Subgroups — #14574793

Order 2432.

326 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927100	C₂	1	1	yes	maximal, characteristic
2	#11927098	C₂	1	1	yes	maximal, characteristic
3	#11926948	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926941	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926893	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926893	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926888	C₂	1	1	yes	maximal, characteristic
8	#11926887	C₂	1	1	yes	maximal, characteristic
9	#11926884	C₂	1	1	yes	maximal, characteristic
10	#11926883	C₂	1	1	yes	maximal, characteristic
11	#11926852	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926851	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926848	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926596	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₉×#125	C₂²	1	1	yes	characteristic
17	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	#10597392	C₂²	1	1	yes	characteristic
19	#10597390	C₂²	1	1	yes	characteristic
20	#10597343	C₂²	1	1	yes	characteristic
21	#10597342	—	2	1	no	—
22	#10597342	—	2	1	no	—
23	#10597342	—	2	1	no	—
24	#10597338	C₂²	1	1	yes	characteristic
25	#10597338	C₂²	1	1	yes	characteristic
26	#10597335	—	2	1	no	—
27	#10597334	C₂²	1	1	yes	characteristic
28	#10597334	C₂²	1	1	yes	characteristic
29	#10597334	C₂²	1	1	yes	characteristic
30	#10597333	—	2	1	no	—
31	#10597333	—	2	1	no	—
32	#10597318	—	2	1	no	—
33	C₄²×D₁₉	C₂²	1	1	yes	characteristic
34	#10597316	C₂²	1	1	yes	characteristic
35	C₄×Dic₃₈	—	2	1	no	—
36	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
37	C₁₉×#107	C₂²	1	1	yes	characteristic
38	C₁₉×#106	C₂²	1	1	yes	characteristic
39	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₉×#103	C₂²	1	1	yes	characteristic
41	C₁₉×#103	C₂²	1	1	yes	characteristic
42	#10597292	C₂²	1	1	yes	characteristic
43	#10597292	C₂²	1	1	yes	characteristic
44	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
45	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
46	#10597275	C₂²	1	1	yes	characteristic
47	#10597274	C₂²	1	1	yes	characteristic
48	#10597273	C₂²	1	1	yes	characteristic
49	#10597273	C₂²	1	1	yes	characteristic
50	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
51	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
52	#10597267	C₂²	1	1	yes	characteristic
53	#10597267	C₂²	1	1	yes	characteristic
54	#10597265	C₂²	1	1	yes	characteristic
55	#10597265	C₂²	1	1	yes	characteristic
56	#10597264	C₂²	1	1	yes	characteristic
57	#10597264	C₂²	1	1	yes	characteristic
58	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
61	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
62	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
63	C₂×Dic₃₈	—	2	1	no	—
64	C₂×Dic₃₈	—	2	1	no	—
65	C₂×Dic₃₈	—	2	1	no	—
66	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
67	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₄⋊C₄×C₁₉	—	2	1	no	—
70	C₄⋊C₄×C₁₉	—	2	1	no	—
71	C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₄²×C₁₉	—	2	1	no	—
76	C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	(C₂×D₁₉)⋊C₄	—	2	1	no	—
78	(C₂×D₁₉)⋊C₄	—	2	1	no	—
79	(C₂×D₁₉)⋊C₄	—	2	1	no	—
80	(C₂×D₁₉)⋊C₄	—	2	1	no	—
81	C₄⋊Dic₁₉	—	2	1	no	—
82	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
84	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
85	Dic₁₉⋊C₄	—	2	1	no	—
