Subgroups — #18082395

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564597	C₂	1	1	yes	maximal, characteristic
2	#14564597	C₂	1	1	yes	maximal, characteristic
3	#14564597	C₂	1	1	yes	maximal, characteristic
4	#14564438	C₂	1	1	yes	maximal, characteristic
5	#14563763	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926265	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#487	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597292	—	2	2	no	—
9	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#11926414	C₂²	1	1	yes	characteristic
12	#11926414	C₂²	1	1	yes	characteristic
13	#11926307	—	2	2	no	—
14	#11926306	—	2	2	no	—
15	#11926306	—	2	2	no	—
16	#11926306	—	2	2	no	—
17	#11926265	—	2	2	no	—
18	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#487	—	2	2	no	—
21	C₁₉×#487	C₄	1	4	yes	complemented
22	C₂×C₁₉×#103	—	2	2	no	—
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	—	2	1	no	—
25	C₂²×Q₈×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	—	2	1	no	—
28	C₁₉×C₄⋊Q₈	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
34	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	—	2	1	no	—
44	C₂×C₄⋊Dic₁₉	—	2	1	no	—
45	C₂×C₄⋊Dic₁₉	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
47	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
48	C₁₉×#103	—	2	8	no	—
49	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₁₉	D₄	1	2	yes	—
51	#10597292	—	4	4	no	—
52	C₄×C₁₉⋊C₈	—	2	1	no	—
53	C₄×C₁₉⋊C₈	—	2	1	no	—
54	C₄×C₁₉⋊C₈	—	2	1	no	—
55	C₄×C₁₉⋊C₈	—	2	1	no	—
56	C₂×Q₈×C₁₉	—	2	2	no	—
57	C₂×Q₈×C₁₉	—	2	2	no	—
58	C₂×Q₈×C₁₉	—	4	1	no	—
59	C₂×Q₈×C₁₉	—	4	1	no	—
60	C₂×Q₈×C₁₉	—	4	2	no	—
61	C₂×Q₈×C₁₉	—	4	2	no	—
62	C₂×Q₈×C₁₉	—	4	2	no	—
63	C₂×Q₈×C₁₉	—	4	2	no	—
64	C₂²×C₄×C₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	—	4	1	no	—
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×Dic₁₉	—	4	1	no	—
70	C₂²×Dic₁₉	—	4	1	no	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
74	C₄⋊C₄×C₁₉	—	2	2	no	—
75	C₄⋊C₄×C₁₉	—	2	2	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₄⋊C₄×C₁₉	—	4	1	no	—
79	C₄⋊C₄×C₁₉	—	4	1	no	—
80	C₄⋊C₄×C₁₉	—	4	1	no	—
81	C₄⋊C₄×C₁₉	—	4	1	no	—
82	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₄²×C₁₉	#41	1	1	yes	characteristic
85	C₄²×C₁₉	#41	1	1	yes	characteristic
86	C₄⋊Dic₁₉	—	4	2	no	—
87	C₄⋊Dic₁₉	—	4	2	no	—
88	C₄⋊Dic₁₉	—	4	2	no	—
89	C₄⋊Dic₁₉	—	4	2	no	—
90	C₄⋊Dic₁₉	—	4	2	no	—
91	C₄⋊Dic₁₉	—	4	2	no	—
92	C₂×C₁₉⋊C₈	—	2	2	no	—
93	C₂×C₁₉⋊C₈	—	2	2	no	—
94	C₂×C₁₉⋊C₈	—	2	2	no	—
95	C₂×C₁₉⋊C₈	—	2	2	no	—
96	C₂×C₁₉⋊C₈	—	2	2	no	—
97	C₂×C₁₉⋊C₈	—	2	2	no	—
98	#9840	—	19	1	no	maximal, Sylow
99	C₂³×C₁₉	#127	1	1	yes	characteristic
100	Q₈×C₁₉	—	4	4	no	—
101	Q₈×C₁₉	—	4	4	no	—
102	Q₈×C₁₉	—	8	2	no	—
103	Q₈×C₁₉	—	8	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	8	1	no	—
107	C₂×C₄×C₁₉	—	8	1	no	—
108	C₂×C₄×C₁₉	—	8	1	no	—
109	C₂×C₄×C₁₉	—	8	1	no	—
110	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
115	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
116	C₂×C₄×C₁₉	#135	1	2	yes	—
117	C₂×C₄×C₁₉	#135	1	2	yes	—
