Subgroups — #16015964

Order 3328.

658 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718562	C₂	1	1	yes	maximal, characteristic
2	#13123432	C₂	1	2	yes	maximal
3	#13116623	C₂	1	4	yes	maximal, complemented
4	#13116622	C₂	1	2	yes	maximal, complemented
5	#13116620	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116619	C₂	1	2	yes	maximal, complemented
7	D₁₃×#367	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#367	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#88155	C₂²	1	1	yes	characteristic
10	#11719209	—	2	2	no	—
11	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#107	C₂²	1	2	yes	—
13	#11718767	C₂²	1	2	yes	—
14	C₂×#88052	C₂²	1	1	yes	characteristic
15	#11718625	—	2	2	no	—
16	#11718562	C₄	1	8	yes	complemented
17	C₂×#88038	C₂²	1	2	yes	—
18	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
19	#11718542	—	2	4	no	—
20	#11718541	C₂²	1	4	yes	—
21	D₁₃×#107	C₂²	1	4	yes	—
22	C₁₃×#367	C₂²	1	2	yes	—
23	C₁₃×#367	C₂²	1	2	yes	—
24	#11718097	C₂²	1	1	yes	characteristic
25	#11718097	C₂²	1	1	yes	characteristic
26	#11718096	C₂²	1	2	yes	—
27	#11718082	C₂²	1	4	yes	—
28	#11718081	C₂²	1	4	yes	—
29	C₂×#6127	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₄×C₂²⋊D₁₃	—	4	4	no	—
33	#88180	—	2	2	no	—
34	C₂×#6099	D₄	1	1	yes	characteristic
35	#88155	C₂×C₄	1	4	yes	—
36	#88155	Q₈	1	4	yes	—
37	C₂×#6094	D₄	1	2	yes	—
38	C₂×C₈×D₁₃	C₂³	1	2	yes	—
39	#88147	—	4	2	no	—
40	#88146	—	2	4	no	—
41	C₄⋊C₄×D₁₃	—	2	4	no	—
42	#88141	—	4	2	no	—
43	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	complemented
44	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
46	C₁₃×#107	—	2	2	no	—
47	C₁₃×#107	C₂³	1	4	yes	—
48	#88058	C₂³	1	2	yes	—
49	#88058	C₂³	1	2	yes	—
50	#88057	—	2	2	no	—
51	#88052	C₂×C₄	1	4	yes	complemented
52	C₂×#6090	C₂³	1	2	yes	—
53	#88048	—	2	4	no	—
54	#88047	—	2	4	no	—
55	#88038	C₂×C₄	1	8	yes	complemented
56	C₁₆×D₁₃	C₂×C₄	1	8	yes	complemented
57	#33411	—	13	1	no	maximal, Sylow
58	C₂²×C₄×C₁₃	—	4	2	no	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₁₃	D₈	1	2	yes	—
61	#6127	C₄⋊C₄	1	4	yes	—
62	#6127	Q₁₆	1	4	yes	—
63	C₂×D₅₂	D₈	1	1	yes	characteristic
64	C₂×C₄×D₁₃	—	4	4	no	—
65	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
66	C₂×Dic₂₆	D₈	1	1	yes	characteristic
67	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
68	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
70	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
71	C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₂²⋊Dic₁₃	—	4	2	no	—
74	#6103	—	4	4	no	—
75	C₄⋊Dic₁₃	—	2	2	no	—
76	C₄⋊Dic₁₃	—	2	2	no	—
77	#6101	—	4	4	no	—
78	C₄×Dic₁₃	—	4	2	no	—
79	C₄×Dic₁₃	—	4	4	no	—
80	#6099	C₄⋊C₄	1	4	yes	—
81	C₂×#1055	C₂×D₄	1	2	yes	—
82	#6094	C₄⋊C₄	1	8	yes	—
83	C₈×D₁₃	C₂²×C₄	1	4	yes	—
84	C₈×D₁₃	C₂×Q₈	1	4	yes	—
85	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
86	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
87	#6090	C₂²×C₄	1	4	yes	—
88	C₂×#504	—	13	1	no	—