86	Dic₁₉⋊C₄	—	2	1	no	—
87	Dic₁₉⋊C₄	—	2	1	no	—
88	Dic₁₉⋊C₄	—	2	1	no	—
89	Dic₁₉⋊C₄	—	2	1	no	—
90	Dic₁₉⋊C₄	—	2	1	no	—
91	Dic₁₉⋊C₄	—	2	1	no	—
92	Dic₁₉⋊C₄	—	2	1	no	—
93	Dic₁₉⋊C₄	—	2	1	no	—
94	C₄×Dic₁₉	—	2	1	no	—
95	C₄×Dic₁₉	—	2	1	no	—
96	C₄×Dic₁₉	—	2	1	no	—
97	C₄×Dic₁₉	D₄	1	1	yes	characteristic
98	C₄×Dic₁₉	D₄	1	1	yes	characteristic
99	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
102	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
103	Q₈×C₁₉	—	2	1	no	—
104	Q₈×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	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	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	C₂×Dic₁₉	—	2	1	no	—
113	C₂×Dic₁₉	—	2	1	no	—
114	C₂×Dic₁₉	—	2	1	no	—
115	C₂×Dic₁₉	—	2	1	no	—
116	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
117	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄×D₁₉	—	2	1	no	—
120	C₄×D₁₉	—	2	1	no	—
121	C₄×D₁₉	—	2	2	no	—
122	C₄×D₁₉	—	2	2	no	—
123	Dic₃₈	—	2	1	no	—
124	Dic₃₈	—	2	1	no	—
125	Dic₃₈	—	4	2	no	—
126	Dic₃₈	—	4	2	no	—
127	Dic₃₈	—	4	2	no	—
128	C₈×C₁₉	—	2	1	no	—
129	C₈×C₁₉	—	2	1	no	—
130	C₁₉⋊C₈	—	2	1	no	—
131	C₁₉⋊C₈	—	2	1	no	—
132	#3231	—	19	1	no	maximal, Sylow
133	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
134	C₂×D₁₉	—	2	1	no	—
135	C₂×D₁₉	—	2	1	no	—
136	C₂×D₁₉	—	2	1	no	—
137	C₄×C₁₉	—	2	1	no	—
138	C₄×C₁₉	—	2	1	no	—
139	C₄×C₁₉	—	4	1	no	—
140	C₄×C₁₉	—	4	1	no	—
141	C₄×C₁₉	—	4	1	no	—
142	C₄×C₁₉	—	4	1	no	—
143	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
144	C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
145	Dic₁₉	—	2	1	no	—
146	Dic₁₉	—	4	1	no	—
147	Dic₁₉	—	4	1	no	—
148	Dic₁₉	—	4	1	no	—
149	Dic₁₉	—	4	1	no	—
150	Dic₁₉	#135	1	2	yes	—
151	Dic₁₉	#137	1	2	yes	—
152	#533	—	19	1	no	—
153	#533	—	19	1	no	—
154	#500	—	19	1	no	—
155	#498	—	19	1	no	—
156	#487	—	19	1	no	—
157	#487	—	19	1	no	—
158	#485	—	19	1	no	—
159	#485	—	19	1	no	—
160	#485	—	19	1	no	—
161	#485	—	19	1	no	—
162	#479	—	19	1	no	—
163	#479	—	19	1	no	—
164	#479	—	19	1	no	—
165	#479	D₁₉	1	1	yes	characteristic, complemented
166	#431	—	19	1	no	—
167	C₂×C₁₉	#536	1	1	yes	characteristic
168	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
169	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
170	D₁₉	—	4	1	no	—
171	C₄⋊Q₈	—	19	1	no	—
172	C₄⋊Q₈	—	19	1	no	—
173	C₄⋊Q₈	—	19	1	no	—
174	C₄⋊Q₈	—	19	1	no	—
175	#125	—	19	1	no	—
176	#125	—	38	1	no	—
177	#125	C₂×D₁₉	1	1	yes	characteristic
178	C₂²⋊Q₈	—	19	1	no	—
179	C₂²⋊Q₈	—	19	1	no	—
180	C₂²⋊Q₈	—	38	1	no	—
181	C₂²⋊Q₈	—	38	1	no	—
182	C₂²⋊Q₈	—	38	1	no	—
183	C₄×Q₈	—	19	1	no	—
184	C₄×Q₈	—	38	1	no	—
185	C₄×Q₈	—	38	1	no	—
186	C₄×Q₈	—	38	1	no	—
187	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
188	#117	—	19	1	no	—
189	#117	—	19	1	no	—
190	#117	—	38	1	no	—
191	C₂×C₄²	—	19	1	no	—
192	#107	—	19	1	no	—
193	#107	—	19	1	no	—
194	#107	—	19	1	no	—
195	#107	C₂×D₁₉	1	1	yes	characteristic
196	#106	—	19	1	no	—
197	#106	—	19	1	no	—
198	#106	—	19	1	no	—
199	#106	C₂×D₁₉	1	1	yes	characteristic
200	C₄⋊C₈	—	19	1	no	—
201	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
202	#103	—	19	1	no	—
203	#103	—	19	1	no	—
204	#103	—	19	1	no	—
205	#103	—	19	1	no	—
206	#103	—	19	1	no	—
207	#103	—	19	1	no	—
208	#103	C₂×D₁₉	1	1	yes	characteristic
209	#103	C₂×D₁₉	1	1	yes	characteristic
210	C₂²⋊C₈	—	19	1	no	—
211	C₂²⋊C₈	—	19	1	no	—
212	C₄×C₈	—	19	1	no	—
213	C₄×C₈	—	19	1	no	—
