Subgroups — C₄⋊#90770 #14272083

Order 1856.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90770	C₂	1	2	yes	maximal
2	C₄×#6597	C₂	1	1	yes	maximal, characteristic
3	C₄²×C₂₉	C₄	1	1	yes	characteristic
4	C₂×#6597	C₄	1	1	yes	characteristic
5	C₂×#6597	C₂²	1	1	yes	characteristic
6	#90770	—	2	2	no	—
7	C₂×C₄×C₂₉	C₈	1	1	yes	characteristic
8	C₂×C₄×C₂₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
10	#6597	—	2	1	no	—
11	#6597	D₄	1	1	yes	characteristic
12	#6597	Q₈	1	1	yes	characteristic
13	C₂²×C₂₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₂₉	—	2	1	no	—
15	C₄×C₂₉	C₁₆	1	2	yes	complemented
16	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₂₉	M₁₆	1	1	yes	characteristic
18	C₄⋊C₁₆	—	29	1	no	maximal, Sylow
19	C₂×C₂₉	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₂₉	C₂×C₁₆	1	1	yes	characteristic
21	C₂×C₂₉	M₃₂	1	1	yes	characteristic
22	C₂×C₁₆	—	29	2	no	—
23	C₄×C₈	—	29	1	no	—
24	C₂₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₈	—	29	1	no	—
26	C₂×C₈	—	29	1	no	—
27	C₄²	#1181	1	1	yes	characteristic
28	C₁₆	—	58	2	no	—
29	C₂×C₄	#6599	1	1	yes	characteristic
30	C₂×C₄	#6599	1	1	yes	characteristic
31	C₂×C₄	C₂×#1181	1	1	yes	characteristic
32	C₈	—	29	1	no	—
33	C₈	—	29	1	no	—
34	C₈	—	58	1	no	—
35	C₂²	C₂×#6599	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#90770	1	2	yes	complemented
38	C₄	#90796	1	1	yes	characteristic
39	C₄	C₄⋊#1181	1	1	yes	characteristic
40	C₂	C₂×#90770	1	1	yes	characteristic
41	C₂	#11745214	1	1	yes	characteristic
42	C₂	C₄⋊#6599	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.