Subgroups — #18087738

Order 4864.

886 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×#11926499	C₂	1	2	yes	maximal
2	C₂×#11926309	C₂	1	1	yes	maximal, characteristic
3	#14563352	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926304	C₂	1	2	yes	maximal
5	C₂²×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	2	yes	—
7	C₂×#10597372	C₂²	1	2	yes	—
8	#11926499	—	2	4	no	—
9	#11926499	C₄	1	8	yes	complemented
10	C₂×#10597272	—	2	2	no	—
11	C₂×C₈×Dic₁₉	—	2	2	no	—
12	#11926309	C₄	1	4	yes	complemented
13	#11926307	C₄	1	4	yes	complemented
14	#11926304	C₄	1	8	yes	complemented
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#97	—	2	4	no	—
19	C₂×C₁₉×#97	C₄	1	4	yes	complemented
20	C₂³×C₄×C₁₉	—	2	1	no	—
21	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂²×C₈×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	—
28	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₉	D₄	1	2	yes	—
30	C₂²×C₈×C₁₉	D₄	1	4	yes	—
31	C₂²×C₈×C₁₉	Q₈	1	2	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
36	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
37	#10597372	—	2	2	no	—
38	#10597372	—	2	2	no	—
39	#10597372	C₂×C₄	1	4	yes	—
40	#10597372	C₂×C₄	1	4	yes	—
41	C₂×C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
42	C₂×C₄×Dic₁₉	—	2	2	no	—
43	C₂×#64520	—	2	2	no	—
44	C₂×#64520	—	2	2	no	—
45	C₂×#64520	—	2	2	no	—
46	C₂×#64520	C₂×C₄	1	4	yes	—
47	C₂×#64520	C₂×C₄	1	4	yes	—
48	C₂×#64520	C₂×C₄	1	4	yes	—
49	C₂²×C₁₉⋊C₈	—	2	2	no	—
50	C₁₉×#97	—	2	8	no	—
51	#10597272	—	2	8	no	—
52	C₈×Dic₁₉	—	2	8	no	—
53	C₂⁴×C₁₉	#41	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	—	2	2	no	—
55	C₂²×C₄×C₁₉	—	2	4	no	—
56	C₂²×C₄×C₁₉	—	4	4	no	—
57	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	#41	1	2	yes	—
67	C₂²×Dic₁₉	—	2	4	no	—
68	C₂×C₈×C₁₉	—	2	2	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	2	4	no	—
71	C₂×C₈×C₁₉	—	2	4	no	—
72	C₂×C₈×C₁₉	C₄²	1	4	yes	—
73	C₂×C₈×C₁₉	C₄²	1	4	yes	—
74	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
75	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
76	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
77	C₂×C₈×C₁₉	C₄⋊C₄	1	8	yes	—
78	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
79	C₄²×C₁₉	—	2	2	no	—
80	C₄²×C₁₉	—	2	4	no	—
81	C₄²×C₁₉	C₄²	1	4	yes	—
82	C₂²⋊Dic₁₉	—	2	4	no	—
83	C₂²⋊Dic₁₉	—	2	4	no	—
84	C₄⋊Dic₁₉	—	2	4	no	—
85	C₄⋊Dic₁₉	C₄²	1	8	yes	—
86	C₄×Dic₁₉	—	2	4	no	—
87	C₄×Dic₁₉	—	2	4	no	—
88	#64520	—	2	4	no	—
89	#64520	—	2	4	no	—
90	#64520	—	2	4	no	—
91	#64520	C₄²	1	8	yes	—
92	C₂×C₁₉⋊C₈	—	2	4	no	—
93	C₂×C₁₉⋊C₈	—	2	4	no	—
94	C₂×C₁₉⋊C₈	—	2	4	no	—
95	#10707	—	19	1	no	maximal, Sylow
96	C₂³×C₁₉	—	2	4	no	—
97	C₂³×C₁₉	#117	1	2	yes	—
98	C₂³×C₁₉	#117	1	1	yes	characteristic
99	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
100	C₂³×C₁₉	C₄×D₄	1	2	yes	—
101	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₉	—	2	4	no	—
103	C₂×C₄×C₁₉	—	4	8	no	—
104	C₂×C₄×C₁₉	—	4	4	no	—
105	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
106	C₂×C₄×C₁₉	C₂×C₄²	1	2	yes	—
107	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
108	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
109	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
112	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
113	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#117	1	2	yes	—
115	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
118	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
