Subgroups — #16840669

Order 3904.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519836	C₂	1	2	yes	maximal
2	#14519765	C₂	1	1	yes	maximal, characteristic
3	C₂×D₂₄₄	C₂²	1	1	yes	characteristic
4	C₂×Dic₁₂₂	C₄	1	1	yes	characteristic, complemented
5	C₂²⋊#6923	—	2	2	no	—
6	C₄²×C₆₁	C₄	1	1	yes	characteristic, complemented
7	#11758198	—	2	2	no	—
8	C₂²×D₆₁	D₄	1	2	yes	—
9	C₂×#6923	—	4	2	no	—
10	C₂×C₄×C₆₁	—	2	1	no	—
11	C₂×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₆₁	—	2	1	no	—
13	D₂₄₄	—	4	1	no	—
14	Dic₁₂₂	—	4	1	no	—
15	C₂²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₆₁	—	2	2	no	—
17	C₂×D₆₁	—	4	2	no	—
18	#6923	—	8	2	no	—
19	C₄×C₆₁	—	2	1	no	—
20	C₄×C₆₁	—	4	1	no	—
21	Dic₆₁	—	4	1	no	—
22	C₂×C₆₁	—	2	1	no	—
23	C₂×C₆₁	#99	1	1	yes	characteristic
24	D₆₁	—	4	2	no	—
25	#354	—	61	1	no	maximal, Sylow
26	C₆₁	#354	1	1	yes	characteristic, complemented, Sylow
27	#124	—	61	1	no	—
28	#99	—	61	2	no	—
29	C₂×Q₈	—	61	1	no	—
30	C₂×D₄	—	61	1	no	—
31	C₂²⋊C₄	—	122	2	no	—
32	C₂²⋊C₄	—	122	2	no	—
33	C₄²	#6923	1	1	yes	characteristic, complemented
34	C₂³	—	61	2	no	—
35	Q₈	—	244	1	no	—
36	D₄	—	244	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	122	1	no	—
39	C₂×C₄	—	244	2	no	—
40	C₂×C₄	C₂×#6923	1	1	yes	characteristic
41	C₂²	—	122	2	no	—
42	C₂²	—	244	2	no	—
43	C₂²	C₂²⋊#6923	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	488	2	no	—
47	C₄	—	244	1	no	—
48	C₂	—	2	1	no	—
49	C₂	—	244	2	no	—
50	C₂	#14519836	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.