Subgroups — C₂×#13130394 #16794932

Order 3328.

854 conjugacy classes of subgroups.

The subgroup lattice has 266 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	#13130394	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718254	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	#11718254	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×#1567	—	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	D₈	1	4	yes	—
57	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
58	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
59	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
60	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
61	C₂×#1057	—	2	8	no	—
62	C₂×#1057	—	4	8	no	—
63	#6118	—	4	16	no	—
64	C₂×C₈×C₁₃	M₁₆	1	8	yes	complemented
65	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
66	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
67	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
68	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
69	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
70	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
72	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
73	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
74	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
75	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
76	C₂×#1055	—	2	4	no	—
77	C₂×#1055	C₂²×C₄	1	4	yes	—
78	C₈×D₁₃	—	2	16	no	—
79	C₂×#423	—	13	2	no	—
80	C₂²×C₄×C₈	—	13	1	no	—
81	#1567	—	13	8	no	—
82	C₂×#335	—	13	4	no	—
83	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂²×D₁₃	—	2	2	no	—
85	C₂²×D₁₃	—	2	2	no	—
86	C₂²×D₁₃	#107	1	4	yes	—
87	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×C₄×C₁₃	#107	1	4	yes	—
89	C₂×C₄×C₁₃	#108	1	4	yes	—
90	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
92	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
94	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
95	C₂×Dic₁₃	—	2	2	no	—
96	C₂×Dic₁₃	—	2	2	no	—
97	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
98	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
99	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
100	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
101	C₂×Dic₁₃	C₂×Q₁₆	1	2	yes	—
102	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
103	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
104	C₄×D₁₃	—	2	4	no	—
105	C₄×D₁₃	—	2	4	no	—
106	C₄×D₁₃	—	2	4	no	—
107	C₄×D₁₃	—	2	4	no	—
108	C₄×D₁₃	#107	1	8	yes	—
109	C₄×D₁₃	C₂×D₈	1	4	yes	—
110	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
111	#1057	—	4	8	no	—
112	C₈×C₁₃	C₂×M₁₆	1	8	yes	complemented
113	#1055	—	2	4	no	—
114	C₂²×M₁₆	—	26	2	no	—
115	C₂³×C₈	—	13	2	no	—
116	C₂²×C₄²	—	13	1	no	—
117	#423	—	13	8	no	—
118	#423	—	26	4	no	—
119	C₂×C₄⋊C₈	—	13	4	no	—
120	C₂×C₄⋊C₈	—	26	2	no	—
121	C₂×C₄×C₈	—	13	2	no	—
122	C₂×C₄×C₈	—	13	1	no	—
123	C₂×C₄×C₈	—	13	4	no	—
124	C₂×C₄×C₈	—	13	4	no	—
125	C₂×C₄×C₈	#261	1	1	yes	characteristic
126	#335	—	13	16	no	—
127	C₂²×C₁₃	#423	1	2	yes	—
128	C₂²×C₁₃	C₂×#107	1	2	yes	—
129	C₂²×C₁₃	C₂×#108	1	2	yes	—
130	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
131	C₂×D₁₃	—	2	8	no	—
132	C₂×D₁₃	—	2	2	no	—
133	C₂×D₁₃	—	2	2	no	—
134	C₂×D₁₃	C₂×#107	1	4	yes	—
135	C₄×C₁₃	#423	1	2	yes	—
136	C₄×C₁₃	C₂×#107	1	4	yes	—
137	C₄×C₁₃	C₂×#108	1	4	yes	—
138	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
139	Dic₁₃	—	2	2	no	—
140	Dic₁₃	—	2	1	no	—
141	Dic₁₃	—	2	1	no	—
142	Dic₁₃	C₂×#107	1	2	yes	—
143	Dic₁₃	C₂²×D₈	1	1	yes	characteristic
144	Dic₁₃	C₂²×Q₁₆	1	1	yes	characteristic
145	C₂³×C₄	—	13	1	no	—
146	C₂³×C₄	—	13	1	no	—
147	C₂³×C₄	—	13	1	no	—
148	C₂×M₁₆	—	26	8	no	—
149	C₂×M₁₆	—	52	8	no	—
150	C₂²×C₈	—	13	2	no	—
151	C₂²×C₈	—	13	8	no	—
152	C₂²×C₈	—	26	8	no	—
153	C₂²×C₈	—	26	4	no	—
