Subgroups — C₂×#13129894 #16789096

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88102	C₂	1	2	yes	maximal
2	#13129894	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄⋊#261	—	2	2	no	—
5	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88102	—	2	2	no	—
7	C₂×#88102	—	2	4	no	—
8	C₂×#88102	C₄	1	8	yes	complemented
9	C₂×#88102	C₂²	1	4	yes	—
10	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂²×#6090	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₆×D₁₃	—	2	4	no	—
13	C₂×C₁₆×D₁₃	C₄	1	2	yes	complemented
14	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
15	C₂³×#261	—	4	2	no	—
16	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
17	C₂×C₄⋊#261	—	2	8	no	—
18	C₂×C₄⋊#261	—	2	4	no	—
19	C₂×C₄⋊#261	—	4	2	no	—
20	C₂×C₄⋊#261	—	4	4	no	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×#1055	Q₈	1	1	yes	characteristic
23	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
25	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
26	C₂×C₈×D₁₃	D₄	1	4	yes	—
27	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
28	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
29	#88102	—	2	8	no	—
30	#88102	—	2	4	no	—
31	#88102	C₂×C₄	1	8	yes	complemented
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	complemented
34	C₂×#6090	—	2	2	no	—
35	C₂×#6090	C₂×C₄	1	2	yes	complemented
36	C₁₆×D₁₃	—	2	4	no	—
37	C₁₆×D₁₃	—	2	4	no	—
38	C₂×#1380	—	13	1	no	maximal, Sylow
39	C₂³×D₁₃	D₈	1	1	yes	characteristic
40	C₂²×#261	—	4	8	no	—
41	C₂²×#261	—	4	4	no	—
42	C₂²×#261	—	8	4	no	—
43	C₂²×#261	—	8	4	no	—
44	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×Dic₁₃	Q₁₆	1	1	yes	characteristic
46	C₂×C₄×D₁₃	C₂²⋊C₄	1	4	yes	—
47	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
49	C₂×C₄×D₁₃	SD₁₆	1	4	yes	—
50	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
51	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
52	C₄⋊#261	—	2	8	no	—
53	C₄⋊#261	—	4	8	no	—
54	C₄⋊#261	—	4	4	no	—
55	C₂×C₈×C₁₃	C₄²	1	2	yes	—
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
60	C₂×#1055	C₄⋊C₄	1	4	yes	—
61	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
62	C₈×D₁₃	C₄²	1	2	yes	—
63	C₈×D₁₃	C₂²⋊C₄	1	4	yes	—
64	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
65	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
66	C₈×D₁₃	C₂²×C₄	1	2	yes	—
67	C₈×D₁₃	C₂×D₄	1	2	yes	—
68	C₁₃×C₁₆	—	2	2	no	—
69	#6090	—	2	2	no	—
70	C₂³×C₁₆	—	13	1	no	—
71	C₂²×#107	—	13	2	no	—
72	#1380	—	13	4	no	—
73	C₂³×C₁₃	#107	1	1	yes	characteristic
74	C₂²×D₁₃	#102	1	4	yes	—
75	C₂²×D₁₃	#107	1	1	yes	characteristic
76	C₂²×D₁₃	D₁₆	1	2	yes	—
77	C₂²×D₁₃	SD₃₂	1	4	yes	—
78	C₂²×D₁₃	Q₃₂	1	2	yes	—
79	C₂²×D₁₃	C₂×D₈	1	1	yes	characteristic
80	C₂×#261	—	4	8	no	—
81	C₂×#261	—	8	16	no	—
82	C₂×#261	—	8	4	no	—
83	C₂×#261	—	8	4	no	—
84	C₂×C₄×C₁₃	#95	1	2	yes	—
85	C₂×C₄×C₁₃	#106	1	2	yes	—
