Subgroups — #18079388

Order 4864.

512 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573118	C₂	1	1	yes	maximal, characteristic
2	#14572744	C₂	1	1	yes	maximal, characteristic
3	#14563656	C₂	1	1	yes	maximal, characteristic
4	#14562307	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561538	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561510	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597388	—	2	1	no	—
9	C₄×#64541	C₂²	1	1	yes	characteristic
10	#11926751	—	2	1	no	—
11	#11926751	C₄	1	2	yes	complemented
12	#11926746	—	2	1	no	—
13	#11926746	C₄	1	2	yes	complemented
14	#11926668	—	2	1	no	—
15	#11926609	—	2	1	no	—
16	C₈×C₂²⋊D₁₉	—	2	2	no	—
17	#11926597	C₂²	1	1	yes	characteristic
18	#11926596	—	2	1	no	—
19	#11926568	C₂²	1	1	yes	characteristic
20	#11926568	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×D₁₉	—	2	1	no	—
22	C₂×#10597262	—	2	1	no	—
23	#11926553	—	2	1	no	—
24	#11926304	—	2	1	no	—
25	#11926290	—	2	1	no	—
26	#11926290	—	2	1	no	—
27	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#340	—	2	2	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂×#64541	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₉	D₄	1	2	yes	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×#64528	—	2	2	no	—
44	#10597388	—	4	2	no	—
45	#10597388	—	4	2	no	—
46	C₂×#64527	—	2	2	no	—
47	C₄×C₂²⋊D₁₉	—	2	1	no	—
48	C₄×C₂²⋊D₁₉	—	2	1	no	—
49	#10597372	D₄	1	1	yes	characteristic
50	C₂×#64520	—	2	1	no	—
51	C₂×#64520	—	2	1	no	—
52	C₂×C₈×D₁₉	—	2	2	no	—
53	C₄×D₇₆	C₂×C₄	1	1	yes	characteristic
54	C₄×D₇₆	D₄	1	1	yes	characteristic
55	#10597318	—	2	1	no	—
56	C₄²×D₁₉	—	2	1	no	—
57	C₄×Dic₃₈	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₃₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	#10597292	—	2	2	no	—
63	#10597292	—	2	2	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
65	(C₂×D₁₉)⋊C₈	—	2	2	no	—
66	Dic₁₉⋊C₈	—	2	2	no	—
67	C₈×Dic₁₉	—	2	2	no	—
68	#10597262	—	4	2	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
73	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
74	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
75	C₄×C₁₉⋊C₈	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	4	1	no	—
78	C₂×Q₈×C₁₉	—	4	1	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×Q₈×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂×C₂²⋊D₁₉	—	2	1	no	—
88	#64541	—	2	1	no	—
89	#64541	—	2	1	no	—
90	#64541	D₈	1	2	yes	—
91	#64541	SD₁₆	1	2	yes	—
92	C₂×D₇₆	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₉	—	2	1	no	—
94	C₂×C₄×D₁₉	—	2	1	no	—
95	C₂×C₄×D₁₉	—	2	1	no	—
96	C₂×Dic₃₈	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	4	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	C₂²⋊Dic₁₉	—	2	1	no	—
112	#64528	—	4	4	no	—
113	#64527	—	4	4	no	—
114	(C₂×D₁₉)⋊C₄	—	2	1	no	—
115	(C₂×D₁₉)⋊C₄	—	2	1	no	—
116	C₄⋊Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₄⋊Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
118	Dic₁₉⋊C₄	—	2	1	no	—
119	Dic₁₉⋊C₄	—	2	1	no	—
120	C₄×Dic₁₉	—	2	1	no	—
121	C₄×Dic₁₉	—	2	1	no	—
122	C₄×Dic₁₉	—	2	1	no	—
123	#64520	—	4	1	no	—
124	#64520	—	4	1	no	—
125	#64520	—	4	1	no	—
126	#64520	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	2	2	no	—
128	C₂×C₁₉⋊C₈	—	2	1	no	—
129	C₂×C₁₉⋊C₈	—	2	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₈×D₁₉	—	8	2	no	—
132	#9316	—	19	1	no	maximal, Sylow
133	C₂³×C₁₉	#121	1	1	yes	characteristic
134	C₂²×D₁₉	—	2	1	no	—
135	Q₈×C₁₉	—	4	2	no	—
136	Q₈×C₁₉	—	4	2	no	—
137	Q₈×C₁₉	—	8	1	no	—
