Subgroups — #27159019

Order 12416.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261859	C₂	1	2	yes	maximal, complemented
2	C₂×#15690900	C₂	1	1	yes	maximal, characteristic
3	#15690900	C₄	1	1	yes	characteristic
4	#15690900	C₂²	1	1	yes	characteristic
5	C₂×#13095514	C₄	1	1	yes	characteristic
6	#13095514	C₈	1	1	yes	characteristic
7	#13095514	C₂×C₄	1	1	yes	characteristic
8	C₂×#11715895	C₈	1	1	yes	characteristic
9	C₂×C₄×C₉₇	C₁₆	1	1	yes	characteristic
10	#11715895	C₁₆	1	1	yes	characteristic
11	#11715895	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₉₇	C₃₂	1	1	yes	characteristic
13	C₄×C₉₇	C₃₂	1	1	yes	characteristic
14	C₄×C₉₇	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₉₇	—	2	1	no	—
16	C₂×C₉₇	C₂×C₃₂	1	1	yes	characteristic
17	M₁₂₈	—	97	1	no	maximal, Sylow
18	C₉₇	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃₂	—	97	1	no	—
20	C₆₄	—	97	2	no	—
21	C₂×C₁₆	—	97	1	no	—
22	C₃₂	—	97	1	no	—
23	C₃₂	—	97	1	no	—
24	C₂×C₈	—	97	1	no	—
25	C₁₆	—	97	1	no	—
26	C₁₆	—	97	1	no	—
27	C₂×C₄	#13095525	1	1	yes	characteristic
28	C₈	—	97	1	no	—
29	C₈	—	97	1	no	—
30	C₂²	#15690909	1	1	yes	characteristic
31	C₄	#15690909	1	1	yes	characteristic
32	C₄	C₂×#13095525	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#15690909	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #20261859	C₂	semidirect
18. C₉₇	M₁₂₈	semidirect

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