Subgroups — C₄×D₂₂₄₈ #31823547

Order 17984.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₂₄₈	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₁₂₄	C₂	1	2	yes	maximal, complemented
3	#22582813	C₂	1	1	yes	maximal, characteristic, complemented
4	#22582801	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₁₂₄	C₂²	1	2	yes	—
7	C₂×C₄×D₂₈₁	—	2	2	no	—
8	D₂₂₄₈	C₄	1	4	yes	direct product factor
9	C₄⋊Dic₂₈₁	C₂²	1	2	yes	—
10	#17985115	—	2	2	no	—
11	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
14	C₂²×D₂₈₁	—	2	2	no	—
15	D₁₁₂₄	—	2	2	no	—
16	D₁₁₂₄	C₂×C₄	1	4	yes	complemented
17	C₂×Dic₂₈₁	—	2	2	no	—
18	C₄×D₂₈₁	—	4	4	no	—
19	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
22	C₈×C₂₈₁	—	2	1	no	—
23	C₈×C₂₈₁	C₂×C₄	1	2	yes	complemented
24	C₂²×C₂₈₁	C₂×D₄	1	1	yes	characteristic
25	C₂×D₂₈₁	—	2	4	no	—
26	C₂×D₂₈₁	—	4	2	no	—
27	C₂×D₂₈₁	—	4	2	no	—
28	C₄×C₂₈₁	—	2	1	no	—
29	C₄×C₂₈₁	D₈	1	2	yes	complemented
30	C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₈₁	#41	1	1	yes	characteristic
32	Dic₂₈₁	—	4	2	no	—
33	C₂×C₂₈₁	C₄×D₄	1	1	yes	characteristic
34	C₂×C₂₈₁	C₂×D₈	1	1	yes	characteristic
35	C₂×C₂₈₁	#135	1	1	yes	characteristic
36	D₂₈₁	—	4	4	no	—
37	C₂₈₁	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
38	C₄×D₈	—	281	1	no	maximal, Sylow
39	C₂×D₈	—	281	1	no	—
40	C₄×D₄	—	281	2	no	—
41	#107	—	281	1	no	—
42	#102	—	281	2	no	—
43	C₄×C₈	D₂₈₁	1	1	yes	characteristic, complemented
44	C₂×D₄	—	281	2	no	—
45	C₂²×C₄	—	562	2	no	—
46	D₈	—	281	4	no	—
47	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
48	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
49	C₄⋊C₄	—	281	2	no	—
50	C₂²⋊C₄	—	562	2	no	—
51	C₄²	C₂×D₂₈₁	1	1	yes	characteristic
52	C₂³	—	562	2	no	—
53	D₄	—	281	4	no	—
54	D₄	—	562	2	no	—
55	C₂×C₄	—	562	2	no	—
56	C₂×C₄	—	1124	4	no	—
57	C₂×C₄	D₁₁₂₄	1	1	yes	characteristic
58	C₂×C₄	D₁₁₂₄	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	C₄×D₂₈₁	1	2	yes	complemented
62	C₂²	—	562	4	no	—
63	C₂²	—	1124	2	no	—
64	C₂²	—	1124	2	no	—
65	C₂²	C₂×D₁₁₂₄	1	1	yes	characteristic
66	C₄	—	2	1	no	—
67	C₄	—	1124	2	no	—
68	C₄	D₂₂₄₈	1	2	yes	direct product factor
69	C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
70	C₄	#17985138	1	1	yes	characteristic
71	C₂	—	1124	4	no	—
72	C₂	C₄×D₁₁₂₄	1	1	yes	characteristic
73	C₂	C₂×D₂₂₄₈	1	1	yes	characteristic
74	C₂	#22582901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₁₂₄
commutator	C₄×C₂₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₈₁
Fitting	C₄×C₈×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×D₄
prime radical	C₂×D₂₂₄₈	C₂
cosocle	C₂×C₄×C₂₈₁	C₂³
hypercenter	C₄×C₈	D₂₈₁
hypocenter	C₂₈₁	C₄×D₈
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×D₁₁₂₄	C₂	semidirect
3. #22582813	C₂	semidirect
4. #22582801	C₂	semidirect
5. C₄×C₈×C₂₈₁	C₂	semidirect
8. D₂₂₄₈	C₄	direct (N × H)
16. D₁₁₂₄	C₂×C₄	semidirect
23. C₈×C₂₈₁	C₂×C₄	semidirect
29. C₄×C₂₈₁	D₈	semidirect
37. C₂₈₁	C₄×D₈	semidirect
43. C₄×C₈	D₂₈₁	semidirect
61. C₈	C₄×D₂₈₁	semidirect
68. C₄	D₂₂₄₈	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×D₂₂₄₈	2
C₄×D₁₁₂₄	2
#22582813	2
#22582801	2
C₄×C₈×C₂₈₁	2
C₄×D₈	281

Subgroups — C4×D2248 #31823547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₂₂₄₈ #31823547