Subgroups — #18091303

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926314	C₂	1	2	yes	maximal
2	C₂×#11926314	C₂	1	2	yes	maximal
3	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2316	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	2	yes	—
7	C₂²×#64520	C₂²	1	2	yes	—
8	#11926314	—	2	4	no	—
9	#11926314	—	2	4	no	—
10	#11926313	—	2	2	no	—
11	#11926313	—	2	2	no	—
12	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#389	—	2	2	no	—
16	C₁₉×#389	—	2	2	no	—
17	C₁₉×#380	C₄	1	4	yes	—
18	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₁₉×#117	—	2	2	no	—
21	C₁₉×#117	—	2	2	no	—
22	C₁₉×#117	—	2	2	no	—
23	C₁₉×#117	—	2	2	no	—
24	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
29	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
30	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
31	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×#64520	—	2	2	no	—
36	C₂×#64520	—	2	2	no	—
37	C₂×#64520	—	2	2	no	—
38	C₂×#64520	—	2	2	no	—
39	C₂×#64520	—	2	2	no	—
40	C₂×#64520	—	2	2	no	—
41	C₂×#64520	—	2	2	no	—
42	C₂×#64520	—	2	2	no	—
43	C₂×#64520	—	2	2	no	—
44	C₂×#64520	—	2	2	no	—
45	C₂×#64520	D₄	1	4	yes	—
46	C₂×#64520	Q₈	1	4	yes	—
47	C₂²×C₁₉⋊C₈	—	2	2	no	—
48	C₂²×C₁₉⋊C₈	—	2	2	no	—
49	C₁₉×#95	—	2	4	no	—
50	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	2	2	no	—
53	C₂²×C₄×C₁₉	—	2	2	no	—
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	8	2	no	—
56	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
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	2	yes	—
61	C₂²×C₄×C₁₉	#41	1	2	yes	—
62	C₂²×C₄×C₁₉	#41	1	2	yes	—
63	C₂²×C₄×C₁₉	#41	1	2	yes	—
64	C₂²×C₄×C₁₉	#41	1	2	yes	—
65	C₄⋊C₄×C₁₉	—	2	4	no	—
66	C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	1	no	—
70	C₄⋊C₄×C₁₉	—	8	4	no	—
71	C₂²⋊C₄×C₁₉	—	2	4	no	—
72	C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₄²×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	—	4	1	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	#64520	—	2	4	no	—
77	#64520	—	2	4	no	—
78	#64520	—	2	4	no	—
79	#64520	—	2	4	no	—
80	#64520	—	4	2	no	—
81	#64520	—	4	2	no	—
82	#64520	—	4	2	no	—
83	#64520	—	4	2	no	—
84	C₂×C₁₉⋊C₈	—	2	4	no	—
85	C₂×C₁₉⋊C₈	—	2	4	no	—
86	C₂×C₁₉⋊C₈	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	C₂×C₁₉⋊C₈	—	4	2	no	—
90	#11352	—	19	1	no	maximal, Sylow
91	C₂³×C₁₉	—	4	1	no	—
92	C₂³×C₁₉	—	4	1	no	—
93	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂³×C₁₉	#117	1	1	yes	characteristic
95	C₂³×C₁₉	#117	1	1	yes	characteristic
96	C₂³×C₁₉	C₄×D₄	1	2	yes	—
97	C₂³×C₁₉	C₄×Q₈	1	2	yes	—
98	C₂×C₄×C₁₉	—	2	4	no	—
99	C₂×C₄×C₁₉	—	4	4	no	—
100	C₂×C₄×C₁₉	—	4	2	no	—
101	C₂×C₄×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	4	2	no	—
103	C₂×C₄×C₁₉	—	4	2	no	—
104	C₂×C₄×C₁₉	—	4	2	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	8	2	no	—
107	C₂×C₄×C₁₉	—	8	2	no	—
108	C₂×C₄×C₁₉	#121	1	2	yes	—
109	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
110	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