119	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
120	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
121	C₂×C₄×C₁₉	C₄×Q₈	1	2	yes	—
122	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
123	C₂×Dic₁₉	—	2	8	no	—
124	C₂×Dic₁₉	—	4	8	no	—
125	C₈×C₁₉	—	2	4	no	—
126	C₈×C₁₉	#95	1	8	yes	—
127	C₁₉⋊C₈	—	2	8	no	—
128	C₂×#405	—	19	2	no	—
129	C₂²×#97	D₁₉	1	1	yes	characteristic
130	C₂×#341	—	19	1	no	—
131	#1735	—	19	1	no	—
132	C₂×#339	—	19	2	no	—
133	C₂²×C₁₉	—	2	4	no	—
134	C₂²×C₁₉	—	2	4	no	—
135	C₂²×C₁₉	—	2	2	no	—
136	C₂²×C₁₉	—	2	2	no	—
137	C₂²×C₁₉	#376	1	1	yes	characteristic
138	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
140	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
141	C₂²×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
142	C₂²×C₁₉	#444	1	4	yes	—
143	C₄×C₁₉	—	4	4	no	—
144	C₄×C₁₉	C₄³	1	1	yes	characteristic
145	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
146	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
147	C₄×C₁₉	C₄×C₂²⋊C₄	1	2	yes	—
148	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
149	C₄×C₁₉	C₄×C₄⋊C₄	1	2	yes	—
150	Dic₁₉	—	4	8	no	—
151	C₂²×M₁₆	—	19	2	no	—
152	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
153	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
154	C₂×#117	—	19	2	no	—
155	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
156	#405	—	19	8	no	—
157	#405	—	38	4	no	—
158	C₂×#97	—	2	4	no	—
159	C₂×#97	—	38	2	no	—
160	C₂×#97	Dic₁₉	1	4	yes	complemented
161	C₂×C₄×C₈	—	38	2	no	—
162	#341	—	19	4	no	—
163	#340	—	19	4	no	—
164	#339	—	19	8	no	—
165	C₂×C₁₉	—	2	1	no	—
166	C₂×C₁₉	—	2	1	no	—
167	C₂×C₁₉	—	2	2	no	—
168	C₂×C₁₉	C₄×#95	1	1	yes	characteristic
169	C₂×C₁₉	#1765	1	4	yes	—
170	C₂×C₁₉	#1773	1	2	yes	—
171	C₂³×C₄	—	2	1	no	—
172	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
173	C₂×M₁₆	—	19	4	no	—
174	C₂×M₁₆	—	19	4	no	—
175	C₂×M₁₆	—	19	4	no	—
176	C₂×M₁₆	—	38	2	no	—
177	C₂×M₁₆	—	38	2	no	—
178	C₂×M₁₆	—	38	2	no	—
179	C₂²×C₈	—	2	2	no	—
180	C₂²×C₈	—	2	2	no	—
181	C₂²×C₈	—	38	2	no	—
182	C₂²×C₈	Dic₃₈	1	2	yes	—
183	C₂²×C₈	C₄×D₁₉	1	2	yes	—
184	C₂²×C₈	C₄×D₁₉	1	2	yes	—
185	C₂²×C₈	C₄×D₁₉	1	4	yes	—
186	C₂²×C₈	D₇₆	1	2	yes	—
187	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
188	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
189	C₂²×C₈	C₂²⋊D₁₉	1	4	yes	—
190	#117	—	19	4	no	—
191	#117	—	19	4	no	—
192	#117	—	38	2	no	—
193	#117	—	38	2	no	—
194	C₂×C₄⋊C₄	—	19	4	no	—
195	C₂×C₂²⋊C₄	—	38	2	no	—
196	C₂×C₄²	—	2	1	no	—
197	C₂×C₄²	—	2	2	no	—
198	C₂×C₄²	—	38	2	no	—
199	C₂×C₄²	C₄×D₁₉	1	4	yes	—
200	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
201	#97	—	2	8	no	—
202	#97	—	38	8	no	—
203	C₄×C₈	—	38	8	no	—
204	C₁₉	#10707	1	1	yes	characteristic, complemented, Sylow
205	C₂⁴	#64541	1	1	yes	characteristic
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	2	4	no	—
208	C₂²×C₄	—	4	4	no	—
209	C₂²×C₄	—	38	4	no	—
210	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
211	C₂²×C₄	C₂×C₄×D₁₉	1	2	yes	—
212	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
213	C₂²×C₄	C₂×C₄×D₁₉	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	#64541	1	1	yes	characteristic
217	C₂²×C₄	#64541	1	2	yes	—
218	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
219	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
220	M₁₆	—	19	8	no	—
221	M₁₆	—	38	4	no	—
222	M₁₆	—	38	4	no	—
223	M₁₆	—	38	4	no	—
