Subgroups — #18079379

Order 4864.

480 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573451	C₂	1	1	yes	maximal, characteristic
2	#14572743	C₂	1	1	yes	maximal, characteristic
3	#14564583	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563656	C₂	1	1	yes	maximal, characteristic
5	#14562315	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561509	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₄×#64541	C₂²	1	1	yes	characteristic
10	#11926840	—	2	1	no	—
11	#11926835	—	2	1	no	—
12	#11926830	C₄	1	2	yes	complemented
13	#11926825	C₄	1	2	yes	complemented
14	C₈×Dic₃₈	—	2	1	no	—
15	C₈×D₇₆	—	2	1	no	—
16	(C₂²⋊D₁₉)⋊C₈	—	2	2	no	—
17	#11926596	—	2	1	no	—
18	#11926586	—	2	1	no	—
19	#11926568	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×D₁₉	—	2	1	no	—
22	C₂×#10597262	—	2	1	no	—
23	#11926546	—	2	1	no	—
24	#11926306	—	2	2	no	—
25	#11926304	—	2	1	no	—
26	#11926292	—	2	1	no	—
27	#11926292	—	2	1	no	—
28	C₁₉×#431	C₂²	1	1	yes	characteristic
29	C₁₉×#423	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×#64541	D₄	1	1	yes	characteristic
32	C₂²×Dic₃₈	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₄×C₂²⋊D₁₉	—	2	1	no	—
38	C₄×C₂²⋊D₁₉	—	2	1	no	—
39	#10597372	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×#64520	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
44	C₂×C₈×D₁₉	—	2	2	no	—
45	C₄×D₇₆	C₂×C₄	1	1	yes	characteristic
46	C₄×D₇₆	D₄	1	1	yes	characteristic
47	#10597318	—	2	1	no	—
48	C₄²×D₁₉	—	2	1	no	—
49	#10597315	—	2	1	no	—
50	#10597315	—	2	1	no	—
51	#10597315	—	2	1	no	—
52	#10597315	C₂×C₄	1	2	yes	—
53	C₄×Dic₃₈	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₃₈	D₄	1	1	yes	characteristic
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
58	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
59	C₁₉×C₂²⋊C₈	—	2	1	no	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	C₁₉×#95	—	2	1	no	—
62	#10597278	—	2	2	no	—
63	(C₂×D₁₉)⋊C₈	—	2	2	no	—
64	#10597275	—	2	2	no	—
65	#10597274	—	2	2	no	—
66	#10597273	—	2	2	no	—
67	Dic₁₉⋊C₈	—	2	2	no	—
68	C₈×Dic₁₉	—	2	2	no	—
69	#10597262	—	4	2	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	4	1	no	—
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
78	C₂×C₂²⋊D₁₉	—	2	1	no	—
79	C₂²×Dic₁₉	—	4	1	no	—
80	#64541	—	2	1	no	—
81	#64541	—	2	1	no	—
82	#64541	SD₁₆	1	2	yes	—
83	#64541	Q₁₆	1	2	yes	—
84	C₂×D₇₆	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₉	—	2	1	no	—
86	C₂×C₄×D₁₉	—	2	1	no	—
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×Dic₃₈	—	2	2	no	—
89	C₂×Dic₃₈	—	4	1	no	—
90	C₂×Dic₃₈	—	8	2	no	—
91	C₂×Dic₃₈	C₂²⋊C₄	1	1	yes	characteristic
92	M₁₆×C₁₉	—	4	1	no	—
93	M₁₆×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	1	no	—
96	C₂×C₈×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄²×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	—	4	1	no	—
