Subgroups — #15781988

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718343	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718156	C₂	1	2	yes	maximal
3	#13112927	C₂	1	2	yes	maximal
4	#13112914	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
7	C₂×#88123	—	2	1	no	—
8	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#103	—	2	1	no	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#391	—	2	1	no	—
12	C₂×#88058	—	2	1	no	—
13	C₂×#88058	C₂²	1	2	yes	—
14	C₂²×#6090	C₂²	1	2	yes	—
15	#11718343	—	2	4	no	—
16	#11718156	—	2	4	no	—
17	C₂²×Q₈×C₁₃	—	2	1	no	—
18	C₂²×Dic₂₆	—	4	1	no	—
19	C₂×C₁₃×Q₁₆	—	2	2	no	—
20	C₂×C₁₃×Q₁₆	—	2	2	no	—
21	C₂×C₁₃×Q₁₆	—	2	1	no	—
22	C₂×C₁₃×Q₁₆	Q₈	1	2	yes	complemented
23	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
26	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₃	—	2	2	no	—
28	C₂×C₄⋊Dic₁₃	—	4	1	no	—
29	#88123	—	2	4	no	—
30	#88123	—	4	2	no	—
31	C₁₃×#107	—	2	2	no	—
32	C₁₃×#103	—	4	2	no	—
33	C₄×C₈×C₁₃	—	2	2	no	—
34	C₁₃×#95	—	4	1	no	—
35	C₁₃×#95	—	4	1	no	—
36	#88058	—	2	4	no	—
37	#88058	—	2	2	no	—
38	#88058	D₄	1	4	yes	—
39	C₂×#6090	—	2	2	no	—
40	C₂×#6090	—	2	2	no	—
41	C₂×#6090	—	2	2	no	—
42	#13364	—	13	1	no	maximal, Sylow
43	C₂×Q₈×C₁₃	—	2	2	no	—
44	C₂×Q₈×C₁₃	—	4	1	no	—
45	C₂×Q₈×C₁₃	—	4	1	no	—
46	C₂×Q₈×C₁₃	—	4	1	no	—
47	C₂×Q₈×C₁₃	—	4	1	no	—
48	C₂×Q₈×C₁₃	—	4	1	no	—
49	C₂²×C₄×C₁₃	—	4	1	no	—
50	C₂²×C₄×C₁₃	—	4	1	no	—
51	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₁₃	—	4	2	no	—
55	C₂×Dic₂₆	—	4	4	no	—
56	C₂×Dic₂₆	—	8	2	no	—
57	C₂×Dic₂₆	—	8	2	no	—
58	C₁₃×Q₁₆	—	2	4	no	—
59	C₁₃×Q₁₆	—	4	2	no	—
60	C₂×C₈×C₁₃	—	2	1	no	—
61	C₂×C₈×C₁₃	—	2	1	no	—
62	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
63	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
64	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₈×C₁₃	#41	1	2	yes	—
66	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
67	C₁₃×C₄⋊C₄	—	4	1	no	—
68	C₁₃×C₄⋊C₄	—	4	1	no	—
69	C₄²×C₁₃	—	2	1	no	—
70	C₄²×C₁₃	—	2	1	no	—
71	C₄⋊Dic₁₃	—	2	4	no	—
72	C₄⋊Dic₁₃	—	4	4	no	—
73	C₄⋊Dic₁₃	—	4	2	no	—
74	#6090	—	4	2	no	—
75	C₂×#500	—	13	1	no	—
76	C₂×#358	—	13	2	no	—
77	#1969	D₁₃	1	1	yes	characteristic
78	#1380	—	13	2	no	—
79	#1374	—	13	1	no	—
80	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
81	Q₈×C₁₃	—	4	2	no	—
82	Q₈×C₁₃	—	4	2	no	—
83	Q₈×C₁₃	—	8	1	no	—
84	Q₈×C₁₃	—	8	1	no	—
85	C₂×C₄×C₁₃	—	2	1	no	—
86	C₂×C₄×C₁₃	—	2	1	no	—
87	C₂×C₄×C₁₃	—	2	1	no	—
88	C₂×C₄×C₁₃	—	2	1	no	—
89	C₂×C₄×C₁₃	—	4	2	no	—
90	C₂×C₄×C₁₃	—	8	1	no	—
91	C₂×C₄×C₁₃	—	8	1	no	—
92	C₂×C₄×C₁₃	—	8	1	no	—
93	C₂×C₄×C₁₃	—	8	1	no	—
94	C₂×C₄×C₁₃	—	8	1	no	—
95	C₂×C₄×C₁₃	SD₃₂	1	2	yes	—
