Subgroups — #15689521

Order 3008.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094024	C₂	1	2	yes	maximal
2	#13093956	C₂	1	4	yes	maximal
3	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₄	—	2	2	no	—
5	C₂×C₈×C₄₇	C₂²	1	2	yes	—
6	C₄²×C₄₇	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₄₇	—	2	2	no	—
8	C₄⋊Dic₄₇	C₂²	1	4	yes	—
9	C₂×C₄×C₄₇	D₄	1	2	yes	—
10	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
11	C₂×Dic₄₇	—	2	4	no	—
12	Dic₉₄	—	4	4	no	—
13	C₈×C₄₇	Q₈	1	4	yes	complemented
14	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
15	C₄×C₄₇	SD₁₆	1	4	yes	—
16	C₄×C₄₇	C₂×Q₈	1	2	yes	—
17	Dic₄₇	—	4	4	no	—
18	C₂×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
19	C₂×C₄₇	C₂×SD₁₆	1	2	yes	—
20	#498	—	47	1	no	maximal, Sylow
21	C₄₇	#498	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊Q₈	—	47	2	no	—
23	#106	—	47	4	no	—
24	C₄×C₈	D₄₇	1	1	yes	characteristic
25	C₂×Q₈	—	94	2	no	—
26	C₂×C₈	C₂×D₄₇	1	2	yes	—
27	C₄⋊C₄	—	47	4	no	—
28	C₄⋊C₄	—	94	2	no	—
29	C₄²	C₂×D₄₇	1	1	yes	characteristic
30	Q₈	—	188	4	no	—
31	C₂×C₄	—	94	4	no	—
32	C₂×C₄	D₁₈₈	1	2	yes	—
33	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
34	C₈	Dic₉₄	1	4	yes	complemented
35	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
36	C₄	—	188	4	no	—
37	C₄	#10625325	1	4	yes	—
38	C₄	C₂×Dic₉₄	1	2	yes	—
39	C₂	#13094024	1	1	yes	characteristic
40	C₂	C₂×#10625325	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.