Subgroups — #18078481

Order 4864.

544 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573107	C₂	1	1	yes	maximal, characteristic
2	#14562194	C₂	1	1	yes	maximal, characteristic
3	#14562129	C₂	1	1	yes	maximal, characteristic
4	#14562030	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561538	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561493	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597388	—	2	1	no	—
9	#11927094	C₂²	1	1	yes	characteristic
10	#11926766	—	2	2	no	—
11	#11926754	C₄	1	2	yes	complemented
12	#11926744	C₄	1	2	yes	complemented
13	#11926597	C₂²	1	1	yes	characteristic
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926568	C₂²	1	1	yes	characteristic
16	#11926543	—	2	1	no	—
17	#11926277	—	2	1	no	—
18	#11926277	—	2	1	no	—
19	#11926277	—	2	2	no	—
20	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#389	—	2	2	no	—
24	C₁₉×#389	—	2	1	no	—
25	C₁₉×#382	—	2	1	no	—
26	C₁₉×#382	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
30	C₂×#64541	—	2	1	no	—
31	C₄×Q₈×C₁₉	—	2	1	no	—
32	C₄×Q₈×C₁₉	—	2	1	no	—
33	C₄×Q₈×C₁₉	—	4	2	no	—
34	C₄×Q₈×C₁₉	—	4	2	no	—
35	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
36	C₄×Q₈×C₁₉	D₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	2	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×#64528	—	2	2	no	—
48	#10597388	—	4	2	no	—
49	#10597388	—	4	2	no	—
50	C₂×#64527	—	2	2	no	—
51	#10597376	—	2	1	no	—
52	#10597376	—	2	1	no	—
53	C₂×#64520	—	2	1	no	—
54	#10597321	—	2	1	no	—
55	#10597320	C₂×C₄	1	1	yes	characteristic
56	C₄×D₇₆	—	2	1	no	—
57	C₄×D₇₆	—	2	1	no	—
58	#10597315	C₂×C₄	1	1	yes	characteristic
59	C₁₉×#95	—	2	2	no	—
60	C₁₉×#95	—	2	1	no	—
61	C₁₉×#95	D₄	1	1	yes	characteristic
62	C₁₉×#95	D₄	1	1	yes	characteristic
63	C₁₉×#95	D₄	1	2	yes	—
64	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	#10597267	—	2	2	no	—
67	#10597266	—	2	2	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₂×Q₈×C₁₉	—	2	1	no	—
75	C₂×Q₈×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	2	1	no	—
77	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
78	C₂×Q₈×C₁₉	D₈	1	2	yes	—
79	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	2	1	no	—
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₂²⋊D₁₉	—	4	1	no	—
89	#64541	—	4	1	no	—
90	#64541	—	4	1	no	—
91	#64541	—	4	1	no	—
92	#64541	—	4	1	no	—
93	C₂×D₇₆	—	2	1	no	—
94	C₂×D₇₆	—	2	1	no	—
95	C₂×D₇₆	—	2	1	no	—
96	C₂×C₄×D₁₉	—	4	1	no	—
97	C₂×Dic₃₈	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	2	no	—
99	C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	4	no	—
103	C₄⋊C₄×C₁₉	—	4	4	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
107	C₄²×C₁₉	—	2	2	no	—
108	C₄²×C₁₉	—	2	2	no	—
109	C₄²×C₁₉	—	4	4	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	—	4	1	no	—
112	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₉	#41	1	1	yes	characteristic
115	C₄²×C₁₉	#41	1	1	yes	characteristic
116	#64528	—	4	4	no	—
117	#64527	—	4	4	no	—
118	(C₂×D₁₉)⋊C₄	—	4	1	no	—
119	(C₂×D₁₉)⋊C₄	—	4	1	no	—
120	C₄⋊Dic₁₉	—	2	1	no	—
121	C₄⋊Dic₁₉	—	2	1	no	—
122	#64520	—	4	1	no	—
123	#64520	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	2	2	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	#9180	—	19	1	no	maximal, Sylow
128	C₂³×C₁₉	#120	1	1	yes	characteristic
