Subgroups — #14272243

Order 1856.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90809	C₂	1	1	yes	maximal, characteristic
2	#11745348	C₂	1	8	yes	maximal, complemented
3	D₂₉⋊M₁₆	C₂	1	6	yes	maximal, complemented
4	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic
5	#90809	C₄	1	4	yes	—
6	#90809	C₂²	1	4	yes	—
7	C₂×D₁₁₆	C₄	1	3	yes	—
8	C₂×C₄×D₂₉	C₂²	1	3	yes	—
9	#90800	C₂²	1	4	yes	—
10	#90796	C₂²	1	12	yes	complemented
11	D₂₉⋊C₈	C₂²	1	12	yes	complemented
12	C₂²×D₂₉	C₂×C₄	1	3	yes	—
13	Q₈×C₂₉	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
15	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
16	D₁₁₆	C₂×C₄	1	12	yes	—
17	C₄×D₂₉	C₂×C₄	1	6	yes	—
18	C₄×D₂₉	C₂³	1	6	yes	—
19	#6599	C₂³	1	8	yes	—
20	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₂₉	—	4	3	no	—
22	C₂×D₂₉	C₂²×C₄	1	6	yes	—
23	C₄×C₂₉	C₂²×C₄	1	6	yes	—
24	Dic₂₉	C₂²×C₄	1	1	yes	characteristic
25	Dic₂₉	C₂⁴	1	1	yes	characteristic
26	#568	—	29	1	no	maximal, Sylow
27	C₂×C₂₉	—	2	1	no	—
28	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
29	D₂₉	—	2	6	no	—
30	C₂×#41	—	29	1	no	—
31	#131	—	29	8	no	—
32	C₂×M₁₆	—	29	6	no	—
33	C₂₉	#568	1	1	yes	characteristic, complemented, Sylow
34	#41	—	29	4	no	—
35	#41	—	29	4	no	—
36	C₂×Q₈	#1181	1	1	yes	characteristic
37	C₂×D₄	—	29	3	no	—
38	C₂²×C₄	—	29	3	no	—
39	M₁₆	—	29	4	no	—
40	M₁₆	—	29	12	no	—
41	C₂×C₈	—	29	12	no	—
42	C₂³	—	29	3	no	—
43	Q₈	C₂×#1181	1	4	yes	—
44	D₄	—	29	12	no	—
45	C₂×C₄	—	29	1	no	—
46	C₂×C₄	—	29	6	no	—
47	C₂×C₄	—	29	6	no	—
48	C₂×C₄	C₂×#1181	1	3	yes	—
49	C₈	—	29	8	no	—
50	C₂²	—	29	6	no	—
51	C₂²	—	116	3	no	—
52	C₂²	C₂²×#1181	1	1	yes	characteristic
53	C₄	—	29	1	no	—
54	C₄	—	29	1	no	—
55	C₄	C₂²×#1181	1	6	yes	—
56	C₂	—	2	1	no	—
57	C₂	—	58	6	no	—
58	C₂	C₂³×#1181	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#1181
commutator, socle	C₂×C₂₉	C₂³×C₄
Fitting	C₂×Q₈×C₂₉	C₄
prime radical	C₂×#90809	C₂
cosocle	Dic₂₉	C₂⁴
hypercenter	C₂×Q₈	#1181
hypocenter	C₂₉	#568
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #11745348	C₂	semidirect
3. D₂₉⋊M₁₆	C₂	semidirect
10. #90796	C₂²	semidirect
11. D₂₉⋊C₈	C₂²	semidirect
33. C₂₉	#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×#90809	2
#11745348	2
D₂₉⋊M₁₆	2
#568	29