Subgroups — #18079352

Order 4864.

514 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572063	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562246	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562069	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562052	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561533	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561506	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3115	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597394	—	2	1	no	—
9	#11926601	C₂²	1	1	yes	characteristic
10	#11926597	C₂²	1	1	yes	characteristic
11	#11926500	—	2	2	no	—
12	#11926500	—	2	1	no	—
13	C₄×#64520	—	2	1	no	—
14	C₄×#64520	C₂²	1	1	yes	characteristic
15	C₂×#10597260	—	2	1	no	—
16	C₂×#10597260	C₂²	1	1	yes	characteristic
17	#11926284	—	2	1	no	—
18	#11926284	—	2	1	no	—
19	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#482	—	2	1	no	—
25	C₁₉×#475	C₄	1	1	yes	characteristic
26	C₁₉×#474	C₄	1	1	yes	characteristic
27	C₁₉×#460	C₄	1	1	yes	characteristic
28	C₁₉×#459	C₄	1	1	yes	characteristic
29	C₁₉×#449	—	2	1	no	—
30	C₁₉×#442	—	2	1	no	—
31	C₁₉×#440	—	2	1	no	—
32	C₁₉×#432	C₂²	1	1	yes	characteristic
33	C₂×#41×C₁₉	—	2	1	no	—
34	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
35	C₂×SD₁₆×C₁₉	—	2	1	no	—
36	C₂×D₈×C₁₉	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
39	C₁₉×#124	—	2	1	no	—
40	C₁₉×#121	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	#10597394	—	2	4	no	—
55	#10597394	—	2	4	no	—
56	C₂×#64520	—	2	2	no	—
57	C₂×#64520	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	2	no	—
59	C₂²×C₁₉⋊C₈	—	2	1	no	—
60	C₁₉×#107	—	2	1	no	—
61	C₁₉×#106	—	2	1	no	—
62	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₁₉×#103	—	2	1	no	—
65	C₁₉×#102	—	2	1	no	—
66	C₁₉×#102	—	2	1	no	—
67	C₁₉×#102	—	2	1	no	—
68	C₁₉×C₂²⋊C₈	—	2	1	no	—
69	C₁₉×#97	—	2	1	no	—
70	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	#10597260	—	2	2	no	—
75	#10597260	—	2	1	no	—
76	#10597260	—	2	1	no	—
77	#10597260	—	2	1	no	—
78	#10597260	D₄	1	1	yes	characteristic
79	#10597260	D₄	1	1	yes	characteristic
80	C₄×C₁₉⋊C₈	—	2	2	no	—
81	C₄×C₁₉⋊C₈	—	2	1	no	—
82	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
83	#41×C₁₉	—	2	2	no	—
84	#41×C₁₉	—	2	2	no	—
85	#41×C₁₉	—	8	2	no	—
86	C₂×Q₈×C₁₉	—	2	1	no	—
87	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	2	1	no	—
92	C₂×D₄×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	—	2	1	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	SD₁₆×C₁₉	—	4	2	no	—
102	D₈×C₁₉	—	4	2	no	—
103	C₂×C₈×C₁₉	—	2	1	no	—
104	C₂×C₈×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂²⋊C₄×C₁₉	—	4	1	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	—	2	1	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	#64520	—	2	8	no	—
124	#64520	—	2	2	no	—
125	#64520	—	2	2	no	—
126	C₂×C₁₉⋊C₈	—	2	8	no	—
127	C₂×C₁₉⋊C₈	—	2	2	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	2	1	no	—
130	C₂×C₁₉⋊C₈	—	2	2	no	—
131	C₂×C₁₉⋊C₈	—	2	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	#9311	—	19	1	no	maximal, Sylow
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	#123	1	1	yes	characteristic
138	Q₈×C₁₉	—	2	1	no	—
139	Q₈×C₁₉	—	8	1	no	—
140	Q₈×C₁₉	#104	1	2	yes	—
141	D₄×C₁₉	—	2	4	no	—
142	D₄×C₁₉	—	2	1	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	—	4	1	no	—
145	D₄×C₁₉	—	4	1	no	—
146	D₄×C₁₉	—	8	1	no	—
147	D₄×C₁₉	—	8	2	no	—
148	D₄×C₁₉	#104	1	2	yes	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	—	8	1	no	—
160	C₂×C₄×C₁₉	—	8	2	no	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
167	C₈×C₁₉	—	4	1	no	—
168	C₈×C₁₉	—	4	1	no	—
169	C₁₉⋊C₈	—	2	2	no	—
170	C₁₉⋊C₈	—	2	2	no	—
171	C₁₉⋊C₈	—	2	4	no	—
172	C₁₉⋊C₈	—	8	1	no	—
173	C₁₉⋊C₈	—	8	1	no	—
174	#3115	D₁₉	1	1	yes	characteristic
175	#2875	—	19	1	no	—
176	#1530	—	19	1	no	—
177	#1488	—	19	1	no	—
178	#1484	—	19	1	no	—
179	#1302	—	19	1	no	—
180	#1291	—	19	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	—	2	2	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	8	1	no	—
188	C₂²×C₁₉	—	8	1	no	—
189	C₂²×C₁₉	—	8	1	no	—
190	C₂²×C₁₉	#386	1	1	yes	characteristic
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	4	1	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
201	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
202	C₂×#131	—	38	1	no	—
203	#532	C₂×D₁₉	1	1	yes	characteristic
204	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
205	#482	—	2	1	no	—
206	#475	Dic₁₉	1	1	yes	characteristic
207	#474	Dic₁₉	1	1	yes	characteristic
208	#460	Dic₁₉	1	1	yes	characteristic
209	#459	Dic₁₉	1	1	yes	characteristic
