Subgroups — C₂×#21443885 #29591565

Order 15616.

254 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839513	C₂	1	2	yes	maximal
2	#21443885	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₁×#346	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#92418	—	2	2	no	—
5	#16839513	—	2	2	no	—
6	#16839513	C₂²	1	4	yes	—
7	C₂²×C₁₆×C₆₁	C₄	1	1	yes	characteristic
8	C₂²×C₁₆×C₆₁	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₆₁×#346	C₄	1	2	yes	—
11	C₆₁×#346	C₂²	1	2	yes	—
12	C₂²×#92418	—	4	2	no	—
13	C₄⋊#92418	—	2	4	no	—
14	C₄⋊#92418	—	4	2	no	—
15	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₆₁	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₆₁	—	2	2	no	—
19	C₂×C₁₆×C₆₁	C₈	1	4	yes	complemented
20	C₂×C₁₆×C₆₁	C₂×C₄	1	2	yes	—
21	C₂×C₁₆×C₆₁	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
24	C₄×C₈×C₆₁	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₄×C₆₁	SD₁₆	1	2	yes	—
28	C₂×C₈×C₆₁	—	2	2	no	—
29	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₆₁	C₂×C₈	1	2	yes	—
32	C₂×C₈×C₆₁	M₁₆	1	2	yes	—
33	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
35	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
36	C₄²×C₆₁	SD₁₆	1	2	yes	—
37	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
38	C₂×#92418	—	4	4	no	—
39	C₂×#92418	—	8	4	no	—
40	C₁₆×C₆₁	—	2	2	no	—
41	C₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
42	C₂³×C₆₁	#106	1	1	yes	characteristic
43	C₂×C₄×C₆₁	—	2	4	no	—
44	C₂×C₄×C₆₁	C₄⋊C₈	1	2	yes	—
45	C₂×C₄×C₆₁	#106	1	2	yes	—
46	C₂×C₄×C₆₁	#106	1	1	yes	characteristic
47	C₂×C₄×C₆₁	#108	1	2	yes	—
48	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
50	C₈×C₆₁	—	2	1	no	—
51	C₈×C₆₁	—	2	1	no	—
52	C₈×C₆₁	C₄⋊C₈	1	2	yes	—
53	C₈×C₆₁	C₂²×C₈	1	1	yes	characteristic
54	C₈×C₆₁	C₂×M₁₆	1	1	yes	characteristic
55	#92418	—	8	4	no	—
56	C₂×#1368	—	61	1	no	maximal, Sylow
57	C₂²×C₆₁	#334	1	2	yes	—
58	C₂²×C₆₁	#365	1	4	yes	—
59	C₂²×C₆₁	C₂×#106	1	1	yes	characteristic
60	C₄×C₆₁	—	2	2	no	—
61	C₄×C₆₁	—	2	2	no	—
62	C₄×C₆₁	#334	1	2	yes	—
63	C₄×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
64	C₄×C₆₁	C₂×#108	1	1	yes	characteristic
65	C₂×#346	D₆₁	1	1	yes	characteristic
66	C₂×#334	—	61	2	no	—
67	#1368	—	61	4	no	—
68	C₂×C₆₁	#1368	1	4	yes	complemented
69	C₂×C₆₁	C₂×#334	1	1	yes	characteristic
70	C₂×C₆₁	C₂×#365	1	2	yes	—
71	C₂²×C₁₆	Dic₆₁	1	1	yes	characteristic
72	C₂²×C₁₆	Dic₆₁	1	1	yes	characteristic
73	C₂×C₄⋊C₈	—	122	2	no	—
74	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
75	#346	Dic₆₁	1	2	yes	—
76	#346	C₂×D₆₁	1	2	yes	—
77	#334	—	61	4	no	—
78	#334	—	122	2	no	—
79	C₆₁	C₂×#1368	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₈	—	244	2	no	—
81	C₂²×C₈	Dic₁₂₂	1	1	yes	characteristic
82	C₂²×C₈	C₂×Dic₆₁	1	1	yes	characteristic
83	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
84	C₂×C₁₆	—	2	2	no	—
85	C₂×C₁₆	#92418	1	4	yes	complemented
86	C₂×C₁₆	C₂×Dic₆₁	1	2	yes	—
87	C₂×C₁₆	C₂×Dic₆₁	1	2	yes	—
88	C₄⋊C₈	—	122	4	no	—
89	C₄⋊C₈	—	244	2	no	—
90	C₄×C₈	Dic₁₂₂	1	1	yes	characteristic
91	C₄×C₈	D₂₄₄	1	1	yes	characteristic
92	C₄×C₈	C₂×Dic₆₁	1	1	yes	characteristic
93	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
94	C₂²×C₄	#11758190	1	2	yes	—
95	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	488	4	no	—
98	C₂×C₈	—	244	4	no	—
99	C₂×C₈	C₂×#92418	1	2	yes	—
100	C₂×C₈	#11758194	1	2	yes	—
101	C₂×C₈	C₄⋊Dic₆₁	1	1	yes	characteristic
102	C₂×C₈	C₄⋊Dic₆₁	1	1	yes	characteristic
103	C₂×C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
104	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
105	C₄²	#11758190	1	2	yes	—
106	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
107	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
108	C₁₆	—	2	2	no	—
109	C₁₆	C₂×#92418	1	4	yes	complemented
110	C₂³	#14519709	1	1	yes	characteristic
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	C₄⋊#92418	1	2	yes	—
113	C₂×C₄	#14519709	1	2	yes	—
114	C₂×C₄	#14519709	1	1	yes	characteristic
115	C₂×C₄	#14519713	1	2	yes	—
116	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
117	C₂×C₄	C₂×#11758190	1	2	yes	—
118	C₈	—	2	1	no	—
119	C₈	—	2	1	no	—
120	C₈	—	488	4	no	—
121	C₈	C₄⋊#92418	1	2	yes	—
122	C₈	C₂²×#92418	1	1	yes	characteristic
123	C₈	C₂×#11758194	1	1	yes	characteristic
124	C₂²	#16839513	1	2	yes	—
125	C₂²	#16839585	1	4	yes	—
126	C₂²	C₂×#14519709	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	2	2	no	—
129	C₄	#16839513	1	2	yes	—
130	C₄	C₂×C₄⋊#92418	1	1	yes	characteristic
131	C₄	C₂×#14519713	1	1	yes	characteristic
132	C₂	#21443885	1	4	yes	direct product factor
133	C₂	C₂×#16839513	1	1	yes	characteristic
134	C₂	C₂×#16839585	1	2	yes	—

	subgroup	G/H
center	C₂³	#14519709
commutator	C₈×C₆₁	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₆₁
Fitting	C₂×C₆₁×#346	C₂
socle, prime radical	C₂³×C₆₁	#106
cosocle	C₄×C₈×C₆₁	C₂³
hypercenter	C₂×#346	D₆₁
hypocenter	C₆₁	C₂×#1368
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. #21443885	C₂	direct (N × H)
19. C₂×C₁₆×C₆₁	C₈	semidirect
41. C₁₆×C₆₁	C₂×C₈	semidirect
68. C₂×C₆₁	#1368	semidirect
79. C₆₁	C₂×#1368	semidirect
85. C₂×C₁₆	#92418	semidirect
109. C₁₆	C₂×#92418	semidirect
132. C₂	#21443885	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×#16839513	2
#21443885	2
C₂×C₆₁×#346	2
C₂×#1368	61

Subgroups — C2×#21443885 #29591565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21443885 #29591565