Subgroups — #14271476

Order 1856.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745292	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#6597	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745157	C₂	1	2	yes	maximal, complemented
5	#11745155	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₉	—	2	1	no	—
7	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₂₉	—	2	1	no	—
9	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₂₉	—	2	1	no	—
11	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
12	#90781	—	2	1	no	—
13	C₄⋊Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×#6597	C₂²	1	2	yes	—
15	C₂³×C₂₉	D₄	1	1	yes	characteristic
16	C₂²×D₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	—	2	2	no	—
19	C₂×C₄×C₂₉	—	4	2	no	—
20	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₂²⋊D₂₉	—	4	2	no	—
23	C₂×Dic₂₉	—	2	1	no	—
24	D₁₁₆	—	2	2	no	—
25	#6597	—	2	2	no	—
26	C₂²×C₂₉	—	2	1	no	—
27	C₂²×C₂₉	—	2	1	no	—
28	C₂²×C₂₉	D₈	1	2	yes	—
29	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
30	C₂×D₂₉	—	4	1	no	—
31	C₂×D₂₉	—	4	1	no	—
32	C₂×D₂₉	—	4	1	no	—
33	C₄×C₂₉	—	2	1	no	—
34	C₄×C₂₉	—	4	2	no	—
35	C₄×C₂₉	#41	1	2	yes	—
36	Dic₂₉	—	4	1	no	—
37	#480	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	—	2	2	no	—
39	C₂×C₂₉	#123	1	1	yes	characteristic
40	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
41	C₂×C₂₉	#137	1	1	yes	characteristic
42	D₂₉	—	8	1	no	—
43	#121	—	29	1	no	—
44	C₂×C₄⋊C₄	D₂₉	1	1	yes	characteristic, complemented
45	#107	—	29	2	no	—
46	#102	—	29	2	no	—
47	C₂²⋊C₈	—	29	1	no	—
48	C₂₉	#480	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	29	1	no	—
50	C₂×D₄	—	58	1	no	—
51	C₂²×C₄	—	2	1	no	—
52	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
53	C₂×C₈	—	29	2	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	29	1	no	—
56	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
57	C₂²⋊C₄	—	58	1	no	—
58	C₂³	—	58	1	no	—
59	C₂³	C₂²⋊D₂₉	1	1	yes	characteristic
60	D₄	—	58	2	no	—
61	D₄	—	116	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	58	1	no	—
66	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
68	C₈	—	58	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	116	1	no	—
72	C₂²	—	116	1	no	—
73	C₂²	—	116	1	no	—
74	C₂²	#90782	1	2	yes	—
75	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	4	2	no	—
78	C₄	—	116	1	no	—
79	C₄	#90805	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	232	1	no	—
82	C₂	#11745291	1	1	yes	characteristic
83	C₂	C₂×#90782	1	1	yes	characteristic
84	C₂	#11745304	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂×C₄⋊C₄×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	#11745292	C₂
hypercenter	C₂×C₄⋊C₄	D₂₉
hypocenter	C₂₉	#480
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊C₄×C₂₉	C₂	semidirect
3. C₂²⋊#6597	C₂	semidirect
4. #11745157	C₂	semidirect
5. #11745155	C₂	semidirect
44. C₂×C₄⋊C₄	D₂₉	semidirect
48. C₂₉	#480	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₂₉	2
#11745292	2
C₂²⋊#6597	2
#11745157	2
#11745155	2
#480	29