Subgroups — #14271537

Order 1856.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#90784	C₂	1	4	yes	maximal, complemented
3	#11745236	C₂	1	1	yes	maximal, characteristic
4	C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
6	C₂×D₁₁₆	—	2	2	no	—
7	C₂×D₁₁₆	C₂²	1	2	yes	—
8	C₄⋊C₄×C₂₉	—	2	2	no	—
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	#90784	—	2	8	no	—
11	C₂×#6597	C₂²	1	2	yes	—
12	C₂²×D₂₉	—	2	2	no	—
13	Q₈×C₂₉	—	2	4	no	—
14	C₂×C₄×C₂₉	—	2	2	no	—
15	C₂×C₄×C₂₉	D₄	1	2	yes	—
16	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	D₁₁₆	—	2	4	no	—
18	D₁₁₆	—	4	4	no	—
19	#6597	D₄	1	4	yes	complemented
20	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
21	C₂×D₂₉	—	4	2	no	—
22	C₂×D₂₉	—	4	4	no	—
23	C₄×C₂₉	—	4	2	no	—
24	C₄×C₂₉	SD₁₆	1	4	yes	complemented
25	C₄×C₂₉	C₂×D₄	1	2	yes	—
26	#492	—	29	1	no	maximal, Sylow
27	C₂×C₂₉	#127	1	1	yes	characteristic
28	C₂×C₂₉	C₂×SD₁₆	1	2	yes	—
29	D₂₉	—	8	2	no	—
30	C₂×SD₁₆	—	29	4	no	—
31	C₄⋊Q₈	D₂₉	1	1	yes	characteristic, complemented
32	#127	—	29	1	no	—
33	C₄×C₈	—	29	1	no	—
34	C₂₉	#492	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	C₂×D₂₉	1	2	yes	—
36	C₂×D₄	—	29	2	no	—
37	C₂×D₄	—	58	2	no	—
38	SD₁₆	—	58	8	no	—
39	C₂×C₈	—	29	2	no	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄²	C₂×D₂₉	1	1	yes	characteristic
42	C₂³	—	58	2	no	—
43	Q₈	—	2	4	no	—
44	D₄	—	58	4	no	—
45	D₄	—	116	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
48	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
49	C₈	—	29	4	no	—
50	C₂²	—	116	2	no	—
51	C₂²	—	116	4	no	—
52	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	#90784	1	4	yes	complemented
55	C₄	D₄×D₂₉	1	2	yes	—
56	C₂	—	232	2	no	—
57	C₂	#11745302	1	1	yes	characteristic
58	C₂	C₂×#90784	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×C₄⋊Q₈	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	#11745236	C₂
hypercenter	C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#492
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₄⋊Q₈	C₂	semidirect
2. C₂×#90784	C₂	semidirect
4. C₄×#6597	C₂	semidirect
19. #6597	D₄	semidirect
24. C₄×C₂₉	SD₁₆	semidirect
31. C₄⋊Q₈	D₂₉	semidirect
34. C₂₉	#492	semidirect
54. C₄	#90784	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×C₄⋊Q₈	2
C₂×#90784	2
#11745236	2
C₄×#6597	2
#492	29