Subgroups — C₂×#11745348 #14272240

Order 1856.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90809	C₂	1	1	yes	maximal, characteristic
2	#11745348	C₂	1	8	yes	maximal, direct product factor
3	C₂×#90796	C₂	1	3	yes	maximal, complemented
4	C₂×D₂₉⋊C₈	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic
6	#90809	C₄	1	4	yes	—
7	#90809	C₂²	1	4	yes	—
8	C₂×D₁₁₆	C₄	1	3	yes	—
9	C₂×C₄×D₂₉	C₂²	1	3	yes	—
10	C₂×#6599	C₂²	1	1	yes	characteristic
11	C₂×#6599	C₂²	1	3	yes	—
12	#90796	C₂²	1	12	yes	complemented
13	D₂₉⋊C₈	C₂²	1	12	yes	complemented
14	C₂²×D₂₉	C₂×C₄	1	3	yes	—
15	Q₈×C₂₉	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
17	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
18	D₁₁₆	C₂×C₄	1	12	yes	—
19	C₄×D₂₉	C₂×C₄	1	6	yes	—
20	C₄×D₂₉	C₂³	1	6	yes	—
21	#6599	C₂³	1	2	yes	—
22	#6599	C₂³	1	6	yes	—
23	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₂₉	—	2	6	no	—
25	C₂×D₂₉	C₂²×C₄	1	6	yes	—
26	C₄×C₂₉	C₂²×C₄	1	6	yes	—
27	Dic₂₉	C₂²×C₄	1	1	yes	characteristic
28	Dic₂₉	C₂⁴	1	1	yes	characteristic
29	C₂×#131	—	29	1	no	maximal, Sylow
30	C₂×C₂₉	#131	1	2	yes	complemented
31	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
32	D₂₉	—	2	6	no	—
33	C₂×#41	—	29	1	no	—
34	#131	—	29	8	no	—
35	C₂×M₁₆	—	29	3	no	—
36	C₂²×C₈	—	29	3	no	—
37	C₂₉	C₂×#131	1	1	yes	characteristic, complemented, Sylow
38	#41	—	29	4	no	—
39	#41	—	29	4	no	—
40	C₂×Q₈	#1181	1	1	yes	characteristic
41	C₂×D₄	—	29	3	no	—
42	C₂²×C₄	—	29	3	no	—
43	M₁₆	—	29	12	no	—
44	C₂×C₈	—	29	1	no	—
45	C₂×C₈	—	29	3	no	—
46	C₂×C₈	—	29	12	no	—
47	C₂³	—	29	3	no	—
48	Q₈	C₂×#1181	1	4	yes	—
49	D₄	—	29	12	no	—
50	C₂×C₄	—	29	1	no	—
51	C₂×C₄	—	29	6	no	—
52	C₂×C₄	—	29	6	no	—
53	C₂×C₄	C₂×#1181	1	3	yes	—
54	C₈	—	29	2	no	—
55	C₈	—	29	6	no	—
56	C₂²	—	29	6	no	—
57	C₂²	—	58	6	no	—
58	C₂²	C₂²×#1181	1	1	yes	characteristic
59	C₄	—	29	1	no	—
60	C₄	—	29	1	no	—
61	C₄	C₂²×#1181	1	6	yes	—
62	C₂	—	58	6	no	—
63	C₂	#11745348	1	2	yes	direct product factor
64	C₂	C₂³×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#1181
commutator	C₂×C₂₉	C₂³×C₄
Frattini	C₂	C₂³×#1181
Fitting	C₂×Q₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂²×C₄
prime radical	C₂×#90809	C₂
cosocle	Dic₂₉	C₂⁴
hypercenter	C₂×Q₈	#1181
hypocenter	C₂₉	C₂×#131
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #11745348	C₂	direct (N × H)
3. C₂×#90796	C₂	semidirect
4. C₂×D₂₉⋊C₈	C₂	semidirect
12. #90796	C₂²	semidirect
13. D₂₉⋊C₈	C₂²	semidirect
30. C₂×C₂₉	#131	semidirect
37. C₂₉	C₂×#131	semidirect
63. C₂	#11745348	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×#90809	2
#11745348	2
C₂×#90796	2
C₂×D₂₉⋊C₈	2
C₂×#131	29

Subgroups — C2×#11745348 #14272240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745348 #14272240