Subgroups — C₂×#13112904 #15774481

Order 3328.

222 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	2	yes	maximal
2	#13112904	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×#88052	—	2	2	no	—
8	C₁₃×#346	C₄	1	2	yes	—
9	C₁₃×#346	C₂²	1	2	yes	—
10	#11718055	—	2	2	no	—
11	#11718055	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
15	C₂×C₁₃×C₁₆	—	2	1	no	—
16	C₂×C₁₃×C₁₆	—	2	1	no	—
17	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
18	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	#88052	—	2	4	no	—
26	#88052	—	4	2	no	—
27	C₂×#6090	—	4	2	no	—
28	C₂×#1369	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	—	2	1	no	—
30	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
36	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
38	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
39	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₄²×C₁₃	—	2	1	no	—
42	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
43	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
44	C₁₃×C₁₆	—	2	2	no	—
45	C₁₃×C₁₆	C₂×C₈	1	4	yes	—
46	#6090	—	4	4	no	—
47	C₂×#364	—	13	2	no	—
48	C₂×#346	D₁₃	1	1	yes	characteristic
49	#1369	—	13	4	no	—
50	C₂³×C₁₃	#108	1	1	yes	characteristic
51	C₂×C₄×C₁₃	—	2	1	no	—
52	C₂×C₄×C₁₃	—	2	1	no	—
53	C₂×C₄×C₁₃	—	4	2	no	—
54	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
57	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
58	C₂×C₄×C₁₃	#108	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
61	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
62	C₈×C₁₃	#106	1	2	yes	—
63	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
64	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
65	C₈×C₁₃	C₂×SD₁₆	1	2	yes	—
66	C₂×M₃₂	—	26	2	no	—
67	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
68	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
70	#364	—	13	4	no	—
71	#364	—	26	2	no	—
72	#346	Dic₁₃	1	2	yes	—
73	#346	C₂×D₁₃	1	2	yes	—
74	C₂²×C₁₃	—	2	2	no	—
75	C₂²×C₁₃	#334	1	1	yes	characteristic
76	C₂²×C₁₃	#334	1	1	yes	characteristic
77	C₂²×C₁₃	C₂×#108	1	1	yes	characteristic
78	C₄×C₁₃	—	4	1	no	—
79	C₄×C₁₃	—	4	1	no	—
80	C₄×C₁₃	#334	1	1	yes	characteristic
81	C₄×C₁₃	#334	1	1	yes	characteristic
82	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
83	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
84	C₂²×C₈	D₅₂	1	1	yes	characteristic
85	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
86	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
87	M₃₂	—	26	4	no	—
88	M₃₂	—	52	2	no	—
89	C₂×C₁₆	—	2	1	no	—
90	C₂×C₁₆	—	2	1	no	—
91	C₂×C₁₆	—	52	2	no	—
92	C₂×C₁₆	#1055	1	2	yes	—
93	C₂×C₁₆	#1055	1	2	yes	—
94	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
95	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
96	C₄×C₈	Dic₂₆	1	1	yes	characteristic
97	C₄×C₈	D₅₂	1	1	yes	characteristic
98	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
99	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
100	C₂×C₁₃	—	2	1	no	—
101	C₂×C₁₃	—	2	1	no	—
102	C₂×C₁₃	#1369	1	2	yes	complemented
103	C₂×C₁₃	C₂×#334	1	1	yes	characteristic
104	C₂²×C₄	—	2	1	no	—
105	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
106	C₂×C₈	#6095	1	2	yes	—
107	C₂×C₈	#6095	1	2	yes	—
108	C₂×C₈	C₂×#1055	1	1	yes	characteristic
109	C₂×C₈	C₂×#1055	1	1	yes	characteristic
110	C₂×C₈	#6099	1	1	yes	characteristic
111	C₂×C₈	#6099	1	1	yes	characteristic
112	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
113	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
114	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
115	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
116	C₄²	—	2	1	no	—
117	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
118	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
119	C₁₆	—	2	2	no	—
120	C₁₆	—	52	4	no	—
121	C₁₆	C₂×#1055	1	4	yes	—
122	C₁₃	C₂×#1369	1	1	yes	characteristic, complemented, Sylow
123	C₂³	#88059	1	1	yes	characteristic
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
128	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
129	C₂×C₄	#88057	1	1	yes	characteristic
130	C₂×C₄	#88057	1	1	yes	characteristic
131	C₂×C₄	#88059	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
133	C₈	C₄⋊#1055	1	1	yes	characteristic
134	C₈	C₄⋊#1055	1	1	yes	characteristic
135	C₈	#88057	1	2	yes	—
136	C₈	C₂×#6095	1	2	yes	—
137	C₈	C₂²×#1055	1	1	yes	characteristic
138	C₈	C₂×#6099	1	1	yes	characteristic
139	C₂²	—	2	2	no	—
140	C₂²	#11718049	1	1	yes	characteristic
141	C₂²	#11718049	1	1	yes	characteristic
142	C₂²	C₂×#88059	1	1	yes	characteristic
143	C₄	—	4	1	no	—
144	C₄	—	4	1	no	—
145	C₄	#11718049	1	1	yes	characteristic
146	C₄	#11718049	1	1	yes	characteristic
147	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
148	C₄	C₂×#88057	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	1	no	—
151	C₂	#13112904	1	2	yes	direct product factor
152	C₂	C₂×#11718049	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88057
commutator	C₈×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#346	C₂
socle	C₂²×C₁₃	#334
prime radical	C₂³×C₁₃	#108
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×#346	D₁₃
hypocenter	C₁₃	C₂×#1369
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. #13112904	C₂	direct (N × H)
102. C₂×C₁₃	#1369	semidirect
122. C₁₃	C₂×#1369	semidirect
151. C₂	#13112904	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×#11718055	2
#13112904	2
C₂×C₁₃×#346	2
C₂×#1369	13

Subgroups — C2×#13112904 #15774481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112904 #15774481