Subgroups — #18075858

Order 4864.

384 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597275	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562398	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562160	C₂	1	2	yes	maximal
4	#14561492	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2966	C₂	1	1	yes	maximal, characteristic
6	#11926601	C₂²	1	2	yes	—
7	C₂×#10597275	—	2	1	no	—
8	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
9	#11926307	—	2	1	no	—
10	#11926297	—	2	1	no	—
11	#11926295	—	2	1	no	—
12	#11926281	—	2	2	no	—
13	#11926278	—	2	2	no	—
14	C₁₉×#529	C₂²	1	1	yes	characteristic
15	C₁₉×#446	C₄	1	1	yes	characteristic, complemented
16	C₈×Q₈×C₁₉	C₄	1	1	yes	characteristic, complemented
17	C₁₉×#436	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#435	—	2	1	no	—
19	C₈×D₄×C₁₉	—	2	1	no	—
20	C₈×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
21	C₁₉×#433	—	2	1	no	—
22	C₁₉×#432	C₂²	1	1	yes	characteristic
23	C₁₉×#405	—	2	1	no	—
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂²×C₈×C₁₉	—	2	1	no	—
27	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₁₉×#126	—	2	1	no	—
30	C₁₉×#125	Q₈	1	1	yes	characteristic
31	C₁₉×#124	Q₈	1	1	yes	characteristic
32	C₁₉×#123	—	2	1	no	—
33	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
34	C₁₉×#121	D₄	1	1	yes	characteristic
35	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₄×D₄×C₁₉	—	2	1	no	—
37	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
38	C₁₉×#117	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₉	—	2	2	no	—
41	C₂×C₄×Dic₁₉	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	2	1	no	—
43	C₁₉×C₄⋊C₈	—	2	1	no	—
44	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₁₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₁₉×C₂²⋊C₈	—	2	1	no	—
47	C₁₉×C₂²⋊C₈	—	2	1	no	—
48	C₁₉×C₂²⋊C₈	—	2	1	no	—
49	C₁₉×#97	—	2	1	no	—
50	C₁₉×#97	—	2	1	no	—
51	C₄×C₈×C₁₉	—	2	1	no	—
52	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
53	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
54	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
55	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
56	C₁₉⋊#95	—	2	2	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
58	#10597275	—	2	4	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
60	#10597260	—	2	2	no	—
61	C₂×Q₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
62	C₂×D₄×C₁₉	—	2	1	no	—
63	C₂×D₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂²×Dic₁₉	—	4	2	no	—
69	M₁₆×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	—	2	1	no	—
72	C₂×C₈×C₁₉	—	2	1	no	—
73	C₂×C₈×C₁₉	—	4	1	no	—
74	C₂×C₈×C₁₉	—	4	2	no	—
75	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₄⋊C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₄²×C₁₉	—	2	1	no	—
91	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
94	C₄²×C₁₉	#41	1	1	yes	characteristic
95	C₄⋊Dic₁₉	—	2	4	no	—
96	C₄⋊Dic₁₉	—	4	2	no	—
97	C₄×Dic₁₉	—	8	2	no	—
98	C₂×C₁₉⋊C₈	—	4	2	no	—
99	#8697	—	19	1	no	maximal, Sylow
100	C₂³×C₁₉	—	2	1	no	—
101	C₂³×C₁₉	#121	1	1	yes	characteristic
102	Q₈×C₁₉	—	4	1	no	—
103	D₄×C₁₉	—	4	1	no	—
104	D₄×C₁₉	—	4	1	no	—
105	D₄×C₁₉	—	4	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	4	1	no	—
114	C₂×C₄×C₁₉	—	4	1	no	—
115	C₂×C₄×C₁₉	—	4	1	no	—
116	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
