Subgroups — #4890

Order 192.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#893	C₂	1	1	yes	maximal, characteristic
2	#888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#821	C₂	1	1	yes	maximal, characteristic
5	Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#809	C₂	1	1	yes	maximal, characteristic
7	#807	C₂	1	1	yes	maximal, characteristic, complemented
8	#474	—	3	1	no	maximal, Sylow
9	C₂×D₁₂	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃	—	2	1	no	—
11	C₂×Dic₆	—	2	1	no	—
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	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	C₄⋊Q₈	—	3	1	no	—
21	C₄×D₄	—	3	1	no	—
22	#107	—	3	1	no	—
23	#107	D₃	1	1	yes	characteristic, complemented
24	C₄⋊C₈	—	3	1	no	—
25	#102	—	3	1	no	—
26	#102	—	3	1	no	—
27	C₂²×D₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
33	C₂×Dic₃	D₄	1	1	yes	characteristic
34	D₁₂	—	2	1	no	—
35	D₁₂	Q₈	1	2	yes	complemented
36	C₄×D₃	—	4	2	no	—
37	Dic₆	—	4	2	no	—
38	C₃×C₈	—	2	1	no	—
39	C₃⋊C₈	—	2	1	no	—
40	C₂×Q₈	—	6	1	no	—
41	C₂×D₄	—	3	1	no	—
42	C₂²×C₄	—	6	1	no	—
43	C₂×C₈	—	3	1	no	—
44	C₂×C₈	C₂×D₃	1	1	yes	characteristic
45	C₄⋊C₄	—	3	1	no	—
46	C₄⋊C₄	—	6	1	no	—
47	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
48	C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
49	C₂²⋊C₄	—	6	1	no	—
50	C₄²	—	3	1	no	—
51	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
52	C₂×D₃	—	2	2	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	C₂×Q₈	1	1	yes	characteristic
58	C₃×C₄	#41	1	1	yes	characteristic
59	Dic₃	—	2	1	no	—
60	Dic₃	—	4	1	no	—
61	Dic₃	D₈	1	2	yes	—
62	C₂³	—	6	1	no	—
63	Q₈	—	12	2	no	—
64	D₄	—	3	2	no	—
65	D₄	—	6	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	6	1	no	—
71	C₂×C₄	—	12	2	no	—
72	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	6	1	no	—
75	C₂×C₃	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₃	C₂×D₈	1	1	yes	characteristic
77	C₂×C₃	#137	1	1	yes	characteristic
78	D₃	—	4	2	no	—
79	C₂²	—	6	2	no	—
80	C₂²	—	12	1	no	—
81	C₂²	—	12	1	no	—
82	C₂²	D₃×D₄	1	1	yes	characteristic
83	C₄	—	3	2	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	6	1	no	—
87	C₄	—	12	1	no	—
88	C₄	#235	1	1	yes	characteristic
89	C₄	D₃×Q₈	1	1	yes	characteristic
90	C₃	#474	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	12	2	no	—
92	C₂	#896	1	1	yes	characteristic
93	C₂	D₃×D₈	1	1	yes	characteristic
94	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×#107	C₂
socle	C₂²×C₃	C₂×D₄
prime radical	C₂×D₁₂	C₂²
hypercenter	#107	D₃
hypocenter	C₃	#474
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
2. #888	C₂	semidirect
3. C₃×#107	C₂	semidirect
5. Dic₃⋊C₈	C₂	semidirect
7. #807	C₂	semidirect
23. #107	D₃	semidirect
35. D₁₂	Q₈	semidirect
90. C₃	#474	semidirect

Maximal subgroups

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

subgroup	index
#893	2
#888	2
C₃×#107	2
#821	2
Dic₃⋊C₈	2
#809	2
#807	2
#474	3