Subgroups — #27139950

Order 12416.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₁₀₄	C₂	1	1	yes	maximal, characteristic
2	#20260454	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₆₄×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅₅₂	—	2	1	no	—
5	Q₃₂×C₉₇	—	2	1	no	—
6	C₃₂×C₉₇	C₂²	1	1	yes	characteristic
7	D₇₇₆	—	4	1	no	—
8	Q₁₆×C₉₇	—	4	1	no	—
9	C₁₆×C₉₇	D₄	1	1	yes	characteristic
10	Q₈×C₉₇	—	8	1	no	—
11	D₃₈₈	—	8	1	no	—
12	C₈×C₉₇	D₈	1	1	yes	characteristic
13	C₂×D₉₇	—	16	1	no	—
14	C₄×C₉₇	—	16	1	no	—
15	C₄×C₉₇	D₁₆	1	1	yes	characteristic
16	C₂×C₉₇	D₃₂	1	1	yes	characteristic
17	D₉₇	—	32	1	no	—
18	SD₁₂₈	—	97	1	no	maximal, Sylow
19	C₉₇	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
20	Q₆₄	D₉₇	1	1	yes	characteristic, complemented
21	D₃₂	—	97	1	no	—
22	C₆₄	—	97	1	no	—
23	Q₃₂	—	2	1	no	—
24	D₁₆	—	194	1	no	—
25	C₃₂	C₂×D₉₇	1	1	yes	characteristic
26	Q₁₆	—	4	1	no	—
27	D₈	—	388	1	no	—
28	C₁₆	C₂²⋊D₉₇	1	1	yes	characteristic
29	Q₈	—	8	1	no	—
30	D₄	—	776	1	no	—
31	C₈	#13095496	1	1	yes	characteristic
32	C₂²	—	1552	1	no	—
33	C₄	—	16	1	no	—
34	C₄	#15690751	1	1	yes	characteristic
35	C₂	—	3104	1	no	—
36	C₂	#20260570	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.