111	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
112	C₂×C₄×C₁₉	#123	1	2	yes	—
113	C₂×C₄×C₁₉	#123	1	2	yes	—
114	C₂×C₄×C₁₉	#123	1	2	yes	—
115	C₂×C₄×C₁₉	#123	1	2	yes	—
116	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
117	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#125	1	2	yes	—
119	C₂×C₄×C₁₉	#125	1	2	yes	—
120	C₂×C₄×C₁₉	#126	1	2	yes	—
121	C₂×C₄×C₁₉	#126	1	2	yes	—
122	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
123	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
124	C₁₉⋊C₈	—	4	4	no	—
125	C₁₉⋊C₈	—	4	4	no	—
126	#2316	D₁₉	1	1	yes	characteristic
127	C₂×#344	—	19	2	no	—
128	C₂×#344	—	19	2	no	—
129	C₂×#343	—	19	1	no	—
130	C₂×#343	—	19	1	no	—
131	C₂²×C₁₉	—	2	1	no	—
132	C₂²×C₁₉	—	2	1	no	—
133	C₂²×C₁₉	—	2	1	no	—
134	C₂²×C₁₉	—	2	1	no	—
135	C₂²×C₁₉	—	2	1	no	—
136	C₂²×C₁₉	—	2	1	no	—
137	C₂²×C₁₉	—	4	2	no	—
138	C₂²×C₁₉	—	4	2	no	—
139	C₂²×C₁₉	#381	1	1	yes	characteristic
140	C₂²×C₁₉	#387	1	2	yes	—
141	C₂²×C₁₉	#387	1	2	yes	—
142	C₂²×C₁₉	#390	1	1	yes	characteristic
143	C₂²×C₁₉	#391	1	1	yes	characteristic
144	C₄×C₁₉	—	4	4	no	—
145	C₄×C₁₉	—	8	2	no	—
146	C₄×C₁₉	—	8	2	no	—
147	C₄×C₁₉	#397	1	2	yes	—
148	C₄×C₁₉	#398	1	2	yes	—
149	C₄×C₁₉	#399	1	2	yes	—
150	C₄×C₁₉	#400	1	2	yes	—
151	C₂²×M₁₆	—	19	2	no	—
152	C₂²×M₁₆	—	19	2	no	—
153	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
154	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
155	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
156	#389	—	2	2	no	—
157	#389	—	2	2	no	—
158	#380	Dic₁₉	1	4	yes	—
159	#344	—	38	4	no	—
160	#344	—	38	4	no	—
161	#343	—	38	2	no	—
162	#343	—	38	2	no	—
163	C₂×C₁₉	—	2	1	no	—
164	C₂×C₁₉	—	2	2	no	—
165	C₂×C₁₉	—	2	2	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	#1445	1	1	yes	characteristic
168	C₂×C₁₉	#1829	1	1	yes	characteristic
169	C₂×C₁₉	#1830	1	1	yes	characteristic
170	C₂³×C₄	C₂×Dic₁₉	1	2	yes	—
171	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
172	C₂×M₁₆	—	19	4	no	—
173	C₂×M₁₆	—	19	4	no	—
174	C₂×M₁₆	—	38	2	no	—
175	C₂×M₁₆	—	38	2	no	—
176	C₂×M₁₆	—	38	2	no	—
177	C₂×M₁₆	—	38	2	no	—
178	C₂×M₁₆	—	38	2	no	—
179	C₂×M₁₆	—	38	2	no	—
180	C₂×M₁₆	—	38	2	no	—
181	C₂×M₁₆	—	38	2	no	—
182	C₂×M₁₆	—	38	2	no	—
183	C₂×M₁₆	—	38	2	no	—
184	C₂²×C₈	—	38	2	no	—
185	C₂²×C₈	—	38	2	no	—
186	#117	—	2	2	no	—
187	#117	—	2	2	no	—
188	#117	—	2	2	no	—
189	#117	—	2	2	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	1	no	—
193	C₂×C₄⋊C₄	—	2	1	no	—
194	C₂×C₄⋊C₄	—	2	4	no	—
195	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
196	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
197	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
198	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
199	C₂×C₄²	—	2	1	no	—
200	C₂×C₄²	—	2	1	no	—
201	#95	—	2	4	no	—
202	C₁₉	#11352	1	1	yes	characteristic, complemented, Sylow
203	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	2	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	8	2	no	—