86	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×Dic₁₃	#103	1	4	yes	—
89	C₂×Dic₁₃	#107	1	1	yes	characteristic
90	C₂×Dic₁₃	C₂×Q₁₆	1	1	yes	characteristic
91	C₄×D₁₃	#95	1	2	yes	—
92	C₄×D₁₃	#102	1	4	yes	—
93	C₄×D₁₃	#103	1	4	yes	—
94	C₄×D₁₃	#106	1	2	yes	—
95	C₄×D₁₃	C₂×C₂²⋊C₄	1	2	yes	—
96	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
97	C₈×C₁₃	#95	1	2	yes	—
98	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
99	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
100	#1055	#95	1	2	yes	—
101	#1055	C₂×C₄⋊C₄	1	2	yes	—
102	C₂³×C₈	—	13	1	no	—
103	C₂²×C₄⋊C₄	—	26	2	no	—
104	C₂²×C₁₆	—	13	1	no	—
105	C₂²×C₁₆	—	13	2	no	—
106	C₂²×C₁₆	—	13	2	no	—
107	C₂²×C₁₆	—	26	4	no	—
108	C₂²×C₁₆	#261	1	1	yes	characteristic, complemented
109	C₂×#107	—	13	4	no	—
110	C₂×#107	—	13	8	no	—
111	C₂×#107	—	26	2	no	—
112	C₂×#107	—	26	4	no	—
113	C₂²×C₁₃	#340	1	2	yes	—
114	C₂²×C₁₃	#366	1	2	yes	—
115	C₂²×C₁₃	#367	1	2	yes	—
116	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
117	C₂×D₁₃	#340	1	2	yes	—
118	C₂×D₁₃	#357	1	8	yes	—
119	C₂×D₁₃	#358	1	8	yes	—
120	C₂×D₁₃	#366	1	2	yes	—
121	C₂×D₁₃	#367	1	2	yes	—
122	C₂×D₁₃	C₂×#102	1	2	yes	—
123	C₂×D₁₃	C₂×D₁₆	1	1	yes	characteristic
124	C₂×D₁₃	C₂×SD₃₂	1	2	yes	—
125	C₂×D₁₃	C₂×Q₃₂	1	1	yes	characteristic
126	#261	—	8	8	no	—
127	C₄×C₁₃	#340	1	2	yes	—
128	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
129	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
130	Dic₁₃	#340	1	2	yes	—
131	Dic₁₃	C₂×#103	1	2	yes	—
132	C₂³×C₄	—	13	1	no	—
133	C₂³×C₄	—	52	2	no	—
134	C₂²×C₈	—	13	1	no	—
135	C₂²×C₈	—	13	4	no	—
136	C₂²×C₈	—	13	1	no	—
137	C₂²×C₈	—	13	1	no	—
138	C₂²×C₈	—	13	4	no	—
139	C₂²×C₈	—	13	1	no	—
140	C₂²×C₈	—	13	1	no	—
141	C₂²×C₈	C₂×#261	1	1	yes	characteristic
142	C₂×C₄⋊C₄	—	26	8	no	—
143	C₂×C₄⋊C₄	—	26	4	no	—
144	C₂×C₄⋊C₄	—	52	4	no	—
145	C₂×C₄⋊C₄	—	52	2	no	—
146	C₂×C₁₆	—	2	2	no	—
147	C₂×C₁₆	—	13	2	no	—
148	C₂×C₁₆	—	26	4	no	—
149	C₂×C₁₆	—	26	4	no	—
150	C₂×C₁₆	—	26	2	no	—
151	C₂×C₁₆	C₂×#261	1	2	yes	complemented
152	#107	—	13	8	no	—
153	#107	—	26	8	no	—
154	#107	—	26	4	no	—
155	C₂×C₁₃	#1380	1	4	yes	complemented
156	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
157	C₂×C₁₃	C₂×#366	1	1	yes	characteristic
158	C₂×C₁₃	C₂×#367	1	1	yes	characteristic
159	D₁₃	#1380	1	4	yes	complemented
160	D₁₃	C₂×#357	1	2	yes	—
161	D₁₃	C₂×#358	1	2	yes	—
162	C₂⁴	—	13	1	no	—
163	C₂²×C₄	—	13	1	no	—
164	C₂²×C₄	—	13	4	no	—
165	C₂²×C₄	—	13	1	no	—
166	C₂²×C₄	—	13	1	no	—
167	C₂²×C₄	—	13	4	no	—
168	C₂²×C₄	—	13	1	no	—
169	C₂²×C₄	—	13	1	no	—
170	C₂²×C₄	—	52	8	no	—
171	C₂²×C₄	—	52	4	no	—
172	C₂²×C₄	—	104	4	no	—
173	C₂²×C₄	—	104	4	no	—
174	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
175	C₂×C₈	—	13	4	no	—
176	C₂×C₈	—	13	1	no	—
177	C₂×C₈	—	13	1	no	—
178	C₂×C₈	—	13	4	no	—
179	C₂×C₈	—	13	4	no	—