138	Q₈×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	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	—	8	1	no	—
146	C₂×C₄×C₁₉	—	8	1	no	—
147	C₂×C₄×C₁₉	—	8	1	no	—
148	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
158	C₂²⋊D₁₉	—	2	2	no	—
159	C₂²⋊D₁₉	—	2	2	no	—
160	C₂×Dic₁₉	—	2	1	no	—
161	C₂×Dic₁₉	—	2	1	no	—
162	C₂×Dic₁₉	—	2	1	no	—
163	D₇₆	—	2	1	no	—
164	D₇₆	#102	1	2	yes	—
165	C₄×D₁₉	—	2	2	no	—
166	C₄×D₁₉	—	2	2	no	—
167	C₄×D₁₉	—	4	1	no	—
168	C₄×D₁₉	—	4	1	no	—
169	C₄×D₁₉	—	8	1	no	—
170	Dic₃₈	—	2	1	no	—
171	Dic₃₈	#102	1	2	yes	—
172	C₈×C₁₉	—	4	2	no	—
173	C₁₉⋊C₈	—	4	2	no	—
174	C₁₉⋊C₈	—	4	1	no	—
175	C₁₉⋊C₈	—	4	1	no	—
176	C₁₉⋊C₈	—	8	1	no	—
177	#3039	—	19	1	no	—
178	#2988	—	19	1	no	—
179	#1988	D₁₉	1	1	yes	characteristic, complemented
180	#1806	—	19	1	no	—
181	#1546	—	19	1	no	—
182	#1303	—	19	1	no	—
183	#1292	—	19	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	#386	1	1	yes	characteristic
187	C₂²×C₁₉	#465	1	1	yes	characteristic
188	C₂²×C₁₉	#466	1	1	yes	characteristic
189	C₂×D₁₉	—	2	2	no	—
190	C₂×D₁₉	—	4	1	no	—
191	C₂×D₁₉	—	4	1	no	—
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	8	2	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
198	C₄×C₁₉	#416	1	1	yes	characteristic
199	C₄×C₁₉	#455	1	1	yes	characteristic
200	C₄×C₁₉	#456	1	1	yes	characteristic
201	C₄×C₁₉	#465	1	1	yes	characteristic
202	C₄×C₁₉	#466	1	1	yes	characteristic
203	Dic₁₉	—	2	2	no	—
204	Dic₁₉	—	4	1	no	—
205	Dic₁₉	—	4	1	no	—
206	C₂×#137	—	38	1	no	—
207	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
208	C₄×#41	—	19	1	no	—
209	#462	—	19	2	no	—
210	#462	—	38	1	no	—
211	#461	—	19	2	no	—
212	#461	—	38	1	no	—
213	C₈×Q₈	—	38	1	no	—
214	C₈×D₄	—	38	1	no	—
215	C₈×D₄	—	38	2	no	—
216	#431	—	19	1	no	—
217	#431	—	38	1	no	—
218	#423	—	19	1	no	—
219	#423	—	19	1	no	—
220	C₂×C₄⋊C₈	—	38	1	no	—
221	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
222	C₂×#104	—	38	1	no	—
223	#419	—	38	1	no	—
224	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
225	#340	—	2	2	no	—
226	#339	—	38	1	no	—
227	#332	—	38	1	no	—
228	#332	—	38	1	no	—
229	C₂×C₁₉	—	2	1	no	—
230	C₂×C₁₉	—	2	1	no	—
231	C₂×C₁₉	#1882	1	1	yes	characteristic
232	C₂×C₁₉	#1893	1	1	yes	characteristic
233	C₂×C₁₉	#1902	1	1	yes	characteristic
234	D₁₉	—	4	2	no	—
235	C₂×#41	—	19	1	no	—
236	C₂²×Q₈	—	2	1	no	—
237	#137	—	76	2	no	—
238	#137	—	76	2	no	—
239	C₂×Q₁₆	—	38	2	no	—
240	C₂×SD₁₆	—	38	2	no	—
241	C₂×M₁₆	—	38	1	no	—
242	C₂×M₁₆	—	38	1	no	—
243	C₂²×C₈	—	38	2	no	—
244	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
249	C₄×Q₈	—	19	1	no	—
250	C₄×Q₈	—	19	1	no	—
251	C₄×D₄	—	19	1	no	—
252	C₄×D₄	—	19	1	no	—
253	C₄×D₄	—	38	1	no	—
254	C₄×D₄	—	38	1	no	—
255	#117	—	19	1	no	—
256	#117	—	38	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	38	1	no	—
262	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	19	2	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	C₄⋊C₈	—	38	1	no	—
272	#104	—	76	2	no	—
273	#103	—	38	2	no	—
274	#103	—	38	2	no	—
275	C₂²⋊C₈	—	38	2	no	—
276	C₂²⋊C₈	—	38	1	no	—
277	C₄×C₈	—	38	2	no	—
278	C₄×C₈	—	38	1	no	—
279	#95	—	2	1	no	—
280	C₁₉	#9316	1	1	yes	characteristic, complemented, Sylow
281	#41	—	19	2	no	—
282	#41	—	19	2	no	—
283	#41	—	38	1	no	—
284	#41	—	38	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×Q₈	—	19	1	no	—
292	C₂×D₄	—	19	1	no	—
293	C₂×D₄	—	38	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	38	1	no	—
297	C₂²×C₄	—	38	1	no	—
298	C₂²×C₄	—	38	1	no	—
299	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	#64543	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
