Subgroups — #18079273

Order 4864.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14574756	C₂	1	1	yes	maximal, characteristic
2	#14564467	C₂	1	1	yes	maximal, characteristic
3	#14562307	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562194	C₂	1	1	yes	maximal, characteristic
5	#14561493	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561464	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927094	C₂²	1	1	yes	characteristic
9	#11926947	C₄	1	2	yes	complemented
10	#11926892	C₄	1	2	yes	complemented
11	#11926857	—	2	2	no	—
12	#11926821	—	2	2	no	—
13	#11926597	C₂²	1	1	yes	characteristic
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926568	C₂²	1	1	yes	characteristic
16	C₂×#10597262	—	2	1	no	—
17	C₂×#10597262	—	2	1	no	—
18	#11926290	—	2	2	no	—
19	#11926277	—	2	2	no	—
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
22	C₁₉×#391	—	2	1	no	—
23	C₁₉×#387	—	2	2	no	—
24	C₁₉×#387	—	2	2	no	—
25	C₁₉×#382	C₂²	1	1	yes	characteristic
26	C₁₉×#376	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	—	2	1	no	—
28	C₂×#64541	—	2	1	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	—	2	1	no	—
31	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
32	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
33	C₄×Q₈×C₁₉	—	4	2	no	—
34	C₄×Q₈×C₁₉	—	4	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
39	C₂×C₄²×C₁₉	—	2	2	no	—
40	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	#10597376	—	2	1	no	—
44	#10597376	—	2	1	no	—
45	C₂×#64520	—	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×#95	—	2	4	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	D₄	1	2	yes	—
56	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
58	#10597266	—	2	4	no	—
59	#10597264	—	2	4	no	—
60	#10597262	—	4	2	no	—
61	#10597262	—	4	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	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	2	no	—
69	C₂×Q₈×C₁₉	—	2	2	no	—
70	C₂×Q₈×C₁₉	—	4	1	no	—
71	C₂×Q₈×C₁₉	—	4	1	no	—
72	C₂×Q₈×C₁₉	—	4	1	no	—
73	C₂×Q₈×C₁₉	—	4	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₂²⋊D₁₉	—	4	1	no	—
82	#64541	—	4	1	no	—
83	#64541	—	4	1	no	—
84	#64541	—	4	1	no	—
85	#64541	—	4	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	—	2	1	no	—
89	C₂×C₄×D₁₉	—	4	1	no	—
90	C₂×Dic₃₈	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₄⋊C₄×C₁₉	—	2	2	no	—
93	C₄⋊C₄×C₁₉	—	2	2	no	—
94	C₄⋊C₄×C₁₉	—	4	4	no	—
95	C₄⋊C₄×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	4	1	no	—
97	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
98	C₄²×C₁₉	—	2	1	no	—
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	—	2	1	no	—
101	C₄²×C₁₉	—	4	4	no	—
102	C₄²×C₁₉	D₈	1	2	yes	—
103	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	C₄²×C₁₉	#41	1	1	yes	characteristic
107	(C₂×D₁₉)⋊C₄	—	4	1	no	—
108	(C₂×D₁₉)⋊C₄	—	4	1	no	—
109	C₄⋊Dic₁₉	—	2	1	no	—
110	C₄⋊Dic₁₉	—	2	1	no	—
111	#64520	—	4	1	no	—
112	#64520	—	4	1	no	—
113	C₂×C₁₉⋊C₈	—	2	2	no	—
114	C₂×C₁₉⋊C₈	—	4	1	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	#9300	—	19	1	no	maximal, Sylow
117	C₂³×C₁₉	#120	1	1	yes	characteristic
118	C₂²×D₁₉	—	4	1	no	—
119	Q₈×C₁₉	—	4	2	no	—
120	Q₈×C₁₉	—	4	2	no	—
121	Q₈×C₁₉	—	4	2	no	—
