Subgroups — C₂×#13130049 #16792606

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719119	C₂	1	2	yes	maximal
2	#13130049	C₂	1	8	yes	maximal, direct product factor
3	C₂×#1057⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂³×#1055	C₄	1	1	yes	characteristic
8	C₂×C₂²⋊#1057	C₄	1	4	yes	—
9	#11719119	C₄	1	8	yes	—
10	#11719119	C₂²	1	8	yes	—
11	C₂×C₄⋊#1057	C₄	1	4	yes	—
12	C₂×C₄×#1057	C₂²	1	4	yes	—
13	C₂×C₈×Dic₁₃	C₄	1	4	yes	—
14	C₂×C₈×Dic₁₃	C₄	1	2	yes	—
15	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
16	C₂×C₈×Dic₁₃	C₂²	1	4	yes	—
17	#1057⋊C₈	C₂²	1	16	yes	complemented
18	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
20	C₂²×#1057	C₂×C₄	1	8	yes	—
21	C₂²×C₈×C₁₃	—	2	4	no	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
28	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
30	C₂²×#1055	—	2	4	no	—
31	C₂²×#1055	C₂×C₄	1	4	yes	—
32	C₂²×#1055	C₂×C₄	1	2	yes	—
33	C₂²⋊#1057	C₂×C₄	1	16	yes	—
34	C₄⋊#1057	C₂×C₄	1	16	yes	—
35	C₄×#1057	C₂×C₄	1	8	yes	—
36	C₄×#1057	C₂³	1	8	yes	—
37	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
38	C₈×Dic₁₃	C₂×C₄	1	8	yes	—
39	C₈×Dic₁₃	C₂³	1	4	yes	—
40	C₂×#1452	—	13	1	no	maximal, Sylow
41	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
43	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
45	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×Dic₁₃	—	2	8	no	—
49	C₂²×Dic₁₃	C₄²	1	2	yes	—
50	C₂²×Dic₁₃	C₄²	1	4	yes	—
51	C₂²×Dic₁₃	C₂²×C₄	1	4	yes	—
52	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
53	C₂×#1057	—	2	16	no	—
54	C₂×#1057	C₂²×C₄	1	16	yes	—
55	C₂×C₈×C₁₃	—	2	8	no	—
56	C₂×C₈×C₁₃	—	2	4	no	—
57	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
58	C₄×Dic₁₃	C₄²	1	2	yes	—
59	C₄×Dic₁₃	C₄²	1	4	yes	—
60	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
61	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
63	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
64	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
65	C₂×#1055	—	2	8	no	—
66	C₂×#1055	—	2	4	no	—
67	C₂×#1055	C₂²×C₄	1	4	yes	—
68	C₂×#431	—	13	2	no	—
69	C₂²×C₄×C₈	—	13	1	no	—
70	#1452	—	13	8	no	—
71	C₂×#322	—	13	4	no	—
72	C₂³×C₁₃	—	2	4	no	—
73	C₂³×C₁₃	#97	1	4	yes	—
74	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
75	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#97	1	8	yes	—
77	C₂×C₄×C₁₃	#97	1	4	yes	—
78	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
79	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
81	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
83	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
84	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
85	C₂×Dic₁₃	—	2	4	no	—
86	C₂×Dic₁₃	—	2	8	no	—
87	C₂×Dic₁₃	—	2	8	no	—
88	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
89	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
90	C₂×Dic₁₃	#131	1	8	yes	—
91	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
92	#1057	—	2	16	no	—
93	C₈×C₁₃	—	2	4	no	—
94	#1055	—	2	4	no	—
95	C₂³×C₈	—	13	1	no	—
96	C₂³×C₈	#261	1	1	yes	characteristic
97	C₂²×C₄²	—	13	1	no	—
98	#431	—	13	8	no	—
99	#431	—	13	8	no	—
100	C₂×C₄⋊C₈	—	13	4	no	—
101	C₂×C₂²⋊C₈	—	13	4	no	—
102	C₂×C₄×C₈	—	13	4	no	—
103	C₂×C₄×C₈	—	13	4	no	—
104	C₂×C₄×C₈	—	13	2	no	—
105	C₂×C₄×C₈	—	13	2	no	—
106	C₂×C₄×C₈	—	13	4	no	—
107	#322	—	13	16	no	—
108	C₂²×C₁₃	—	2	4	no	—
109	C₂²×C₁₃	—	2	8	no	—
110	C₂²×C₁₃	C₂×#97	1	4	yes	—
111	C₂²×C₁₃	C₂×#97	1	2	yes	—
112	C₂²×C₁₃	#405	1	4	yes	—
113	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
