Subgroups — #14271542

Order 1856.

122 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
2	C₂×#90785	C₂	1	4	yes	maximal
3	#11745231	C₂	1	1	yes	maximal, characteristic
4	C₄×#6597	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
6	C₂×Dic₅₈	C₂²	1	2	yes	—
7	C₄⋊C₄×C₂₉	—	2	2	no	—
8	C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	#90785	—	2	8	no	—
10	C₄⋊Dic₂₉	—	2	2	no	—
11	C₂×#6597	C₂²	1	2	yes	—
12	Q₈×C₂₉	—	2	4	no	—
13	C₂×C₄×C₂₉	—	2	2	no	—
14	C₂×C₄×C₂₉	D₄	1	2	yes	—
15	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	C₂×Dic₂₉	—	2	2	no	—
17	Dic₅₈	—	2	4	no	—
18	#6597	D₄	1	4	yes	—
19	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
20	C₄×C₂₉	—	4	2	no	—
21	C₄×C₂₉	Q₁₆	1	4	yes	complemented
22	C₄×C₂₉	C₂×D₄	1	2	yes	—
23	Dic₂₉	—	4	2	no	—
24	#494	—	29	1	no	maximal, Sylow
25	C₂×C₂₉	#127	1	1	yes	characteristic
26	C₂×C₂₉	C₂×Q₁₆	1	2	yes	—
27	C₂×Q₁₆	—	29	4	no	—
28	C₄⋊Q₈	—	29	1	no	—
29	C₄⋊Q₈	D₂₉	1	1	yes	characteristic
30	C₄×C₈	—	29	1	no	—
31	C₂₉	#494	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₈	—	29	2	no	—
33	C₂×Q₈	C₂×D₂₉	1	2	yes	—
34	Q₁₆	—	58	8	no	—
35	C₂×C₈	—	29	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	—	58	2	no	—
38	C₄²	C₂×D₂₉	1	1	yes	characteristic
39	Q₈	—	2	4	no	—
40	Q₈	—	58	4	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	58	2	no	—
43	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
44	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
45	C₈	—	29	4	no	—
46	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
47	C₄	—	4	2	no	—
48	C₄	—	116	2	no	—
49	C₄	#90785	1	4	yes	complemented
50	C₄	D₄×D₂₉	1	2	yes	—
51	C₂	#11745302	1	1	yes	characteristic
52	C₂	C₂×#90785	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, prime radical	C₂²×C₂₉	C₂×D₄
hypercenter	C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#494
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
21. C₄×C₂₉	Q₁₆	semidirect
31. C₂₉	#494	semidirect
49. C₄	#90785	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×#90785	2
#11745231	2
C₄×#6597	2
#494	29