Subgroups — C₂×#13130758 #16798169

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719060	C₂	1	2	yes	maximal
2	#13130758	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718265	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊#261	C₂²	1	4	yes	—
6	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×(C₂×#261)⋊C₄	—	2	4	no	—
9	#11719060	—	2	4	no	—
10	#11719060	C₂²	1	8	yes	—
11	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
12	C₂×C₈×Dic₁₃	C₄	1	2	yes	complemented
13	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
14	C₄×C₈×D₁₃	C₄	1	4	yes	complemented
15	C₄×C₈×D₁₃	C₂²	1	4	yes	—
16	#11718265	C₂²	1	16	yes	—
17	C₂³×#261	—	2	4	no	—
18	C₂²×C₄×D₁₃	D₄	1	2	yes	—
19	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₄⋊#261	—	2	16	no	—
21	C₂×C₄⋊#261	—	2	4	no	—
22	C₂×C₄⋊#261	C₂³	1	8	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	Q₈	1	2	yes	—
27	C₂²×#1055	C₂×C₄	1	2	yes	—
28	C₂×C₈×D₁₃	—	2	8	no	—
29	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
30	C₂×C₈×D₁₃	C₂³	1	4	yes	—
31	C₄²×D₁₃	C₂×C₄	1	2	yes	—
32	C₄²×D₁₃	D₄	1	2	yes	—
33	C₄²×D₁₃	Q₈	1	2	yes	—
34	C₄²×D₁₃	C₂³	1	2	yes	—
35	(C₂×#261)⋊C₄	—	2	16	no	—
36	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
37	C₈×Dic₁₃	C₂×C₄	1	8	yes	complemented
38	C₄×#1055	C₂×C₄	1	4	yes	complemented
39	C₂×#1835	—	13	1	no	maximal, Sylow
40	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×#261	—	2	8	no	—
42	C₂²×#261	—	4	8	no	—
43	C₂²×#261	—	4	16	no	—
44	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
47	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₄×D₁₃	—	2	8	no	—
49	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
50	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×D₁₃	C₂×D₄	1	4	yes	—
52	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₄×D₁₃	#41	1	8	yes	—
55	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
56	C₄⋊#261	—	2	16	no	—
57	C₄⋊#261	—	4	8	no	—
58	C₂×C₈×C₁₃	—	2	4	no	—
59	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
60	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
61	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
62	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
63	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
64	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
65	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
66	C₂×#1055	—	2	4	no	—
67	C₂×#1055	C₂²×C₄	1	4	yes	—
68	C₈×D₁₃	—	2	8	no	—
69	C₈×D₁₃	—	2	8	no	—
70	C₂²×C₄×C₈	—	13	1	no	—
71	C₂×#382	—	13	2	no	—
72	#1835	—	13	8	no	—
73	C₂×#340	—	13	4	no	—
74	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×D₁₃	#124	1	4	yes	—
77	C₂²×D₁₃	#135	1	8	yes	—
78	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
79	C₂×#261	—	4	8	no	—
80	C₂×#261	—	4	16	no	—
81	C₂×#261	—	8	16	no	—
82	C₂×C₄×C₁₃	—	2	4	no	—
83	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
84	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#117	1	4	yes	—
86	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
87	C₂×Dic₁₃	—	2	4	no	—
88	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
89	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×Dic₁₃	#125	1	4	yes	—
91	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
92	C₄×D₁₃	—	2	8	no	—
93	C₄×D₁₃	—	2	8	no	—
94	C₄×D₁₃	#117	1	4	yes	—
95	C₄×D₁₃	#124	1	4	yes	—
96	C₄×D₁₃	#125	1	4	yes	—
97	C₄×D₁₃	C₂×#41	1	4	yes	—
98	C₈×C₁₃	—	2	4	no	—
99	#1055	—	2	4	no	—
100	C₂³×C₈	—	13	2	no	—
101	C₂²×C₄⋊C₄	—	13	4	no	—
102	C₂²×C₄²	—	13	1	no	—
103	C₂×C₄×C₈	—	13	2	no	—
104	C₂×C₄×C₈	—	13	1	no	—
105	C₂×C₄×C₈	—	13	4	no	—
106	C₂×C₄×C₈	—	13	4	no	—
107	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
108	#382	—	13	8	no	—
109	#382	—	26	4	no	—
110	C₂×#95	—	26	4	no	—
111	#340	—	13	16	no	—
112	C₂²×C₁₃	#382	1	2	yes	—
113	C₂²×C₁₃	#427	1	4	yes	—
