Subgroups — #4516

Order 192.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#819	C₂	1	1	yes	maximal, characteristic, complemented
4	#361	—	3	1	no	maximal, Sylow
5	C₂×D₁₂	—	2	1	no	—
6	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
7	#208	—	2	1	no	—
8	D₂₄	—	2	1	no	—
9	D₂₄	C₄	1	2	yes	—
10	C₃×C₁₆	—	2	1	no	—
11	C₂×D₈	—	3	1	no	—
12	M₃₂	D₃	1	1	yes	characteristic, complemented
13	#108	—	3	1	no	—
14	C₂²×D₃	—	4	1	no	—
15	C₂×C₃×C₄	D₄	1	1	yes	characteristic
16	D₁₂	—	2	2	no	—
17	D₁₂	—	4	1	no	—
18	C₃×C₈	C₂×C₄	1	1	yes	characteristic
19	C₃×C₈	D₄	1	1	yes	characteristic
20	C₃⋊C₈	—	4	1	no	—
21	C₂×D₄	—	6	1	no	—
22	D₈	—	3	2	no	—
23	D₈	—	6	1	no	—
24	M₁₆	—	6	1	no	—
25	C₂×C₈	C₂×D₃	1	1	yes	characteristic
26	C₁₆	—	2	1	no	—
27	C₂²×C₃	SD₁₆	1	1	yes	characteristic
28	C₂×D₃	—	4	2	no	—
29	C₂×D₃	—	8	2	no	—
30	C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
31	C₃×C₄	D₈	1	1	yes	characteristic
32	C₂³	—	12	1	no	—
33	D₄	—	6	2	no	—
34	D₄	—	12	1	no	—
35	C₂×C₄	D₁₂	1	1	yes	characteristic
36	C₈	—	12	1	no	—
37	C₈	C₄×D₃	1	1	yes	characteristic
38	C₈	#67	1	1	yes	characteristic
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	#102	1	1	yes	characteristic
41	D₃	—	8	2	no	—
42	C₂²	—	12	2	no	—
43	C₂²	—	24	2	no	—
44	C₂²	#204	1	1	yes	characteristic
45	C₄	D₂₄	1	1	yes	characteristic
46	C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
47	C₃	#361	1	1	yes	characteristic, complemented, Sylow
48	C₂	—	2	1	no	—
49	C₂	—	24	2	no	—
50	C₂	#821	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.