89	#2913	—	13	2	no	—
90	#2159	—	13	2	no	—
91	#2159	—	13	4	no	—
92	#2158	—	13	1	no	—
93	#2158	—	13	2	no	—
94	C₂×#367	—	13	2	no	—
95	C₂×#367	D₁₃	1	1	yes	characteristic, complemented
96	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
97	C₂²×D₁₃	C₂×D₈	1	2	yes	—
98	C₂×C₄×C₁₃	—	4	4	no	—
99	C₂×C₄×C₁₃	—	16	2	no	—
100	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
101	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
103	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
104	C₂²⋊D₁₃	#107	1	8	yes	—
105	C₂×Dic₁₃	—	4	2	no	—
106	C₂×Dic₁₃	—	4	2	no	—
107	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
108	D₅₂	#107	1	4	yes	—
109	C₄×D₁₃	—	16	4	no	—
110	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
111	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
112	Dic₂₆	#107	1	4	yes	—
113	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
114	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
115	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
116	#1055	C₂×C₄⋊C₄	1	4	yes	—
117	C₂×#131	—	13	1	no	—
118	#520	—	26	2	no	—
119	#504	—	13	8	no	—
120	C₂×M₃₂	—	13	1	no	—
121	C₂×M₃₂	—	13	2	no	—
122	C₂²×C₁₆	—	13	2	no	—
123	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
124	#428	—	26	4	no	—
125	#428	—	26	2	no	—
126	#427	—	13	2	no	—
127	#427	—	13	4	no	—
128	C₂×#107	—	13	4	no	—
129	C₂×#107	C₂×D₁₃	1	2	yes	—
130	#367	—	13	1	no	—
131	#367	—	13	1	no	—
132	#367	—	13	4	no	—
133	#367	C₂×D₁₃	1	2	yes	—
134	#367	C₂×D₁₃	1	2	yes	—
135	#366	—	13	2	no	—
136	#366	—	13	4	no	—
137	C₂²×C₁₃	—	2	2	no	—
138	C₂²×C₁₃	C₂×#107	1	2	yes	—
139	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
140	C₂×D₁₃	—	2	4	no	—
141	C₂×D₁₃	C₂×#107	1	4	yes	—
142	C₄×C₁₃	—	8	4	no	—
143	C₄×C₁₃	C₂×#107	1	2	yes	—
144	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
145	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
146	Dic₁₃	—	8	2	no	—
147	Dic₁₃	—	8	2	no	—
148	Dic₁₃	C₂×#107	1	4	yes	—
149	C₂×#41	—	13	1	no	—
150	#131	—	13	4	no	—
151	#131	—	13	4	no	—
152	C₂×M₁₆	—	13	1	no	—
153	C₂×M₁₆	—	13	2	no	—
154	C₂²×C₈	—	13	2	no	—
155	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
156	C₄×Q₈	—	52	2	no	—
157	C₄×D₄	—	52	2	no	—
158	C₄×D₄	—	52	4	no	—
159	#117	—	26	4	no	—
160	#117	—	26	2	no	—
161	C₂×C₄⋊C₄	—	2	2	no	—
162	C₂×C₄⋊C₄	—	26	4	no	—
163	M₃₂	—	13	4	no	—
164	M₃₂	—	13	8	no	—
165	C₂×C₁₆	—	13	2	no	—
166	C₂×C₁₆	—	13	8	no	—
167	C₂×C₁₆	C₄×D₁₃	1	4	yes	complemented
168	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
169	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
170	#107	—	2	2	no	—
171	#107	—	13	2	no	—
172	#107	—	13	2	no	—
173	#107	—	26	4	no	—
174	#107	C₂²×D₁₃	1	4	yes	—
175	#106	—	26	4	no	—
176	#106	—	26	2	no	—
177	C₂×C₁₃	—	2	2	no	—
178	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
179	C₂×C₁₃	#3416	1	2	yes	—
180	D₁₃	—	2	4	no	—
181	#41	—	13	4	no	—
182	#41	—	13	4	no	—
183	C₂×Q₈	—	13	1	no	—
184	C₂×D₄	—	13	2	no	—
185	C₂×D₄	—	13	1	no	—