302	Q₁₆	—	76	4	no	—
303	SD₁₆	—	76	4	no	—
304	M₁₆	—	76	1	no	—
305	M₁₆	—	76	1	no	—
306	M₁₆	—	76	1	no	—
307	M₁₆	—	76	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	38	1	no	—
311	C₂×C₈	—	38	1	no	—
312	C₂×C₈	—	38	2	no	—
313	C₂×C₈	—	76	1	no	—
314	C₂×C₈	—	152	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	19	1	no	—
322	C₄⋊C₄	—	19	1	no	—
323	C₄⋊C₄	—	38	1	no	—
324	C₄⋊C₄	—	38	1	no	—
325	C₂²⋊C₄	—	38	1	no	—
326	C₂²⋊C₄	—	38	1	no	—
327	C₂²⋊C₄	—	38	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	—	38	1	no	—
331	C₄²	—	38	1	no	—
332	C₄²	—	38	1	no	—
333	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
334	C₄²	#64541	1	1	yes	characteristic
335	C₄²	D₄×D₁₉	1	1	yes	characteristic
336	C₄²	D₄×D₁₉	1	1	yes	characteristic
337	C₂³	—	38	1	no	—
338	C₂³	#10597384	1	1	yes	characteristic
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	8	1	no	—
342	Q₈	—	8	1	no	—
343	Q₈	—	19	2	no	—
344	Q₈	—	38	1	no	—
345	D₄	—	19	2	no	—
346	D₄	—	38	2	no	—
347	D₄	—	38	2	no	—
348	D₄	—	38	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	—	8	1	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	—	38	1	no	—
359	C₂×C₄	—	38	2	no	—
360	C₂×C₄	—	38	2	no	—
361	C₂×C₄	—	38	1	no	—
362	C₂×C₄	—	38	1	no	—
363	C₂×C₄	—	76	1	no	—
364	C₂×C₄	—	76	1	no	—
365	C₂×C₄	—	152	1	no	—
366	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
367	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
368	C₂×C₄	#10597329	1	1	yes	characteristic
369	C₂×C₄	#10597330	1	1	yes	characteristic
370	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
371	C₂×C₄	#10597358	1	1	yes	characteristic
372	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
373	C₂×C₄	#10597362	1	1	yes	characteristic
374	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
375	C₂×C₄	#10597383	1	1	yes	characteristic
376	C₈	—	4	2	no	—
377	C₈	—	76	2	no	—
378	C₈	—	76	1	no	—
379	C₈	—	76	1	no	—
380	C₈	—	152	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	38	2	no	—
384	C₂²	—	76	1	no	—
385	C₂²	—	76	1	no	—
386	C₂²	#11926420	1	1	yes	characteristic
387	C₂²	#11926770	1	1	yes	characteristic
388	C₂²	#11926777	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	2	no	—
394	C₄	—	38	2	no	—
395	C₄	—	76	1	no	—
396	C₄	—	76	1	no	—
397	C₄	#102×D₁₉	1	1	yes	characteristic
398	C₄	#11926537	1	1	yes	characteristic
399	C₄	#11926721	1	1	yes	characteristic
400	C₄	#11926726	1	1	yes	characteristic
401	C₄	#11926772	1	1	yes	characteristic
402	C₄	#11926779	1	1	yes	characteristic
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	76	2	no	—
406	C₂	#14564007	1	1	yes	characteristic
407	C₂	#14564060	1	1	yes	characteristic
408	C₂	#14564105	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926420
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1988	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#64541	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1988	D₁₉
hypocenter	C₁₉	#9316
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1988

Complements

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

N	H ≅ G/N	type
4. #14562307	C₂	semidirect
5. #14561538	C₂	semidirect
6. #14561510	C₂	semidirect
7. C₁₉×#1988	C₂	semidirect
11. #11926751	C₄	semidirect
13. #11926746	C₄	semidirect
179. #1988	D₁₉	semidirect
280. C₁₉	#9316	semidirect

Maximal subgroups

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

subgroup	index
#14573118	2
#14572744	2
#14563656	2
#14562307	2
#14561538	2
#14561510	2
C₁₉×#1988	2
#9316	19