Subgroups — #18079336

Order 4864.

518 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573099	C₂	1	1	yes	maximal, characteristic
2	#14563645	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562196	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562035	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561531	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597378	—	2	1	no	—
9	#11927094	C₂²	1	1	yes	characteristic
10	#11926759	—	2	2	no	—
11	#11926749	C₄	1	2	yes	complemented
12	#11926739	C₄	1	2	yes	complemented
13	#11926568	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	#11926543	—	2	1	no	—
16	C₂×#10597289	—	2	1	no	—
17	#11926410	C₂²	1	1	yes	characteristic
18	#11926306	—	2	1	no	—
19	#11926279	—	2	2	no	—
20	#11926273	—	2	2	no	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#436	—	2	2	no	—
23	C₁₉×#436	—	2	2	no	—
24	C₁₉×#431	C₂²	1	1	yes	characteristic
25	C₁₉×#431	C₂²	1	1	yes	characteristic
26	C₁₉×#407	—	2	2	no	—
27	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	—	2	1	no	—
29	C₂×#64541	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	4	no	—
31	C₄×D₄×C₁₉	—	2	1	no	—
32	C₄×D₄×C₁₉	—	2	1	no	—
33	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
34	C₄×D₄×C₁₉	D₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×#64526	—	2	2	no	—
39	#10597378	—	4	2	no	—
40	#10597378	—	4	2	no	—
41	C₂×#64525	—	2	2	no	—
42	#10597376	—	2	1	no	—
43	#10597376	—	2	1	no	—
44	C₂×C₄⋊Dic₁₉	—	2	1	no	—
45	C₂×#64520	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	#10597321	—	2	1	no	—
48	#10597320	C₂×C₄	1	1	yes	characteristic
49	C₄×D₇₆	—	2	1	no	—
50	C₄×D₇₆	—	2	1	no	—
51	#10597315	C₂×C₄	1	1	yes	characteristic
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₂²⋊C₈	—	2	4	no	—
55	C₁₉×C₂²⋊C₈	—	2	1	no	—
56	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
57	C₄×C₈×C₁₉	—	2	1	no	—
58	C₄×C₈×C₁₉	D₄	1	2	yes	—
59	#10597289	—	4	2	no	—
60	C₁₉⋊#95	—	2	1	no	—
61	C₁₉⋊#95	—	2	1	no	—
62	#10597267	—	2	2	no	—
63	#10597266	—	2	2	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
68	C₂⁴×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	—	2	1	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	—	2	1	no	—
72	C₂×D₄×C₁₉	—	2	1	no	—
73	C₂×D₄×C₁₉	—	2	1	no	—
74	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	8	2	no	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
82	C₂×C₂²⋊D₁₉	—	4	1	no	—
83	C₂²×Dic₁₉	—	4	1	no	—
84	#64541	—	4	1	no	—
85	#64541	—	4	1	no	—
86	#64541	—	4	1	no	—
87	#64541	—	4	1	no	—
88	C₂×D₇₆	—	2	1	no	—
89	C₂×D₇₆	—	2	1	no	—
90	C₂×D₇₆	—	2	1	no	—
91	C₂×C₄×D₁₉	—	4	1	no	—
92	C₂×Dic₃₈	—	2	1	no	—
93	M₁₆×C₁₉	—	8	4	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
98	C₂²⋊C₄×C₁₉	—	2	2	no	—
99	C₂²⋊C₄×C₁₉	—	2	2	no	—
100	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	#64526	—	4	4	no	—
105	#64525	—	4	4	no	—
106	(C₂×D₁₉)⋊C₄	—	4	1	no	—
107	(C₂×D₁₉)⋊C₄	—	4	1	no	—
108	C₄⋊Dic₁₉	—	2	1	no	—
109	C₄⋊Dic₁₉	—	2	1	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	#64520	—	4	1	no	—
113	#64520	—	4	1	no	—
114	C₂×C₁₉⋊C₈	—	2	2	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	#9309	—	19	1	no	maximal, Sylow
119	C₂³×C₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	4	1	no	—
121	C₂³×C₁₉	—	4	1	no	—
122	C₂³×C₁₉	—	8	1	no	—
123	C₂³×C₁₉	—	8	1	no	—
124	C₂³×C₁₉	#121	1	1	yes	characteristic
125	C₂²×D₁₉	—	4	1	no	—
126	D₄×C₁₉	—	2	2	no	—
127	D₄×C₁₉	—	2	2	no	—
128	D₄×C₁₉	—	4	1	no	—
129	D₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	2	2	no	—