118	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
119	C₂×C₄×C₁₉	#137	1	2	yes	—
120	C₂×C₄×C₁₉	#137	1	2	yes	—
121	C₂×C₄×C₁₉	#137	1	2	yes	—
122	C₂×Dic₁₉	—	8	1	no	—
123	C₂×Dic₁₉	—	8	1	no	—
124	C₂×Dic₁₉	—	8	1	no	—
125	C₂×Dic₁₉	—	8	1	no	—
126	C₂×Dic₁₉	—	8	1	no	—
127	C₂×Dic₁₉	—	8	1	no	—
128	C₈×C₁₉	—	2	4	no	—
129	C₁₉⋊C₈	—	4	2	no	—
130	C₁₉⋊C₈	—	4	2	no	—
131	C₂×#487	D₁₉	1	1	yes	characteristic
132	#1990	—	19	1	no	—
133	#1990	—	19	1	no	—
134	#1990	—	19	1	no	—
135	#1956	—	19	1	no	—
136	#1834	—	19	1	no	—
137	C₂×#322	—	19	1	no	—
138	C₂²×C₁₉	#390	1	1	yes	characteristic
139	C₂²×C₁₉	#495	1	1	yes	characteristic
140	C₂²×C₁₉	#495	1	1	yes	characteristic
141	C₂²×C₁₉	#496	1	1	yes	characteristic
142	C₂²×C₁₉	#497	1	1	yes	characteristic
143	C₂²×C₁₉	#497	1	1	yes	characteristic
144	C₂²×C₁₉	#497	1	1	yes	characteristic
145	C₄×C₁₉	—	8	2	no	—
146	C₄×C₁₉	—	8	2	no	—
147	C₄×C₁₉	#416	1	2	yes	—
148	C₄×C₁₉	#440	1	2	yes	—
149	C₄×C₁₉	#441	1	2	yes	—
150	C₄×C₁₉	#468	1	2	yes	—
151	C₄×C₁₉	#470	1	2	yes	—
152	C₄×C₁₉	#488	1	2	yes	—
153	Dic₁₉	—	16	1	no	—
154	Dic₁₉	—	16	1	no	—
155	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
156	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
157	#487	—	2	2	no	—
158	#487	Dic₁₉	1	4	yes	complemented
159	C₂×#103	—	2	2	no	—
160	C₂×#103	—	38	2	no	—
161	C₂×C₄×C₈	—	19	1	no	—
162	C₂×C₄×C₈	—	19	1	no	—
163	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
164	#384	—	19	1	no	—
165	#384	—	19	1	no	—
166	#340	—	38	2	no	—
167	#340	—	38	2	no	—
168	#340	—	38	2	no	—
169	#340	—	38	2	no	—
170	#322	—	38	2	no	—
171	C₂×C₁₉	#1718	1	1	yes	characteristic
172	C₂×C₁₉	#1718	1	1	yes	characteristic
173	C₂×C₁₉	#1719	1	1	yes	characteristic
174	C₂×C₁₉	#1720	1	1	yes	characteristic
175	C₂×C₁₉	#1958	1	1	yes	characteristic
176	C₂×C₁₉	#1971	1	1	yes	characteristic
177	C₂×C₁₉	#1973	1	1	yes	characteristic
178	C₂²×Q₈	—	2	1	no	—
179	C₂²×Q₈	—	2	1	no	—
180	C₂²×C₈	—	19	2	no	—
181	C₂²×C₈	—	19	2	no	—
182	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
183	C₄⋊Q₈	—	2	1	no	—
184	C₄⋊Q₈	—	2	1	no	—
185	C₄⋊Q₈	—	2	1	no	—
186	C₄⋊Q₈	—	2	1	no	—
187	C₄⋊Q₈	—	2	1	no	—
188	C₄⋊Q₈	—	2	1	no	—
189	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
190	C₄⋊Q₈	C₂×Dic₁₉	1	2	yes	—
191	C₂×C₄⋊C₄	—	2	1	no	—
192	C₂×C₄⋊C₄	—	2	1	no	—
193	C₂×C₄⋊C₄	—	2	1	no	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₄⋊C₄	—	38	1	no	—
196	C₂×C₄⋊C₄	—	38	1	no	—
197	C₂×C₄⋊C₄	—	38	1	no	—
198	C₂×C₄⋊C₄	—	38	1	no	—
199	C₂×C₄⋊C₄	—	38	1	no	—
200	C₂×C₄⋊C₄	—	38	1	no	—
201	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
202	#103	—	2	8	no	—
203	#103	—	76	4	no	—
204	C₄×C₈	—	38	1	no	—
205	C₄×C₈	—	38	1	no	—
206	C₄×C₈	—	38	1	no	—
207	C₄×C₈	—	38	1	no	—
208	C₄×C₈	C₂×Dic₁₉	1	2	yes	—
209	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
210	C₁₉	#9840	1	1	yes	characteristic, complemented, Sylow
211	C₂×Q₈	—	2	2	no	—
212	C₂×Q₈	—	2	2	no	—
213	C₂×Q₈	—	4	1	no	—
214	C₂×Q₈	—	4	1	no	—
215	C₂×Q₈	—	4	2	no	—
216	C₂×Q₈	—	4	2	no	—
217	C₂×Q₈	—	4	2	no	—
218	C₂×Q₈	—	4	2	no	—
219	C₂²×C₄	—	4	1	no	—
220	C₂²×C₄	—	4	1	no	—
221	C₂²×C₄	—	76	1	no	—