101	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₉	#41	1	1	yes	characteristic
105	C₂²⋊Dic₁₉	—	2	1	no	—
106	(C₂×D₁₉)⋊C₄	—	2	1	no	—
107	(C₂×D₁₉)⋊C₄	—	2	1	no	—
108	C₄⋊Dic₁₉	—	2	2	no	—
109	C₄⋊Dic₁₉	—	2	2	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₄⋊Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
114	Dic₁₉⋊C₄	—	2	1	no	—
115	Dic₁₉⋊C₄	—	2	1	no	—
116	C₄×Dic₁₉	—	2	1	no	—
117	C₄×Dic₁₉	—	2	1	no	—
118	C₄×Dic₁₉	—	2	1	no	—
119	#64520	—	4	1	no	—
120	#64520	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	2	2	no	—
122	C₂×C₁₉⋊C₈	—	4	2	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₈×D₁₉	—	8	2	no	—
125	#9315	—	19	1	no	maximal, Sylow
126	C₂³×C₁₉	#121	1	1	yes	characteristic
127	C₂²×D₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	4	1	no	—
131	C₂×C₄×C₁₉	—	4	2	no	—
132	C₂×C₄×C₁₉	—	8	1	no	—
133	C₂×C₄×C₁₉	—	8	1	no	—
134	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
138	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
139	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
144	C₂²⋊D₁₉	—	2	2	no	—
145	C₂²⋊D₁₉	—	2	2	no	—
146	C₂×Dic₁₉	—	2	1	no	—
147	C₂×Dic₁₉	—	2	1	no	—
148	C₂×Dic₁₉	—	2	1	no	—
149	C₂×Dic₁₉	—	4	2	no	—
150	C₂×Dic₁₉	—	8	2	no	—
151	D₇₆	—	2	1	no	—
152	D₇₆	#103	1	2	yes	—
153	C₄×D₁₉	—	2	2	no	—
154	C₄×D₁₉	—	2	2	no	—
155	C₄×D₁₉	—	4	1	no	—
156	C₄×D₁₉	—	4	1	no	—
157	C₄×D₁₉	—	8	1	no	—
158	Dic₃₈	—	2	1	no	—
159	Dic₃₈	—	8	2	no	—
160	Dic₃₈	—	8	2	no	—
161	Dic₃₈	#103	1	2	yes	—
162	C₈×C₁₉	—	4	2	no	—
163	C₈×C₁₉	—	4	1	no	—
164	C₈×C₁₉	—	4	1	no	—
165	C₁₉⋊C₈	—	4	2	no	—
166	C₁₉⋊C₈	—	8	1	no	—
167	#3079	—	19	1	no	—
168	#2988	—	19	1	no	—
169	#1987	—	19	1	no	—
170	#1806	—	19	1	no	—
171	#1548	—	19	1	no	—
172	#1303	D₁₉	1	1	yes	characteristic, complemented
173	#1292	—	19	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	#386	1	1	yes	characteristic
177	C₂²×C₁₉	#465	1	1	yes	characteristic
178	C₂²×C₁₉	#467	1	1	yes	characteristic
179	C₂×D₁₉	—	2	2	no	—
180	C₂×D₁₉	—	4	1	no	—
181	C₂×D₁₉	—	4	1	no	—
182	C₄×C₁₉	—	2	1	no	—
183	C₄×C₁₉	—	2	1	no	—
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	8	2	no	—
186	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
187	C₄×C₁₉	#416	1	1	yes	characteristic
188	C₄×C₁₉	#455	1	1	yes	characteristic
189	C₄×C₁₉	#456	1	1	yes	characteristic
190	C₄×C₁₉	#465	1	1	yes	characteristic
191	C₄×C₁₉	#467	1	1	yes	characteristic
192	Dic₁₉	—	2	2	no	—
193	Dic₁₉	—	4	1	no	—
194	Dic₁₉	—	4	1	no	—
195	Dic₁₉	—	8	2	no	—
196	C₂×C₄⋊Q₈	—	19	1	no	—
197	C₄×#41	—	19	1	no	—
198	#477	—	38	1	no	—
199	#476	—	38	1	no	—
200	#475	—	19	2	no	—
201	#474	—	19	2	no	—
202	C₈×Q₈	—	38	1	no	—
203	C₈×D₄	—	38	1	no	—
204	C₈×D₄	—	38	2	no	—
205	#431	—	38	1	no	—
206	#431	C₂×D₁₉	1	1	yes	characteristic
207	#428	—	38	1	no	—
208	#423	—	19	1	no	—
209	#423	C₂×D₁₉	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	19	1	no	—
