Subgroups — #37580915

Order 24448.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259319	C₂	1	14	yes	maximal, complemented
2	C₄³×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₇₆₄	C₂²	1	28	yes	—
4	#20259319	—	2	56	no	—
5	C₂×C₄²×C₁₉₁	C₂²	1	7	yes	—
6	C₂³×D₁₉₁	C₂³	1	8	yes	—
7	C₂×D₇₆₄	—	2	168	no	—
8	C₂²×C₄×C₁₉₁	C₂³	1	7	yes	—
9	C₄²×C₁₉₁	D₄	1	28	yes	complemented
10	C₂²×D₁₉₁	—	2	56	no	—
11	D₇₆₄	—	4	112	no	—
12	C₂³×C₁₉₁	C₂⁴	1	1	yes	characteristic
13	C₂×C₄×C₁₉₁	C₂×D₄	1	42	yes	—
14	C₂²×C₁₉₁	C₂²×D₄	1	7	yes	—
15	C₂×D₁₉₁	—	4	56	no	—
16	C₄×C₁₉₁	#127	1	28	yes	complemented
17	C₂×C₁₉₁	C₂×#127	1	7	yes	—
18	D₁₉₁	—	8	8	no	—
19	C₁₉₁	#2867	1	1	yes	characteristic, complemented, Sylow
20	#2867	—	191	1	no	maximal, Sylow
21	C₂×#127	—	191	14	no	—
22	C₄³	D₁₉₁	1	1	yes	characteristic, complemented
23	C₂²×D₄	—	191	28	no	—
24	#127	—	382	56	no	—
25	C₂×C₄²	C₂×D₁₉₁	1	7	yes	—
26	C₂⁴	—	191	8	no	—
27	C₂×D₄	—	382	168	no	—
28	C₂²×C₄	C₂²×D₁₉₁	1	7	yes	—
29	C₄²	D₇₆₄	1	28	yes	complemented
30	C₂³	—	382	56	no	—
31	C₂³	C₂³×D₁₉₁	1	1	yes	characteristic
32	D₄	—	764	112	no	—
33	C₂×C₄	C₂×D₇₆₄	1	42	yes	—
34	C₂²	—	764	56	no	—
35	C₂²	C₂²×D₇₆₄	1	7	yes	—
36	C₄	#20259319	1	28	yes	complemented
37	C₂	—	1528	8	no	—
38	C₂	C₂×#20259319	1	7	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.