222	C₂²×C₄	—	76	1	no	—
223	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
224	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	38	2	no	—
229	C₂×C₈	—	38	2	no	—
230	C₂×C₈	—	38	2	no	—
231	C₂×C₈	—	38	2	no	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	—	38	2	no	—
234	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	—	2	2	no	—
238	C₄⋊C₄	—	2	2	no	—
239	C₄⋊C₄	—	4	1	no	—
240	C₄⋊C₄	—	4	1	no	—
241	C₄⋊C₄	—	4	1	no	—
242	C₄⋊C₄	—	4	1	no	—
243	C₄⋊C₄	—	76	2	no	—
244	C₄⋊C₄	—	76	2	no	—
245	C₄⋊C₄	—	76	2	no	—
246	C₄⋊C₄	—	76	2	no	—
247	C₄⋊C₄	—	76	2	no	—
248	C₄⋊C₄	—	76	2	no	—
249	C₄²	#64543	1	1	yes	characteristic
250	C₄²	#64543	1	1	yes	characteristic
251	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
252	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
253	C₂³	#10597386	1	1	yes	characteristic
254	Q₈	—	4	4	no	—
255	Q₈	—	4	4	no	—
256	Q₈	—	8	2	no	—
257	Q₈	—	8	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	8	1	no	—
261	C₂×C₄	—	8	1	no	—
262	C₂×C₄	—	8	1	no	—
263	C₂×C₄	—	8	1	no	—
264	C₂×C₄	—	152	1	no	—
265	C₂×C₄	—	152	1	no	—
266	C₂×C₄	—	152	1	no	—
267	C₂×C₄	—	152	1	no	—
268	C₂×C₄	—	152	1	no	—
269	C₂×C₄	—	152	1	no	—
270	C₂×C₄	#10597360	1	2	yes	—
271	C₂×C₄	#10597361	1	2	yes	—
272	C₂×C₄	#10597364	1	2	yes	—
273	C₂×C₄	#10597364	1	2	yes	—
274	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
275	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
276	C₂×C₄	#10597382	1	1	yes	characteristic
277	C₂×C₄	#10597384	1	1	yes	characteristic
278	C₂×C₄	#10597384	1	1	yes	characteristic
279	C₂×C₄	#10597396	1	2	yes	—
280	C₂×C₄	#10597396	1	2	yes	—
281	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
282	C₈	—	2	4	no	—
283	C₈	—	76	2	no	—
284	C₈	—	76	2	no	—
285	C₂²	#11926447	1	1	yes	characteristic
286	C₂²	#11926926	1	1	yes	characteristic
287	C₂²	#11926926	1	1	yes	characteristic
288	C₂²	#11926930	1	1	yes	characteristic
289	C₂²	#11926935	1	1	yes	characteristic
290	C₂²	#11926937	1	1	yes	characteristic
291	C₂²	#11926937	1	1	yes	characteristic
292	C₄	—	8	2	no	—
293	C₄	—	8	2	no	—
294	C₄	—	304	1	no	—
295	C₄	—	304	1	no	—
296	C₄	#11926540	1	2	yes	—
297	C₄	#11926645	1	2	yes	—
298	C₄	#11926651	1	2	yes	—
299	C₄	#11926787	1	2	yes	—
300	C₄	#11926799	1	2	yes	—
301	C₄	#11926898	1	2	yes	—
302	C₂	#14563278	1	1	yes	characteristic
303	C₂	#14563282	1	1	yes	characteristic
304	C₂	#14563289	1	1	yes	characteristic
305	C₂	#14563292	1	1	yes	characteristic
306	C₂	#14564447	1	1	yes	characteristic
307	C₂	#14564507	1	1	yes	characteristic
308	C₂	#14564518	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#487	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#487	D₁₉
hypocenter	C₁₉	#9840
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#487

Complements

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

N	H ≅ G/N	type
21. C₁₉×#487	C₄	semidirect
158. #487	Dic₁₉	semidirect
210. C₁₉	#9840	semidirect

Maximal subgroups

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

subgroup	index
#14564597	2
#14564438	2
#14563763	2
C₂×#11926265	2
C₂×C₁₉×#487	2
#9840	19