Subgroups — #4540

Order 192.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#124	C₂	1	1	yes	maximal, characteristic
2	#803	C₂	1	2	yes	maximal, complemented
3	#329	—	3	1	no	maximal, Sylow
4	C₂×C₃×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₃×D₄	C₄	1	1	yes	characteristic
6	C₃×C₂²⋊C₄	—	2	2	no	—
7	C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊C₈	—	2	2	no	—
9	#124	D₃	1	1	yes	characteristic
10	#97	—	3	2	no	—
11	C₂³×C₃	—	2	1	no	—
12	C₃×Q₈	—	4	1	no	—
13	C₃×D₄	—	4	1	no	—
14	C₂×C₃×C₄	—	2	1	no	—
15	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₄	D₄	1	2	yes	—
17	C₃⋊C₈	—	2	4	no	—
18	C₂×Q₈	Dic₃	1	1	yes	characteristic
19	C₂×D₄	Dic₃	1	1	yes	characteristic
20	C₂×C₈	—	6	2	no	—
21	C₂²⋊C₄	—	2	2	no	—
22	C₄²	C₂×D₃	1	1	yes	characteristic
23	C₂²×C₃	—	4	1	no	—
24	C₂²×C₃	—	4	2	no	—
25	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₃×C₄	—	2	1	no	—
27	C₃×C₄	—	2	2	no	—
28	C₃×C₄	—	4	1	no	—
29	C₂³	—	2	1	no	—
30	Q₈	—	4	1	no	—
31	D₄	—	4	1	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
34	C₂×C₄	#67	1	2	yes	—
35	C₈	—	6	4	no	—
36	C₂×C₃	—	8	1	no	—
37	C₂×C₃	#100	1	1	yes	characteristic
38	C₂×C₃	#104	1	2	yes	—
39	C₂²	—	4	1	no	—
40	C₂²	—	4	2	no	—
41	C₂²	#217	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	2	2	no	—
44	C₄	—	4	1	no	—
45	C₃	#329	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	8	1	no	—
47	C₂	#833	1	1	yes	characteristic
48	C₂	#837	1	2	yes	—

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

N	H ≅ G/N	type
2. #803	C₂	semidirect
45. C₃	#329	semidirect

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