Subgroups — Q₁₆×#11745021 #28412519

Order 14656.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#11745021	C₂	1	2	yes	maximal
2	#20301057	C₂	1	1	yes	maximal, characteristic
3	#20301051	C₂	1	2	yes	maximal
4	C₈×#11745021	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₂₂₉	C₂	1	1	yes	maximal, characteristic
6	D₂₂₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊#11745021	—	2	2	no	—
8	C₄⋊#11745021	C₂²	1	2	yes	—
9	C₄×#11745021	—	2	2	no	—
10	C₄×#11745021	C₂²	1	1	yes	characteristic
11	Q₈×D₂₂₉	C₂²	1	2	yes	—
12	Dic₉₁₆	C₄	1	1	yes	characteristic, complemented
13	#16814656	C₄	1	2	yes	complemented
14	C₈×D₂₂₉	C₂²	1	1	yes	characteristic
15	Q₁₆×C₂₂₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#11745021	—	2	2	no	—
17	C₂×#11745021	D₄	1	1	yes	characteristic
18	C₂×#11745021	D₄	1	1	yes	characteristic
19	#14270087	—	2	1	no	—
20	Dic₄₅₈	—	2	2	no	—
21	Dic₄₅₈	C₂×C₄	1	2	yes	—
22	C₄×D₂₂₉	—	2	2	no	—
23	C₄×D₂₂₉	C₂³	1	1	yes	characteristic
24	#14270080	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₂₂₉	C₂×C₄	1	2	yes	—
26	C₈×C₂₂₉	C₂×C₄	1	1	yes	characteristic
27	C₂×D₂₂₉	C₂×D₄	1	1	yes	characteristic
28	#11745021	—	2	1	no	—
29	#11745021	—	4	2	no	—
30	#11745021	Q₁₆	1	2	yes	direct product factor
31	C₄×C₂₂₉	—	2	2	no	—
32	C₄×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
33	Dic₂₂₉	—	2	2	no	—
34	Dic₂₂₉	#41	1	1	yes	characteristic
35	C₂×C₂₂₉	C₄×D₄	1	1	yes	characteristic
36	D₂₂₉	C₂×Q₁₆	1	1	yes	characteristic
37	D₂₂₉	#135	1	1	yes	characteristic
38	C₂₂₉	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₄×Q₁₆	—	229	1	no	maximal, Sylow
40	C₂×Q₁₆	—	229	1	no	—
41	C₄×Q₈	—	229	2	no	—
42	#107	—	229	1	no	—
43	#103	—	229	2	no	—
44	C₄×C₈	—	229	1	no	—
45	C₂×Q₈	—	229	2	no	—
46	Q₁₆	—	229	2	no	—
47	Q₁₆	—	229	1	no	—
48	Q₁₆	#11745021	1	1	yes	characteristic, direct product factor
49	C₂×C₈	—	229	1	no	—
50	C₂×C₈	—	229	1	no	—
51	C₄⋊C₄	—	458	2	no	—
52	C₄⋊C₄	—	229	2	no	—
53	C₄²	—	458	2	no	—
54	C₄²	—	229	1	no	—
55	Q₈	—	458	2	no	—
56	Q₈	—	229	2	no	—
57	Q₈	C₂×#11745021	1	2	yes	—
58	C₂×C₄	—	458	2	no	—
59	C₂×C₄	—	458	2	no	—
60	C₂×C₄	—	229	1	no	—
61	C₂×C₄	—	229	1	no	—
62	C₂×C₄	—	229	1	no	—
63	C₈	—	458	1	no	—
64	C₈	—	229	1	no	—
65	C₈	C₂×#11745021	1	1	yes	characteristic
66	C₂²	—	229	1	no	—
67	C₄	—	2	2	no	—
68	C₄	—	916	2	no	—
69	C₄	—	458	1	no	—
70	C₄	—	458	2	no	—
71	C₄	—	229	2	no	—
72	C₄	—	229	1	no	—
73	C₄	C₂²×#11745021	1	1	yes	characteristic
74	C₂	—	229	1	no	—
75	C₂	—	229	1	no	—
76	C₂	D₄×#11745021	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#11745021
commutator	C₄×C₂₂₉	C₂²×C₄
Frattini	C₄	C₂²×#11745021
Fitting	Q₁₆×C₂₂₉	C₄
socle	C₂×C₂₂₉	C₄×D₄
prime radical	C₂×D₂₂₉	C₂×D₄
cosocle	C₄×D₂₂₉	C₂³
hypercenter	Q₁₆	#11745021
hypocenter	C₂₂₉	C₄×Q₁₆
LCS	G ▷ C₄×C₂₂₉ ▷ C₂×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Dic₉₁₆	C₄	semidirect
13. #16814656	C₄	semidirect
15. Q₁₆×C₂₂₉	C₄	semidirect
30. #11745021	Q₁₆	direct (N × H)
38. C₂₂₉	C₄×Q₁₆	semidirect
48. Q₁₆	#11745021	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×#11745021	2
#20301057	2
#20301051	2
C₈×#11745021	2
Q₁₆×D₂₂₉	2
C₄×Q₁₆	229

Subgroups — Q16×#11745021 #28412519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#11745021 #28412519