Subgroups — #4797

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#944	C₂	1	1	yes	maximal, characteristic
2	#890	C₂	1	1	yes	maximal, characteristic
3	C₃×#103	C₂	1	1	yes	maximal, characteristic
4	#835	C₂	1	1	yes	maximal, characteristic
5	#816	C₂	1	1	yes	maximal, characteristic
6	#815	C₂	1	1	yes	maximal, characteristic
7	#810	C₂	1	1	yes	maximal, characteristic
8	#491	—	3	1	no	maximal, Sylow
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×Dic₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₃	—	2	1	no	—
14	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
15	Dic₃⋊C₄	—	2	1	no	—
16	Dic₃⋊C₄	—	2	1	no	—
17	Dic₃⋊C₄	—	2	1	no	—
18	C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈	—	3	1	no	—
21	#125	—	3	1	no	—
22	#103	—	3	1	no	—
23	#103	—	3	1	no	—
24	#103	—	3	1	no	—
25	#103	D₃	1	1	yes	characteristic
26	#97	—	3	1	no	—
27	C₃×Q₈	—	2	1	no	—
28	C₃×Q₈	—	2	1	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₂×Dic₃	—	2	1	no	—
33	C₂×Dic₃	—	2	1	no	—
34	C₂×Dic₃	D₄	1	1	yes	characteristic
35	C₂×Dic₃	D₄	1	1	yes	characteristic
36	Dic₆	—	2	1	no	—
37	Dic₆	—	2	1	no	—
38	C₃×C₈	—	2	1	no	—
39	C₃⋊C₈	—	2	1	no	—
40	C₂×Q₈	—	3	1	no	—
41	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
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	—	6	1	no	—
48	C₄⋊C₄	—	6	1	no	—
49	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
50	C₄²	—	3	1	no	—
51	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
52	C₃×C₄	—	4	1	no	—
53	C₃×C₄	—	4	1	no	—
54	C₃×C₄	#41	1	1	yes	characteristic
55	C₃×C₄	#41	1	1	yes	characteristic
56	Dic₃	—	2	1	no	—
57	Dic₃	—	2	1	no	—
58	Dic₃	—	4	1	no	—
59	Dic₃	—	4	1	no	—
60	Q₈	—	2	1	no	—
61	Q₈	—	2	1	no	—
62	Q₈	—	6	1	no	—
63	Q₈	—	6	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	3	1	no	—
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	6	1	no	—
69	C₂×C₄	—	6	1	no	—
70	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	6	1	no	—
73	C₂×C₃	#124	1	1	yes	characteristic
74	C₂×C₃	#137	1	1	yes	characteristic
75	C₂×C₃	#137	1	1	yes	characteristic
76	C₂²	D₃×D₄	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	4	1	no	—
79	C₄	—	6	1	no	—
80	C₄	—	6	1	no	—
81	C₄	—	12	1	no	—
82	C₄	—	12	1	no	—
83	C₄	#235	1	1	yes	characteristic
84	C₄	#237	1	1	yes	characteristic
85	C₃	#491	1	1	yes	characteristic, complemented, Sylow
86	C₂	#885	1	1	yes	characteristic
87	C₂	#915	1	1	yes	characteristic
88	C₂	#918	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, prime radical	C₂²×C₃	C₂×D₄
hypercenter	#103	D₃
hypocenter	C₃	#491
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
85. C₃	#491	semidirect

Maximal subgroups

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

subgroup	index
#944	2
#890	2
C₃×#103	2
#835	2
#816	2
#815	2
#810	2
#491	3