Subgroups — #18077770

Order 4864.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14574190	C₂	1	1	yes	maximal, characteristic
2	#14572578	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564555	C₂	1	1	yes	maximal, characteristic
4	#14562135	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561471	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1480	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926940	C₄	1	1	yes	characteristic, complemented
10	#11926916	C₄	1	1	yes	characteristic, complemented
11	#11926896	C₄	1	1	yes	characteristic, complemented
12	#11926890	C₄	1	1	yes	characteristic, complemented
13	#11926771	—	2	2	no	—
14	#11926673	—	2	2	no	—
15	#11926671	—	2	1	no	—
16	#11926668	—	2	1	no	—
17	C₄×#64526	—	2	2	no	—
18	#11926570	—	2	1	no	—
19	C₂×#10597294	—	2	1	no	—
20	C₂×#10597294	—	2	1	no	—
21	#11926499	—	2	1	no	—
22	C₄×#64520	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	#11926282	—	2	2	no	—
26	C₁₉×#532	C₂²	1	1	yes	characteristic
27	C₁₉×#431	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×D₄⋊C₈	—	2	1	no	—
30	C₁₉×D₄⋊C₈	—	2	1	no	—
31	C₂×#41×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
34	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
35	C₁₉×#124	—	2	1	no	—
36	C₁₉×#121	—	2	1	no	—
37	C₁₉×#121	—	2	1	no	—
38	C₄×D₄×C₁₉	—	2	1	no	—
39	C₄×D₄×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×#64526	—	2	2	no	—
42	#10597372	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	—	2	1	no	—
44	#10597370	—	2	1	no	—
45	#10597370	D₄	1	2	yes	—
46	C₂×C₄×Dic₁₉	—	2	1	no	—
47	C₂×#64520	D₄	1	1	yes	characteristic
48	C₂×#64520	D₄	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	—	2	1	no	—
50	#10597316	—	2	1	no	—
51	#10597315	C₂×C₄	1	1	yes	characteristic
52	#10597315	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₃₈	—	2	1	no	—
54	C₄×Dic₃₈	D₄	1	2	yes	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
59	C₁₉×C₂²⋊C₈	—	2	1	no	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	#10597294	—	4	2	no	—
62	#10597294	—	4	2	no	—
63	#10597289	—	2	2	no	—
64	C₁₉⋊#95	—	2	1	no	—
65	#10597272	—	2	2	no	—
66	Dic₁₉⋊C₈	—	2	2	no	—
67	Dic₁₉⋊C₈	—	2	2	no	—
68	C₈×Dic₁₉	—	2	2	no	—
69	#10597267	—	2	2	no	—
70	#10597265	—	2	2	no	—
71	#10597260	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
76	#41×C₁₉	—	4	1	no	—
77	#41×C₁₉	—	4	1	no	—
78	#41×C₁₉	—	4	1	no	—
79	#41×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×Dic₁₉	—	4	1	no	—
90	C₂×Dic₃₈	—	2	1	no	—
91	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
92	C₂×C₈×C₁₉	—	2	1	no	—
93	C₂×C₈×C₁₉	—	2	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₂²⋊C₄×C₁₉	—	4	1	no	—
100	C₂²⋊C₄×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₉	#41	1	1	yes	characteristic
105	C₂²⋊Dic₁₉	—	2	2	no	—
106	#64526	—	4	4	no	—
107	C₄⋊Dic₁₉	—	2	1	no	—
108	C₄⋊Dic₁₉	—	2	1	no	—
109	C₄⋊Dic₁₉	—	2	1	no	—
110	C₄⋊Dic₁₉	—	2	2	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
113	Dic₁₉⋊C₄	—	2	2	no	—
114	Dic₁₉⋊C₄	—	2	2	no	—
115	C₄×Dic₁₉	—	2	2	no	—
116	C₄×Dic₁₉	—	4	1	no	—
117	C₄×Dic₁₉	—	4	1	no	—
118	#64520	—	2	1	no	—
119	#64520	—	2	1	no	—
120	#64520	—	2	1	no	—
121	#64520	SD₁₆	1	2	yes	complemented
122	C₂×C₁₉⋊C₈	—	2	1	no	—
123	C₂×C₁₉⋊C₈	—	2	1	no	—
124	C₂×C₁₉⋊C₈	—	2	1	no	—
125	C₂×C₁₉⋊C₈	—	2	1	no	—
126	C₂×C₁₉⋊C₈	—	4	2	no	—
127	#9054	—	19	1	no	maximal, Sylow
128	C₂³×C₁₉	—	4	1	no	—
129	C₂³×C₁₉	#121	1	1	yes	characteristic
130	Q₈×C₁₉	—	4	1	no	—
131	Q₈×C₁₉	—	4	1	no	—
132	D₄×C₁₉	—	4	2	no	—
133	D₄×C₁₉	—	4	1	no	—
134	D₄×C₁₉	—	4	1	no	—
135	D₄×C₁₉	—	4	1	no	—