214	C₁₉	#3231	1	1	yes	characteristic, complemented, Sylow
215	C₂×Q₈	—	19	1	no	—
216	C₂×Q₈	—	38	1	no	—
217	C₂×Q₈	—	38	1	no	—
218	C₂×Q₈	—	38	1	no	—
219	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
220	C₂²×C₄	—	19	1	no	—
221	C₂²×C₄	—	19	1	no	—
222	C₂²×C₄	—	19	1	no	—
223	C₂×C₈	—	19	1	no	—
224	C₂×C₈	—	19	1	no	—
225	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
226	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
227	C₄⋊C₄	—	2	1	no	—
228	C₄⋊C₄	—	2	1	no	—
229	C₄⋊C₄	—	2	1	no	—
230	C₄⋊C₄	—	19	1	no	—
231	C₄⋊C₄	—	19	1	no	—
232	C₄⋊C₄	—	19	1	no	—
233	C₄⋊C₄	—	38	1	no	—
234	C₄⋊C₄	—	38	1	no	—
235	C₄⋊C₄	—	38	1	no	—
236	C₄⋊C₄	—	38	1	no	—
237	C₄⋊C₄	—	38	1	no	—
238	C₄⋊C₄	—	38	1	no	—
239	C₄⋊C₄	—	38	1	no	—
240	C₄⋊C₄	—	38	1	no	—
241	C₄⋊C₄	—	38	1	no	—
242	C₄⋊C₄	—	38	1	no	—
243	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
244	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
245	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
246	C₂²⋊C₄	—	38	1	no	—
247	C₂²⋊C₄	—	38	1	no	—
248	C₂²⋊C₄	—	38	1	no	—
249	C₂²⋊C₄	—	38	1	no	—
250	C₄²	—	2	1	no	—
251	C₄²	—	19	1	no	—
252	C₄²	—	19	1	no	—
253	C₄²	—	19	1	no	—
254	C₄²	—	38	1	no	—
255	C₄²	—	38	1	no	—
256	C₄²	—	38	1	no	—
257	C₄²	C₂²×D₁₉	1	1	yes	characteristic
258	C₂³	—	19	1	no	—
259	Q₈	—	2	1	no	—
260	Q₈	—	2	1	no	—
261	Q₈	—	38	1	no	—
262	Q₈	—	38	1	no	—
263	Q₈	—	76	2	no	—
264	Q₈	—	76	2	no	—
265	Q₈	—	76	2	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	19	1	no	—
271	C₂×C₄	—	19	1	no	—
272	C₂×C₄	—	19	1	no	—
273	C₂×C₄	—	38	2	no	—
274	C₂×C₄	—	38	2	no	—
275	C₂×C₄	—	38	1	no	—
276	C₂×C₄	—	38	1	no	—
277	C₂×C₄	—	38	1	no	—
278	C₂×C₄	—	38	1	no	—
279	C₂×C₄	—	38	1	no	—
280	C₂×C₄	—	38	1	no	—
281	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
282	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
283	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
284	C₈	—	2	1	no	—
285	C₈	—	2	1	no	—
286	C₈	—	38	1	no	—
287	C₈	—	38	1	no	—
288	C₂²	—	38	1	no	—
289	C₂²	—	38	1	no	—
290	C₂²	—	38	1	no	—
291	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
292	C₄	—	2	1	no	—
293	C₄	—	2	1	no	—
294	C₄	—	4	1	no	—
295	C₄	—	4	1	no	—
296	C₄	—	4	1	no	—
297	C₄	—	4	1	no	—
298	C₄	—	19	2	no	—
299	C₄	—	19	2	no	—
300	C₄	—	38	1	no	—
301	C₄	—	76	1	no	—
302	C₄	—	76	1	no	—
303	C₄	—	76	1	no	—
304	C₄	—	76	1	no	—
305	C₄	#10597433	1	1	yes	characteristic
306	C₄	#10597436	1	1	yes	characteristic
307	C₂	—	76	1	no	—
308	C₂	#11927117	1	1	yes	characteristic
309	C₂	#135×D₁₉	1	1	yes	characteristic
310	C₂	#137×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#479	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₁₉	C₂×D₄
hypercenter	#479	D₁₉
hypocenter	C₁₉	#3231
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #479

Complements

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

N	H ≅ G/N	type
3. #11926948	C₂	semidirect
4. #11926941	C₂	semidirect
5. #11926893	C₂	semidirect
6. #11926893	C₂	semidirect
11. #11926852	C₂	semidirect
12. #11926851	C₂	semidirect
13. #11926848	C₂	semidirect
15. C₁₉×#479	C₂	semidirect
165. #479	D₁₉	semidirect
214. C₁₉	#3231	semidirect

Maximal subgroups

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

subgroup	index
#11927100	2
#11927098	2
#11926948	2
#11926941	2
#11926893	2
#11926888	2
#11926887	2
#11926884	2
#11926883	2
#11926852	2
#11926851	2
#11926848	2
#11926596	2
C₁₉×#479	2
#3231	19