96	C₂×C₄×C₁₃	Q₃₂	1	2	yes	—
97	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
103	C₂×Dic₁₃	—	4	4	no	—
104	C₂×Dic₁₃	—	8	2	no	—
105	C₂×Dic₁₃	—	8	2	no	—
106	Dic₂₆	—	8	8	no	—
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
109	C₈×C₁₃	#124	1	2	yes	—
110	C₂²×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
111	C₂×C₄⋊Q₈	—	26	1	no	—
112	C₂²×C₁₆	—	13	2	no	—
113	#500	—	26	4	no	—
114	C₂×#107	—	13	2	no	—
115	C₂×#107	—	26	1	no	—
116	C₂×#107	C₂×D₁₃	1	1	yes	characteristic
117	C₂×#103	—	2	1	no	—
118	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
119	#391	—	2	1	no	—
120	#358	—	26	4	no	—
121	C₂²×C₁₃	#447	1	1	yes	characteristic
122	C₂²×C₁₃	#474	1	1	yes	characteristic
123	C₂²×C₁₃	#486	1	1	yes	characteristic
124	C₂²×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
125	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
126	C₂²×C₁₃	#509	1	1	yes	characteristic
127	C₂²×C₁₃	#510	1	1	yes	characteristic
128	C₄×C₁₃	—	2	2	no	—
129	C₄×C₁₃	—	2	2	no	—
130	C₄×C₁₃	—	8	2	no	—
131	C₄×C₁₃	—	16	1	no	—
132	C₄×C₁₃	#393	1	1	yes	characteristic
133	C₄×C₁₃	#448	1	1	yes	characteristic
134	C₄×C₁₃	#476	1	1	yes	characteristic
135	C₄×C₁₃	#489	1	1	yes	characteristic
136	Dic₁₃	—	8	4	no	—
137	C₂²×Q₈	—	2	1	no	—
138	C₂²×Q₈	—	52	1	no	—
139	C₂×Q₁₆	—	2	1	no	—
140	C₂×Q₁₆	—	2	2	no	—
141	C₂×Q₁₆	—	2	2	no	—
142	C₂×Q₁₆	Dic₂₆	1	2	yes	complemented
143	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
144	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
145	C₄⋊Q₈	—	26	4	no	—
146	C₄⋊Q₈	—	52	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	26	2	no	—
149	C₂×C₄⋊C₄	—	52	1	no	—
150	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
151	C₂×C₁₆	—	26	2	no	—
152	C₂×C₁₆	—	26	2	no	—
153	C₂×C₁₆	—	26	2	no	—
154	#107	—	2	2	no	—
155	#107	—	13	4	no	—
156	#107	—	26	4	no	—
157	#107	—	26	2	no	—
158	#103	—	4	2	no	—
159	C₄×C₈	—	2	2	no	—
160	#95	—	4	1	no	—
161	#95	—	4	1	no	—
162	C₂×C₁₃	#2023	1	1	yes	characteristic
163	C₂×C₁₃	#2187	1	1	yes	characteristic
164	C₂×C₁₃	#2188	1	1	yes	characteristic
165	C₂×C₁₃	#2225	1	1	yes	characteristic
166	C₂×C₁₃	#2227	1	1	yes	characteristic
167	C₂×C₁₃	#2241	1	1	yes	characteristic
168	C₂×C₁₃	#2243	1	1	yes	characteristic
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	4	1	no	—
171	C₂×Q₈	—	4	1	no	—
172	C₂×Q₈	—	4	1	no	—
173	C₂×Q₈	—	4	1	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	52	4	no	—
176	C₂×Q₈	—	104	2	no	—
177	C₂×Q₈	—	104	2	no	—
178	C₂²×C₄	—	4	1	no	—
179	C₂²×C₄	—	4	1	no	—
180	C₂²×C₄	—	52	2	no	—
181	C₂²×C₄	#6104	1	1	yes	characteristic
182	C₂²×C₄	#6104	1	1	yes	characteristic
183	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
