Subgroups — #18088364

Order 4864.

998 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926414	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926410	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926307	C₂	1	4	yes	maximal
4	C₂²×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₁₉	—	2	2	no	—
6	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₁₉	C₂²	1	2	yes	—
8	#11926414	—	2	2	no	—
9	#11926414	C₄	1	4	yes	complemented
10	#11926410	—	2	2	no	—
11	#11926410	C₄	1	4	yes	complemented
12	C₂×C₁₉⋊#95	—	2	2	no	—
13	#11926307	—	2	8	no	—
14	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#97	—	2	2	no	—
17	C₂×C₁₉×#97	—	2	2	no	—
18	C₂×C₁₉×#97	C₄	1	4	yes	complemented
19	C₂³×C₄×C₁₉	D₄	1	2	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂³×Dic₁₉	—	2	2	no	—
22	C₂³×Dic₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	—	2	2	no	—
26	C₂²×C₈×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
28	C₂²×C₈×C₁₉	D₄	1	4	yes	—
29	C₂²×C₈×C₁₉	Q₈	1	4	yes	—
30	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄²×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
36	C₂×C₄⋊Dic₁₉	—	2	4	no	—
37	C₂×C₄⋊Dic₁₉	—	2	4	no	—
38	C₂×C₄⋊Dic₁₉	—	2	4	no	—
39	C₂×C₄⋊Dic₁₉	—	2	4	no	—
40	C₂×C₄⋊Dic₁₉	—	2	8	no	—
41	C₂×C₄⋊Dic₁₉	—	2	2	no	—
42	C₂×C₄⋊Dic₁₉	—	2	2	no	—
43	C₂×C₄⋊Dic₁₉	—	4	8	no	—
44	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
45	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
46	C₁₉×#97	—	2	8	no	—
47	C₁₉⋊#95	—	2	8	no	—
48	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	—	2	4	no	—
50	C₂²×C₄×C₁₉	—	2	4	no	—
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
53	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
54	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
62	C₂²×C₄×C₁₉	#41	1	2	yes	—
63	C₂²×C₄×C₁₉	#41	1	2	yes	—
64	C₂²×Dic₁₉	—	2	4	no	—
65	C₂²×Dic₁₉	—	2	4	no	—
66	C₂²×Dic₁₉	—	4	2	no	—
67	C₂²×Dic₁₉	—	4	2	no	—
68	C₂²×Dic₁₉	—	4	2	no	—
69	C₂²×Dic₁₉	—	4	2	no	—
70	C₂²×Dic₁₉	—	4	4	no	—
71	C₂²×Dic₁₉	—	4	8	no	—
72	C₂²×Dic₁₉	—	4	4	no	—
73	C₂×C₈×C₁₉	—	2	4	no	—
74	C₂×C₈×C₁₉	—	2	4	no	—
75	C₂×C₈×C₁₉	—	2	4	no	—
76	C₂×C₈×C₁₉	—	2	4	no	—
77	C₂×C₈×C₁₉	—	2	4	no	—
78	C₂×C₈×C₁₉	—	2	4	no	—
79	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	complemented
80	C₄²×C₁₉	C₄²	1	4	yes	—
81	C₄²×C₁₉	C₂²⋊C₄	1	4	yes	—
82	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
83	C₄²×C₁₉	C₄⋊C₄	1	4	yes	—
84	C₄⋊Dic₁₉	—	2	8	no	—
85	C₄⋊Dic₁₉	—	2	8	no	—
86	C₄⋊Dic₁₉	—	4	16	no	—
87	C₄⋊Dic₁₉	—	4	4	no	—
88	C₄⋊Dic₁₉	—	4	4	no	—
89	#10843	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂³×C₁₉	#124	1	1	yes	characteristic
94	C₂³×C₁₉	#124	1	1	yes	characteristic
