Subgroups — C₂×#888 #5497

Order 192.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
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	#888	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄⋊Q₈	—	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	2	yes	—
11	C₂²×Dic₃	C₂²	1	1	yes	characteristic
12	C₂²×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₆	—	2	8	no	—
14	C₂×Dic₆	C₂²	1	8	yes	—
15	C₃×C₄⋊C₄	C₂²	1	4	yes	—
16	C₄⋊Dic₃	C₂²	1	4	yes	—
17	Dic₃⋊C₄	C₂²	1	8	yes	—
18	C₄×Dic₃	C₂²	1	4	yes	—
19	C₂²×Q₈	—	3	2	no	—
20	C₄⋊Q₈	—	3	8	no	—
21	C₂×C₄⋊C₄	—	3	2	no	—
22	C₂×C₄⋊C₄	—	3	1	no	—
23	C₂×C₄⋊C₄	D₃	1	1	yes	characteristic
24	C₂×C₄²	—	3	1	no	—
25	C₂³×C₃	C₂³	1	1	yes	characteristic
26	C₂×C₃×C₄	—	2	4	no	—
27	C₂×C₃×C₄	Q₈	1	4	yes	complemented
28	C₂×C₃×C₄	C₂³	1	4	yes	—
29	C₂×C₃×C₄	C₂³	1	2	yes	—
30	C₂×Dic₃	—	2	4	no	—
31	C₂×Dic₃	D₄	1	4	yes	—
32	C₂×Dic₃	Q₈	1	4	yes	complemented
33	C₂×Dic₃	C₂³	1	4	yes	—
34	C₂×Dic₃	C₂³	1	2	yes	—
35	C₂×Dic₃	C₂³	1	2	yes	—
36	Dic₆	—	2	16	no	—
37	C₂×Q₈	—	3	8	no	—
38	C₂×Q₈	—	6	8	no	—
39	C₂²×C₄	—	3	1	no	—
40	C₂²×C₄	—	3	1	no	—
41	C₂²×C₄	—	3	2	no	—
42	C₂²×C₄	C₂×D₃	1	2	yes	—
43	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
44	C₄⋊C₄	—	3	8	no	—
45	C₄⋊C₄	—	3	4	no	—
46	C₄⋊C₄	C₂×D₃	1	4	yes	—
47	C₄²	—	3	4	no	—
48	C₂²×C₃	C₂×D₄	1	2	yes	—
49	C₂²×C₃	C₂×Q₈	1	2	yes	—
50	C₂²×C₃	C₂×Q₈	1	2	yes	—
51	C₂²×C₃	C₂⁴	1	1	yes	characteristic
52	C₃×C₄	—	2	4	no	—
53	C₃×C₄	C₂×Q₈	1	4	yes	complemented
54	Dic₃	—	2	4	no	—
55	Dic₃	C₂×D₄	1	4	yes	—
56	Dic₃	C₂×Q₈	1	4	yes	complemented
57	C₂³	C₂²×D₃	1	1	yes	characteristic
58	Q₈	—	6	16	no	—
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	3	4	no	—
61	C₂×C₄	—	3	4	no	—
62	C₂×C₄	—	3	2	no	—
63	C₂×C₄	—	3	2	no	—
64	C₂×C₄	—	3	4	no	—
65	C₂×C₄	—	6	4	no	—
66	C₂×C₄	Dic₆	1	4	yes	complemented
67	C₂×C₄	C₂²×D₃	1	4	yes	—
68	C₂×C₄	C₂²×D₃	1	2	yes	—
69	C₂×C₃	C₄⋊Q₈	1	4	yes	complemented
70	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
71	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
72	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
73	C₂²	C₂×Dic₆	1	2	yes	—
74	C₂²	D₃×D₄	1	2	yes	—
75	C₂²	D₃×Q₈	1	2	yes	—
76	C₂²	C₂³×D₃	1	1	yes	characteristic
77	C₄	—	2	4	no	—
78	C₄	—	3	4	no	—
79	C₄	—	3	4	no	—
80	C₄	—	6	4	no	—
81	C₄	C₂×Dic₆	1	4	yes	complemented
82	C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
83	C₂	#888	1	4	yes	direct product factor
84	C₂	C₂²×Dic₆	1	1	yes	characteristic
85	C₂	C₂×D₃×D₄	1	1	yes	characteristic
86	C₂	C₂×D₃×Q₈	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×C₄⋊Q₈
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. #888	C₂	direct (N × H)
27. C₂×C₃×C₄	Q₈	semidirect
32. C₂×Dic₃	Q₈	semidirect
53. C₃×C₄	C₂×Q₈	semidirect
56. Dic₃	C₂×Q₈	semidirect
66. C₂×C₄	Dic₆	semidirect
69. C₂×C₃	C₄⋊Q₈	semidirect
81. C₄	C₂×Dic₆	semidirect
82. C₃	C₂×C₄⋊Q₈	semidirect
83. C₂	#888	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×Dic₆	2
C₂×C₃×C₄⋊C₄	2
C₂×C₄⋊Dic₃	2
C₂×Dic₃⋊C₄	2
C₂×C₄×Dic₃	2
#888	2
C₂×C₄⋊Q₈	3

Subgroups — C2×#888 #5497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#888 #5497