Subgroups — C₂×#13130777 #16798280

Order 3328.

1046 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88104	C₂	1	4	yes	maximal
2	C₂×#11719052	C₂	1	2	yes	maximal
3	#13130777	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6118	C₂²	1	4	yes	—
6	C₂²×C₈×D₁₃	C₂²	1	2	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊#1057	—	2	4	no	—
9	C₂×#88104	—	2	16	no	—
10	C₂×#88104	C₂²	1	16	yes	—
11	#11719052	—	2	4	no	—
12	#11719052	C₂²	1	8	yes	—
13	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₁₃	C₄	1	2	yes	—
15	C₂×C₄×#1055	C₄	1	1	yes	characteristic
16	C₄×C₈×D₁₃	C₄	1	4	yes	—
17	C₄×C₈×D₁₃	C₂²	1	4	yes	—
18	C₂²×C₄×D₁₃	Q₈	1	2	yes	—
19	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
20	C₂²×#1057	—	2	4	no	—
21	C₂×#6118	—	2	16	no	—
22	C₂×#6118	—	2	4	no	—
23	C₂×#6118	C₂³	1	8	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
28	C₂²×#1055	C₂×C₄	1	2	yes	—
29	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
30	C₂×C₈×D₁₃	D₄	1	8	yes	—
31	C₂×C₈×D₁₃	Q₈	1	8	yes	—
32	C₂×C₈×D₁₃	C₂³	1	4	yes	—
33	C₄²×D₁₃	C₂×C₄	1	2	yes	—
34	C₄²×D₁₃	D₄	1	2	yes	—
35	C₄²×D₁₃	Q₈	1	2	yes	—
36	C₄²×D₁₃	C₂³	1	2	yes	—
37	C₄⋊#1057	—	2	16	no	—
38	#88104	—	2	32	no	—
39	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
40	C₈×Dic₁₃	C₂×C₄	1	8	yes	—
41	C₄×#1055	C₂×C₄	1	4	yes	—
42	C₂×#1848	—	13	1	no	maximal, Sylow
43	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
47	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×D₁₃	—	2	8	no	—
49	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
50	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×D₁₃	C₂×D₄	1	4	yes	—
52	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×D₁₃	C₂×Q₈	1	4	yes	—
54	C₂×C₄×D₁₃	C₂×Q₈	1	4	yes	—
55	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
57	C₂×#1057	—	2	8	no	—
58	C₂×#1057	—	4	8	no	—
59	#6118	—	2	16	no	—
60	#6118	—	4	8	no	—
61	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
62	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
63	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
64	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
65	C₄×Dic₁₃	C₄⋊C₄	1	4	yes	—
66	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
67	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
68	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
69	C₂×#1055	C₄⋊C₄	1	8	yes	—
70	C₂×#1055	C₂²×C₄	1	4	yes	—
71	C₈×D₁₃	C₄⋊C₄	1	16	yes	—
72	C₈×D₁₃	C₂×D₄	1	8	yes	—
73	C₈×D₁₃	C₂×Q₈	1	8	yes	—
74	C₂²×#108	—	13	4	no	—
75	C₂×#423	—	13	2	no	—
76	C₂²×C₄×C₈	—	13	1	no	—
77	#1848	—	13	8	no	—
78	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂²×D₁₃	—	2	4	no	—