95	C₂³×C₁₉	#127	1	1	yes	characteristic
96	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
97	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
98	C₂³×C₁₉	#137	1	4	yes	—
99	C₂×C₄×C₁₉	—	2	8	no	—
100	C₂×C₄×C₁₉	—	2	4	no	—
101	C₂×C₄×C₁₉	—	2	4	no	—
102	C₂×C₄×C₁₉	—	2	8	no	—
103	C₂×C₄×C₁₉	#95	1	8	yes	—
104	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
105	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
109	C₂×C₄×C₁₉	#117	1	2	yes	—
110	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
112	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
113	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
114	C₂×C₄×C₁₉	#121	1	2	yes	—
115	C₂×C₄×C₁₉	#121	1	2	yes	—
116	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
117	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
118	C₂×C₄×C₁₉	#125	1	2	yes	—
119	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
120	C₂×Dic₁₉	—	4	4	no	—
121	C₂×Dic₁₉	—	4	4	no	—
122	C₂×Dic₁₉	—	4	8	no	—
123	C₂×Dic₁₉	—	4	8	no	—
124	C₂×Dic₁₉	—	8	4	no	—
125	C₂×Dic₁₉	—	8	4	no	—
126	C₂×Dic₁₉	—	8	2	no	—
127	C₂×Dic₁₉	—	8	4	no	—
128	C₂×Dic₁₉	—	8	2	no	—
129	C₈×C₁₉	—	2	8	no	—
130	C₂²×#97	D₁₉	1	1	yes	characteristic
131	C₂×#384	—	19	1	no	—
132	C₂×#382	—	19	1	no	—
133	C₂×#340	—	19	4	no	—
134	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
135	C₂²×C₁₉	#382	1	1	yes	characteristic
136	C₂²×C₁₉	#384	1	1	yes	characteristic
137	C₂²×C₁₉	#390	1	1	yes	characteristic
138	C₂²×C₁₉	#390	1	1	yes	characteristic
139	C₂²×C₁₉	#391	1	1	yes	characteristic
140	C₂²×C₁₉	#391	1	1	yes	characteristic
141	C₂²×C₁₉	#417	1	4	yes	—
142	C₂²×C₁₉	#418	1	2	yes	—
143	C₂²×C₁₉	#419	1	2	yes	—
144	C₂²×C₁₉	#428	1	4	yes	—
145	C₂²×C₁₉	#489	1	4	yes	—
146	C₂²×C₁₉	#490	1	2	yes	—
147	C₂²×C₁₉	#491	1	2	yes	—
148	C₂²×C₁₉	#496	1	2	yes	—
149	C₂²×C₁₉	#497	1	2	yes	—
150	C₂²×C₁₉	#501	1	4	yes	—
151	C₄×C₁₉	—	2	8	no	—
152	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
153	C₄×C₁₉	#380	1	2	yes	—
154	C₄×C₁₉	#389	1	2	yes	—
155	C₄×C₁₉	#389	1	2	yes	—
156	Dic₁₉	—	8	4	no	—
157	Dic₁₉	—	8	4	no	—
158	C₂³×C₈	C₂×D₁₉	1	2	yes	—
159	C₂²×C₄⋊C₄	—	19	2	no	—
160	C₂²×C₄⋊C₄	—	19	2	no	—
161	C₂²×C₄⋊C₄	—	38	2	no	—
162	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
163	C₂×#97	—	2	2	no	—
164	C₂×#97	—	2	2	no	—
165	C₂×#97	Dic₁₉	1	4	yes	complemented
166	#384	—	19	4	no	—
167	#384	—	38	2	no	—
168	#382	—	19	4	no	—
169	#382	—	38	2	no	—
170	C₂×#95	—	38	2	no	—
171	#340	—	38	8	no	—
172	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
173	C₂×C₁₉	#1736	1	2	yes	—
174	C₂×C₁₉	#1836	1	2	yes	—
175	C₂×C₁₉	#1847	1	2	yes	—
176	C₂×C₁₉	#1959	1	2	yes	—
177	C₂×C₁₉	#1960	1	1	yes	characteristic
