Subgroups — #14573470

Order 2432.

362 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927171	C₂	1	1	yes	maximal, characteristic
2	#11927020	C₂	1	1	yes	maximal, characteristic
3	#11926854	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926852	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926851	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926849	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926837	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926836	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926828	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926583	C₂	1	1	yes	maximal, characteristic
11	#11926579	C₂	1	1	yes	maximal, characteristic
12	#11926569	C₂	1	1	yes	maximal, characteristic
13	#11926551	C₂	1	1	yes	maximal, characteristic
14	#103×D₁₉	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	#10597392	—	2	1	no	—
20	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
21	#10597390	—	2	1	no	—
22	C₂×#64515	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
24	#10597342	—	2	1	no	—
25	#10597338	—	2	1	no	—
26	#10597338	C₂²	1	1	yes	characteristic
27	#10597338	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
29	#10597336	C₂²	1	1	yes	characteristic
30	#10597335	—	2	1	no	—
31	#10597334	C₂²	1	1	yes	characteristic
32	#10597333	—	2	1	no	—
33	#10597333	C₂²	1	1	yes	characteristic
34	#10597318	—	2	1	no	—
35	#10597318	C₂²	1	1	yes	characteristic
36	#10597316	C₂²	1	1	yes	characteristic
37	C₄×Dic₃₈	—	2	1	no	—
38	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
39	C₁₉×#106	C₂²	1	1	yes	characteristic
40	C₁₉×#106	C₂²	1	1	yes	characteristic
41	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₉×#103	C₂²	1	1	yes	characteristic
43	C₁₉×#103	C₂²	1	1	yes	characteristic
44	#10597292	C₂²	1	1	yes	characteristic
45	#10597292	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	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
51	Dic₁₉⋊C₈	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	#10597264	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	—	2	1	no	—
60	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	Q₈×D₁₉	—	2	2	no	—
62	Q₈×D₁₉	Q₈	1	4	yes	complemented
63	C₂×C₄×D₁₉	—	2	1	no	—
64	C₂×C₄×D₁₉	—	2	1	no	—
65	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
66	C₂×Dic₃₈	—	2	1	no	—
67	C₂×Dic₃₈	—	2	1	no	—
68	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
71	C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₄²×C₁₉	—	2	1	no	—
77	C₄²×C₁₉	C₂³	1	1	yes	characteristic
78	(C₂×D₁₉)⋊C₄	—	2	1	no	—
79	(C₂×D₁₉)⋊C₄	—	2	1	no	—
80	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
81	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
82	C₄⋊Dic₁₉	—	2	1	no	—
83	C₄⋊Dic₁₉	—	2	1	no	—
84	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
85	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
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	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
95	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
96	C₄×Dic₁₉	—	2	1	no	—
97	C₄×Dic₁₉	—	2	1	no	—
98	C₄×Dic₁₉	—	2	1	no	—
99	C₄×Dic₁₉	—	2	1	no	—
100	C₄×Dic₁₉	—	2	1	no	—
101	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