211	C₂×C₄⋊C₈	—	38	1	no	—
212	C₂×#104	—	38	1	no	—
213	#417	—	38	1	no	—
214	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
215	#340	—	38	2	no	—
216	#339	—	38	1	no	—
217	#333	—	38	1	no	—
218	#333	—	38	1	no	—
219	C₂×C₁₉	—	2	1	no	—
220	C₂×C₁₉	—	2	1	no	—
221	C₂×C₁₉	#1882	1	1	yes	characteristic
222	C₂×C₁₉	#1892	1	1	yes	characteristic
223	C₂×C₁₉	#1903	1	1	yes	characteristic
224	D₁₉	—	4	2	no	—
225	C₂×#41	—	19	1	no	—
226	C₂²×Q₈	—	38	1	no	—
227	C₂×M₁₆	—	2	1	no	—
228	C₂×M₁₆	—	38	1	no	—
229	C₂²×C₈	—	19	2	no	—
230	C₂²×C₈	—	38	2	no	—
231	C₄⋊Q₈	—	19	2	no	—
232	C₄⋊Q₈	—	38	1	no	—
233	C₄⋊Q₈	—	38	1	no	—
234	C₄⋊Q₈	—	38	1	no	—
235	C₄×Q₈	—	19	1	no	—
236	C₄×Q₈	—	19	1	no	—
237	C₄×D₄	—	19	1	no	—
238	C₄×D₄	—	19	1	no	—
239	C₄×D₄	—	38	1	no	—
240	C₄×D₄	—	38	1	no	—
241	#117	—	19	1	no	—
242	#117	—	38	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	38	1	no	—
245	C₂×C₄⋊C₄	—	38	1	no	—
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	—	38	1	no	—
248	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
249	#107	—	38	2	no	—
250	#106	—	38	2	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	38	2	no	—
253	C₄⋊C₈	—	38	1	no	—
254	C₄⋊C₈	—	38	1	no	—
255	C₄⋊C₈	—	38	1	no	—
256	C₄⋊C₈	—	38	1	no	—
257	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
258	C₄⋊C₈	D₇₆	1	1	yes	characteristic
259	C₄⋊C₈	D₇₆	1	1	yes	characteristic
260	#104	—	76	2	no	—
261	#103	—	38	2	no	—
262	#102	—	38	2	no	—
263	C₂²⋊C₈	—	2	1	no	—
264	C₂²⋊C₈	—	38	2	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	38	2	no	—
267	#95	—	2	1	no	—
268	C₁₉	#9315	1	1	yes	characteristic, complemented, Sylow
269	#41	—	19	2	no	—
270	#41	—	19	2	no	—
271	#41	—	38	1	no	—
272	#41	—	38	1	no	—
273	C₂×Q₈	—	19	1	no	—
274	C₂×Q₈	—	38	2	no	—
275	C₂×Q₈	—	76	1	no	—
276	C₂×Q₈	—	152	2	no	—
277	C₂×D₄	—	19	1	no	—
278	C₂×D₄	—	38	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	38	1	no	—
281	C₂²×C₄	—	38	1	no	—
282	C₂²×C₄	—	38	1	no	—
283	C₂²×C₄	—	76	1	no	—
284	C₂²×C₄	#64541	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
286	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
287	M₁₆	—	4	1	no	—
288	M₁₆	—	4	1	no	—
289	M₁₆	—	76	1	no	—
290	M₁₆	—	76	1	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	38	2	no	—
295	C₂×C₈	—	76	2	no	—
296	C₂×C₈	—	76	1	no	—
297	C₂×C₈	—	152	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	4	1	no	—
300	C₄⋊C₄	—	19	1	no	—
301	C₄⋊C₄	—	19	1	no	—
302	C₄⋊C₄	—	38	1	no	—
303	C₄⋊C₄	—	38	1	no	—
304	C₄⋊C₄	—	38	2	no	—
305	C₄⋊C₄	—	38	2	no	—
306	C₄⋊C₄	—	76	1	no	—
307	C₄⋊C₄	—	76	1	no	—
308	C₂²⋊C₄	—	38	1	no	—
309	C₂²⋊C₄	—	38	1	no	—
310	C₂²⋊C₄	—	38	1	no	—
311	C₄²	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	38	1	no	—
314	C₄²	—	38	1	no	—
315	C₄²	—	38	1	no	—
316	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