178	C₂×C₁₉	#1961	1	1	yes	characteristic
179	C₂×C₁₉	#1992	1	2	yes	—
180	C₂×C₁₉	#1993	1	2	yes	—
181	C₂³×C₄	—	38	2	no	—
182	C₂³×C₄	—	38	2	no	—
183	C₂³×C₄	D₇₆	1	2	yes	—
184	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
185	C₂²×C₈	—	2	2	no	—
186	C₂²×C₈	—	2	2	no	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	2	no	—
189	C₂²×C₈	Dic₃₈	1	4	yes	—
190	C₂²×C₈	D₇₆	1	4	yes	—
191	C₂²×C₈	C₂×Dic₁₉	1	4	yes	—
192	C₂×C₄⋊C₄	—	19	4	no	—
193	C₂×C₄⋊C₄	—	19	4	no	—
194	C₂×C₄⋊C₄	—	38	4	no	—
195	C₂×C₄⋊C₄	—	38	4	no	—
196	C₂×C₄⋊C₄	—	38	4	no	—
197	C₂×C₄⋊C₄	—	38	4	no	—
198	C₂×C₄⋊C₄	—	38	8	no	—
199	C₂×C₄⋊C₄	—	38	2	no	—
200	C₂×C₄⋊C₄	—	38	2	no	—
201	C₂×C₄⋊C₄	—	76	8	no	—
202	C₂×C₄²	Dic₃₈	1	2	yes	—
203	C₂×C₄²	C₄×D₁₉	1	2	yes	—
204	C₂×C₄²	C₄×D₁₉	1	2	yes	—
205	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
206	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
207	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
208	#97	—	2	8	no	—
209	#95	—	38	8	no	—
210	C₁₉	#10843	1	1	yes	characteristic, complemented, Sylow
211	C₂⁴	C₂×D₇₆	1	1	yes	characteristic
212	C₂²×C₄	—	2	4	no	—
213	C₂²×C₄	—	2	4	no	—
214	C₂²×C₄	—	38	4	no	—
215	C₂²×C₄	—	38	4	no	—
216	C₂²×C₄	—	76	2	no	—
217	C₂²×C₄	—	76	2	no	—
218	C₂²×C₄	—	76	2	no	—
219	C₂²×C₄	—	76	2	no	—
220	C₂²×C₄	—	76	8	no	—
221	C₂²×C₄	—	76	4	no	—
222	C₂²×C₄	—	76	4	no	—
223	C₂²×C₄	C₄⋊Dic₁₉	1	4	yes	—
224	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
225	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
226	C₂²×C₄	C₂×Dic₃₈	1	2	yes	—
227	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
229	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
230	C₂²×C₄	C₂×D₇₆	1	2	yes	—
231	C₂²×C₄	#64541	1	2	yes	—
232	C₂²×C₄	#64541	1	2	yes	—
233	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
234	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
235	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
236	C₂×C₈	—	2	4	no	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	—	2	4	no	—
240	C₂×C₈	—	2	4	no	—
241	C₂×C₈	—	2	4	no	—
242	C₂×C₈	C₄⋊Dic₁₉	1	8	yes	complemented
243	C₄⋊C₄	—	38	8	no	—
244	C₄⋊C₄	—	38	8	no	—
245	C₄⋊C₄	—	76	16	no	—
246	C₄⋊C₄	—	76	4	no	—
247	C₄⋊C₄	—	76	4	no	—
248	C₄²	C₄×Dic₁₉	1	4	yes	—
249	C₄²	Dic₁₉⋊C₄	1	4	yes	—
250	C₄²	Dic₁₉⋊C₄	1	4	yes	—
251	C₄²	C₂²⋊Dic₁₉	1	4	yes	—
252	C₂³	#10597315	1	1	yes	characteristic
253	C₂³	#10597320	1	1	yes	characteristic
254	C₂³	#10597321	1	1	yes	characteristic
255	C₂³	#10597321	1	1	yes	characteristic
256	C₂³	#10597354	1	4	yes	—
257	C₂³	#10597355	1	4	yes	—
258	C₂³	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
259	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
