Subgroups — C₂×#11719089 #13131394

Order 1664.

592 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×#88237	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	#11719089	C₂	1	8	yes	maximal, direct product factor
5	C₂×#88100	C₂	1	2	yes	maximal, complemented
6	C₂×C₈×#261	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊#261	C₄	1	2	yes	—
9	C₂×#6122	C₄	1	2	yes	complemented
10	#88237	C₄	1	4	yes	—
11	#88237	C₂²	1	4	yes	—
12	C₂×C₄⋊#261	C₄	1	2	yes	—
13	C₂×C₄×#261	C₂²	1	2	yes	—
14	D₁₃⋊M₁₆	C₄	1	4	yes	complemented
15	D₁₃⋊M₁₆	C₂²	1	4	yes	—
16	C₂×#6118	C₄	1	2	yes	complemented
17	C₂×D₁₃⋊C₈	C₂²	1	2	yes	—
18	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
19	C₂²×#1055	C₄	1	1	yes	characteristic, complemented
20	C₂×C₈×D₁₃	C₄	1	4	yes	complemented
21	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
22	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
23	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₈×D₁₃	C₂²	1	4	yes	—
26	#88100	C₂²	1	8	yes	complemented
27	C₈×#261	C₂²	1	8	yes	complemented
28	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×#261	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
39	C₂×C₄×D₁₃	C₂³	1	2	yes	—
40	C₂²⋊#261	C₂×C₄	1	8	yes	—
41	#6122	C₂×C₄	1	8	yes	complemented
42	C₂×#1057	C₂×C₄	1	4	yes	—
43	C₄⋊#261	C₂×C₄	1	8	yes	—
44	C₄×#261	C₂×C₄	1	4	yes	—
45	C₄×#261	C₂³	1	4	yes	—
46	#6118	C₂×C₄	1	8	yes	complemented
47	D₁₃⋊C₈	C₂×C₄	1	4	yes	—
48	D₁₃⋊C₈	C₂³	1	4	yes	—
49	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
52	C₂×#1055	C₂×C₄	1	1	yes	characteristic
53	C₂×#1055	C₂×C₄	1	1	yes	characteristic
54	C₂×#1055	C₂×C₄	1	4	yes	complemented
55	C₈×D₁₃	C₂×C₄	1	2	yes	—
56	C₈×D₁₃	C₂×C₄	1	2	yes	—
57	C₈×D₁₃	C₂×C₄	1	4	yes	complemented
58	C₈×D₁₃	C₂×C₄	1	4	yes	complemented
59	C₈×D₁₃	C₂³	1	2	yes	—
60	C₈×D₁₃	C₂³	1	2	yes	—
61	C₂×#405	—	13	1	no	maximal, Sylow
62	C₂³×C₁₃	C₄²	1	1	yes	characteristic
63	C₂²×D₁₃	—	2	4	no	—
64	C₂²×D₁₃	C₄²	1	1	yes	characteristic
65	C₂²×D₁₃	C₄²	1	2	yes	—
66	C₂²×D₁₃	C₂²×C₄	1	2	yes	—
67	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
68	C₂×#261	—	2	8	no	—
69	C₂×#261	C₂²×C₄	1	8	yes	—
70	C₂×C₄×C₁₃	C₄²	1	2	yes	—
71	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
74	C₂×Dic₁₃	C₄²	1	2	yes	—
75	C₂×Dic₁₃	C₄²	1	1	yes	characteristic
76	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
78	C₄×D₁₃	C₄²	1	2	yes	—
79	C₄×D₁₃	C₄²	1	2	yes	—
80	C₄×D₁₃	C₄²	1	2	yes	—
81	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₄×D₁₃	C₂²×C₄	1	2	yes	—
83	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₄×D₁₃	C₂²×C₄	1	2	yes	—
