Subgroups — C₂×#21440696 #29508674

Order 15424.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16838778	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11757210	C₂	1	1	yes	maximal, characteristic
3	#21440696	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×D₂₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11757210	C₄	1	2	yes	—
6	#16838778	C₄	1	2	yes	complemented
7	#16838778	C₂²	1	2	yes	—
8	C₂×#14515356	C₄	1	2	yes	complemented
9	C₄×#11757210	C₄	1	2	yes	—
10	C₄×#11757210	C₂²	1	2	yes	—
11	C₂×C₄×D₂₄₁	C₂²	1	1	yes	characteristic
12	C₂×#14515349	C₄	1	1	yes	characteristic, complemented
13	C₈×D₂₄₁	C₄	1	2	yes	complemented
14	C₈×D₂₄₁	C₂²	1	2	yes	—
15	C₂×C₈×C₂₄₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#11757210	—	2	4	no	—
17	C₂×#11757210	C₂×C₄	1	4	yes	—
18	#14515356	C₂×C₄	1	4	yes	complemented
19	C₂²×D₂₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
21	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
22	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
23	C₄×D₂₄₁	C₂×C₄	1	1	yes	characteristic
24	C₄×D₂₄₁	C₂³	1	1	yes	characteristic
25	#14515349	C₂×C₄	1	2	yes	complemented
26	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
27	C₈×C₂₄₁	C₂×C₄	1	2	yes	complemented
28	C₂²×C₂₄₁	C₄²	1	1	yes	characteristic
29	C₂×D₂₄₁	C₄²	1	1	yes	characteristic
30	C₂×D₂₄₁	M₁₆	1	4	yes	—
31	C₂×D₂₄₁	C₂²×C₄	1	1	yes	characteristic
32	#11757210	—	2	4	no	—
33	C₄×C₂₄₁	C₄²	1	1	yes	characteristic
34	C₄×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
35	Dic₂₄₁	C₄²	1	1	yes	characteristic
36	Dic₂₄₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₂₄₁	#97	1	2	yes	complemented
38	C₂×C₂₄₁	C₂×C₄²	1	1	yes	characteristic
39	D₂₄₁	#97	1	2	yes	complemented
40	D₂₄₁	C₂×M₁₆	1	2	yes	—
41	C₂₄₁	C₂×#97	1	1	yes	characteristic, complemented, Sylow
42	C₂×#97	—	241	1	no	maximal, Sylow
43	C₂²×C₈	—	241	1	no	—
44	C₂²×C₈	—	241	1	no	—
45	C₂×C₄²	—	241	1	no	—
46	#97	—	241	4	no	—
47	C₂²×C₄	—	241	2	no	—
48	C₂²×C₄	—	241	1	no	—
49	C₂×C₈	—	241	2	no	—
50	C₂×C₈	—	241	2	no	—
51	C₂×C₈	—	241	2	no	—
52	C₂×C₈	—	241	1	no	—
53	C₂×C₈	—	241	2	no	—
54	C₂×C₈	—	241	2	no	—
55	C₂×C₈	#11757210	1	1	yes	characteristic, complemented
56	C₄²	—	241	2	no	—
57	C₄²	—	241	2	no	—
58	C₂³	—	241	1	no	—
59	C₂×C₄	—	482	4	no	—
60	C₂×C₄	—	241	4	no	—
61	C₂×C₄	—	241	1	no	—
62	C₂×C₄	—	241	1	no	—
63	C₂×C₄	—	241	1	no	—
64	C₂×C₄	—	241	1	no	—
65	C₂×C₄	—	241	1	no	—
66	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
67	C₈	—	241	4	no	—
68	C₈	—	241	2	no	—
69	C₈	C₂×#11757210	1	2	yes	complemented
70	C₂²	—	241	4	no	—
71	C₂²	—	241	1	no	—
72	C₂²	—	241	1	no	—
73	C₂²	C₄×#11757210	1	1	yes	characteristic
74	C₄	—	482	4	no	—
75	C₄	—	241	1	no	—
76	C₄	—	241	1	no	—
77	C₄	C₄×#11757210	1	1	yes	characteristic
78	C₄	C₂²×#11757210	1	1	yes	characteristic
79	C₂	—	241	2	no	—
80	C₂	—	241	2	no	—
81	C₂	#21440696	1	2	yes	direct product factor
82	C₂	C₂×C₄×#11757210	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11757210
commutator	C₂×C₂₄₁	C₂×C₄²
Frattini	C₄	C₂²×#11757210
Fitting	C₂×C₈×C₂₄₁	C₄
socle	C₂²×C₂₄₁	C₄²
prime radical	C₂²×D₂₄₁	C₂×C₄
cosocle	C₄×D₂₄₁	C₂³
hypercenter	C₂×C₈	#11757210
hypocenter	C₂₄₁	C₂×#97
LCS	G ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. #21440696	C₂	direct (N × H)
6. #16838778	C₄	semidirect
8. C₂×#14515356	C₄	semidirect
12. C₂×#14515349	C₄	semidirect
13. C₈×D₂₄₁	C₄	semidirect
15. C₂×C₈×C₂₄₁	C₄	semidirect
18. #14515356	C₂×C₄	semidirect
25. #14515349	C₂×C₄	semidirect
27. C₈×C₂₄₁	C₂×C₄	semidirect
37. C₂×C₂₄₁	#97	semidirect
39. D₂₄₁	#97	semidirect
41. C₂₄₁	C₂×#97	semidirect
55. C₂×C₈	#11757210	semidirect
69. C₈	C₂×#11757210	semidirect
81. C₂	#21440696	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×#16838778	2
C₂×C₄×#11757210	2
#21440696	2
C₂×C₈×D₂₄₁	2
C₂×#97	241

Subgroups — C2×#21440696 #29508674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21440696 #29508674