Subgroups — #18075396

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926595	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	2	yes	maximal
3	C₂×#11926295	C₂	1	1	yes	maximal, characteristic, complemented
4	#14561469	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
7	#11926595	—	2	2	no	—
8	#11926595	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×Dic₁₉⋊C₈	C₄	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	C₄	1	1	yes	characteristic
12	C₂×(C₂×D₁₉)⋊C₈	—	2	2	no	—
13	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
14	C₂×(C₂×D₁₉)⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926298	—	2	2	no	—
17	#11926295	—	2	2	no	—
18	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#335	—	2	2	no	—
21	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×D₁₉	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₉	Q₈	1	1	yes	characteristic
31	C₂²×C₁₉⋊C₈	—	2	2	no	—
32	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₄²×D₁₉	—	2	1	no	—
35	C₄²×D₁₉	—	2	1	no	—
36	C₄²×D₁₉	—	2	1	no	—
37	C₄²×D₁₉	—	2	1	no	—
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₄×C₈×C₁₉	D₄	1	2	yes	—
42	(C₂×D₁₉)⋊C₈	—	2	2	no	—
43	(C₂×D₁₉)⋊C₈	—	2	2	no	—
44	(C₂×D₁₉)⋊C₈	—	4	4	no	—
45	Dic₁₉⋊C₈	—	2	2	no	—
46	Dic₁₉⋊C₈	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
49	C₄×C₁₉⋊C₈	—	2	1	no	—
50	C₄×C₁₉⋊C₈	—	2	1	no	—
51	C₂³×D₁₉	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×Dic₁₉	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×D₁₉	—	2	2	no	—
59	C₂×C₄×D₁₉	—	2	1	no	—
60	C₂×C₄×D₁₉	—	2	1	no	—
61	C₂×C₄×D₁₉	—	2	2	no	—
62	C₂×C₄×D₁₉	—	2	1	no	—
63	C₂×C₄×D₁₉	—	2	1	no	—
64	C₂×C₄×D₁₉	—	2	1	no	—
65	C₂×C₄×D₁₉	—	2	1	no	—
66	C₂×C₄×D₁₉	—	2	2	no	—
67	C₂×C₄×D₁₉	—	2	2	no	—
68	C₂×C₄×D₁₉	—	2	2	no	—
69	C₂×C₄×D₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	2	2	no	—
72	C₂×C₈×C₁₉	—	4	2	no	—
73	C₂×C₈×C₁₉	—	4	2	no	—
74	C₂×C₈×C₁₉	—	4	2	no	—
75	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
76	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	#41	1	1	yes	characteristic
80	C₄²×C₁₉	#41	1	1	yes	characteristic
81	C₄×Dic₁₉	—	2	1	no	—
82	C₄×Dic₁₉	—	2	1	no	—
83	C₄×Dic₁₉	—	2	1	no	—
84	C₄×Dic₁₉	—	2	1	no	—
85	C₄×Dic₁₉	—	2	1	no	—
86	C₄×Dic₁₉	—	2	1	no	—
87	C₂×C₁₉⋊C₈	—	2	1	no	—
88	C₂×C₁₉⋊C₈	—	2	1	no	—
89	C₂×C₁₉⋊C₈	—	2	2	no	—
90	C₂×C₁₉⋊C₈	—	2	2	no	—
91	C₂×C₁₉⋊C₈	—	4	2	no	—
92	C₂×C₁₉⋊C₈	—	4	2	no	—
93	C₂×C₁₉⋊C₈	—	4	2	no	—
94	#8600	—	19	1	no	maximal, Sylow
95	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂²×D₁₉	—	2	1	no	—
97	C₂²×D₁₉	—	2	2	no	—
98	C₂²×D₁₉	—	2	2	no	—
99	C₂²×D₁₉	—	2	1	no	—
100	C₂²×D₁₉	#108	1	2	yes	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
105	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
107	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
109	C₂×C₄×C₁₉	#131	1	2	yes	—
110	C₂×C₄×C₁₉	#131	1	2	yes	—
111	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
112	C₂×C₄×C₁₉	#137	1	2	yes	—
113	C₂×Dic₁₉	—	2	1	no	—
114	C₂×Dic₁₉	—	2	1	no	—
115	C₂×Dic₁₉	—	2	1	no	—
116	C₂×Dic₁₉	—	2	1	no	—
117	C₂×Dic₁₉	—	2	2	no	—
118	C₂×Dic₁₉	—	2	2	no	—
