Subgroups — #16817319

Order 3712.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6597	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₉	C₄	1	2	yes	—
4	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
5	C₂²×#6597	C₄	1	4	yes	—
6	C₄×C₈×C₂₉	—	2	2	no	—
7	C₄×#6597	—	2	2	no	—
8	C₄×#6597	—	2	2	no	—
9	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₂₉	—	2	2	no	—
12	C₂×C₈×C₂₉	—	2	2	no	—
13	C₂×C₈×C₂₉	C₈	1	4	yes	complemented
14	C₄²×C₂₉	D₄	1	1	yes	characteristic
15	C₄²×C₂₉	D₄	1	2	yes	—
16	C₄²×C₂₉	Q₈	1	1	yes	characteristic
17	C₂×#6597	—	2	4	no	—
18	C₂×#6597	—	2	4	no	—
19	C₂×#6597	C₈	1	8	yes	complemented
20	C₂³×C₂₉	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
26	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₉	M₁₆	1	4	yes	—
28	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
29	C₈×C₂₉	—	2	4	no	—
30	#6597	—	2	8	no	—
31	#1273	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	#95	1	1	yes	characteristic
33	C₂²×C₂₉	C₄×C₈	1	1	yes	characteristic
34	C₂²×C₂₉	C₄×C₈	1	2	yes	—
35	C₂²×C₂₉	#97	1	1	yes	characteristic
36	C₂²×C₂₉	#97	1	2	yes	—
37	C₄×C₂₉	C₂²⋊C₈	1	4	yes	—
38	C₄×C₂₉	C₂²⋊C₈	1	2	yes	—
39	C₄×C₂₉	C₄⋊C₈	1	2	yes	—
40	C₄×C₂₉	C₄⋊C₈	1	4	yes	—
41	C₂×C₄×C₈	—	29	2	no	—
42	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
43	C₂×C₂₉	C₈²	1	1	yes	characteristic
44	C₂×C₂₉	#322	1	1	yes	characteristic
45	C₂×C₂₉	#322	1	2	yes	—
46	C₂×C₂₉	#336	1	2	yes	—
47	C₂×C₂₉	#336	1	1	yes	characteristic
48	C₂²×C₈	—	29	4	no	—
49	C₂²×C₈	Dic₂₉	1	2	yes	—
50	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
51	C₄×C₈	—	2	2	no	—
52	C₄×C₈	—	58	2	no	—
53	C₄×C₈	—	58	2	no	—
54	C₂₉	#1273	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₄	C₄×D₂₉	1	2	yes	—
56	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	—	2	2	no	—
59	C₂×C₈	—	29	8	no	—
60	C₂×C₈	—	58	4	no	—
61	C₂×C₈	—	58	4	no	—
62	C₂×C₈	#6597	1	4	yes	complemented
63	C₄²	Dic₅₈	1	1	yes	characteristic
64	C₄²	D₁₁₆	1	1	yes	characteristic
65	C₄²	C₂²⋊D₂₉	1	2	yes	—
66	C₂³	C₄×Dic₂₉	1	1	yes	characteristic
67	C₂×C₄	C₈×D₂₉	1	4	yes	—
68	C₂×C₄	#90772	1	4	yes	—
69	C₂×C₄	C₂×#6597	1	2	yes	—
70	C₂×C₄	#90777	1	2	yes	—
71	C₂×C₄	#90779	1	2	yes	—
72	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
73	C₂×C₄	#90781	1	2	yes	—
74	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
75	C₈	—	2	4	no	—
76	C₈	—	58	8	no	—
77	C₂²	C₄×#6597	1	1	yes	characteristic
78	C₂²	#11745151	1	1	yes	characteristic
79	C₂²	C₈×Dic₂₉	1	2	yes	—
80	C₂²	#11745163	1	2	yes	—
81	C₂²	#11745179	1	1	yes	characteristic
82	C₄	C₄⋊#6597	1	2	yes	—
83	C₄	#11745162	1	4	yes	—
84	C₄	#11745168	1	4	yes	—
85	C₄	C₂²⋊#6597	1	2	yes	—
86	C₂	C₈×#6597	1	1	yes	characteristic
87	C₂	#14270884	1	1	yes	characteristic
88	C₂	#14270885	1	2	yes	—
89	C₂	#14270917	1	2	yes	—
90	C₂	#14270918	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂×D₂₉
commutator	C₂×C₂₉	C₈²
Fitting	C₂×C₄×C₈×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₄²
cosocle	C₂×C₄²×C₂₉	C₂²
hypercenter	C₂×C₄×C₈	D₂₉
hypocenter	C₂₉	#1273
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
13. C₂×C₈×C₂₉	C₈	semidirect
19. C₂×#6597	C₈	semidirect
54. C₂₉	#1273	semidirect
62. C₂×C₈	#6597	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#6597	2
C₂×C₄×C₈×C₂₉	2
#1273	29