136	D₄×C₁₉	—	4	1	no	—
137	D₄×C₁₉	—	8	1	no	—
138	D₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
153	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
155	C₂×Dic₁₉	—	2	2	no	—
156	C₂×Dic₁₉	—	2	2	no	—
157	C₂×Dic₁₉	—	4	2	no	—
158	C₂×Dic₁₉	—	8	1	no	—
159	C₂×Dic₁₉	—	8	1	no	—
160	Dic₃₈	—	4	1	no	—
161	Dic₃₈	—	4	1	no	—
162	Dic₃₈	—	4	2	no	—
163	C₈×C₁₉	—	4	1	no	—
164	C₈×C₁₉	—	4	1	no	—
165	C₈×C₁₉	—	8	1	no	—
166	C₁₉⋊C₈	—	2	2	no	—
167	C₁₉⋊C₈	—	2	2	no	—
168	C₁₉⋊C₈	—	4	1	no	—
169	C₁₉⋊C₈	—	4	1	no	—
170	#3167	—	19	1	no	—
171	#2962	—	19	1	no	—
172	#1980	—	19	1	no	—
173	#1503	—	19	1	no	—
174	#1480	D₁₉	1	1	yes	characteristic
175	#1279	—	19	1	no	—
176	#1278	—	19	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	8	1	no	—
180	C₂²×C₁₉	—	8	1	no	—
181	C₂²×C₁₉	—	8	1	no	—
182	C₂²×C₁₉	#386	1	1	yes	characteristic
183	C₂²×C₁₉	#460	1	1	yes	characteristic
184	C₂²×C₁₉	#464	1	1	yes	characteristic
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	8	1	no	—
189	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
190	C₄×C₁₉	#440	1	1	yes	characteristic
191	C₄×C₁₉	#443	1	1	yes	characteristic
192	C₄×C₁₉	#444	1	1	yes	characteristic
193	C₄×C₁₉	#448	1	1	yes	characteristic
194	C₄×C₁₉	#449	1	1	yes	characteristic
195	Dic₁₉	—	4	2	no	—
196	Dic₁₉	—	4	2	no	—
197	Dic₁₉	—	8	2	no	—
198	#533	—	19	1	no	—
199	#532	C₂×D₁₉	1	1	yes	characteristic
200	#498	—	19	1	no	—
201	#492	—	19	1	no	—
202	#487	—	19	1	no	—
203	#486	—	19	1	no	—
204	#465	—	38	2	no	—
205	#446	—	38	2	no	—
206	#446	—	38	1	no	—
207	C₈×Q₈	—	38	1	no	—
208	C₄×SD₁₆	—	38	2	no	—
209	#431	C₂×D₁₉	1	1	yes	characteristic
210	#424	—	38	1	no	—
211	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
212	C₂×#104	—	38	1	no	—
213	C₂×#104	—	38	1	no	—
214	#405	—	38	1	no	—
215	C₄×M₁₆	—	19	1	no	—
216	C₂×C₄×C₈	—	19	1	no	—
217	C₄×C₄⋊C₄	—	19	1	no	—
218	#328	—	38	2	no	—
219	D₄⋊C₈	—	2	1	no	—
220	D₄⋊C₈	—	2	1	no	—
221	C₂×C₁₉	—	2	1	no	—
222	C₂×C₁₉	—	2	1	no	—
223	C₂×C₁₉	—	16	1	no	—
224	C₂×C₁₉	#1876	1	1	yes	characteristic
225	C₂×C₁₉	#1880	1	1	yes	characteristic
226	C₂×C₁₉	#1884	1	1	yes	characteristic
227	C₂×#41	—	2	1	no	—
228	C₂×SD₁₆	—	38	2	no	—
229	C₂×M₁₆	—	19	1	no	—
230	C₂×M₁₆	—	19	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	38	1	no	—
233	C₄⋊Q₈	—	19	1	no	—
234	C₄⋊Q₈	—	19	1	no	—
235	C₄⋊Q₈	C₄×D₁₉	1	1	yes	characteristic
236	#127	C₄×D₁₉	1	1	yes	characteristic
237	#125	—	38	1	no	—
238	#124	—	2	1	no	—
239	C₂²⋊Q₈	—	19	2	no	—
240	C₂²⋊Q₈	—	38	1	no	—
241	#121	—	2	1	no	—
242	#121	—	2	1	no	—
243	C₄×Q₈	—	19	2	no	—
244	C₄×Q₈	—	38	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	#117	—	38	1	no	—
248	C₂×C₄⋊C₄	—	38	1	no	—
249	C₂×C₄²	—	38	1	no	—
250	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
251	#106	—	38	2	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	38	2	no	—
255	C₄⋊C₈	—	38	2	no	—
256	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
257	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
258	#104	—	76	2	no	—
259	#104	—	76	2	no	—
260	#103	—	38	2	no	—
261	#102	—	38	2	no	—
262	C₂²⋊C₈	—	2	1	no	—
263	#97	—	38	2	no	—
264	#97	—	38	1	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	19	1	no	—
267	C₄×C₈	—	19	1	no	—
268	C₄×C₈	—	38	2	no	—
269	C₄×C₈	—	38	1	no	—
270	C₄×C₈	—	38	1	no	—
271	#95	—	38	1	no	—
272	C₁₉	#9054	1	1	yes	characteristic, complemented, Sylow
273	#41	—	4	1	no	—
274	#41	—	4	1	no	—
275	#41	—	4	1	no	—
276	#41	—	4	1	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	19	2	no	—
279	C₂×Q₈	—	38	1	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	76	1	no	—
