Subgroups — C₂×#11719099 #13131398

Order 1664.

592 conjugacy classes of subgroups.

The subgroup lattice has 224 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	C₂²×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	#11719099	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	C₂²×#1057	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	C₂×D₁₃⋊C₈	C₄	1	4	yes	complemented
15	C₂×D₁₃⋊C₈	C₄	1	2	yes	complemented
16	C₂×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×D₁₃⋊C₈	C₂²	1	4	yes	—
19	C₂×C₁₃×M₁₆	C₄	1	1	yes	characteristic, complemented
20	C₂×#6099	C₄	1	1	yes	characteristic, complemented
21	M₁₆×D₁₃	C₄	1	4	yes	complemented
22	M₁₆×D₁₃	C₂²	1	4	yes	—
23	C₂×#6094	C₄	1	2	yes	complemented
24	C₂×C₈×D₁₃	C₂²	1	2	yes	—
25	#88100	C₂²	1	8	yes	complemented
26	C₈×#261	C₂²	1	8	yes	complemented
27	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×#261	C₂×C₄	1	4	yes	—
29	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₄×D₁₃	C₂³	1	2	yes	—
39	C₂²⋊#261	C₂×C₄	1	8	yes	—
40	C₂×#1057	C₂×C₄	1	2	yes	—
41	C₂×#1057	C₂×C₄	1	2	yes	—
42	C₂×#1057	C₂×C₄	1	8	yes	complemented
43	C₄⋊#261	C₂×C₄	1	8	yes	—
44	C₄×#261	C₂×C₄	1	4	yes	—
45	C₄×#261	C₂³	1	4	yes	—
46	D₁₃⋊C₈	C₂×C₄	1	2	yes	—
47	D₁₃⋊C₈	C₂×C₄	1	2	yes	—
48	D₁₃⋊C₈	C₂×C₄	1	8	yes	complemented
49	D₁₃⋊C₈	C₂³	1	2	yes	—
50	D₁₃⋊C₈	C₂³	1	2	yes	—
51	C₁₃×M₁₆	C₂×C₄	1	4	yes	complemented
52	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
53	#6099	C₂×C₄	1	4	yes	complemented
54	C₂×#1055	C₂×C₄	1	2	yes	—
55	#6094	C₂×C₄	1	8	yes	complemented
56	C₈×D₁₃	C₂×C₄	1	4	yes	—
57	C₈×D₁₃	C₂³	1	4	yes	—
58	C₂×#405	—	13	1	no	maximal, Sylow
59	C₂³×C₁₃	C₄²	1	1	yes	characteristic
60	C₂²×D₁₃	—	2	4	no	—
61	C₂²×D₁₃	C₄²	1	1	yes	characteristic
62	C₂²×D₁₃	C₄²	1	2	yes	—
63	C₂²×D₁₃	C₂²×C₄	1	2	yes	—
64	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×#261	—	2	8	no	—
66	C₂×#261	C₂²×C₄	1	8	yes	—
67	C₂×C₄×C₁₃	C₄²	1	2	yes	—
68	C₂×C₄×C₁₃	C₄²	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×Dic₁₃	C₄²	1	2	yes	—
72	C₂×Dic₁₃	C₄²	1	1	yes	characteristic
73	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×Dic₁₃	C₂²×C₄	1	2	yes	—
75	C₄×D₁₃	C₄²	1	2	yes	—
76	C₄×D₁₃	C₄²	1	2	yes	—
77	C₄×D₁₃	C₄²	1	2	yes	—
78	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₄×D₁₃	C₂²×C₄	1	2	yes	—
80	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₄×D₁₃	C₂²×C₄	1	2	yes	—
82	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₄×D₁₃	C₂²×C₄	1	2	yes	—
