Subgroups — #16785594

Order 3328.

678 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×#11718268	C₂	1	2	yes	maximal
2	C₂×#11718268	C₂	1	2	yes	maximal
3	#13130500	C₂	1	2	yes	maximal
4	C₂×D₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6118	C₂²	1	4	yes	—
6	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
10	C₂×#88055	C₄	1	1	yes	characteristic
11	C₂×#88055	C₄	1	1	yes	characteristic
12	C₂×#88043	C₄	1	1	yes	characteristic
13	D₁₃×#97	—	2	4	no	—
14	#11718290	—	2	4	no	—
15	#11718268	—	2	4	no	—
16	#11718268	C₄	1	8	yes	complemented
17	C₂²×C₄×D₁₃	Q₈	1	2	yes	—
18	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
19	C₂²×#1057	—	2	4	no	—
20	C₂×#6118	—	2	4	no	—
21	C₂×#6118	—	2	4	no	—
22	C₂×#6118	—	2	4	no	—
23	C₂×#6118	—	2	4	no	—
24	C₂×#6118	—	2	4	no	—
25	C₂×#6118	C₂×C₄	1	8	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
31	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
32	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
33	C₂×C₈×D₁₃	—	2	2	no	—
34	C₂×C₈×D₁₃	—	2	2	no	—
35	C₂×C₈×D₁₃	—	2	2	no	—
36	C₂×C₈×D₁₃	—	2	2	no	—
37	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
38	C₂×C₈×D₁₃	D₄	1	4	yes	—
39	C₄²×D₁₃	—	2	2	no	—
40	C₄²×D₁₃	—	2	2	no	—
41	C₁₃×#97	—	2	2	no	—
42	#88055	—	2	2	no	—
43	#88055	—	2	2	no	—
44	#88043	—	2	2	no	—
45	#10823	—	13	1	no	maximal, Sylow
46	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
50	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×D₁₃	—	2	4	no	—
52	C₂×C₄×D₁₃	—	4	4	no	—
53	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
54	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
55	C₂×C₄×D₁₃	#41	1	2	yes	—
56	C₂×C₄×D₁₃	#41	1	2	yes	—
57	C₂×C₄×D₁₃	#41	1	2	yes	—
58	C₂×C₄×D₁₃	#41	1	2	yes	—
59	C₂×#1057	—	2	8	no	—
60	C₂×#1057	—	4	4	no	—
61	C₂×#1057	—	4	4	no	—
62	#6118	—	2	8	no	—
63	#6118	—	2	8	no	—
64	#6118	—	4	4	no	—
65	#6118	—	4	4	no	—
66	C₂×C₈×C₁₃	—	2	1	no	—
67	C₂×C₈×C₁₃	—	2	1	no	—
68	C₂×C₈×C₁₃	—	2	1	no	—
69	C₂×C₈×C₁₃	—	2	1	no	—
70	C₂×C₈×C₁₃	C₄²	1	2	yes	—
71	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
72	C₄²×C₁₃	—	2	1	no	—
73	C₄²×C₁₃	—	2	1	no	—
74	C₄×Dic₁₃	—	2	1	no	—
75	C₄×Dic₁₃	—	2	1	no	—
76	C₄×Dic₁₃	—	2	4	no	—
77	C₂×#1055	—	2	1	no	—
78	C₂×#1055	—	2	1	no	—
79	C₂×#1055	—	2	1	no	—
80	C₂×#1055	—	2	1	no	—
81	C₂×#1055	C₄²	1	2	yes	—
82	C₂×#1055	C₂²⋊C₄	1	2	yes	—
83	C₈×D₁₃	—	2	8	no	—
84	C₈×D₁₃	—	2	8	no	—
85	C₂²×#97	—	13	1	no	—
86	C₂×#341	—	13	2	no	—
87	C₂×#341	—	13	2	no	—
88	#1728	—	13	2	no	—
89	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₂²×D₁₃	—	2	4	no	—