154	C₂²×C₈	C₂×#261	1	2	yes	—
155	C₂×C₄²	—	13	1	no	—
156	C₂×C₄²	—	13	1	no	—
157	C₂×C₄²	—	13	1	no	—
158	C₂×C₄²	—	13	2	no	—
159	C₂×C₄²	—	13	2	no	—
160	C₂×C₄²	—	13	2	no	—
161	C₂×C₄²	—	13	2	no	—
162	C₂×C₄²	C₂×#261	1	1	yes	characteristic
163	C₄⋊C₈	—	13	8	no	—
164	C₄⋊C₈	—	26	4	no	—
165	C₄⋊C₈	—	26	8	no	—
166	C₄×C₈	—	13	4	no	—
167	C₄×C₈	—	13	4	no	—
168	C₄×C₈	—	13	4	no	—
169	C₄×C₈	C₂×#261	1	4	yes	—
170	C₂×C₁₃	#1567	1	4	yes	complemented
171	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
172	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
173	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
174	D₁₃	—	2	4	no	—
175	C₂⁴	—	13	1	no	—
176	C₂²×C₄	—	13	1	no	—
177	C₂²×C₄	—	13	4	no	—
178	C₂²×C₄	—	13	4	no	—
179	C₂²×C₄	—	13	2	no	—
180	C₂²×C₄	—	13	2	no	—
181	C₂²×C₄	—	13	1	no	—
182	C₂²×C₄	—	13	1	no	—
183	C₂²×C₄	—	13	2	no	—
184	C₂²×C₄	—	13	2	no	—
185	C₂²×C₄	—	13	2	no	—
186	C₂²×C₄	—	13	2	no	—
187	C₂²×C₄	—	26	4	no	—
188	C₂²×C₄	—	26	4	no	—
189	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
190	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
191	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
192	M₁₆	—	52	16	no	—
193	C₂×C₈	—	13	4	no	—
194	C₂×C₈	—	26	4	no	—
195	C₂×C₈	—	26	16	no	—
196	C₂×C₈	—	26	8	no	—
197	C₂×C₈	—	52	8	no	—
198	C₂×C₈	#6118	1	8	yes	complemented
199	C₂×C₈	C₂²×#261	1	4	yes	—
200	C₄²	—	13	1	no	—
201	C₄²	—	13	2	no	—
202	C₄²	—	13	2	no	—
203	C₄²	—	13	2	no	—
204	C₄²	—	13	1	no	—
205	C₄²	—	13	2	no	—
206	C₄²	—	13	1	no	—
207	C₄²	—	13	1	no	—
208	C₄²	C₄⋊#261	1	2	yes	—
209	C₄²	C₂²×#261	1	2	yes	—
210	C₁₃	C₂×#1567	1	1	yes	characteristic, complemented, Sylow
211	C₂³	—	13	4	no	—
212	C₂³	—	13	2	no	—
213	C₂³	—	26	2	no	—
214	C₂³	—	26	2	no	—
215	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
216	C₂×C₄	—	13	2	no	—
217	C₂×C₄	—	13	2	no	—
218	C₂×C₄	—	13	1	no	—
219	C₂×C₄	—	13	1	no	—
220	C₂×C₄	—	13	4	no	—
221	C₂×C₄	—	13	8	no	—
222	C₂×C₄	—	13	4	no	—
223	C₂×C₄	—	13	2	no	—
224	C₂×C₄	—	13	1	no	—
225	C₂×C₄	—	13	1	no	—
226	C₂×C₄	—	26	2	no	—
227	C₂×C₄	—	26	2	no	—
228	C₂×C₄	—	26	4	no	—
229	C₂×C₄	—	26	4	no	—
230	C₂×C₄	—	26	4	no	—
231	C₂×C₄	—	26	4	no	—
232	C₂×C₄	#88102	1	4	yes	—
233	C₂×C₄	#88104	1	4	yes	—
234	C₂×C₄	C₂×#6118	1	4	yes	—
235	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
236	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
237	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
238	C₂×C₄	C₂³×#261	1	1	yes	characteristic
239	C₈	—	26	4	no	—
240	C₈	—	52	8	no	—
241	C₈	C₂×#6118	1	8	yes	complemented
242	C₂²	—	13	4	no	—
243	C₂²	—	26	8	no	—
244	C₂²	—	26	2	no	—
245	C₂²	—	26	2	no	—
246	C₂²	#11719052	1	2	yes	—
247	C₂²	C₂×#88102	1	2	yes	—
248	C₂²	C₂×#88104	1	2	yes	—
249	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
250	C₄	—	13	1	no	—
251	C₄	—	13	1	no	—
252	C₄	—	13	2	no	—
253	C₄	—	26	2	no	—
254	C₄	—	26	1	no	—
255	C₄	—	26	1	no	—
256	C₄	#11719052	1	2	yes	—
257	C₄	C₂×#88102	1	4	yes	—
258	C₄	C₂×#88104	1	4	yes	—
259	C₄	C₂²×#6118	1	2	yes	—
260	C₂	—	26	4	no	—
261	C₂	#13130394	1	4	yes	direct product factor
262	C₂	C₂×#11719052	1	1	yes	characteristic
263	C₂	C₂²×#88102	1	1	yes	characteristic
264	C₂	C₂²×#88104	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×#1567
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. #13130394	C₂	direct (N × H)
3. C₂×#11718254	C₂	semidirect
17. #11718254	C₂²	semidirect
64. C₂×C₈×C₁₃	M₁₆	semidirect
112. C₈×C₁₃	C₂×M₁₆	semidirect
170. C₂×C₁₃	#1567	semidirect
198. C₂×C₈	#6118	semidirect
210. C₁₃	C₂×#1567	semidirect
241. C₈	C₂×#6118	semidirect
261. C₂	#13130394	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
#13130394	2
C₂×#11718254	2
C₂×C₄×C₈×D₁₃	2
C₂×#1567	13

Subgroups — C2×#13130394 #16794932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130394 #16794932