Subgroups — C₄×#16814676 #28412443

Order 14656.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16814676	C₂	1	2	yes	maximal
2	#20301043	C₂	1	2	yes	maximal, complemented
3	C₄×#14270087	C₂	1	2	yes	maximal, complemented
4	C₄²×D₂₂₉	C₂	1	1	yes	maximal, characteristic
5	#16814676	C₄	1	8	yes	direct product factor
6	C₂×#14270087	C₂²	1	4	yes	—
7	C₂×C₄×D₂₂₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₂₂₉	C₄	1	1	yes	characteristic
9	C₂×C₄×D₂₂₉	C₂²	1	1	yes	characteristic
10	C₄×Dic₂₂₉	C₄	1	1	yes	characteristic
11	C₄×Dic₂₂₉	C₂²	1	1	yes	characteristic
12	C₄×Dic₂₂₉	C₂²	1	1	yes	characteristic
13	C₄²×C₂₂₉	C₄	1	1	yes	characteristic
14	#14270087	C₂×C₄	1	8	yes	complemented
15	C₂²×D₂₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₂₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₂₂₉	C₂³	1	1	yes	characteristic
19	C₄×D₂₂₉	—	2	2	no	—
20	C₄×D₂₂₉	—	2	2	no	—
21	C₄×D₂₂₉	C₂×C₄	1	4	yes	—
22	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₂₂₉	—	2	1	no	—
27	C₂×D₂₂₉	—	2	1	no	—
28	C₂×D₂₂₉	C₄²	1	2	yes	—
29	C₄×C₂₂₉	—	2	1	no	—
30	C₄×C₂₂₉	C₄²	1	2	yes	—
31	C₄×C₂₂₉	M₁₆	1	2	yes	complemented
32	Dic₂₂₉	—	2	1	no	—
33	Dic₂₂₉	M₁₆	1	2	yes	complemented
34	Dic₂₂₉	C₂²×C₄	1	2	yes	—
35	C₂×C₂₂₉	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₂₂₉	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₂₂₉	C₂×M₁₆	1	1	yes	characteristic
38	D₂₂₉	—	2	2	no	—
39	C₂₂₉	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₄×M₁₆	—	229	1	no	maximal, Sylow
41	C₂×M₁₆	—	229	2	no	—
42	C₂×C₄²	—	229	1	no	—
43	#97	—	229	2	no	—
44	C₄×C₈	—	229	2	no	—
45	C₂²×C₄	—	229	1	no	—
46	C₂²×C₄	—	229	1	no	—
47	C₂²×C₄	—	229	1	no	—
48	M₁₆	—	229	8	no	—
49	C₂×C₈	—	229	4	no	—
50	C₄²	—	229	1	no	—
51	C₄²	—	229	1	no	—
52	C₄²	—	229	1	no	—
53	C₄²	#11745021	1	1	yes	characteristic
54	C₂³	—	229	1	no	—
55	C₂×C₄	—	458	2	no	—
56	C₂×C₄	—	458	2	no	—
57	C₂×C₄	—	229	1	no	—
58	C₂×C₄	—	229	1	no	—
59	C₂×C₄	—	229	1	no	—
60	C₂×C₄	—	229	4	no	—
61	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
62	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
63	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
64	C₈	—	229	8	no	—
65	C₂²	—	458	1	no	—
66	C₂²	—	458	1	no	—
67	C₂²	—	229	2	no	—
68	C₂²	C₂²×#11745021	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	458	1	no	—
71	C₄	—	229	2	no	—
72	C₄	—	229	2	no	—
73	C₄	C₄×#11745021	1	2	yes	—
74	C₄	#16814676	1	2	yes	direct product factor
75	C₂	—	458	2	no	—
76	C₂	C₂×C₄×#11745021	1	1	yes	characteristic
77	C₂	D₂₂₉⋊M₁₆	1	1	yes	characteristic
78	C₂	C₂×#16814676	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#11745021
commutator	C₂×C₂₂₉	C₂×C₄²
Frattini	C₂²	C₂²×#11745021
Fitting	C₄²×C₂₂₉	C₄
socle	C₂²×C₂₂₉	C₂²×C₄
prime radical	C₂²×D₂₂₉	C₂×C₄
cosocle	C₂×Dic₂₂₉	C₂³
hypercenter	C₄²	#11745021
hypocenter	C₂₂₉	C₄×M₁₆
LCS	G ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #20301043	C₂	semidirect
3. C₄×#14270087	C₂	semidirect
5. #16814676	C₄	direct (N × H)
14. #14270087	C₂×C₄	semidirect
31. C₄×C₂₂₉	M₁₆	semidirect
33. Dic₂₂₉	M₁₆	semidirect
39. C₂₂₉	C₄×M₁₆	semidirect
74. C₄	#16814676	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×#16814676	2
#20301043	2
C₄×#14270087	2
C₄²×D₂₂₉	2
C₄×M₁₆	229

Subgroups — C4×#16814676 #28412443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16814676 #28412443