Subgroups — #16817436

Order 3712.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14270889	C₂	1	2	yes	maximal
2	C₂₉×#382	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
6	C₂₉×#95	—	2	2	no	—
7	C₂²⋊#6597	—	2	2	no	—
8	C₂²×C₄×C₂₉	—	2	1	no	—
9	C₂²×C₄×C₂₉	—	2	1	no	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₉	D₄	1	2	yes	—
12	C₄⋊C₄×C₂₉	—	4	1	no	—
13	C₄⋊C₄×C₂₉	—	4	1	no	—
14	C₄²×C₂₉	—	2	1	no	—
15	C₄²×C₂₉	C₈	1	2	yes	complemented
16	C₂×#6597	—	4	2	no	—
17	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	1	no	—
19	C₂×C₄×C₂₉	—	2	1	no	—
20	C₂×C₄×C₂₉	—	2	2	no	—
21	C₂×C₄×C₂₉	—	2	2	no	—
22	C₂×C₄×C₂₉	—	4	1	no	—
23	C₂×C₄×C₂₉	—	4	1	no	—
24	C₂×C₄×C₂₉	—	4	2	no	—
25	C₂×C₄×C₂₉	—	4	2	no	—
26	C₂×C₄×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
29	#6597	—	8	2	no	—
30	#1324	—	29	1	no	maximal, Sylow
31	C₂²×C₂₉	—	2	1	no	—
32	C₂²×C₂₉	—	2	1	no	—
33	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
34	C₂²×C₂₉	#99	1	1	yes	characteristic
35	C₂²×C₂₉	#101	1	1	yes	characteristic
36	C₄×C₂₉	—	2	1	no	—
37	C₄×C₂₉	—	2	1	no	—
38	C₄×C₂₉	—	4	2	no	—
39	C₄×C₂₉	—	4	2	no	—
40	C₄×C₂₉	—	8	1	no	—
41	#382	D₂₉	1	1	yes	characteristic
42	#324	—	29	2	no	—
43	C₂×C₂₉	—	2	1	no	—
44	C₂×C₂₉	—	2	1	no	—
45	C₂×C₂₉	#324	1	1	yes	characteristic
46	C₂×C₂₉	#354	1	1	yes	characteristic
47	C₂×C₂₉	#355	1	1	yes	characteristic
48	C₂×C₄⋊C₄	Dic₂₉	1	1	yes	characteristic
49	C₂×C₄⋊C₄	C₂×D₂₉	1	1	yes	characteristic
50	C₂×C₄²	Dic₂₉	1	1	yes	characteristic
51	C₂²⋊C₈	—	58	2	no	—
52	#95	—	2	2	no	—
53	C₂₉	#1324	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	—	2	1	no	—
56	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
57	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
58	C₂×C₈	—	116	2	no	—
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄²	—	2	1	no	—
62	C₄²	#6597	1	2	yes	complemented
63	C₂³	C₂²⋊Dic₂₉	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	4	2	no	—
72	C₂×C₄	—	4	1	no	—
73	C₂×C₄	C₂×#6597	1	1	yes	characteristic
74	C₂×C₄	#90777	1	1	yes	characteristic
75	C₈	—	232	2	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	C₂²⋊#6597	1	1	yes	characteristic
79	C₂²	#11745182	1	1	yes	characteristic
80	C₂²	#11745184	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	4	2	no	—
84	C₄	—	4	2	no	—
85	C₄	—	8	1	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	#14270889	1	1	yes	characteristic
89	C₂	#14270958	1	1	yes	characteristic
90	C₂	#14270960	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745182
commutator	C₂×C₄×C₂₉	C₂×C₈
Frattini	C₂×C₄⋊C₄	C₂×D₂₉
Fitting	C₂₉×#382	C₂
socle	C₂²×C₂₉	#99
prime radical	C₂³×C₂₉	C₂²⋊C₄
cosocle	C₂×C₄⋊C₄×C₂₉	C₂²
hypercenter	#382	D₂₉
hypocenter	C₂₉	#1324
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #382

Complements

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

N	H ≅ G/N	type
15. C₄²×C₂₉	C₈	semidirect
53. C₂₉	#1324	semidirect
62. C₄²	#6597	semidirect

Maximal subgroups

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

subgroup	index
#14270889	2
C₂₉×#382	2
#1324	29