Subgroups — #16835149

Order 3712.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745218	C₂	1	3	yes	maximal
2	C₂×C₄×#6599	C₂	1	3	yes	maximal
3	#14271008	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6599	C₂²	1	1	yes	characteristic
5	C₂²×#6599	C₂²	1	3	yes	—
6	C₂×C₄×Dic₂₉	C₂²	1	3	yes	—
7	#11745218	C₄	1	12	yes	complemented
8	C₄×#6599	C₄	1	12	yes	complemented
9	C₂₉×#95	C₄	1	1	yes	characteristic
10	#11745179	C₄	1	3	yes	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	3	yes	—
12	C₂²×Dic₂₉	C₂×C₄	1	3	yes	—
13	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
14	C₂×#6599	C₂×C₄	1	6	yes	—
15	C₂×#6599	C₂×C₄	1	6	yes	—
16	C₂×#6599	C₂×C₄	1	12	yes	—
17	C₄×Dic₂₉	C₂×C₄	1	6	yes	—
18	C₄×Dic₂₉	C₂×C₄	1	6	yes	—
19	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	—	2	6	no	—
21	C₂×C₄×C₂₉	C₄²	1	6	yes	—
22	C₂×Dic₂₉	—	2	3	no	—
23	C₂×Dic₂₉	—	2	3	no	—
24	C₂×Dic₂₉	C₄²	1	6	yes	—
25	C₂×Dic₂₉	C₂²×C₄	1	3	yes	—
26	C₂×Dic₂₉	C₂²×C₄	1	3	yes	—
27	#6599	C₄²	1	4	yes	—
28	#6599	C₄²	1	12	yes	—
29	#1726	—	29	1	no	maximal, Sylow
30	C₂²×C₂₉	C₂×C₄²	1	3	yes	—
31	C₂²×C₂₉	#131	1	3	yes	—
32	C₂²×C₂₉	#131	1	1	yes	characteristic
33	C₄×C₂₉	—	2	6	no	—
34	Dic₂₉	—	2	6	no	—
35	Dic₂₉	C₂×C₄²	1	1	yes	characteristic
36	Dic₂₉	C₂×C₄²	1	3	yes	—
37	C₂×#97	—	29	3	no	—
38	C₂×C₄×C₈	—	29	3	no	—
39	#376	—	29	1	no	—
40	C₂×C₂₉	C₄³	1	1	yes	characteristic
41	C₂×C₂₉	#405	1	3	yes	—
42	C₂×C₂₉	#405	1	3	yes	—
43	C₂²×C₈	—	29	1	no	—
44	C₂²×C₈	—	29	3	no	—
45	C₂×C₄²	—	29	3	no	—
46	#97	—	29	12	no	—
47	C₄×C₈	—	29	12	no	—
48	#95	—	29	3	no	—
49	#95	#1181	1	1	yes	characteristic
50	C₂₉	#1726	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	—	29	1	no	—
52	C₂²×C₄	—	29	3	no	—
53	C₂²×C₄	C₂×#1181	1	3	yes	—
54	C₂×C₈	—	29	6	no	—
55	C₂×C₈	—	29	6	no	—
56	C₂×C₈	—	29	12	no	—
57	C₄²	—	29	6	no	—
58	C₄²	—	29	6	no	—
59	C₂³	C₂²×#1181	1	1	yes	characteristic
60	C₂×C₄	—	2	6	no	—
61	C₂×C₄	—	29	3	no	—
62	C₂×C₄	—	29	3	no	—
63	C₂×C₄	—	29	6	no	—
64	C₂×C₄	—	58	3	no	—
65	C₂×C₄	—	58	3	no	—
66	C₂×C₄	C₄×#1181	1	6	yes	—
67	C₈	—	29	4	no	—
68	C₈	—	29	12	no	—
69	C₂²	C₂×C₄×#1181	1	3	yes	—
70	C₂²	#11745346	1	3	yes	—
71	C₂²	#11745348	1	1	yes	characteristic
72	C₄	—	2	6	no	—
73	C₄	—	29	1	no	—
74	C₄	—	29	3	no	—
75	C₄	—	58	6	no	—
76	C₂	C₄²×#1181	1	1	yes	characteristic
77	C₂	#14272127	1	3	yes	—
78	C₂	#14272128	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator	C₂×C₂₉	C₄³
Fitting	C₂₉×#95	C₄
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	#95	#1181
hypocenter	C₂₉	#1726
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
7. #11745218	C₄	semidirect
8. C₄×#6599	C₄	semidirect
50. C₂₉	#1726	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745218	2
C₂×C₄×#6599	2
#14271008	2
#1726	29