Subgroups — C₂×C₈×#6597 #16817765

Order 3712.

280 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	C₈×#6597	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	C₄	1	2	yes	—
5	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²×#6597	C₄	1	4	yes	—
7	C₄×C₈×C₂₉	C₄	1	2	yes	—
8	C₄×C₈×C₂₉	C₂²	1	2	yes	—
9	C₄×#6597	C₄	1	4	yes	—
10	C₄×#6597	C₂²	1	4	yes	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₂₉	C₈	1	8	yes	complemented
14	C₂×C₈×C₂₉	C₂×C₄	1	4	yes	—
15	C₄²×C₂₉	C₂×C₄	1	2	yes	—
16	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×#6597	C₈	1	16	yes	direct product factor
19	C₂×#6597	C₂×C₄	1	8	yes	—
20	C₂³×C₂₉	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₄²	1	2	yes	—
23	C₂×C₄×C₂₉	C₂×C₈	1	8	yes	—
24	C₂×C₄×C₂₉	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
26	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₈×C₂₉	C₂×C₈	1	8	yes	complemented
28	#6597	C₂×C₈	1	16	yes	direct product factor
29	C₂×C₈²	—	29	1	no	maximal, Sylow
30	C₂²×C₂₉	C₄×C₈	1	2	yes	—
31	C₂²×C₂₉	C₄×C₈	1	4	yes	—
32	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
33	C₄×C₂₉	C₄×C₈	1	2	yes	—
34	C₄×C₂₉	C₄×C₈	1	4	yes	—
35	C₄×C₂₉	C₂²×C₈	1	2	yes	—
36	C₄×C₂₉	C₂²×C₈	1	4	yes	—
37	C₂×C₄×C₈	—	29	2	no	—
38	C₂×C₄×C₈	D₂₉	1	1	yes	characteristic
39	C₈²	—	29	4	no	—
40	C₂×C₂₉	C₈²	1	4	yes	complemented
41	C₂×C₂₉	C₂×C₄×C₈	1	2	yes	—
42	C₂×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
43	C₂²×C₈	—	29	4	no	—
44	C₂²×C₈	Dic₂₉	1	2	yes	—
45	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
46	C₄×C₈	—	29	4	no	—
47	C₄×C₈	—	29	4	no	—
48	C₄×C₈	Dic₂₉	1	2	yes	—
49	C₄×C₈	C₂×D₂₉	1	2	yes	—
50	C₂₉	C₂×C₈²	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₄	C₄×D₂₉	1	2	yes	—
52	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
53	C₂×C₈	—	29	16	no	—
54	C₂×C₈	—	29	8	no	—
55	C₂×C₈	#6597	1	8	yes	direct product factor
56	C₂×C₈	C₂×Dic₂₉	1	4	yes	—
57	C₄²	C₄×D₂₉	1	2	yes	—
58	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
59	C₄²	C₂²×D₂₉	1	1	yes	characteristic
60	C₂³	C₄×Dic₂₉	1	1	yes	characteristic
61	C₂×C₄	C₈×D₂₉	1	8	yes	—
62	C₂×C₄	C₂×#6597	1	4	yes	—
63	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
64	C₂×C₄	C₄×Dic₂₉	1	2	yes	—
65	C₂×C₄	C₂×C₄×D₂₉	1	2	yes	—
66	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
67	C₈	—	29	16	no	—
68	C₈	C₂×#6597	1	8	yes	direct product factor
69	C₂²	C₄×#6597	1	2	yes	—
70	C₂²	C₈×Dic₂₉	1	4	yes	—
71	C₂²	C₂×C₄×Dic₂₉	1	1	yes	characteristic
72	C₄	C₄×#6597	1	2	yes	—
73	C₄	C₈×Dic₂₉	1	4	yes	—
74	C₄	C₂×C₈×D₂₉	1	4	yes	—
75	C₄	C₂²×#6597	1	2	yes	—
76	C₂	C₈×#6597	1	4	yes	direct product factor
77	C₂	C₂×C₈×Dic₂₉	1	2	yes	—
78	C₂	C₂×C₄×#6597	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₈×#6597	C₂	direct (N × H)
13. C₂×C₈×C₂₉	C₈	semidirect
18. C₂×#6597	C₈	direct (N × H)
27. C₈×C₂₉	C₂×C₈	semidirect
28. #6597	C₂×C₈	direct (N × H)
40. C₂×C₂₉	C₈²	semidirect
50. C₂₉	C₂×C₈²	semidirect
55. C₂×C₈	#6597	direct (N × H)
68. C₈	C₂×#6597	direct (N × H)
76. C₂	C₈×#6597	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×#6597	2
C₈×#6597	2
C₂×C₄×C₈×C₂₉	2
C₂×C₈²	29

Subgroups — C2×C8×#6597 #16817765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#6597 #16817765