Subgroups — #15768528

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718116	C₂	1	2	yes	maximal
2	C₂×#11718116	C₂	1	2	yes	maximal
3	C₂×#11718116	C₂	1	2	yes	maximal
4	C₂×C₁₃×#376	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂³×#1055	C₂²	1	4	yes	—
9	C₁₃×#376	—	2	4	no	—
10	C₂×C₁₃×#95	C₄	1	4	yes	—
11	#11718116	—	2	4	no	—
12	#11718116	—	2	4	no	—
13	#11718116	C₄	1	8	yes	complemented
14	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
15	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
16	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	—	2	2	no	—
19	C₂×C₄²×C₁₃	—	2	2	no	—
20	C₂×C₄²×C₁₃	—	2	2	no	—
21	C₂×C₄²×C₁₃	—	2	2	no	—
22	C₂×C₄²×C₁₃	—	2	2	no	—
23	C₂×C₄²×C₁₃	—	2	2	no	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₃	D₄	1	2	yes	—
26	C₂×C₄²×C₁₃	D₄	1	4	yes	—
27	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
28	C₂²×#1055	—	2	4	no	—
29	C₂²×#1055	—	2	4	no	—
30	C₂²×#1055	—	2	4	no	—
31	C₂²×#1055	—	2	4	no	—
32	C₂²×#1055	—	2	4	no	—
33	C₂²×#1055	—	2	4	no	—
34	C₂²×#1055	C₂×C₄	1	8	yes	—
35	C₁₃×#95	—	2	8	no	—
36	#10796	—	13	1	no	maximal, Sylow
37	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	—	2	2	no	—
39	C₂²×C₄×C₁₃	—	2	2	no	—
40	C₂²×C₄×C₁₃	—	2	2	no	—
41	C₂²×C₄×C₁₃	—	2	2	no	—
42	C₂²×C₄×C₁₃	—	2	2	no	—
43	C₂²×C₄×C₁₃	—	2	2	no	—
44	C₂²×C₄×C₁₃	—	2	8	no	—
45	C₂²×C₄×C₁₃	—	2	8	no	—
46	C₂²×C₄×C₁₃	—	2	8	no	—
47	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
48	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
49	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
50	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	#41	1	2	yes	—
55	C₂²×C₄×C₁₃	#41	1	2	yes	—
56	C₂²×C₄×C₁₃	#41	1	2	yes	—
57	C₂²×C₄×C₁₃	#41	1	2	yes	—
58	C₄²×C₁₃	—	2	8	no	—
59	C₄²×C₁₃	—	2	4	no	—
60	C₄²×C₁₃	—	2	4	no	—
61	C₄²×C₁₃	—	2	8	no	—
62	C₂×#1055	—	2	8	no	—
63	C₂×#1055	—	2	8	no	—
64	C₂×#1055	—	2	8	no	—
65	C₂×#1055	—	4	4	no	—
66	C₂×#1055	—	4	4	no	—
67	C₂×#1055	—	4	4	no	—
68	C₂×#1055	—	4	4	no	—
69	C₂×#376	D₁₃	1	1	yes	characteristic
70	C₂×#336	—	13	2	no	—
71	C₂×#336	—	13	2	no	—
72	C₂×#336	—	13	2	no	—
73	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
74	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂³×C₁₃	#117	1	1	yes	characteristic
77	C₂³×C₁₃	#117	1	1	yes	characteristic
78	C₂³×C₁₃	#117	1	1	yes	characteristic
79	C₂³×C₁₃	#117	1	1	yes	characteristic
80	C₂³×C₁₃	#131	1	8	yes	—
81	C₂×C₄×C₁₃	—	2	4	no	—
82	C₂×C₄×C₁₃	—	2	4	no	—
83	C₂×C₄×C₁₃	—	2	4	no	—
84	C₂×C₄×C₁₃	—	2	8	no	—
85	C₂×C₄×C₁₃	—	2	8	no	—
86	C₂×C₄×C₁₃	—	2	8	no	—
87	C₂×C₄×C₁₃	—	4	4	no	—
88	C₂×C₄×C₁₃	—	4	4	no	—
89	C₂×C₄×C₁₃	—	4	4	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	—	4	4	no	—
