Subgroups — C₂×C₈×#6599 #16834683

Order 3712.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6599	C₂	1	2	yes	maximal
2	C₈×#6599	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6599	C₄	1	4	yes	—
5	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
7	C₂²×#6597	C₄	1	1	yes	characteristic
8	C₄×#6599	C₄	1	4	yes	—
9	C₄×#6599	C₂²	1	4	yes	—
10	C₈×Dic₂₉	C₄	1	2	yes	—
11	C₈×Dic₂₉	C₂²	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
14	C₂×#6599	C₈	1	16	yes	direct product factor
15	C₂×#6599	C₂×C₄	1	8	yes	—
16	C₂×C₈×C₂₉	C₈	1	4	yes	complemented
17	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
18	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
21	C₂×#6597	C₈	1	4	yes	complemented
22	C₂×#6597	C₂×C₄	1	2	yes	—
23	C₂³×C₂₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₂₉	C₄²	1	2	yes	—
29	C₂×Dic₂₉	C₂×C₈	1	8	yes	—
30	C₂×Dic₂₉	C₂²×C₄	1	2	yes	—
31	#6599	C₂×C₈	1	16	yes	direct product factor
32	C₈×C₂₉	C₂×C₈	1	4	yes	complemented
33	#6597	C₂×C₈	1	4	yes	complemented
34	C₂×C₈²	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	C₄×C₈	1	4	yes	—
36	C₂²×C₂₉	C₄×C₈	1	2	yes	—
37	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
38	C₄×C₂₉	C₄×C₈	1	2	yes	—
39	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
41	Dic₂₉	C₄×C₈	1	4	yes	—
42	Dic₂₉	C₂²×C₈	1	4	yes	—
43	C₂×C₄×C₈	—	29	2	no	—
44	C₂×C₄×C₈	—	29	1	no	—
45	C₈²	—	29	4	no	—
46	C₂×C₂₉	C₈²	1	4	yes	complemented
47	C₂×C₂₉	C₂×C₄×C₈	1	2	yes	—
48	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂²×C₈	—	29	4	no	—
50	C₂²×C₈	—	29	1	no	—
51	C₂²×C₈	#1181	1	1	yes	characteristic
52	C₂×C₄²	—	29	1	no	—
53	C₄×C₈	—	29	4	no	—
54	C₄×C₈	—	29	4	no	—
55	C₄×C₈	—	29	2	no	—
56	C₄×C₈	—	29	2	no	—
57	C₂₉	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	29	2	no	—
59	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
60	C₂×C₈	—	29	8	no	—
61	C₂×C₈	—	29	16	no	—
62	C₂×C₈	—	29	4	no	—
63	C₂×C₈	—	29	2	no	—
64	C₂×C₈	#6599	1	4	yes	direct product factor
65	C₂×C₈	C₂×#1181	1	2	yes	—
66	C₄²	—	29	2	no	—
67	C₄²	—	29	1	no	—
68	C₄²	—	29	1	no	—
69	C₂³	C₄×#1181	1	1	yes	characteristic
70	C₂×C₄	—	29	2	no	—
71	C₂×C₄	—	29	2	no	—
72	C₂×C₄	—	29	8	no	—
73	C₂×C₄	D₂₉⋊C₈	1	2	yes	—
74	C₂×C₄	C₄×#1181	1	1	yes	characteristic
75	C₂×C₄	C₂×#6599	1	2	yes	—
76	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
77	C₈	—	29	16	no	—
78	C₈	—	29	4	no	—
79	C₈	C₂×#6599	1	4	yes	direct product factor
80	C₂²	C₈×#1181	1	4	yes	—
81	C₂²	C₄×#6599	1	2	yes	—
82	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
83	C₄	—	29	4	no	—
84	C₄	—	29	4	no	—
85	C₄	C₄×#6599	1	2	yes	—
86	C₄	C₂×D₂₉⋊C₈	1	1	yes	characteristic
87	C₄	C₂²×#6599	1	1	yes	characteristic
88	C₂	C₈×#6599	1	4	yes	direct product factor
89	C₂	C₂×C₈×#1181	1	2	yes	—
90	C₂	C₂×C₄×#6599	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	#1181
commutator, hypocenter	C₂₉	C₂×C₈²
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂²×C₈×C₂₉	C₄
socle, prime radical	C₂³×C₂₉	C₄²
cosocle	C₄×Dic₂₉	C₂³
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₈×#6599	C₂	direct (N × H)
14. C₂×#6599	C₈	direct (N × H)
16. C₂×C₈×C₂₉	C₈	semidirect
21. C₂×#6597	C₈	semidirect
31. #6599	C₂×C₈	direct (N × H)
32. C₈×C₂₉	C₂×C₈	semidirect
33. #6597	C₂×C₈	semidirect
46. C₂×C₂₉	C₈²	semidirect
57. C₂₉	C₂×C₈²	semidirect
64. C₂×C₈	#6599	direct (N × H)
79. C₈	C₂×#6599	direct (N × H)
88. C₂	C₈×#6599	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#6599	2
C₈×#6599	2
C₂×C₈×Dic₂₉	2
C₂×C₈²	29

Subgroups — C2×C8×#6599 #16834683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#6599 #16834683