Subgroups — #27159033

Order 12416.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20261866	C₂	1	3	yes	maximal, complemented
2	#20261864	C₂	1	3	yes	maximal, complemented
3	#20261857	C₂	1	1	yes	maximal, characteristic
4	#15690909	C₂²	1	1	yes	characteristic
5	#15690909	C₂²	1	3	yes	—
6	#15690907	C₄	1	3	yes	—
7	#15690905	C₂²	1	3	yes	—
8	#15690898	C₄	1	1	yes	characteristic
9	#13095523	C₂×C₄	1	3	yes	—
10	#13095523	C₂³	1	1	yes	characteristic
11	#13095521	C₈	1	3	yes	—
12	#13095519	C₂×C₄	1	3	yes	—
13	#13095512	C₈	1	1	yes	characteristic
14	Q₈×C₉₇	C₁₆	1	1	yes	characteristic
15	D₃₈₈	C₁₆	1	3	yes	—
16	C₄×D₉₇	C₂×C₈	1	3	yes	—
17	#11715897	C₂×C₈	1	3	yes	—
18	#11715897	C₂²×C₄	1	1	yes	characteristic
19	C₂×D₉₇	C₂×C₁₆	1	3	yes	—
20	C₄×C₉₇	C₂×C₁₆	1	3	yes	—
21	Dic₉₇	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₉₇	C₂²×C₁₆	1	1	yes	characteristic
23	D₉₇	—	2	3	no	—
24	#2258	—	97	1	no	maximal, Sylow
25	C₉₇	#2258	1	1	yes	characteristic, complemented, Sylow
26	#504	—	97	1	no	—
27	M₆₄	—	97	3	no	—
28	C₂×C₃₂	—	97	3	no	—
29	#131	—	97	1	no	—
30	M₃₂	—	97	3	no	—
31	C₂×C₁₆	—	97	3	no	—
32	C₃₂	—	97	1	no	—
33	C₃₂	—	97	3	no	—
34	#41	—	97	1	no	—
35	M₁₆	—	97	3	no	—
36	C₂×C₈	—	97	3	no	—
37	C₁₆	—	97	1	no	—
38	C₁₆	—	97	3	no	—
39	Q₈	#13095525	1	1	yes	characteristic
40	D₄	—	97	3	no	—
41	C₂×C₄	—	97	3	no	—
42	C₈	—	97	1	no	—
43	C₈	—	97	3	no	—
44	C₂²	—	97	3	no	—
45	C₄	—	97	1	no	—
46	C₄	C₂×#13095525	1	3	yes	—
47	C₂	—	194	3	no	—
48	C₂	C₂²×#13095525	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.