186	C₂²×C₄	—	4	2	no	—
187	C₂²×C₄	—	13	2	no	—
188	C₂²×C₄	—	52	4	no	—
189	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
190	M₁₆	—	13	4	no	—
191	M₁₆	—	13	8	no	—
192	C₂×C₈	—	13	2	no	—
193	C₂×C₈	—	13	4	no	—
194	C₂×C₈	—	13	4	no	—
195	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
196	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
197	C₂×C₈	Q₈×D₁₃	1	2	yes	—
198	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
199	C₄⋊C₄	—	2	4	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	26	2	no	—
202	C₄⋊C₄	—	26	2	no	—
203	C₄⋊C₄	—	52	4	no	—
204	C₂²⋊C₄	—	52	4	no	—
205	C₂²⋊C₄	—	52	2	no	—
206	C₄²	—	52	4	no	—
207	C₄²	—	52	2	no	—
208	C₁₆	—	13	4	no	—
209	C₁₆	C₂×C₄×D₁₃	1	2	yes	—
210	C₁₆	C₂×C₄×D₁₃	1	2	yes	—
211	C₁₃	#33411	1	1	yes	characteristic, complemented, Sylow
212	C₂³	—	13	2	no	—
213	C₂³	D₈×D₁₃	1	1	yes	characteristic
214	Q₈	—	13	4	no	—
215	D₄	—	13	8	no	—
216	D₄	—	13	4	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	—	13	2	no	—
219	C₂×C₄	—	13	4	no	—
220	C₂×C₄	—	13	4	no	—
221	C₂×C₄	—	16	2	no	—
222	C₂×C₄	—	52	2	no	—
223	C₂×C₄	—	52	2	no	—
224	C₂×C₄	—	208	4	no	—
225	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
226	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
227	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
228	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
229	C₈	—	13	4	no	—
230	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
231	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
232	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
233	C₂²	—	2	2	no	—
234	C₂²	—	13	4	no	—
235	C₂²	—	26	4	no	—
236	C₂²	D₁₃×#107	1	2	yes	—
237	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
238	C₄	—	8	4	no	—
239	C₄	—	13	4	no	—
240	C₄	—	104	2	no	—
241	C₄	—	104	2	no	—
242	C₄	D₁₃×#107	1	2	yes	—
243	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
244	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
245	C₂	—	2	2	no	—
246	C₂	—	26	4	no	—
247	C₂	C₂×D₁₃×#107	1	1	yes	characteristic
248	C₂	#13127978	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#367	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×#6127	D₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#367	D₁₃
hypocenter	C₁₃	#33411
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#367

Complements

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

N	H ≅ G/N	type
3. #13116623	C₂	semidirect
4. #13116622	C₂	semidirect
5. #13116620	C₂	semidirect
6. #13116619	C₂	semidirect
7. D₁₃×#367	C₂	semidirect
8. C₂×C₁₃×#367	C₂	semidirect
16. #11718562	C₄	semidirect
43. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
51. #88052	C₂×C₄	semidirect
55. #88038	C₂×C₄	semidirect
56. C₁₆×D₁₃	C₂×C₄	semidirect
95. C₂×#367	D₁₃	semidirect
167. C₂×C₁₆	C₄×D₁₃	semidirect
211. C₁₃	#33411	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718562	2
#13123432	2
#13116623	2
#13116622	2
#13116620	2
#13116619	2
D₁₃×#367	2
C₂×C₁₃×#367	2
#33411	13