Subgroups — C₂×#13112971 #15783103

Order 3328.

222 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718091	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718094	C₂	1	1	yes	maximal, characteristic
3	#13112971	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
7	C₂²×#6090	C₄	1	1	yes	characteristic
8	C₁₃×M₆₄	C₄	1	2	yes	complemented
9	C₁₃×M₆₄	C₂²	1	2	yes	—
10	C₂×C₁₃×C₃₂	C₄	1	2	yes	complemented
11	#11718094	C₄	1	2	yes	—
12	#11718094	C₂²	1	2	yes	—
13	#11718091	C₄	1	2	yes	complemented
14	#11718091	C₂²	1	2	yes	—
15	C₂×#88034	C₄	1	2	yes	complemented
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₃	C₈	1	1	yes	characteristic
18	C₂²×#1055	C₈	1	1	yes	characteristic
19	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
25	C₈×Dic₁₃	C₈	1	2	yes	—
26	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
27	C₂×#6090	C₈	1	2	yes	—
28	C₂×#6090	C₈	1	2	yes	—
29	C₂×#6090	C₂×C₄	1	2	yes	—
30	C₁₃×C₃₂	C₂×C₄	1	4	yes	complemented
31	#88034	C₂×C₄	1	4	yes	complemented
32	C₂×#1398	—	13	1	no	maximal, Sylow
33	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂²×Dic₁₃	—	2	1	no	—
35	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×Dic₁₃	—	2	1	no	—
42	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
43	C₂×#1055	—	2	1	no	—
44	C₂×#1055	—	2	1	no	—
45	C₂×#1055	C₂×C₈	1	2	yes	—
46	C₁₃×C₁₆	C₄²	1	1	yes	characteristic
47	C₁₃×C₁₆	C₄²	1	1	yes	characteristic
48	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
49	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
50	#6090	C₂×C₈	1	4	yes	—
51	C₂×M₆₄	—	13	1	no	—
52	C₂×M₆₄	D₁₃	1	1	yes	characteristic
53	C₂×#346	—	13	1	no	—
54	#1398	—	13	4	no	—
55	C₂³×C₁₃	M₃₂	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
59	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
60	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
62	C₂×Dic₁₃	—	2	2	no	—
63	C₂×Dic₁₃	—	4	2	no	—
64	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
65	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
66	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
67	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
68	#1055	—	2	2	no	—
69	C₂²×C₁₆	—	13	1	no	—
70	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
71	C₂×C₄×C₈	—	13	1	no	—
72	M₆₄	—	13	2	no	—
73	M₆₄	—	13	2	no	—
74	M₆₄	Dic₁₃	1	2	yes	complemented
75	M₆₄	C₂×D₁₃	1	2	yes	—
76	C₂×C₃₂	—	13	2	no	—
77	C₂×C₃₂	Dic₁₃	1	2	yes	complemented
78	#346	—	13	2	no	—
79	#346	—	13	2	no	—
80	C₂²×C₁₃	—	2	2	no	—
81	C₂²×C₁₃	#346	1	1	yes	characteristic
82	C₂²×C₁₃	#346	1	1	yes	characteristic
83	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
84	C₄×C₁₃	#346	1	1	yes	characteristic
85	C₄×C₁₃	#346	1	1	yes	characteristic
86	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
87	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
88	Dic₁₃	—	4	2	no	—
89	C₂²×C₈	—	13	1	no	—
90	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
91	C₂×C₄²	—	13	1	no	—
92	C₂×C₁₆	—	13	2	no	—
93	C₂×C₁₆	—	13	2	no	—
94	C₂×C₁₆	—	13	2	no	—
95	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
96	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
97	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
98	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
99	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
100	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
101	C₄×C₈	—	13	2	no	—
102	C₄×C₈	—	13	2	no	—
103	C₃₂	—	13	4	no	—
104	C₃₂	C₂×Dic₁₃	1	4	yes	complemented
105	C₂×C₁₃	—	2	1	no	—
106	C₂×C₁₃	—	2	1	no	—
107	C₂×C₁₃	#1398	1	2	yes	complemented
108	C₂×C₁₃	C₂×#346	1	1	yes	characteristic
109	C₂²×C₄	—	26	1	no	—
110	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
111	C₂×C₈	—	13	2	no	—
112	C₂×C₈	—	26	1	no	—
113	C₂×C₈	—	26	1	no	—
114	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
115	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
116	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
117	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
118	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
119	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
120	C₄²	—	13	2	no	—
121	C₄²	—	26	1	no	—
122	C₁₆	—	13	4	no	—
123	C₁₆	C₄×Dic₁₃	1	1	yes	characteristic
124	C₁₆	C₄×Dic₁₃	1	1	yes	characteristic
125	C₁₆	C₂×C₄×D₁₃	1	1	yes	characteristic
126	C₁₆	C₂²×Dic₁₃	1	1	yes	characteristic
127	C₁₃	C₂×#1398	1	1	yes	characteristic, complemented, Sylow
128	C₂³	#88038	1	1	yes	characteristic
129	C₂×C₄	—	26	2	no	—
130	C₂×C₄	—	52	2	no	—
131	C₂×C₄	#88038	1	1	yes	characteristic
132	C₂×C₄	#88038	1	1	yes	characteristic
133	C₂×C₄	#88038	1	1	yes	characteristic
134	C₂×C₄	C₈×Dic₁₃	1	1	yes	characteristic
135	C₂×C₄	C₈×Dic₁₃	1	1	yes	characteristic
136	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
137	C₈	—	26	2	no	—
138	C₈	C₈×Dic₁₃	1	1	yes	characteristic
139	C₈	C₈×Dic₁₃	1	1	yes	characteristic
140	C₈	C₂×C₈×D₁₃	1	1	yes	characteristic
141	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
142	C₂²	—	2	2	no	—
143	C₂²	#11718094	1	1	yes	characteristic
144	C₂²	#11718094	1	1	yes	characteristic
145	C₂²	C₂×#88038	1	1	yes	characteristic
146	C₄	—	52	2	no	—
147	C₄	#11718094	1	1	yes	characteristic
148	C₄	#11718094	1	1	yes	characteristic
149	C₄	C₂×#88038	1	1	yes	characteristic
150	C₄	C₂×C₈×Dic₁₃	1	1	yes	characteristic
151	C₂	—	2	1	no	—
152	C₂	—	2	1	no	—
153	C₂	#13112971	1	2	yes	direct product factor
154	C₂	C₂×#11718094	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄×Dic₁₃
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×M₆₄	C₂
socle	C₂²×C₁₃	#346
prime radical	C₂³×C₁₃	M₃₂
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₂×M₆₄	D₁₃
hypocenter	C₁₃	C₂×#1398
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
3. #13112971	C₂	direct (N × H)
8. C₁₃×M₆₄	C₄	semidirect
10. C₂×C₁₃×C₃₂	C₄	semidirect
13. #11718091	C₄	semidirect
15. C₂×#88034	C₄	semidirect
30. C₁₃×C₃₂	C₂×C₄	semidirect
31. #88034	C₂×C₄	semidirect
74. M₆₄	Dic₁₃	semidirect
77. C₂×C₃₂	Dic₁₃	semidirect
104. C₃₂	C₂×Dic₁₃	semidirect
107. C₂×C₁₃	#1398	semidirect
127. C₁₃	C₂×#1398	semidirect
153. C₂	#13112971	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×#11718091	2
C₂×#11718094	2
#13112971	2
C₂×C₁₃×M₆₄	2
C₂×#1398	13

Subgroups — C2×#13112971 #15783103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112971 #15783103