Subgroups — #18079343

Order 4864.

470 conjugacy classes of subgroups.

The subgroup lattice has 368 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	#14563650	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562196	C₂	1	1	yes	maximal, characteristic
4	#14562035	C₂	1	1	yes	maximal, characteristic
5	#14561531	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2983	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	#11926568	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	#11926543	—	2	1	no	—
16	C₂×#10597292	—	2	1	no	—
17	#11926410	C₂²	1	1	yes	characteristic
18	#11926306	—	2	1	no	—
19	#11926279	—	2	2	no	—
20	#11926273	—	2	2	no	—
21	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#446	—	2	2	no	—
23	C₁₉×#446	—	2	2	no	—
24	C₁₉×#432	—	2	2	no	—
25	C₁₉×#431	C₂²	1	1	yes	characteristic
26	C₁₉×#431	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂×#64541	—	2	1	no	—
29	C₄×Q₈×C₁₉	—	2	1	no	—
30	C₄×Q₈×C₁₉	—	2	1	no	—
31	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
32	C₄×Q₈×C₁₉	D₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×#64528	—	2	2	no	—
38	#10597388	—	4	2	no	—
39	#10597388	—	4	2	no	—
40	C₂×#64527	—	2	2	no	—
41	#10597376	—	2	1	no	—
42	#10597376	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	—	2	1	no	—
44	C₂×#64520	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	#10597321	—	2	1	no	—
47	#10597320	C₂×C₄	1	1	yes	characteristic
48	C₄×D₇₆	—	2	1	no	—
49	C₄×D₇₆	—	2	1	no	—
50	#10597315	C₂×C₄	1	1	yes	characteristic
51	C₁₉×C₄⋊C₈	—	2	4	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₁₉×C₂²⋊C₈	—	2	1	no	—
55	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
56	C₁₉×#97	—	2	4	no	—
57	C₄×C₈×C₁₉	—	2	1	no	—
58	C₄×C₈×C₁₉	D₄	1	2	yes	—
59	#10597292	—	4	2	no	—
60	C₁₉⋊#95	—	2	1	no	—
61	C₁₉⋊#95	—	2	1	no	—
62	#10597267	—	2	2	no	—
63	#10597266	—	2	2	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
68	C₂×Q₈×C₁₉	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂×C₂²⋊D₁₉	—	4	1	no	—
80	C₂²×Dic₁₉	—	4	1	no	—
81	#64541	—	4	1	no	—
82	#64541	—	4	1	no	—
83	#64541	—	4	1	no	—
84	#64541	—	4	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×C₄×D₁₉	—	4	1	no	—
89	C₂×Dic₃₈	—	2	1	no	—
90	C₂×C₈×C₁₉	—	2	2	no	—
91	C₂×C₈×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	2	no	—
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	—	2	2	no	—
95	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₁₉	—	2	2	no	—
97	C₄²×C₁₉	—	2	2	no	—
98	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₉	#41	1	1	yes	characteristic
102	#64528	—	4	4	no	—
103	#64527	—	4	4	no	—
104	(C₂×D₁₉)⋊C₄	—	4	1	no	—
105	(C₂×D₁₉)⋊C₄	—	4	1	no	—
106	C₄⋊Dic₁₉	—	2	1	no	—
107	C₄⋊Dic₁₉	—	2	1	no	—
108	C₄⋊Dic₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	1	no	—
110	#64520	—	4	1	no	—
111	#64520	—	4	1	no	—
112	C₂×C₁₉⋊C₈	—	2	2	no	—
113	C₂×C₁₉⋊C₈	—	4	1	no	—
114	C₂×C₁₉⋊C₈	—	4	1	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	#9310	—	19	1	no	maximal, Sylow
117	C₂³×C₁₉	#121	1	1	yes	characteristic
118	C₂²×D₁₉	—	4	1	no	—
119	Q₈×C₁₉	—	2	2	no	—
120	Q₈×C₁₉	—	2	2	no	—
121	Q₈×C₁₉	—	4	1	no	—
122	Q₈×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	1	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	1	no	—
129	C₂×C₄×C₁₉	—	8	1	no	—
130	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
