Subgroups — C₂×#13112902 #15774471

Order 3328.

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×#11718049	C₂	1	2	yes	maximal
2	#13112902	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	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊#1055	—	2	2	no	—
8	C₁₃×#346	C₄	1	2	yes	—
9	C₁₃×#346	C₂²	1	2	yes	—
10	#11718049	—	2	2	no	—
11	#11718049	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
15	C₂²×#1055	—	4	2	no	—
16	C₂×C₁₃×C₁₆	—	2	2	no	—
17	C₂×C₁₃×C₁₆	C₈	1	4	yes	complemented
18	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₄⋊#1055	—	2	4	no	—
25	C₄⋊#1055	—	4	2	no	—
26	C₂×#1368	—	13	1	no	maximal, Sylow
27	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
33	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
34	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
37	C₄²×C₁₃	SD₁₆	1	2	yes	—
38	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×#1055	—	4	4	no	—
40	C₂×#1055	—	8	4	no	—
41	C₁₃×C₁₆	—	2	2	no	—
42	C₁₃×C₁₆	C₂×C₈	1	4	yes	complemented
43	C₂×#346	D₁₃	1	1	yes	characteristic
44	C₂×#334	—	13	2	no	—
45	#1368	—	13	4	no	—
46	C₂³×C₁₃	#106	1	1	yes	characteristic
47	C₂×C₄×C₁₃	—	2	4	no	—
48	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
49	C₂×C₄×C₁₃	#106	1	2	yes	—
50	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
51	C₂×C₄×C₁₃	#108	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
54	C₈×C₁₃	—	2	1	no	—
55	C₈×C₁₃	—	2	1	no	—
56	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
57	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
58	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
59	#1055	—	8	4	no	—
60	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
61	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
62	C₂×C₄⋊C₈	—	26	2	no	—
63	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
64	#346	Dic₁₃	1	2	yes	—
65	#346	C₂×D₁₃	1	2	yes	—
66	#334	—	13	4	no	—
67	#334	—	26	2	no	—
68	C₂²×C₁₃	#334	1	2	yes	—
69	C₂²×C₁₃	#365	1	4	yes	—
70	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
71	C₄×C₁₃	—	2	2	no	—
72	C₄×C₁₃	—	2	2	no	—
73	C₄×C₁₃	#334	1	2	yes	—
74	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
75	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
76	C₂²×C₈	—	52	2	no	—
77	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
78	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
79	C₂×C₄²	D₅₂	1	1	yes	characteristic
80	C₂×C₁₆	—	2	2	no	—
81	C₂×C₁₆	#1055	1	4	yes	complemented
82	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
83	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
84	C₄⋊C₈	—	26	4	no	—
85	C₄⋊C₈	—	52	2	no	—
86	C₄×C₈	Dic₂₆	1	1	yes	characteristic
87	C₄×C₈	D₅₂	1	1	yes	characteristic
88	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
89	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
90	C₂×C₁₃	#1368	1	4	yes	complemented
91	C₂×C₁₃	C₂×#334	1	1	yes	characteristic
92	C₂×C₁₃	C₂×#365	1	2	yes	—
93	C₂²×C₄	#6095	1	2	yes	—
94	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	52	4	no	—
97	C₂×C₈	—	104	4	no	—
98	C₂×C₈	C₂×#1055	1	2	yes	—
99	C₂×C₈	#6099	1	2	yes	—
100	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
101	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
102	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
103	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
104	C₄²	#6095	1	2	yes	—
105	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
106	C₄²	C₂×D₅₂	1	1	yes	characteristic
107	C₁₆	—	2	2	no	—
108	C₁₆	C₂×#1055	1	4	yes	complemented
109	C₁₃	C₂×#1368	1	1	yes	characteristic, complemented, Sylow
110	C₂³	#88057	1	1	yes	characteristic
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	C₄⋊#1055	1	2	yes	—
113	C₂×C₄	#88057	1	2	yes	—
114	C₂×C₄	#88057	1	1	yes	characteristic
115	C₂×C₄	#88059	1	2	yes	—
116	C₂×C₄	C₂×#6095	1	2	yes	—
117	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
118	C₈	—	2	1	no	—
119	C₈	—	2	1	no	—
120	C₈	—	104	4	no	—
121	C₈	C₄⋊#1055	1	2	yes	—
122	C₈	C₂²×#1055	1	1	yes	characteristic
123	C₈	C₂×#6099	1	1	yes	characteristic
124	C₂²	#11718049	1	2	yes	—
125	C₂²	#11718105	1	4	yes	—
126	C₂²	C₂×#88057	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	2	2	no	—
129	C₄	#11718049	1	2	yes	—
130	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
131	C₄	C₂×#88059	1	1	yes	characteristic
132	C₂	#13112902	1	4	yes	direct product factor
133	C₂	C₂×#11718049	1	1	yes	characteristic
134	C₂	C₂×#11718105	1	2	yes	—

	subgroup	G/H
center	C₂³	#88057
commutator	C₈×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#346	C₂
socle, prime radical	C₂³×C₁₃	#106
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×#346	D₁₃
hypocenter	C₁₃	C₂×#1368
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
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. #13112902	C₂	direct (N × H)
17. C₂×C₁₃×C₁₆	C₈	semidirect
42. C₁₃×C₁₆	C₂×C₈	semidirect
81. C₂×C₁₆	#1055	semidirect
90. C₂×C₁₃	#1368	semidirect
108. C₁₆	C₂×#1055	semidirect
109. C₁₃	C₂×#1368	semidirect
132. C₂	#13112902	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×#11718049	2
#13112902	2
C₂×C₁₃×#346	2
C₂×#1368	13

Subgroups — C2×#13112902 #15774471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112902 #15774471