84	C₄×D₁₃	C₂⁴	1	1	yes	characteristic
85	#1057	C₂²×C₄	1	4	yes	—
86	#1057	C₂²×C₄	1	4	yes	—
87	C₈×C₁₃	C₂²×C₄	1	4	yes	—
88	#1055	C₂²×C₄	1	4	yes	—
89	C₂²×M₁₆	—	13	1	no	—
90	C₂³×C₈	—	13	1	no	—
91	C₂×#117	—	13	1	no	—
92	#405	—	13	8	no	—
93	C₂×#97	—	13	2	no	—
94	C₂×C₄×C₈	—	13	2	no	—
95	C₂²×C₁₃	—	2	2	no	—
96	C₂²×C₁₃	C₂×C₄²	1	2	yes	—
97	C₂²×C₁₃	C₂×C₄²	1	1	yes	characteristic
98	C₂×D₁₃	—	2	2	no	—
99	C₂×D₁₃	—	2	4	no	—
100	C₂×D₁₃	—	2	4	no	—
101	C₂×D₁₃	C₂×C₄²	1	2	yes	—
102	C₂×D₁₃	C₂×C₄²	1	1	yes	characteristic
103	C₂×D₁₃	#131	1	4	yes	—
104	C₂×D₁₃	C₂³×C₄	1	1	yes	characteristic
105	#261	—	2	8	no	—
106	C₄×C₁₃	C₂×C₄²	1	2	yes	—
107	C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
108	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
109	Dic₁₃	C₂×C₄²	1	1	yes	characteristic
110	Dic₁₃	C₂×C₄²	1	2	yes	—
111	Dic₁₃	C₂³×C₄	1	1	yes	characteristic
112	C₂³×C₄	—	13	1	no	—
113	C₂×M₁₆	—	13	1	no	—
114	C₂×M₁₆	—	13	4	no	—
115	C₂×M₁₆	—	13	4	no	—
116	C₂×M₁₆	—	13	2	no	—
117	C₂×M₁₆	#261	1	1	yes	characteristic, complemented
118	C₂²×C₈	—	13	1	no	—
119	C₂²×C₈	—	13	1	no	—
120	C₂²×C₈	—	13	4	no	—
121	C₂²×C₈	—	13	4	no	—
122	C₂²×C₈	—	13	2	no	—
123	C₂²×C₈	—	13	2	no	—
124	C₂²×C₈	—	13	2	no	—
125	#117	—	13	4	no	—
126	#117	—	13	4	no	—
127	C₂×C₄⋊C₄	—	13	2	no	—
128	C₂×C₂²⋊C₄	—	13	2	no	—
129	C₂×C₄²	—	13	2	no	—
130	#97	—	13	8	no	—
131	C₄×C₈	—	13	8	no	—
132	C₂×C₁₃	—	2	2	no	—
133	C₂×C₁₃	#405	1	2	yes	complemented
134	C₂×C₁₃	C₂²×C₄²	1	1	yes	characteristic
135	D₁₃	—	2	2	no	—
136	D₁₃	#405	1	2	yes	complemented
137	D₁₃	C₂×#131	1	2	yes	—
138	C₂⁴	—	13	1	no	—
139	C₂²×C₄	—	13	1	no	—
140	C₂²×C₄	—	13	1	no	—
141	C₂²×C₄	—	13	2	no	—
142	C₂²×C₄	—	13	2	no	—
143	C₂²×C₄	—	13	1	no	—
144	C₂²×C₄	—	13	2	no	—
145	C₂²×C₄	—	13	2	no	—
146	C₂²×C₄	—	13	1	no	—
147	C₂²×C₄	—	13	1	no	—
148	C₂²×C₄	—	13	4	no	—
149	C₂²×C₄	C₂×#261	1	1	yes	characteristic
150	M₁₆	—	13	4	no	—
151	M₁₆	—	13	8	no	—
152	M₁₆	C₂×#261	1	4	yes	complemented
153	C₂×C₈	—	13	2	no	—
154	C₂×C₈	—	13	2	no	—
155	C₂×C₈	—	13	2	no	—
156	C₂×C₈	—	13	2	no	—
157	C₂×C₈	—	13	8	no	—
158	C₂×C₈	—	13	2	no	—
159	C₂×C₈	—	13	2	no	—
160	C₂×C₈	—	13	8	no	—
161	C₂×C₈	—	13	2	no	—
162	C₂×C₈	—	13	4	no	—
163	C₂×C₈	—	13	4	no	—
164	C₂×C₈	C₂×#261	1	2	yes	—
165	C₄⋊C₄	—	13	8	no	—
166	C₂²⋊C₄	—	13	8	no	—
167	C₄²	—	13	4	no	—
168	C₄²	—	13	4	no	—
169	C₁₃	C₂×#405	1	1	yes	characteristic, complemented, Sylow
170	C₂³	—	13	1	no	—
171	C₂³	—	13	2	no	—