91	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
92	C₂²×D₁₃	C₂²⋊Q₈	1	2	yes	—
93	C₂²×D₁₃	#125	1	2	yes	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	4	no	—
96	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
100	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
101	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
102	C₂×Dic₁₃	—	2	2	no	—
103	C₂×Dic₁₃	—	2	4	no	—
104	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
105	C₂×Dic₁₃	#121	1	2	yes	—
106	C₂×Dic₁₃	#124	1	2	yes	—
107	C₄×D₁₃	—	4	8	no	—
108	C₄×D₁₃	#117	1	4	yes	—
109	C₄×D₁₃	C₄×D₄	1	4	yes	—
110	C₄×D₁₃	#123	1	4	yes	—
111	C₄×D₁₃	#126	1	4	yes	—
112	#1057	—	4	8	no	—
113	C₈×C₁₃	—	2	2	no	—
114	C₈×C₁₃	—	2	2	no	—
115	#1055	—	2	2	no	—
116	#1055	—	2	2	no	—
117	C₂²×M₁₆	—	13	4	no	—
118	C₂³×C₈	—	13	1	no	—
119	C₂³×C₈	—	13	1	no	—
120	C₂²×C₄²	—	13	1	no	—
121	C₂×#97	—	13	1	no	—
122	C₂×#97	—	13	1	no	—
123	C₂×#97	—	13	1	no	—
124	C₂×#97	—	26	4	no	—
125	C₂×#97	#261	1	1	yes	characteristic
126	#341	—	13	8	no	—
127	#341	—	26	4	no	—
128	#336	—	26	4	no	—
129	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
130	C₂²×C₁₃	#380	1	1	yes	characteristic
131	C₂²×C₁₃	#382	1	1	yes	characteristic
132	C₂²×C₁₃	#430	1	4	yes	—
133	C₂×D₁₃	—	2	4	no	—
134	C₂×D₁₃	—	2	4	no	—
135	C₂×D₁₃	—	2	4	no	—
136	C₂×D₁₃	#387	1	4	yes	—
137	C₄×C₁₃	—	4	2	no	—
138	C₄×C₁₃	#376	1	1	yes	characteristic
139	C₄×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
140	C₄×C₁₃	#381	1	1	yes	characteristic
141	C₄×C₁₃	#383	1	1	yes	characteristic
142	Dic₁₃	—	4	2	no	—
143	Dic₁₃	#388	1	4	yes	—
144	C₂³×C₄	—	13	1	no	—
145	C₂³×C₄	—	13	2	no	—
146	C₂×M₁₆	—	13	8	no	—
147	C₂×M₁₆	—	26	4	no	—
148	C₂×M₁₆	—	26	4	no	—
149	C₂×M₁₆	—	26	4	no	—
150	C₂×M₁₆	—	26	4	no	—
151	C₂×M₁₆	—	26	4	no	—
152	C₂²×C₈	—	13	1	no	—
153	C₂²×C₈	—	13	1	no	—
154	C₂²×C₈	—	13	4	no	—
155	C₂²×C₈	—	13	4	no	—
156	C₂²×C₈	—	26	2	no	—
157	C₂²×C₈	—	26	2	no	—
158	C₂²×C₈	—	26	2	no	—
159	C₂²×C₈	—	26	2	no	—
160	C₂²×C₈	—	26	4	no	—
161	C₂²×C₈	C₂×#261	1	1	yes	characteristic
162	C₂²×C₈	C₂×#261	1	1	yes	characteristic
163	C₂×C₄²	—	13	2	no	—
164	C₂×C₄²	—	13	1	no	—
165	C₂×C₄²	—	26	2	no	—
166	C₂×C₄²	—	26	2	no	—
167	C₂×C₄²	C₂×#261	1	1	yes	characteristic
168	#97	—	2	2	no	—
169	#97	—	26	2	no	—
170	#97	—	26	2	no	—
171	#97	—	26	2	no	—
172	C₂×C₁₃	#1434	1	1	yes	characteristic
173	C₂×C₁₃	#1778	1	2	yes	—
174	C₂×C₁₃	#1811	1	2	yes	—
175	C₂×C₁₃	#1838	1	2	yes	—
176	D₁₃	—	2	4	no	—
177	C₂⁴	—	13	1	no	—
178	C₂²×C₄	—	13	1	no	—
179	C₂²×C₄	—	13	2	no	—
180	C₂²×C₄	—	13	2	no	—
181	C₂²×C₄	—	13	2	no	—
182	C₂²×C₄	—	13	2	no	—
