Subgroups — #18087593

Order 4864.

442 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564597	C₂	1	1	yes	maximal, characteristic
2	#14564438	C₂	1	1	yes	maximal, characteristic
3	#14563795	C₂	1	1	yes	maximal, characteristic
4	#14563794	C₂	1	1	yes	maximal, characteristic
5	#14563794	C₂	1	1	yes	maximal, characteristic
6	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1990	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597275	—	2	2	no	—
9	C₂×#10597264	—	2	2	no	—
10	C₂×#10597264	—	2	2	no	—
11	C₂×#10597292	—	2	2	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11926414	C₂²	1	1	yes	characteristic
15	#11926414	C₂²	1	1	yes	characteristic
16	#11926306	—	2	2	no	—
17	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#384	C₂²	1	1	yes	characteristic
20	C₁₉×#340	—	2	2	no	—
21	C₂²×Q₈×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	—	2	1	no	—
24	C₁₉×C₄⋊Q₈	—	2	1	no	—
25	C₁₉×C₄⋊Q₈	—	2	1	no	—
26	C₁₉×C₄⋊Q₈	Q₈	1	2	yes	—
27	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×C₄⋊Dic₁₉	—	2	1	no	—
34	C₂×C₄⋊Dic₁₉	—	2	1	no	—
35	C₂×C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
40	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
41	C₄×C₈×C₁₉	—	2	1	no	—
42	C₄×C₈×C₁₉	—	2	1	no	—
43	#10597292	—	4	4	no	—
44	#10597275	—	4	4	no	—
45	#10597264	—	4	4	no	—
46	#10597264	—	4	4	no	—
47	C₄×C₁₉⋊C₈	—	2	1	no	—
48	C₄×C₁₉⋊C₈	—	2	1	no	—
49	C₄×C₁₉⋊C₈	—	2	1	no	—
50	C₄×C₁₉⋊C₈	—	2	1	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	4	1	no	—
53	C₂×Q₈×C₁₉	—	4	2	no	—
54	C₂×Q₈×C₁₉	—	4	2	no	—
55	C₂²×C₄×C₁₉	—	4	1	no	—
56	C₂²×C₄×C₁₉	—	4	1	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×Dic₁₉	—	4	1	no	—
61	C₂²×Dic₁₉	—	4	1	no	—
62	C₂×C₈×C₁₉	—	2	2	no	—
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
65	C₄⋊C₄×C₁₉	—	2	2	no	—
66	C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₄⋊C₄×C₁₉	—	4	1	no	—
68	C₄⋊C₄×C₁₉	—	4	1	no	—
69	C₄⋊C₄×C₁₉	—	4	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₄²×C₁₉	#41	1	1	yes	characteristic
76	C₄⋊Dic₁₉	—	4	2	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	4	2	no	—
79	C₄⋊Dic₁₉	—	4	2	no	—
80	C₄⋊Dic₁₉	—	4	2	no	—
81	C₄⋊Dic₁₉	—	4	2	no	—
82	C₂×C₁₉⋊C₈	—	2	2	no	—
83	C₂×C₁₉⋊C₈	—	2	2	no	—
84	C₂×C₁₉⋊C₈	—	2	2	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	D₈	1	4	yes	—
87	C₂×C₁₉⋊C₈	Q₁₆	1	4	yes	—
88	#10674	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	#127	1	1	yes	characteristic
90	Q₈×C₁₉	—	4	4	no	—
91	Q₈×C₁₉	—	8	2	no	—
92	C₂×C₄×C₁₉	—	4	2	no	—
93	C₂×C₄×C₁₉	—	8	1	no	—
94	C₂×C₄×C₁₉	—	8	1	no	—
95	C₂×C₄×C₁₉	—	8	1	no	—
96	C₂×C₄×C₁₉	—	8	1	no	—
97	C₂×C₄×C₁₉	—	8	1	no	—
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
104	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
105	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
106	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
107	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