172	C₂³	—	13	2	no	—
173	C₂³	—	13	1	no	—
174	C₂³	—	26	4	no	—
175	C₂³	C₄×#261	1	1	yes	characteristic
176	C₂×C₄	—	13	2	no	—
177	C₂×C₄	—	13	1	no	—
178	C₂×C₄	—	13	2	no	—
179	C₂×C₄	—	13	1	no	—
180	C₂×C₄	—	13	1	no	—
181	C₂×C₄	—	13	2	no	—
182	C₂×C₄	—	13	2	no	—
183	C₂×C₄	—	13	1	no	—
184	C₂×C₄	—	13	2	no	—
185	C₂×C₄	—	13	2	no	—
186	C₂×C₄	—	13	2	no	—
187	C₂×C₄	—	13	1	no	—
188	C₂×C₄	—	13	1	no	—
189	C₂×C₄	—	13	2	no	—
190	C₂×C₄	—	13	8	no	—
191	C₂×C₄	—	26	8	no	—
192	C₂×C₄	C₄×#261	1	1	yes	characteristic
193	C₂×C₄	C₄×#261	1	2	yes	—
194	C₂×C₄	C₂²×#261	1	2	yes	—
195	C₂×C₄	C₂²×#261	1	1	yes	characteristic
196	C₈	—	13	4	no	—
197	C₈	—	13	4	no	—
198	C₈	—	13	4	no	—
199	C₈	C₂²×#261	1	4	yes	—
200	C₂²	—	2	2	no	—
201	C₂²	—	13	4	no	—
202	C₂²	—	13	1	no	—
203	C₂²	—	13	1	no	—
204	C₂²	—	13	2	no	—
205	C₂²	—	26	4	no	—
206	C₂²	—	26	4	no	—
207	C₂²	—	26	2	no	—
208	C₂²	C₂×C₄×#261	1	2	yes	—
209	C₂²	C₂×C₄×#261	1	1	yes	characteristic
210	C₄	—	13	1	no	—
211	C₄	—	13	2	no	—
212	C₄	—	13	1	no	—
213	C₄	—	26	8	no	—
214	C₄	C₂×C₄×#261	1	2	yes	—
215	C₄	C₂×C₄×#261	1	1	yes	characteristic
216	C₄	C₂³×#261	1	1	yes	characteristic
217	C₂	—	2	2	no	—
218	C₂	—	13	2	no	—
219	C₂	—	13	2	no	—
220	C₂	—	26	2	no	—
221	C₂	#11719099	1	2	yes	direct product factor
222	C₂	C₂²×C₄×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₄²
Frattini	C₄	C₂³×#261
Fitting	C₂×C₁₃×M₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₂×C₄
cosocle	C₄×D₁₃	C₂⁴
hypercenter	C₂×M₁₆	#261
hypocenter	C₁₃	C₂×#405
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #11719099	C₂	direct (N × H)
5. C₂×#88100	C₂	semidirect
6. C₂×C₈×#261	C₂	semidirect
9. C₂²×#1057	C₄	semidirect
14. C₂×D₁₃⋊C₈	C₄	semidirect
15. C₂×D₁₃⋊C₈	C₄	semidirect
19. C₂×C₁₃×M₁₆	C₄	semidirect
20. C₂×#6099	C₄	semidirect
21. M₁₆×D₁₃	C₄	semidirect
23. C₂×#6094	C₄	semidirect
25. #88100	C₂²	semidirect
26. C₈×#261	C₂²	semidirect
42. C₂×#1057	C₂×C₄	semidirect
48. D₁₃⋊C₈	C₂×C₄	semidirect
51. C₁₃×M₁₆	C₂×C₄	semidirect
53. #6099	C₂×C₄	semidirect
55. #6094	C₂×C₄	semidirect
117. C₂×M₁₆	#261	semidirect
133. C₂×C₁₃	#405	semidirect
136. D₁₃	#405	semidirect
152. M₁₆	C₂×#261	semidirect
169. C₁₃	C₂×#405	semidirect
221. C₂	#11719099	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
C₂²×D₁₃⋊C₈	2
C₂×M₁₆×D₁₃	2
#11719099	2
C₂×#88100	2
C₂×C₈×#261	2
C₂×#405	13

Subgroups — C2×#11719099 #13131398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719099 #13131398