Subgroups — C₄×#16838780 #29508679

Order 15424.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16838780	C₂	1	2	yes	maximal
2	#21440697	C₂	1	2	yes	maximal, complemented
3	C₄×#14515356	C₂	1	2	yes	maximal, complemented
4	C₄²×D₂₄₁	C₂	1	1	yes	maximal, characteristic
5	#16838780	C₄	1	8	yes	direct product factor
6	C₂×#14515356	C₂²	1	4	yes	—
7	C₂×C₄×D₂₄₁	C₄	1	1	yes	characteristic
8	C₂×C₄×D₂₄₁	C₄	1	1	yes	characteristic
9	C₂×C₄×D₂₄₁	C₂²	1	1	yes	characteristic
10	C₄×Dic₂₄₁	C₄	1	1	yes	characteristic
11	C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
12	C₄×Dic₂₄₁	C₂²	1	1	yes	characteristic
13	C₄²×C₂₄₁	C₄	1	1	yes	characteristic
14	#14515356	C₂×C₄	1	8	yes	complemented
15	C₂²×D₂₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₂₄₁	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₂₄₁	C₂³	1	1	yes	characteristic
19	C₄×D₂₄₁	—	2	2	no	—
20	C₄×D₂₄₁	—	2	2	no	—
21	C₄×D₂₄₁	C₂×C₄	1	4	yes	—
22	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₄₁	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₂₄₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₂₄₁	—	2	1	no	—
27	C₂×D₂₄₁	—	2	1	no	—
28	C₂×D₂₄₁	C₄²	1	2	yes	—
29	C₄×C₂₄₁	—	2	1	no	—
30	C₄×C₂₄₁	C₄²	1	2	yes	—
31	C₄×C₂₄₁	M₁₆	1	2	yes	complemented
32	Dic₂₄₁	—	2	1	no	—
33	Dic₂₄₁	M₁₆	1	2	yes	complemented
34	Dic₂₄₁	C₂²×C₄	1	2	yes	—
35	C₂×C₂₄₁	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₂₄₁	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₂₄₁	C₂×M₁₆	1	1	yes	characteristic
38	D₂₄₁	—	2	2	no	—
39	C₂₄₁	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₄×M₁₆	—	241	1	no	maximal, Sylow
41	C₂×M₁₆	—	241	2	no	—
42	C₂×C₄²	—	241	1	no	—
43	#97	—	241	2	no	—
44	C₄×C₈	—	241	2	no	—
45	C₂²×C₄	—	241	1	no	—
46	C₂²×C₄	—	241	1	no	—
47	C₂²×C₄	—	241	1	no	—
48	M₁₆	—	241	8	no	—
49	C₂×C₈	—	241	4	no	—
50	C₄²	—	241	1	no	—
51	C₄²	—	241	1	no	—
52	C₄²	—	241	1	no	—
53	C₄²	#11757210	1	1	yes	characteristic
54	C₂³	—	241	1	no	—
55	C₂×C₄	—	482	2	no	—
56	C₂×C₄	—	482	2	no	—
57	C₂×C₄	—	241	1	no	—
58	C₂×C₄	—	241	1	no	—
59	C₂×C₄	—	241	1	no	—
60	C₂×C₄	—	241	4	no	—
61	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
62	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
63	C₂×C₄	C₂×#11757210	1	1	yes	characteristic
64	C₈	—	241	8	no	—
65	C₂²	—	482	1	no	—
66	C₂²	—	482	1	no	—
67	C₂²	—	241	2	no	—
68	C₂²	C₂²×#11757210	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	482	1	no	—
71	C₄	—	241	2	no	—
72	C₄	—	241	2	no	—
73	C₄	C₄×#11757210	1	2	yes	—
74	C₄	#16838780	1	2	yes	direct product factor
75	C₂	—	482	2	no	—
76	C₂	C₂×C₄×#11757210	1	1	yes	characteristic
77	C₂	D₂₄₁⋊M₁₆	1	1	yes	characteristic
78	C₂	C₂×#16838780	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11757210
commutator	C₂×C₂₄₁	C₂×C₄²
Frattini	C₂²	C₂²×#11757210
Fitting	C₄²×C₂₄₁	C₄
socle	C₂²×C₂₄₁	C₂²×C₄
prime radical	C₂²×D₂₄₁	C₂×C₄
cosocle	C₂×Dic₂₄₁	C₂³
hypercenter	C₄²	#11757210
hypocenter	C₂₄₁	C₄×M₁₆
LCS	G ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #21440697	C₂	semidirect
3. C₄×#14515356	C₂	semidirect
5. #16838780	C₄	direct (N × H)
14. #14515356	C₂×C₄	semidirect
31. C₄×C₂₄₁	M₁₆	semidirect
33. Dic₂₄₁	M₁₆	semidirect
39. C₂₄₁	C₄×M₁₆	semidirect
74. C₄	#16838780	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×#16838780	2
#21440697	2
C₄×#14515356	2
C₄²×D₂₄₁	2
C₄×M₁₆	241

Subgroups — C4×#16838780 #29508679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16838780 #29508679