Subgroups — #16834357

Order 3712.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272184	C₂	1	2	yes	maximal
2	C₂×#11745162	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
5	C₂²×#6597	C₄	1	1	yes	characteristic
6	C₂²⋊#6599	—	2	2	no	—
7	#11745218	C₄	1	4	yes	—
8	C₄⋊#6599	—	2	2	no	—
9	#11745162	—	2	2	no	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₂₉	D₄	1	1	yes	characteristic
12	C₂²×Dic₂₉	Q₈	1	1	yes	characteristic
13	C₂×#6599	—	2	4	no	—
14	C₂×C₈×C₂₉	—	2	1	no	—
15	C₂×C₈×C₂₉	—	4	1	no	—
16	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
17	C₄×Dic₂₉	D₄	1	2	yes	—
18	C₂×#6597	—	2	1	no	—
19	C₂×#6597	—	4	1	no	—
20	C₂³×C₂₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₂₉	—	2	1	no	—
26	C₂×Dic₂₉	—	2	1	no	—
27	C₂×Dic₂₉	—	4	1	no	—
28	C₂×Dic₂₉	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
30	#6599	—	4	4	no	—
31	C₈×C₂₉	—	4	1	no	—
32	#6597	—	4	1	no	—
33	#1290	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	—	2	1	no	—
35	C₂²×C₂₉	—	2	1	no	—
36	C₂²×C₂₉	#95	1	1	yes	characteristic
37	C₂²×C₂₉	#108	1	1	yes	characteristic
38	C₂²×C₂₉	#108	1	1	yes	characteristic
39	C₄×C₂₉	—	2	1	no	—
40	C₄×C₂₉	#100	1	1	yes	characteristic
41	C₄×C₂₉	#101	1	1	yes	characteristic
42	Dic₂₉	—	2	2	no	—
43	Dic₂₉	—	2	2	no	—
44	#432	—	29	2	no	—
45	C₂×C₄⋊C₈	—	29	1	no	—
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	—	2	1	no	—
48	C₂×C₂₉	H(3,ℤ/4)	1	1	yes	characteristic
49	C₂×C₂₉	#341	1	1	yes	characteristic
50	C₂×C₂₉	#343	1	1	yes	characteristic
51	C₂²×C₈	—	29	1	no	—
52	C₂²×C₈	#1181	1	1	yes	characteristic
53	C₂×C₄²	—	29	1	no	—
54	C₄⋊C₈	—	58	2	no	—
55	C₄⋊C₈	—	58	2	no	—
56	C₂²⋊C₈	—	58	2	no	—
57	#97	—	29	4	no	—
58	C₂₉	#1290	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₄	—	29	1	no	—
60	C₂²×C₄	—	29	1	no	—
61	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
62	C₂×C₈	—	2	1	no	—
63	C₂×C₈	—	4	1	no	—
64	C₂×C₈	—	58	4	no	—
65	C₂×C₈	—	58	1	no	—
66	C₂×C₈	—	116	1	no	—
67	C₄²	—	29	2	no	—
68	C₄²	—	29	2	no	—
69	C₂³	C₄⋊#1181	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	29	2	no	—
73	C₂×C₄	—	29	2	no	—
74	C₂×C₄	—	58	1	no	—
75	C₂×C₄	—	58	1	no	—
76	C₂×C₄	—	116	1	no	—
77	C₂×C₄	C₄×#1181	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
79	C₈	—	4	1	no	—
80	C₈	—	116	4	no	—
81	C₈	—	116	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	1	no	—
84	C₂²	#11745211	1	1	yes	characteristic
85	C₂²	#11745212	1	1	yes	characteristic
86	C₂²	(C₂×#1181)⋊C₄	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	58	2	no	—
89	C₄	—	58	2	no	—
90	C₄	#11745221	1	1	yes	characteristic
91	C₄	#11745229	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	2	1	no	—
94	C₂	#14272031	1	1	yes	characteristic
95	C₂	#14272039	1	1	yes	characteristic
96	C₂	#14272043	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#1181)⋊C₄
commutator	C₂×C₄×C₂₉	C₄²
Frattini	C₂²×C₄	C₂×#1181
Fitting	C₂²×C₈×C₂₉	C₄
socle	C₂²×C₂₉	#95
prime radical	C₂³×C₂₉	C₄⋊C₄
cosocle	C₂×C₄×Dic₂₉	C₂²
hypercenter	C₂²×C₈	#1181
hypocenter	C₂₉	#1290
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
58. C₂₉	#1290	semidirect

Maximal subgroups

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

subgroup	index
#14272184	2
C₂×#11745162	2
#1290	29