Subgroups — C₂²⋊#20259013 #37566992

Order 24352.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259013	C₂	1	2	yes	maximal, complemented
2	C₂²×#15690200	C₂	1	1	yes	maximal, characteristic
3	#20259013	—	2	2	no	—
4	C₂×#15690200	—	2	2	no	—
5	C₂×#15690200	C₄	1	1	yes	characteristic
6	C₂×#15690200	C₂²	1	1	yes	characteristic
7	C₂²×D₇₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₇₆₁	C₈	1	1	yes	characteristic, complemented
9	C₂×D₇₆₁	—	2	1	no	—
10	C₂×D₇₆₁	—	2	1	no	—
11	C₂×D₇₆₁	C₈	1	1	yes	characteristic, complemented
12	C₂×D₇₆₁	C₂×C₄	1	1	yes	characteristic
13	#15690200	—	2	1	no	—
14	#15690200	D₄	1	2	yes	—
15	C₂×C₇₆₁	—	2	1	no	—
16	C₂×C₇₆₁	C₂×C₈	1	1	yes	characteristic
17	D₇₆₁	—	2	1	no	—
18	D₇₆₁	C₂²⋊C₄	1	1	yes	characteristic
19	D₇₆₁	M₁₆	1	1	yes	characteristic
20	C₇₆₁	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
21	C₂²⋊C₈	—	761	1	no	maximal, Sylow
22	C₂²×C₄	—	761	1	no	—
23	C₂×C₈	—	761	2	no	—
24	C₂³	—	761	1	no	—
25	C₂×C₄	—	1522	2	no	—
26	C₂×C₄	—	761	1	no	—
27	C₂×C₄	—	761	1	no	—
28	C₈	—	1522	2	no	—
29	C₂²	—	1522	1	no	—
30	C₂²	—	1522	1	no	—
31	C₂²	—	761	1	no	—
32	C₂²	—	761	1	no	—
33	C₂²	#20259013	1	1	yes	characteristic, complemented
34	C₄	—	1522	1	no	—
35	C₄	—	761	2	no	—
36	C₂	—	2	1	no	—
37	C₂	—	1522	1	no	—
38	C₂	—	761	1	no	—
39	C₂	—	761	1	no	—
40	C₂	C₂×#20259013	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.