Subgroups — #14569050

Order 2432.

428 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926486	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926478	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926467	C₂	1	1	yes	maximal, characteristic
4	#11926467	C₂	1	1	yes	maximal, characteristic
5	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926441	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926437	C₂	1	1	yes	maximal, characteristic
9	#11926437	C₂	1	1	yes	maximal, characteristic
10	#11926431	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926428	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926417	C₂	1	1	yes	maximal, characteristic
13	#11926417	C₂	1	1	yes	maximal, characteristic
14	C₄×Dic₁₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#95	C₂²	1	1	yes	characteristic
40	C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₁₉⋊#95	C₂²	1	1	yes	characteristic
42	C₁₉⋊#95	C₂²	1	1	yes	characteristic
43	C₁₉⋊#95	C₂²	1	1	yes	characteristic
44	C₁₉⋊#95	C₂²	1	1	yes	characteristic
45	C₁₉⋊#95	C₂²	1	1	yes	characteristic
46	C₁₉⋊#95	C₂²	1	1	yes	characteristic
47	C₁₉⋊#95	C₂²	1	1	yes	characteristic
48	C₁₉⋊#95	C₂²	1	1	yes	characteristic
49	C₁₉⋊#95	C₂²	1	1	yes	characteristic
50	C₁₉⋊#95	C₂²	1	1	yes	characteristic
51	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	4	1	no	—
54	C₂²×C₄×C₁₉	—	4	1	no	—
55	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
66	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
67	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
68	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
69	C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂²⋊C₄×C₁₉	Q₈	1	4	yes	—
71	C₄²×C₁₉	—	4	1	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₂²⋊Dic₁₉	—	2	2	no	—
74	C₂²⋊Dic₁₉	—	2	2	no	—
75	C₂²⋊Dic₁₉	—	4	1	no	—
76	C₂²⋊Dic₁₉	—	4	1	no	—
77	C₄⋊Dic₁₉	—	2	2	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	C₄⋊Dic₁₉	—	4	1	no	—
80	C₄⋊Dic₁₉	—	4	1	no	—
81	Dic₁₉⋊C₄	—	2	2	no	—
82	Dic₁₉⋊C₄	—	2	2	no	—
83	Dic₁₉⋊C₄	—	2	2	no	—
84	Dic₁₉⋊C₄	—	2	2	no	—
85	Dic₁₉⋊C₄	—	2	2	no	—
86	Dic₁₉⋊C₄	—	4	1	no	—
87	Dic₁₉⋊C₄	—	4	1	no	—
88	Dic₁₉⋊C₄	—	4	1	no	—
89	C₄×Dic₁₉	—	2	2	no	—
90	C₄×Dic₁₉	—	4	1	no	—
91	C₂³×C₁₉	—	2	1	no	—
92	C₂³×C₁₉	—	2	1	no	—
93	C₂³×C₁₉	—	2	1	no	—
94	C₂³×C₁₉	—	2	1	no	—
95	C₂³×C₁₉	—	2	1	no	—
96	C₂³×C₁₉	—	2	1	no	—
97	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
98	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	4	4	no	—
114	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
115	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
116	C₂×C₄×C₁₉	#41	1	2	yes	—
117	C₂×C₄×C₁₉	#41	1	2	yes	—
118	C₂×Dic₁₉	—	2	1	no	—
119	C₂×Dic₁₉	—	2	1	no	—
120	C₂×Dic₁₉	—	2	1	no	—
121	C₂×Dic₁₉	—	2	1	no	—
122	C₂×Dic₁₉	—	2	1	no	—
123	C₂×Dic₁₉	—	2	1	no	—
124	C₂×Dic₁₉	—	2	1	no	—
125	C₂×Dic₁₉	—	2	1	no	—
126	C₂×Dic₁₉	—	2	1	no	—
127	C₂×Dic₁₉	—	2	1	no	—
128	C₂×Dic₁₉	—	2	1	no	—
129	C₂×Dic₁₉	—	2	1	no	—
130	C₂×Dic₁₉	—	2	1	no	—
131	C₂×Dic₁₉	—	2	1	no	—
132	C₂×Dic₁₉	—	2	1	no	—
133	C₂×Dic₁₉	—	2	1	no	—
134	C₂×Dic₁₉	—	2	1	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	—	2	1	no	—
140	C₂×Dic₁₉	#41	1	2	yes	—
