Subgroups — #27139938

Order 12416.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20260561	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic
3	#15690744	—	2	2	no	—
4	C₂×C₁₆×C₉₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₉₇	C₄	1	2	yes	complemented
6	C₄⋊Dic₉₇	—	4	2	no	—
7	C₂×C₈×C₉₇	D₄	1	1	yes	characteristic
8	C₁₆×C₉₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₉₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₉₇	D₈	1	1	yes	characteristic
11	C₂×Dic₉₇	—	8	2	no	—
12	C₈×C₉₇	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₉₇	Q₁₆	1	1	yes	characteristic
14	C₂²×C₉₇	D₁₆	1	1	yes	characteristic
15	C₄×C₉₇	#107	1	1	yes	characteristic
16	C₄×C₉₇	Q₃₂	1	1	yes	characteristic
17	Dic₉₇	—	16	2	no	—
18	C₂×C₉₇	#366	1	1	yes	characteristic
19	C₂×C₉₇	SD₆₄	1	2	yes	—
20	#1424	—	97	1	no	maximal, Sylow
21	C₉₇	#1424	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃₂	D₉₇	1	1	yes	characteristic
23	#366	—	97	2	no	—
24	C₂×C₁₆	C₂×D₉₇	1	1	yes	characteristic
25	#107	—	194	2	no	—
26	C₃₂	Dic₉₇	1	2	yes	complemented
27	C₂×C₈	D₃₈₈	1	1	yes	characteristic
28	C₄⋊C₄	—	388	2	no	—
29	C₁₆	Dic₁₉₄	1	1	yes	characteristic
30	C₁₆	C₂×Dic₉₇	1	1	yes	characteristic
31	C₂×C₄	—	776	2	no	—
32	C₂×C₄	D₇₇₆	1	1	yes	characteristic
33	C₈	C₄⋊Dic₉₇	1	1	yes	characteristic
34	C₈	Dic₃₈₈	1	1	yes	characteristic
35	C₂²	D₁₅₅₂	1	1	yes	characteristic
36	C₄	—	1552	2	no	—
37	C₄	#15690744	1	1	yes	characteristic
38	C₄	Dic₇₇₆	1	1	yes	characteristic
39	C₂	#20260561	1	1	yes	characteristic
40	C₂	#20260574	1	2	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.