Subgroups — #16827879

Order 3712.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271061	C₂	1	4	yes	maximal
2	#14271047	C₂	1	8	yes	maximal
3	#14271029	C₂	1	2	yes	maximal
4	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₂₉	C₂²	1	4	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₂₉	C₂²	1	4	yes	—
9	C₂×#90779	C₂²	1	8	yes	—
10	#11745179	C₂²	1	8	yes	—
11	#11745179	C₂²	1	8	yes	—
12	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
13	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₂₉	C₂³	1	8	yes	—
16	C₄²×C₂₉	—	2	8	no	—
17	C₄²×C₂₉	—	2	4	no	—
18	C₄²×C₂₉	Q₈	1	4	yes	—
19	C₄⋊Dic₂₉	—	2	8	no	—
20	#90779	—	2	16	no	—
21	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
22	C₂×C₄×C₂₉	—	2	4	no	—
23	C₂×C₄×C₂₉	—	2	4	no	—
24	C₂×C₄×C₂₉	—	2	4	no	—
25	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
26	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
27	C₂×C₄×C₂₉	#41	1	8	yes	—
28	C₂×C₄×C₂₉	#41	1	4	yes	—
29	C₂×Dic₂₉	—	2	16	no	—
30	C₂×Dic₂₉	—	2	8	no	—
31	#2864	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	C₂²×Q₈	1	1	yes	characteristic
33	C₂²×C₂₉	C₂×#41	1	2	yes	—
34	C₂²×C₂₉	C₂×#41	1	4	yes	—
35	C₄×C₂₉	—	2	8	no	—
36	C₄×C₂₉	—	2	4	no	—
37	C₄×C₂₉	#125	1	4	yes	—
38	Dic₂₉	—	4	8	no	—
39	#389	—	29	4	no	—
40	#387	—	29	8	no	—
41	#382	—	29	2	no	—
42	C₄³	D₂₉	1	1	yes	characteristic
43	C₂×C₂₉	C₂×#125	1	1	yes	characteristic
44	C₂×C₂₉	#529	1	4	yes	—
45	C₂×C₂₉	#533	1	2	yes	—
46	C₂×C₄⋊C₄	—	29	8	no	—
47	C₂×C₄⋊C₄	—	29	4	no	—
48	C₂×C₄²	C₂×D₂₉	1	4	yes	—
49	C₂×C₄²	C₂×D₂₉	1	2	yes	—
50	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
51	#95	—	29	8	no	—
52	#95	—	29	8	no	—
53	C₂₉	#2864	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	—	29	8	no	—
55	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
56	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
57	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
58	C₄⋊C₄	—	58	16	no	—
59	C₄⋊C₄	—	58	8	no	—
60	C₄²	—	2	8	no	—
61	C₄²	—	2	4	no	—
62	C₄²	Dic₅₈	1	4	yes	—
63	C₂³	C₂³×D₂₉	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	58	8	no	—
68	C₂×C₄	—	58	16	no	—
69	C₂×C₄	C₂×Dic₅₈	1	4	yes	—
70	C₂×C₄	C₂×Dic₅₈	1	2	yes	—
71	C₂×C₄	#90805	1	8	yes	—
72	C₂×C₄	#90805	1	4	yes	—
73	C₂²	C₂²×Dic₅₈	1	1	yes	characteristic
74	C₂²	C₂×#90805	1	2	yes	—
75	C₂²	C₂×#90805	1	4	yes	—
76	C₄	—	2	8	no	—
77	C₄	—	2	4	no	—
78	C₄	—	116	8	no	—
79	C₄	#11745232	1	4	yes	—
80	C₂	C₂×#11745232	1	1	yes	characteristic
81	C₂	#14271697	1	4	yes	—
82	C₂	#14271720	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₄³×C₂₉	C₂
hypercenter	C₄³	D₂₉
hypocenter	C₂₉	#2864
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
53. C₂₉	#2864	semidirect

Maximal subgroups

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

subgroup	index
#14271061	2
#14271047	2
#14271029	2
C₄³×C₂₉	2
#2864	29