Subgroups — #4683

Order 192.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#870	C₂	1	2	yes	maximal
2	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#818	C₂	1	2	yes	maximal
4	#817	C₂	1	2	yes	maximal
5	#499	—	3	1	no	maximal, Sylow
6	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
8	C₃×C₄²	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₃	C₂²	1	4	yes	—
10	Dic₃⋊C₄	—	2	4	no	—
11	#125	—	3	2	no	—
12	#107	—	3	2	no	—
13	#106	—	3	2	no	—
14	C₄×C₈	D₃	1	1	yes	characteristic
15	C₂×C₃×C₄	D₄	1	2	yes	—
16	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
17	C₂×Dic₃	—	2	4	no	—
18	C₃×C₈	Q₈	1	2	yes	—
19	C₃×C₈	Q₈	1	2	yes	—
20	C₂×C₈	C₂×D₃	1	1	yes	characteristic
21	C₂×C₈	C₂×D₃	1	1	yes	characteristic
22	C₄⋊C₄	—	3	4	no	—
23	C₄⋊C₄	—	6	4	no	—
24	C₄²	C₂×D₃	1	1	yes	characteristic
25	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
26	C₃×C₄	—	2	2	no	—
27	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
28	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
29	Dic₃	—	4	4	no	—
30	C₂×C₄	—	6	4	no	—
31	C₂×C₄	D₁₂	1	2	yes	—
32	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
33	C₈	Dic₆	1	2	yes	—
34	C₈	Dic₆	1	2	yes	—
35	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
36	C₂×C₃	#135	1	2	yes	—
37	C₂²	C₂×D₁₂	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	—	12	4	no	—
40	C₄	C₂×Dic₆	1	1	yes	characteristic
41	C₄	C₂×Dic₆	1	1	yes	characteristic
42	C₃	#499	1	1	yes	characteristic, complemented, Sylow
43	C₂	#869	1	1	yes	characteristic
44	C₂	#904	1	2	yes	—

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

N	H ≅ G/N	type
42. C₃	#499	semidirect

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