	1	2	yes	—
22	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₂₉	—	2	2	no	—
24	C₄×C₂₉	C₄²	1	2	yes	—
25	C₄×C₂₉	M₁₆	1	4	yes	complemented
26	C₄×C₂₉	C₂²×C₄	1	2	yes	—
27	C₄×M₁₆	—	29	1	no	maximal, Sylow
28	C₂×C₂₉	—	2	2	no	—
29	C₂×C₂₉	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₂₉	C₂×M₁₆	1	2	yes	—
31	C₂×M₁₆	—	29	2	no	—
32	C₂×C₄²	D₂₉	1	1	yes	characteristic
33	#97	—	29	2	no	—
34	C₄×C₈	—	29	2	no	—
35	C₂₉	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₄	Dic₂₉	1	2	yes	—
37	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
38	M₁₆	—	29	8	no	—
39	C₂×C₈	—	29	4	no	—
40	C₄²	Dic₂₉	1	2	yes	—
41	C₄²	C₂×D₂₉	1	1	yes	characteristic
42	C₄²	C₂×D₂₉	1	1	yes	characteristic
43	C₂³	C₂×Dic₂₉	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	C₄×D₂₉	1	4	yes	—
46	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
47	C₂×C₄	C₂×Dic₂₉	1	2	yes	—
48	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
49	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
50	C₈	—	29	8	no	—
51	C₂²	—	2	2	no	—
52	C₂²	C₄×Dic₂₉	1	2	yes	—
53	C₂²	C₂²×Dic₂₉	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	#90777	1	4	yes	direct product factor
56	C₄	C₄×Dic₂₉	1	2	yes	—
57	C₄	C₂×C₄×D₂₉	1	2	yes	—
58	C₂	—	2	2	no	—
59	C₂	C₂×#90777	1	2	yes	—
60	C₂	C₂×C₄×Dic₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂×C₄²×C₂₉	C₂
socle	C₂²×C₂₉	C₂²×C₄
prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₂×C₄²	D₂₉
hypocenter	C₂₉	C₄×M₁₆
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #11745151	C₂	semidirect
4. C₄×#6597	C₂	semidirect
10. #90777	C₄	direct (N × H)
19. #6597	C₂×C₄	semidirect
25. C₄×C₂₉	M₁₆	semidirect
35. C₂₉	C₄×M₁₆	semidirect
55. C₄	#90777	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×C₄²×C₂₉	2
C₂×#90777	2
#11745151	2
C₄×#6597	2
C₄×M₁₆	29

Subgroups — C4×#90777 #14271116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#90777 #14271116