Subgroups — #16835862

Order 3712.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272085	C₂	1	2	yes	maximal, complemented
2	#14272059	C₂	1	2	yes	maximal
3	#14272056	C₂	1	2	yes	maximal, complemented
4	M₁₆×Dic₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
7	C₂×#90777	C₂²	1	1	yes	characteristic
8	#11745214	C₂²	1	4	yes	—
9	#11745163	C₄	1	1	yes	characteristic
10	#11745163	C₂²	1	1	yes	characteristic
11	C₈×Dic₂₉	C₄	1	1	yes	characteristic
12	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₂₉	—	2	1	no	—
15	M₁₆×C₂₉	—	2	2	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₂₉	—	2	1	no	—
19	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	#90777	—	2	2	no	—
22	C₂×#6597	C₂×C₄	1	1	yes	characteristic
23	C₂×#6597	C₂³	1	1	yes	characteristic
24	#90770	—	2	4	no	—
25	C₂³×C₂₉	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₂₉	—	2	1	no	—
27	C₂×C₄×C₂₉	—	2	1	no	—
28	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₂₉	—	2	1	no	—
31	C₂×Dic₂₉	—	2	1	no	—
32	C₂×Dic₂₉	—	4	2	no	—
33	C₈×C₂₉	—	2	1	no	—
34	C₈×C₂₉	M₁₆	1	2	yes	—
35	#6597	—	2	1	no	—
36	#6597	#41	1	2	yes	—
37	#2165	—	29	1	no	maximal, Sylow
38	C₂²×C₂₉	—	2	1	no	—
39	C₂²×C₂₉	—	4	1	no	—
40	C₂²×C₂₉	C₂×M₁₆	1	1	yes	characteristic
41	C₄×C₂₉	—	2	1	no	—
42	C₄×C₂₉	#117	1	1	yes	characteristic
43	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
44	Dic₂₉	—	2	2	no	—
45	Dic₂₉	—	4	1	no	—
46	C₄×M₁₆	—	29	1	no	—
47	#364	—	29	2	no	—
48	#349	—	29	2	no	—
49	#347	—	29	2	no	—
50	C₂×C₂₉	—	2	1	no	—
51	C₂×C₂₉	—	4	1	no	—
52	C₂×C₂₉	#432	1	1	yes	characteristic
53	C₂×M₁₆	—	29	1	no	—
54	C₂×M₁₆	#1181	1	1	yes	characteristic
55	C₂×C₄²	—	29	1	no	—
56	M₃₂	—	29	4	no	—
57	#97	—	29	1	no	—
58	#97	—	29	1	no	—
59	C₄×C₈	—	29	1	no	—
60	C₄×C₈	—	29	1	no	—
61	C₂₉	#2165	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	58	1	no	—
63	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	58	2	no	—
66	C₂×C₈	—	29	1	no	—
67	C₂×C₈	—	29	1	no	—
68	C₂×C₈	C₂×#1181	1	1	yes	characteristic
69	C₂×C₈	C₂×#1181	1	1	yes	characteristic
70	C₄²	—	29	1	no	—
71	C₄²	—	29	1	no	—
72	C₄²	—	58	1	no	—
73	C₁₆	—	58	4	no	—
74	C₂³	#90796	1	1	yes	characteristic
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	58	1	no	—
78	C₂×C₄	—	58	1	no	—
79	C₂×C₄	—	116	2	no	—
80	C₂×C₄	#90796	1	1	yes	characteristic
81	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	29	2	no	—
84	C₈	—	58	1	no	—
85	C₈	#90800	1	2	yes	—
86	C₂²	—	2	1	no	—
87	C₂²	—	4	1	no	—
88	C₂²	C₂×#90796	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	58	2	no	—
91	C₄	—	116	1	no	—
92	C₄	#11745345	1	1	yes	characteristic
93	C₄	C₂×#90800	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#14272184	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745345
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂×M₁₆×C₂₉	C₄
socle	C₂×C₂₉	#432
prime radical	C₂³×C₂₉	M₁₆
cosocle	C₂×#6597	C₂³
hypercenter	C₂×M₁₆	#1181
hypocenter	C₂₉	#2165
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. #14272085	C₂	semidirect
3. #14272056	C₂	semidirect
61. C₂₉	#2165	semidirect

Maximal subgroups

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

subgroup	index
#14272085	2
#14272059	2
#14272056	2
M₁₆×Dic₂₉	2
#2165	29