Subgroups — #16817442

Order 3712.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271186	C₂	1	1	yes	maximal, characteristic
2	#14270945	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#349	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
6	C₂×#90777	C₄	1	1	yes	characteristic
7	C₂₉×M₃₂	—	2	1	no	—
8	#11745162	—	2	1	no	—
9	#11745162	—	2	1	no	—
10	#11745160	—	2	1	no	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₂₉	—	2	1	no	—
13	M₁₆×C₂₉	—	4	1	no	—
14	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₄×Dic₂₉	—	2	1	no	—
17	C₄×Dic₂₉	C₈	1	1	yes	characteristic
18	C₄×Dic₂₉	C₈	1	1	yes	characteristic
19	#90777	—	4	1	no	—
20	C₂×#6597	—	2	1	no	—
21	C₁₆×C₂₉	—	4	1	no	—
22	#90768	—	4	1	no	—
23	C₂³×C₂₉	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₂₉	—	2	1	no	—
25	C₂×C₄×C₂₉	—	2	1	no	—
26	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₂₉	—	2	1	no	—
29	C₂×Dic₂₉	—	2	1	no	—
30	C₂×Dic₂₉	—	4	2	no	—
31	C₈×C₂₉	—	2	1	no	—
32	C₈×C₂₉	—	2	1	no	—
33	#6597	—	4	1	no	—
34	#1327	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	—	2	1	no	—
36	C₂²×C₂₉	—	4	1	no	—
37	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₄×C₂₉	—	2	1	no	—
39	C₄×C₂₉	#99	1	1	yes	characteristic
40	C₄×C₂₉	#101	1	1	yes	characteristic
41	Dic₂₉	—	2	2	no	—
42	Dic₂₉	—	4	1	no	—
43	#423	—	29	1	no	—
44	#349	—	29	1	no	—
45	#349	D₂₉	1	1	yes	characteristic
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	—	4	1	no	—
48	C₂×C₂₉	#324	1	1	yes	characteristic
49	C₂×M₁₆	—	29	1	no	—
50	C₂×M₁₆	C₂×D₂₉	1	1	yes	characteristic
51	C₂×C₄²	—	29	1	no	—
52	M₃₂	—	2	1	no	—
53	M₃₂	—	58	1	no	—
54	C₄⋊C₈	—	58	1	no	—
55	C₄⋊C₈	—	58	1	no	—
56	C₂₉	#1327	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₄	—	58	1	no	—
58	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
59	M₁₆	—	4	1	no	—
60	M₁₆	—	116	1	no	—
61	C₂×C₈	—	58	1	no	—
62	C₂×C₈	D₁₁₆	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₂₉	1	1	yes	characteristic
64	C₄²	—	29	1	no	—
65	C₄²	—	29	1	no	—
66	C₄²	—	58	1	no	—
67	C₁₆	—	4	1	no	—
68	C₁₆	—	116	1	no	—
69	C₂³	#90772	1	1	yes	characteristic
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	58	1	no	—
73	C₂×C₄	—	58	1	no	—
74	C₂×C₄	—	116	2	no	—
75	C₂×C₄	C₈×D₂₉	1	1	yes	characteristic
76	C₂×C₄	#90781	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	116	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	#11745168	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	58	2	no	—
85	C₄	—	116	1	no	—
86	C₄	#11745154	1	1	yes	characteristic
87	C₄	#11745172	1	1	yes	characteristic
88	C₂	—	2	1	no	—
89	C₂	—	4	1	no	—
90	C₂	#14270888	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745154
commutator	C₂×C₄×C₂₉	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₂₉
Fitting	C₂₉×#349	C₂
socle	C₂×C₂₉	#324
prime radical	C₂³×C₂₉	M₁₆
cosocle	C₂×M₁₆×C₂₉	C₂²
hypercenter	#349	D₂₉
hypocenter	C₂₉	#1327
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
56. C₂₉	#1327	semidirect

Maximal subgroups

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

subgroup	index
#14271186	2
#14270945	2
C₂₉×#349	2
#1327	29