Subgroups — Q₈×#6599 #14272211

Order 1856.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#6599	C₂	1	3	yes	maximal
3	C₄×#6599	C₂	1	3	yes	maximal
4	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂×#6599	C₂²	1	3	yes	—
6	C₂×#6599	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₂₉	C₄	1	3	yes	—
8	C₄×Dic₂₉	C₂²	1	3	yes	—
9	Q₈×C₂₉	C₈	1	4	yes	complemented
10	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
11	C₂×Dic₂₉	C₂×C₄	1	3	yes	—
12	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
13	#6599	—	2	3	no	—
14	#6599	Q₈	1	2	yes	direct product factor
15	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₂₉	C₂×C₈	1	6	yes	—
17	Dic₂₉	—	2	3	no	—
18	Dic₂₉	C₂×Q₈	1	1	yes	characteristic
19	Dic₂₉	#41	1	1	yes	characteristic
20	C₈×Q₈	—	29	1	no	maximal, Sylow
21	C₂×C₂₉	C₄×Q₈	1	1	yes	characteristic
22	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
23	C₂×C₂₉	#131	1	1	yes	characteristic
24	C₄×Q₈	—	29	1	no	—
25	C₄⋊C₈	—	29	3	no	—
26	C₄×C₈	—	29	3	no	—
27	C₂₉	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₈	#1181	1	1	yes	characteristic
29	C₂×C₈	—	29	1	no	—
30	C₂×C₈	—	29	3	no	—
31	C₄⋊C₄	—	29	3	no	—
32	C₄²	—	29	3	no	—
33	Q₈	#6599	1	4	yes	direct product factor
34	C₂×C₄	—	29	1	no	—
35	C₂×C₄	—	29	3	no	—
36	C₂×C₄	C₂×#1181	1	3	yes	—
37	C₈	—	29	2	no	—
38	C₈	—	58	3	no	—
39	C₂²	C₂²×#1181	1	1	yes	characteristic
40	C₄	—	29	1	no	—
41	C₄	—	29	1	no	—
42	C₄	—	58	3	no	—
43	C₄	C₂×#6599	1	6	yes	—
44	C₂	#11745348	1	1	yes	characteristic
45	C₂	Q₈×#1181	1	1	yes	characteristic
46	C₂	C₂²×#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.