122	Q₈×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	2	4	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	—	4	2	no	—
130	C₂×C₄×C₁₉	—	4	2	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	4	1	no	—
133	C₂×C₄×C₁₉	—	4	2	no	—
134	C₂×C₄×C₁₉	—	4	1	no	—
135	C₂×C₄×C₁₉	—	4	2	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
145	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂²⋊D₁₉	—	8	1	no	—
148	C₂²⋊D₁₉	—	8	1	no	—
149	C₂×Dic₁₉	—	4	1	no	—
150	D₇₆	—	4	2	no	—
151	D₇₆	—	4	1	no	—
152	D₇₆	—	4	1	no	—
153	D₇₆	—	8	1	no	—
154	C₄×D₁₉	—	8	1	no	—
155	C₄×D₁₉	—	8	1	no	—
156	Dic₃₈	—	4	1	no	—
157	Dic₃₈	—	4	1	no	—
158	C₁₉⋊C₈	—	4	2	no	—
159	C₁₉⋊C₈	—	8	1	no	—
160	C₁₉⋊C₈	—	8	1	no	—
161	#3226	—	19	1	no	—
162	#2327	D₁₉	1	1	yes	characteristic, complemented
163	#1963	—	19	1	no	—
164	#1546	—	19	1	no	—
165	#1517	—	19	1	no	—
166	#1286	—	19	1	no	—
167	#1274	—	19	1	no	—
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	#386	1	1	yes	characteristic
171	C₂²×C₁₉	#447	1	1	yes	characteristic
172	C₂²×C₁₉	#449	1	1	yes	characteristic
173	C₂×D₁₉	—	8	1	no	—
174	C₂×D₁₉	—	8	1	no	—
175	C₂×D₁₉	—	8	1	no	—
176	C₄×C₁₉	—	2	1	no	—
177	C₄×C₁₉	—	2	1	no	—
178	C₄×C₁₉	—	2	1	no	—
179	C₄×C₁₉	—	2	1	no	—
180	C₄×C₁₉	—	4	2	no	—
181	C₄×C₁₉	—	4	4	no	—
182	C₄×C₁₉	—	8	2	no	—
183	C₄×C₁₉	—	8	1	no	—
184	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
185	C₄×C₁₉	#442	1	1	yes	characteristic
186	C₄×C₁₉	#459	1	1	yes	characteristic
187	C₄×C₁₉	#463	1	1	yes	characteristic
188	Dic₁₉	—	8	1	no	—
189	#532	—	19	1	no	—
190	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
191	C₂×C₄×Q₈	—	2	1	no	—
192	#500	—	19	2	no	—
193	#486	—	19	2	no	—
194	#480	—	38	2	no	—
195	#474	—	38	2	no	—
196	#431	—	19	1	no	—
197	#431	—	19	1	no	—
198	#423	—	19	1	no	—
199	C₂×#104	—	38	1	no	—
200	C₂×#104	—	38	1	no	—
201	#391	—	2	1	no	—
202	#387	—	2	2	no	—
203	#387	—	2	2	no	—
204	#382	C₂×D₁₉	1	1	yes	characteristic
205	#376	C₂×D₁₉	1	1	yes	characteristic
206	#332	—	38	2	no	—
207	#327	—	38	2	no	—
208	C₂×C₁₉	—	2	1	no	—
209	C₂×C₁₉	—	2	1	no	—
210	C₂×C₁₉	#1879	1	1	yes	characteristic
211	C₂×C₁₉	#1905	1	1	yes	characteristic
212	C₂×C₁₉	#1912	1	1	yes	characteristic
213	D₁₉	—	16	1	no	—
214	C₂×#41	—	38	1	no	—
215	C₂²×Q₈	—	2	1	no	—
216	C₂×M₁₆	—	38	1	no	—
217	C₄⋊Q₈	—	2	1	no	—
218	C₄⋊Q₈	—	2	1	no	—
219	C₄⋊Q₈	—	19	1	no	—
220	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
221	C₄⋊Q₈	D₇₆	1	2	yes	—
222	#127	—	19	1	no	—
223	#124	—	38	1	no	—
224	#121	—	38	1	no	—
225	#121	—	38	1	no	—
226	C₄×Q₈	—	4	2	no	—
227	C₄×Q₈	—	4	2	no	—
228	C₄×D₄	—	38	1	no	—
229	C₄×D₄	—	38	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
234	C₂×C₄²	—	2	2	no	—
235	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
236	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
238	#107	—	38	4	no	—
239	C₄⋊C₈	—	38	1	no	—
240	C₄⋊C₈	—	38	1	no	—
241	C₄⋊C₈	—	38	1	no	—
242	C₄⋊C₈	—	38	1	no	—
243	#104	—	76	2	no	—
244	#104	—	76	2	no	—
245	#102	—	38	4	no	—
246	C₂²⋊C₈	—	38	1	no	—
247	C₂²⋊C₈	—	38	1	no	—
248	C₄×C₈	—	19	2	no	—
249	C₄×C₈	—	38	1	no	—
250	#95	—	2	4	no	—
251	#95	—	2	1	no	—
252	#95	—	2	1	no	—
253	#95	—	2	1	no	—
254	#95	C₂²⋊D₁₉	1	2	yes	—
255	C₁₉	#9300	1	1	yes	characteristic, complemented, Sylow
256	#41	—	76	1	no	—
257	#41	—	76	1	no	—
258	#41	—	76	1	no	—