85	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₄×D₁₃	C₂²×C₄	1	2	yes	—
87	C₄×D₁₃	C₂⁴	1	1	yes	characteristic
88	#1057	C₂²×C₄	1	8	yes	—
89	C₈×C₁₃	C₂²×C₄	1	2	yes	—
90	C₈×C₁₃	C₂²×C₄	1	2	yes	—
91	#1055	C₂²×C₄	1	2	yes	—
92	#1055	C₂²×C₄	1	2	yes	—
93	C₂²×M₁₆	—	13	1	no	—
94	C₂³×C₈	—	13	1	no	—
95	C₂×#117	—	13	1	no	—
96	#405	—	13	8	no	—
97	C₂×#97	—	13	2	no	—
98	C₂×C₄×C₈	—	13	2	no	—
99	C₂²×C₁₃	—	2	2	no	—
100	C₂²×C₁₃	C₂×C₄²	1	2	yes	—
101	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
102	C₂×D₁₃	—	2	2	no	—
103	C₂×D₁₃	—	2	4	no	—
104	C₂×D₁₃	—	2	4	no	—
105	C₂×D₁₃	C₂×C₄²	1	2	yes	—
106	C₂×D₁₃	C₂×C₄²	1	1	yes	characteristic
107	C₂×D₁₃	#131	1	4	yes	—
108	C₂×D₁₃	C₂³×C₄	1	1	yes	characteristic
109	#261	—	2	8	no	—
110	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
111	C₄×C₁₃	C₂×C₄²	1	2	yes	—
112	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
113	Dic₁₃	C₂×C₄²	1	1	yes	characteristic
114	Dic₁₃	C₂×C₄²	1	2	yes	—
115	Dic₁₃	C₂³×C₄	1	1	yes	characteristic
116	C₂³×C₄	—	13	1	no	—
117	C₂×M₁₆	—	13	4	no	—
118	C₂×M₁₆	—	13	2	no	—
119	C₂×M₁₆	—	13	4	no	—
120	C₂×M₁₆	—	13	2	no	—
121	C₂²×C₈	—	13	2	no	—
122	C₂²×C₈	—	13	1	no	—
123	C₂²×C₈	—	13	1	no	—
124	C₂²×C₈	—	13	1	no	—
125	C₂²×C₈	—	13	1	no	—
126	C₂²×C₈	—	13	1	no	—
127	C₂²×C₈	—	13	4	no	—
128	C₂²×C₈	—	13	4	no	—
129	C₂²×C₈	#261	1	1	yes	characteristic, complemented
130	#117	—	13	4	no	—
131	#117	—	13	4	no	—
132	C₂×C₄⋊C₄	—	13	2	no	—
133	C₂×C₂²⋊C₄	—	13	2	no	—
134	C₂×C₄²	—	13	2	no	—
135	#97	—	13	8	no	—
136	C₄×C₈	—	13	8	no	—
137	C₂×C₁₃	—	2	2	no	—
138	C₂×C₁₃	#405	1	2	yes	complemented
139	C₂×C₁₃	C₂²×C₄²	1	1	yes	characteristic
140	D₁₃	—	2	2	no	—
141	D₁₃	#405	1	2	yes	complemented
142	D₁₃	C₂×#131	1	2	yes	—
143	C₂⁴	—	13	1	no	—
144	C₂²×C₄	—	13	1	no	—
145	C₂²×C₄	—	13	1	no	—
146	C₂²×C₄	—	13	2	no	—
147	C₂²×C₄	—	13	1	no	—
148	C₂²×C₄	—	13	2	no	—
149	C₂²×C₄	—	13	1	no	—
150	C₂²×C₄	—	13	2	no	—
151	C₂²×C₄	—	13	1	no	—
152	C₂²×C₄	—	13	2	no	—
153	C₂²×C₄	—	13	4	no	—
154	C₂²×C₄	C₂×#261	1	1	yes	characteristic
155	M₁₆	—	13	8	no	—
156	M₁₆	—	13	8	no	—
157	C₂×C₈	—	13	4	no	—
158	C₂×C₈	—	13	4	no	—
159	C₂×C₈	—	13	4	no	—
160	C₂×C₈	—	13	1	no	—
161	C₂×C₈	—	13	1	no	—
162	C₂×C₈	—	13	4	no	—
163	C₂×C₈	—	13	2	no	—
164	C₂×C₈	—	13	2	no	—
165	C₂×C₈	—	13	2	no	—
166	C₂×C₈	—	13	2	no	—
167	C₂×C₈	—	13	4	no	—
168	C₂×C₈	—	13	4	no	—
169	C₂×C₈	C₂×#261	1	1	yes	characteristic
170	C₂×C₈	C₂×#261	1	1	yes	characteristic
171	C₂×C₈	C₂×#261	1	4	yes	complemented
172	C₄⋊C₄	—	13	8	no	—
173	C₂²⋊C₄	—	13	8	no	—
174	C₄²	—	13	4	no	—
175	C₄²	—	13	4	no	—
176	C₁₃	C₂×#405	1	1	yes	characteristic, complemented, Sylow