80	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂²×D₁₃	C₄⋊Q₈	1	4	yes	—
82	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	#108	1	8	yes	complemented
84	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
85	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
87	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
88	C₂×Dic₁₃	—	2	4	no	—
89	C₂×Dic₁₃	C₂×C₄⋊C₄	1	4	yes	—
90	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂×Dic₁₃	#127	1	2	yes	—
92	C₂×Dic₁₃	C₄⋊Q₈	1	2	yes	—
93	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
94	C₄×D₁₃	—	2	8	no	—
95	C₄×D₁₃	—	2	8	no	—
96	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
97	C₄×D₁₃	#127	1	2	yes	—
98	C₄×D₁₃	C₄⋊Q₈	1	2	yes	—
99	C₄×D₁₃	C₄⋊Q₈	1	4	yes	—
100	C₄×D₁₃	C₂²×D₄	1	2	yes	—
101	C₄×D₁₃	C₂²×Q₈	1	2	yes	—
102	#1057	—	4	8	no	—
103	C₈×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
104	#1055	C₂×C₄⋊C₄	1	8	yes	—
105	C₂²×M₁₆	—	13	4	no	—
106	C₂³×C₈	—	13	2	no	—
107	C₂²×C₄²	—	13	1	no	—
108	C₂×#108	—	13	16	no	—
109	C₂×#108	—	26	16	no	—
110	#423	—	13	8	no	—
111	#423	—	26	4	no	—
112	C₂×C₄⋊C₈	—	26	4	no	—
113	C₂×C₄×C₈	—	13	2	no	—
114	C₂×C₄×C₈	—	13	1	no	—
115	C₂×C₄×C₈	—	13	4	no	—
116	C₂×C₄×C₈	—	13	4	no	—
117	C₂×C₄×C₈	#261	1	1	yes	characteristic
118	C₂²×C₁₃	#384	1	2	yes	—
119	C₂²×C₁₃	C₂×#108	1	4	yes	—
120	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
121	C₂×D₁₃	—	2	8	no	—
122	C₂×D₁₃	—	2	2	no	—
123	C₂×D₁₃	—	2	2	no	—
124	C₂×D₁₃	#384	1	2	yes	—
125	C₂×D₁₃	C₂×C₄⋊Q₈	1	2	yes	—
126	C₄×C₁₃	#384	1	2	yes	—
127	C₄×C₁₃	C₂×#108	1	8	yes	complemented
128	C₄×C₁₃	C₂²×C₄⋊C₄	1	2	yes	—
129	Dic₁₃	—	2	4	no	—
130	Dic₁₃	#384	1	2	yes	—
131	Dic₁₃	C₂×#127	1	1	yes	characteristic
132	Dic₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
133	C₂³×C₄	—	13	1	no	—
134	C₂³×C₄	—	13	2	no	—
135	C₂×M₁₆	—	13	8	no	—
136	C₂×M₁₆	—	26	4	no	—
137	C₂×M₁₆	—	26	16	no	—
138	C₂²×C₈	—	13	2	no	—
139	C₂²×C₈	—	13	8	no	—
140	C₂²×C₈	—	13	8	no	—
141	C₂²×C₈	—	13	4	no	—
142	C₂²×C₈	—	13	4	no	—
143	C₂²×C₈	—	26	4	no	—
144	C₂²×C₈	C₂×#261	1	2	yes	—
145	C₂×C₄²	—	13	2	no	—
146	C₂×C₄²	—	13	1	no	—
147	C₂×C₄²	—	13	2	no	—
148	C₂×C₄²	—	13	2	no	—
149	C₂×C₄²	—	13	2	no	—
150	C₂×C₄²	—	13	2	no	—
151	C₂×C₄²	C₂×#261	1	1	yes	characteristic
152	#108	—	26	32	no	—
153	C₄⋊C₈	—	26	16	no	—
154	C₄×C₈	—	13	8	no	—
155	C₄×C₈	—	13	4	no	—
156	C₄×C₈	C₂×#261	1	4	yes	—
157	C₂×C₁₃	#1848	1	4	yes	complemented
158	C₂×C₁₃	C₂×#384	1	1	yes	characteristic
159	C₂×C₁₃	C₂²×#108	1	2	yes	—
160	D₁₃	—	2	2	no	—
161	D₁₃	—	2	2	no	—
162	C₂⁴	—	13	1	no	—
163	C₂²×C₄	—	13	1	no	—
164	C₂²×C₄	—	13	1	no	—
165	C₂²×C₄	—	13	1	no	—
166	C₂²×C₄	—	13	4	no	—
