Subgroups — #4800

Order 192.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#947	C₂	1	1	yes	maximal, characteristic
2	#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	#835	C₂	1	1	yes	maximal, characteristic, complemented
5	#821	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#809	C₂	1	1	yes	maximal, characteristic
8	#488	—	3	1	no	maximal, Sylow
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×D₁₂	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	(C₂×D₃)⋊C₄	—	2	1	no	—
14	(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₃	—	2	1	no	—
16	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	Dic₃⋊C₄	—	2	1	no	—
18	C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	#125	—	3	1	no	—
21	#124	—	3	1	no	—
22	#103	—	3	1	no	—
23	#103	D₃	1	1	yes	characteristic, complemented
24	#102	—	3	1	no	—
25	#102	—	3	1	no	—
26	C₄×C₈	—	3	1	no	—
27	C₂²×D₃	—	2	1	no	—
28	C₃×Q₈	—	2	1	no	—
29	C₃×Q₈	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
33	C₂×Dic₃	—	2	1	no	—
34	C₂×Dic₃	D₄	1	1	yes	characteristic
35	C₂×Dic₃	D₄	1	1	yes	characteristic
36	D₁₂	—	2	1	no	—
37	D₁₂	—	2	1	no	—
38	C₃×C₈	—	2	1	no	—
39	C₃⋊C₈	—	2	1	no	—
40	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
41	C₂×D₄	—	3	1	no	—
42	C₂×C₈	—	3	1	no	—
43	C₂×C₈	C₂×D₃	1	1	yes	characteristic
44	C₄⋊C₄	—	3	1	no	—
45	C₄⋊C₄	—	6	1	no	—
46	C₄⋊C₄	—	6	1	no	—
47	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
48	C₂²⋊C₄	—	6	1	no	—
49	C₂²⋊C₄	—	6	1	no	—
50	C₄²	—	3	1	no	—
51	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
52	C₂×D₃	—	4	1	no	—
53	C₂×D₃	—	4	1	no	—
54	C₂×D₃	—	4	1	no	—
55	C₃×C₄	—	4	1	no	—
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	#41	1	1	yes	characteristic
58	C₃×C₄	#41	1	1	yes	characteristic
59	Dic₃	—	2	1	no	—
60	Dic₃	—	2	1	no	—
61	Dic₃	—	4	1	no	—
62	C₂³	—	6	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	2	1	no	—
65	D₄	—	6	1	no	—
66	D₄	—	6	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	6	1	no	—
72	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	6	1	no	—
75	C₂×C₃	#124	1	1	yes	characteristic
76	C₂×C₃	#135	1	1	yes	characteristic
77	C₂×C₃	#135	1	1	yes	characteristic
78	D₃	—	8	1	no	—
79	C₂²	—	12	1	no	—
80	C₂²	—	12	1	no	—
81	C₂²	—	12	1	no	—
82	C₂²	D₃×D₄	1	1	yes	characteristic
83	C₄	—	4	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	6	1	no	—
86	C₄	—	6	1	no	—
87	C₄	—	12	1	no	—
88	C₄	#235	1	1	yes	characteristic
89	C₄	#237	1	1	yes	characteristic
90	C₃	#488	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	24	1	no	—
92	C₂	#885	1	1	yes	characteristic
93	C₂	#916	1	1	yes	characteristic
94	C₂	#919	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#103	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	C₂×D₁₂	C₂²
hypercenter	#103	D₃
hypocenter	C₃	#488
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
2. #890	C₂	semidirect
3. C₃×#103	C₂	semidirect
4. #835	C₂	semidirect
6. C₈×Dic₃	C₂	semidirect
23. #103	D₃	semidirect
90. C₃	#488	semidirect

Maximal subgroups

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

subgroup	index
#947	2
#890	2
C₃×#103	2
#835	2
#821	2
C₈×Dic₃	2
#809	2
#488	3