177	C₂³	—	13	1	no	—
178	C₂³	—	13	2	no	—
179	C₂³	—	13	2	no	—
180	C₂³	—	13	1	no	—
181	C₂³	—	26	4	no	—
182	C₂³	C₄×#261	1	1	yes	characteristic
183	C₂×C₄	—	13	1	no	—
184	C₂×C₄	—	13	2	no	—
185	C₂×C₄	—	13	2	no	—
186	C₂×C₄	—	13	1	no	—
187	C₂×C₄	—	13	1	no	—
188	C₂×C₄	—	13	2	no	—
189	C₂×C₄	—	13	1	no	—
190	C₂×C₄	—	13	2	no	—
191	C₂×C₄	—	13	2	no	—
192	C₂×C₄	—	13	2	no	—
193	C₂×C₄	—	13	2	no	—
194	C₂×C₄	—	13	1	no	—
195	C₂×C₄	—	13	1	no	—
196	C₂×C₄	—	13	2	no	—
197	C₂×C₄	—	13	8	no	—
198	C₂×C₄	—	26	8	no	—
199	C₂×C₄	C₄×#261	1	2	yes	—
200	C₂×C₄	C₄×#261	1	1	yes	characteristic
201	C₂×C₄	C₂²×#261	1	1	yes	characteristic
202	C₂×C₄	C₂²×#261	1	2	yes	—
203	C₈	—	13	8	no	—
204	C₈	—	13	2	no	—
205	C₈	—	13	2	no	—
206	C₈	C₂²×#261	1	2	yes	—
207	C₈	C₂²×#261	1	2	yes	—
208	C₂²	—	2	2	no	—
209	C₂²	—	13	4	no	—
210	C₂²	—	13	1	no	—
211	C₂²	—	13	1	no	—
212	C₂²	—	13	2	no	—
213	C₂²	—	26	4	no	—
214	C₂²	—	26	4	no	—
215	C₂²	—	26	2	no	—
216	C₂²	C₂×C₄×#261	1	2	yes	—
217	C₂²	C₂×C₄×#261	1	1	yes	characteristic
218	C₄	—	13	1	no	—
219	C₄	—	13	2	no	—
220	C₄	—	13	1	no	—
221	C₄	—	26	8	no	—
222	C₄	C₂×C₄×#261	1	1	yes	characteristic
223	C₄	C₂×C₄×#261	1	2	yes	—
224	C₄	C₂³×#261	1	1	yes	characteristic
225	C₂	—	2	2	no	—
226	C₂	—	13	2	no	—
227	C₂	—	13	2	no	—
228	C₂	—	26	2	no	—
229	C₂	#11719089	1	2	yes	direct product factor
230	C₂	C₂²×C₄×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄²
Frattini	C₄	C₂³×#261
Fitting	C₂²×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₂×C₄
cosocle	C₄×D₁₃	C₂⁴
hypercenter	C₂²×C₈	#261
hypocenter	C₁₃	C₂×#405
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #11719089	C₂	direct (N × H)
5. C₂×#88100	C₂	semidirect
6. C₂×C₈×#261	C₂	semidirect
9. C₂×#6122	C₄	semidirect
14. D₁₃⋊M₁₆	C₄	semidirect
16. C₂×#6118	C₄	semidirect
18. C₂²×C₈×C₁₃	C₄	semidirect
19. C₂²×#1055	C₄	semidirect
20. C₂×C₈×D₁₃	C₄	semidirect
21. C₂×C₈×D₁₃	C₄	semidirect
22. C₂×C₈×D₁₃	C₄	semidirect
26. #88100	C₂²	semidirect
27. C₈×#261	C₂²	semidirect
41. #6122	C₂×C₄	semidirect
46. #6118	C₂×C₄	semidirect
51. C₂×C₈×C₁₃	C₂×C₄	semidirect
54. C₂×#1055	C₂×C₄	semidirect
57. C₈×D₁₃	C₂×C₄	semidirect
58. C₈×D₁₃	C₂×C₄	semidirect
129. C₂²×C₈	#261	semidirect
138. C₂×C₁₃	#405	semidirect
141. D₁₃	#405	semidirect
171. C₂×C₈	C₂×#261	semidirect
176. C₁₃	C₂×#405	semidirect
229. C₂	#11719089	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×#88237	2
C₂×D₁₃⋊M₁₆	2
C₂²×C₈×D₁₃	2
#11719089	2
C₂×#88100	2
C₂×C₈×#261	2
C₂×#405	13

Subgroups — C2×#11719089 #13131394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719089 #13131394