141	C₂×Dic₁₉	#41	1	2	yes	—
142	#2587	—	19	1	no	maximal, Sylow
143	C₂²×C₁₉	—	2	2	no	—
144	C₂²×C₁₉	—	2	2	no	—
145	C₂²×C₁₉	—	2	2	no	—
146	C₂²×C₁₉	—	4	1	no	—
147	C₂²×C₁₉	—	4	1	no	—
148	C₂²×C₁₉	—	4	1	no	—
149	C₂²×C₁₉	—	4	1	no	—
150	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
151	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
152	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
153	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
154	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
155	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
157	C₄×C₁₉	—	2	2	no	—
158	C₄×C₁₉	—	2	2	no	—
159	C₄×C₁₉	—	2	2	no	—
160	C₄×C₁₉	—	2	2	no	—
161	C₄×C₁₉	—	4	1	no	—
162	C₄×C₁₉	—	4	1	no	—
163	Dic₁₉	—	2	2	no	—
164	Dic₁₉	—	2	2	no	—
165	Dic₁₉	—	4	1	no	—
166	Dic₁₉	—	4	1	no	—
167	Dic₁₉	—	4	1	no	—
168	Dic₁₉	—	4	1	no	—
169	Dic₁₉	—	4	1	no	—
170	Dic₁₉	—	4	1	no	—
171	#400	—	19	1	no	—
172	#398	—	19	1	no	—
173	#396	—	19	1	no	—
174	#396	—	19	1	no	—
175	#389	—	19	1	no	—
176	#389	—	19	1	no	—
177	#389	—	19	1	no	—
178	#388	—	19	1	no	—
179	#388	—	19	1	no	—
180	#387	—	19	1	no	—
181	#387	—	19	1	no	—
182	#385	—	19	1	no	—
183	#385	—	19	1	no	—
184	C₄×C₄⋊C₄	—	19	1	no	—
185	C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
186	C₂×C₁₉	—	4	2	no	—
187	C₂×C₁₉	#529	1	1	yes	characteristic
188	C₂×C₁₉	#533	1	1	yes	characteristic
189	C₂×C₁₉	#538	1	1	yes	characteristic
190	C₂×C₁₉	#553	1	1	yes	characteristic
191	C₂×C₁₉	#553	1	1	yes	characteristic
192	C₂×C₁₉	#554	1	1	yes	characteristic
193	C₂×C₁₉	#554	1	1	yes	characteristic
194	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
195	C₂×C₄⋊C₄	—	19	1	no	—
196	C₂×C₄⋊C₄	—	19	1	no	—
197	C₂×C₄⋊C₄	—	19	1	no	—
198	C₂×C₄⋊C₄	—	19	1	no	—
199	C₂×C₄⋊C₄	—	19	1	no	—
200	C₂×C₄⋊C₄	—	19	1	no	—
201	C₂×C₄⋊C₄	—	19	1	no	—
202	C₂×C₄⋊C₄	—	19	1	no	—
203	C₂×C₄⋊C₄	—	19	1	no	—
204	C₂×C₄⋊C₄	—	19	1	no	—
205	C₂×C₄⋊C₄	—	19	1	no	—
206	C₂×C₄⋊C₄	—	19	1	no	—
207	C₂×C₂²⋊C₄	—	19	1	no	—
208	C₂×C₂²⋊C₄	—	19	1	no	—
209	C₂×C₂²⋊C₄	—	19	1	no	—
210	C₂×C₂²⋊C₄	—	19	1	no	—
211	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
212	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
213	C₂×C₄²	—	19	1	no	—
214	C₂×C₄²	—	19	1	no	—
215	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
217	#95	—	19	1	no	—
218	#95	—	19	1	no	—
219	#95	—	19	1	no	—
220	#95	—	19	1	no	—
221	#95	—	19	1	no	—
222	#95	—	19	1	no	—
223	#95	—	19	1	no	—
224	#95	—	19	1	no	—
225	#95	—	19	1	no	—
226	#95	—	19	1	no	—
227	#95	C₂×D₁₉	1	1	yes	characteristic
228	#95	C₂×D₁₉	1	1	yes	characteristic
229	C₁₉	#2587	1	1	yes	characteristic, complemented, Sylow
230	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	4	1	no	—
233	C₂²×C₄	—	4	1	no	—
234	C₂²×C₄	—	19	1	no	—
235	C₂²×C₄	—	19	1	no	—
236	C₂²×C₄	—	19	1	no	—
237	C₂²×C₄	—	19	1	no	—
238	C₂²×C₄	—	19	1	no	—
239	C₂²×C₄	—	19	1	no	—
240	C₂²×C₄	—	19	1	no	—
241	C₂²×C₄	—	19	1	no	—
242	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
243	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
244	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
245	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
246	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
