Subgroups — C₂×#11745177 #14271590

Order 1856.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₁₆	C₂	1	1	yes	maximal, characteristic
3	#11745177	C₂	1	4	yes	maximal, direct product factor
4	C₂×#90768	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₉	—	2	1	no	—
6	C₂×Dic₅₈	—	2	1	no	—
7	Q₁₆×C₂₉	—	2	1	no	—
8	Q₁₆×C₂₉	C₂²	1	2	yes	—
9	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	Dic₁₁₆	—	2	1	no	—
11	Dic₁₁₆	C₂²	1	2	yes	—
12	#90768	C₂²	1	2	yes	—
13	Q₈×C₂₉	—	2	2	no	—
14	Q₈×C₂₉	—	4	1	no	—
15	C₂×C₄×C₂₉	—	4	1	no	—
16	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
17	C₂×Dic₂₉	—	4	1	no	—
18	Dic₅₈	—	2	2	no	—
19	Dic₅₈	—	4	1	no	—
20	C₈×C₂₉	D₄	1	1	yes	characteristic
21	C₈×C₂₉	C₂³	1	1	yes	characteristic
22	C₂²×C₂₉	D₈	1	1	yes	characteristic
23	C₄×C₂₉	—	4	2	no	—
24	C₄×C₂₉	D₈	1	1	yes	characteristic
25	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
26	Dic₂₉	—	4	2	no	—
27	C₂×Q₃₂	—	29	1	no	maximal, Sylow
28	C₂×C₂₉	Q₃₂	1	2	yes	complemented
29	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
30	C₂×Q₁₆	—	29	1	no	—
31	C₂×Q₁₆	D₂₉	1	1	yes	characteristic
32	Q₃₂	—	29	4	no	—
33	C₂×C₁₆	—	29	1	no	—
34	C₂₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	58	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	29	2	no	—
39	Q₁₆	—	58	1	no	—
40	Q₁₆	C₂×D₂₉	1	2	yes	—
41	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
42	C₁₆	—	29	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	58	2	no	—
46	Q₈	—	116	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	116	1	no	—
49	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
50	C₈	C₂²⋊D₂₉	1	1	yes	characteristic
51	C₈	C₂²×D₂₉	1	1	yes	characteristic
52	C₂²	#90782	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	116	2	no	—
55	C₄	#90782	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
57	C₂	#11745177	1	2	yes	direct product factor
58	C₂	C₂×#90782	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#90782
commutator, cosocle	C₈×C₂₉	C₂³
Frattini	C₈	C₂²×D₂₉
Fitting	C₂×Q₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	D₈
hypercenter	C₂×Q₁₆	D₂₉
hypocenter	C₂₉	C₂×Q₃₂
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #11745177	C₂	direct (N × H)
28. C₂×C₂₉	Q₃₂	semidirect
34. C₂₉	C₂×Q₃₂	semidirect
57. C₂	#11745177	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×Q₁₆×C₂₉	2
C₂×Dic₁₁₆	2
#11745177	2
C₂×#90768	2
C₂×Q₃₂	29

Subgroups — C2×#11745177 #14271590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745177 #14271590