Subgroups — C₂×#11745237 #14271680

Order 1856.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₅₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄²×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#90781	C₂	1	4	yes	maximal, complemented
5	#11745237	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₂₉	C₂²	1	2	yes	—
7	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
8	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₂₉	C₂²	1	2	yes	—
10	C₂×D₁₁₆	—	2	4	no	—
11	C₂×D₁₁₆	C₂²	1	4	yes	—
12	C₂×Dic₅₈	—	2	4	no	—
13	C₂×Dic₅₈	C₂²	1	4	yes	complemented
14	C₄²×C₂₉	C₂²	1	4	yes	complemented
15	#90781	C₂²	1	16	yes	complemented
16	C₂³×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×D₂₉	—	2	4	no	—
18	C₂²×D₂₉	—	2	8	no	—
19	C₂²×D₂₉	C₂³	1	4	yes	—
20	C₂×C₄×C₂₉	—	2	4	no	—
21	C₂×C₄×C₂₉	D₄	1	4	yes	—
22	C₂×C₄×C₂₉	C₂³	1	4	yes	—
23	C₂×C₄×C₂₉	C₂³	1	2	yes	—
24	C₂×Dic₂₉	—	2	4	no	—
25	C₂×Dic₂₉	C₂³	1	4	yes	—
26	D₁₁₆	—	2	8	no	—
27	Dic₅₈	—	2	8	no	—
28	C₂²×C₂₉	C₂×D₄	1	2	yes	—
29	C₂²×C₂₉	#41	1	4	yes	—
30	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
31	C₂×D₂₉	—	2	4	no	—
32	C₂×D₂₉	—	2	8	no	—
33	C₂×D₂₉	—	4	8	no	—
34	C₄×C₂₉	—	2	4	no	—
35	C₄×C₂₉	C₂×D₄	1	4	yes	—
36	Dic₂₉	—	2	4	no	—
37	C₂×#124	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	#124	1	4	yes	complemented
39	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
40	C₂×C₂₉	C₂×#41	1	2	yes	—
41	D₂₉	—	4	4	no	—
42	C₂²×Q₈	—	29	1	no	—
43	C₂²×D₄	—	29	1	no	—
44	#124	—	29	8	no	—
45	C₂×C₂²⋊C₄	—	29	4	no	—
46	C₂×C₄²	D₂₉	1	1	yes	characteristic, complemented
47	C₂₉	C₂×#124	1	1	yes	characteristic, complemented, Sylow
48	C₂⁴	—	29	2	no	—
49	C₂×Q₈	—	29	4	no	—
50	C₂×Q₈	—	58	4	no	—
51	C₂×D₄	—	29	4	no	—
52	C₂×D₄	—	58	4	no	—
53	C₂²×C₄	—	29	2	no	—
54	C₂²×C₄	C₂×D₂₉	1	2	yes	—
55	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
56	C₂²⋊C₄	—	29	16	no	—
57	C₄²	C₂×D₂₉	1	4	yes	complemented
58	C₂³	—	29	4	no	—
59	C₂³	—	58	4	no	—
60	C₂³	—	58	8	no	—
61	C₂³	C₂²×D₂₉	1	1	yes	characteristic
62	Q₈	—	58	8	no	—
63	D₄	—	58	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	29	4	no	—
66	C₂×C₄	—	58	4	no	—
67	C₂×C₄	D₁₁₆	1	4	yes	—
68	C₂×C₄	C₂²×D₂₉	1	4	yes	—
69	C₂×C₄	C₂²×D₂₉	1	2	yes	—
70	C₂²	—	58	4	no	—
71	C₂²	—	58	8	no	—
72	C₂²	—	116	8	no	—
73	C₂²	C₂×D₁₁₆	1	2	yes	—
74	C₂²	#90805	1	4	yes	—
75	C₂²	C₂³×D₂₉	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	58	4	no	—
78	C₄	C₂×D₁₁₆	1	4	yes	—
79	C₂	—	116	4	no	—
80	C₂	#11745237	1	4	yes	direct product factor
81	C₂	C₂²×D₁₁₆	1	1	yes	characteristic
82	C₂	C₂×#90805	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₂₉
commutator, cosocle	C₂²×C₂₉	C₂⁴
Frattini	C₂²	C₂³×D₂₉
Fitting	C₂×C₄²×C₂₉	C₂
socle	C₂³×C₂₉	C₂³
prime radical	C₂²×D₁₁₆	C₂
hypercenter	C₂×C₄²	D₂₉
hypocenter	C₂₉	C₂×#124
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₅₈	C₂	semidirect
3. C₂×C₄²×C₂₉	C₂	semidirect
4. C₂×#90781	C₂	semidirect
5. #11745237	C₂	direct (N × H)
13. C₂×Dic₅₈	C₂²	semidirect
14. C₄²×C₂₉	C₂²	semidirect
15. #90781	C₂²	semidirect
38. C₂×C₂₉	#124	semidirect
46. C₂×C₄²	D₂₉	semidirect
47. C₂₉	C₂×#124	semidirect
57. C₄²	C₂×D₂₉	semidirect
80. C₂	#11745237	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₁₆	2
C₂²×Dic₅₈	2
C₂×C₄²×C₂₉	2
C₂×#90781	2
#11745237	2
C₂×#124	29

Subgroups — C2×#11745237 #14271680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745237 #14271680