Subgroups — C₂×#21448113 #29838122

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21448113	C₂	1	8	yes	maximal, direct product factor
2	C₂×#16839596	C₂	1	3	yes	maximal, complemented
3	C₂²×#14519683	C₂	1	3	yes	maximal, complemented
4	C₂×C₆₁×#504	C₂	1	1	yes	maximal, characteristic
5	#16839596	C₂²	1	12	yes	complemented
6	C₂×#14519683	C₂²	1	1	yes	characteristic
7	C₂×#14519683	C₂²	1	3	yes	—
8	C₂×#14519683	C₂²	1	12	yes	complemented
9	C₂×#131×C₆₁	C₄	1	1	yes	characteristic
10	C₆₁×#504	C₄	1	4	yes	—
11	C₆₁×#504	C₂²	1	4	yes	—
12	C₂×M₃₂×C₆₁	C₄	1	3	yes	—
13	C₂²×C₁₆×C₆₁	C₂²	1	3	yes	—
14	#14519683	C₂³	1	2	yes	—
15	#14519683	C₂³	1	6	yes	—
16	C₂×#41×C₆₁	C₈	1	1	yes	characteristic
17	#131×C₆₁	C₈	1	4	yes	—
18	#131×C₆₁	C₂×C₄	1	4	yes	—
19	C₂×M₁₆×C₆₁	C₈	1	3	yes	—
20	C₂²×C₈×C₆₁	C₂×C₄	1	3	yes	—
21	M₃₂×C₆₁	C₂×C₄	1	12	yes	—
22	C₂×C₁₆×C₆₁	C₂×C₄	1	3	yes	—
23	C₂×C₁₆×C₆₁	C₂×C₄	1	6	yes	—
24	C₂×C₁₆×C₆₁	C₂³	1	6	yes	—
25	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
26	#41×C₆₁	C₁₆	1	4	yes	—
27	#41×C₆₁	C₂×C₈	1	4	yes	—
28	C₂×Q₈×C₆₁	C₁₆	1	1	yes	characteristic
29	C₂×D₄×C₆₁	C₁₆	1	3	yes	—
30	C₂²×C₄×C₆₁	C₂×C₈	1	3	yes	—
31	M₁₆×C₆₁	C₂×C₈	1	12	yes	—
32	C₂×C₈×C₆₁	C₂×C₈	1	3	yes	—
33	C₂×C₈×C₆₁	C₂×C₈	1	6	yes	—
34	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₆₁	C₂²×C₄	1	6	yes	—
36	C₁₆×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₁₆×C₆₁	C₂²×C₄	1	6	yes	—
38	C₁₆×C₆₁	C₂⁴	1	1	yes	characteristic
39	C₂³×C₆₁	C₂×C₁₆	1	3	yes	—
40	Q₈×C₆₁	C₂×C₁₆	1	4	yes	—
41	D₄×C₆₁	C₂×C₁₆	1	12	yes	—
42	C₂×C₄×C₆₁	C₂×C₁₆	1	3	yes	—
43	C₂×C₄×C₆₁	C₂×C₁₆	1	6	yes	—
44	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
45	C₂×C₄×C₆₁	C₂²×C₈	1	6	yes	—
46	C₈×C₆₁	C₂²×C₈	1	1	yes	characteristic
47	C₈×C₆₁	C₂²×C₈	1	6	yes	—
48	C₈×C₆₁	C₂³×C₄	1	1	yes	characteristic
49	C₂×#2258	—	61	1	no	maximal, Sylow
50	C₂²×C₆₁	—	2	6	no	—
51	C₂²×C₆₁	C₂²×C₁₆	1	6	yes	—
52	C₂²×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
53	C₄×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
54	C₄×C₆₁	C₂²×C₁₆	1	6	yes	—
55	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
56	C₂×#504	D₆₁	1	1	yes	characteristic
57	#2258	—	61	8	no	—
58	C₂×M₆₄	—	61	3	no	—
59	C₂²×C₃₂	—	61	3	no	—
60	C₂×C₆₁	—	2	6	no	—
61	C₂×C₆₁	#2258	1	2	yes	complemented
62	C₂×C₆₁	C₂³×C₁₆	1	1	yes	characteristic
63	C₂×#131	Dic₆₁	1	1	yes	characteristic
64	#504	Dic₆₁	1	4	yes	—
65	#504	C₂×D₆₁	1	4	yes	—
66	C₂×M₃₂	Dic₆₁	1	3	yes	—
67	C₂²×C₁₆	C₂×D₆₁	1	3	yes	—
