Subgroups — C₄×C₂²⋊Dic₂₂₃ #28383428

Order 14272.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊Dic₂₂₃	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₂₂₃	C₂	1	2	yes	maximal, complemented
3	C₂₂₃⋊#95	C₂	1	2	yes	maximal, complemented
4	C₂³×C₄×C₂₂₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₂₂₃	C₂²	1	4	yes	—
6	C₂²⋊Dic₂₂₃	C₄	1	8	yes	direct product factor
7	C₄×Dic₂₂₃	—	2	4	no	—
8	C₂⁴×C₂₂₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₂₂₃	—	2	4	no	—
10	C₂²×C₄×C₂₂₃	C₄	1	4	yes	complemented
11	C₂²×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₂₃	—	2	4	no	—
14	C₂×Dic₂₂₃	—	2	4	no	—
15	C₂×Dic₂₂₃	C₂×C₄	1	8	yes	complemented
16	C₂³×C₂₂₃	—	2	2	no	—
17	C₂³×C₂₂₃	—	2	2	no	—
18	C₂³×C₂₂₃	C₂×C₄	1	4	yes	—
19	C₂³×C₂₂₃	C₂×C₄	1	2	yes	—
20	C₂³×C₂₂₃	C₂³	1	1	yes	characteristic
21	C₂×C₄×C₂₂₃	—	2	2	no	—
22	C₂×C₄×C₂₂₃	—	2	8	no	—
23	C₂×C₄×C₂₂₃	C₂×C₄	1	2	yes	—
24	C₂×C₄×C₂₂₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₂₃	D₄	1	4	yes	—
26	C₂²×C₂₂₃	—	2	2	no	—
27	C₂²×C₂₂₃	—	2	2	no	—
28	C₂²×C₂₂₃	—	2	8	no	—
29	C₂²×C₂₂₃	C₄²	1	4	yes	complemented
30	C₂²×C₂₂₃	C₂²×C₄	1	2	yes	—
31	C₂²×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₂₂₃	C₂×D₄	1	2	yes	—
33	C₂²×C₂₂₃	#41	1	2	yes	—
34	C₄×C₂₂₃	—	2	2	no	—
35	C₄×C₂₂₃	C₂²⋊C₄	1	4	yes	complemented
36	Dic₂₂₃	—	2	8	no	—
37	C₂×C₂₂₃	—	2	4	no	—
38	C₂×C₂₂₃	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₂₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₂₂₃	#117	1	1	yes	characteristic
41	C₂×C₂₂₃	C₄×D₄	1	4	yes	—
42	C₂₂₃	C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
43	C₄×C₂²⋊C₄	—	223	1	no	maximal, Sylow
44	C₂³×C₄	D₂₂₃	1	1	yes	characteristic
45	C₂×C₂²⋊C₄	—	223	2	no	—
46	C₂×C₄²	—	223	2	no	—
47	#95	—	223	2	no	—
48	C₂⁴	C₂×D₂₂₃	1	1	yes	characteristic
49	C₂²×C₄	—	2	4	no	—
50	C₂²×C₄	—	223	4	no	—
51	C₂²×C₄	Dic₂₂₃	1	4	yes	complemented
52	C₂²×C₄	C₂×D₂₂₃	1	1	yes	characteristic
53	C₂²×C₄	C₂×D₂₂₃	1	1	yes	characteristic
54	C₂²⋊C₄	—	223	8	no	—
55	C₄²	—	446	4	no	—
56	C₂³	—	2	2	no	—
57	C₂³	—	2	2	no	—
58	C₂³	C₄×D₂₂₃	1	4	yes	—
59	C₂³	C₂×Dic₂₂₃	1	2	yes	—
60	C₂³	C₂²×D₂₂₃	1	1	yes	characteristic
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	8	no	—
63	C₂×C₄	—	446	4	no	—
64	C₂×C₄	—	446	4	no	—
65	C₂×C₄	—	223	8	no	—
66	C₂×C₄	C₂×Dic₂₂₃	1	2	yes	—
67	C₂×C₄	C₂×Dic₂₂₃	1	2	yes	—
68	C₂×C₄	C₂²⋊D₂₂₃	1	4	yes	—
69	C₂²	—	2	2	no	—
70	C₂²	—	2	2	no	—
71	C₂²	—	2	8	no	—
72	C₂²	C₄×Dic₂₂₃	1	4	yes	complemented
73	C₂²	C₂×C₄×D₂₂₃	1	2	yes	—
74	C₂²	C₂²×Dic₂₂₃	1	1	yes	characteristic
75	C₂²	C₂×C₂²⋊D₂₂₃	1	2	yes	—
76	C₂²	#16813170	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	—	446	8	no	—
79	C₄	C₂²⋊Dic₂₂₃	1	4	yes	direct product factor
80	C₂	—	2	4	no	—
81	C₂	C₂×C₄×Dic₂₂₃	1	1	yes	characteristic
82	C₂	C₂×C₂²⋊Dic₂₂₃	1	1	yes	characteristic
83	C₂	#20297263	1	1	yes	characteristic
84	C₂	C₄×C₂²⋊D₂₂₃	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₂₃
commutator	C₂×C₂₂₃	C₂×C₄²
Frattini	C₂³	C₂²×D₂₂₃
Fitting	C₂³×C₄×C₂₂₃	C₂
socle, cosocle	C₂³×C₂₂₃	C₂³
prime radical	C₂⁴×C₂₂₃	C₂²
hypercenter	C₂³×C₄	D₂₂₃
hypocenter	C₂₂₃	C₄×C₂²⋊C₄
LCS	G ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₂₂₃	C₂	semidirect
3. C₂₂₃⋊#95	C₂	semidirect
6. C₂²⋊Dic₂₂₃	C₄	direct (N × H)
10. C₂²×C₄×C₂₂₃	C₄	semidirect
15. C₂×Dic₂₂₃	C₂×C₄	semidirect
29. C₂²×C₂₂₃	C₄²	semidirect
35. C₄×C₂₂₃	C₂²⋊C₄	semidirect
42. C₂₂₃	C₄×C₂²⋊C₄	semidirect
51. C₂²×C₄	Dic₂₂₃	semidirect
72. C₂²	C₄×Dic₂₂₃	semidirect
79. C₄	C₂²⋊Dic₂₂₃	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×C₂²⋊Dic₂₂₃	2
C₂×C₄×Dic₂₂₃	2
C₂₂₃⋊#95	2
C₂³×C₄×C₂₂₃	2
C₄×C₂²⋊C₄	223

Subgroups — C4×C22⋊Dic223 #28383428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂²⋊Dic₂₂₃ #28383428