Subgroups — #27150131

Order 12416.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690807	C₂	1	14	yes	maximal, complemented
2	C₄³×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₃₈₈	C₂²	1	28	yes	—
4	#15690807	—	2	56	no	—
5	C₂×C₄²×C₉₇	C₂²	1	7	yes	—
6	C₂³×D₉₇	C₂³	1	8	yes	—
7	C₂×D₃₈₈	—	2	168	no	—
8	C₂²×C₄×C₉₇	C₂³	1	7	yes	—
9	C₄²×C₉₇	D₄	1	28	yes	complemented
10	C₂³×C₉₇	C₂⁴	1	1	yes	characteristic
11	C₂²×D₉₇	—	2	56	no	—
12	C₂×C₄×C₉₇	C₂×D₄	1	42	yes	—
13	D₃₈₈	—	4	112	no	—
14	C₂²×C₉₇	C₂²×D₄	1	7	yes	—
15	C₂×D₉₇	—	4	56	no	—
16	C₄×C₉₇	#127	1	28	yes	complemented
17	C₂×C₉₇	C₂×#127	1	7	yes	—
18	D₉₇	—	8	8	no	—
19	#2867	—	97	1	no	maximal, Sylow
20	C₉₇	#2867	1	1	yes	characteristic, complemented, Sylow
21	C₂×#127	—	97	14	no	—
22	C₄³	D₉₇	1	1	yes	characteristic, complemented
23	C₂²×D₄	—	97	28	no	—
24	#127	—	194	56	no	—
25	C₂×C₄²	C₂×D₉₇	1	7	yes	—
26	C₂⁴	—	97	8	no	—
27	C₂×D₄	—	194	168	no	—
28	C₂²×C₄	C₂²×D₉₇	1	7	yes	—
29	C₄²	D₃₈₈	1	28	yes	complemented
30	C₂³	—	194	56	no	—
31	C₂³	C₂³×D₉₇	1	1	yes	characteristic
32	D₄	—	388	112	no	—
33	C₂×C₄	C₂×D₃₈₈	1	42	yes	—
34	C₂²	—	388	56	no	—
35	C₂²	C₂²×D₃₈₈	1	7	yes	—
36	C₄	#15690807	1	28	yes	complemented
37	C₂	—	776	8	no	—
38	C₂	C₂×#15690807	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.