119	C₂×Dic₁₉	#108	1	2	yes	—
120	C₄×D₁₉	—	2	4	no	—
121	C₄×D₁₉	—	2	4	no	—
122	C₄×D₁₉	—	4	1	no	—
123	C₄×D₁₉	—	4	1	no	—
124	C₄×D₁₉	—	4	2	no	—
125	C₄×D₁₉	—	4	2	no	—
126	C₄×D₁₉	—	4	1	no	—
127	C₄×D₁₉	—	4	1	no	—
128	C₈×C₁₉	—	2	2	no	—
129	C₈×C₁₉	—	2	2	no	—
130	C₈×C₁₉	—	8	2	no	—
131	C₁₉⋊C₈	—	4	1	no	—
132	C₁₉⋊C₈	—	4	1	no	—
133	C₁₉⋊C₈	—	8	2	no	—
134	C₂×#431	—	19	1	no	—
135	#1797	—	19	2	no	—
136	C₂×#335	D₁₉	1	1	yes	characteristic, complemented
137	C₂×#334	—	19	1	no	—
138	#1277	—	19	2	no	—
139	C₂²×C₁₉	#380	1	1	yes	characteristic
140	C₂²×C₁₉	#424	1	2	yes	—
141	C₂²×C₁₉	#428	1	2	yes	—
142	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
143	C₂²×C₁₉	C₂×#108	1	1	yes	characteristic
144	C₂×D₁₉	—	2	2	no	—
145	C₂×D₁₉	—	2	4	no	—
146	C₂×D₁₉	—	4	1	no	—
147	C₂×D₁₉	—	4	1	no	—
148	C₂×D₁₉	—	4	2	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	#408	1	1	yes	characteristic
152	C₄×C₁₉	#408	1	1	yes	characteristic
153	C₄×C₁₉	#433	1	2	yes	—
154	C₄×C₁₉	#468	1	2	yes	—
155	C₄×C₁₉	#469	1	1	yes	characteristic
156	C₄×C₁₉	#470	1	1	yes	characteristic
157	Dic₁₉	—	2	2	no	—
158	Dic₁₉	—	4	1	no	—
159	Dic₁₉	—	4	1	no	—
160	C₂²×C₄²	—	19	1	no	—
161	#431	—	38	2	no	—
162	#431	—	38	2	no	—
163	C₂×C₄⋊C₈	—	19	1	no	—
164	C₂×C₄⋊C₈	—	19	1	no	—
165	C₂×C₄⋊C₈	—	19	2	no	—
166	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
167	C₂×C₂²⋊C₈	—	19	1	no	—
168	C₂×C₂²⋊C₈	—	19	1	no	—
169	C₂×C₂²⋊C₈	—	38	2	no	—
170	C₂×C₄×C₈	—	19	1	no	—
171	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
172	#336	—	38	2	no	—
173	#335	—	2	2	no	—
174	#334	—	38	2	no	—
175	C₂×C₁₉	#1573	1	2	yes	—
176	C₂×C₁₉	#1574	1	2	yes	—
177	C₂×C₁₉	#1798	1	1	yes	characteristic
178	C₂×C₁₉	#1809	1	1	yes	characteristic
179	C₂×C₁₉	#1810	1	1	yes	characteristic
180	D₁₉	—	4	2	no	—
181	C₂³×C₄	—	19	1	no	—
182	C₂³×C₄	—	19	1	no	—
183	C₂³×C₄	—	19	1	no	—
184	C₂²×C₈	—	2	2	no	—
185	C₂²×C₈	—	19	1	no	—
186	C₂²×C₈	—	19	1	no	—
187	C₂²×C₈	—	38	2	no	—
188	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
189	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
190	C₂×C₄²	—	19	1	no	—
191	C₂×C₄²	—	19	1	no	—
192	C₂×C₄²	—	19	1	no	—
193	C₂×C₄²	—	38	1	no	—
194	C₂×C₄²	—	38	1	no	—
195	C₂×C₄²	—	38	1	no	—
196	C₂×C₄²	—	38	1	no	—
197	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
198	C₄⋊C₈	—	2	2	no	—
199	C₄⋊C₈	—	2	2	no	—
200	C₄⋊C₈	—	38	2	no	—
201	C₄⋊C₈	—	38	2	no	—
202	C₄⋊C₈	—	38	2	no	—
203	C₄⋊C₈	—	38	2	no	—
204	C₂²⋊C₈	—	38	2	no	—
205	C₂²⋊C₈	—	38	2	no	—
206	C₂²⋊C₈	—	76	4	no	—
207	C₄×C₈	—	38	1	no	—
208	C₄×C₈	—	38	1	no	—
209	C₄×C₈	D₇₆	1	2	yes	—
210	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
211	C₁₉	#8600	1	1	yes	characteristic, complemented, Sylow
212	C₂⁴	—	19	1	no	—
213	C₂²×C₄	—	19	1	no	—
214	C₂²×C₄	—	19	1	no	—
215	C₂²×C₄	—	19	1	no	—
216	C₂²×C₄	—	38	2	no	—
217	C₂²×C₄	—	38	2	no	—
218	C₂²×C₄	—	38	1	no	—
219	C₂²×C₄	—	38	1	no	—
220	C₂²×C₄	—	38	1	no	—
221	C₂²×C₄	—	38	1	no	—
222	C₂²×C₄	—	38	1	no	—
223	C₂²×C₄	—	38	2	no	—
224	C₂²×C₄	—	38	2	no	—
225	C₂²×C₄	—	38	2	no	—
226	C₂²×C₄	—	38	2	no	—
227	C₂²×C₄	—	38	1	no	—
228	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