260	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
261	C₂×C₄	—	2	8	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	2	4	no	—
264	C₂×C₄	—	2	8	no	—
265	C₂×C₄	—	76	8	no	—
266	C₂×C₄	—	76	8	no	—
267	C₂×C₄	—	76	4	no	—
268	C₂×C₄	—	76	4	no	—
269	C₂×C₄	—	152	4	no	—
270	C₂×C₄	—	152	4	no	—
271	C₂×C₄	—	152	2	no	—
272	C₂×C₄	—	152	4	no	—
273	C₂×C₄	—	152	2	no	—
274	C₂×C₄	C₁₉⋊#95	1	8	yes	—
275	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
276	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
277	C₂×C₄	#10597315	1	2	yes	—
278	C₂×C₄	#10597316	1	2	yes	—
279	C₂×C₄	C₄×D₇₆	1	2	yes	—
280	C₂×C₄	C₄×D₇₆	1	2	yes	—
281	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
282	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
283	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
284	C₂×C₄	#10597370	1	2	yes	—
285	C₂×C₄	#10597370	1	2	yes	—
286	C₂×C₄	C₂×C₄⋊Dic₁₉	1	2	yes	—
287	C₂×C₄	#10597372	1	2	yes	—
288	C₂×C₄	#10597376	1	2	yes	—
289	C₂×C₄	#10597376	1	2	yes	—
290	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
291	C₈	—	2	8	no	—
292	C₂²	C₂×C₁₉⋊#95	1	1	yes	characteristic
293	C₂²	#11926410	1	1	yes	characteristic
294	C₂²	#11926414	1	1	yes	characteristic
295	C₂²	#11926446	1	1	yes	characteristic
296	C₂²	#11926446	1	1	yes	characteristic
297	C₂²	#11926450	1	1	yes	characteristic
298	C₂²	#11926450	1	1	yes	characteristic
299	C₂²	#11926546	1	4	yes	—
300	C₂²	#11926550	1	2	yes	—
301	C₂²	#11926554	1	2	yes	—
302	C₂²	#11926586	1	4	yes	—
303	C₂²	#11926904	1	4	yes	—
304	C₂²	#11926909	1	2	yes	—
305	C₂²	#11926913	1	2	yes	—
306	C₂²	#11926933	1	2	yes	—
307	C₂²	#11926938	1	2	yes	—
308	C₂²	#11926953	1	4	yes	—
309	C₄	—	2	8	no	—
310	C₄	—	152	4	no	—
311	C₄	—	152	4	no	—
312	C₄	C₄×C₄⋊Dic₁₉	1	2	yes	—
313	C₄	#11926404	1	2	yes	—
314	C₄	#11926442	1	2	yes	—
315	C₄	#11926442	1	2	yes	—
316	C₂	#14561865	1	1	yes	characteristic
317	C₂	#14563355	1	2	yes	—
318	C₂	#14563769	1	2	yes	—
319	C₂	#14563803	1	2	yes	—
320	C₂	#14564451	1	2	yes	—
321	C₂	#14564455	1	1	yes	characteristic
322	C₂	#14564459	1	1	yes	characteristic
323	C₂	#14564604	1	2	yes	—
324	C₂	#14564608	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#97	C₂
socle, prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#97	D₁₉
hypocenter	C₁₉	#10843
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
9. #11926414	C₄	semidirect
11. #11926410	C₄	semidirect
18. C₂×C₁₉×#97	C₄	semidirect
79. C₂×C₈×C₁₉	C₄⋊C₄	semidirect
165. C₂×#97	Dic₁₉	semidirect
210. C₁₉	#10843	semidirect
242. C₂×C₈	C₄⋊Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926414	2
C₂×#11926410	2
C₂×#11926307	2
C₂²×C₁₉×#97	2
#10843	19