Subgroups — #16832595

Order 3712.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271580	C₂	1	8	yes	maximal, complemented
2	C₂×#11745160	C₂	1	6	yes	maximal, complemented
3	C₂×C₂₉×#131	C₂	1	1	yes	maximal, characteristic
4	C₂×#41×C₂₉	C₄	1	1	yes	characteristic
5	C₂₉×#131	C₄	1	4	yes	—
6	C₂₉×#131	C₂²	1	4	yes	—
7	C₂×M₁₆×C₂₉	C₄	1	3	yes	—
8	C₂²×C₈×C₂₉	C₂²	1	3	yes	—
9	#11745160	C₂²	1	4	yes	—
10	#11745160	C₂²	1	12	yes	complemented
11	C₂×#90768	C₂²	1	12	yes	complemented
12	#41×C₂₉	C₈	1	4	yes	—
13	#41×C₂₉	C₂×C₄	1	4	yes	—
14	C₂×Q₈×C₂₉	C₈	1	1	yes	characteristic
15	C₂×D₄×C₂₉	C₈	1	3	yes	—
16	C₂²×C₄×C₂₉	C₂×C₄	1	3	yes	—
17	M₁₆×C₂₉	C₂×C₄	1	12	yes	—
18	C₂×C₈×C₂₉	C₂×C₄	1	3	yes	—
19	C₂×C₈×C₂₉	C₂×C₄	1	6	yes	—
20	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₂₉	C₂³	1	6	yes	—
22	#90768	C₂³	1	8	yes	—
23	C₂³×C₂₉	C₂×C₈	1	3	yes	—
24	Q₈×C₂₉	C₂×C₈	1	4	yes	—
25	D₄×C₂₉	C₂×C₈	1	12	yes	—
26	C₂×C₄×C₂₉	C₂×C₈	1	3	yes	—
27	C₂×C₄×C₂₉	C₂×C₈	1	6	yes	—
28	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂²×C₄	1	6	yes	—
30	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₈×C₂₉	C₂²×C₄	1	6	yes	—
32	C₈×C₂₉	C₂⁴	1	1	yes	characteristic
33	#3407	—	29	1	no	maximal, Sylow
34	C₂²×C₂₉	—	4	3	no	—
35	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
36	C₂²×C₂₉	C₂²×C₈	1	6	yes	—
37	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
38	C₄×C₂₉	C₂²×C₈	1	6	yes	—
39	C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
40	C₂×#131	D₂₉	1	1	yes	characteristic
41	#504	—	29	8	no	—
42	C₂×M₃₂	—	29	6	no	—
43	C₂×C₂₉	—	2	1	no	—
44	C₂×C₂₉	—	2	6	no	—
45	C₂×C₂₉	C₂³×C₈	1	1	yes	characteristic
46	C₂×#41	Dic₂₉	1	1	yes	characteristic
47	#131	Dic₂₉	1	4	yes	—
48	#131	C₂×D₂₉	1	4	yes	—
49	C₂×M₁₆	Dic₂₉	1	3	yes	—
50	C₂²×C₈	C₂×D₂₉	1	3	yes	—
51	M₃₂	—	29	4	no	—
52	M₃₂	—	29	12	no	—
53	C₂×C₁₆	—	29	12	no	—
54	C₂₉	#3407	1	1	yes	characteristic, complemented, Sylow
55	#41	#6597	1	4	yes	—
56	#41	C₂×Dic₂₉	1	4	yes	—
57	C₂×Q₈	#6597	1	1	yes	characteristic
58	C₂×D₄	#6597	1	3	yes	—
59	C₂²×C₄	C₂×Dic₂₉	1	3	yes	—
60	M₁₆	C₂×Dic₂₉	1	12	yes	—
61	C₂×C₈	C₂×Dic₂₉	1	3	yes	—
62	C₂×C₈	C₂×Dic₂₉	1	6	yes	—
63	C₂×C₈	C₂²×D₂₉	1	6	yes	—
64	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
65	C₁₆	—	29	8	no	—
66	C₂³	C₂×#6597	1	3	yes	—
67	Q₈	C₂×#6597	1	4	yes	—
68	D₄	C₂×#6597	1	12	yes	—
69	C₂×C₄	C₂×#6597	1	3	yes	—
70	C₂×C₄	C₂×#6597	1	6	yes	—
71	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
72	C₂×C₄	C₂²×Dic₂₉	1	6	yes	—
73	C₈	C₂²×Dic₂₉	1	1	yes	characteristic
74	C₈	C₂²×Dic₂₉	1	6	yes	—
75	C₈	C₂³×D₂₉	1	1	yes	characteristic
76	C₂²	—	4	3	no	—
77	C₂²	C₂²×#6597	1	1	yes	characteristic
78	C₂²	C₂²×#6597	1	6	yes	—
79	C₄	C₂²×#6597	1	1	yes	characteristic
80	C₄	C₂²×#6597	1	6	yes	—
81	C₄	C₂³×Dic₂₉	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	2	6	no	—
84	C₂	C₂³×#6597	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂³×D₂₉
commutator, socle	C₂×C₂₉	C₂³×C₈
Fitting	C₂×C₂₉×#131	C₂
prime radical	C₂×#41×C₂₉	C₄
cosocle	C₈×C₂₉	C₂⁴
hypercenter	C₂×#131	D₂₉
hypocenter	C₂₉	#3407
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. #14271580	C₂	semidirect
2. C₂×#11745160	C₂	semidirect
10. #11745160	C₂²	semidirect
11. C₂×#90768	C₂²	semidirect
54. C₂₉	#3407	semidirect

Maximal subgroups

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

subgroup	index
#14271580	2
C₂×#11745160	2
C₂×C₂₉×#131	2
#3407	29