103	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
104	#64515	—	2	2	no	—
105	C₈×D₁₉	—	2	2	no	—
106	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
107	Q₈×C₁₉	—	2	1	no	—
108	Q₈×C₁₉	—	8	1	no	—
109	Q₈×C₁₉	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
114	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
117	C₂×Dic₁₉	—	2	1	no	—
118	C₂×Dic₁₉	—	2	1	no	—
119	C₂×Dic₁₉	—	2	1	no	—
120	C₂×Dic₁₉	—	2	1	no	—
121	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
124	C₄×D₁₉	—	2	4	no	—
125	C₄×D₁₉	—	8	1	no	—
126	C₄×D₁₉	C₂×Q₈	1	2	yes	—
127	C₄×D₁₉	#41	1	2	yes	—
128	Dic₃₈	—	2	1	no	—
129	Dic₃₈	—	2	4	no	—
130	Dic₃₈	—	8	1	no	—
131	Dic₃₈	C₂×Q₈	1	2	yes	—
132	C₈×C₁₉	—	2	1	no	—
133	C₈×C₁₉	—	2	1	no	—
134	C₁₉⋊C₈	—	2	1	no	—
135	C₁₉⋊C₈	—	2	1	no	—
136	#3082	—	19	1	no	maximal, Sylow
137	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
138	C₂×D₁₉	—	2	1	no	—
139	C₂×D₁₉	—	2	1	no	—
140	C₂×D₁₉	C₂²⋊Q₈	1	2	yes	—
141	C₄×C₁₉	—	2	2	no	—
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	4	1	no	—
145	C₄×C₁₉	—	4	1	no	—
146	C₄×C₁₉	—	4	1	no	—
147	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
148	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
149	Dic₁₉	—	2	2	no	—
150	Dic₁₉	—	2	1	no	—
151	Dic₁₉	—	2	1	no	—
152	Dic₁₉	—	4	1	no	—
153	Dic₁₉	—	4	1	no	—
154	Dic₁₉	—	4	1	no	—
155	Dic₁₉	C₂²⋊Q₈	1	2	yes	—
156	#544	—	19	1	no	—
157	#519	—	19	1	no	—
158	#479	—	19	1	no	—
159	#479	—	19	1	no	—
160	#479	—	19	1	no	—
161	#479	—	19	1	no	—
162	#477	—	19	1	no	—
163	#477	—	19	1	no	—
164	#475	—	19	1	no	—
165	#475	D₁₉	1	1	yes	characteristic, complemented
166	#428	—	19	1	no	—
167	#427	—	19	1	no	—
168	#424	—	19	1	no	—
169	#419	—	19	1	no	—
170	C₂×#103	—	19	1	no	—
171	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
172	C₂×C₁₉	#577	1	1	yes	characteristic
173	C₂×C₁₉	#578	1	1	yes	characteristic
174	D₁₉	—	2	2	no	—
175	C₂²×Q₈	—	19	1	no	—
176	C₂×M₁₆	—	19	1	no	—
177	C₂²×C₈	—	19	1	no	—
178	C₄⋊Q₈	—	19	1	no	—
179	C₄⋊Q₈	—	38	1	no	—
180	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
181	#125	—	19	1	no	—
182	#125	—	19	1	no	—
183	#125	—	38	1	no	—
184	C₂²⋊Q₈	—	38	1	no	—
185	C₂²⋊Q₈	—	38	1	no	—
186	C₄×Q₈	—	19	1	no	—
187	C₄×Q₈	—	19	1	no	—
188	C₄×Q₈	—	19	1	no	—
189	C₄×Q₈	—	38	1	no	—
190	C₄×Q₈	—	38	1	no	—
191	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
192	#117	—	19	1	no	—
193	#117	—	19	1	no	—
194	#117	—	19	1	no	—
195	#117	—	38	1	no	—
196	#117	—	38	1	no	—
197	C₂×C₄⋊C₄	—	19	1	no	—
198	#107	—	19	1	no	—
199	#107	—	19	1	no	—
200	#107	—	19	1	no	—
201	#107	—	19	1	no	—
202	#106	—	19	1	no	—
203	#106	—	19	1	no	—
204	#106	C₂×D₁₉	1	1	yes	characteristic
205	#106	C₂×D₁₉	1	1	yes	characteristic
206	C₄⋊C₈	—	19	1	no	—
207	C₄⋊C₈	—	19	1	no	—
208	C₄⋊C₈	—	19	1	no	—
209	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
210	#103	—	19	1	no	—
211	#103	—	19	1	no	—
212	#103	—	19	1	no	—
213	#103	—	19	1	no	—
214	#103	—	19	1	no	—
215	#103	—	19	1	no	—
216	#103	C₂×D₁₉	1	1	yes	characteristic
217	#103	C₂×D₁₉	1	1	yes	characteristic
218	C₁₉	#3082	1	1	yes	characteristic, complemented, Sylow
219	C₂×Q₈	—	2	1	no	—
220	C₂×Q₈	—	19	4	no	—
221	C₂×Q₈	—	19	1	no	—
222	C₂×Q₈	—	38	1	no	—
223	C₂×Q₈	—	38	1	no	—
224	C₂×Q₈	—	38	2	no	—
225	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
