Subgroups — #15756655

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114987	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718049	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718072	C₂	1	2	yes	maximal
5	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88054	—	2	4	no	—
9	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
13	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#1055	C₂²	1	2	yes	—
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₁₃×#334	—	2	2	no	—
17	#11718072	—	2	4	no	—
18	#11718049	—	2	2	no	—
19	C₂²×C₈×C₁₃	—	2	2	no	—
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
26	C₂×C₄×Dic₁₃	Q₈	1	2	yes	—
27	C₂²×#1055	—	2	2	no	—
28	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
29	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
30	C₁₃×C₄⋊C₈	—	2	2	no	—
31	C₁₃×C₄⋊C₈	—	2	2	no	—
32	C₄×C₈×C₁₃	D₄	1	2	yes	—
33	C₄×C₈×C₁₃	Q₈	1	2	yes	—
34	#88054	—	4	8	no	—
35	C₈×Dic₁₃	—	2	2	no	—
36	C₈×Dic₁₃	—	2	2	no	—
37	C₈×Dic₁₃	—	2	2	no	—
38	C₈×Dic₁₃	C₈	1	4	yes	complemented
39	C₄⋊#1055	—	2	2	no	—
40	C₄⋊#1055	—	2	2	no	—
41	C₄×#1055	D₄	1	2	yes	—
42	C₄×#1055	Q₈	1	2	yes	—
43	#8805	—	13	1	no	maximal, Sylow
44	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
48	C₂²×Dic₁₃	C₄⋊C₄	1	2	yes	—
49	C₂×C₈×C₁₃	—	2	1	no	—
50	C₂×C₈×C₁₃	—	2	1	no	—
51	C₂×C₈×C₁₃	—	4	2	no	—
52	C₂×C₈×C₁₃	—	4	4	no	—
53	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
54	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
56	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
57	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
60	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
61	C₄×Dic₁₃	—	2	1	no	—
62	C₄×Dic₁₃	—	2	1	no	—
63	C₄×Dic₁₃	—	2	4	no	—
64	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
65	C₄×Dic₁₃	M₁₆	1	2	yes	—
66	C₄×Dic₁₃	SD₁₆	1	8	yes	—
67	C₂×#1055	—	2	1	no	—
68	C₂×#1055	—	2	1	no	—
69	C₂×#1055	—	4	2	no	—
70	C₂×#1055	—	4	4	no	—
71	C₂×#1055	C₄⋊C₄	1	2	yes	—
72	C₂×#1055	C₄⋊C₄	1	2	yes	—
73	C₂×#1055	C₂×C₈	1	2	yes	—
74	C₂×#1055	M₁₆	1	2	yes	—
75	#1842	—	13	2	no	—
76	C₄²×C₈	—	13	1	no	—
77	C₂×#334	—	13	2	no	—
78	C₂×#334	—	13	1	no	—
79	C₂×#334	D₁₃	1	1	yes	characteristic
80	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	—
93	C₂×Dic₁₃	—	2	2	no	—
94	C₂×Dic₁₃	—	2	2	no	—
95	C₂×Dic₁₃	C₄⋊C₈	1	4	yes	—
96	C₂×Dic₁₃	#106	1	4	yes	—
97	C₂×Dic₁₃	#106	1	4	yes	—
98	C₂×Dic₁₃	#108	1	4	yes	—
99	C₈×C₁₃	—	2	2	no	—
100	C₈×C₁₃	—	8	2	no	—
101	C₈×C₁₃	C₄⋊C₈	1	4	yes	complemented
102	#1055	—	2	2	no	—
103	#1055	—	8	2	no	—
104	#1055	C₄⋊C₈	1	4	yes	complemented
105	C₂×C₄⋊C₈	—	13	2	no	—
106	C₂×C₄⋊C₈	—	26	4	no	—
107	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
108	C₂×C₄×C₈	—	13	1	no	—
109	C₂×C₄×C₈	—	13	1	no	—
110	C₂×C₄×C₈	—	13	1	no	—
111	C₂×C₄×C₈	—	13	1	no	—
112	C₂×C₄×C₈	—	13	1	no	—
113	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
114	C₄³	—	13	1	no	—
115	#334	—	2	2	no	—
116	#334	—	26	4	no	—
117	#334	—	26	2	no	—
118	C₂²×C₁₃	#384	1	1	yes	characteristic
119	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
120	C₂²×C₁₃	#423	1	1	yes	characteristic
121	C₂²×C₁₃	C₂×#106	1	2	yes	—
122	C₂²×C₁₃	C₂×#108	1	2	yes	—
123	C₄×C₁₃	—	2	1	no	—
124	C₄×C₁₃	—	2	1	no	—
125	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
126	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
127	C₄×C₁₃	#423	1	1	yes	characteristic
128	C₄×C₁₃	#423	1	1	yes	characteristic
129	C₄×C₁₃	#492	1	2	yes	—
130	C₄×C₁₃	#498	1	2	yes	—
131	Dic₁₃	—	2	4	no	—
132	Dic₁₃	#334	1	8	yes	complemented
133	C₂²×C₈	—	2	2	no	—
134	C₂²×C₈	—	13	1	no	—
135	C₂²×C₈	—	13	1	no	—
136	C₂²×C₈	—	26	2	no	—
137	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
138	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