184	Q₁₆	—	2	4	no	—
185	Q₁₆	—	4	2	no	—
186	C₂×C₈	—	2	1	no	—
187	C₂×C₈	—	2	1	no	—
188	C₂×C₈	#6105	1	2	yes	—
189	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
190	C₂×C₈	#6127	1	1	yes	characteristic
191	C₂×C₈	D₄×D₁₃	1	2	yes	—
192	C₂×C₈	#6129	1	2	yes	—
193	C₄⋊C₄	—	4	1	no	—
194	C₄⋊C₄	—	4	1	no	—
195	C₄⋊C₄	—	26	4	no	—
196	C₄⋊C₄	—	52	4	no	—
197	C₄⋊C₄	—	52	2	no	—
198	C₄²	—	2	1	no	—
199	C₄²	—	2	1	no	—
200	C₁₆	—	52	2	no	—
201	C₁₃	#13364	1	1	yes	characteristic, complemented, Sylow
202	C₂³	C₂×#6104	1	1	yes	characteristic
203	Q₈	—	4	2	no	—
204	Q₈	—	4	2	no	—
205	Q₈	—	8	1	no	—
206	Q₈	—	8	1	no	—
207	Q₈	—	104	8	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	8	1	no	—
214	C₂×C₄	—	8	1	no	—
215	C₂×C₄	—	8	1	no	—
216	C₂×C₄	—	8	1	no	—
217	C₂×C₄	—	8	1	no	—
218	C₂×C₄	—	52	4	no	—
219	C₂×C₄	—	104	2	no	—
220	C₂×C₄	—	104	2	no	—
221	C₂×C₄	#88068	1	2	yes	—
222	C₂×C₄	#88069	1	2	yes	—
223	C₂×C₄	#88178	1	1	yes	characteristic
224	C₂×C₄	C₂×#6105	1	1	yes	characteristic
225	C₂×C₄	#88190	1	1	yes	characteristic
226	C₂×C₄	#88191	1	1	yes	characteristic
227	C₂×C₄	#88203	1	1	yes	characteristic
228	C₂×C₄	#88205	1	1	yes	characteristic
229	C₈	—	2	2	no	—
230	C₈	#88132	1	2	yes	—
231	C₈	#88139	1	2	yes	—
232	C₂²	#11718668	1	1	yes	characteristic
233	C₂²	#11718697	1	1	yes	characteristic
234	C₂²	#11718731	1	1	yes	characteristic
235	C₂²	C₂×#88068	1	1	yes	characteristic
236	C₂²	C₂×#88069	1	1	yes	characteristic
237	C₂²	#11718854	1	1	yes	characteristic
238	C₂²	#11718856	1	1	yes	characteristic
239	C₄	—	2	2	no	—
240	C₄	—	2	2	no	—
241	C₄	—	8	2	no	—
242	C₄	—	16	1	no	—
243	C₄	—	104	4	no	—
244	C₄	#11718608	1	1	yes	characteristic
245	C₄	#11718669	1	1	yes	characteristic
246	C₄	#11718701	1	1	yes	characteristic
247	C₄	#11718716	1	1	yes	characteristic
248	C₂	#13115972	1	1	yes	characteristic
249	C₂	#13116764	1	1	yes	characteristic
250	C₂	#13116769	1	1	yes	characteristic
251	C₂	#13116978	1	1	yes	characteristic
252	C₂	#13116988	1	1	yes	characteristic
253	C₂	#13117063	1	1	yes	characteristic
254	C₂	#13117072	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#6104
commutator, cosocle	C₂²×C₈×C₁₃	C₂³
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1969	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	#1969	D₁₃
hypocenter	C₁₃	#13364
LCS	G ▷ C₂²×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1969

Complements

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

N	H ≅ G/N	type
22. C₂×C₁₃×Q₁₆	Q₈	semidirect
142. C₂×Q₁₆	Dic₂₆	semidirect
201. C₁₃	#13364	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718343	2
C₂×#11718156	2
#13112927	2
#13112914	2
C₁₃×#1969	2
#13364	13