119	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
122	C₂×Dic₁₉	—	4	4	no	—
123	C₂×Dic₁₉	—	8	2	no	—
124	C₂×Dic₁₉	—	8	2	no	—
125	C₈×C₁₉	—	2	1	no	—
126	C₈×C₁₉	—	2	1	no	—
127	C₈×C₁₉	—	2	1	no	—
128	C₈×C₁₉	—	4	1	no	—
129	C₈×C₁₉	—	4	1	no	—
130	C₈×C₁₉	#104	1	2	yes	—
131	C₁₉⋊C₈	—	8	2	no	—
132	#2966	D₁₉	1	1	yes	characteristic
133	C₄×#107	—	19	1	no	—
134	#1568	—	19	1	no	—
135	#1509	—	19	2	no	—
136	#1285	—	19	2	no	—
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	—	2	1	no	—
139	C₂²×C₁₉	—	4	1	no	—
140	C₂²×C₁₉	—	4	1	no	—
141	C₂²×C₁₉	—	4	1	no	—
142	C₂²×C₁₉	#380	1	1	yes	characteristic
143	C₂²×C₁₉	#472	1	1	yes	characteristic
144	C₂²×C₁₉	#473	1	1	yes	characteristic
145	C₄×C₁₉	—	2	1	no	—
146	C₄×C₁₉	—	2	1	no	—
147	C₄×C₁₉	—	2	1	no	—
148	C₄×C₁₉	—	2	1	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	4	1	no	—
151	C₄×C₁₉	—	4	1	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
154	C₄×C₁₉	#421	1	1	yes	characteristic
155	Dic₁₉	—	8	4	no	—
156	#529	C₂×D₁₉	1	1	yes	characteristic
157	#446	Dic₁₉	1	1	yes	characteristic, complemented
158	C₈×Q₈	Dic₁₉	1	1	yes	characteristic, complemented
159	#436	Dic₁₉	1	1	yes	characteristic, complemented
160	#435	—	2	1	no	—
161	C₈×D₄	—	2	1	no	—
162	C₈×D₄	Dic₁₉	1	1	yes	characteristic, complemented
163	#433	—	2	1	no	—
164	#432	—	19	2	no	—
165	#432	C₂×D₁₉	1	1	yes	characteristic
166	C₂×#107	—	38	1	no	—
167	#405	—	2	1	no	—
168	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
169	C₄×C₄⋊C₄	—	19	2	no	—
170	#340	—	38	1	no	—
171	#335	—	38	1	no	—
172	#334	—	38	1	no	—
173	#328	—	38	2	no	—
174	#327	—	38	2	no	—
175	C₂×C₁₉	—	2	1	no	—
176	C₂×C₁₉	—	2	1	no	—
177	C₂×C₁₉	—	8	1	no	—
178	C₂×C₁₉	#1806	1	1	yes	characteristic
179	C₂×C₁₉	#1812	1	1	yes	characteristic
180	C₂×C₁₉	#1816	1	1	yes	characteristic
181	C₂×M₁₆	—	2	1	no	—
182	C₂²×C₈	—	2	1	no	—
183	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
184	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
185	#126	—	2	1	no	—
186	#125	Dic₃₈	1	1	yes	characteristic
187	#124	Dic₃₈	1	1	yes	characteristic
188	#123	—	2	1	no	—
189	C₂²⋊Q₈	D₇₆	1	1	yes	characteristic
190	#121	D₇₆	1	1	yes	characteristic
191	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
192	C₄×D₄	—	2	1	no	—
193	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
194	#117	—	2	1	no	—
195	C₂×C₄⋊C₄	—	38	2	no	—
196	C₂×C₄²	—	38	2	no	—
197	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
198	#107	—	38	4	no	—
199	C₄⋊C₈	—	2	1	no	—
200	C₄⋊C₈	—	2	1	no	—
201	C₄⋊C₈	—	38	2	no	—
202	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
203	C₄⋊C₈	C₂×Dic₁₉	1	1	yes	characteristic
204	C₂²⋊C₈	—	2	1	no	—
205	C₂²⋊C₈	—	2	1	no	—
206	C₂²⋊C₈	—	2	1	no	—
207	C₂²⋊C₈	—	38	2	no	—
208	#97	—	2	1	no	—
209	#97	—	2	1	no	—
210	#97	—	38	2	no	—
211	C₄×C₈	—	2	1	no	—
212	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
213	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
214	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
215	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
216	#95	—	38	2	no	—
217	C₁₉	#8697	1	1	yes	characteristic, complemented, Sylow
218	C₂×Q₈	C₄⋊Dic₁₉	1	1	yes	characteristic
219	C₂×D₄	—	2	1	no	—
220	C₂×D₄	C₄⋊Dic₁₉	1	1	yes	characteristic
221	C₂²×C₄	—	2	1	no	—
222	C₂²×C₄	—	76	2	no	—
223	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