68	M₆₄	—	61	12	no	—
69	C₂×C₃₂	—	61	12	no	—
70	C₂×C₃₂	—	61	1	no	—
71	C₂×C₃₂	—	61	3	no	—
72	C₆₁	C₂×#2258	1	1	yes	characteristic, complemented, Sylow
73	C₂×#41	#92418	1	1	yes	characteristic
74	#131	#92418	1	4	yes	—
75	#131	C₂×Dic₆₁	1	4	yes	—
76	C₂×M₁₆	#92418	1	3	yes	—
77	C₂²×C₈	C₂×Dic₆₁	1	3	yes	—
78	M₃₂	C₂×Dic₆₁	1	12	yes	—
79	C₂×C₁₆	C₂×Dic₆₁	1	3	yes	—
80	C₂×C₁₆	C₂×Dic₆₁	1	6	yes	—
81	C₂×C₁₆	C₂²×D₆₁	1	6	yes	—
82	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
83	C₃₂	—	61	2	no	—
84	C₃₂	—	61	6	no	—
85	#41	#11758185	1	4	yes	—
86	#41	C₂×#92418	1	4	yes	—
87	C₂×Q₈	#11758185	1	1	yes	characteristic
88	C₂×D₄	#11758185	1	3	yes	—
89	C₂²×C₄	C₂×#92418	1	3	yes	—
90	M₁₆	C₂×#92418	1	12	yes	—
91	C₂×C₈	C₂×#92418	1	3	yes	—
92	C₂×C₈	C₂×#92418	1	6	yes	—
93	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
94	C₂×C₈	C₂²×Dic₆₁	1	6	yes	—
95	C₁₆	C₂²×Dic₆₁	1	1	yes	characteristic
96	C₁₆	C₂²×Dic₆₁	1	6	yes	—
97	C₁₆	C₂³×D₆₁	1	1	yes	characteristic
98	C₂³	C₂×#11758185	1	3	yes	—
99	Q₈	C₂×#11758185	1	4	yes	—
100	D₄	C₂×#11758185	1	12	yes	—
101	C₂×C₄	C₂×#11758185	1	3	yes	—
102	C₂×C₄	C₂×#11758185	1	6	yes	—
103	C₂×C₄	C₂²×#92418	1	1	yes	characteristic
104	C₂×C₄	C₂²×#92418	1	6	yes	—
105	C₈	C₂²×#92418	1	1	yes	characteristic
106	C₈	C₂²×#92418	1	6	yes	—
107	C₈	C₂³×Dic₆₁	1	1	yes	characteristic
108	C₂²	—	2	6	no	—
109	C₂²	C₂²×#11758185	1	6	yes	—
110	C₂²	C₂²×#11758185	1	1	yes	characteristic
111	C₄	C₂²×#11758185	1	1	yes	characteristic
112	C₄	C₂²×#11758185	1	6	yes	—
113	C₄	C₂³×#92418	1	1	yes	characteristic
114	C₂	—	2	6	no	—
115	C₂	#21448113	1	2	yes	direct product factor
116	C₂	C₂³×#11758185	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₆₁
commutator	C₂×C₆₁	C₂³×C₁₆
Frattini	C₁₆	C₂³×D₆₁
Fitting	C₂×C₆₁×#504	C₂
socle	C₂²×C₆₁	C₂²×C₁₆
prime radical	C₂×#41×C₆₁	C₈
cosocle	C₁₆×C₆₁	C₂⁴
hypercenter	C₂×#504	D₆₁
hypocenter	C₆₁	C₂×#2258
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. #21448113	C₂	direct (N × H)
2. C₂×#16839596	C₂	semidirect
3. C₂²×#14519683	C₂	semidirect
5. #16839596	C₂²	semidirect
8. C₂×#14519683	C₂²	semidirect
61. C₂×C₆₁	#2258	semidirect
72. C₆₁	C₂×#2258	semidirect
115. C₂	#21448113	direct (N × H)

Maximal subgroups

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

subgroup	index
#21448113	2
C₂×#16839596	2
C₂²×#14519683	2
C₂×C₆₁×#504	2
C₂×#2258	61

Subgroups — C2×#21448113 #29838122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21448113 #29838122