Subgroups — #14573163

Order 2432.

458 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597361	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927114	C₂	1	1	yes	maximal, characteristic
4	#11927020	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926765	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926764	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926763	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926755	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926754	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926753	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926752	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926569	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926551	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926537	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
18	C₂×#64543	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#124	C₂²	1	1	yes	characteristic
22	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
24	#10597390	C₂²	1	1	yes	characteristic
25	C₂×#64528	C₂²	1	1	yes	characteristic
26	C₂×#64528	C₂²	1	1	yes	characteristic
27	C₂×#64528	C₂²	1	1	yes	characteristic
28	#10597382	C₂²	1	1	yes	characteristic
29	C₂×#64526	C₂²	1	1	yes	characteristic
30	Q₁₆×D₁₉	—	2	4	no	—
31	#10597361	—	2	4	no	—
32	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
33	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
34	C₂×#64515	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
36	#10597338	—	2	1	no	—
37	#10597338	C₂²	1	1	yes	characteristic
38	#10597333	—	2	1	no	—
39	#10597333	C₂²	1	1	yes	characteristic
40	#10597329	—	2	1	no	—
41	#10597329	—	2	1	no	—
42	#10597324	—	2	1	no	—
43	#10597324	—	2	1	no	—
44	#10597318	—	2	1	no	—
45	#10597318	C₂²	1	1	yes	characteristic
46	#10597315	C₂²	1	1	yes	characteristic
47	C₄×Dic₃₈	—	2	1	no	—
48	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
49	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₉×#103	C₂²	1	1	yes	characteristic
51	C₁₉×#102	C₂²	1	1	yes	characteristic
52	#10597292	C₂²	1	1	yes	characteristic
53	#10597289	C₂²	1	1	yes	characteristic
54	#10597273	C₂²	1	1	yes	characteristic
55	#10597273	C₂²	1	1	yes	characteristic
56	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
57	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
58	#10597267	C₂²	1	1	yes	characteristic
59	#10597267	C₂²	1	1	yes	characteristic
60	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
61	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₉	—	2	1	no	—
65	C₂²×Dic₁₉	—	2	1	no	—
66	Q₈×D₁₉	—	2	2	no	—
67	Q₈×D₁₉	—	2	2	no	—
68	Q₈×D₁₉	—	2	2	no	—
69	Q₈×D₁₉	D₄	1	4	yes	—
70	#64543	—	2	2	no	—
71	#64543	—	2	2	no	—
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×C₄×D₁₉	—	2	1	no	—
74	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
75	C₂×Dic₃₈	—	2	1	no	—
76	C₂×Dic₃₈	—	2	1	no	—
77	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
78	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
79	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
80	Q₁₆×C₁₉	—	2	2	no	—
81	SD₁₆×C₁₉	—	2	2	no	—
82	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₄²×C₁₉	—	2	1	no	—
89	C₄²×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²⋊Dic₁₉	—	2	1	no	—
91	C₂²⋊Dic₁₉	—	2	1	no	—
92	#64528	—	2	2	no	—
93	#64528	—	2	2	no	—
94	#64528	—	2	2	no	—
95	#64526	—	2	2	no	—
96	(C₂×D₁₉)⋊C₄	—	2	1	no	—
97	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
98	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
99	C₄⋊Dic₁₉	—	2	1	no	—
100	C₄⋊Dic₁₉	—	2	1	no	—
101	C₄⋊Dic₁₉	—	2	1	no	—
102	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
103	Dic₁₉⋊C₄	—	2	1	no	—
104	Dic₁₉⋊C₄	—	2	1	no	—
105	Dic₁₉⋊C₄	—	2	1	no	—
