Subgroups — #27139940

Order 12416.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20260565	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic
3	#15690746	—	2	2	no	—
4	C₂×C₁₆×C₉₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₉₇	C₄	1	2	yes	—
6	#13095495	—	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	C₈×C₉₇	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₉₇	Q₁₆	1	1	yes	characteristic
13	#11715895	—	8	2	no	—
14	C₂²×C₉₇	Q₃₂	1	1	yes	characteristic
15	C₄×C₉₇	#107	1	1	yes	characteristic
16	C₄×C₉₇	D₁₆	1	1	yes	characteristic
17	C₂×C₉₇	—	2	1	no	—
18	C₂×C₉₇	#366	1	1	yes	characteristic
19	#1425	—	97	1	no	maximal, Sylow
20	C₉₇	#1425	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃₂	D₉₇	1	1	yes	characteristic
22	#368	—	97	2	no	—
23	C₂×C₁₆	C₂×D₉₇	1	1	yes	characteristic
24	#108	—	194	2	no	—
25	C₃₂	Dic₉₇	1	2	yes	—
26	M₁₆	—	388	2	no	—
27	C₂×C₈	D₃₈₈	1	1	yes	characteristic
28	C₁₆	Dic₁₉₄	1	1	yes	characteristic
29	C₁₆	C₂×Dic₉₇	1	1	yes	characteristic
30	C₂×C₄	D₇₇₆	1	1	yes	characteristic
31	C₈	—	776	2	no	—
32	C₈	C₄⋊Dic₉₇	1	1	yes	characteristic
33	C₈	Dic₃₈₈	1	1	yes	characteristic
34	C₂²	Dic₇₇₆	1	1	yes	characteristic
35	C₄	#15690744	1	1	yes	characteristic
36	C₄	D₁₅₅₂	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#20260561	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
20. C₉₇	#1425	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.