Subgroups — #27158825

Order 12416.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261843	C₂	1	2	yes	maximal
2	#20261624	C₂	1	1	yes	maximal, characteristic
3	#15690900	C₄	1	4	yes	complemented
4	C₂×#13095514	C₄	1	1	yes	characteristic
5	C₂×#13095514	C₂²	1	1	yes	characteristic
6	C₈×Dic₉₇	C₄	1	1	yes	characteristic
7	#13095514	C₈	1	2	yes	—
8	#13095514	C₂×C₄	1	2	yes	—
9	C₂×#11715895	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₉₇	C₈	1	1	yes	characteristic
11	C₂×C₈×C₉₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
13	C₂×Dic₉₇	—	2	1	no	—
14	C₈×C₉₇	—	2	1	no	—
15	#11715895	C₄²	1	1	yes	characteristic
16	#11715895	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₉₇	M₃₂	1	1	yes	characteristic
18	C₄×C₉₇	C₄×C₈	1	1	yes	characteristic
19	C₄×C₉₇	M₃₂	1	1	yes	characteristic
20	Dic₉₇	—	4	1	no	—
21	C₂×C₉₇	—	2	1	no	—
22	C₂×C₉₇	#346	1	1	yes	characteristic
23	#1398	—	97	1	no	maximal, Sylow
24	C₉₇	#1398	1	1	yes	characteristic, complemented, Sylow
25	M₆₄	—	97	2	no	—
26	#346	—	97	1	no	—
27	C₂×C₁₆	—	97	1	no	—
28	C₂×C₁₆	—	97	1	no	—
29	C₄×C₈	—	97	1	no	—
30	C₃₂	—	97	4	no	—
31	C₂×C₈	—	97	1	no	—
32	C₂×C₈	#11715906	1	1	yes	characteristic
33	C₄²	—	97	1	no	—
34	C₁₆	—	97	2	no	—
35	C₁₆	—	97	2	no	—
36	C₂×C₄	—	194	1	no	—
37	C₂×C₄	C₂×#11715906	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	—	97	1	no	—
40	C₈	—	97	1	no	—
41	C₂²	#15690907	1	1	yes	characteristic
42	C₄	—	388	1	no	—
43	C₄	C₄×#11715906	1	1	yes	characteristic
44	C₄	#15690906	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#20261829	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #15690900	C₄	semidirect
24. C₉₇	#1398	semidirect

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