Subgroups — #18079280

Order 4864.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14574560	C₂	1	1	yes	maximal, characteristic
2	#14564467	C₂	1	1	yes	maximal, characteristic
3	#14562316	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×#2331	C₂	1	1	yes	maximal, characteristic, complemented
8	#11927094	C₂²	1	1	yes	characteristic
9	#11926918	C₄	1	2	yes	complemented
10	#11926894	C₄	1	2	yes	complemented
11	#11926746	—	2	2	no	—
12	#11926683	—	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	#11926293	—	2	2	no	—
19	#11926277	—	2	2	no	—
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#391	—	2	2	no	—
22	C₁₉×#389	—	2	1	no	—
23	C₁₉×#387	—	2	2	no	—
24	C₁₉×#382	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₁₉×#376	C₂²	1	1	yes	characteristic
27	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
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	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄²×C₁₉	—	2	2	no	—
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	C₂×#64527	—	2	4	no	—
42	#10597376	—	2	1	no	—
43	#10597376	—	2	1	no	—
44	C₂×#64520	—	2	1	no	—
45	#10597321	—	2	1	no	—
46	#10597320	C₂×C₄	1	1	yes	characteristic
47	C₄×D₇₆	—	2	1	no	—
48	C₄×D₇₆	—	2	1	no	—
49	#10597315	C₂×C₄	1	1	yes	characteristic
50	C₁₉×#95	—	2	2	no	—
51	C₁₉×#95	—	2	2	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	#10597292	—	2	4	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
58	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
59	#10597262	—	4	2	no	—
60	#10597262	—	4	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	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	C₂×C₄	1	2	yes	—
67	C₂×Q₈×C₁₉	—	2	2	no	—
68	C₂×Q₈×C₁₉	—	8	2	no	—
69	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₂²⋊D₁₉	—	4	1	no	—
78	#64541	—	4	1	no	—
79	#64541	—	4	1	no	—
80	#64541	—	4	1	no	—
81	#64541	—	4	1	no	—
82	C₂×D₇₆	—	2	1	no	—
83	C₂×D₇₆	—	2	1	no	—
84	C₂×D₇₆	—	2	1	no	—
85	C₂×C₄×D₁₉	—	4	1	no	—
86	C₂×Dic₃₈	—	2	1	no	—
87	C₄⋊C₄×C₁₉	—	2	2	no	—
88	C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₄⋊C₄×C₁₉	—	8	2	no	—
94	C₄²×C₁₉	—	2	1	no	—
95	C₄²×C₁₉	—	2	1	no	—
96	C₄²×C₁₉	—	2	1	no	—
97	C₄²×C₁₉	—	8	2	no	—
98	C₄²×C₁₉	SD₁₆	1	2	yes	complemented
99	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
100	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₉	#41	1	1	yes	characteristic
102	C₄²×C₁₉	#41	1	1	yes	characteristic
103	#64527	—	8	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	#64520	—	4	1	no	—
109	#64520	—	4	1	no	—
110	C₂×C₁₉⋊C₈	—	2	2	no	—
111	C₂×C₁₉⋊C₈	—	4	1	no	—
112	C₂×C₁₉⋊C₈	—	4	1	no	—
113	#9301	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	#120	1	1	yes	characteristic
115	C₂²×D₁₉	—	4	1	no	—
116	Q₈×C₁₉	—	4	4	no	—
117	Q₈×C₁₉	—	8	2	no	—
118	C₂×C₄×C₁₉	—	2	4	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	4	1	no	—
121	C₂×C₄×C₁₉	—	4	1	no	—
122	C₂×C₄×C₁₉	—	4	1	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	—	4	2	no	—
125	C₂×C₄×C₁₉	—	4	1	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	—	4	1	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	—	4	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