108	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
109	C₂×C₄×C₁₉	#137	1	2	yes	—
110	C₂×Dic₁₉	—	8	1	no	—
111	C₂×Dic₁₉	—	8	1	no	—
112	C₂×Dic₁₉	—	8	1	no	—
113	C₂×Dic₁₉	—	8	1	no	—
114	C₂×Dic₁₉	—	8	1	no	—
115	C₂×Dic₁₉	—	8	1	no	—
116	C₈×C₁₉	—	2	4	no	—
117	C₁₉⋊C₈	—	2	4	no	—
118	C₁₉⋊C₈	—	2	4	no	—
119	#1990	—	19	1	no	—
120	#1990	D₁₉	1	1	yes	characteristic
121	#1956	—	19	1	no	—
122	#1845	—	19	1	no	—
123	#1845	—	19	1	no	—
124	#1845	—	19	1	no	—
125	#1273	—	19	1	no	—
126	C₂²×C₁₉	#399	1	1	yes	characteristic
127	C₂²×C₁₉	#493	1	1	yes	characteristic
128	C₂²×C₁₉	#494	1	1	yes	characteristic
129	C₂²×C₁₉	#494	1	1	yes	characteristic
130	C₂²×C₁₉	#496	1	1	yes	characteristic
131	C₂²×C₁₉	#496	1	1	yes	characteristic
132	C₂²×C₁₉	#497	1	1	yes	characteristic
133	C₄×C₁₉	—	8	2	no	—
134	C₄×C₁₉	—	16	1	no	—
135	C₄×C₁₉	#474	1	2	yes	—
136	C₄×C₁₉	#477	1	2	yes	—
137	C₄×C₁₉	#477	1	2	yes	—
138	C₄×C₁₉	#480	1	2	yes	—
139	C₄×C₁₉	#484	1	2	yes	—
140	C₄×C₁₉	#484	1	2	yes	—
141	Dic₁₉	—	16	1	no	—
142	Dic₁₉	—	16	1	no	—
143	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
144	C₂×#107	—	38	2	no	—
145	C₂×#107	—	38	2	no	—
146	C₂×#107	—	38	2	no	—
147	C₂×#103	—	38	2	no	—
148	C₂×C₄×C₈	—	19	1	no	—
149	C₂×C₄×C₈	—	19	1	no	—
150	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
151	#384	—	19	1	no	—
152	#384	—	19	1	no	—
153	#384	C₂×D₁₉	1	1	yes	characteristic
154	#340	—	2	2	no	—
155	#340	—	38	2	no	—
156	C₂×C₁₉	#1713	1	1	yes	characteristic
157	C₂×C₁₉	#1721	1	1	yes	characteristic
158	C₂×C₁₉	#1723	1	1	yes	characteristic
159	C₂×C₁₉	#1723	1	1	yes	characteristic
160	C₂×C₁₉	#2093	1	1	yes	characteristic
161	C₂×C₁₉	#2095	1	1	yes	characteristic
162	C₂×C₁₉	#2095	1	1	yes	characteristic
163	C₂²×Q₈	—	2	1	no	—
164	C₂²×C₈	—	19	2	no	—
165	C₂²×C₈	—	19	2	no	—
166	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
167	C₄⋊Q₈	—	2	1	no	—
168	C₄⋊Q₈	—	2	1	no	—
169	C₄⋊Q₈	—	2	1	no	—
170	C₄⋊Q₈	Dic₃₈	1	2	yes	—
171	C₂×C₄⋊C₄	—	2	1	no	—
172	C₂×C₄⋊C₄	—	2	1	no	—
173	C₂×C₄⋊C₄	—	2	1	no	—
174	C₂×C₄⋊C₄	—	2	1	no	—
175	C₂×C₄⋊C₄	—	2	1	no	—
176	C₂×C₄⋊C₄	—	38	1	no	—
177	C₂×C₄⋊C₄	—	38	1	no	—
178	C₂×C₄⋊C₄	—	38	1	no	—
179	C₂×C₄⋊C₄	—	38	1	no	—
180	C₂×C₄⋊C₄	—	38	1	no	—
181	C₂×C₄⋊C₄	—	38	1	no	—
182	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
183	#107	—	76	4	no	—
184	#107	—	76	4	no	—
185	#107	—	76	4	no	—
186	#103	—	76	4	no	—
187	C₄×C₈	—	2	1	no	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	38	1	no	—
190	C₄×C₈	—	38	1	no	—
191	C₄×C₈	—	38	1	no	—
192	C₄×C₈	—	38	1	no	—
193	C₁₉	#10674	1	1	yes	characteristic, complemented, Sylow
194	C₂×Q₈	—	2	2	no	—
195	C₂×Q₈	—	4	1	no	—
196	C₂×Q₈	—	4	2	no	—
197	C₂×Q₈	—	4	2	no	—
198	C₂²×C₄	—	4	1	no	—
199	C₂²×C₄	—	4	1	no	—
200	C₂²×C₄	—	76	1	no	—
201	C₂²×C₄	—	76	1	no	—
202	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
203	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