106	Dic₁₉⋊C₄	—	2	1	no	—
107	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
108	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
109	C₄×Dic₁₉	—	2	1	no	—
110	C₄×Dic₁₉	—	2	1	no	—
111	C₄×Dic₁₉	—	2	1	no	—
112	C₄×Dic₁₉	—	2	1	no	—
113	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
115	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
116	Dic₇₆	—	2	2	no	—
117	Dic₇₆	—	2	2	no	—
118	#64515	—	2	2	no	—
119	C₈×D₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
122	Q₈×C₁₉	—	2	1	no	—
123	Q₈×C₁₉	—	2	1	no	—
124	Q₈×C₁₉	—	2	1	no	—
125	Q₈×C₁₉	C₂×D₄	1	2	yes	—
126	D₄×C₁₉	—	2	1	no	—
127	D₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂²⋊D₁₉	—	4	2	no	—
135	C₂×Dic₁₉	—	2	1	no	—
136	C₂×Dic₁₉	—	2	1	no	—
137	C₂×Dic₁₉	—	2	1	no	—
138	C₂×Dic₁₉	—	2	1	no	—
139	C₂×Dic₁₉	—	4	2	no	—
140	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
143	C₄×D₁₉	—	2	4	no	—
144	C₄×D₁₉	—	4	2	no	—
145	C₄×D₁₉	C₂×D₄	1	2	yes	—
146	C₄×D₁₉	#41	1	2	yes	—
147	Dic₃₈	—	2	1	no	—
148	Dic₃₈	—	2	4	no	—
149	Dic₃₈	—	2	1	no	—
150	Dic₃₈	—	2	1	no	—
151	Dic₃₈	—	2	1	no	—
152	Dic₃₈	—	2	1	no	—
153	Dic₃₈	—	4	2	no	—
154	Dic₃₈	C₂×D₄	1	2	yes	—
155	C₈×C₁₉	—	2	1	no	—
156	C₈×C₁₉	—	2	1	no	—
157	C₁₉⋊C₈	—	2	1	no	—
158	C₁₉⋊C₈	—	2	1	no	—
159	#3044	—	19	1	no	maximal, Sylow
160	C₂²×C₁₉	—	4	1	no	—
161	C₂²×C₁₉	—	4	1	no	—
162	C₂²×C₁₉	—	4	1	no	—
163	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×D₁₉	—	2	1	no	—
165	C₂×D₁₉	—	2	1	no	—
166	C₂×D₁₉	#121	1	2	yes	—
167	C₄×C₁₉	—	2	2	no	—
168	C₄×C₁₉	—	2	1	no	—
169	C₄×C₁₉	—	2	1	no	—
170	C₄×C₁₉	—	4	1	no	—
171	C₄×C₁₉	—	4	1	no	—
172	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
173	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
174	Dic₁₉	—	2	2	no	—
175	Dic₁₉	—	2	1	no	—
176	Dic₁₉	—	2	1	no	—
177	Dic₁₉	—	4	1	no	—
178	Dic₁₉	—	4	1	no	—
179	Dic₁₉	—	4	1	no	—
180	Dic₁₉	#121	1	2	yes	—
181	C₂×#137	—	19	1	no	—
182	C₂²×Q₁₆	—	19	1	no	—
183	#536	—	19	1	no	—
184	#519	—	19	1	no	—
185	#464	—	19	1	no	—
186	#464	—	19	1	no	—
187	#464	—	19	1	no	—
188	#464	D₁₉	1	1	yes	characteristic, complemented
189	#462	—	19	1	no	—
190	#462	—	19	1	no	—
191	#462	—	19	1	no	—
192	#462	—	19	1	no	—
193	#424	—	19	1	no	—
194	#419	—	19	1	no	—
195	#416	—	19	1	no	—
196	C₂×C₁₉	—	8	1	no	—
197	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
198	C₂×C₁₉	#578	1	1	yes	characteristic
199	C₂×C₁₉	#578	1	1	yes	characteristic
200	D₁₉	—	2	2	no	—
201	C₂×#41	—	19	1	no	—
202	C₂²×Q₈	—	19	1	no	—
203	C₂²×Q₈	—	19	1	no	—
204	#137	—	38	4	no	—
205	C₂×Q₁₆	—	19	1	no	—
206	C₂×Q₁₆	—	19	1	no	—
207	C₂×Q₁₆	—	19	1	no	—
208	C₂×Q₁₆	—	19	1	no	—
209	C₂×Q₁₆	—	19	1	no	—
210	C₂×Q₁₆	—	38	4	no	—
211	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
212	C₂×SD₁₆	—	19	1	no	—
213	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
214	C₂×M₁₆	—	19	1	no	—
215	C₂²×C₈	—	19	1	no	—
216	C₄⋊Q₈	—	19	1	no	—
217	C₄⋊Q₈	—	19	1	no	—
218	#124	—	19	1	no	—
219	#124	C₂×D₁₉	1	1	yes	characteristic
220	#123	—	38	1	no	—
221	#123	—	38	1	no	—
222	C₂²⋊Q₈	—	38	1	no	—
223	C₂²⋊Q₈	—	38	1	no	—
224	C₄×Q₈	—	19	1	no	—
225	C₄×Q₈	—	19	1	no	—
226	C₄×Q₈	—	19	1	no	—
227	C₄×Q₈	—	38	1	no	—
228	C₄×Q₈	—	38	1	no	—
229	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
230	#117	—	19	1	no	—
231	#117	—	19	1	no	—
232	#117	—	38	1	no	—
233	#117	—	38	1	no	—
234	C₄⋊C₈	—	19	1	no	—
235	C₄⋊C₈	—	19	1	no	—
236	C₄⋊C₈	—	19	1	no	—
237	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
238	#103	—	19	1	no	—
239	#103	—	19	1	no	—
240	#103	—	19	1	no	—
241	#103	—	19	1	no	—
242	#103	—	19	1	no	—
243	#103	C₂×D₁₉	1	1	yes	characteristic
244	#102	—	19	1	no	—
245	#102	C₂×D₁₉	1	1	yes	characteristic
246	C₁₉	#3044	1	1	yes	characteristic, complemented, Sylow
247	#41	—	38	2	no	—
248	#41	—	38	2	no	—
249	C₂×Q₈	—	19	4	no	—
250	C₂×Q₈	—	19	1	no	—
