Subgroups — #27163093

Order 12704.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₈₈	C₂	1	6	yes	maximal, complemented
2	C₄²×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₃₉₇	C₂²	1	4	yes	—
4	D₁₅₈₈	—	2	12	no	—
5	C₂×C₄×C₃₉₇	C₂²	1	3	yes	—
6	C₂²×C₃₉₇	C₂³	1	1	yes	characteristic
7	C₂×D₃₉₇	—	2	12	no	—
8	C₄×C₃₉₇	D₄	1	6	yes	complemented
9	C₂×C₃₉₇	C₂×D₄	1	3	yes	—
10	D₃₉₇	—	4	4	no	—
11	C₃₉₇	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	397	1	no	maximal, Sylow
13	C₂×D₄	—	397	6	no	—
14	C₄²	D₃₉₇	1	1	yes	characteristic, complemented
15	C₂³	—	397	4	no	—
16	D₄	—	794	12	no	—
17	C₂×C₄	C₂×D₃₉₇	1	3	yes	—
18	C₂²	—	794	12	no	—
19	C₂²	C₂²×D₃₉₇	1	1	yes	characteristic
20	C₄	D₁₅₈₈	1	6	yes	complemented
21	C₂	—	1588	4	no	—
22	C₂	C₂×D₁₅₈₈	1	3	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.