Subgroups — #18075960

Order 4864.

630 conjugacy classes of subgroups.

The subgroup lattice has 304 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	#14563615	C₂	1	1	yes	maximal, characteristic
3	#14561519	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
6	C₂²×C₄⋊Dic₁₉	—	2	1	no	—
7	C₂²×C₄⋊Dic₁₉	C₄	1	2	yes	—
8	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	#11926414	—	2	1	no	—
11	#11926414	—	2	1	no	—
12	#11926414	C₄	1	2	yes	—
13	#11926414	C₂²	1	2	yes	—
14	#11926299	—	2	1	no	—
15	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊C₈	—	2	1	no	—
18	C₁₉×#336	—	2	1	no	—
19	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂³×Dic₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂×C₄²×C₁₉	—	2	4	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	C₂×C₄⋊Dic₁₉	—	2	2	no	—
31	C₂×C₄⋊Dic₁₉	—	2	2	no	—
32	C₂×C₄⋊Dic₁₉	—	2	2	no	—
33	C₂×C₄⋊Dic₁₉	—	2	2	no	—
34	C₂×C₄⋊Dic₁₉	—	4	4	no	—
35	C₂×C₄⋊Dic₁₉	—	4	4	no	—
36	C₂×C₄⋊Dic₁₉	—	4	4	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	4	no	—
40	C₁₉×C₂²⋊C₈	—	4	2	no	—
41	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
43	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	2	no	—
48	C₂²×C₄×C₁₉	—	2	2	no	—
49	C₂²×C₄×C₁₉	—	2	2	no	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
55	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
56	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
57	C₂²×C₄×C₁₉	Q₁₆	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×Dic₁₉	—	2	4	no	—
62	C₂²×Dic₁₉	—	4	4	no	—
63	C₂²×Dic₁₉	—	4	4	no	—
64	C₂²×Dic₁₉	—	4	4	no	—
65	C₂×C₈×C₁₉	—	4	2	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₄²×C₁₉	—	2	2	no	—
69	C₄²×C₁₉	—	2	2	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	#41	1	4	yes	—
72	C₄⋊Dic₁₉	—	4	4	no	—
73	C₄⋊Dic₁₉	—	4	4	no	—
74	C₄⋊Dic₁₉	—	4	4	no	—
75	C₄⋊Dic₁₉	—	4	4	no	—
76	C₄⋊Dic₁₉	—	4	4	no	—
77	C₄⋊Dic₁₉	—	4	4	no	—
78	C₂×C₁₉⋊C₈	—	4	2	no	—
79	C₂×C₁₉⋊C₈	—	4	2	no	—
80	C₂×C₁₉⋊C₈	—	4	2	no	—
81	#8725	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	—	2	1	no	—
83	C₂³×C₁₉	—	2	1	no	—
84	C₂³×C₁₉	—	2	1	no	—
85	C₂³×C₁₉	—	2	1	no	—
86	C₂³×C₁₉	#100	1	2	yes	—
87	C₂³×C₁₉	#103	1	2	yes	—
88	C₂³×C₁₉	#103	1	2	yes	—
89	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₁₉	—	2	8	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	2	1	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	4	no	—
100	C₂×C₄×C₁₉	—	2	4	no	—
101	C₂×C₄×C₁₉	—	2	4	no	—
102	C₂×C₄×C₁₉	—	2	4	no	—
103	C₂×C₄×C₁₉	#101	1	2	yes	—
104	C₂×C₄×C₁₉	#103	1	2	yes	—
105	C₂×C₄×C₁₉	#103	1	2	yes	—
106	C₂×C₄×C₁₉	#117	1	2	yes	—
107	C₂×C₄×C₁₉	#123	1	2	yes	—
108	C₂×C₄×C₁₉	#123	1	2	yes	—
109	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
112	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
114	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
115	C₂×Dic₁₉	—	4	4	no	—
116	C₂×Dic₁₉	—	4	4	no	—
117	C₂×Dic₁₉	—	4	4	no	—
118	C₂×Dic₁₉	—	8	8	no	—