136	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
137	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
140	C₂²⋊D₁₉	—	8	1	no	—
141	C₂²⋊D₁₉	—	8	1	no	—
142	C₂×Dic₁₉	—	4	1	no	—
143	C₂×Dic₁₉	—	8	1	no	—
144	C₂×Dic₁₉	—	8	1	no	—
145	C₂×Dic₁₉	—	8	1	no	—
146	D₇₆	—	4	2	no	—
147	D₇₆	—	4	1	no	—
148	D₇₆	—	4	1	no	—
149	D₇₆	—	8	1	no	—
150	C₄×D₁₉	—	8	1	no	—
151	C₄×D₁₉	—	8	1	no	—
152	Dic₃₈	—	4	1	no	—
153	Dic₃₈	—	4	1	no	—
154	C₈×C₁₉	—	4	2	no	—
155	C₈×C₁₉	—	4	2	no	—
156	C₁₉⋊C₈	—	4	2	no	—
157	C₁₉⋊C₈	—	8	1	no	—
158	#3037	—	19	1	no	—
159	#2983	D₁₉	1	1	yes	characteristic, complemented
160	#1805	—	19	1	no	—
161	#1517	—	19	1	no	—
162	#1480	—	19	1	no	—
163	#1301	—	19	1	no	—
164	#1286	—	19	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	—	2	1	no	—
167	C₂²×C₁₉	#386	1	1	yes	characteristic
168	C₂²×C₁₉	#468	1	1	yes	characteristic
169	C₂²×C₁₉	#469	1	1	yes	characteristic
170	C₂×D₁₉	—	8	1	no	—
171	C₂×D₁₉	—	8	1	no	—
172	C₂×D₁₉	—	8	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	2	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	4	2	no	—
178	C₄×C₁₉	—	4	2	no	—
179	C₄×C₁₉	#417	1	1	yes	characteristic
180	C₄×C₁₉	#418	1	1	yes	characteristic
181	C₄×C₁₉	#468	1	1	yes	characteristic
182	C₄×C₁₉	#469	1	1	yes	characteristic
183	Dic₁₉	—	8	1	no	—
184	Dic₁₉	—	16	1	no	—
185	C₂×#137	—	38	1	no	—
186	#532	—	19	1	no	—
187	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
188	#464	—	38	2	no	—
189	#462	—	19	2	no	—
190	#460	—	19	2	no	—
191	#446	—	2	2	no	—
192	#446	—	2	2	no	—
193	#432	—	2	2	no	—
194	#431	C₂×D₁₉	1	1	yes	characteristic
195	#431	C₂×D₁₉	1	1	yes	characteristic
196	#423	—	19	1	no	—
197	C₂×C₄⋊C₈	—	19	1	no	—
198	#417	—	38	1	no	—
199	C₂×#103	—	38	1	no	—
200	#382	—	19	1	no	—
201	#340	—	38	1	no	—
202	#327	—	38	2	no	—
203	D₄⋊C₈	—	38	2	no	—
204	C₂×C₁₉	—	2	1	no	—
205	C₂×C₁₉	—	2	1	no	—
206	C₂×C₁₉	#1881	1	1	yes	characteristic
207	C₂×C₁₉	#1895	1	1	yes	characteristic
208	C₂×C₁₉	#1905	1	1	yes	characteristic
209	D₁₉	—	16	1	no	—
210	C₂×#41	—	38	1	no	—
211	C₂²×Q₈	D₇₆	1	1	yes	characteristic
212	#137	—	76	2	no	—
213	#137	—	76	2	no	—
214	C₂×Q₁₆	—	38	2	no	—
215	C₂×SD₁₆	—	38	2	no	—
216	C₂×M₁₆	—	38	1	no	—
217	C₂²×C₈	—	38	1	no	—
218	C₄⋊Q₈	—	19	1	no	—
219	#127	—	19	1	no	—
220	#124	—	38	1	no	—
221	#121	—	38	1	no	—
222	#121	—	38	1	no	—
223	C₄×Q₈	—	2	1	no	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	C₄×D₁₉	1	2	yes	—
226	C₄×Q₈	C₂²⋊D₁₉	1	2	yes	—
227	C₄×D₄	—	38	1	no	—
228	C₄×D₄	—	38	1	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	38	1	no	—
231	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
234	C₄⋊C₈	—	2	4	no	—
235	C₄⋊C₈	—	2	1	no	—
236	C₄⋊C₈	—	2	1	no	—
237	C₄⋊C₈	—	19	2	no	—
238	C₄⋊C₈	—	38	1	no	—
239	C₄⋊C₈	—	38	1	no	—
240	C₄⋊C₈	—	38	1	no	—
241	#103	—	38	2	no	—
242	#103	—	76	2	no	—
243	#102	—	38	2	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	C₂²⋊C₈	C₂²⋊D₁₉	1	2	yes	—
246	#97	—	2	4	no	—
247	C₄×C₈	—	2	1	no	—
248	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
249	#95	—	38	1	no	—
250	#95	—	38	1	no	—
251	C₁₉	#9310	1	1	yes	characteristic, complemented, Sylow
252	#41	—	76	1	no	—
253	#41	—	76	1	no	—
254	#41	—	76	1	no	—
255	#41	—	76	1	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	2	1	no	—
258	C₂×Q₈	—	2	1	no	—
259	C₂×Q₈	—	2	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	38	1	no	—