129	C₂²×D₁₉	—	4	1	no	—
130	Q₈×C₁₉	—	2	2	no	—
131	Q₈×C₁₉	—	2	2	no	—
132	Q₈×C₁₉	—	2	2	no	—
133	Q₈×C₁₉	#102	1	4	yes	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	2	2	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
160	C₂²⋊D₁₉	—	8	1	no	—
161	C₂²⋊D₁₉	—	8	1	no	—
162	C₂×Dic₁₉	—	4	1	no	—
163	D₇₆	—	4	1	no	—
164	D₇₆	—	4	1	no	—
165	D₇₆	—	8	1	no	—
166	D₇₆	—	8	1	no	—
167	C₄×D₁₉	—	8	1	no	—
168	C₄×D₁₉	—	8	1	no	—
169	Dic₃₈	—	4	1	no	—
170	Dic₃₈	—	4	1	no	—
171	C₁₉⋊C₈	—	4	2	no	—
172	C₁₉⋊C₈	—	8	1	no	—
173	C₁₉⋊C₈	—	8	1	no	—
174	#3037	—	19	1	no	—
175	#2351	D₁₉	1	1	yes	characteristic, complemented
176	#1517	—	19	1	no	—
177	#1502	—	19	1	no	—
178	#1479	—	19	1	no	—
179	#1303	—	19	1	no	—
180	#1286	—	19	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	#386	1	1	yes	characteristic
184	C₂²×C₁₉	#447	1	1	yes	characteristic
185	C₂²×C₁₉	#448	1	1	yes	characteristic
186	C₂×D₁₉	—	8	1	no	—
187	C₂×D₁₉	—	8	1	no	—
188	C₂×D₁₉	—	8	1	no	—
189	C₄×C₁₉	—	2	4	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	2	1	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	4	2	no	—
195	C₄×C₁₉	—	4	2	no	—
196	C₄×C₁₉	—	8	2	no	—
197	C₄×C₁₉	—	8	1	no	—
198	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
199	C₄×C₁₉	#417	1	1	yes	characteristic
200	C₄×C₁₉	#480	1	1	yes	characteristic
201	C₄×C₁₉	#481	1	1	yes	characteristic
202	Dic₁₉	—	8	1	no	—
203	C₂×#137	—	38	1	no	—
204	#532	—	19	1	no	—
205	C₂×C₄×Q₈	—	2	1	no	—
206	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
207	#464	—	38	2	no	—
208	#462	—	19	2	no	—
209	#460	—	19	2	no	—
210	#431	—	19	1	no	—
211	#431	—	19	1	no	—
212	#423	—	19	1	no	—
213	#417	—	38	1	no	—
214	#389	—	2	1	no	—
215	#389	—	2	2	no	—
216	#382	—	2	1	no	—
217	#382	C₂×D₁₉	1	1	yes	characteristic
218	C₄×C₄⋊C₄	—	2	1	no	—
219	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
220	#327	—	38	1	no	—
221	#327	—	38	1	no	—
222	#327	—	38	2	no	—
223	Q₈⋊C₈	—	38	2	no	—
224	C₂×C₁₉	—	2	1	no	—
225	C₂×C₁₉	—	2	1	no	—
226	C₂×C₁₉	#1874	1	1	yes	characteristic
227	C₂×C₁₉	#1905	1	1	yes	characteristic
228	C₂×C₁₉	#1906	1	1	yes	characteristic
229	D₁₉	—	16	1	no	—
230	C₂×#41	—	38	1	no	—
231	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
232	#137	—	76	2	no	—
233	#137	—	76	2	no	—
234	C₂×Q₁₆	—	38	2	no	—
235	C₂×SD₁₆	—	38	2	no	—
236	C₂×M₁₆	—	38	1	no	—
237	C₄⋊Q₈	—	19	1	no	—
238	#127	—	19	1	no	—
239	#124	—	38	1	no	—
240	#121	—	38	1	no	—
241	#121	—	38	1	no	—
242	C₄×Q₈	—	2	1	no	—
243	C₄×Q₈	—	2	1	no	—
244	C₄×Q₈	—	4	2	no	—
245	C₄×Q₈	—	4	2	no	—
246	C₄×Q₈	C₄×D₁₉	1	2	yes	—
247	C₄×Q₈	D₇₆	1	2	yes	—
248	C₄×D₄	—	38	1	no	—
249	C₄×D₄	—	38	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
260	C₄⋊C₈	—	19	2	no	—
261	C₄⋊C₈	—	38	1	no	—
262	C₄⋊C₈	—	38	1	no	—
263	C₄⋊C₈	—	38	1	no	—
264	#103	—	38	2	no	—
265	#102	—	38	2	no	—
266	C₂²⋊C₈	—	38	1	no	—
267	C₂²⋊C₈	—	38	1	no	—
268	C₄×C₈	—	38	1	no	—
269	C₄×C₈	—	38	1	no	—
270	#95	—	2	2	no	—
271	#95	—	2	1	no	—
272	#95	C₂²⋊D₁₉	1	1	yes	characteristic
273	#95	C₂²⋊D₁₉	1	1	yes	characteristic
274	#95	C₂²⋊D₁₉	1	2	yes	—
275	C₁₉	#9180	1	1	yes	characteristic, complemented, Sylow
276	#41	—	76	1	no	—
277	#41	—	76	1	no	—
278	#41	—	76	1	no	—
279	#41	—	76	1	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	38	1	no	—
