Subgroups — #16827870

Order 3712.

504 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745231	C₂	1	2	yes	maximal
2	#14271069	C₂	1	8	yes	maximal
3	#14271029	C₂	1	4	yes	maximal
4	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₅₈	C₂²	1	4	yes	—
6	C₂×C₄²×C₂₉	C₂²	1	4	yes	—
7	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₂₉	C₂²	1	4	yes	—
10	C₂×C₄⋊Dic₂₉	C₂²	1	4	yes	—
11	#11745231	—	2	8	no	—
12	#11745179	C₂²	1	16	yes	—
13	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
16	C₂²×Dic₂₉	C₂³	1	8	yes	—
17	C₂×Dic₅₈	—	2	8	no	—
18	C₂×Dic₅₈	—	2	16	no	—
19	C₄²×C₂₉	—	2	8	no	—
20	C₄²×C₂₉	D₄	1	4	yes	—
21	C₄²×C₂₉	Q₈	1	8	yes	complemented
22	C₄⋊Dic₂₉	—	2	8	no	—
23	C₄⋊Dic₂₉	—	2	8	no	—
24	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₂₉	—	2	8	no	—
26	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
27	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
28	C₂×C₄×C₂₉	C₂×Q₈	1	8	yes	—
29	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
30	C₂×C₄×C₂₉	#41	1	8	yes	—
31	C₂×Dic₂₉	—	2	8	no	—
32	C₂×Dic₂₉	—	2	16	no	—
33	Dic₅₈	—	4	16	no	—
34	#2862	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
36	C₂²×C₂₉	C₂²×Q₈	1	2	yes	—
37	C₂²×C₂₉	C₂×#41	1	4	yes	—
38	C₄×C₂₉	—	2	8	no	—
39	C₄×C₂₉	#124	1	8	yes	—
40	C₄×C₂₉	C₄⋊Q₈	1	4	yes	—
41	Dic₂₉	—	4	8	no	—
42	C₂×C₄⋊Q₈	—	29	2	no	—
43	#391	—	29	8	no	—
44	#382	—	29	4	no	—
45	C₄³	D₂₉	1	1	yes	characteristic
46	C₂×C₂₉	C₂×#124	1	2	yes	—
47	C₂×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
48	C₂×C₂₉	#533	1	4	yes	—
49	C₂²×Q₈	—	29	4	no	—
50	C₄⋊Q₈	—	58	8	no	—
51	C₂×C₄⋊C₄	—	29	4	no	—
52	C₂×C₄⋊C₄	—	29	4	no	—
53	C₂×C₄²	C₂×D₂₉	1	4	yes	—
54	C₂×C₄²	C₂×D₂₉	1	2	yes	—
55	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
56	#95	—	29	16	no	—
57	C₂₉	#2862	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₈	—	58	8	no	—
59	C₂×Q₈	—	58	16	no	—
60	C₂²×C₄	—	29	8	no	—
61	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
62	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
63	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
64	C₄⋊C₄	—	58	8	no	—
65	C₄⋊C₄	—	58	8	no	—
66	C₄²	—	2	8	no	—
67	C₄²	Dic₅₈	1	8	yes	complemented
68	C₄²	D₁₁₆	1	4	yes	—
69	C₂³	C₂³×D₂₉	1	1	yes	characteristic
70	Q₈	—	116	16	no	—
71	C₂×C₄	—	2	8	no	—
72	C₂×C₄	—	58	8	no	—
73	C₂×C₄	—	58	16	no	—
74	C₂×C₄	C₂×Dic₅₈	1	8	yes	—
75	C₂×C₄	C₂×Dic₅₈	1	4	yes	—
76	C₂×C₄	C₂×D₁₁₆	1	2	yes	—
77	C₂×C₄	C₂×D₁₁₆	1	4	yes	—
78	C₂×C₄	#90805	1	8	yes	—
79	C₂²	C₂²×Dic₅₈	1	2	yes	—
80	C₂²	C₂²×D₁₁₆	1	1	yes	characteristic
81	C₂²	C₂×#90805	1	4	yes	—
82	C₄	—	2	8	no	—
83	C₄	—	116	8	no	—
84	C₄	#11745231	1	4	yes	—
85	C₄	#11745237	1	8	yes	—
86	C₂	C₂×#11745237	1	2	yes	—
87	C₂	C₂×#11745231	1	1	yes	characteristic
88	C₂	#14271720	1	4	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	#2862
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
21. C₄²×C₂₉	Q₈	semidirect
57. C₂₉	#2862	semidirect
67. C₄²	Dic₅₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745231	2
#14271069	2
#14271029	2
C₄³×C₂₉	2
#2862	29