Subgroups — #29505170

Order 15296.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21439960	C₂	1	2	yes	maximal
2	#21439892	C₂	1	4	yes	maximal
3	C₄×C₈×C₂₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₇₈	—	2	2	no	—
5	C₄⋊Dic₂₃₉	—	2	2	no	—
6	C₄⋊Dic₂₃₉	C₂²	1	4	yes	—
7	C₂×C₈×C₂₃₉	C₂²	1	2	yes	—
8	C₄²×C₂₃₉	C₂²	1	1	yes	characteristic
9	Dic₄₇₈	—	4	4	no	—
10	C₂×Dic₂₃₉	—	2	4	no	—
11	C₂×C₄×C₂₃₉	D₄	1	2	yes	—
12	C₂×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
13	C₈×C₂₃₉	Q₈	1	4	yes	complemented
14	C₂²×C₂₃₉	C₂×D₄	1	1	yes	characteristic
15	C₄×C₂₃₉	SD₁₆	1	4	yes	—
16	C₄×C₂₃₉	C₂×Q₈	1	2	yes	—
17	Dic₂₃₉	—	4	4	no	—
18	C₂×C₂₃₉	C₄⋊Q₈	1	1	yes	characteristic
19	C₂×C₂₃₉	C₂×SD₁₆	1	2	yes	—
20	C₂₃₉	#498	1	1	yes	characteristic, complemented, Sylow
21	#498	—	239	1	no	maximal, Sylow
22	C₄⋊Q₈	—	239	2	no	—
23	#106	—	239	4	no	—
24	C₄×C₈	D₂₃₉	1	1	yes	characteristic
25	C₂×Q₈	—	478	2	no	—
26	C₂×C₈	C₂×D₂₃₉	1	2	yes	—
27	C₄⋊C₄	—	478	2	no	—
28	C₄⋊C₄	—	239	4	no	—
29	C₄²	C₂×D₂₃₉	1	1	yes	characteristic
30	Q₈	—	956	4	no	—
31	C₂×C₄	—	478	4	no	—
32	C₂×C₄	D₉₅₆	1	2	yes	—
33	C₂×C₄	C₂²×D₂₃₉	1	1	yes	characteristic
34	C₈	Dic₄₇₈	1	4	yes	complemented
35	C₂²	C₂×D₉₅₆	1	1	yes	characteristic
36	C₄	—	956	4	no	—
37	C₄	#16838537	1	4	yes	—
38	C₄	C₂×Dic₄₇₈	1	2	yes	—
39	C₂	#21439960	1	1	yes	characteristic
40	C₂	C₂×#16838537	1	2	yes	—

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.