204	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	—	19	4	no	—
208	C₂×C₈	—	19	4	no	—
209	C₂×C₈	—	38	2	no	—
210	C₂×C₈	—	38	2	no	—
211	C₂×C₈	—	38	2	no	—
212	C₂×C₈	—	38	2	no	—
213	C₂×C₈	#64528	1	4	yes	—
214	C₄⋊C₄	—	2	2	no	—
215	C₄⋊C₄	—	2	2	no	—
216	C₄⋊C₄	—	4	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄⋊C₄	—	4	2	no	—
219	C₄⋊C₄	—	4	2	no	—
220	C₄⋊C₄	—	4	2	no	—
221	C₄⋊C₄	—	76	2	no	—
222	C₄⋊C₄	—	76	2	no	—
223	C₄⋊C₄	—	76	2	no	—
224	C₄⋊C₄	—	76	2	no	—
225	C₄⋊C₄	—	76	2	no	—
226	C₄⋊C₄	—	76	2	no	—
227	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
228	C₄²	#64541	1	1	yes	characteristic
229	C₄²	#64543	1	1	yes	characteristic
230	C₄²	#64543	1	1	yes	characteristic
231	C₂³	#10597386	1	1	yes	characteristic
232	Q₈	—	4	4	no	—
233	Q₈	—	8	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	8	1	no	—
236	C₂×C₄	—	8	1	no	—
237	C₂×C₄	—	8	1	no	—
238	C₂×C₄	—	8	1	no	—
239	C₂×C₄	—	8	1	no	—
240	C₂×C₄	—	152	1	no	—
241	C₂×C₄	—	152	1	no	—
242	C₂×C₄	—	152	1	no	—
243	C₂×C₄	—	152	1	no	—
244	C₂×C₄	—	152	1	no	—
245	C₂×C₄	—	152	1	no	—
246	C₂×C₄	#10597324	1	1	yes	characteristic
247	C₂×C₄	#10597324	1	1	yes	characteristic
248	C₂×C₄	#10597329	1	1	yes	characteristic
249	C₂×C₄	#10597329	1	1	yes	characteristic
250	C₂×C₄	D₈×D₁₉	1	2	yes	—
251	C₂×C₄	#10597360	1	2	yes	—
252	C₂×C₄	#10597361	1	2	yes	—
253	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
254	C₂×C₄	#10597370	1	1	yes	characteristic
255	C₂×C₄	#10597381	1	1	yes	characteristic
256	C₂×C₄	C₂×#64528	1	2	yes	—
257	C₂×C₄	#10597395	1	2	yes	—
258	C₈	—	2	4	no	—
259	C₈	—	38	4	no	—
260	C₈	—	38	4	no	—
261	C₂²	#11926480	1	1	yes	characteristic
262	C₂²	#11926919	1	1	yes	characteristic
263	C₂²	#11926922	1	1	yes	characteristic
264	C₂²	#11926923	1	1	yes	characteristic
265	C₂²	#11926930	1	1	yes	characteristic
266	C₂²	#11926934	1	1	yes	characteristic
267	C₂²	#11926935	1	1	yes	characteristic
268	C₄	—	8	2	no	—
269	C₄	—	16	1	no	—
270	C₄	—	304	1	no	—
271	C₄	—	304	1	no	—
272	C₄	#11926822	1	2	yes	—
273	C₄	#11926837	1	2	yes	—
274	C₄	#11926839	1	2	yes	—
275	C₄	#11926856	1	2	yes	—
276	C₄	#11926877	1	2	yes	—
277	C₄	#11926878	1	2	yes	—
278	C₂	#14563252	1	1	yes	characteristic
279	C₂	#14563303	1	1	yes	characteristic
280	C₂	#14563309	1	1	yes	characteristic
281	C₂	#14563314	1	1	yes	characteristic
282	C₂	#14565161	1	1	yes	characteristic
283	C₂	#14565171	1	1	yes	characteristic
284	C₂	#14565173	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1990	C₂
socle, prime radical	C₂³×C₁₉	#127
hypercenter	#1990	D₁₉
hypocenter	C₁₉	#10674
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1990

Complements

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

N	H ≅ G/N	type
193. C₁₉	#10674	semidirect

Maximal subgroups

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

subgroup	index
#14564597	2
#14564438	2
#14563795	2
#14563794	2
C₁₉⋊#1273	2
C₁₉×#1990	2
#10674	19