247	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
248	C₄⋊C₄	—	38	2	no	—
249	C₄⋊C₄	—	38	2	no	—
250	C₄⋊C₄	—	38	2	no	—
251	C₄⋊C₄	—	38	2	no	—
252	C₄⋊C₄	—	38	2	no	—
253	C₄⋊C₄	—	38	2	no	—
254	C₄⋊C₄	—	38	2	no	—
255	C₄⋊C₄	—	76	1	no	—
256	C₄⋊C₄	—	76	1	no	—
257	C₄⋊C₄	—	76	1	no	—
258	C₄⋊C₄	—	76	1	no	—
259	C₄⋊C₄	—	76	1	no	—
260	C₂²⋊C₄	—	2	2	no	—
261	C₂²⋊C₄	—	38	2	no	—
262	C₂²⋊C₄	—	38	2	no	—
263	C₂²⋊C₄	—	76	1	no	—
264	C₂²⋊C₄	—	76	1	no	—
265	C₂²⋊C₄	Dic₃₈	1	4	yes	—
266	C₄²	—	4	1	no	—
267	C₄²	—	4	1	no	—
268	C₄²	—	38	2	no	—
269	C₄²	—	76	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	1	no	—
273	C₂³	—	2	1	no	—
274	C₂³	—	2	1	no	—
275	C₂³	—	2	1	no	—
276	C₂³	C₂×Dic₃₈	1	2	yes	—
277	C₂³	C₂³×D₁₉	1	1	yes	characteristic
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	4	4	no	—
293	C₂×C₄	—	19	2	no	—
294	C₂×C₄	—	19	2	no	—
295	C₂×C₄	—	38	1	no	—
296	C₂×C₄	—	38	1	no	—
297	C₂×C₄	—	38	1	no	—
298	C₂×C₄	—	38	1	no	—
299	C₂×C₄	—	38	1	no	—
300	C₂×C₄	—	38	1	no	—
301	C₂×C₄	—	38	1	no	—
302	C₂×C₄	—	38	1	no	—
303	C₂×C₄	—	38	1	no	—
304	C₂×C₄	—	38	1	no	—
305	C₂×C₄	—	38	1	no	—
306	C₂×C₄	—	38	1	no	—
307	C₂×C₄	—	38	1	no	—
308	C₂×C₄	—	38	1	no	—
309	C₂×C₄	—	38	1	no	—
310	C₂×C₄	—	38	1	no	—
311	C₂×C₄	—	38	1	no	—
312	C₂×C₄	—	38	1	no	—
313	C₂×C₄	—	38	1	no	—
314	C₂×C₄	—	38	1	no	—
315	C₂×C₄	—	38	1	no	—
316	C₂×C₄	—	38	1	no	—
317	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
318	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
319	C₂×C₄	#64541	1	2	yes	—
320	C₂×C₄	#64541	1	2	yes	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	1	no	—
327	C₂²	—	4	1	no	—
328	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
329	C₂²	C₂×#64541	1	1	yes	characteristic
330	C₂²	C₂×#64541	1	1	yes	characteristic
331	C₂²	#10597430	1	1	yes	characteristic
332	C₂²	#10597430	1	1	yes	characteristic
333	C₂²	#41×D₁₉	1	1	yes	characteristic
334	C₂²	#41×D₁₉	1	1	yes	characteristic
335	C₄	—	2	2	no	—
336	C₄	—	2	2	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	4	1	no	—
340	C₄	—	4	1	no	—
341	C₄	—	38	2	no	—
342	C₄	—	38	2	no	—
343	C₄	—	76	1	no	—
344	C₄	—	76	1	no	—
345	C₄	—	76	1	no	—
346	C₄	—	76	1	no	—
347	C₄	—	76	1	no	—
348	C₄	—	76	1	no	—
349	C₂	—	4	2	no	—
350	C₂	#11927072	1	1	yes	characteristic
351	C₂	#11927101	1	1	yes	characteristic
352	C₂	#11927132	1	1	yes	characteristic
353	C₂	#11927243	1	1	yes	characteristic
354	C₂	#11927244	1	1	yes	characteristic
355	C₂	#11927253	1	1	yes	characteristic
356	C₂	#11927253	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₂²⋊C₄×C₁₉	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#2587
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #11926486	C₂	semidirect
2. #11926478	C₂	semidirect
5. #11926442	C₂	semidirect
6. #11926442	C₂	semidirect
7. #11926441	C₂	semidirect
10. #11926431	C₂	semidirect
11. #11926428	C₂	semidirect
14. C₄×Dic₁₉⋊C₄	C₂	semidirect
229. C₁₉	#2587	semidirect

Maximal subgroups

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

subgroup	index
#11926486	2
#11926478	2
#11926467	2
#11926442	2
#11926441	2
#11926437	2
#11926431	2
#11926428	2
#11926417	2
C₄×Dic₁₉⋊C₄	2
C₄×C₂²⋊C₄×C₁₉	2
#2587	19