114	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
115	C₂×D₁₃	#382	1	2	yes	—
116	C₂×D₁₃	#427	1	4	yes	—
117	C₂×D₁₃	#488	1	16	yes	—
118	C₂×D₁₃	C₂×#124	1	2	yes	—
119	C₂×D₁₃	C₂×#135	1	4	yes	—
120	#261	—	8	8	no	—
121	C₄×C₁₃	—	2	4	no	—
122	C₄×C₁₃	#382	1	2	yes	—
123	C₄×C₁₃	C₂×#117	1	2	yes	—
124	Dic₁₃	—	2	4	no	—
125	Dic₁₃	#382	1	2	yes	—
126	Dic₁₃	C₂×#125	1	2	yes	—
127	C₂³×C₄	—	13	1	no	—
128	C₂³×C₄	—	13	2	no	—
129	C₂³×C₄	—	26	4	no	—
130	C₂²×C₈	—	13	2	no	—
131	C₂²×C₈	—	13	4	no	—
132	C₂²×C₈	—	13	4	no	—
133	C₂²×C₈	—	26	8	no	—
134	C₂²×C₈	C₂×#261	1	2	yes	—
135	C₂×C₄⋊C₄	—	13	8	no	—
136	C₂×C₄⋊C₄	—	26	16	no	—
137	C₂×C₄⋊C₄	—	26	4	no	—
138	C₂×C₄²	—	13	2	no	—
139	C₂×C₄²	—	13	1	no	—
140	C₂×C₄²	—	13	2	no	—
141	C₂×C₄²	—	13	2	no	—
142	C₂×C₄²	—	13	2	no	—
143	C₂×C₄²	—	13	2	no	—
144	C₂×C₄²	C₂×#261	1	1	yes	characteristic
145	C₄×C₈	—	13	8	no	—
146	C₄×C₈	—	13	4	no	—
147	C₄×C₈	C₂×#261	1	4	yes	complemented
148	#95	—	26	16	no	—
149	C₂×C₁₃	#1835	1	4	yes	complemented
150	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
151	C₂×C₁₃	C₂×#427	1	2	yes	—
152	D₁₃	#1835	1	4	yes	complemented
153	D₁₃	C₂×#488	1	4	yes	—
154	C₂⁴	—	13	1	no	—
155	C₂²×C₄	—	13	1	no	—
156	C₂²×C₄	—	13	1	no	—
157	C₂²×C₄	—	13	1	no	—
158	C₂²×C₄	—	13	8	no	—
159	C₂²×C₄	—	13	1	no	—
160	C₂²×C₄	—	13	1	no	—
161	C₂²×C₄	—	13	2	no	—
162	C₂²×C₄	—	13	4	no	—
163	C₂²×C₄	—	13	4	no	—
164	C₂²×C₄	—	26	8	no	—
165	C₂²×C₄	—	26	8	no	—
166	C₂²×C₄	—	52	8	no	—
167	C₂²×C₄	—	52	16	no	—
168	C₂²×C₄	C₄⋊#261	1	2	yes	—
169	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	—	13	4	no	—
172	C₂×C₈	—	26	8	no	—
173	C₂×C₈	—	26	8	no	—
174	C₂×C₈	—	26	4	no	—
175	C₂×C₈	C₂²×#261	1	4	yes	—
176	C₄⋊C₄	—	26	16	no	—
177	C₄⋊C₄	—	52	8	no	—
178	C₄²	—	13	4	no	—
179	C₄²	—	13	2	no	—
180	C₄²	—	13	4	no	—
181	C₄²	—	13	2	no	—
182	C₄²	C₄⋊#261	1	2	yes	—
183	C₄²	C₂²×#261	1	2	yes	—
184	C₁₃	C₂×#1835	1	1	yes	characteristic, complemented, Sylow
185	C₂³	—	13	4	no	—
186	C₂³	—	13	8	no	—
187	C₂³	—	13	1	no	—
188	C₂³	—	13	1	no	—
189	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	13	4	no	—
192	C₂×C₄	—	13	1	no	—
193	C₂×C₄	—	13	1	no	—
194	C₂×C₄	—	13	4	no	—
195	C₂×C₄	—	13	4	no	—
196	C₂×C₄	—	13	4	no	—
197	C₂×C₄	—	13	4	no	—
198	C₂×C₄	—	13	4	no	—
199	C₂×C₄	—	26	8	no	—
200	C₂×C₄	—	26	8	no	—
201	C₂×C₄	—	26	4	no	—
202	C₂×C₄	—	52	8	no	—
203	C₂×C₄	—	52	16	no	—
204	C₂×C₄	—	104	16	no	—
205	C₂×C₄	C₂×C₄⋊#261	1	4	yes	—
206	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
207	C₂×C₄	#88237	1	4	yes	—
208	C₂×C₄	C₂³×#261	1	1	yes	characteristic
209	C₈	—	2	4	no	—
210	C₈	—	26	4	no	—
211	C₂²	—	13	16	no	—
212	C₂²	—	13	2	no	—
213	C₂²	—	13	2	no	—
214	C₂²	—	13	4	no	—
215	C₂²	—	13	4	no	—
216	C₂²	#11719060	1	2	yes	—
217	C₂²	#11719092	1	4	yes	—
218	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
219	C₄	—	2	4	no	—
220	C₄	—	13	2	no	—
221	C₄	—	13	2	no	—
222	C₄	—	26	4	no	—
223	C₄	—	104	8	no	—
224	C₄	#11719060	1	2	yes	—
225	C₄	C₂×#88237	1	2	yes	—
226	C₂	—	13	4	no	—
227	C₂	—	13	4	no	—
228	C₂	#13130758	1	4	yes	direct product factor
229	C₂	C₂×#11719060	1	1	yes	characteristic
230	C₂	C₂×#11719092	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1835
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130758	C₂	direct (N × H)
11. C₂×C₄×C₈×C₁₃	C₄	semidirect
12. C₂×C₈×Dic₁₃	C₄	semidirect
13. C₂×C₄×#1055	C₄	semidirect
14. C₄×C₈×D₁₃	C₄	semidirect
36. C₄×C₈×C₁₃	C₂×C₄	semidirect
37. C₈×Dic₁₃	C₂×C₄	semidirect
38. C₄×#1055	C₂×C₄	semidirect
107. C₂×C₄×C₈	#261	semidirect
147. C₄×C₈	C₂×#261	semidirect
149. C₂×C₁₃	#1835	semidirect
152. D₁₃	#1835	semidirect
184. C₁₃	C₂×#1835	semidirect
228. C₂	#13130758	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×#11719060	2
#13130758	2
C₂×#11718265	2
C₂×C₄×C₈×D₁₃	2
C₂×#1835	13

Subgroups — C2×#13130758 #16798169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130758 #16798169