284	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
285	C₂×Q₈	#64525	1	2	yes	—
286	C₂×Q₈	#64527	1	2	yes	—
287	C₂×D₄	—	38	1	no	—
288	C₂×D₄	—	38	1	no	—
289	C₂×D₄	—	38	1	no	—
290	C₂×D₄	—	76	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	76	1	no	—
297	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
300	Q₁₆	—	76	4	no	—
301	SD₁₆	—	76	4	no	—
302	M₁₆	—	76	1	no	—
303	M₁₆	—	76	1	no	—
304	C₂×C₈	—	38	2	no	—
305	C₂×C₈	—	76	1	no	—
306	C₂×C₈	—	76	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	38	1	no	—
316	C₄⋊C₄	—	38	1	no	—
317	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
318	C₂²⋊C₄	—	76	1	no	—
319	C₂²⋊C₄	—	76	1	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	4	4	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	4	1	no	—
325	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
326	C₄²	C₂×D₇₆	1	1	yes	characteristic
327	C₄²	#64541	1	1	yes	characteristic
328	C₄²	#64541	1	1	yes	characteristic
329	C₂³	—	76	1	no	—
330	C₂³	#10597399	1	1	yes	characteristic
331	Q₈	—	2	2	no	—
332	Q₈	—	2	2	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	76	1	no	—
335	Q₈	—	76	1	no	—
336	Q₈	#10597266	1	4	yes	—
337	D₄	—	76	1	no	—
338	D₄	—	76	1	no	—
339	D₄	—	152	1	no	—
340	D₄	—	152	1	no	—
341	D₄	—	152	1	no	—
342	D₄	—	152	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	76	1	no	—
360	C₂×C₄	—	152	1	no	—
361	C₂×C₄	—	152	1	no	—
362	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
364	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
365	C₂×C₄	#10597375	1	1	yes	characteristic
366	C₂×C₄	#10597376	1	1	yes	characteristic
367	C₂×C₄	#10597376	1	1	yes	characteristic
368	C₂×C₄	C₂×#64525	1	1	yes	characteristic
369	C₂×C₄	#10597378	1	1	yes	characteristic
370	C₂×C₄	C₂×#64527	1	1	yes	characteristic
371	C₂×C₄	#10597388	1	1	yes	characteristic
372	C₈	—	76	2	no	—
373	C₈	—	152	1	no	—
374	C₈	—	152	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	152	1	no	—
378	C₂²	—	152	1	no	—
379	C₂²	—	152	1	no	—
380	C₂²	#11926423	1	1	yes	characteristic
381	C₂²	#11926678	1	1	yes	characteristic
382	C₂²	#11926683	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	4	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	1	no	—
392	C₄	—	152	1	no	—
393	C₄	C₂×#10597266	1	1	yes	characteristic
394	C₄	#11926543	1	1	yes	characteristic
395	C₄	#11926857	1	1	yes	characteristic
396	C₄	#11926862	1	1	yes	characteristic
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	304	1	no	—
400	C₂	#14563952	1	1	yes	characteristic
401	C₂	#14564129	1	1	yes	characteristic
402	C₂	#14564136	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2351	C₂
socle	C₂²×C₁₉	#386
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2351	D₁₉
hypocenter	C₁₉	#9180
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2351

Complements

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

N	H ≅ G/N	type
4. #14562030	C₂	semidirect
5. #14561538	C₂	semidirect
6. #14561493	C₂	semidirect
7. C₁₉×#2351	C₂	semidirect
11. #11926754	C₄	semidirect
12. #11926744	C₄	semidirect
175. #2351	D₁₉	semidirect
275. C₁₉	#9180	semidirect

Maximal subgroups

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

subgroup	index
#14573107	2
#14562194	2
#14562129	2
#14562030	2
#14561538	2
#14561493	2
C₁₉×#2351	2
#9180	19