Subgroups — C₂×#944 #5810

Order 192.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₆	C₂	1	1	yes	maximal, characteristic
3	#944	C₂	1	8	yes	maximal, direct product factor
4	C₂×Dic₃⋊C₄	C₂	1	4	yes	maximal
5	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Q₈	—	3	1	no	maximal, Sylow
7	C₂×C₃×Q₈	—	2	4	no	—
8	C₂×C₃×Q₈	C₂²	1	4	yes	—
9	C₂²×C₃×C₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃	C₂²	1	2	yes	—
12	C₂²×Dic₃	C₂²	1	2	yes	—
13	C₂×Dic₆	—	2	4	no	—
14	C₂×Dic₆	C₂²	1	4	yes	—
15	Dic₃⋊C₄	C₂²	1	16	yes	—
16	C₄×Dic₃	C₂²	1	4	yes	—
17	C₂²×Q₈	—	3	1	no	—
18	C₂²×Q₈	D₃	1	1	yes	characteristic
19	C₄⋊Q₈	—	3	8	no	—
20	C₂×C₄⋊C₄	—	3	4	no	—
21	C₂×C₄²	—	3	1	no	—
22	C₂³×C₃	C₂³	1	1	yes	characteristic
23	C₃×Q₈	—	2	8	no	—
24	C₂×C₃×C₄	—	2	4	no	—
25	C₂×C₃×C₄	D₄	1	4	yes	—
26	C₂×C₃×C₄	C₂³	1	4	yes	—
27	C₂×C₃×C₄	C₂³	1	2	yes	—
28	C₂×Dic₃	—	2	4	no	—
29	C₂×Dic₃	Q₈	1	8	yes	complemented
30	C₂×Dic₃	C₂³	1	4	yes	—
31	C₂×Dic₃	C₂³	1	4	yes	—
32	Dic₆	—	2	8	no	—
33	C₂×Q₈	—	2	4	no	—
34	C₂×Q₈	—	3	4	no	—
35	C₂×Q₈	—	6	4	no	—
36	C₂×Q₈	C₂×D₃	1	4	yes	—
37	C₂²×C₄	—	3	2	no	—
38	C₂²×C₄	—	3	2	no	—
39	C₂²×C₄	C₂×D₃	1	2	yes	—
40	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
41	C₄⋊C₄	—	3	16	no	—
42	C₄²	—	3	4	no	—
43	C₂²×C₃	C₂×D₄	1	2	yes	—
44	C₂²×C₃	C₂×Q₈	1	4	yes	—
45	C₂²×C₃	C₂⁴	1	1	yes	characteristic
46	C₃×C₄	—	2	4	no	—
47	C₃×C₄	C₂×D₄	1	4	yes	—
48	Dic₃	—	2	4	no	—
49	Dic₃	C₂×Q₈	1	8	yes	complemented
50	C₂³	C₂²×D₃	1	1	yes	characteristic
51	Q₈	—	2	8	no	—
52	Q₈	—	6	8	no	—
53	C₂×C₄	—	2	4	no	—
54	C₂×C₄	—	3	8	no	—
55	C₂×C₄	—	3	4	no	—
56	C₂×C₄	—	3	4	no	—
57	C₂×C₄	—	6	4	no	—
58	C₂×C₄	#67	1	4	yes	—
59	C₂×C₄	C₂²×D₃	1	4	yes	—
60	C₂×C₄	C₂²×D₃	1	2	yes	—
61	C₂×C₃	C₄⋊Q₈	1	4	yes	complemented
62	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
63	C₂×C₃	C₂²×Q₈	1	2	yes	—
64	C₂²	D₃×Q₈	1	4	yes	—
65	C₂²	C₂×#67	1	2	yes	—
66	C₂²	C₂³×D₃	1	1	yes	characteristic
67	C₄	—	2	4	no	—
68	C₄	—	3	8	no	—
69	C₄	—	6	4	no	—
70	C₄	C₂×#67	1	4	yes	—
71	C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
72	C₂	#944	1	4	yes	direct product factor
73	C₂	C₂×D₃×Q₈	1	2	yes	—
74	C₂	C₂²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴
Frattini	C₂²	C₂³×D₃
Fitting	C₂²×C₃×Q₈	C₂
socle, prime radical	C₂³×C₃	C₂³
hypercenter	C₂²×Q₈	D₃
hypocenter	C₃	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
3. #944	C₂	direct (N × H)
29. C₂×Dic₃	Q₈	semidirect
49. Dic₃	C₂×Q₈	semidirect
61. C₂×C₃	C₄⋊Q₈	semidirect
71. C₃	C₂×C₄⋊Q₈	semidirect
72. C₂	#944	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×C₃×Q₈	2
C₂²×Dic₆	2
#944	2
C₂×Dic₃⋊C₄	2
C₂×C₄×Dic₃	2
C₂×C₄⋊Q₈	3

Subgroups — C2×#944 #5810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#944 #5810