Subgroups — C₂×#13130391 #16794928

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719052	C₂	1	2	yes	maximal
2	#13130391	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718253	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6118	—	2	2	no	—
6	C₂²×C₈×D₁₃	C₄	1	2	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊#1057	—	2	2	no	—
9	C₂×C₄⋊#1057	C₂²	1	4	yes	—
10	#11719052	—	2	4	no	—
11	#11719052	C₂²	1	8	yes	—
12	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
14	C₂×C₄×#1055	C₄	1	1	yes	characteristic
15	C₄×C₈×D₁₃	C₄	1	4	yes	—
16	C₄×C₈×D₁₃	C₂²	1	4	yes	—
17	#11718253	C₂²	1	16	yes	complemented
18	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
21	C₂²×#1057	—	2	4	no	—
22	C₂×#6118	—	2	8	no	—
23	C₂×#6118	—	4	8	no	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
27	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
28	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
29	C₂²×#1055	C₂×C₄	1	2	yes	—
30	C₂×C₈×D₁₃	—	2	8	no	—
31	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
32	C₄²×D₁₃	C₂×C₄	1	2	yes	—
33	C₄²×D₁₃	D₄	1	2	yes	—
34	C₄²×D₁₃	Q₈	1	2	yes	—
35	C₄²×D₁₃	C₂³	1	2	yes	—
36	C₄⋊#1057	—	2	4	no	—
37	C₄⋊#1057	—	2	8	no	—
38	C₄⋊#1057	C₂³	1	8	yes	—
39	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
40	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
41	C₈×Dic₁₃	C₂³	1	4	yes	—
42	C₄×#1055	C₂×C₄	1	4	yes	—
43	C₂×#1566	—	13	1	no	maximal, Sylow
44	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
49	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄×D₁₃	—	2	4	no	—
52	C₂×C₄×D₁₃	—	2	4	no	—
53	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
54	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
55	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
56	C₂×C₄×D₁₃	SD₁₆	1	8	yes	—
57	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
58	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
59	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
60	C₂×#1057	—	2	8	no	—
61	C₂×#1057	—	4	8	no	—
62	#6118	—	4	16	no	—
63	C₂×C₈×C₁₃	M₁₆	1	8	yes	complemented
64	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
65	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
66	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
67	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
68	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
69	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
71	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
72	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
73	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
74	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
75	C₂×#1055	—	2	4	no	—
76	C₂×#1055	C₂²×C₄	1	4	yes	—
77	C₈×D₁₃	—	2	16	no	—
78	C₂×#423	—	13	2	no	—
79	C₂²×C₄×C₈	—	13	1	no	—
80	#1566	—	13	8	no	—
81	C₂×#334	—	13	4	no	—
82	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂²×D₁₃	—	2	2	no	—