92	C₂×C₄×C₁₃	—	4	4	no	—
93	C₂×C₄×C₁₃	#117	1	4	yes	—
94	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
95	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
96	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
97	C₂×C₄×C₁₃	#121	1	2	yes	—
98	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
99	C₂×C₄×C₁₃	#123	1	4	yes	—
100	C₂×C₄×C₁₃	#124	1	2	yes	—
101	C₂×C₄×C₁₃	#125	1	2	yes	—
102	C₂×C₄×C₁₃	#126	1	4	yes	—
103	#1055	—	4	8	no	—
104	C₂³×C₈	—	13	4	no	—
105	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
106	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
107	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
108	#376	—	2	4	no	—
109	C₂×#95	Dic₁₃	1	4	yes	—
110	#336	—	13	8	no	—
111	#336	—	26	4	no	—
112	#336	—	26	4	no	—
113	C₂²×C₁₃	#376	1	1	yes	characteristic
114	C₂²×C₁₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₁₃	#380	1	1	yes	characteristic
117	C₂²×C₁₃	#381	1	1	yes	characteristic
118	C₂²×C₁₃	#382	1	1	yes	characteristic
119	C₂²×C₁₃	#383	1	1	yes	characteristic
120	C₂²×C₁₃	#405	1	4	yes	—
121	C₂²×C₁₃	#408	1	4	yes	—
122	C₂²×C₁₃	#424	1	4	yes	—
123	C₂²×C₁₃	#433	1	4	yes	—
124	C₂²×C₁₃	#433	1	4	yes	—
125	C₂²×C₁₃	#433	1	4	yes	—
126	C₂²×C₁₃	#433	1	4	yes	—
127	C₄×C₁₃	—	4	4	no	—
128	C₄×C₁₃	—	4	4	no	—
129	C₄×C₁₃	—	4	4	no	—
130	C₄×C₁₃	#387	1	4	yes	—
131	C₄×C₁₃	#388	1	4	yes	—
132	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
133	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
134	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
135	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
136	C₂²×C₈	—	13	8	no	—
137	C₂²×C₈	—	26	4	no	—
138	C₂²×C₈	—	26	4	no	—
139	C₂²×C₈	—	26	4	no	—
140	C₂²×C₈	—	26	4	no	—
141	C₂²×C₈	—	26	4	no	—
142	C₂²×C₈	—	26	4	no	—
143	C₂×C₄²	—	2	2	no	—
144	C₂×C₄²	—	2	2	no	—
145	C₂×C₄²	—	2	2	no	—
146	C₂×C₄²	—	2	2	no	—
147	C₂×C₄²	—	2	2	no	—
148	C₂×C₄²	—	2	2	no	—
149	C₂×C₄²	Dic₂₆	1	2	yes	—
150	C₂×C₄²	C₄×D₁₃	1	4	yes	—
151	C₂×C₄²	D₅₂	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
153	#95	—	2	8	no	—
154	C₂×C₁₃	#1434	1	1	yes	characteristic
155	C₂×C₁₃	#1746	1	2	yes	—
156	C₂×C₁₃	#1750	1	2	yes	—
157	C₂×C₁₃	#1768	1	2	yes	—
158	C₂×C₁₃	#1798	1	2	yes	—
159	C₂×C₁₃	#1818	1	2	yes	—
160	C₂×C₁₃	#1832	1	2	yes	—
161	C₂×C₁₃	#1840	1	2	yes	—
162	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	8	no	—
168	C₂²×C₄	—	2	8	no	—
169	C₂²×C₄	—	2	8	no	—
170	C₂²×C₄	—	2	2	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
173	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
174	C₂²×C₄	C₂²⋊Dic₁₃	1	4	yes	—
175	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
177	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
178	C₂²×C₄	#6127	1	2	yes	—