119	C₈×C₁₉	—	8	2	no	—
120	C₁₉⋊C₈	—	8	2	no	—
121	C₂×#384	—	19	1	no	—
122	#1797	—	19	1	no	—
123	#1797	D₁₉	1	1	yes	characteristic
124	#1296	—	19	4	no	—
125	C₂²×C₁₉	—	2	2	no	—
126	C₂²×C₁₉	—	2	2	no	—
127	C₂²×C₁₉	—	2	2	no	—
128	C₂²×C₁₉	—	2	2	no	—
129	C₂²×C₁₉	—	2	2	no	—
130	C₂²×C₁₉	—	2	2	no	—
131	C₂²×C₁₉	#333	1	4	yes	—
132	C₂²×C₁₉	#381	1	1	yes	characteristic
133	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
134	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
135	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
136	C₂²×C₁₉	C₂×#103	1	1	yes	characteristic
137	C₂²×C₁₉	#418	1	1	yes	characteristic
138	C₂²×C₁₉	#418	1	1	yes	characteristic
139	C₄×C₁₉	—	2	2	no	—
140	C₄×C₁₉	—	2	2	no	—
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	2	no	—
143	C₄×C₁₉	#481	1	2	yes	—
144	C₄×C₁₉	#481	1	2	yes	—
145	C₄×C₁₉	#484	1	2	yes	—
146	C₄×C₁₉	#484	1	2	yes	—
147	Dic₁₉	—	8	4	no	—
148	C₂²×C₄⋊C₄	—	19	2	no	—
149	C₂²×C₄⋊C₄	—	38	1	no	—
150	C₂²×C₄⋊C₄	—	38	1	no	—
151	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
152	C₂×C₄⋊C₈	—	19	2	no	—
153	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
154	C₂×C₂²⋊C₈	—	2	1	no	—
155	C₂×C₂²⋊C₈	—	38	1	no	—
156	#384	—	19	2	no	—
157	#384	—	19	2	no	—
158	#384	—	38	1	no	—
159	#384	—	38	1	no	—
160	#336	—	2	1	no	—
161	#336	—	38	1	no	—
162	C₂×C₁₉	—	2	4	no	—
163	C₂×C₁₉	C₂×#333	1	1	yes	characteristic
164	C₂×C₁₉	#1549	1	1	yes	characteristic
165	C₂×C₁₉	#1549	1	1	yes	characteristic
166	C₂×C₁₉	#1555	1	1	yes	characteristic
167	C₂×C₁₉	#1821	1	1	yes	characteristic
168	C₂×C₁₉	#1824	1	1	yes	characteristic
169	C₂×C₁₉	#1824	1	1	yes	characteristic
170	C₂³×C₄	—	38	2	no	—
171	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
172	C₂³×C₄	D₇₆	1	1	yes	characteristic
173	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
174	C₂²×C₈	—	2	2	no	—
175	C₂²×C₈	—	38	2	no	—
176	C₂×C₄⋊C₄	—	19	4	no	—
177	C₂×C₄⋊C₄	—	38	2	no	—
178	C₂×C₄⋊C₄	—	38	2	no	—
179	C₂×C₄⋊C₄	—	38	2	no	—
180	C₂×C₄⋊C₄	—	38	2	no	—
181	C₂×C₄⋊C₄	—	38	2	no	—
182	C₂×C₄⋊C₄	—	76	4	no	—
183	C₂×C₄⋊C₄	—	76	4	no	—
184	C₂×C₄⋊C₄	—	76	4	no	—
185	C₂×C₄²	—	2	4	no	—
186	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
187	C₂×C₄²	D₇₆	1	1	yes	characteristic
188	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
189	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
190	C₄⋊C₈	—	2	4	no	—
191	C₄⋊C₈	—	38	4	no	—
192	C₂²⋊C₈	—	4	2	no	—
193	C₂²⋊C₈	—	76	2	no	—
194	C₁₉	#8725	1	1	yes	characteristic, complemented, Sylow
195	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	—	2	2	no	—
199	C₂²×C₄	—	2	2	no	—
200	C₂²×C₄	—	2	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	2	2	no	—
203	C₂²×C₄	—	38	4	no	—
204	C₂²×C₄	—	76	4	no	—
205	C₂²×C₄	—	76	4	no	—
206	C₂²×C₄	—	76	4	no	—
207	C₂²×C₄	#64516	1	2	yes	—
208	C₂²×C₄	Dic₇₆	1	2	yes	—
209	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
210	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
