Subgroups — C₂²⋊#20259004 #37566813

Order 24352.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259004	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×C₇₆₁	C₂	1	1	yes	maximal, characteristic
3	#20259004	—	2	2	no	—
4	C₂³×C₇₆₁	C₄	1	1	yes	characteristic
5	C₂×C₄×C₇₆₁	—	2	2	no	—
6	C₂×C₄×C₇₆₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₇₆₁	C₂²	1	1	yes	characteristic
8	C₂²×C₇₆₁	—	2	1	no	—
9	C₂²×C₇₆₁	—	2	1	no	—
10	C₂²×C₇₆₁	C₈	1	2	yes	complemented
11	C₂²×C₇₆₁	C₂×C₄	1	1	yes	characteristic
12	C₄×C₇₆₁	—	2	1	no	—
13	C₄×C₇₆₁	D₄	1	2	yes	—
14	C₂×C₇₆₁	—	2	2	no	—
15	C₂×C₇₆₁	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₇₆₁	C₂×C₈	1	1	yes	characteristic
17	C₂×C₇₆₁	M₁₆	1	1	yes	characteristic
18	C₇₆₁	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	761	1	no	maximal, Sylow
20	C₂²×C₄	D₇₆₁	1	1	yes	characteristic
21	C₂×C₈	—	761	2	no	—
22	C₂³	Dic₇₆₁	1	1	yes	characteristic
23	C₂×C₄	—	2	2	no	—
24	C₂×C₄	Dic₇₆₁	1	1	yes	characteristic
25	C₂×C₄	C₂×D₇₆₁	1	1	yes	characteristic
26	C₈	—	1522	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	#20259004	1	2	yes	complemented
30	C₂²	C₂×Dic₇₆₁	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	C₂²⋊D₇₆₁	1	2	yes	—
33	C₂	—	2	2	no	—
34	C₂	C₂²⋊Dic₇₆₁	1	1	yes	characteristic
35	C₂	C₂×#20259004	1	1	yes	characteristic
36	C₂	#27131633	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.