210	#449	—	2	1	no	—
211	#442	—	2	1	no	—
212	#440	—	2	1	no	—
213	#432	—	19	1	no	—
214	#432	C₂×D₁₉	1	1	yes	characteristic
215	#431	—	19	1	no	—
216	#405	—	38	2	no	—
217	#405	—	38	1	no	—
218	C₄×M₁₆	—	19	1	no	—
219	C₄×M₁₆	—	38	1	no	—
220	C₂×#97	—	19	1	no	—
221	C₂×#97	—	38	1	no	—
222	#329	—	38	1	no	—
223	#329	—	38	1	no	—
224	Q₈⋊C₈	—	38	1	no	—
225	D₄⋊C₈	—	38	2	no	—
226	D₄⋊C₈	—	38	1	no	—
227	C₂×C₁₉	—	4	1	no	—
228	C₂×C₁₉	—	4	2	no	—
229	C₂×C₁₉	—	16	1	no	—
230	C₂×C₁₉	#1881	1	1	yes	characteristic
231	C₂×C₁₉	#1896	1	1	yes	characteristic
232	C₂×C₁₉	#1903	1	1	yes	characteristic
233	C₂×#41	—	2	1	no	—
234	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
235	C₂×SD₁₆	—	2	1	no	—
236	C₂×D₈	—	2	1	no	—
237	#131	—	38	4	no	—
238	#131	—	38	4	no	—
239	C₂×M₁₆	—	38	2	no	—
240	C₂×M₁₆	—	38	1	no	—
241	C₂²×C₈	—	38	2	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic
244	#127	C₂×Dic₁₉	1	1	yes	characteristic
245	#124	—	2	1	no	—
246	#121	—	2	1	no	—
247	#121	—	2	1	no	—
248	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
249	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
255	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
256	#117	—	2	1	no	—
257	#117	C₂²⋊D₁₉	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
260	#107	—	2	1	no	—
261	#106	—	2	1	no	—
262	C₄⋊C₈	—	38	1	no	—
263	C₄⋊C₈	—	38	1	no	—
264	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
265	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
266	#103	—	2	1	no	—
267	#102	—	2	1	no	—
268	#102	—	2	1	no	—
269	#102	—	2	1	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	38	1	no	—
272	C₂²⋊C₈	—	38	1	no	—
273	#97	—	2	1	no	—
274	#97	—	19	1	no	—
275	#97	—	19	1	no	—
276	#97	—	38	2	no	—
277	#97	—	38	1	no	—
278	#97	—	38	1	no	—
279	#97	—	38	1	no	—
280	C₄×C₈	—	19	2	no	—
281	C₄×C₈	—	38	2	no	—
282	C₄×C₈	—	38	1	no	—
283	C₁₉	#9311	1	1	yes	characteristic, complemented, Sylow
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	#41	—	8	2	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	#64543	1	1	yes	characteristic
300	C₂²×C₄	#64543	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
302	SD₁₆	—	4	2	no	—
303	D₈	—	4	2	no	—
304	M₁₆	—	38	8	no	—
305	M₁₆	—	38	2	no	—
306	M₁₆	—	38	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	38	8	no	—
310	C₂×C₈	—	38	2	no	—
311	C₂×C₈	—	38	2	no	—
312	C₂×C₈	—	38	2	no	—
313	C₂×C₈	—	38	1	no	—
314	C₂×C₈	—	38	1	no	—
315	C₂×C₈	—	76	1	no	—
316	C₂×C₈	—	76	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
322	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	D₄×D₁₉	1	1	yes	characteristic
332	C₄²	D₄×D₁₉	1	1	yes	characteristic
333	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
335	C₂³	—	2	1	no	—
336	C₂³	—	4	1	no	—
337	C₂³	#10597381	1	1	yes	characteristic
338	Q₈	—	2	1	no	—
339	Q₈	—	8	1	no	—
340	Q₈	#10597294	1	2	yes	—
341	D₄	—	2	4	no	—
342	D₄	—	2	1	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	1	no	—
345	D₄	—	4	1	no	—
346	D₄	—	8	1	no	—
347	D₄	—	8	2	no	—
348	D₄	#10597294	1	2	yes	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	8	1	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
362	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
363	C₂×C₄	#10597383	1	1	yes	characteristic
364	C₂×C₄	#10597385	1	1	yes	characteristic
365	C₂×C₄	#10597385	1	1	yes	characteristic
366	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
367	C₈	—	4	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	38	2	no	—
370	C₈	—	38	4	no	—
371	C₈	—	38	2	no	—
372	C₈	—	152	1	no	—
373	C₈	—	152	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	#11926424	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	8	1	no	—
393	C₄	C₂×#10597294	1	1	yes	characteristic
394	C₄	C₂×#10597294	1	1	yes	characteristic
395	C₂	—	4	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	16	1	no	—
398	C₂	#14563999	1	1	yes	characteristic
399	C₂	#14564079	1	1	yes	characteristic
400	C₂	#14564117	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3115	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3115	D₁₉
hypocenter	C₁₉	#9311
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3115

Complements

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

N	H ≅ G/N	type
1. #14572063	C₂	semidirect
2. #14562246	C₂	semidirect
3. #14562069	C₂	semidirect
4. #14562052	C₂	semidirect
5. #14561533	C₂	semidirect
6. #14561506	C₂	semidirect
283. C₁₉	#9311	semidirect

Maximal subgroups

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

subgroup	index
#14572063	2
#14562246	2
#14562069	2
#14562052	2
#14561533	2
#14561506	2
C₁₉×#3115	2
#9311	19