Subgroups — C₂²×#90768 #14271575

Order 1856.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#90768	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₄×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₈×C₂₉	C₄	1	3	yes	—
5	C₂×C₈×C₂₉	C₂²	1	3	yes	—
6	#90768	C₂²	1	4	yes	direct product factor
7	C₂³×C₂₉	C₈	1	1	yes	characteristic
8	C₂×C₄×C₂₉	C₈	1	3	yes	—
9	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
10	C₈×C₂₉	C₂×C₄	1	3	yes	—
11	C₈×C₂₉	C₂³	1	1	yes	characteristic
12	C₂²×C₂₉	C₁₆	1	4	yes	complemented
13	C₂²×C₂₉	C₂×C₈	1	3	yes	—
14	C₄×C₂₉	C₂×C₈	1	3	yes	—
15	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
16	C₂²×C₁₆	—	29	1	no	maximal, Sylow
17	C₂×C₂₉	C₂×C₁₆	1	6	yes	complemented
18	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
19	C₂²×C₈	D₂₉	1	1	yes	characteristic
20	C₂×C₁₆	—	29	6	no	—
21	C₂₉	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₄	Dic₂₉	1	1	yes	characteristic
23	C₂×C₈	Dic₂₉	1	3	yes	—
24	C₂×C₈	C₂×D₂₉	1	3	yes	—
25	C₁₆	—	29	4	no	—
26	C₂³	#6597	1	1	yes	characteristic
27	C₂×C₄	#6597	1	3	yes	—
28	C₂×C₄	C₂×Dic₂₉	1	3	yes	—
29	C₈	C₂×Dic₂₉	1	3	yes	—
30	C₈	C₂²×D₂₉	1	1	yes	characteristic
31	C₂²	#90768	1	4	yes	direct product factor
32	C₂²	C₂×#6597	1	3	yes	—
33	C₄	C₂×#6597	1	3	yes	—
34	C₄	C₂²×Dic₂₉	1	1	yes	characteristic
35	C₂	C₂×#90768	1	6	yes	direct product factor
36	C₂	C₂²×#6597	1	1	yes	characteristic

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

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