Subgroups — C₄×Dic₁₈₈ #15689219

Order 3008.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₉₄	C₂	1	2	yes	maximal
3	#13093958	C₂	1	1	yes	maximal, characteristic
4	#13093949	C₂	1	2	yes	maximal
5	C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₄	C₂²	1	2	yes	—
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₄²×C₄₇	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	Dic₄₇⋊C₄	—	2	2	no	—
12	C₄×Dic₄₇	—	2	2	no	—
13	Dic₁₈₈	C₄	1	4	yes	direct product factor
14	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₇	—	2	2	no	—
18	C₂×Dic₄₇	—	2	2	no	—
19	Dic₉₄	—	2	2	no	—
20	Dic₉₄	C₂×C₄	1	4	yes	—
21	C₈×C₄₇	—	2	1	no	—
22	C₈×C₄₇	C₂×C₄	1	2	yes	—
23	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₇	—	2	1	no	—
25	C₄×C₄₇	Q₁₆	1	2	yes	complemented
26	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₇	#41	1	1	yes	characteristic
28	Dic₄₇	—	2	4	no	—
29	Dic₄₇	—	4	2	no	—
30	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
31	C₂×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₄₇	#135	1	1	yes	characteristic
33	C₄×Q₁₆	—	47	1	no	maximal, Sylow
34	C₄₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	47	1	no	—
36	C₄×Q₈	—	47	2	no	—
37	#107	—	47	1	no	—
38	#103	—	47	2	no	—
39	C₄×C₈	D₄₇	1	1	yes	characteristic
40	C₂×Q₈	—	47	2	no	—
41	Q₁₆	—	47	4	no	—
42	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
43	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
44	C₄⋊C₄	—	47	2	no	—
45	C₄⋊C₄	—	94	2	no	—
46	C₄²	—	94	2	no	—
47	C₄²	C₂×D₄₇	1	1	yes	characteristic
48	Q₈	—	47	4	no	—
49	Q₈	—	94	2	no	—
50	C₂×C₄	—	94	2	no	—
51	C₂×C₄	—	94	2	no	—
52	C₂×C₄	D₁₈₈	1	1	yes	characteristic
53	C₂×C₄	D₁₈₈	1	1	yes	characteristic
54	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₄×D₄₇	1	2	yes	—
57	C₂²	C₂×D₁₈₈	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	94	4	no	—
60	C₄	—	188	2	no	—
61	C₄	Dic₁₈₈	1	2	yes	direct product factor
62	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
63	C₄	#10625350	1	1	yes	characteristic
64	C₂	C₄×D₁₈₈	1	1	yes	characteristic
65	C₂	C₂×Dic₁₈₈	1	1	yes	characteristic
66	C₂	#13094046	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₈₈
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₄×C₈×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₄×C₈	D₄₇
hypocenter	C₄₇	C₄×Q₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
13. Dic₁₈₈	C₄	direct (N × H)
25. C₄×C₄₇	Q₁₆	semidirect
34. C₄₇	C₄×Q₁₆	semidirect
61. C₄	Dic₁₈₈	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×Dic₁₈₈	2
C₄×Dic₉₄	2
#13093958	2
#13093949	2
C₄×C₈×C₄₇	2
C₄×Q₁₆	47

Subgroups — C4×Dic188 #15689219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₁₈₈ #15689219