259	#41	—	76	1	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	—	4	1	no	—
264	C₂×Q₈	—	4	1	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂×Q₈	—	38	1	no	—
267	C₂×D₄	—	38	1	no	—
268	C₂×D₄	—	38	1	no	—
269	C₂×D₄	—	38	1	no	—
270	C₂×D₄	—	76	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	76	1	no	—
276	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
279	M₁₆	—	76	1	no	—
280	M₁₆	—	76	1	no	—
281	C₂×C₈	—	38	2	no	—
282	C₂×C₈	—	76	1	no	—
283	C₂×C₈	—	76	1	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	4	4	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	—	38	1	no	—
291	C₄⋊C₄	—	38	1	no	—
292	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
293	C₂²⋊C₄	—	76	1	no	—
294	C₂²⋊C₄	—	76	1	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	4	4	no	—
299	C₄²	#64525	1	2	yes	—
300	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
301	C₄²	C₂×D₇₆	1	1	yes	characteristic
302	C₄²	#64541	1	1	yes	characteristic
303	C₄²	#64541	1	1	yes	characteristic
304	C₂³	—	76	1	no	—
305	C₂³	#10597399	1	1	yes	characteristic
306	Q₈	—	4	2	no	—
307	Q₈	—	4	2	no	—
308	Q₈	—	4	2	no	—
309	Q₈	—	4	2	no	—
310	Q₈	—	76	1	no	—
311	Q₈	—	76	1	no	—
312	D₄	—	76	2	no	—
313	D₄	—	76	1	no	—
314	D₄	—	76	1	no	—
315	D₄	—	152	1	no	—
316	D₄	—	152	1	no	—
317	D₄	—	152	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	76	1	no	—
333	C₂×C₄	—	152	1	no	—
334	C₂×C₄	—	152	1	no	—
335	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
337	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
338	C₂×C₄	#10597375	1	1	yes	characteristic
339	C₂×C₄	#10597376	1	1	yes	characteristic
340	C₂×C₄	#10597376	1	1	yes	characteristic
341	C₂×C₄	C₂×#64525	1	1	yes	characteristic
342	C₂×C₄	#10597378	1	1	yes	characteristic
343	C₂×C₄	#10597395	1	1	yes	characteristic
344	C₂×C₄	#10597396	1	1	yes	characteristic
345	C₈	—	76	2	no	—
346	C₈	—	152	1	no	—
347	C₈	—	152	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	152	1	no	—
351	C₂²	—	152	1	no	—
352	C₂²	—	152	1	no	—
353	C₂²	#11926423	1	1	yes	characteristic
354	C₂²	#11926678	1	1	yes	characteristic
355	C₂²	#11926689	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	4	no	—
362	C₄	—	8	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	152	1	no	—
365	C₄	C₄×#64525	1	1	yes	characteristic
366	C₄	#11926654	1	1	yes	characteristic
367	C₄	#11926739	1	1	yes	characteristic
368	C₄	#11926759	1	1	yes	characteristic
369	C₂	—	2	1	no	—
370	C₂	—	2	1	no	—
371	C₂	—	304	1	no	—
372	C₂	#14563983	1	1	yes	characteristic
373	C₂	#14564129	1	1	yes	characteristic
374	C₂	#14564172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2327	C₂
socle	C₂²×C₁₉	#386
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2327	D₁₉
hypocenter	C₁₉	#9300
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2327

Complements

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

N	H ≅ G/N	type
3. #14562307	C₂	semidirect
5. #14561493	C₂	semidirect
6. #14561464	C₂	semidirect
7. C₁₉×#2327	C₂	semidirect
9. #11926947	C₄	semidirect
10. #11926892	C₄	semidirect
162. #2327	D₁₉	semidirect
255. C₁₉	#9300	semidirect

Maximal subgroups

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

subgroup	index
#14574756	2
#14564467	2
#14562307	2
#14562194	2
#14561493	2
#14561464	2
C₁₉×#2327	2
#9300	19