179	C₂²×C₄	#6127	1	2	yes	—
180	C₂²×C₄	#6127	1	2	yes	—
181	C₂²×C₄	#6127	1	2	yes	—
182	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
183	C₂×C₈	—	26	8	no	—
184	C₂×C₈	—	26	8	no	—
185	C₂×C₈	—	26	8	no	—
186	C₂×C₈	—	52	4	no	—
187	C₂×C₈	—	52	4	no	—
188	C₂×C₈	—	52	4	no	—
189	C₂×C₈	—	52	4	no	—
190	C₄²	—	2	4	no	—
191	C₄²	—	2	8	no	—
192	C₄²	—	2	8	no	—
193	C₄²	—	2	4	no	—
194	C₁₃	#10796	1	1	yes	characteristic, complemented, Sylow
195	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
196	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
197	C₂³	#88180	1	1	yes	characteristic
198	C₂³	#88180	1	1	yes	characteristic
199	C₂³	#88180	1	1	yes	characteristic
200	C₂³	#88180	1	1	yes	characteristic
201	C₂³	#88202	1	8	yes	—
202	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	2	8	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	2	8	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	4	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	4	4	no	—
214	C₂×C₄	—	4	4	no	—
215	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
216	C₂×C₄	#88124	1	2	yes	—
217	C₂×C₄	#88126	1	4	yes	—
218	C₂×C₄	C₄×D₅₂	1	2	yes	—
219	C₂×C₄	#88129	1	2	yes	—
220	C₂×C₄	#88130	1	4	yes	—
221	C₂×C₄	#88178	1	2	yes	—
222	C₂×C₄	C₄×C₂²⋊D₁₃	1	4	yes	—
223	C₂×C₄	#88183	1	4	yes	—
224	C₂×C₄	#88184	1	2	yes	—
225	C₈	—	52	8	no	—
226	C₂²	#11718593	1	1	yes	characteristic
227	C₂²	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
228	C₂²	#11718597	1	1	yes	characteristic
229	C₂²	#11718598	1	1	yes	characteristic
230	C₂²	#11718658	1	4	yes	—
231	C₂²	#11718660	1	4	yes	—
232	C₂²	#11718661	1	4	yes	—
233	C₂²	#11718661	1	4	yes	—
234	C₂²	#11718661	1	4	yes	—
235	C₂²	#11718661	1	4	yes	—
236	C₂²	C₄×C₂²⋊Dic₁₃	1	1	yes	characteristic
237	C₂²	#11718872	1	1	yes	characteristic
238	C₂²	#11718873	1	1	yes	characteristic
239	C₂²	#11718895	1	4	yes	—
240	C₄	—	4	4	no	—
241	C₄	—	4	4	no	—
242	C₄	—	4	4	no	—
243	C₄	#11718594	1	4	yes	—
244	C₄	#11718601	1	4	yes	—
245	C₂	#13113063	1	1	yes	characteristic
246	C₂	#13114588	1	2	yes	—
247	C₂	#13114602	1	2	yes	—
248	C₂	#13114693	1	2	yes	—
249	C₂	#13114820	1	2	yes	—
250	C₂	#13114907	1	2	yes	—
251	C₂	#13114956	1	2	yes	—
252	C₂	#13114981	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₁₃
commutator	C₂³×C₁₃	C₂×C₄²
Fitting	C₂×C₁₃×#376	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×#376	D₁₃
hypocenter	C₁₃	#10796
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#376

Complements

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

N	H ≅ G/N	type
13. #11718116	C₄	semidirect
194. C₁₃	#10796	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718116	2
C₂×C₁₃×#376	2
#10796	13