84	C₂²×D₁₃	—	2	2	no	—
85	C₂²×D₁₃	#106	1	4	yes	—
86	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
87	C₂×C₄×C₁₃	#106	1	4	yes	—
88	C₂×C₄×C₁₃	#108	1	4	yes	—
89	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
91	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
93	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
94	C₂×Dic₁₃	—	2	2	no	—
95	C₂×Dic₁₃	—	2	2	no	—
96	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
98	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×Dic₁₃	C₂×SD₁₆	1	4	yes	—
100	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
101	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
102	C₄×D₁₃	—	2	4	no	—
103	C₄×D₁₃	—	2	4	no	—
104	C₄×D₁₃	—	2	4	no	—
105	C₄×D₁₃	—	2	4	no	—
106	C₄×D₁₃	#106	1	8	yes	—
107	C₄×D₁₃	C₂×SD₁₆	1	8	yes	—
108	#1057	—	4	8	no	—
109	C₈×C₁₃	C₂×M₁₆	1	8	yes	complemented
110	#1055	—	2	4	no	—
111	C₂²×M₁₆	—	26	2	no	—
112	C₂³×C₈	—	13	2	no	—
113	C₂²×C₄²	—	13	1	no	—
114	#423	—	13	8	no	—
115	#423	—	26	4	no	—
116	C₂×C₄⋊C₈	—	13	4	no	—
117	C₂×C₄⋊C₈	—	26	2	no	—
118	C₂×C₄×C₈	—	13	2	no	—
119	C₂×C₄×C₈	—	13	1	no	—
120	C₂×C₄×C₈	—	13	4	no	—
121	C₂×C₄×C₈	—	13	4	no	—
122	C₂×C₄×C₈	#261	1	1	yes	characteristic
123	#334	—	13	16	no	—
124	C₂²×C₁₃	#423	1	2	yes	—
125	C₂²×C₁₃	C₂×#106	1	2	yes	—
126	C₂²×C₁₃	C₂×#108	1	2	yes	—
127	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
128	C₂×D₁₃	—	2	8	no	—
129	C₂×D₁₃	—	2	2	no	—
130	C₂×D₁₃	—	2	2	no	—
131	C₂×D₁₃	C₂×#106	1	4	yes	—
132	C₄×C₁₃	#423	1	2	yes	—
133	C₄×C₁₃	C₂×#106	1	4	yes	—
134	C₄×C₁₃	C₂×#108	1	4	yes	—
135	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
136	Dic₁₃	—	2	2	no	—
137	Dic₁₃	—	2	1	no	—
138	Dic₁₃	—	2	1	no	—
139	Dic₁₃	C₂×#106	1	2	yes	—
140	Dic₁₃	C₂²×SD₁₆	1	2	yes	—
141	C₂³×C₄	—	13	1	no	—
142	C₂³×C₄	—	13	1	no	—
143	C₂³×C₄	—	13	1	no	—
144	C₂×M₁₆	—	26	8	no	—
145	C₂×M₁₆	—	52	8	no	—
146	C₂²×C₈	—	13	2	no	—
147	C₂²×C₈	—	13	8	no	—
148	C₂²×C₈	—	26	8	no	—
149	C₂²×C₈	—	26	4	no	—
150	C₂²×C₈	C₂×#261	1	2	yes	—
151	C₂×C₄²	—	13	1	no	—
152	C₂×C₄²	—	13	1	no	—
153	C₂×C₄²	—	13	1	no	—
154	C₂×C₄²	—	13	2	no	—
155	C₂×C₄²	—	13	2	no	—
156	C₂×C₄²	—	13	2	no	—
157	C₂×C₄²	—	13	2	no	—
158	C₂×C₄²	C₂×#261	1	1	yes	characteristic
159	C₄⋊C₈	—	13	8	no	—
160	C₄⋊C₈	—	26	4	no	—
161	C₄⋊C₈	—	26	8	no	—
162	C₄×C₈	—	13	4	no	—
163	C₄×C₈	—	13	4	no	—
164	C₄×C₈	—	13	4	no	—
165	C₄×C₈	C₂×#261	1	4	yes	—
166	C₂×C₁₃	#1566	1	4	yes	complemented
167	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
168	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
169	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
170	D₁₃	—	2	4	no	—
171	C₂⁴	—	13	1	no	—
172	C₂²×C₄	—	13	1	no	—
173	C₂²×C₄	—	13	8	no	—
174	C₂²×C₄	—	13	2	no	—
175	C₂²×C₄	—	13	2	no	—
176	C₂²×C₄	—	13	1	no	—
177	C₂²×C₄	—	13	1	no	—
178	C₂²×C₄	—	13	2	no	—
179	C₂²×C₄	—	13	2	no	—
180	C₂²×C₄	—	13	2	no	—
181	C₂²×C₄	—	13	2	no	—
