Subgroups — #4884

Order 192.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#897	C₂	1	1	yes	maximal, characteristic
2	D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#816	C₂	1	1	yes	maximal, characteristic, complemented
6	#810	C₂	1	1	yes	maximal, characteristic, complemented
7	#807	C₂	1	1	yes	maximal, characteristic, complemented
8	#484	—	3	1	no	maximal, Sylow
9	C₂×C₄×D₃	—	2	1	no	—
10	C₂×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	(C₂×D₃)⋊C₄	—	2	1	no	—
16	C₄⋊Dic₃	—	2	1	no	—
17	C₄⋊Dic₃	C₂²	1	1	yes	characteristic
18	Dic₃⋊C₄	—	2	1	no	—
19	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂²⋊Q₈	—	3	1	no	—
21	C₂×C₄⋊C₄	—	3	1	no	—
22	#107	—	3	1	no	—
23	#107	D₃	1	1	yes	characteristic, complemented
24	#103	—	3	1	no	—
25	#103	—	3	1	no	—
26	C₂²⋊C₈	—	3	1	no	—
27	C₂²×D₃	D₄	1	1	yes	characteristic
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₂×Dic₃	—	2	1	no	—
32	C₂×Dic₃	—	2	1	no	—
33	C₂×Dic₃	D₄	1	1	yes	characteristic
34	C₄×D₃	—	2	1	no	—
35	C₄×D₃	—	2	1	no	—
36	C₄×D₃	—	4	2	no	—
37	Dic₆	—	2	1	no	—
38	Dic₆	—	2	1	no	—
39	C₃×C₈	—	2	1	no	—
40	C₃⋊C₈	—	2	1	no	—
41	C₂×Q₈	—	3	1	no	—
42	C₂²×C₄	—	3	1	no	—
43	C₂²×C₄	—	6	1	no	—
44	C₂×C₈	—	3	1	no	—
45	C₂×C₈	C₂×D₃	1	1	yes	characteristic
46	C₄⋊C₄	—	3	1	no	—
47	C₄⋊C₄	—	6	1	no	—
48	C₄⋊C₄	—	6	1	no	—
49	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
50	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
51	C₂²⋊C₄	—	6	1	no	—
52	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
53	C₂×D₃	—	2	1	no	—
54	C₂×D₃	—	2	1	no	—
55	C₂×D₃	Q₁₆	1	2	yes	—
56	C₃×C₄	—	4	1	no	—
57	C₃×C₄	—	4	1	no	—
58	C₃×C₄	#41	1	1	yes	characteristic
59	C₃×C₄	#41	1	1	yes	characteristic
60	Dic₃	—	2	1	no	—
61	Dic₃	—	4	1	no	—
62	Dic₃	—	4	1	no	—
63	C₂³	—	3	1	no	—
64	Q₈	—	6	1	no	—
65	Q₈	—	6	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	6	1	no	—
70	C₂×C₄	—	6	1	no	—
71	C₂×C₄	—	6	1	no	—
72	C₂×C₄	—	6	1	no	—
73	C₂×C₄	—	12	2	no	—
74	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	6	1	no	—
77	C₂×C₃	#123	1	1	yes	characteristic
78	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
79	C₂×C₃	AGL(1,ℤ/8)	1	1	yes	characteristic
80	D₃	—	2	2	no	—
81	C₂²	—	3	2	no	—
82	C₂²	—	6	1	no	—
83	C₂²	—	6	1	no	—
84	C₂²	D₃×D₄	1	1	yes	characteristic
85	C₄	—	4	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	6	1	no	—
88	C₄	—	12	1	no	—
89	C₄	—	12	1	no	—
90	C₄	#235	1	1	yes	characteristic
91	C₄	#239	1	1	yes	characteristic
92	C₃	#484	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	6	2	no	—
94	C₂	#894	1	1	yes	characteristic
95	C₂	#911	1	1	yes	characteristic
96	C₂	D₃×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#107	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	C₂²×D₃	D₄
hypercenter	#107	D₃
hypocenter	C₃	#484
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. C₃×#107	C₂	semidirect
5. #816	C₂	semidirect
6. #810	C₂	semidirect
7. #807	C₂	semidirect
23. #107	D₃	semidirect
92. C₃	#484	semidirect

Maximal subgroups

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

subgroup	index
#897	2
D₃×C₄⋊C₄	2
C₃×#107	2
(C₂×D₃)⋊C₈	2
#816	2
#810	2
#807	2
#484	3