167	C₂²×C₄	—	13	4	no	—
168	C₂²×C₄	—	13	1	no	—
169	C₂²×C₄	—	13	1	no	—
170	C₂²×C₄	—	13	2	no	—
171	C₂²×C₄	—	13	4	no	—
172	C₂²×C₄	—	13	4	no	—
173	C₂²×C₄	—	26	8	no	—
174	C₂²×C₄	C₄⋊#261	1	2	yes	—
175	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
176	M₁₆	—	26	16	no	—
177	M₁₆	—	52	8	no	—
178	C₂×C₈	—	13	8	no	—
179	C₂×C₈	—	13	4	no	—
180	C₂×C₈	—	13	8	no	—
181	C₂×C₈	—	13	16	no	—
182	C₂×C₈	—	13	8	no	—
183	C₂×C₈	—	26	8	no	—
184	C₂×C₈	—	52	8	no	—
185	C₂×C₈	C₄⋊#261	1	8	yes	—
186	C₂×C₈	C₂²×#261	1	4	yes	—
187	C₄²	—	13	4	no	—
188	C₄²	—	13	4	no	—
189	C₄²	—	13	2	no	—
190	C₄²	—	13	2	no	—
191	C₄²	C₄⋊#261	1	2	yes	—
192	C₄²	C₂²×#261	1	2	yes	—
193	C₁₃	C₂×#1848	1	1	yes	characteristic, complemented, Sylow
194	C₂³	—	13	4	no	—
195	C₂³	—	13	1	no	—
196	C₂³	—	13	1	no	—
197	C₂³	—	26	4	no	—
198	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
199	C₂×C₄	—	13	2	no	—
200	C₂×C₄	—	13	2	no	—
201	C₂×C₄	—	13	1	no	—
202	C₂×C₄	—	13	1	no	—
203	C₂×C₄	—	13	2	no	—
204	C₂×C₄	—	13	2	no	—
205	C₂×C₄	—	13	4	no	—
206	C₂×C₄	—	13	2	no	—
207	C₂×C₄	—	13	4	no	—
208	C₂×C₄	—	13	2	no	—
209	C₂×C₄	—	13	4	no	—
210	C₂×C₄	—	26	4	no	—
211	C₂×C₄	—	26	8	no	—
212	C₂×C₄	—	26	8	no	—
213	C₂×C₄	#88104	1	8	yes	complemented
214	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
215	C₂×C₄	C₂×C₄⋊#261	1	4	yes	—
216	C₂×C₄	C₂×C₄⋊#261	1	4	yes	—
217	C₂×C₄	C₂³×#261	1	1	yes	characteristic
218	C₈	—	13	8	no	—
219	C₈	—	52	8	no	—
220	C₈	C₂×C₄⋊#261	1	8	yes	—
221	C₂²	—	13	2	no	—
222	C₂²	—	13	2	no	—
223	C₂²	—	26	8	no	—
224	C₂²	—	26	2	no	—
225	C₂²	—	26	2	no	—
226	C₂²	#11719059	1	2	yes	—
227	C₂²	C₂×#88104	1	4	yes	—
228	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
229	C₄	—	13	1	no	—
230	C₄	—	13	1	no	—
231	C₄	—	13	2	no	—
232	C₄	—	26	4	no	—
233	C₄	#11719059	1	2	yes	—
234	C₄	C₂×#88104	1	8	yes	complemented
235	C₄	C₂²×C₄⋊#261	1	2	yes	—
236	C₂	—	26	2	no	—
237	C₂	—	26	2	no	—
238	C₂	#13130777	1	4	yes	direct product factor
239	C₂	C₂×#11719059	1	1	yes	characteristic
240	C₂	C₂²×#88104	1	2	yes	—

	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	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1848
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
3. #13130777	C₂	direct (N × H)
83. C₂×C₄×C₁₃	#108	semidirect
127. C₄×C₁₃	C₂×#108	semidirect
157. C₂×C₁₃	#1848	semidirect
193. C₁₃	C₂×#1848	semidirect
213. C₂×C₄	#88104	semidirect
234. C₄	C₂×#88104	semidirect
238. C₂	#13130777	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×#88104	2
C₂×#11719052	2
#13130777	2
C₂×C₄×C₈×D₁₃	2
C₂×#1848	13

Subgroups — C2×#13130777 #16798280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130777 #16798280