Subgroups — #16817775

Order 3712.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271216	C₂	1	2	yes	maximal
2	#14270884	C₂	1	2	yes	maximal, complemented
3	C₈×#6597	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₂₉	C₄	1	2	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₂₉	C₄	1	2	yes	—
8	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂²⋊#6597	C₄	1	4	yes	—
11	C₄⋊#6597	C₄	1	4	yes	—
12	C₄×#6597	C₂²	1	4	yes	—
13	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₉	C₈	1	8	yes	complemented
16	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
18	C₄²×C₂₉	C₂×C₄	1	2	yes	—
19	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₂₉	C₂³	1	1	yes	characteristic
21	C₂×#6597	C₂×C₄	1	8	yes	—
22	C₂³×C₂₉	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₉	—	2	4	no	—
24	C₂×C₄×C₂₉	C₄²	1	2	yes	—
25	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
27	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₂₉	C₂×C₈	1	4	yes	—
30	C₈×C₂₉	C₂×C₈	1	4	yes	—
31	#6597	—	2	8	no	—
32	#1450	—	29	1	no	maximal, Sylow
33	C₂²×C₂₉	—	2	2	no	—
34	C₂²×C₂₉	C₄×C₈	1	2	yes	—
35	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
36	C₄×C₂₉	—	2	2	no	—
37	C₄×C₂₉	C₄×C₈	1	2	yes	—
38	C₄×C₂₉	C₂²×C₈	1	2	yes	—
39	C₄×C₂₉	#131	1	4	yes	—
40	#431	—	29	2	no	—
41	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
42	#322	—	29	2	no	—
43	C₈²	—	29	2	no	—
44	C₂×C₂₉	—	2	2	no	—
45	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
46	C₂×C₂₉	#405	1	2	yes	—
47	C₂²×C₈	Dic₂₉	1	2	yes	—
48	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
49	C₄⋊C₈	—	29	4	no	—
50	C₂²⋊C₈	—	29	4	no	—
51	C₄×C₈	—	29	4	no	—
52	C₄×C₈	Dic₂₉	1	2	yes	—
53	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
54	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
55	C₂₉	#1450	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	C₄×D₂₉	1	2	yes	—
57	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
58	C₂×C₈	—	29	8	no	—
59	C₂×C₈	#6597	1	8	yes	complemented
60	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
61	C₂×C₈	C₂×Dic₂₉	1	2	yes	—
62	C₄²	C₄×D₂₉	1	2	yes	—
63	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
64	C₄²	C₂²×D₂₉	1	1	yes	characteristic
65	C₂³	C₄×Dic₂₉	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	C₂×#6597	1	4	yes	—
68	C₂×C₄	C₄×Dic₂₉	1	2	yes	—
69	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
70	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
71	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
72	C₈	—	58	8	no	—
73	C₈	C₂×#6597	1	4	yes	—
74	C₈	C₂×#6597	1	4	yes	—
75	C₂²	—	2	2	no	—
76	C₂²	C₄×#6597	1	2	yes	—
77	C₂²	C₂×C₄×Dic₂₉	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	C₄×#6597	1	2	yes	—
80	C₄	#11745263	1	4	yes	—
81	C₄	C₂²×#6597	1	2	yes	—
82	C₂	—	2	2	no	—
83	C₂	C₂×C₄×#6597	1	1	yes	characteristic
84	C₂	#14271118	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₄×C₈
Frattini	C₄²	C₂²×D₂₉
Fitting	C₂×C₄×C₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×C₄²
prime radical	C₂³×C₂₉	C₄²
cosocle	C₄²×C₂₉	C₂³
hypercenter	C₂×C₄×C₈	D₂₉
hypocenter	C₂₉	#1450
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #14270884	C₂	semidirect
3. C₈×#6597	C₂	semidirect
15. C₂×C₈×C₂₉	C₈	semidirect
55. C₂₉	#1450	semidirect
59. C₂×C₈	#6597	semidirect

Maximal subgroups

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

subgroup	index
#14271216	2
#14270884	2
C₈×#6597	2
C₂×C₄×C₈×C₂₉	2
#1450	29