Subgroups — C₄×D₃×Q₈ #5571

Order 192.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₄⋊C₄	C₂	1	3	yes	maximal
5	#887	C₂	1	3	yes	maximal, complemented
6	C₄²×D₃	C₂	1	3	yes	maximal
7	C₄×Dic₆	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×Q₈	—	3	1	no	maximal, Sylow
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	D₃×Q₈	C₄	1	8	yes	direct product factor
11	C₂×C₄×D₃	C₂²	1	3	yes	—
12	C₂×C₄×D₃	C₂²	1	3	yes	—
13	C₂×C₄×D₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₆	C₂²	1	3	yes	—
15	C₃×C₄⋊C₄	C₂²	1	3	yes	—
16	C₃×C₄²	C₂²	1	3	yes	—
17	C₄⋊Dic₃	C₂²	1	3	yes	—
18	Dic₃⋊C₄	C₂²	1	6	yes	—
19	C₄×Dic₃	C₂²	1	3	yes	—
20	C₄×Dic₃	C₂²	1	3	yes	—
21	C₄×Dic₃	C₂²	1	3	yes	—
22	C₂²×Q₈	—	3	1	no	—
23	C₄×Q₈	—	3	1	no	—
24	C₄×Q₈	—	3	3	no	—
25	C₄×Q₈	—	3	3	no	—
26	C₄×Q₈	D₃	1	1	yes	characteristic, direct product factor
27	C₂×C₄⋊C₄	—	3	3	no	—
28	C₂×C₄²	—	3	3	no	—
29	C₂²×D₃	C₂³	1	1	yes	characteristic
30	C₃×Q₈	C₂×C₄	1	4	yes	complemented
31	C₂×C₃×C₄	C₂³	1	3	yes	—
32	C₂×C₃×C₄	C₂³	1	3	yes	—
33	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
34	C₂×Dic₃	C₂³	1	3	yes	—
35	C₂×Dic₃	C₂³	1	3	yes	—
36	C₂×Dic₃	C₂³	1	1	yes	characteristic
37	C₄×D₃	—	2	6	no	—
38	C₄×D₃	C₂×C₄	1	12	yes	—
39	C₄×D₃	Q₈	1	4	yes	direct product factor
40	Dic₆	C₂×C₄	1	12	yes	complemented
41	C₂×Q₈	—	3	8	no	—
42	C₂×Q₈	—	3	3	no	—
43	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
44	C₂²×C₄	—	3	3	no	—
45	C₂²×C₄	—	3	1	no	—
46	C₂²×C₄	—	3	3	no	—
47	C₄⋊C₄	—	3	6	no	—
48	C₄⋊C₄	—	3	3	no	—
49	C₄⋊C₄	C₂×D₃	1	3	yes	—
50	C₄²	—	3	3	no	—
51	C₄²	—	3	3	no	—
52	C₄²	—	3	3	no	—
53	C₄²	C₂×D₃	1	3	yes	—
54	C₂²×C₃	C₂⁴	1	1	yes	characteristic
55	C₂×D₃	C₂²×C₄	1	2	yes	—
56	C₂×D₃	C₂×Q₈	1	2	yes	—
57	C₂×D₃	#41	1	2	yes	—
58	C₃×C₄	—	2	3	no	—
59	C₃×C₄	C₂²×C₄	1	6	yes	—
60	C₃×C₄	C₂×Q₈	1	2	yes	complemented
61	Dic₃	—	2	3	no	—
62	Dic₃	C₂²×C₄	1	6	yes	—
63	Dic₃	C₂×Q₈	1	2	yes	complemented
64	C₂³	—	3	1	no	—
65	Q₈	—	3	12	no	—
66	Q₈	C₄×D₃	1	4	yes	direct product factor
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	3	3	no	—
69	C₂×C₄	—	3	12	no	—
70	C₂×C₄	—	3	4	no	—
71	C₂×C₄	—	3	3	no	—
72	C₂×C₄	—	6	6	no	—
73	C₂×C₄	C₂²×D₃	1	3	yes	—
74	C₂×C₄	C₂²×D₃	1	3	yes	—
75	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
76	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
77	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
78	C₂×C₃	C₂×#41	1	1	yes	characteristic
79	D₃	C₄×Q₈	1	4	yes	direct product factor
80	C₂²	—	3	2	no	—
81	C₂²	—	3	2	no	—
82	C₂²	—	3	2	no	—
83	C₂²	C₂³×D₃	1	1	yes	characteristic
84	C₄	—	2	3	no	—
85	C₄	—	3	6	no	—
86	C₄	—	3	2	no	—
87	C₄	—	6	3	no	—
88	C₄	C₂×C₄×D₃	1	6	yes	—
89	C₄	D₃×Q₈	1	2	yes	direct product factor
90	C₃	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	3	4	no	—
92	C₂	C₂²×C₄×D₃	1	1	yes	characteristic
93	C₂	C₂×D₃×Q₈	1	1	yes	characteristic
94	C₂	D₃×#41	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×Q₈	C₂	semidirect
3. Q₈×Dic₃	C₂	semidirect
5. #887	C₂	semidirect
7. C₄×Dic₆	C₂	semidirect
10. D₃×Q₈	C₄	direct (N × H)
26. C₄×Q₈	D₃	direct (N × H)
30. C₃×Q₈	C₂×C₄	semidirect
39. C₄×D₃	Q₈	direct (N × H)
40. Dic₆	C₂×C₄	semidirect
60. C₃×C₄	C₂×Q₈	semidirect
63. Dic₃	C₂×Q₈	semidirect
66. Q₈	C₄×D₃	direct (N × H)
79. D₃	C₄×Q₈	direct (N × H)
89. C₄	D₃×Q₈	direct (N × H)
90. C₃	C₂×C₄×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Q₈	2
C₃×C₄×Q₈	2
Q₈×Dic₃	2
D₃×C₄⋊C₄	2
#887	2
C₄²×D₃	2
C₄×Dic₆	2
C₂×C₄×Q₈	3

Subgroups — C4×D3×Q8 #5571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃×Q₈ #5571