262	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
263	C₂×D₄	—	38	1	no	—
264	C₂×D₄	—	38	1	no	—
265	C₂×D₄	—	38	1	no	—
266	C₂×D₄	—	76	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	76	1	no	—
270	C₂²×C₄	—	76	1	no	—
271	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
272	C₂²×C₄	#64541	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
274	Q₁₆	—	76	4	no	—
275	SD₁₆	—	76	4	no	—
276	M₁₆	—	76	1	no	—
277	M₁₆	—	76	1	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	38	2	no	—
281	C₂×C₈	—	76	1	no	—
282	C₂×C₈	—	76	1	no	—
283	C₂×C₈	—	76	1	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	38	1	no	—
288	C₄⋊C₄	—	38	1	no	—
289	C₄⋊C₄	—	76	1	no	—
290	C₄⋊C₄	—	76	1	no	—
291	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
292	C₂²⋊C₄	—	76	1	no	—
293	C₂²⋊C₄	—	76	1	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
297	C₄²	#64541	1	1	yes	characteristic
298	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
299	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
300	C₂³	—	76	1	no	—
301	C₂³	#10597376	1	1	yes	characteristic
302	Q₈	—	2	2	no	—
303	Q₈	—	2	2	no	—
304	Q₈	—	4	1	no	—
305	Q₈	—	4	1	no	—
306	Q₈	—	76	1	no	—
307	Q₈	—	76	1	no	—
308	D₄	—	76	2	no	—
309	D₄	—	76	1	no	—
310	D₄	—	76	1	no	—
311	D₄	—	152	1	no	—
312	D₄	—	152	1	no	—
313	D₄	—	152	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	8	1	no	—
321	C₂×C₄	—	76	1	no	—
322	C₂×C₄	—	152	1	no	—
323	C₂×C₄	—	152	1	no	—
324	C₂×C₄	—	152	1	no	—
325	C₂×C₄	—	152	1	no	—
326	C₂×C₄	—	152	1	no	—
327	C₂×C₄	#10597354	1	1	yes	characteristic
328	C₂×C₄	#10597354	1	1	yes	characteristic
329	C₂×C₄	#10597354	1	1	yes	characteristic
330	C₂×C₄	#10597355	1	1	yes	characteristic
331	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
333	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
334	C₂×C₄	#10597375	1	1	yes	characteristic
335	C₂×C₄	#10597376	1	1	yes	characteristic
336	C₂×C₄	#10597399	1	1	yes	characteristic
337	C₈	—	4	2	no	—
338	C₈	—	4	2	no	—
339	C₈	—	76	2	no	—
340	C₈	—	152	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	152	1	no	—
344	C₂²	—	152	1	no	—
345	C₂²	—	152	1	no	—
346	C₂²	#11926423	1	1	yes	characteristic
347	C₂²	#11926790	1	1	yes	characteristic
348	C₂²	#11926797	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	304	1	no	—
356	C₄	—	152	1	no	—
357	C₄	#11926546	1	1	yes	characteristic
358	C₄	#11926550	1	1	yes	characteristic
359	C₄	#11926790	1	1	yes	characteristic
360	C₄	#11926797	1	1	yes	characteristic
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	—	304	1	no	—
364	C₂	#14563997	1	1	yes	characteristic
365	C₂	#14564073	1	1	yes	characteristic
366	C₂	#14564129	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2983	C₂
socle	C₂²×C₁₉	#386
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2983	D₁₉
hypocenter	C₁₉	#9310
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2983

Complements

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

N	H ≅ G/N	type
2. #14563650	C₂	semidirect
5. #14561531	C₂	semidirect
6. #14561494	C₂	semidirect
7. C₁₉×#2983	C₂	semidirect
11. #11926754	C₄	semidirect
12. #11926744	C₄	semidirect
159. #2983	D₁₉	semidirect
251. C₁₉	#9310	semidirect

Maximal subgroups

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

subgroup	index
#14573107	2
#14563650	2
#14562196	2
#14562035	2
#14561531	2
#14561494	2
C₁₉×#2983	2
#9310	19