180	C₂×C₈	—	13	2	no	—
181	C₂×C₈	—	13	2	no	—
182	C₂×C₈	—	13	2	no	—
183	C₂×C₈	—	13	2	no	—
184	C₂×C₈	C₄×#261	1	2	yes	—
185	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
186	C₂×C₈	C₂²⋊#261	1	2	yes	—
187	C₂×C₈	C₂²×#261	1	1	yes	characteristic
188	C₄⋊C₄	—	26	8	no	—
189	C₄⋊C₄	—	52	8	no	—
190	C₄⋊C₄	—	52	4	no	—
191	C₁₆	—	2	2	no	—
192	C₁₆	—	26	2	no	—
193	C₁₃	C₂×#1380	1	1	yes	characteristic, complemented, Sylow
194	C₂³	—	13	2	no	—
195	C₂³	—	13	2	no	—
196	C₂³	—	13	4	no	—
197	C₂³	—	13	4	no	—
198	C₂³	—	13	1	no	—
199	C₂³	—	13	1	no	—
200	C₂³	#88102	1	1	yes	characteristic
201	C₂×C₄	—	13	4	no	—
202	C₂×C₄	—	13	1	no	—
203	C₂×C₄	—	13	1	no	—
204	C₂×C₄	—	13	4	no	—
205	C₂×C₄	—	13	4	no	—
206	C₂×C₄	—	13	2	no	—
207	C₂×C₄	—	13	2	no	—
208	C₂×C₄	—	13	2	no	—
209	C₂×C₄	—	13	2	no	—
210	C₂×C₄	—	52	8	no	—
211	C₂×C₄	—	104	16	no	—
212	C₂×C₄	—	104	4	no	—
213	C₂×C₄	—	104	4	no	—
214	C₂×C₄	#88101	1	2	yes	—
215	C₂×C₄	#88102	1	1	yes	characteristic
216	C₂×C₄	(C₂×#261)⋊C₄	1	2	yes	—
217	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
218	C₈	—	13	2	no	—
219	C₈	—	13	2	no	—
220	C₈	(C₂×#261)⋊C₄	1	2	yes	—
221	C₈	C₂×C₄×#261	1	1	yes	characteristic
222	C₈	C₂×C₂²⋊#261	1	1	yes	characteristic
223	C₂²	—	13	2	no	—
224	C₂²	—	13	2	no	—
225	C₂²	—	13	8	no	—
226	C₂²	—	13	8	no	—
227	C₂²	—	13	2	no	—
228	C₂²	—	13	1	no	—
229	C₂²	—	13	1	no	—
230	C₂²	—	13	2	no	—
231	C₂²	—	13	2	no	—
232	C₂²	#11718221	1	2	yes	—
233	C₂²	#11718222	1	2	yes	—
234	C₂²	#11718265	1	2	yes	—
235	C₂²	C₂×#88102	1	1	yes	characteristic
236	C₄	—	13	2	no	—
237	C₄	—	13	2	no	—
238	C₄	—	104	8	no	—
239	C₄	#11718265	1	2	yes	—
240	C₄	C₂×#88101	1	1	yes	characteristic
241	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
242	C₂	—	13	2	no	—
243	C₂	—	13	2	no	—
244	C₂	—	13	4	no	—
245	C₂	#13129894	1	4	yes	direct product factor
246	C₂	C₂×#11718265	1	1	yes	characteristic
247	C₂	C₂×#11718221	1	1	yes	characteristic
248	C₂	C₂×#11718222	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88102
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle	C₂³×C₁₃	#107
prime radical	C₂³×D₁₃	D₈
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	C₂×#1380
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13129894	C₂	direct (N × H)
8. C₂×#88102	C₄	semidirect
10. C₂²×C₁₃×C₁₆	C₄	semidirect
11. C₂²×#6090	C₄	semidirect
13. C₂×C₁₆×D₁₃	C₄	semidirect
31. #88102	C₂×C₄	semidirect
33. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
35. C₂×#6090	C₂×C₄	semidirect
108. C₂²×C₁₆	#261	semidirect
151. C₂×C₁₆	C₂×#261	semidirect
155. C₂×C₁₃	#1380	semidirect
159. D₁₃	#1380	semidirect
193. C₁₃	C₂×#1380	semidirect
245. C₂	#13129894	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#88102	2
#13129894	2
C₂²×C₁₆×D₁₃	2
C₂×#1380	13

Subgroups — C2×#13129894 #16789096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129894 #16789096