182	C₂²×C₄	—	26	4	no	—
183	C₂²×C₄	—	26	4	no	—
184	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
185	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
186	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
187	M₁₆	—	52	16	no	—
188	C₂×C₈	—	13	4	no	—
189	C₂×C₈	—	26	4	no	—
190	C₂×C₈	—	26	16	no	—
191	C₂×C₈	—	26	8	no	—
192	C₂×C₈	—	52	8	no	—
193	C₂×C₈	#6118	1	8	yes	complemented
194	C₂×C₈	C₂²×#261	1	4	yes	—
195	C₄²	—	13	1	no	—
196	C₄²	—	13	2	no	—
197	C₄²	—	13	2	no	—
198	C₄²	—	13	2	no	—
199	C₄²	—	13	1	no	—
200	C₄²	—	13	2	no	—
201	C₄²	—	13	1	no	—
202	C₄²	—	13	1	no	—
203	C₄²	C₄⋊#261	1	2	yes	—
204	C₄²	C₂²×#261	1	2	yes	—
205	C₁₃	C₂×#1566	1	1	yes	characteristic, complemented, Sylow
206	C₂³	—	13	4	no	—
207	C₂³	—	13	2	no	—
208	C₂³	—	26	2	no	—
209	C₂³	—	26	2	no	—
210	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
211	C₂×C₄	—	13	4	no	—
212	C₂×C₄	—	13	1	no	—
213	C₂×C₄	—	13	1	no	—
214	C₂×C₄	—	13	8	no	—
215	C₂×C₄	—	13	8	no	—
216	C₂×C₄	—	13	2	no	—
217	C₂×C₄	—	13	1	no	—
218	C₂×C₄	—	13	1	no	—
219	C₂×C₄	—	26	2	no	—
220	C₂×C₄	—	26	2	no	—
221	C₂×C₄	—	26	4	no	—
222	C₂×C₄	—	26	4	no	—
223	C₂×C₄	—	26	4	no	—
224	C₂×C₄	—	26	4	no	—
225	C₂×C₄	#88101	1	4	yes	—
226	C₂×C₄	#88103	1	4	yes	—
227	C₂×C₄	C₂×#6118	1	4	yes	—
228	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
229	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
230	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
231	C₂×C₄	C₂³×#261	1	1	yes	characteristic
232	C₈	—	26	4	no	—
233	C₈	—	52	8	no	—
234	C₈	C₂×#6118	1	8	yes	complemented
235	C₂²	—	13	4	no	—
236	C₂²	—	26	8	no	—
237	C₂²	—	26	2	no	—
238	C₂²	—	26	2	no	—
239	C₂²	#11719052	1	2	yes	—
240	C₂²	C₂×#88101	1	2	yes	—
241	C₂²	C₂×#88103	1	2	yes	—
242	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
243	C₄	—	13	2	no	—
244	C₄	—	13	2	no	—
245	C₄	—	26	2	no	—
246	C₄	—	26	1	no	—
247	C₄	—	26	1	no	—
248	C₄	#11719052	1	2	yes	—
249	C₄	C₂×#88101	1	4	yes	—
250	C₄	C₂×#88103	1	4	yes	—
251	C₄	C₂²×#6118	1	2	yes	—
252	C₂	—	26	4	no	—
253	C₂	#13130391	1	4	yes	direct product factor
254	C₂	C₂×#11719052	1	1	yes	characteristic
255	C₂	C₂²×#88101	1	1	yes	characteristic
256	C₂	C₂²×#88103	1	1	yes	characteristic

	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	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1566
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. #13130391	C₂	direct (N × H)
3. C₂×#11718253	C₂	semidirect
17. #11718253	C₂²	semidirect
63. C₂×C₈×C₁₃	M₁₆	semidirect
109. C₈×C₁₃	C₂×M₁₆	semidirect
166. C₂×C₁₃	#1566	semidirect
193. C₂×C₈	#6118	semidirect
205. C₁₃	C₂×#1566	semidirect
234. C₈	C₂×#6118	semidirect
253. C₂	#13130391	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×#11719052	2
#13130391	2
C₂×#11718253	2
C₂×C₄×C₈×D₁₃	2
C₂×#1566	13

Subgroups — C2×#13130391 #16794928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130391 #16794928