131	C₂×C₄×C₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	4	no	—
134	C₂×C₄×C₁₉	—	8	2	no	—
135	C₂×C₄×C₁₉	—	8	1	no	—
136	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
142	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
143	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
146	C₂²⋊D₁₉	—	8	1	no	—
147	C₂²⋊D₁₉	—	8	1	no	—
148	C₂×Dic₁₉	—	4	1	no	—
149	C₂×Dic₁₉	—	8	1	no	—
150	C₂×Dic₁₉	—	8	1	no	—
151	C₂×Dic₁₉	—	8	1	no	—
152	D₇₆	—	4	2	no	—
153	D₇₆	—	4	1	no	—
154	D₇₆	—	4	1	no	—
155	D₇₆	—	8	1	no	—
156	C₄×D₁₉	—	8	1	no	—
157	C₄×D₁₉	—	8	1	no	—
158	Dic₃₈	—	4	1	no	—
159	Dic₃₈	—	4	1	no	—
160	C₈×C₁₉	—	4	2	no	—
161	C₈×C₁₉	—	4	2	no	—
162	C₁₉⋊C₈	—	4	2	no	—
163	C₁₉⋊C₈	—	8	1	no	—
164	#3036	—	19	1	no	—
165	#2975	D₁₉	1	1	yes	characteristic, complemented
166	#1804	—	19	1	no	—
167	#1517	—	19	1	no	—
168	#1480	—	19	1	no	—
169	#1301	—	19	1	no	—
170	#1286	—	19	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	4	2	no	—
174	C₂²×C₁₉	—	4	2	no	—
175	C₂²×C₁₉	—	4	2	no	—
176	C₂²×C₁₉	—	8	2	no	—
177	C₂²×C₁₉	—	8	2	no	—
178	C₂²×C₁₉	#386	1	1	yes	characteristic
179	C₂²×C₁₉	#468	1	1	yes	characteristic
180	C₂²×C₁₉	#469	1	1	yes	characteristic
181	C₂×D₁₉	—	8	1	no	—
182	C₂×D₁₉	—	8	1	no	—
183	C₂×D₁₉	—	8	1	no	—
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	4	2	no	—
189	C₄×C₁₉	#417	1	1	yes	characteristic
190	C₄×C₁₉	#418	1	1	yes	characteristic
191	C₄×C₁₉	#468	1	1	yes	characteristic
192	C₄×C₁₉	#469	1	1	yes	characteristic
193	Dic₁₉	—	8	1	no	—
194	Dic₁₉	—	16	1	no	—
195	C₂×AGL(1,ℤ/8)	—	38	1	no	—
196	#532	—	19	1	no	—
197	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
198	#463	—	38	2	no	—
199	#461	—	19	2	no	—
200	#459	—	19	2	no	—
201	#436	—	2	2	no	—
202	#436	—	2	2	no	—
203	#431	C₂×D₁₉	1	1	yes	characteristic
204	#431	C₂×D₁₉	1	1	yes	characteristic
205	#423	—	19	1	no	—
206	C₂×C₄⋊C₈	—	19	1	no	—
207	#417	—	38	1	no	—
208	C₂×#102	—	38	1	no	—
209	#407	—	2	2	no	—
210	#382	—	19	1	no	—
211	#340	—	38	1	no	—
212	#327	—	38	2	no	—
213	D₄⋊C₈	—	38	2	no	—
214	C₂×C₁₉	—	2	1	no	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	—	8	2	no	—
217	C₂×C₁₉	#1881	1	1	yes	characteristic
218	C₂×C₁₉	#1895	1	1	yes	characteristic
219	C₂×C₁₉	#1904	1	1	yes	characteristic
220	D₁₉	—	16	1	no	—
221	C₂×#41	—	38	1	no	—
222	C₂²×D₄	D₇₆	1	1	yes	characteristic
223	C₂³×C₄	—	2	1	no	—
224	AGL(1,ℤ/8)	—	76	2	no	—
225	AGL(1,ℤ/8)	—	76	2	no	—
226	C₂×SD₁₆	—	38	2	no	—
227	C₂×D₈	—	38	2	no	—
228	C₂×M₁₆	—	2	4	no	—
229	C₂×M₁₆	—	38	1	no	—
230	C₂²×C₈	—	38	1	no	—
231	C₄⋊Q₈	—	19	1	no	—
232	#127	—	19	1	no	—
233	#124	—	38	1	no	—
234	#121	—	38	1	no	—
235	#121	—	38	1	no	—
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	38	1	no	—
239	C₄×D₄	—	38	1	no	—
240	C₄×D₄	C₄×D₁₉	1	2	yes	—
241	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
242	C₂×C₄⋊C₄	—	38	1	no	—
243	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	1	no	—
248	C₄⋊C₈	—	19	2	no	—
249	C₄⋊C₈	—	38	1	no	—
250	C₄⋊C₈	—	38	1	no	—
251	C₄⋊C₈	—	38	1	no	—
252	#103	—	38	2	no	—
253	#102	—	38	2	no	—
254	#102	—	76	2	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	C₂²⋊D₁₉	1	2	yes	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
260	#95	—	38	1	no	—
261	#95	—	38	1	no	—
262	C₁₉	#9309	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	2	1	no	—
264	#41	—	76	1	no	—
265	#41	—	76	1	no	—
266	#41	—	76	1	no	—
267	#41	—	76	1	no	—
268	C₂×Q₈	—	38	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	38	1	no	—
275	C₂×D₄	—	38	1	no	—
276	C₂×D₄	—	38	1	no	—