211	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
212	C₂²×C₄	#64526	1	2	yes	—
213	C₂²×C₄	#64528	1	2	yes	—
214	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
215	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
216	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
217	C₂×C₈	—	4	2	no	—
218	C₂×C₈	—	4	2	no	—
219	C₂×C₈	—	4	2	no	—
220	C₂×C₈	—	76	2	no	—
221	C₂×C₈	—	76	2	no	—
222	C₂×C₈	—	76	2	no	—
223	C₄⋊C₄	—	76	4	no	—
224	C₄⋊C₄	—	76	4	no	—
225	C₄⋊C₄	—	76	4	no	—
226	C₄⋊C₄	—	76	4	no	—
227	C₄⋊C₄	—	76	4	no	—
228	C₄⋊C₄	—	76	4	no	—
229	C₄²	—	2	2	no	—
230	C₄²	—	2	2	no	—
231	C₄²	—	2	2	no	—
232	C₄²	#64543	1	4	yes	—
233	C₂³	—	2	1	no	—
234	C₂³	—	2	1	no	—
235	C₂³	—	2	1	no	—
236	C₂³	—	2	1	no	—
237	C₂³	#10597267	1	2	yes	—
238	C₂³	#10597273	1	2	yes	—
239	C₂³	#10597280	1	2	yes	—
240	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
241	C₂×C₄	—	2	8	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	2	4	no	—
254	C₂×C₄	—	76	4	no	—
255	C₂×C₄	—	76	4	no	—
256	C₂×C₄	—	76	4	no	—
257	C₂×C₄	—	152	8	no	—
258	C₂×C₄	#10597267	1	2	yes	—
259	C₂×C₄	#10597273	1	2	yes	—
260	C₂×C₄	#10597281	1	2	yes	—
261	C₂×C₄	#10597323	1	2	yes	—
262	C₂×C₄	#10597332	1	2	yes	—
263	C₂×C₄	C₂×#64516	1	1	yes	characteristic
264	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
265	C₂×C₄	#10597354	1	2	yes	—
266	C₂×C₄	C₂×#64526	1	1	yes	characteristic
267	C₂×C₄	#10597381	1	2	yes	—
268	C₂×C₄	C₂×#64528	1	1	yes	characteristic
269	C₂×C₄	#10597395	1	2	yes	—
270	C₈	—	8	2	no	—
271	C₈	—	152	2	no	—
272	C₂²	—	2	2	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	2	no	—
275	C₂²	—	2	2	no	—
276	C₂²	—	2	2	no	—
277	C₂²	—	2	2	no	—
278	C₂²	#11926292	1	4	yes	—
279	C₂²	#11926405	1	1	yes	characteristic
280	C₂²	C₂×#10597280	1	1	yes	characteristic
281	C₂²	C₂×#10597281	1	1	yes	characteristic
282	C₂²	C₂×#10597267	1	1	yes	characteristic
283	C₂²	C₂×#10597273	1	1	yes	characteristic
284	C₂²	#11926548	1	1	yes	characteristic
285	C₂²	#11926550	1	1	yes	characteristic
286	C₄	—	2	2	no	—
287	C₄	—	2	2	no	—
288	C₄	—	2	2	no	—
289	C₄	—	2	2	no	—
290	C₄	—	152	4	no	—
291	C₄	#11926860	1	2	yes	—
292	C₄	#11926863	1	2	yes	—
293	C₄	#11926877	1	2	yes	—
294	C₄	#11926880	1	2	yes	—
295	C₂	—	2	4	no	—
296	C₂	C₂×#11926292	1	1	yes	characteristic
297	C₂	#14562319	1	1	yes	characteristic
298	C₂	#14562321	1	1	yes	characteristic
299	C₂	#14562348	1	1	yes	characteristic
300	C₂	#14563713	1	1	yes	characteristic
301	C₂	#14563723	1	1	yes	characteristic
302	C₂	#14563726	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1797	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1797	D₁₉
hypocenter	C₁₉	#8725
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #1797

Complements

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

N	H ≅ G/N	type
3. #14561519	C₂	semidirect
194. C₁₉	#8725	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
#14563615	2
#14561519	2
C₁₉×#1797	2
#8725	19