Subgroups — C₂×#821 #5112

Order 192.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#821	C₂	1	4	yes	maximal, direct product factor
5	C₂×#102	—	3	1	no	maximal, Sylow
6	C₂³×D₃	—	2	1	no	—
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃	—	2	1	no	—
9	C₂×D₁₂	—	2	1	no	—
10	C₂×D₁₂	—	2	2	no	—
11	C₂×D₁₂	C₄	1	4	yes	complemented
12	C₂×D₁₂	C₂²	1	2	yes	—
13	C₂×C₃×C₈	—	2	2	no	—
14	C₂×C₃×C₈	C₂²	1	2	yes	complemented
15	C₄⋊Dic₃	—	2	1	no	—
16	C₄⋊Dic₃	C₂²	1	2	yes	complemented
17	C₂²×D₄	—	3	1	no	—
18	C₂²×C₈	D₃	1	1	yes	characteristic, complemented
19	C₂×C₄⋊C₄	—	3	1	no	—
20	#102	—	3	4	no	—
21	C₂³×C₃	D₄	1	1	yes	characteristic
22	C₂²×D₃	—	2	4	no	—
23	C₂²×D₃	—	2	2	no	—
24	C₂²×D₃	—	4	2	no	—
25	C₂²×D₃	—	4	2	no	—
26	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
27	C₂×C₃×C₄	D₄	1	1	yes	characteristic
28	C₂×C₃×C₄	D₄	1	2	yes	—
29	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
30	C₂×Dic₃	—	2	2	no	—
31	C₂×Dic₃	—	4	2	no	—
32	D₁₂	—	2	4	no	—
33	D₁₂	—	2	2	no	—
34	D₁₂	C₂×C₄	1	4	yes	complemented
35	C₃×C₈	—	2	2	no	—
36	C₂⁴	—	6	1	no	—
37	C₂×D₄	—	3	4	no	—
38	C₂×D₄	—	3	2	no	—
39	C₂×D₄	—	6	1	no	—
40	C₂×D₄	—	6	2	no	—
41	C₂²×C₄	—	6	1	no	—
42	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
43	C₂×C₈	—	2	2	no	—
44	C₂×C₈	C₂×D₃	1	2	yes	complemented
45	C₄⋊C₄	—	3	2	no	—
46	C₄⋊C₄	—	6	1	no	—
47	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₃	D₈	1	2	yes	—
49	C₂²×C₃	SD₁₆	1	2	yes	—
50	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
51	C₂×D₃	—	2	4	no	—
52	C₂×D₃	—	4	8	no	—
53	C₂×D₃	—	4	2	no	—
54	C₂×D₃	—	4	2	no	—
55	C₃×C₄	C₂²⋊C₄	1	2	yes	—
56	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
57	C₃×C₄	C₂×D₄	1	1	yes	characteristic
58	Dic₃	—	4	2	no	—
59	C₂³	—	6	4	no	—
60	C₂³	—	6	2	no	—
61	C₂³	—	12	2	no	—
62	C₂³	—	12	2	no	—
63	C₂³	D₁₂	1	1	yes	characteristic
64	D₄	—	3	4	no	—
65	D₄	—	6	4	no	—
66	D₄	—	6	2	no	—
67	C₂×C₄	—	6	2	no	—
68	C₂×C₄	—	12	2	no	—
69	C₂×C₄	C₄×D₃	1	2	yes	—
70	C₂×C₄	D₁₂	1	1	yes	characteristic
71	C₂×C₄	#67	1	2	yes	—
72	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₂×C₃	#102	1	4	yes	complemented
75	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₃	C₂×D₈	1	1	yes	characteristic
77	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
78	D₃	—	4	4	no	—
79	C₂²	—	6	4	no	—
80	C₂²	—	12	8	no	—
81	C₂²	—	12	2	no	—
82	C₂²	—	12	2	no	—
83	C₂²	#204	1	2	yes	—
84	C₂²	D₂₄	1	2	yes	—
85	C₂²	(C₂×D₃)⋊C₄	1	2	yes	—
86	C₂²	C₂×D₁₂	1	1	yes	characteristic
87	C₄	—	12	2	no	—
88	C₄	(C₂×D₃)⋊C₄	1	2	yes	—
89	C₄	C₂×C₄×D₃	1	1	yes	characteristic
90	C₄	C₂×#67	1	1	yes	characteristic
91	C₃	C₂×#102	1	1	yes	characteristic, complemented, Sylow
92	C₂	—	12	4	no	—
93	C₂	#821	1	4	yes	direct product factor
94	C₂	C₂×#204	1	1	yes	characteristic
95	C₂	C₂×D₂₄	1	1	yes	characteristic
96	C₂	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₂
commutator	C₃×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₂²×C₃×C₈	C₂
socle	C₂³×C₃	D₄
prime radical	C₂²×D₁₂	C₂
cosocle	C₂×C₃×C₄	C₂³
hypercenter	C₂²×C₈	D₃
hypocenter	C₃	C₂×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₈	C₂	semidirect
3. C₂×C₄⋊Dic₃	C₂	semidirect
4. #821	C₂	direct (N × H)
11. C₂×D₁₂	C₄	semidirect
14. C₂×C₃×C₈	C₂²	semidirect
16. C₄⋊Dic₃	C₂²	semidirect
18. C₂²×C₈	D₃	semidirect
34. D₁₂	C₂×C₄	semidirect
44. C₂×C₈	C₂×D₃	semidirect
74. C₂×C₃	#102	semidirect
91. C₃	C₂×#102	semidirect
93. C₂	#821	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₂	2
C₂²×C₃×C₈	2
C₂×C₄⋊Dic₃	2
#821	2
C₂×#102	3

Subgroups — C2×#821 #5112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#821 #5112