Subgroups — #14271276

Order 1856.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₁₆	C₂	1	2	yes	maximal, complemented
3	C₂₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745169	C₂	1	2	yes	maximal, complemented
5	#11745165	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₁₆	C₂²	1	2	yes	—
7	C₂×C₄×D₂₉	—	2	2	no	—
8	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	#90781	—	2	2	no	—
12	C₄⋊Dic₂₉	C₂²	1	2	yes	—
13	D₂₃₂	C₄	1	4	yes	complemented
14	C₂²×D₂₉	—	2	2	no	—
15	C₂×C₄×C₂₉	D₄	1	2	yes	—
16	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₉	—	2	2	no	—
18	D₁₁₆	—	2	2	no	—
19	D₁₁₆	C₂×C₄	1	4	yes	complemented
20	C₄×D₂₉	—	4	4	no	—
21	C₈×C₂₉	—	2	1	no	—
22	C₈×C₂₉	C₂×C₄	1	2	yes	complemented
23	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₂×D₂₉	—	2	4	no	—
25	C₂×D₂₉	—	4	2	no	—
26	C₂×D₂₉	—	4	2	no	—
27	C₄×C₂₉	—	2	2	no	—
28	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₂₉	#41	1	1	yes	characteristic
30	Dic₂₉	—	4	2	no	—
31	#442	—	29	1	no	maximal, Sylow
32	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
33	C₂×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
34	D₂₉	—	4	4	no	—
35	C₂×D₈	—	29	1	no	—
36	C₄×D₄	—	29	2	no	—
37	#106	—	29	1	no	—
38	#102	—	29	2	no	—
39	#97	D₂₉	1	1	yes	characteristic, complemented
40	C₂₉	#442	1	1	yes	characteristic, complemented, Sylow
41	C₂×D₄	—	29	2	no	—
42	C₂²×C₄	—	58	2	no	—
43	D₈	—	29	4	no	—
44	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
45	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
46	C₄⋊C₄	—	29	2	no	—
47	C₂²⋊C₄	—	58	2	no	—
48	C₄²	C₂×D₂₉	1	1	yes	characteristic
49	C₂³	—	58	2	no	—
50	D₄	—	29	4	no	—
51	D₄	—	58	2	no	—
52	C₂×C₄	—	58	2	no	—
53	C₂×C₄	—	116	4	no	—
54	C₂×C₄	D₁₁₆	1	2	yes	—
55	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	C₄×D₂₉	1	2	yes	complemented
58	C₂²	—	58	4	no	—
59	C₂²	—	116	2	no	—
60	C₂²	—	116	2	no	—
61	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
62	C₄	—	2	2	no	—
63	C₄	—	116	2	no	—
64	C₄	C₂×C₄×D₂₉	1	1	yes	characteristic
65	C₄	#90805	1	1	yes	characteristic
66	C₂	—	116	4	no	—
67	C₂	C₄×D₁₁₆	1	1	yes	characteristic
68	C₂	#11745270	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#97	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂×D₂₃₂	C₂
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#97	D₂₉
hypocenter	C₂₉	#442
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. C₄×D₁₁₆	C₂	semidirect
3. C₂₉×#97	C₂	semidirect
4. #11745169	C₂	semidirect
5. #11745165	C₂	semidirect
13. D₂₃₂	C₄	semidirect
19. D₁₁₆	C₂×C₄	semidirect
22. C₈×C₂₉	C₂×C₄	semidirect
39. #97	D₂₉	semidirect
40. C₂₉	#442	semidirect
57. C₈	C₄×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₃₂	2
C₄×D₁₁₆	2
C₂₉×#97	2
#11745169	2
#11745165	2
#442	29