Subgroups — C₂³×#6599 #14272233

Order 1856.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6599	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₂₉	C₄	1	1	yes	characteristic
4	C₂²×Dic₂₉	C₄	1	7	yes	—
5	C₂²×Dic₂₉	C₂²	1	7	yes	—
6	C₂×#6599	C₂²	1	28	yes	direct product factor
7	C₂³×C₂₉	C₈	1	8	yes	complemented
8	C₂³×C₂₉	C₂×C₄	1	7	yes	—
9	C₂×Dic₂₉	C₂×C₄	1	21	yes	—
10	C₂×Dic₂₉	C₂³	1	7	yes	—
11	#6599	C₂³	1	8	yes	direct product factor
12	C₂²×C₂₉	C₂×C₈	1	28	yes	complemented
13	C₂²×C₂₉	C₂²×C₄	1	7	yes	—
14	Dic₂₉	C₂²×C₄	1	7	yes	—
15	Dic₂₉	C₂⁴	1	1	yes	characteristic
16	C₂³×C₈	—	29	1	no	maximal, Sylow
17	C₂×C₂₉	C₂²×C₈	1	14	yes	complemented
18	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
19	C₂³×C₄	—	29	1	no	—
20	C₂²×C₈	—	29	14	no	—
21	C₂₉	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂⁴	#1181	1	1	yes	characteristic
23	C₂²×C₄	—	29	7	no	—
24	C₂²×C₄	—	29	7	no	—
25	C₂×C₈	—	29	28	no	—
26	C₂³	#6599	1	8	yes	direct product factor
27	C₂³	C₂×#1181	1	7	yes	—
28	C₂×C₄	—	29	7	no	—
29	C₂×C₄	—	29	21	no	—
30	C₈	—	29	8	no	—
31	C₂²	C₂×#6599	1	28	yes	direct product factor
32	C₂²	C₂²×#1181	1	7	yes	—
33	C₄	—	29	1	no	—
34	C₄	—	29	7	no	—
35	C₂	C₂²×#6599	1	14	yes	direct product factor
36	C₂	C₂³×#1181	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.