277	C₂×D₄	—	76	1	no	—
278	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	8	2	no	—
283	C₂²×C₄	—	76	1	no	—
284	C₂²×C₄	—	76	1	no	—
285	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
286	C₂²×C₄	#64541	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
288	SD₁₆	—	76	4	no	—
289	D₈	—	76	4	no	—
290	M₁₆	—	8	4	no	—
291	M₁₆	—	76	1	no	—
292	M₁₆	—	76	1	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	38	2	no	—
296	C₂×C₈	—	76	1	no	—
297	C₂×C₈	—	76	1	no	—
298	C₂×C₈	—	76	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	38	1	no	—
301	C₄⋊C₄	—	38	1	no	—
302	C₄⋊C₄	—	76	1	no	—
303	C₄⋊C₄	—	76	1	no	—
304	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	76	1	no	—
308	C₂²⋊C₄	—	76	1	no	—
309	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
310	C₄²	#64541	1	1	yes	characteristic
311	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
312	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	C₂³	—	2	2	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	8	1	no	—
317	C₂³	—	8	1	no	—
318	C₂³	—	76	1	no	—
319	C₂³	#10597376	1	1	yes	characteristic
320	Q₈	—	76	1	no	—
321	Q₈	—	76	1	no	—
322	D₄	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	4	1	no	—
325	D₄	—	4	1	no	—
326	D₄	—	76	2	no	—
327	D₄	—	76	1	no	—
328	D₄	—	76	1	no	—
329	D₄	—	152	1	no	—
330	D₄	—	152	1	no	—
331	D₄	—	152	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	1	no	—
338	C₂×C₄	—	76	1	no	—
339	C₂×C₄	—	152	1	no	—
340	C₂×C₄	—	152	1	no	—
341	C₂×C₄	—	152	1	no	—
342	C₂×C₄	—	152	1	no	—
343	C₂×C₄	—	152	1	no	—
344	C₂×C₄	#10597354	1	1	yes	characteristic
345	C₂×C₄	#10597354	1	1	yes	characteristic
346	C₂×C₄	#10597354	1	1	yes	characteristic
347	C₂×C₄	#10597355	1	1	yes	characteristic
348	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
350	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
351	C₂×C₄	#10597375	1	1	yes	characteristic
352	C₂×C₄	#10597376	1	1	yes	characteristic
353	C₂×C₄	#10597399	1	1	yes	characteristic
354	C₈	—	4	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	76	2	no	—
357	C₈	—	152	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	152	1	no	—
366	C₂²	—	152	1	no	—
367	C₂²	—	152	1	no	—
368	C₂²	#11926423	1	1	yes	characteristic
369	C₂²	#11926790	1	1	yes	characteristic
370	C₂²	#11926797	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	304	1	no	—
377	C₄	—	152	1	no	—
378	C₄	#11926546	1	1	yes	characteristic
379	C₄	#11926550	1	1	yes	characteristic
380	C₄	#11926790	1	1	yes	characteristic
381	C₄	#11926797	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	8	2	no	—
385	C₂	—	304	1	no	—
386	C₂	#14563997	1	1	yes	characteristic
387	C₂	#14564073	1	1	yes	characteristic
388	C₂	#14564122	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2975	C₂
socle	C₂²×C₁₉	#386
prime radical	#14573099	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2975	D₁₉
hypocenter	C₁₉	#9309
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2975

Complements

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

N	H ≅ G/N	type
2. #14563645	C₂	semidirect
3. #14562196	C₂	semidirect
4. #14562035	C₂	semidirect
5. #14561531	C₂	semidirect
6. #14561494	C₂	semidirect
7. C₁₉×#2975	C₂	semidirect
11. #11926749	C₄	semidirect
12. #11926739	C₄	semidirect
165. #2975	D₁₉	semidirect
262. C₁₉	#9309	semidirect

Maximal subgroups

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

subgroup	index
#14573099	2
#14563645	2
#14562196	2
#14562035	2
#14561531	2
#14561494	2
C₁₉×#2975	2
#9309	19