Subgroups — C₂×#21440567 #29507709

Order 15424.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₈₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₂₄₁	C₂	1	1	yes	maximal, characteristic
3	#21440567	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₂₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₄₈₂	—	2	2	no	—
6	C₂×Dic₄₈₂	—	2	1	no	—
7	C₂×Dic₄₈₂	C₄	1	4	yes	complemented
8	C₂×Dic₄₈₂	C₂²	1	2	yes	—
9	C₂²×Dic₂₄₁	—	2	1	no	—
10	C₂²×Dic₂₄₁	—	2	1	no	—
11	C₄⋊Dic₂₄₁	—	2	1	no	—
12	C₄⋊Dic₂₄₁	C₂²	1	2	yes	—
13	C₂²×C₄×C₂₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₂₄₁	—	2	2	no	—
15	C₂×C₈×C₂₄₁	C₂²	1	2	yes	—
16	Dic₄₈₂	—	2	4	no	—
17	Dic₄₈₂	—	2	2	no	—
18	Dic₄₈₂	C₂×C₄	1	4	yes	complemented
19	C₂×Dic₂₄₁	—	2	4	no	—
20	C₂×Dic₂₄₁	—	2	2	no	—
21	C₂×Dic₂₄₁	—	2	2	no	—
22	C₂×Dic₂₄₁	—	4	2	no	—
23	C₂³×C₂₄₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₄₁	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₄₁	D₄	1	2	yes	—
26	C₂×C₄×C₂₄₁	D₄	1	1	yes	characteristic
27	C₂×C₄×C₂₄₁	C₂³	1	1	yes	characteristic
28	C₈×C₂₄₁	—	2	2	no	—
29	C₂²×C₂₄₁	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₂₄₁	SD₁₆	1	2	yes	—
31	C₂²×C₂₄₁	Q₁₆	1	2	yes	—
32	C₂²×C₂₄₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₄₁	C₂²⋊C₄	1	2	yes	—
34	C₄×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
36	Dic₂₄₁	—	2	4	no	—
37	Dic₂₄₁	—	4	2	no	—
38	C₂×C₂₄₁	#103	1	4	yes	complemented
39	C₂×C₂₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₂₄₁	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₂₄₁	C₂×Q₁₆	1	1	yes	characteristic
42	C₂₄₁	C₂×#103	1	1	yes	characteristic, complemented, Sylow
43	C₂×#103	—	241	1	no	maximal, Sylow
44	C₂²×Q₈	—	241	1	no	—
45	C₂²×C₈	D₂₄₁	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	241	1	no	—
47	#103	—	241	4	no	—
48	C₂×Q₈	—	482	2	no	—
49	C₂×Q₈	—	482	1	no	—
50	C₂×Q₈	—	241	4	no	—
51	C₂×Q₈	—	241	2	no	—
52	C₂²×C₄	—	482	1	no	—
53	C₂²×C₄	—	482	1	no	—
54	C₂²×C₄	C₂×D₂₄₁	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	C₂×D₂₄₁	1	2	yes	—
57	C₄⋊C₄	—	482	1	no	—
58	C₄⋊C₄	—	241	2	no	—
59	C₂³	D₉₆₄	1	1	yes	characteristic
60	Q₈	—	482	4	no	—
61	Q₈	—	482	2	no	—
62	Q₈	—	241	4	no	—
63	C₂×C₄	—	964	2	no	—
64	C₂×C₄	—	482	2	no	—
65	C₂×C₄	—	482	4	no	—
66	C₂×C₄	—	482	2	no	—
67	C₂×C₄	C₄×D₂₄₁	1	2	yes	—
68	C₂×C₄	C₂²⋊D₂₄₁	1	2	yes	—
69	C₂×C₄	D₉₆₄	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₂₄₁	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₂²	#16838747	1	2	yes	—
73	C₂²	#16838759	1	2	yes	—
74	C₂²	Dic₉₆₄	1	2	yes	—
75	C₂²	C₂×D₉₆₄	1	1	yes	characteristic
76	C₄	—	964	2	no	—
77	C₄	—	482	4	no	—
78	C₄	#16838747	1	2	yes	—
79	C₄	C₂×C₄×D₂₄₁	1	1	yes	characteristic
80	C₄	C₂×C₂²⋊D₂₄₁	1	1	yes	characteristic
81	C₂	#21440567	1	4	yes	direct product factor
82	C₂	C₂×#16838747	1	1	yes	characteristic
83	C₂	C₂×#16838759	1	1	yes	characteristic
84	C₂	C₂×Dic₉₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₉₆₄
commutator	C₄×C₂₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₄₁
Fitting	C₂²×C₈×C₂₄₁	C₂
socle, prime radical	C₂³×C₂₄₁	D₄
cosocle	C₂×C₄×C₂₄₁	C₂³
hypercenter	C₂²×C₈	D₂₄₁
hypocenter	C₂₄₁	C₂×#103
LCS	G ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #21440567	C₂	direct (N × H)
7. C₂×Dic₄₈₂	C₄	semidirect
18. Dic₄₈₂	C₂×C₄	semidirect
38. C₂×C₂₄₁	#103	semidirect
42. C₂₄₁	C₂×#103	semidirect
81. C₂	#21440567	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×Dic₄₈₂	2
C₂×C₄⋊Dic₂₄₁	2
#21440567	2
C₂²×C₈×C₂₄₁	2
C₂×#103	241

Subgroups — C2×#21440567 #29507709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21440567 #29507709