Subgroups — #14271454

Order 1856.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₁₆	C₂	1	1	yes	maximal, characteristic
2	#11745231	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745169	C₂	1	2	yes	maximal
5	#11745165	C₂	1	2	yes	maximal, complemented
6	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₂₉	—	2	1	no	—
8	C₂×Dic₅₈	—	2	1	no	—
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	#90781	—	2	1	no	—
12	C₄⋊Dic₂₉	—	2	1	no	—
13	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₂₉	C₂²	1	2	yes	—
15	C₂²×D₂₉	—	2	1	no	—
16	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	—	2	2	no	—
20	C₂×Dic₂₉	—	2	1	no	—
21	D₁₁₆	—	2	1	no	—
22	D₁₁₆	Q₈	1	2	yes	complemented
23	C₄×D₂₉	—	4	2	no	—
24	Dic₅₈	—	4	2	no	—
25	C₈×C₂₉	—	2	2	no	—
26	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₂₉	—	2	2	no	—
28	C₂×D₂₉	—	4	1	no	—
29	C₂×D₂₉	—	4	1	no	—
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	SD₁₆	1	2	yes	—
32	C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₂₉	#41	1	1	yes	characteristic
34	Dic₂₉	—	4	1	no	—
35	Dic₂₉	—	4	2	no	—
36	#476	—	29	1	no	maximal, Sylow
37	C₂×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
38	C₂×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
39	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
40	D₂₉	—	4	2	no	—
41	C₄⋊Q₈	—	29	1	no	—
42	C₄×D₄	—	29	1	no	—
43	#106	—	29	2	no	—
44	C₄⋊C₈	D₂₉	1	1	yes	characteristic, complemented
45	#102	—	29	2	no	—
46	C₂₉	#476	1	1	yes	characteristic, complemented, Sylow
47	C₂×Q₈	—	58	1	no	—
48	C₂×D₄	—	29	1	no	—
49	C₂²×C₄	—	58	1	no	—
50	C₂×C₈	C₂×D₂₉	1	2	yes	—
51	C₄⋊C₄	—	29	2	no	—
52	C₄⋊C₄	—	29	1	no	—
53	C₄⋊C₄	—	58	1	no	—
54	C₂²⋊C₄	—	58	1	no	—
55	C₄²	C₂×D₂₉	1	1	yes	characteristic
56	C₂³	—	58	1	no	—
57	Q₈	—	116	2	no	—
58	D₄	—	29	2	no	—
59	D₄	—	58	1	no	—
60	C₂×C₄	—	58	1	no	—
61	C₂×C₄	—	58	2	no	—
62	C₂×C₄	—	116	2	no	—
63	C₂×C₄	D₁₁₆	1	1	yes	characteristic
64	C₂×C₄	D₁₁₆	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₂²	—	58	2	no	—
68	C₂²	—	116	1	no	—
69	C₂²	—	116	1	no	—
70	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	116	1	no	—
73	C₄	—	116	2	no	—
74	C₄	#90773	1	2	yes	—
75	C₄	#90807	1	1	yes	characteristic
76	C₄	Q₈×D₂₉	1	1	yes	characteristic
77	C₂	—	116	2	no	—
78	C₂	#11745259	1	1	yes	characteristic
79	C₂	C₂×#90773	1	1	yes	characteristic
80	C₂	#11745270	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×C₄⋊C₈	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	C₂×D₁₁₆	C₂²
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#476
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #11745231	C₂	semidirect
3. C₂₉×C₄⋊C₈	C₂	semidirect
5. #11745165	C₂	semidirect
22. D₁₁₆	Q₈	semidirect
44. C₄⋊C₈	D₂₉	semidirect
46. C₂₉	#476	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₁₆	2
#11745231	2
C₂₉×C₄⋊C₈	2
#11745169	2
#11745165	2
#476	29