Subgroups — #16817325

Order 3712.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271216	C₂	1	2	yes	maximal
2	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₉	—	2	2	no	—
4	C₂×C₄²×C₂₉	C₄	1	2	yes	—
5	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²⋊#6597	—	2	2	no	—
7	C₄⋊#6597	C₄	1	4	yes	complemented
8	C₄×#6597	—	2	2	no	—
9	C₂²×C₄×C₂₉	—	2	2	no	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₉	D₄	1	2	yes	—
12	C₄²×C₂₉	—	2	8	no	—
13	C₄²×C₂₉	—	2	2	no	—
14	C₄²×C₂₉	C₈	1	4	yes	complemented
15	C₄²×C₂₉	C₂×C₄	1	2	yes	—
16	C₄²×C₂₉	D₄	1	1	yes	characteristic
17	C₄²×C₂₉	Q₈	1	1	yes	characteristic
18	C₂×#6597	—	2	4	no	—
19	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	—	2	8	no	—
21	C₂×C₄×C₂₉	—	2	4	no	—
22	C₂×C₄×C₂₉	—	2	4	no	—
23	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
28	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
29	#6597	—	4	4	no	—
30	#1276	—	29	1	no	maximal, Sylow
31	C₂²×C₂₉	—	2	2	no	—
32	C₂²×C₂₉	#95	1	1	yes	characteristic
33	C₂²×C₂₉	C₂²⋊C₈	1	2	yes	—
34	C₄×C₂₉	—	2	8	no	—
35	C₄×C₂₉	—	2	2	no	—
36	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
37	C₄×C₂₉	#97	1	1	yes	characteristic
38	C₄×C₂₉	#104	1	4	yes	—
39	C₄×C₂₉	C₄⋊C₈	1	2	yes	—
40	#431	—	29	2	no	—
41	C₄³	D₂₉	1	1	yes	characteristic
42	C₂×C₂₉	—	2	2	no	—
43	C₂×C₂₉	#336	1	1	yes	characteristic
44	C₂×C₂₉	#339	1	2	yes	—
45	C₂×C₄²	—	2	2	no	—
46	C₂×C₄²	Dic₂₉	1	2	yes	—
47	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
48	C₄⋊C₈	—	29	4	no	—
49	C₂²⋊C₈	—	58	2	no	—
50	C₄×C₈	—	58	2	no	—
51	C₂₉	#1276	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₄	—	2	2	no	—
53	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
54	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
55	C₂×C₈	—	58	4	no	—
56	C₄²	—	2	8	no	—
57	C₄²	—	2	2	no	—
58	C₄²	#6597	1	4	yes	complemented
59	C₄²	Dic₅₈	1	1	yes	characteristic
60	C₄²	C₄×D₂₉	1	2	yes	—
61	C₄²	D₁₁₆	1	1	yes	characteristic
62	C₂³	C₂²⋊Dic₂₉	1	1	yes	characteristic
63	C₂×C₄	—	2	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₂×#6597	1	2	yes	—
67	C₂×C₄	#90777	1	2	yes	—
68	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
69	C₂×C₄	#90779	1	2	yes	—
70	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
71	C₂×C₄	#90781	1	2	yes	—
72	C₈	—	116	4	no	—
73	C₂²	—	2	2	no	—
74	C₂²	C₂²⋊#6597	1	2	yes	—
75	C₂²	#11745179	1	1	yes	characteristic
76	C₄	—	2	8	no	—
77	C₄	—	2	2	no	—
78	C₄	C₄×#6597	1	1	yes	characteristic
79	C₄	#11745151	1	1	yes	characteristic
80	C₄	C₄⋊#6597	1	2	yes	—
81	C₄	#11745153	1	4	yes	—
82	C₂	—	2	2	no	—
83	C₂	#14270918	1	1	yes	characteristic
84	C₂	#14270923	1	2	yes	—

	subgroup	G/H
center	C₄²	D₁₁₆
commutator	C₄×C₂₉	C₄×C₈
Frattini	C₂×C₄²	C₂×D₂₉
Fitting	C₄³×C₂₉	C₂
socle	C₂²×C₂₉	#95
prime radical	C₂³×C₂₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₂₉	C₂²
hypercenter	C₄³	D₂₉
hypocenter	C₂₉	#1276
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄³

Complements

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

N	H ≅ G/N	type
7. C₄⋊#6597	C₄	semidirect
14. C₄²×C₂₉	C₈	semidirect
51. C₂₉	#1276	semidirect
58. C₄²	#6597	semidirect

Maximal subgroups

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

subgroup	index
#14271216	2
C₄³×C₂₉	2
#1276	29