114	C₄×C₁₃	C₂×#97	1	4	yes	—
115	C₄×C₁₃	C₂×#97	1	2	yes	—
116	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
117	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
118	Dic₁₃	—	2	4	no	—
119	Dic₁₃	#405	1	4	yes	—
120	Dic₁₃	C₂×#131	1	4	yes	—
121	C₂³×C₄	—	13	2	no	—
122	C₂³×C₄	C₂×#261	1	1	yes	characteristic
123	C₂²×C₈	—	2	4	no	—
124	C₂²×C₈	—	13	8	no	—
125	C₂²×C₈	—	13	4	no	—
126	C₂²×C₈	—	13	2	no	—
127	C₂²×C₈	—	26	4	no	—
128	C₂²×C₈	C₂×#261	1	4	yes	—
129	C₂²×C₈	C₂×#261	1	2	yes	—
130	C₂×C₄²	—	13	2	no	—
131	C₂×C₄²	—	13	4	no	—
132	C₂×C₄²	—	13	2	no	—
133	C₂×C₄²	—	13	2	no	—
134	C₂×C₄²	—	13	1	no	—
135	C₂×C₄²	—	13	1	no	—
136	C₄⋊C₈	—	13	16	no	—
137	C₂²⋊C₈	—	13	16	no	—
138	C₄×C₈	—	13	8	no	—
139	C₄×C₈	—	13	8	no	—
140	C₄×C₈	—	13	4	no	—
141	C₄×C₈	—	13	4	no	—
142	C₄×C₈	—	13	8	no	—
143	C₂×C₁₃	—	2	4	no	—
144	C₂×C₁₃	#1452	1	4	yes	complemented
145	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
146	C₂×C₁₃	C₂×#405	1	2	yes	—
147	C₂⁴	C₄×#261	1	1	yes	characteristic
148	C₂²×C₄	—	13	2	no	—
149	C₂²×C₄	—	13	4	no	—
150	C₂²×C₄	—	13	4	no	—
151	C₂²×C₄	—	13	2	no	—
152	C₂²×C₄	—	26	8	no	—
153	C₂²×C₄	#6118	1	4	yes	—
154	C₂²×C₄	C₄×#261	1	1	yes	characteristic
155	C₂²×C₄	C₄×#261	1	2	yes	—
156	C₂²×C₄	#6122	1	4	yes	—
157	C₂²×C₄	C₂²×#261	1	2	yes	—
158	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
159	C₂×C₈	—	2	8	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	13	16	no	—
162	C₂×C₈	—	13	4	no	—
163	C₂×C₈	—	26	16	no	—
164	C₂×C₈	—	26	8	no	—
165	C₂×C₈	—	26	4	no	—
166	C₂×C₈	C₂²×#261	1	4	yes	—
167	C₄²	—	13	2	no	—
168	C₄²	—	13	4	no	—
169	C₄²	—	13	4	no	—
170	C₄²	—	13	2	no	—
171	C₄²	—	13	1	no	—
172	C₄²	—	13	1	no	—
173	C₄²	—	13	2	no	—
174	C₁₃	C₂×#1452	1	1	yes	characteristic, complemented, Sylow
175	C₂³	—	2	4	no	—
176	C₂³	#88110	1	4	yes	—
177	C₂³	C₂×C₄×#261	1	2	yes	—
178	C₂³	C₂×C₄×#261	1	1	yes	characteristic
179	C₂×C₄	—	13	8	no	—
180	C₂×C₄	—	13	2	no	—
181	C₂×C₄	—	13	2	no	—
182	C₂×C₄	—	13	4	no	—
183	C₂×C₄	—	26	8	no	—
184	C₂×C₄	—	26	8	no	—
185	C₂×C₄	—	26	4	no	—
186	C₂×C₄	#88110	1	8	yes	—
187	C₂×C₄	#88110	1	4	yes	—
188	C₂×C₄	C₂×#6118	1	4	yes	—
189	C₂×C₄	C₂×#6118	1	2	yes	—
190	C₂×C₄	C₂×C₄×#261	1	2	yes	—
191	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
192	C₂×C₄	C₂×#6122	1	4	yes	—
193	C₂×C₄	C₂×#6122	1	2	yes	—
194	C₂×C₄	C₂³×#261	1	1	yes	characteristic
195	C₈	—	2	4	no	—
196	C₈	—	26	16	no	—
197	C₈	—	26	4	no	—
198	C₂²	—	2	8	no	—
199	C₂²	—	2	4	no	—
200	C₂²	#11719089	1	4	yes	—
201	C₂²	C₂×#88110	1	4	yes	—
202	C₂²	C₂×#88110	1	2	yes	—
203	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
204	C₄	—	13	4	no	—
205	C₄	—	13	4	no	—
206	C₄	—	26	4	no	—
207	C₄	C₂×#88110	1	4	yes	—
208	C₄	C₂×#88110	1	2	yes	—
209	C₄	C₂²×#6118	1	1	yes	characteristic
210	C₄	C₂²×#6122	1	1	yes	characteristic
211	C₂	—	2	4	no	—
212	C₂	#13130049	1	4	yes	direct product factor
213	C₂	C₂²×#88110	1	1	yes	characteristic
214	C₂	C₂×#11719089	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×#261
commutator	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	C₂×#1452
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. #13130049	C₂	direct (N × H)
3. C₂×#1057⋊C₈	C₂	semidirect
17. #1057⋊C₈	C₂²	semidirect
144. C₂×C₁₃	#1452	semidirect
174. C₁₃	C₂×#1452	semidirect
212. C₂	#13130049	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×#11719119	2
#13130049	2
C₂×#1057⋊C₈	2
C₂²×C₈×Dic₁₃	2
C₂×#1452	13

Subgroups — C2×#13130049 #16792606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130049 #16792606