229	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
230	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	2	2	no	—
233	C₂×C₈	—	4	2	no	—
234	C₂×C₈	—	4	2	no	—
235	C₂×C₈	—	4	2	no	—
236	C₂×C₈	—	38	2	no	—
237	C₂×C₈	—	38	2	no	—
238	C₂×C₈	—	38	1	no	—
239	C₂×C₈	—	38	1	no	—
240	C₂×C₈	—	76	2	no	—
241	C₂×C₈	—	76	2	no	—
242	C₂×C₈	—	76	2	no	—
243	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
244	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
245	C₄²	—	38	1	no	—
246	C₄²	—	38	1	no	—
247	C₄²	—	38	1	no	—
248	C₄²	—	38	1	no	—
249	C₄²	—	38	1	no	—
250	C₄²	—	38	1	no	—
251	C₄²	C₂×D₇₆	1	1	yes	characteristic
252	C₄²	#64543	1	1	yes	characteristic
253	C₄²	#64545	1	1	yes	characteristic
254	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂³	—	19	2	no	—
256	C₂³	—	38	2	no	—
257	C₂³	—	38	2	no	—
258	C₂³	—	38	1	no	—
259	C₂³	—	38	1	no	—
260	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	19	2	no	—
264	C₂×C₄	—	38	4	no	—
265	C₂×C₄	—	38	4	no	—
266	C₂×C₄	—	38	1	no	—
267	C₂×C₄	—	38	1	no	—
268	C₂×C₄	—	38	2	no	—
269	C₂×C₄	—	38	2	no	—
270	C₂×C₄	—	38	1	no	—
271	C₂×C₄	—	38	1	no	—
272	C₂×C₄	—	76	2	no	—
273	C₂×C₄	—	76	1	no	—
274	C₂×C₄	—	76	1	no	—
275	C₂×C₄	—	76	2	no	—
276	C₂×C₄	—	76	1	no	—
277	C₂×C₄	—	76	1	no	—
278	C₂×C₄	#10597338	1	1	yes	characteristic
279	C₂×C₄	#10597341	1	1	yes	characteristic
280	C₂×C₄	#10597343	1	1	yes	characteristic
281	C₂×C₄	#10597347	1	2	yes	—
282	C₂×C₄	#10597353	1	2	yes	—
283	C₂×C₄	#10597357	1	2	yes	—
284	C₂×C₄	#10597364	1	2	yes	—
285	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
286	C₂×C₄	#10597384	1	1	yes	characteristic
287	C₂×C₄	#10597392	1	1	yes	characteristic
288	C₈	—	2	2	no	—
289	C₈	—	2	2	no	—
290	C₈	—	8	2	no	—
291	C₈	—	76	1	no	—
292	C₈	—	76	1	no	—
293	C₈	—	152	2	no	—
294	C₂²	—	38	2	no	—
295	C₂²	—	38	4	no	—
296	C₂²	—	76	1	no	—
297	C₂²	—	76	1	no	—
298	C₂²	—	76	2	no	—
299	C₂²	#11926401	1	1	yes	characteristic
300	C₂²	#11926569	1	2	yes	—
301	C₂²	#11926585	1	2	yes	—
302	C₂²	#108×D₁₉	1	1	yes	characteristic
303	C₂²	#108×D₁₉	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	2	1	no	—
306	C₄	—	38	2	no	—
307	C₄	—	76	1	no	—
308	C₄	—	76	1	no	—
309	C₄	#11926510	1	1	yes	characteristic
310	C₄	#11926512	1	1	yes	characteristic
311	C₄	#11926604	1	2	yes	—
312	C₄	#11926791	1	2	yes	—
313	C₄	#11926794	1	1	yes	characteristic
314	C₄	#11926799	1	1	yes	characteristic
315	C₂	—	76	2	no	—
316	C₂	#14562419	1	2	yes	—
317	C₂	#14562425	1	2	yes	—
318	C₂	#14563616	1	1	yes	characteristic
319	C₂	#14563669	1	1	yes	characteristic
320	C₂	#14563670	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#335	C₂
socle	C₂³×C₁₉	C₂×C₄⋊C₄
prime radical	C₂³×D₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#335	D₁₉
hypocenter	C₁₉	#8600
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. C₂×#11926295	C₂	semidirect
4. #14561469	C₂	semidirect
5. C₂×C₁₉×#335	C₂	semidirect
136. C₂×#335	D₁₉	semidirect
211. C₁₉	#8600	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926595	2
#14563612	2
C₂×#11926295	2
#14561469	2
C₂×C₁₉×#335	2
#8600	19