139	C₂×C₄²	—	13	1	no	—
140	C₂×C₄²	—	13	2	no	—
141	C₂×C₄²	—	13	1	no	—
142	C₂×C₄²	—	13	2	no	—
143	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
144	C₄⋊C₈	—	2	2	no	—
145	C₄⋊C₈	—	2	2	no	—
146	C₄⋊C₈	—	26	2	no	—
147	C₄⋊C₈	—	26	2	no	—
148	C₄⋊C₈	—	52	8	no	—
149	C₄×C₈	—	13	4	no	—
150	C₄×C₈	—	13	2	no	—
151	C₄×C₈	—	13	2	no	—
152	C₄×C₈	—	26	2	no	—
153	C₄×C₈	—	26	2	no	—
154	C₄×C₈	—	26	2	no	—
155	C₄×C₈	Dic₂₆	1	2	yes	—
156	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
157	C₂×C₁₃	C₂×#334	1	2	yes	—
158	C₂×C₁₃	#1566	1	2	yes	—
159	C₂×C₁₃	#1842	1	1	yes	characteristic
160	C₂×C₁₃	#1844	1	1	yes	characteristic
161	C₂×C₁₃	#1848	1	1	yes	characteristic
162	C₂²×C₄	—	13	2	no	—
163	C₂²×C₄	—	13	2	no	—
164	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
165	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
166	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
167	C₂×C₈	—	2	1	no	—
168	C₂×C₈	—	2	1	no	—
169	C₂×C₈	—	4	4	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	13	2	no	—
172	C₂×C₈	—	13	2	no	—
173	C₂×C₈	—	13	2	no	—
174	C₂×C₈	—	13	2	no	—
175	C₂×C₈	—	26	1	no	—
176	C₂×C₈	—	26	1	no	—
177	C₂×C₈	—	52	4	no	—
178	C₂×C₈	—	52	2	no	—
179	C₂×C₈	C₈×D₁₃	1	2	yes	—
180	C₂×C₈	#6094	1	2	yes	—
181	C₂×C₈	#6101	1	2	yes	—
182	C₂×C₈	#6101	1	2	yes	—
183	C₄²	—	13	2	no	—
184	C₄²	—	13	2	no	—
185	C₄²	—	13	8	no	—
186	C₄²	—	26	4	no	—
187	C₄²	—	26	1	no	—
188	C₄²	—	26	1	no	—
189	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
190	C₄²	D₄×D₁₃	1	1	yes	characteristic
191	C₄²	Q₈×D₁₃	1	1	yes	characteristic
192	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
193	C₁₃	#8805	1	1	yes	characteristic, complemented, Sylow
194	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	13	4	no	—
197	C₂×C₄	—	13	4	no	—
198	C₂×C₄	—	13	4	no	—
199	C₂×C₄	—	13	4	no	—
200	C₂×C₄	—	26	2	no	—
201	C₂×C₄	—	26	2	no	—
202	C₂×C₄	#88142	1	1	yes	characteristic
203	C₂×C₄	#88142	1	1	yes	characteristic
204	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
205	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
206	C₂×C₄	C₂×#6094	1	1	yes	characteristic
207	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
208	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
209	C₂×C₄	SD₁₆×D₁₃	1	4	yes	—
210	C₂×C₄	C₂×#6101	1	1	yes	characteristic
211	C₂×C₄	#88194	1	1	yes	characteristic
212	C₂×C₄	#88198	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	8	2	no	—
215	C₈	—	13	4	no	—
216	C₈	—	26	2	no	—
217	C₈	—	104	2	no	—
218	C₈	#88054	1	4	yes	complemented
219	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
220	C₂²	#11718498	1	1	yes	characteristic
221	C₂²	D₁₃×#106	1	2	yes	—
222	C₂²	D₁₃×#108	1	2	yes	—
223	C₂²	#11718637	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	13	8	no	—
227	C₄	—	26	4	no	—
228	C₄	D₁₃×C₄⋊C₈	1	1	yes	characteristic
229	C₄	#11718498	1	1	yes	characteristic
230	C₄	#11718516	1	2	yes	—
231	C₄	C₂×#88054	1	1	yes	characteristic
232	C₄	#11718779	1	1	yes	characteristic
233	C₄	#11718836	1	2	yes	—
234	C₂	D₁₃×#334	1	2	yes	—
235	C₂	#13113590	1	2	yes	—
236	C₂	#13114987	1	1	yes	characteristic
237	C₂	#13114991	1	1	yes	characteristic
238	C₂	#13115006	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#334	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#334	D₁₃
hypocenter	C₁₃	#8805
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
38. C₈×Dic₁₃	C₈	semidirect
101. C₈×C₁₃	C₄⋊C₈	semidirect
104. #1055	C₄⋊C₈	semidirect
132. Dic₁₃	#334	semidirect
193. C₁₃	#8805	semidirect
218. C₈	#88054	semidirect

Maximal subgroups

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

subgroup	index
#13114987	2
C₄×C₈×Dic₁₃	2
C₂×#11718049	2
C₂×#11718072	2
C₂×C₁₃×#334	2
#8805	13