Subgroups — C₂²×C₄⋊#4223 #14581398

Order 2624.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#4223	C₂	1	2	yes	maximal
2	C₂×C₄⋊#4223	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄×D₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×D₄₁	C₂²	1	1	yes	characteristic
5	C₂²×#4223	—	2	8	no	—
6	C₂²×#4223	C₂²	1	12	yes	—
7	C₂²×C₄×C₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂²×Dic₄₁	C₄	1	1	yes	characteristic, complemented
9	C₂×C₄×D₄₁	C₄	1	6	yes	complemented
10	C₂×C₄×D₄₁	C₂²	1	6	yes	—
11	C₄⋊#4223	C₂²	1	16	yes	direct product factor
12	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×D₄₁	C₂×C₄	1	3	yes	—
14	C₂²×D₄₁	D₄	1	4	yes	—
15	C₂²×D₄₁	Q₈	1	4	yes	—
16	C₂²×D₄₁	C₂³	1	3	yes	—
17	C₂×#4223	—	2	24	no	—
18	C₂×#4223	C₂³	1	8	yes	—
19	C₂×C₄×C₄₁	C₂×C₄	1	6	yes	complemented
20	C₂×Dic₄₁	C₂×C₄	1	6	yes	complemented
21	C₄×D₄₁	C₂×C₄	1	12	yes	complemented
22	C₄×D₄₁	C₂³	1	4	yes	—
23	C₂²×C₄₁	C₄⋊C₄	1	4	yes	complemented
24	C₂²×C₄₁	C₂²×C₄	1	3	yes	—
25	C₂×D₄₁	C₄⋊C₄	1	12	yes	complemented
26	C₂×D₄₁	C₂²×C₄	1	3	yes	—
27	C₂×D₄₁	C₂×D₄	1	6	yes	—
28	C₂×D₄₁	C₂×Q₈	1	6	yes	—
29	C₂×D₄₁	C₂⁴	1	1	yes	characteristic
30	#4223	—	2	8	no	—
31	C₄×C₄₁	C₂²×C₄	1	4	yes	complemented
32	Dic₄₁	C₂²×C₄	1	4	yes	complemented
33	C₂×C₄₁	C₂×C₄⋊C₄	1	6	yes	complemented
34	C₂×C₄₁	C₂³×C₄	1	1	yes	characteristic
35	D₄₁	C₂×C₄⋊C₄	1	6	yes	complemented
36	D₄₁	C₂²×D₄	1	1	yes	characteristic
37	D₄₁	C₂²×Q₈	1	1	yes	characteristic
38	C₂²×C₄⋊C₄	—	41	1	no	maximal, Sylow
39	C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
40	C₂³×C₄	—	41	1	no	—
41	C₂³×C₄	—	41	2	no	—
42	C₂×C₄⋊C₄	—	41	12	no	—
43	C₂⁴	—	41	1	no	—
44	C₂²×C₄	—	41	1	no	—
45	C₂²×C₄	—	41	6	no	—
46	C₂²×C₄	—	41	6	no	—
47	C₂²×C₄	—	41	12	no	—
48	C₂²×C₄	—	82	8	no	—
49	C₂²×C₄	#4223	1	1	yes	characteristic, complemented
50	C₄⋊C₄	—	41	16	no	—
51	C₂³	—	41	4	no	—
52	C₂³	—	41	4	no	—
53	C₂³	—	41	3	no	—
54	C₂³	—	41	3	no	—
55	C₂³	C₂×#4223	1	1	yes	characteristic
56	C₂×C₄	—	41	6	no	—
57	C₂×C₄	—	41	4	no	—
58	C₂×C₄	—	41	12	no	—
59	C₂×C₄	—	41	8	no	—
60	C₂×C₄	—	82	24	no	—
61	C₂×C₄	C₂×#4223	1	6	yes	complemented
62	C₂²	—	41	6	no	—
63	C₂²	—	41	12	no	—
64	C₂²	—	41	6	no	—
65	C₂²	—	41	1	no	—
66	C₂²	—	41	3	no	—
67	C₂²	C₄⋊#4223	1	4	yes	direct product factor
68	C₂²	C₂²×#4223	1	3	yes	—
69	C₄	—	41	4	no	—
70	C₄	—	82	8	no	—
71	C₄	C₂²×#4223	1	4	yes	complemented
72	C₂	—	41	1	no	—
73	C₂	—	41	6	no	—
74	C₂	—	41	1	no	—
75	C₂	C₂×C₄⋊#4223	1	6	yes	direct product factor
76	C₂	C₂³×#4223	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#4223
commutator	C₂×C₄₁	C₂³×C₄
Frattini	C₂	C₂³×#4223
Fitting	C₂²×C₄×C₄₁	C₄
socle	C₂³×C₄₁	C₂×C₄
prime radical	C₂³×D₄₁	C₂²
cosocle	C₂×D₄₁	C₂⁴
hypercenter	C₂²×C₄	#4223
hypocenter	C₄₁	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊#4223	C₂	direct (N × H)
7. C₂²×C₄×C₄₁	C₄	semidirect
8. C₂²×Dic₄₁	C₄	semidirect
9. C₂×C₄×D₄₁	C₄	semidirect
11. C₄⋊#4223	C₂²	direct (N × H)
19. C₂×C₄×C₄₁	C₂×C₄	semidirect
20. C₂×Dic₄₁	C₂×C₄	semidirect
21. C₄×D₄₁	C₂×C₄	semidirect
23. C₂²×C₄₁	C₄⋊C₄	semidirect
25. C₂×D₄₁	C₄⋊C₄	semidirect
31. C₄×C₄₁	C₂²×C₄	semidirect
32. Dic₄₁	C₂²×C₄	semidirect
33. C₂×C₄₁	C₂×C₄⋊C₄	semidirect
35. D₄₁	C₂×C₄⋊C₄	semidirect
39. C₄₁	C₂²×C₄⋊C₄	semidirect
49. C₂²×C₄	#4223	semidirect
61. C₂×C₄	C₂×#4223	semidirect
67. C₂²	C₄⋊#4223	direct (N × H)
71. C₄	C₂²×#4223	semidirect
75. C₂	C₂×C₄⋊#4223	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#4223	2
C₂×C₄⋊#4223	2
C₂²×C₄×D₄₁	2
C₂²×C₄⋊C₄	41

Subgroups — C22×C4⋊#4223 #14581398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄⋊#4223 #14581398