183	C₂²×C₄	—	13	2	no	—
184	C₂²×C₄	—	13	2	no	—
185	C₂²×C₄	—	13	2	no	—
186	C₂²×C₄	—	26	4	no	—
187	C₂²×C₄	—	52	4	no	—
188	C₂²×C₄	C₄⋊#261	1	2	yes	—
189	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
190	M₁₆	—	26	8	no	—
191	M₁₆	—	26	8	no	—
192	M₁₆	—	52	4	no	—
193	M₁₆	—	52	4	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	2	1	no	—
198	C₂×C₈	—	13	2	no	—
199	C₂×C₈	—	13	2	no	—
200	C₂×C₈	—	26	8	no	—
201	C₂×C₈	—	26	8	no	—
202	C₂×C₈	—	26	1	no	—
203	C₂×C₈	—	26	1	no	—
204	C₂×C₈	—	26	1	no	—
205	C₂×C₈	—	26	1	no	—
206	C₂×C₈	—	26	8	no	—
207	C₂×C₈	—	52	4	no	—
208	C₂×C₈	—	52	4	no	—
209	C₂×C₈	C₄×#261	1	2	yes	—
210	C₂×C₈	C₂²⋊#261	1	2	yes	—
211	C₄²	—	2	1	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	26	4	no	—
214	C₄²	—	26	1	no	—
215	C₄²	—	26	1	no	—
216	C₁₃	#10823	1	1	yes	characteristic, complemented, Sylow
217	C₂³	—	13	2	no	—
218	C₂³	—	13	2	no	—
219	C₂³	—	13	2	no	—
220	C₂³	—	26	4	no	—
221	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	13	2	no	—
225	C₂×C₄	—	13	2	no	—
226	C₂×C₄	—	13	2	no	—
227	C₂×C₄	—	13	4	no	—
228	C₂×C₄	—	13	4	no	—
229	C₂×C₄	—	13	4	no	—
230	C₂×C₄	—	13	4	no	—
231	C₂×C₄	—	26	4	no	—
232	C₂×C₄	—	26	2	no	—
233	C₂×C₄	—	52	8	no	—
234	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
235	C₂×C₄	#88237	1	1	yes	characteristic
236	C₂×C₄	#88237	1	1	yes	characteristic
237	C₂×C₄	#88237	1	1	yes	characteristic
238	C₂×C₄	#88237	1	1	yes	characteristic
239	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
240	C₈	—	2	2	no	—
241	C₈	—	2	2	no	—
242	C₈	—	26	2	no	—
243	C₈	—	26	2	no	—
244	C₈	—	52	8	no	—
245	C₂²	—	13	4	no	—
246	C₂²	—	26	4	no	—
247	C₂²	—	26	4	no	—
248	C₂²	—	26	4	no	—
249	C₂²	C₄×C₄⋊#261	1	1	yes	characteristic
250	C₂²	#11719060	1	1	yes	characteristic
251	C₂²	#11719100	1	4	yes	—
252	C₂²	#11719136	1	1	yes	characteristic
253	C₄	—	4	2	no	—
254	C₄	—	13	4	no	—
255	C₄	—	52	2	no	—
256	C₄	#11719057	1	1	yes	characteristic
257	C₄	#11719061	1	1	yes	characteristic
258	C₄	C₄×C₂²⋊#261	1	1	yes	characteristic
259	C₄	#11719135	1	1	yes	characteristic
260	C₂	—	26	4	no	—
261	C₂	#13130012	1	1	yes	characteristic
262	C₂	#13130656	1	2	yes	—
263	C₂	#13130717	1	2	yes	—
264	C₂	#13130762	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₁₃×#97	C₄
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂²×C₄×D₁₃	C₂³
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#10823
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
16. #11718268	C₄	semidirect
216. C₁₃	#10823	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718268	2
#13130500	2
C₂×D₁₃×#97	2
#10823	13