Subgroups — #16827956

Order 3712.

716 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271641	C₂	1	2	yes	maximal, complemented
2	#14271137	C₂	1	12	yes	maximal, complemented
3	C₂×C₂₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
4	C₂₉×2₋¹⁺⁴	—	2	8	no	—
5	C₂×#41×C₂₉	C₄	1	4	yes	complemented
6	C₂×#41×C₂₉	C₂²	1	6	yes	—
7	C₂²×Q₈×C₂₉	C₄	1	4	yes	complemented
8	C₂²×Q₈×C₂₉	C₂²	1	1	yes	characteristic
9	Q₈×Dic₂₉	—	2	8	no	—
10	#11745288	C₂²	1	12	yes	—
11	#11745182	C₂²	1	16	yes	—
12	#41×C₂₉	—	2	16	no	—
13	#41×C₂₉	—	2	24	no	—
14	C₂×Q₈×C₂₉	—	2	16	no	—
15	C₂×Q₈×C₂₉	C₂×C₄	1	6	yes	—
16	C₂×Q₈×C₂₉	C₂×C₄	1	4	yes	—
17	C₂×Q₈×C₂₉	D₄	1	8	yes	—
18	C₂×D₄×C₂₉	C₂×C₄	1	6	yes	—
19	C₂×D₄×C₂₉	C₂³	1	4	yes	—
20	C₂²×C₄×C₂₉	C₂×C₄	1	12	yes	—
21	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
22	C₂²⋊Dic₂₉	C₂³	1	8	yes	—
23	C₄⋊Dic₂₉	—	2	12	no	—
24	C₄×Dic₂₉	—	2	12	no	—
25	C₂³×C₂₉	C₂²×C₄	1	4	yes	—
26	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
27	Q₈×C₂₉	—	2	12	no	—
28	Q₈×C₂₉	C₂²⋊C₄	1	16	yes	—
29	D₄×C₂₉	—	2	8	no	—
30	D₄×C₂₉	—	2	12	no	—
31	C₂×C₄×C₂₉	—	2	24	no	—
32	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
33	C₂×C₄×C₂₉	C₂²×C₄	1	6	yes	—
34	C₂×C₄×C₂₉	C₂×D₄	1	12	yes	—
35	C₂×Dic₂₉	—	2	8	no	—
36	#2884	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	—	2	4	no	—
38	C₂²×C₂₉	—	4	1	no	—
39	C₂²×C₂₉	—	4	4	no	—
40	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
41	C₂²×C₂₉	C₂²×D₄	1	2	yes	—
42	C₄×C₂₉	—	2	4	no	—
43	C₄×C₂₉	C₂×C₂²⋊C₄	1	12	yes	—
44	Dic₂₉	—	4	8	no	—
45	C₂×2₋¹⁺⁴	D₂₉	1	1	yes	characteristic
46	#519	—	29	2	no	—
47	#410	—	29	12	no	—
48	C₂×C₂₉	—	2	2	no	—
49	C₂×C₂₉	—	2	1	no	—
50	C₂×C₂₉	—	4	4	no	—
51	C₂×C₂₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
52	2₋¹⁺⁴	—	2	8	no	—
53	C₂×#41	Dic₂₉	1	4	yes	complemented
54	C₂×#41	C₂×D₂₉	1	6	yes	—
55	C₂²×Q₈	Dic₂₉	1	4	yes	complemented
56	C₂²×Q₈	C₂×D₂₉	1	1	yes	characteristic
57	C₄×Q₈	—	58	8	no	—
58	#117	—	29	12	no	—
59	#99	—	29	16	no	—
60	C₂₉	#2884	1	1	yes	characteristic, complemented, Sylow
61	#41	—	2	16	no	—
62	#41	—	2	24	no	—
63	C₂×Q₈	—	2	16	no	—
64	C₂×Q₈	C₂×Dic₂₉	1	6	yes	—
65	C₂×Q₈	C₂×Dic₂₉	1	4	yes	—
66	C₂×Q₈	C₂²⋊D₂₉	1	8	yes	—
67	C₂×D₄	C₂×Dic₂₉	1	6	yes	—
68	C₂×D₄	C₂²×D₂₉	1	4	yes	—
69	C₂²×C₄	C₂×Dic₂₉	1	12	yes	—
70	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
71	C₄⋊C₄	—	58	12	no	—
72	C₂²⋊C₄	—	29	8	no	—
73	C₄²	—	58	12	no	—
74	C₂³	C₂²×Dic₂₉	1	4	yes	—
75	C₂³	C₂³×D₂₉	1	1	yes	characteristic
76	Q₈	—	2	12	no	—
77	Q₈	C₂²⋊Dic₂₉	1	16	yes	—
78	D₄	—	2	8	no	—
79	D₄	—	2	12	no	—
80	C₂×C₄	—	2	24	no	—
81	C₂×C₄	—	58	8	no	—
82	C₂×C₄	C₂²×Dic₂₉	1	4	yes	—
83	C₂×C₄	C₂²×Dic₂₉	1	6	yes	—
84	C₂×C₄	C₂×C₂²⋊D₂₉	1	12	yes	—
85	C₂²	—	2	4	no	—
86	C₂²	—	4	1	no	—
87	C₂²	—	4	4	no	—
88	C₂²	C₂³×Dic₂₉	1	1	yes	characteristic
89	C₂²	C₂²×C₂²⋊D₂₉	1	2	yes	—
90	C₄	—	2	4	no	—
91	C₄	—	116	8	no	—
92	C₄	C₂×C₂²⋊Dic₂₉	1	12	yes	—
93	C₂	—	2	2	no	—
94	C₂	—	2	1	no	—
95	C₂	—	4	4	no	—
96	C₂	C₂²×C₂²⋊Dic₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×C₂²⋊Dic₂₉
commutator	C₂²×C₂₉	C₂³×C₄
Frattini	C₂³	C₂³×D₂₉
Fitting, prime radical	C₂×C₂₉×2₋¹⁺⁴	C₂
socle	C₂×C₂₉	C₂²×C₂²⋊C₄
cosocle	C₂³×C₂₉	C₂⁴
hypercenter	C₂×2₋¹⁺⁴	D₂₉
hypocenter	C₂₉	#2884
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂²×Q₈ ◁ C₂×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. #14271641	C₂	semidirect
2. #14271137	C₂	semidirect
5. C₂×#41×C₂₉	C₄	semidirect
7. C₂²×Q₈×C₂₉	C₄	semidirect
53. C₂×#41	Dic₂₉	semidirect
55. C₂²×Q₈	Dic₂₉	semidirect
60. C₂₉	#2884	semidirect

Maximal subgroups

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

subgroup	index
#14271641	2
#14271137	2
C₂×C₂₉×2₋¹⁺⁴	2
#2884	29