Subgroups — #14272035

Order 1856.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745345	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#1181	C₂	1	1	yes	maximal, characteristic
3	M₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#1181	—	2	1	no	—
5	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
6	C₂²⋊#1181	—	2	1	no	—
7	C₄⋊#1181	C₄	1	2	yes	complemented
8	C₄×#1181	—	2	1	no	—
9	C₄×#1181	—	2	1	no	—
10	C₄×#1181	C₄	1	2	yes	complemented
11	M₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
12	#90777	C₄	1	1	yes	characteristic, complemented
13	#90772	—	2	1	no	—
14	C₈×D₂₉	—	2	1	no	—
15	C₂²×D₂₉	D₄	1	1	yes	characteristic
16	C₂×#1181	—	2	4	no	—
17	C₂×#1181	—	2	2	no	—
18	C₂×#1181	—	2	2	no	—
19	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₉	Q₈	1	1	yes	characteristic
21	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄×D₂₉	D₄	1	1	yes	characteristic
24	C₄×D₂₉	D₄	1	1	yes	characteristic
25	C₈×C₂₉	—	2	1	no	—
26	#6597	—	2	1	no	—
27	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₂₉	—	2	2	no	—
29	C₂×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
31	#1181	—	2	4	no	—
32	#1181	—	4	2	no	—
33	C₄×C₂₉	C₄²	1	1	yes	characteristic
34	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
35	Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
36	Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
37	#339	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	—	2	1	no	—
39	C₂×C₂₉	#95	1	1	yes	characteristic
40	D₂₉	—	2	1	no	—
41	D₂₉	#104	1	2	yes	—
42	C₂×M₁₆	—	29	1	no	—
43	#117	—	29	1	no	—
44	C₂×C₄²	—	29	1	no	—
45	C₂₉	#339	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	—	29	1	no	—
47	C₂²×C₄	—	58	1	no	—
48	M₁₆	—	29	1	no	—
49	M₁₆	—	58	1	no	—
50	M₁₆	#1181	1	1	yes	characteristic, complemented
51	C₂×C₈	—	58	1	no	—
52	C₄⋊C₄	—	29	2	no	—
53	C₂²⋊C₄	—	58	1	no	—
54	C₄²	—	29	2	no	—
55	C₄²	—	58	1	no	—
56	C₄²	—	58	1	no	—
57	C₂³	—	29	1	no	—
58	C₂×C₄	—	29	1	no	—
59	C₂×C₄	—	29	1	no	—
60	C₂×C₄	—	29	1	no	—
61	C₂×C₄	—	29	1	no	—
62	C₂×C₄	—	29	1	no	—
63	C₂×C₄	—	58	2	no	—
64	C₂×C₄	—	58	4	no	—
65	C₂×C₄	—	58	2	no	—
66	C₂×C₄	C₂×#1181	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	—	58	1	no	—
69	C₂²	—	29	1	no	—
70	C₂²	—	29	1	no	—
71	C₂²	—	58	2	no	—
72	C₂²	C₄⋊#1181	1	1	yes	characteristic
73	C₄	—	29	1	no	—
74	C₄	—	29	1	no	—
75	C₄	—	58	4	no	—
76	C₄	—	116	2	no	—
77	C₄	C₄×#1181	1	1	yes	characteristic
78	C₄	C₂²⋊#1181	1	1	yes	characteristic
79	C₂	—	2	1	no	—
80	C₂	—	29	2	no	—
81	C₂	—	58	1	no	—
82	C₂	(C₂×#1181)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#1181
commutator	C₄×C₂₉	C₄²
Frattini	C₂×C₄	C₂×#1181
Fitting	M₁₆×C₂₉	C₄
socle	C₂×C₂₉	#95
prime radical	C₂²×D₂₉	D₄
cosocle	C₂×C₄×D₂₉	C₂²
hypercenter	M₁₆	#1181
hypocenter	C₂₉	#339
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
7. C₄⋊#1181	C₄	semidirect
10. C₄×#1181	C₄	semidirect
11. M₁₆×C₂₉	C₄	semidirect
12. #90777	C₄	semidirect
45. C₂₉	#339	semidirect
50. M₁₆	#1181	semidirect

Maximal subgroups

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

subgroup	index
#11745345	2
C₂×C₄×#1181	2
M₁₆×D₂₉	2
#339	29