317	C₄²	C₂×D₇₆	1	1	yes	characteristic
318	C₄²	D₄×D₁₉	1	1	yes	characteristic
319	C₄²	#64545	1	1	yes	characteristic
320	C₂³	—	38	1	no	—
321	C₂³	#10597330	1	1	yes	characteristic
322	Q₈	—	19	2	no	—
323	Q₈	—	38	1	no	—
324	Q₈	—	152	2	no	—
325	Q₈	—	152	2	no	—
326	D₄	—	19	2	no	—
327	D₄	—	38	2	no	—
328	D₄	—	38	2	no	—
329	D₄	—	38	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	1	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	38	1	no	—
337	C₂×C₄	—	38	2	no	—
338	C₂×C₄	—	38	2	no	—
339	C₂×C₄	—	38	1	no	—
340	C₂×C₄	—	38	1	no	—
341	C₂×C₄	—	76	1	no	—
342	C₂×C₄	—	76	1	no	—
343	C₂×C₄	—	76	2	no	—
344	C₂×C₄	—	152	1	no	—
345	C₂×C₄	—	152	2	no	—
346	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
347	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
348	C₂×C₄	#10597328	1	1	yes	characteristic
349	C₂×C₄	#10597339	1	1	yes	characteristic
350	C₂×C₄	#10597340	1	1	yes	characteristic
351	C₂×C₄	#10597341	1	1	yes	characteristic
352	C₂×C₄	#10597358	1	1	yes	characteristic
353	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
354	C₂×C₄	#10597362	1	1	yes	characteristic
355	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
356	C₈	—	4	2	no	—
357	C₈	—	4	1	no	—
358	C₈	—	4	1	no	—
359	C₈	—	76	2	no	—
360	C₈	—	152	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	38	2	no	—
364	C₂²	—	76	1	no	—
365	C₂²	—	76	1	no	—
366	C₂²	#11926422	1	1	yes	characteristic
367	C₂²	#11926772	1	1	yes	characteristic
368	C₂²	#11926784	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	8	2	no	—
373	C₄	—	38	2	no	—
374	C₄	—	76	1	no	—
375	C₄	—	76	1	no	—
376	C₄	—	152	2	no	—
377	C₄	#103×D₁₉	1	1	yes	characteristic
378	C₄	#11926537	1	1	yes	characteristic
379	C₄	#11926723	1	1	yes	characteristic
380	C₄	#11926728	1	1	yes	characteristic
381	C₄	#11926774	1	1	yes	characteristic
382	C₄	#11926786	1	1	yes	characteristic
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	—	76	2	no	—
386	C₂	#14564005	1	1	yes	characteristic
387	C₂	#14564057	1	1	yes	characteristic
388	C₂	#14564114	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926422
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1303	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#64541	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1303	D₁₉
hypocenter	C₁₉	#9315
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1303

Complements

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

N	H ≅ G/N	type
3. #14564583	C₂	semidirect
5. #14562315	C₂	semidirect
6. #14561509	C₂	semidirect
7. C₁₉×#1303	C₂	semidirect
12. #11926830	C₄	semidirect
13. #11926825	C₄	semidirect
172. #1303	D₁₉	semidirect
268. C₁₉	#9315	semidirect

Maximal subgroups

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

subgroup	index
#14573451	2
#14572743	2
#14564583	2
#14563656	2
#14562315	2
#14561509	2
C₁₉×#1303	2
#9315	19