Subgroups — #36376168

Order 22432.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14584149	C₂	1	2	yes	maximal
2	C₈×D₇₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#14584149	—	2	2	no	—
4	C₄×D₇₀₁	C₂²	1	1	yes	characteristic
5	#19150480	C₄	1	1	yes	characteristic, complemented
6	C₈×C₇₀₁	C₄	1	1	yes	characteristic, complemented
7	C₂×D₇₀₁	D₄	1	1	yes	characteristic
8	#14584149	—	4	2	no	—
9	C₄×C₇₀₁	C₂×C₄	1	1	yes	characteristic
10	Dic₇₀₁	Q₈	1	1	yes	characteristic
11	C₂×C₇₀₁	C₄⋊C₄	1	1	yes	characteristic
12	D₇₀₁	SD₁₆	1	2	yes	—
13	C₇₀₁	#106	1	1	yes	characteristic, complemented, Sylow
14	#106	—	701	1	no	maximal, Sylow
15	C₂×C₈	—	701	1	no	—
16	C₄⋊C₄	—	701	2	no	—
17	C₂×C₄	—	1402	2	no	—
18	C₂×C₄	—	701	1	no	—
19	C₈	—	701	1	no	—
20	C₈	#14584149	1	1	yes	characteristic, complemented
21	C₂²	—	701	1	no	—
22	C₄	—	701	1	no	—
23	C₄	—	2804	2	no	—
24	C₄	C₂×#14584149	1	1	yes	characteristic
25	C₂	—	701	2	no	—
26	C₂	C₄⋊#14584149	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.