224	C₂²×C₄	#64541	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
226	M₁₆	—	4	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	1	no	—
229	C₂×C₈	—	2	1	no	—
230	C₂×C₈	—	4	1	no	—
231	C₂×C₈	—	4	2	no	—
232	C₂×C₈	—	76	2	no	—
233	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
234	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
235	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
236	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
237	C₄⋊C₄	—	2	1	no	—
238	C₄⋊C₄	—	2	1	no	—
239	C₄⋊C₄	—	2	1	no	—
240	C₄⋊C₄	—	2	1	no	—
241	C₄⋊C₄	—	38	4	no	—
242	C₄⋊C₄	—	76	2	no	—
243	C₄⋊C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
244	C₄⋊C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
245	C₂²⋊C₄	—	2	1	no	—
246	C₂²⋊C₄	—	2	1	no	—
247	C₂²⋊C₄	—	2	1	no	—
248	C₂²⋊C₄	—	2	1	no	—
249	C₂²⋊C₄	—	2	1	no	—
250	C₄²	—	2	1	no	—
251	C₄²	—	152	2	no	—
252	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
253	C₄²	#64541	1	1	yes	characteristic
254	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
255	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂³	—	2	1	no	—
257	C₂³	#10597376	1	1	yes	characteristic
258	Q₈	—	4	1	no	—
259	D₄	—	4	1	no	—
260	D₄	—	4	1	no	—
261	D₄	—	4	1	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	4	1	no	—
270	C₂×C₄	—	4	1	no	—
271	C₂×C₄	—	4	1	no	—
272	C₂×C₄	—	76	4	no	—
273	C₂×C₄	—	152	2	no	—
274	C₂×C₄	—	152	2	no	—
275	C₂×C₄	#10597370	1	1	yes	characteristic
276	C₂×C₄	#10597370	1	1	yes	characteristic
277	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
278	C₂×C₄	#10597372	1	1	yes	characteristic
279	C₂×C₄	#10597376	1	1	yes	characteristic
280	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
281	C₈	—	2	1	no	—
282	C₈	—	2	1	no	—
283	C₈	—	2	1	no	—
284	C₈	—	4	1	no	—
285	C₈	—	4	1	no	—
286	C₈	—	152	2	no	—
287	C₈	#10597294	1	2	yes	—
288	C₂²	—	2	1	no	—
289	C₂²	—	2	1	no	—
290	C₂²	—	4	1	no	—
291	C₂²	—	4	1	no	—
292	C₂²	—	4	1	no	—
293	C₂²	#11926404	1	1	yes	characteristic
294	C₂²	#11926814	1	1	yes	characteristic
295	C₂²	#11926819	1	1	yes	characteristic
296	C₄	—	2	1	no	—
297	C₄	—	2	1	no	—
298	C₄	—	2	1	no	—
299	C₄	—	2	1	no	—
300	C₄	—	2	1	no	—
301	C₄	—	4	1	no	—
302	C₄	—	4	1	no	—
303	C₄	—	4	1	no	—
304	C₄	—	152	4	no	—
305	C₄	C₂×#10597294	1	1	yes	characteristic
306	C₄	#11926561	1	1	yes	characteristic
307	C₂	—	2	1	no	—
308	C₂	—	2	1	no	—
309	C₂	—	8	1	no	—
310	C₂	#14563655	1	1	yes	characteristic
311	C₂	#14563681	1	1	yes	characteristic
312	C₂	#14563699	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926404
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2966	C₂
socle	C₂²×C₁₉	#380
prime radical	C₁₉×#121	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2966	D₁₉
hypocenter	C₁₉	#8697
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2966

Complements

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

N	H ≅ G/N	type
1. C₄×#10597275	C₂	semidirect
2. #14562398	C₂	semidirect
4. #14561492	C₂	semidirect
15. C₁₉×#446	C₄	semidirect
16. C₈×Q₈×C₁₉	C₄	semidirect
17. C₁₉×#436	C₄	semidirect
20. C₈×D₄×C₁₉	C₄	semidirect
157. #446	Dic₁₉	semidirect
158. C₈×Q₈	Dic₁₉	semidirect
159. #436	Dic₁₉	semidirect
162. C₈×D₄	Dic₁₉	semidirect
217. C₁₉	#8697	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10597275	2
#14562398	2
#14562160	2
#14561492	2
C₁₉×#2966	2
#8697	19