138	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
140	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
142	C₂²⋊D₁₉	—	8	1	no	—
143	C₂²⋊D₁₉	—	8	1	no	—
144	C₂×Dic₁₉	—	4	1	no	—
145	D₇₆	—	4	2	no	—
146	D₇₆	—	4	1	no	—
147	D₇₆	—	4	1	no	—
148	D₇₆	—	8	1	no	—
149	C₄×D₁₉	—	8	1	no	—
150	C₄×D₁₉	—	8	1	no	—
151	Dic₃₈	—	4	1	no	—
152	Dic₃₈	—	4	1	no	—
153	C₁₉⋊C₈	—	4	2	no	—
154	C₁₉⋊C₈	—	8	1	no	—
155	C₁₉⋊C₈	—	8	1	no	—
156	#3206	—	19	1	no	—
157	#2331	D₁₉	1	1	yes	characteristic, complemented
158	#1963	—	19	1	no	—
159	#1548	—	19	1	no	—
160	#1517	—	19	1	no	—
161	#1286	—	19	1	no	—
162	#1274	—	19	1	no	—
163	C₂²×C₁₉	—	2	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	#386	1	1	yes	characteristic
166	C₂²×C₁₉	#448	1	1	yes	characteristic
167	C₂²×C₁₉	#449	1	1	yes	characteristic
168	C₂×D₁₉	—	8	1	no	—
169	C₂×D₁₉	—	8	1	no	—
170	C₂×D₁₉	—	8	1	no	—
171	C₄×C₁₉	—	2	1	no	—
172	C₄×C₁₉	—	2	1	no	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	4	2	no	—
176	C₄×C₁₉	—	4	4	no	—
177	C₄×C₁₉	—	8	2	no	—
178	C₄×C₁₉	—	8	1	no	—
179	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
180	C₄×C₁₉	#440	1	1	yes	characteristic
181	C₄×C₁₉	#460	1	1	yes	characteristic
182	C₄×C₁₉	#464	1	1	yes	characteristic
183	Dic₁₉	—	8	1	no	—
184	#532	—	19	1	no	—
185	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
186	#492	—	19	2	no	—
187	#487	—	19	2	no	—
188	#461	—	38	2	no	—
189	#448	—	38	2	no	—
190	#431	—	19	1	no	—
191	#431	—	19	1	no	—
192	#423	—	19	1	no	—
193	C₂×#104	—	38	1	no	—
194	C₂×#104	—	38	1	no	—
195	#391	—	2	2	no	—
196	#389	—	2	1	no	—
197	#387	—	2	2	no	—
198	#382	C₂×D₁₉	1	1	yes	characteristic
199	C₄×C₄⋊C₄	—	2	1	no	—
200	#376	C₂×D₁₉	1	1	yes	characteristic
201	#333	—	38	2	no	—
202	#327	—	38	2	no	—
203	C₂×C₁₉	—	2	1	no	—
204	C₂×C₁₉	—	2	1	no	—
205	C₂×C₁₉	#1880	1	1	yes	characteristic
206	C₂×C₁₉	#1905	1	1	yes	characteristic
207	C₂×C₁₉	#1911	1	1	yes	characteristic
208	D₁₉	—	16	1	no	—
209	C₂×#41	—	38	1	no	—
210	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
211	C₂×SD₁₆	—	38	4	no	—
212	C₂×M₁₆	—	38	1	no	—
213	C₄⋊Q₈	—	2	1	no	—
214	C₄⋊Q₈	—	2	1	no	—
215	C₄⋊Q₈	—	19	1	no	—
216	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
217	C₄⋊Q₈	D₇₆	1	2	yes	—
218	#127	—	19	1	no	—
219	#124	—	38	1	no	—
220	#121	—	38	1	no	—
221	#121	—	38	1	no	—
222	C₄×D₄	—	38	1	no	—
223	C₄×D₄	—	38	1	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
231	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
232	C₄⋊C₈	—	38	1	no	—
233	C₄⋊C₈	—	38	1	no	—
234	C₄⋊C₈	—	38	1	no	—
235	C₄⋊C₈	—	38	1	no	—
236	#104	—	76	2	no	—
237	#104	—	76	2	no	—
238	#103	—	38	4	no	—
239	C₂²⋊C₈	—	38	1	no	—
240	C₂²⋊C₈	—	38	1	no	—
241	C₄×C₈	—	19	2	no	—
242	C₄×C₈	—	38	1	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	2	1	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	C₂²⋊D₁₉	1	2	yes	—
249	C₁₉	#9301	1	1	yes	characteristic, complemented, Sylow
250	#41	—	76	1	no	—
251	#41	—	76	1	no	—
252	#41	—	76	1	no	—
253	#41	—	76	1	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	8	2	no	—
256	C₂×Q₈	—	38	1	no	—