226	C₂²×C₄	—	19	1	no	—
227	C₂²×C₄	—	38	1	no	—
228	C₂²×C₄	—	38	1	no	—
229	M₁₆	—	38	2	no	—
230	C₂×C₈	—	19	1	no	—
231	C₂×C₈	—	19	1	no	—
232	C₂×C₈	—	38	2	no	—
233	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
234	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
235	C₄⋊C₄	—	2	1	no	—
236	C₄⋊C₄	—	2	1	no	—
237	C₄⋊C₄	—	19	1	no	—
238	C₄⋊C₄	—	19	1	no	—
239	C₄⋊C₄	—	19	1	no	—
240	C₄⋊C₄	—	19	1	no	—
241	C₄⋊C₄	—	19	1	no	—
242	C₄⋊C₄	—	38	1	no	—
243	C₄⋊C₄	—	38	1	no	—
244	C₄⋊C₄	—	38	1	no	—
245	C₄⋊C₄	—	38	1	no	—
246	C₄⋊C₄	—	38	1	no	—
247	C₄⋊C₄	—	38	1	no	—
248	C₄⋊C₄	—	38	1	no	—
249	C₄⋊C₄	—	38	1	no	—
250	C₄⋊C₄	—	38	1	no	—
251	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
252	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
253	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
254	C₂²⋊C₄	—	19	1	no	—
255	C₂²⋊C₄	—	19	1	no	—
256	C₂²⋊C₄	—	38	1	no	—
257	C₂²⋊C₄	—	38	1	no	—
258	C₄²	—	2	1	no	—
259	C₄²	—	19	1	no	—
260	C₄²	—	38	1	no	—
261	C₄²	—	38	1	no	—
262	C₄²	—	38	1	no	—
263	C₄²	—	38	1	no	—
264	C₄²	—	38	1	no	—
265	C₄²	C₂²×D₁₉	1	1	yes	characteristic
266	C₂³	—	19	1	no	—
267	Q₈	—	2	1	no	—
268	Q₈	—	8	1	no	—
269	Q₈	—	19	2	no	—
270	Q₈	—	38	4	no	—
271	Q₈	—	38	1	no	—
272	Q₈	—	152	1	no	—
273	Q₈	Q₈×D₁₉	1	2	yes	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	19	1	no	—
279	C₂×C₄	—	19	2	no	—
280	C₂×C₄	—	19	2	no	—
281	C₂×C₄	—	19	1	no	—
282	C₂×C₄	—	19	1	no	—
283	C₂×C₄	—	38	4	no	—
284	C₂×C₄	—	38	1	no	—
285	C₂×C₄	—	38	1	no	—
286	C₂×C₄	—	38	1	no	—
287	C₂×C₄	—	38	1	no	—
288	C₂×C₄	—	152	1	no	—
289	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
290	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
291	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
292	C₈	—	2	1	no	—
293	C₈	—	2	1	no	—
294	C₈	—	38	1	no	—
295	C₈	—	38	1	no	—
296	C₂²	—	19	2	no	—
297	C₂²	—	38	1	no	—
298	C₂²	—	38	1	no	—
299	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	2	no	—
303	C₄	—	4	1	no	—
304	C₄	—	4	1	no	—
305	C₄	—	4	1	no	—
306	C₄	—	19	2	no	—
307	C₄	—	38	1	no	—
308	C₄	—	38	1	no	—
309	C₄	—	38	2	no	—
310	C₄	—	76	1	no	—
311	C₄	—	76	1	no	—
312	C₄	—	76	1	no	—
313	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
314	C₄	#41×D₁₉	1	1	yes	characteristic
315	C₂	—	38	2	no	—
316	C₂	C₂²⋊Q₈×D₁₉	1	1	yes	characteristic
317	C₂	#11927350	1	1	yes	characteristic
318	C₂	#11927360	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×#475	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₁₉	C₂×D₄
hypercenter	#475	D₁₉
hypocenter	C₁₉	#3082
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

Complements

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

N	H ≅ G/N	type
3. #11926854	C₂	semidirect
4. #11926852	C₂	semidirect
5. #11926851	C₂	semidirect
6. #11926849	C₂	semidirect
7. #11926837	C₂	semidirect
8. #11926836	C₂	semidirect
9. #11926828	C₂	semidirect
15. C₁₉×#475	C₂	semidirect
62. Q₈×D₁₉	Q₈	semidirect
165. #475	D₁₉	semidirect
218. C₁₉	#3082	semidirect

Maximal subgroups

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

subgroup	index
#11927171	2
#11927020	2
#11926854	2
#11926852	2
#11926851	2
#11926849	2
#11926837	2
#11926836	2
#11926828	2
#11926583	2
#11926579	2
#11926569	2
#11926551	2
#103×D₁₉	2
C₁₉×#475	2
#3082	19