Subgroups — #14270977

Order 1856.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₁₆	—	2	1	no	—
5	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	#90777	—	2	1	no	—
7	D₂₃₂	—	2	1	no	—
8	D₂₃₂	C₄	1	2	yes	—
9	C₁₆×C₂₉	—	2	1	no	—
10	C₂²×D₂₉	—	4	1	no	—
11	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
12	D₁₁₆	—	2	2	no	—
13	D₁₁₆	—	4	1	no	—
14	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₂₉	D₄	1	1	yes	characteristic
16	#6597	—	4	1	no	—
17	C₂²×C₂₉	SD₁₆	1	1	yes	characteristic
18	C₂×D₂₉	—	4	2	no	—
19	C₂×D₂₉	—	8	2	no	—
20	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₉	D₈	1	1	yes	characteristic
22	#361	—	29	1	no	maximal, Sylow
23	C₂×C₂₉	—	2	1	no	—
24	C₂×C₂₉	#102	1	1	yes	characteristic
25	D₂₉	—	8	2	no	—
26	C₂×D₈	—	29	1	no	—
27	M₃₂	D₂₉	1	1	yes	characteristic, complemented
28	#108	—	29	1	no	—
29	C₂₉	#361	1	1	yes	characteristic, complemented, Sylow
30	C₂×D₄	—	58	1	no	—
31	D₈	—	29	2	no	—
32	D₈	—	58	1	no	—
33	M₁₆	—	58	1	no	—
34	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	116	1	no	—
37	D₄	—	58	2	no	—
38	D₄	—	116	1	no	—
39	C₂×C₄	D₁₁₆	1	1	yes	characteristic
40	C₈	—	116	1	no	—
41	C₈	C₄×D₂₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₂₉	1	1	yes	characteristic
43	C₂²	—	116	2	no	—
44	C₂²	—	232	2	no	—
45	C₂²	#90773	1	1	yes	characteristic
46	C₄	D₂₃₂	1	1	yes	characteristic
47	C₄	#90781	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	232	2	no	—
50	C₂	#11745169	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11745169
commutator	C₈×C₂₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₉
Fitting	C₂₉×M₃₂	C₂
socle	C₂×C₂₉	#102
prime radical	C₂×D₂₃₂	C₂
cosocle	C₂×C₈×C₂₉	C₂²
hypercenter	M₃₂	D₂₉
hypocenter	C₂₉	#361
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂₉×M₃₂	C₂	semidirect
3. #11745167	C₂	semidirect
27. M₃₂	D₂₉	semidirect
29. C₂₉	#361	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₃₂	2
C₂₉×M₃₂	2
#11745167	2
#361	29