224	C₂×C₈	—	2	2	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	4	no	—
227	C₂×C₈	—	2	4	no	—
228	C₂×C₈	—	38	4	no	—
229	C₂×C₈	—	38	4	no	—
230	C₂×C₈	—	38	4	no	—
231	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
232	C₂×C₈	C₄×Dic₁₉	1	4	yes	—
233	C₂×C₈	Dic₁₉⋊C₄	1	8	yes	—
234	C₂×C₈	C₄⋊Dic₁₉	1	4	yes	—
235	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
236	C₂×C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
237	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
238	C₄⋊C₄	—	19	8	no	—
239	C₄⋊C₄	—	38	4	no	—
240	C₂²⋊C₄	—	38	4	no	—
241	C₂²⋊C₄	—	38	4	no	—
242	C₄²	—	2	2	no	—
243	C₄²	—	2	4	no	—
244	C₄²	—	38	4	no	—
245	C₄²	—	38	4	no	—
246	C₄²	C₄×Dic₁₉	1	4	yes	—
247	C₂³	—	2	4	no	—
248	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
249	C₂³	#10597318	1	2	yes	—
250	C₂³	C₄×D₇₆	1	1	yes	characteristic
251	C₂³	#10597372	1	1	yes	characteristic
252	C₂³	C₄×C₂²⋊D₁₉	1	2	yes	—
253	C₂×C₄	—	2	4	no	—
254	C₂×C₄	—	4	8	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	—	38	8	no	—
257	C₂×C₄	—	76	8	no	—
258	C₂×C₄	C₄×Dic₃₈	1	2	yes	—
259	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
260	C₂×C₄	C₄²×D₁₉	1	2	yes	—
261	C₂×C₄	C₄²×D₁₉	1	2	yes	—
262	C₂×C₄	#10597318	1	2	yes	—
263	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
264	C₂×C₄	C₄×D₇₆	1	2	yes	—
265	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
266	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
267	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
268	C₂×C₄	C₂×Dic₁₉⋊C₄	1	2	yes	—
269	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
270	C₂×C₄	#10597372	1	1	yes	characteristic
271	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	2	yes	—
272	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
273	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
274	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
275	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
276	C₈	—	2	4	no	—
277	C₈	—	38	8	no	—
278	C₈	C₁₉⋊#95	1	8	yes	—
279	C₂²	—	2	4	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	2	2	no	—
282	C₂²	—	2	2	no	—
283	C₂²	#11926390	1	1	yes	characteristic
284	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
285	C₂²	C₄×(C₂×D₁₉)⋊C₄	1	2	yes	—
286	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
287	C₂²	C₄×Dic₁₉⋊C₄	1	2	yes	—
288	C₂²	#11926667	1	4	yes	—
289	C₄	—	4	4	no	—
290	C₄	—	76	8	no	—
291	C₄	C₄²×Dic₁₉	1	1	yes	characteristic
292	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
293	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
294	C₄	C₄×(C₂×D₁₉)⋊C₄	1	2	yes	—
295	C₄	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
296	C₄	C₄×Dic₁₉⋊C₄	1	2	yes	—
297	C₂	—	2	1	no	—
298	C₂	—	2	1	no	—
299	C₂	—	2	2	no	—
300	C₂	C₄×C₁₉⋊#95	1	1	yes	characteristic
301	C₂	#14563479	1	4	yes	—
302	C₂	#14563519	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₄×C₁₉	C₄³
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂²×C₁₉×#97	C₂
socle	C₂³×C₁₉	C₄×D₄
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂²×#97	D₁₉
hypocenter	C₁₉	#10707
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
9. #11926499	C₄	semidirect
12. #11926309	C₄	semidirect
13. #11926307	C₄	semidirect
14. #11926304	C₄	semidirect
19. C₂×C₁₉×#97	C₄	semidirect
160. C₂×#97	Dic₁₉	semidirect
204. C₁₉	#10707	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926499	2
C₂×#11926309	2
#14563352	2
C₂×#11926304	2
C₂²×C₁₉×#97	2
#10707	19