Subgroups — C₂×#13112972 #15783104

Order 3328.

222 conjugacy classes of subgroups.

The subgroup lattice has 138 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	2	yes	maximal
2	#13112972	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₁₃×#346	C₄	1	2	yes	—
8	C₁₃×#346	C₂²	1	2	yes	—
9	#11718091	C₄	1	4	yes	complemented
10	#11718091	C₂²	1	4	yes	—
11	C₂×#88034	C₄	1	4	yes	complemented
12	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
15	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
16	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
17	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
22	C₄×C₈×C₁₃	C₈	1	2	yes	—
23	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	#88034	C₂×C₄	1	8	yes	complemented
25	C₂×#1398	—	13	1	no	maximal, Sylow
26	C₂²×C₄×C₁₃	—	2	1	no	—
27	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₈×C₁₃	—	2	1	no	—
29	C₂×C₈×C₁₃	—	2	1	no	—
30	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
33	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₄²×C₁₃	—	2	1	no	—
38	C₄²×C₁₃	C₂×C₈	1	2	yes	—
39	C₁₃×C₁₆	C₄²	1	2	yes	—
40	C₁₃×C₁₆	C₂×C₈	1	4	yes	—
41	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
42	C₂×M₆₄	—	13	2	no	—
43	C₂×#346	D₁₃	1	1	yes	characteristic
44	#1398	—	13	4	no	—
45	C₂³×C₁₃	M₃₂	1	1	yes	characteristic
46	C₂×C₄×C₁₃	—	2	2	no	—
47	C₂×C₄×C₁₃	—	4	2	no	—
48	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
51	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
52	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
54	C₈×C₁₃	—	2	2	no	—
55	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
56	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
57	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
58	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
59	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
60	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
61	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
62	M₆₄	—	13	4	no	—
63	M₆₄	—	13	4	no	—
64	C₂×C₃₂	—	13	4	no	—
65	#346	Dic₁₃	1	2	yes	—
66	#346	C₂×D₁₃	1	2	yes	—
67	C₂²×C₁₃	—	2	2	no	—
68	C₂²×C₁₃	#346	1	1	yes	characteristic
69	C₂²×C₁₃	#346	1	1	yes	characteristic
70	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
71	C₄×C₁₃	—	4	2	no	—
72	C₄×C₁₃	#346	1	1	yes	characteristic
73	C₄×C₁₃	#346	1	1	yes	characteristic
74	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
75	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
76	C₂²×C₈	#1055	1	1	yes	characteristic
77	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
78	C₂×C₄²	#1055	1	1	yes	characteristic
79	C₂×C₁₆	#1055	1	2	yes	—
80	C₂×C₁₆	#1055	1	2	yes	—
81	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
82	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
83	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
84	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
85	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
86	C₄×C₈	#1055	1	2	yes	—
87	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
88	C₃₂	—	13	8	no	—
89	C₂×C₁₃	—	2	1	no	—
90	C₂×C₁₃	—	2	1	no	—
91	C₂×C₁₃	#1398	1	2	yes	complemented
92	C₂×C₁₃	C₂×#346	1	1	yes	characteristic
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	C₂×#1055	1	2	yes	—
98	C₂×C₈	C₂×#1055	1	1	yes	characteristic
99	C₂×C₈	C₂×#1055	1	1	yes	characteristic
100	C₂×C₈	C₂×#1055	1	1	yes	characteristic
101	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
102	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
103	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
104	C₄²	—	2	1	no	—
105	C₄²	C₂×#1055	1	2	yes	—
106	C₁₆	C₂×#1055	1	4	yes	—
107	C₁₆	C₄×Dic₁₃	1	2	yes	—
108	C₁₆	C₂×C₄×D₁₃	1	2	yes	—
109	C₁₃	C₂×#1398	1	1	yes	characteristic, complemented, Sylow
110	C₂³	#88052	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	4	2	no	—
113	C₂×C₄	C₄×#1055	1	1	yes	characteristic
114	C₂×C₄	C₄×#1055	1	1	yes	characteristic
115	C₂×C₄	#88052	1	1	yes	characteristic
116	C₂×C₄	#88052	1	1	yes	characteristic
117	C₂×C₄	#88052	1	1	yes	characteristic
118	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
119	C₈	—	2	2	no	—
120	C₈	C₄×#1055	1	1	yes	characteristic
121	C₈	C₄×#1055	1	1	yes	characteristic
122	C₈	C₂²×#1055	1	1	yes	characteristic
123	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
124	C₂²	—	2	2	no	—
125	C₂²	#11718053	1	1	yes	characteristic
126	C₂²	#11718053	1	1	yes	characteristic
127	C₂²	C₂×#88052	1	1	yes	characteristic
128	C₄	—	4	2	no	—
129	C₄	#11718053	1	1	yes	characteristic
130	C₄	#11718053	1	1	yes	characteristic
131	C₄	C₂×C₄×#1055	1	1	yes	characteristic
132	C₄	C₂×#88052	1	1	yes	characteristic
133	C₂	—	2	1	no	—
134	C₂	—	2	1	no	—
135	C₂	#13112972	1	2	yes	direct product factor
136	C₂	C₂×#11718053	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×#346	C₂
socle	C₂²×C₁₃	#346
prime radical	C₂³×C₁₃	M₃₂
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₂×#346	D₁₃
hypocenter	C₁₃	C₂×#1398
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. #13112972	C₂	direct (N × H)
9. #11718091	C₄	semidirect
11. C₂×#88034	C₄	semidirect
24. #88034	C₂×C₄	semidirect
91. C₂×C₁₃	#1398	semidirect
109. C₁₃	C₂×#1398	semidirect
135. C₂	#13112972	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
#13112972	2
C₂×C₁₃×#346	2
C₂×#1398	13

Subgroups — C2×#13112972 #15783104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112972 #15783104