Subgroups — C₂×#890 #5499

Order 192.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
6	#890	C₂	1	8	yes	maximal, direct product factor
7	C₂×#125	—	3	1	no	maximal, Sylow
8	C₂²×C₃×C₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂²×Dic₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃	C₂²	1	2	yes	—
13	C₃×C₄⋊C₄	C₂²	1	4	yes	—
14	C₄⋊Dic₃	C₂²	1	8	yes	—
15	C₄⋊Dic₃	C₂²	1	4	yes	—
16	Dic₃⋊C₄	C₂²	1	8	yes	—
17	C₄×Dic₃	C₂²	1	4	yes	—
18	#125	—	3	8	no	—
19	C₂×C₄⋊C₄	—	3	2	no	—
20	C₂×C₄⋊C₄	—	3	2	no	—
21	C₂×C₄⋊C₄	—	3	1	no	—
22	C₂×C₄⋊C₄	D₃	1	1	yes	characteristic
23	C₂×C₄²	—	3	1	no	—
24	C₂³×C₃	C₂³	1	1	yes	characteristic
25	C₂×C₃×C₄	—	2	4	no	—
26	C₂×C₃×C₄	Q₈	1	4	yes	—
27	C₂×C₃×C₄	C₂³	1	4	yes	—
28	C₂×C₃×C₄	C₂³	1	2	yes	—
29	C₂×Dic₃	—	2	2	no	—
30	C₂×Dic₃	—	2	2	no	—
31	C₂×Dic₃	—	2	4	no	—
32	C₂×Dic₃	C₂³	1	2	yes	—
33	C₂×Dic₃	C₂³	1	2	yes	—
34	C₂×Dic₃	C₂³	1	4	yes	—
35	C₂²×C₄	—	3	1	no	—
36	C₂²×C₄	—	3	1	no	—
37	C₂²×C₄	—	3	2	no	—
38	C₂²×C₄	C₂×D₃	1	2	yes	—
39	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
40	C₄⋊C₄	—	3	8	no	—
41	C₄⋊C₄	—	3	8	no	—
42	C₄⋊C₄	—	3	4	no	—
43	C₄⋊C₄	C₂×D₃	1	4	yes	—
44	C₄²	—	3	4	no	—
45	C₂²×C₃	C₂×Q₈	1	2	yes	—
46	C₂²×C₃	#41	1	2	yes	—
47	C₂²×C₃	#41	1	2	yes	—
48	C₂²×C₃	C₂⁴	1	1	yes	characteristic
49	C₃×C₄	—	2	4	no	—
50	C₃×C₄	C₂×Q₈	1	4	yes	—
51	Dic₃	—	2	2	no	—
52	Dic₃	—	2	2	no	—
53	Dic₃	—	2	4	no	—
54	C₂³	C₂²×D₃	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	3	2	no	—
57	C₂×C₄	—	3	2	no	—
58	C₂×C₄	—	3	4	no	—
59	C₂×C₄	—	6	2	no	—
60	C₂×C₄	—	6	2	no	—
61	C₂×C₄	—	6	4	no	—
62	C₂×C₄	Dic₆	1	4	yes	—
63	C₂×C₄	C₂²×D₃	1	4	yes	—
64	C₂×C₄	C₂²×D₃	1	2	yes	—
65	C₂×C₃	#125	1	4	yes	complemented
66	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
67	C₂×C₃	C₂×#41	1	1	yes	characteristic
68	C₂×C₃	C₂×#41	1	1	yes	characteristic
69	C₂²	C₂×Dic₆	1	2	yes	—
70	C₂²	#237	1	2	yes	—
71	C₂²	#239	1	2	yes	—
72	C₂²	C₂³×D₃	1	1	yes	characteristic
73	C₄	—	2	4	no	—
74	C₄	—	6	2	no	—
75	C₄	—	6	2	no	—
76	C₄	—	6	4	no	—
77	C₄	C₂×Dic₆	1	4	yes	—
78	C₃	C₂×#125	1	1	yes	characteristic, complemented, Sylow
79	C₂	#890	1	4	yes	direct product factor
80	C₂	C₂²×Dic₆	1	1	yes	characteristic
81	C₂	C₂×#237	1	1	yes	characteristic
82	C₂	C₂×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴
Frattini	C₂²	C₂³×D₃
Fitting	C₂×C₃×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₃
hypocenter	C₃	C₂×#125
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #890	C₂	direct (N × H)
65. C₂×C₃	#125	semidirect
78. C₃	C₂×#125	semidirect
79. C₂	#890	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄⋊C₄	2
C₂×C₄⋊Dic₃	2
C₂×Dic₃⋊C₄	2
C₂×C₄×Dic₃	2
#890	2
C₂×#125	3

Subgroups — C2×#890 #5499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#890 #5499