209	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
210	C₂²×C₄	#64541	1	2	yes	—
211	C₂²×C₄	#64541	1	2	yes	—
212	C₂²×C₄	D₄×D₁₉	1	2	yes	—
213	C₂²×C₄	#64543	1	2	yes	—
214	C₂²×C₄	Q₈×D₁₉	1	2	yes	—
215	C₂²×C₄	#64545	1	2	yes	—
216	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
218	M₁₆	—	38	4	no	—
219	M₁₆	—	38	4	no	—
220	M₁₆	—	38	4	no	—
221	M₁₆	—	38	4	no	—
222	M₁₆	—	76	2	no	—
223	M₁₆	—	76	2	no	—
224	M₁₆	—	76	2	no	—
225	M₁₆	—	76	2	no	—
226	C₂×C₈	—	38	4	no	—
227	C₂×C₈	—	38	4	no	—
228	C₂×C₈	—	76	2	no	—
229	C₂×C₈	—	76	2	no	—
230	C₂×C₈	—	76	2	no	—
231	C₂×C₈	—	76	2	no	—
232	C₄⋊C₄	—	2	4	no	—
233	C₄⋊C₄	—	2	4	no	—
234	C₄⋊C₄	—	4	1	no	—
235	C₄⋊C₄	—	4	2	no	—
236	C₄⋊C₄	—	4	1	no	—
237	C₄⋊C₄	—	8	4	no	—
238	C₂²⋊C₄	—	2	4	no	—
239	C₂²⋊C₄	—	2	4	no	—
240	C₄²	—	4	1	no	—
241	C₄²	—	4	2	no	—
242	C₄²	—	4	1	no	—
243	C₂³	—	4	1	no	—
244	C₂³	—	4	1	no	—
245	C₂³	#10597372	1	1	yes	characteristic
246	C₂³	#10597372	1	1	yes	characteristic
247	C₂³	D₄×Dic₁₉	1	2	yes	—
248	C₂³	Q₈×Dic₁₉	1	2	yes	—
249	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	4	4	no	—
252	C₂×C₄	—	4	2	no	—
253	C₂×C₄	—	4	2	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	8	2	no	—
259	C₂×C₄	—	8	2	no	—
260	C₂×C₄	#10597335	1	2	yes	—
261	C₂×C₄	#10597335	1	2	yes	—
262	C₂×C₄	#10597340	1	2	yes	—
263	C₂×C₄	#10597340	1	2	yes	—
264	C₂×C₄	#10597342	1	2	yes	—
265	C₂×C₄	#10597342	1	2	yes	—
266	C₂×C₄	#10597344	1	2	yes	—
267	C₂×C₄	#10597344	1	2	yes	—
268	C₂×C₄	#10597375	1	2	yes	—
269	C₂×C₄	#10597375	1	2	yes	—
270	C₂×C₄	#10597382	1	1	yes	characteristic
271	C₂×C₄	#10597384	1	2	yes	—
272	C₂×C₄	#10597386	1	1	yes	characteristic
273	C₂×C₄	#10597390	1	1	yes	characteristic
274	C₂×C₄	#10597392	1	2	yes	—
275	C₂×C₄	#10597393	1	1	yes	characteristic
276	C₈	—	76	4	no	—
277	C₈	—	76	4	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	2	1	no	—
280	C₂²	—	2	1	no	—
281	C₂²	—	2	1	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	2	1	no	—
284	C₂²	—	4	2	no	—
285	C₂²	—	4	2	no	—
286	C₂²	#11926407	1	1	yes	characteristic
287	C₂²	#11926430	1	2	yes	—
288	C₂²	#11926430	1	2	yes	—
289	C₂²	#11926447	1	1	yes	characteristic
290	C₂²	#11926451	1	1	yes	characteristic
291	C₄	—	4	4	no	—
292	C₄	—	8	2	no	—
293	C₄	—	8	2	no	—
294	C₄	#11926470	1	2	yes	—
295	C₄	#11926475	1	2	yes	—
296	C₄	#11926479	1	2	yes	—
297	C₄	#11926482	1	2	yes	—
298	C₂	—	2	1	no	—
299	C₂	—	2	2	no	—
300	C₂	—	2	2	no	—
301	C₂	—	2	1	no	—
302	C₂	#14561903	1	1	yes	characteristic
303	C₂	#14563746	1	1	yes	characteristic
304	C₂	#14563749	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926407
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2316	C₂
socle	C₂²×C₁₉	#381
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2316	D₁₉
hypocenter	C₁₉	#11352
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2316

Complements

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

N	H ≅ G/N	type
202. C₁₉	#11352	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926314	2
C₂×#11926313	2
C₁₉×#2316	2
#11352	19