Subgroups — C₂²×Dic₁₄₄₈ #37546834

Order 23168.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₂₄	C₂	1	2	yes	maximal
2	C₂×Dic₁₄₄₈	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₃₆₂	—	2	2	no	—
5	C₂×Dic₇₂₄	—	2	6	no	—
6	C₂×Dic₇₂₄	C₂²	1	12	yes	—
7	Dic₁₄₄₈	C₂²	1	16	yes	direct product factor
8	C₂²×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₈₁	C₂²	1	6	yes	—
10	C₂×Dic₃₆₂	—	2	12	no	—
11	C₂×Dic₃₆₂	—	4	6	no	—
12	C₂²×Dic₁₈₁	—	4	2	no	—
13	Dic₇₂₄	—	2	12	no	—
14	Dic₇₂₄	C₂³	1	8	yes	—
15	C₂²×C₄×C₁₈₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₈₁	D₄	1	3	yes	—
17	C₂×C₈×C₁₈₁	C₂³	1	3	yes	—
18	C₁₆×C₁₈₁	C₂³	1	4	yes	—
19	Dic₃₆₂	—	2	8	no	—
20	Dic₃₆₂	—	4	12	no	—
21	C₂×Dic₁₈₁	—	4	12	no	—
22	C₂³×C₁₈₁	D₈	1	1	yes	characteristic
23	C₂×C₄×C₁₈₁	D₈	1	3	yes	—
24	C₂×C₄×C₁₈₁	C₂×D₄	1	3	yes	—
25	C₈×C₁₈₁	C₂×D₄	1	3	yes	—
26	C₈×C₁₈₁	C₂⁴	1	1	yes	characteristic
27	C₂²×C₁₈₁	Q₃₂	1	4	yes	complemented
28	C₂²×C₁₈₁	C₂×D₈	1	3	yes	—
29	C₄×C₁₈₁	C₂×D₈	1	3	yes	—
30	C₄×C₁₈₁	C₂²×D₄	1	1	yes	characteristic
31	Dic₁₈₁	—	4	8	no	—
32	C₂×C₁₈₁	C₂×Q₃₂	1	6	yes	complemented
33	C₂×C₁₈₁	C₂²×D₈	1	1	yes	characteristic
34	C₁₈₁	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
35	C₂²×Q₃₂	—	181	1	no	maximal, Sylow
36	C₂²×Q₁₆	—	181	2	no	—
37	C₂×Q₃₂	—	181	12	no	—
38	C₂²×C₁₆	D₁₈₁	1	1	yes	characteristic
39	C₂²×Q₈	—	362	2	no	—
40	C₂×Q₁₆	—	362	6	no	—
41	C₂×Q₁₆	—	181	12	no	—
42	C₂²×C₈	C₂×D₁₈₁	1	1	yes	characteristic
43	Q₃₂	—	181	16	no	—
44	C₂×C₁₆	C₂×D₁₈₁	1	6	yes	—
45	C₂×Q₈	—	362	12	no	—
46	C₂×Q₈	—	724	6	no	—
47	C₂²×C₄	—	724	2	no	—
48	C₂²×C₄	D₇₂₄	1	1	yes	characteristic
49	Q₁₆	—	362	12	no	—
50	Q₁₆	—	181	8	no	—
51	C₂×C₈	D₇₂₄	1	3	yes	—
52	C₂×C₈	C₂²×D₁₈₁	1	3	yes	—
53	C₁₆	C₂²×D₁₈₁	1	4	yes	—
54	C₂³	D₁₄₄₈	1	1	yes	characteristic
55	Q₈	—	362	8	no	—
56	Q₈	—	724	12	no	—
57	C₂×C₄	—	724	12	no	—
58	C₂×C₄	D₁₄₄₈	1	3	yes	—
59	C₂×C₄	C₂×D₇₂₄	1	3	yes	—
60	C₈	C₂×D₇₂₄	1	3	yes	—
61	C₈	C₂³×D₁₈₁	1	1	yes	characteristic
62	C₂²	Dic₁₄₄₈	1	4	yes	direct product factor
63	C₂²	C₂×D₁₄₄₈	1	3	yes	—
64	C₄	—	724	8	no	—
65	C₄	C₂×D₁₄₄₈	1	3	yes	—
66	C₄	C₂²×D₇₂₄	1	1	yes	characteristic
67	C₂	C₂×Dic₁₄₄₈	1	6	yes	direct product factor
68	C₂	C₂²×D₁₄₄₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₄₄₈
commutator, cosocle	C₈×C₁₈₁	C₂⁴
Frattini	C₈	C₂³×D₁₈₁
Fitting	C₂²×C₁₆×C₁₈₁	C₂
socle, prime radical	C₂³×C₁₈₁	D₈
hypercenter	C₂²×C₁₆	D₁₈₁
hypocenter	C₁₈₁	C₂²×Q₃₂
LCS	G ▷ C₈×C₁₈₁ ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₄₄₈	C₂	direct (N × H)
7. Dic₁₄₄₈	C₂²	direct (N × H)
27. C₂²×C₁₈₁	Q₃₂	semidirect
32. C₂×C₁₈₁	C₂×Q₃₂	semidirect
34. C₁₈₁	C₂²×Q₃₂	semidirect
62. C₂²	Dic₁₄₄₈	direct (N × H)
67. C₂	C₂×Dic₁₄₄₈	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×Dic₇₂₄	2
C₂×Dic₁₄₄₈	2
C₂²×C₁₆×C₁₈₁	2
C₂²×Q₃₂	181

Subgroups — C22×Dic1448 #37546834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₁₄₄₈ #37546834