251	C₂×Q₈	—	19	1	no	—
252	C₂×Q₈	—	19	1	no	—
253	C₂×Q₈	—	38	1	no	—
254	C₂×Q₈	—	38	1	no	—
255	C₂×Q₈	—	38	2	no	—
256	C₂×Q₈	—	38	2	no	—
257	C₂×Q₈	—	38	2	no	—
258	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
259	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
260	C₂×D₄	—	38	1	no	—
261	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
262	C₂²×C₄	—	19	1	no	—
263	C₂²×C₄	—	38	1	no	—
264	C₂²×C₄	—	38	1	no	—
265	C₂²×C₄	—	38	1	no	—
266	Q₁₆	—	2	2	no	—
267	Q₁₆	—	38	2	no	—
268	Q₁₆	—	38	2	no	—
269	Q₁₆	—	38	2	no	—
270	Q₁₆	—	38	2	no	—
271	Q₁₆	—	38	2	no	—
272	SD₁₆	—	2	2	no	—
273	SD₁₆	—	38	2	no	—
274	M₁₆	—	38	2	no	—
275	C₂×C₈	—	19	1	no	—
276	C₂×C₈	—	19	1	no	—
277	C₂×C₈	—	38	2	no	—
278	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
279	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	19	1	no	—
282	C₄⋊C₄	—	19	1	no	—
283	C₄⋊C₄	—	19	1	no	—
284	C₄⋊C₄	—	38	1	no	—
285	C₄⋊C₄	—	38	1	no	—
286	C₄⋊C₄	—	38	1	no	—
287	C₄⋊C₄	—	38	1	no	—
288	C₄⋊C₄	—	38	1	no	—
289	C₄⋊C₄	—	38	1	no	—
290	C₄⋊C₄	—	38	1	no	—
291	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	19	1	no	—
295	C₂²⋊C₄	—	19	1	no	—
296	C₂²⋊C₄	—	38	1	no	—
297	C₂²⋊C₄	—	38	1	no	—
298	C₂²⋊C₄	—	38	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	19	1	no	—
301	C₄²	—	38	1	no	—
302	C₄²	—	38	1	no	—
303	C₄²	—	38	1	no	—
304	C₄²	—	38	1	no	—
305	C₄²	C₂²×D₁₉	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	19	1	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	2	1	no	—
310	Q₈	—	2	1	no	—
311	Q₈	—	19	2	no	—
312	Q₈	—	38	4	no	—
313	Q₈	—	38	1	no	—
314	Q₈	—	38	1	no	—
315	Q₈	—	38	1	no	—
316	Q₈	—	38	1	no	—
317	Q₈	—	38	1	no	—
318	Q₈	—	76	2	no	—
319	Q₈	D₄×D₁₉	1	2	yes	—
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	76	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	19	1	no	—
327	C₂×C₄	—	19	2	no	—
328	C₂×C₄	—	19	2	no	—
329	C₂×C₄	—	19	1	no	—
330	C₂×C₄	—	19	1	no	—
331	C₂×C₄	—	38	4	no	—
332	C₂×C₄	—	38	1	no	—
333	C₂×C₄	—	38	1	no	—
334	C₂×C₄	—	38	1	no	—
335	C₂×C₄	—	38	1	no	—
336	C₂×C₄	—	76	2	no	—
337	C₂×C₄	—	76	2	no	—
338	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
339	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	2	1	no	—
343	C₈	—	38	1	no	—
344	C₈	—	38	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	19	2	no	—
349	C₂²	—	38	1	no	—
350	C₂²	—	38	1	no	—
351	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	2	no	—
355	C₄	—	4	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	19	2	no	—
358	C₄	—	38	1	no	—
359	C₄	—	38	1	no	—
360	C₄	—	38	2	no	—
361	C₄	—	76	1	no	—
362	C₄	—	76	1	no	—
363	C₄	—	76	1	no	—
364	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
365	C₄	#41×D₁₉	1	1	yes	characteristic
366	C₂	—	8	1	no	—
367	C₂	—	38	2	no	—
368	C₂	#121×D₁₉	1	1	yes	characteristic
369	C₂	#11927358	1	1	yes	characteristic
370	C₂	#11927360	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#464	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#64543	C₂²
hypercenter	#464	D₁₉
hypocenter	C₁₉	#3044
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #464

Complements

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

N	H ≅ G/N	type
2. C₂×Q₁₆×D₁₉	C₂	semidirect
4. #11927020	C₂	semidirect
5. #11926765	C₂	semidirect
6. #11926764	C₂	semidirect
7. #11926763	C₂	semidirect
8. #11926755	C₂	semidirect
9. #11926754	C₂	semidirect
10. #11926753	C₂	semidirect
11. #11926752	C₂	semidirect
12. #11926569	C₂	semidirect
13. #11926551	C₂	semidirect
15. C₁₉×#464	C₂	semidirect
188. #464	D₁₉	semidirect
246. C₁₉	#3044	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597361	2
C₂×Q₁₆×D₁₉	2
#11927114	2
#11927020	2
#11926765	2
#11926764	2
#11926763	2
#11926755	2
#11926754	2
#11926753	2
#11926752	2
#11926569	2
#11926551	2
#11926537	2
C₁₉×#464	2
#3044	19