257	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
258	C₂×D₄	—	38	1	no	—
259	C₂×D₄	—	38	1	no	—
260	C₂×D₄	—	38	1	no	—
261	C₂×D₄	—	76	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	76	1	no	—
267	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
270	SD₁₆	—	152	4	no	—
271	M₁₆	—	76	1	no	—
272	M₁₆	—	76	1	no	—
273	C₂×C₈	—	38	2	no	—
274	C₂×C₈	—	76	1	no	—
275	C₂×C₈	—	76	1	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	4	1	no	—
281	C₄⋊C₄	—	4	1	no	—
282	C₄⋊C₄	—	8	2	no	—
283	C₄⋊C₄	—	38	1	no	—
284	C₄⋊C₄	—	38	1	no	—
285	C₂²⋊C₄	—	76	1	no	—
286	C₂²⋊C₄	—	76	1	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	8	2	no	—
291	C₄²	#64527	1	2	yes	complemented
292	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
293	C₄²	C₂×D₇₆	1	1	yes	characteristic
294	C₄²	#64541	1	1	yes	characteristic
295	C₄²	#64541	1	1	yes	characteristic
296	C₂³	—	76	1	no	—
297	C₂³	#10597399	1	1	yes	characteristic
298	Q₈	—	4	4	no	—
299	Q₈	—	8	2	no	—
300	Q₈	—	76	1	no	—
301	Q₈	—	76	1	no	—
302	D₄	—	76	2	no	—
303	D₄	—	76	1	no	—
304	D₄	—	76	1	no	—
305	D₄	—	152	1	no	—
306	D₄	—	152	1	no	—
307	D₄	—	152	1	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	76	1	no	—
323	C₂×C₄	—	152	1	no	—
324	C₂×C₄	—	152	1	no	—
325	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
327	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
328	C₂×C₄	#10597375	1	1	yes	characteristic
329	C₂×C₄	#10597376	1	1	yes	characteristic
330	C₂×C₄	#10597376	1	1	yes	characteristic
331	C₂×C₄	C₂×#64527	1	1	yes	characteristic
332	C₂×C₄	#10597388	1	1	yes	characteristic
333	C₂×C₄	#10597395	1	1	yes	characteristic
334	C₂×C₄	#10597396	1	1	yes	characteristic
335	C₈	—	76	2	no	—
336	C₈	—	152	1	no	—
337	C₈	—	152	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	152	1	no	—
341	C₂²	—	152	1	no	—
342	C₂²	—	152	1	no	—
343	C₂²	#11926423	1	1	yes	characteristic
344	C₂²	#11926683	1	1	yes	characteristic
345	C₂²	#11926689	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	4	no	—
352	C₄	—	8	2	no	—
353	C₄	—	8	1	no	—
354	C₄	—	152	1	no	—
355	C₄	C₄×#64527	1	1	yes	characteristic
356	C₄	#11926642	1	1	yes	characteristic
357	C₄	#11926744	1	1	yes	characteristic
358	C₄	#11926766	1	1	yes	characteristic
359	C₂	—	2	1	no	—
360	C₂	—	2	1	no	—
361	C₂	—	304	1	no	—
362	C₂	#14563990	1	1	yes	characteristic
363	C₂	#14564129	1	1	yes	characteristic
364	C₂	#14564167	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2331	C₂
socle	C₂²×C₁₉	#386
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2331	D₁₉
hypocenter	C₁₉	#9301
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2331

Complements

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

N	H ≅ G/N	type
3. #14562316	C₂	semidirect
5. #14561493	C₂	semidirect
6. #14561464	C₂	semidirect
7. C₁₉×#2331	C₂	semidirect
9. #11926918	C₄	semidirect
10. #11926894	C₄	semidirect
98. C₄²×C₁₉	SD₁₆	semidirect
157. #2331	D₁₉	semidirect
249. C₁₉	#9301	semidirect
291. C₄²	#64527	semidirect

Maximal subgroups

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

subgroup	index
#14574560	2
#14564467	2
#14562316	2
#14562194	2
#14561493	2
#14561464	2
C₁₉×#2331	2
#9301	19