Subgroups — #5082

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#870	C₂	1	1	yes	maximal, characteristic
3	#835	C₂	1	4	yes	maximal
4	#803	C₂	1	1	yes	maximal, characteristic
5	#491	—	3	1	no	maximal, Sylow
6	C₂×C₃×Q₈	C₂²	1	2	yes	—
7	C₃×C₄⋊C₄	—	2	2	no	—
8	C₃×C₄²	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₃	C₂²	1	2	yes	—
10	Dic₃⋊C₄	—	2	2	no	—
11	C₂×C₃⋊C₈	C₂²	1	2	yes	—
12	C₄⋊Q₈	D₃	1	1	yes	characteristic
13	#125	—	3	1	no	—
14	#103	—	3	4	no	—
15	#97	—	3	1	no	—
16	C₃×Q₈	—	2	4	no	—
17	C₂×C₃×C₄	—	2	2	no	—
18	C₂×C₃×C₄	D₄	1	2	yes	—
19	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
20	C₂×Dic₃	—	2	2	no	—
21	C₃⋊C₈	—	2	2	no	—
22	C₂×Q₈	C₂×D₃	1	2	yes	—
23	C₂×C₈	—	3	2	no	—
24	C₄⋊C₄	—	2	2	no	—
25	C₄⋊C₄	—	3	2	no	—
26	C₄⋊C₄	—	6	2	no	—
27	C₄²	C₂×D₃	1	1	yes	characteristic
28	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
29	C₃×C₄	—	2	2	no	—
30	C₃×C₄	—	4	2	no	—
31	C₃×C₄	#41	1	2	yes	—
32	Dic₃	—	4	2	no	—
33	Q₈	—	2	4	no	—
34	C₂×C₄	—	2	2	no	—
35	C₂×C₄	—	6	2	no	—
36	C₂×C₄	#67	1	2	yes	—
37	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
38	C₈	—	6	2	no	—
39	C₂×C₃	#124	1	1	yes	characteristic
40	C₂×C₃	#137	1	2	yes	—
41	C₂²	C₂×#67	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	4	2	no	—
44	C₄	—	12	2	no	—
45	C₄	#237	1	2	yes	—
46	C₃	#491	1	1	yes	characteristic, complemented, Sylow
47	C₂	#936	1	1	yes	characteristic
48	C₂	#942	1	2	yes	—

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

N	H ≅ G/N	type
46. C₃	#491	semidirect

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