286	C₂²×C₄	#64541	1	1	yes	characteristic
287	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
288	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
289	SD₁₆	—	76	4	no	—
290	M₁₆	—	19	2	no	—
291	M₁₆	—	38	1	no	—
292	M₁₆	—	38	1	no	—
293	M₁₆	—	38	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	38	1	no	—
300	C₂×C₈	—	38	1	no	—
301	C₂×C₈	—	38	1	no	—
302	C₂×C₈	—	38	1	no	—
303	C₂×C₈	—	76	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	19	2	no	—
307	C₄⋊C₄	—	38	2	no	—
308	C₄⋊C₄	—	38	2	no	—
309	C₄⋊C₄	—	38	1	no	—
310	C₄⋊C₄	—	38	1	no	—
311	C₄⋊C₄	—	38	2	no	—
312	C₄⋊C₄	—	38	1	no	—
313	C₄⋊C₄	—	76	1	no	—
314	C₂²⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	38	2	no	—
317	C₄²	—	38	2	no	—
318	C₄²	—	76	1	no	—
319	C₄²	—	76	1	no	—
320	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
321	C₄²	D₄×D₁₉	1	1	yes	characteristic
322	C₄²	#64543	1	1	yes	characteristic
323	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
324	C₂³	—	4	1	no	—
325	C₂³	#10597330	1	1	yes	characteristic
326	Q₈	—	4	1	no	—
327	Q₈	—	4	1	no	—
328	Q₈	—	76	2	no	—
329	Q₈	—	76	1	no	—
330	Q₈	—	76	1	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	1	no	—
333	D₄	—	4	1	no	—
334	D₄	—	4	1	no	—
335	D₄	—	4	1	no	—
336	D₄	—	8	1	no	—
337	D₄	—	8	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	8	1	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	38	2	no	—
345	C₂×C₄	—	38	2	no	—
346	C₂×C₄	—	76	2	no	—
347	C₂×C₄	—	152	1	no	—
348	C₂×C₄	—	152	1	no	—
349	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
350	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
351	C₂×C₄	#10597329	1	1	yes	characteristic
352	C₂×C₄	#10597357	1	1	yes	characteristic
353	C₂×C₄	#10597358	1	1	yes	characteristic
354	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
355	C₂×C₄	#10597361	1	1	yes	characteristic
356	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
357	C₂×C₄	#10597383	1	1	yes	characteristic
358	C₂×C₄	#10597384	1	1	yes	characteristic
359	C₈	—	4	1	no	—
360	C₈	—	4	1	no	—
361	C₈	—	8	1	no	—
362	C₈	—	38	2	no	—
363	C₈	—	38	2	no	—
364	C₈	—	76	1	no	—
365	C₈	—	76	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	#11926420	1	1	yes	characteristic
372	C₂²	#11926743	1	1	yes	characteristic
373	C₂²	#11926765	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	1	no	—
378	C₄	—	76	2	no	—
379	C₄	—	76	2	no	—
380	C₄	—	152	2	no	—
381	C₄	#11926635	1	1	yes	characteristic
382	C₄	#11926641	1	1	yes	characteristic
383	C₄	#11926659	1	1	yes	characteristic
384	C₄	#11926664	1	1	yes	characteristic
385	C₄	#11926681	1	1	yes	characteristic
386	C₄	#11926686	1	1	yes	characteristic
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	16	1	no	—
390	C₂	#14563965	1	1	yes	characteristic
391	C₂	#14563987	1	1	yes	characteristic
392	C₂	#14564015	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1480	C₂
socle	C₂²×C₁₉	#386
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1480	D₁₉
hypocenter	C₁₉	#9054
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1480

Complements

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

N	H ≅ G/N	type
2. #14572578	C₂	semidirect
4. #14562135	C₂	semidirect
5. #14561474	C₂	semidirect
6. #14561471	C₂	semidirect
9. #11926940	C₄	semidirect
10. #11926916	C₄	semidirect
11. #11926896	C₄	semidirect
12. #11926890	C₄	semidirect
121. #64520	SD₁₆	semidirect
272. C₁₉	#9054	semidirect

Maximal subgroups

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

subgroup	index
#14574190	2
#14572578	2
#14564555	2
#14562135	2
#14561474	2
#14561471	2
C₁₉×#1480	2
#9054	19