Subgroups — C₂×#20297245 #28384000

Order 14272.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₇₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#20297245	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₂₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈₉₂	—	2	1	no	—
6	D₁₇₈₄	—	2	1	no	—
7	D₁₇₈₄	C₂²	1	2	yes	complemented
8	C₂₂₃⋊C₁₆	C₂²	1	2	yes	complemented
9	C₂×D₄×C₂₂₃	—	2	1	no	—
10	D₈×C₂₂₃	—	2	1	no	—
11	D₈×C₂₂₃	C₂²	1	2	yes	complemented
12	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
13	C₂²×D₂₂₃	—	4	1	no	—
14	D₈₉₂	—	2	2	no	—
15	D₈₉₂	—	4	1	no	—
16	C₂³×C₂₂₃	—	4	1	no	—
17	D₄×C₂₂₃	—	2	2	no	—
18	D₄×C₂₂₃	—	4	1	no	—
19	C₂×C₄×C₂₂₃	D₄	1	1	yes	characteristic
20	C₈×C₂₂₃	D₄	1	1	yes	characteristic
21	C₈×C₂₂₃	C₂³	1	1	yes	characteristic
22	C₂²×C₂₂₃	—	4	2	no	—
23	C₂²×C₂₂₃	—	8	2	no	—
24	C₂²×C₂₂₃	D₈	1	1	yes	characteristic
25	C₂×D₂₂₃	—	4	2	no	—
26	C₂×D₂₂₃	—	8	2	no	—
27	C₄×C₂₂₃	D₈	1	1	yes	characteristic
28	C₄×C₂₂₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₂₂₃	—	8	2	no	—
30	C₂×C₂₂₃	D₁₆	1	2	yes	complemented
31	C₂×C₂₂₃	C₂×D₈	1	1	yes	characteristic
32	D₂₂₃	—	8	2	no	—
33	C₂₂₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₁₆	—	223	1	no	maximal, Sylow
35	C₂×D₈	—	223	1	no	—
36	C₂×D₈	D₂₂₃	1	1	yes	characteristic, complemented
37	D₁₆	—	223	4	no	—
38	C₂×C₁₆	—	223	1	no	—
39	C₂×D₄	—	2	1	no	—
40	C₂×D₄	—	446	1	no	—
41	D₈	—	2	1	no	—
42	D₈	—	446	1	no	—
43	D₈	—	223	2	no	—
44	D₈	C₂×D₂₂₃	1	2	yes	complemented
45	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
46	C₁₆	—	223	2	no	—
47	C₂³	—	4	1	no	—
48	C₂³	—	892	1	no	—
49	D₄	—	2	2	no	—
50	D₄	—	4	1	no	—
51	D₄	—	892	1	no	—
52	D₄	—	446	2	no	—
53	C₂×C₄	C₂²⋊D₂₂₃	1	1	yes	characteristic
54	C₈	C₂²⋊D₂₂₃	1	1	yes	characteristic
55	C₈	C₂²×D₂₂₃	1	1	yes	characteristic
56	C₂²	—	4	2	no	—
57	C₂²	—	8	2	no	—
58	C₂²	—	892	2	no	—
59	C₂²	—	1784	2	no	—
60	C₂²	#16813155	1	1	yes	characteristic
61	C₄	#16813155	1	1	yes	characteristic
62	C₄	C₂×C₂²⋊D₂₂₃	1	1	yes	characteristic
63	C₂	—	8	2	no	—
64	C₂	—	1784	2	no	—
65	C₂	#20297245	1	2	yes	direct product factor
66	C₂	C₂×#16813155	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16813155
commutator, cosocle	C₈×C₂₂₃	C₂³
Frattini	C₈	C₂²×D₂₂₃
Fitting	C₂×D₈×C₂₂₃	C₂
socle	C₂²×C₂₂₃	D₈
hypercenter	C₂×D₈	D₂₂₃
hypocenter	C₂₂₃	C₂×D₁₆
LCS	G ▷ C₈×C₂₂₃ ▷ C₄×C₂₂₃ ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₇₈₄	C₂	semidirect
2. #20297245	C₂	direct (N × H)
3. C₂×C₂₂₃⋊C₁₆	C₂	semidirect
4. C₂×D₈×C₂₂₃	C₂	semidirect
7. D₁₇₈₄	C₂²	semidirect
8. C₂₂₃⋊C₁₆	C₂²	semidirect
11. D₈×C₂₂₃	C₂²	semidirect
30. C₂×C₂₂₃	D₁₆	semidirect
33. C₂₂₃	C₂×D₁₆	semidirect
36. C₂×D₈	D₂₂₃	semidirect
44. D₈	C₂×D₂₂₃	semidirect
65. C₂	#20297245	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×D₁₇₈₄	2
#20297245	2
C₂×C₂₂₃⋊C₁₆	2
C₂×D₈×C₂₂₃	2
C₂×D₁₆	223

Subgroups — C2×#20297245 #28384000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20297245 #28384000