Subgroups — #14573763

Order 2432.

380 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927098	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926876	C₂	1	1	yes	maximal, characteristic
4	#11926873	C₂	1	1	yes	maximal, characteristic
5	#11926828	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926827	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926753	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926752	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926701	C₂	1	1	yes	maximal, characteristic
10	#11926698	C₂	1	1	yes	maximal, characteristic
11	#11926652	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926649	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926649	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926599	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
17	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	#10597392	C₂²	1	1	yes	characteristic
21	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
22	#10597390	C₂²	1	1	yes	characteristic
23	C₂×#64528	C₂²	1	1	yes	characteristic
24	C₂×#64528	C₂²	1	1	yes	characteristic
25	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
26	#10597343	C₂²	1	1	yes	characteristic
27	#10597342	—	2	1	no	—
28	C₄⋊C₄×D₁₉	—	2	1	no	—
29	C₄⋊C₄×D₁₉	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	C₄²×D₁₉	—	2	1	no	—
36	C₄²×D₁₉	C₂²	1	1	yes	characteristic
37	C₄×Dic₃₈	—	2	1	no	—
38	C₄×Dic₃₈	—	2	1	no	—
39	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
40	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
41	C₁₉×#106	C₂²	1	1	yes	characteristic
42	C₁₉×#103	C₂²	1	1	yes	characteristic
43	C₁₉×#103	C₂²	1	1	yes	characteristic
44	C₁₉×#97	C₂²	1	1	yes	characteristic
45	#10597292	C₂²	1	1	yes	characteristic
46	#10597292	C₂²	1	1	yes	characteristic
47	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
49	#10597274	C₂²	1	1	yes	characteristic
50	#10597273	C₂²	1	1	yes	characteristic
51	#10597273	C₂²	1	1	yes	characteristic
52	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
53	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
54	#10597267	C₂²	1	1	yes	characteristic
55	#10597267	C₂²	1	1	yes	characteristic
56	#10597265	C₂²	1	1	yes	characteristic
57	#10597265	C₂²	1	1	yes	characteristic
58	#10597260	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	Q₈×D₁₉	—	2	2	no	—
62	Q₈×D₁₉	—	2	2	no	—
63	C₂×C₄×D₁₉	—	2	1	no	—
64	C₂×C₄×D₁₉	—	2	1	no	—
65	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
67	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
68	C₂×Dic₃₈	—	2	1	no	—
69	C₂×Dic₃₈	—	2	1	no	—
70	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
71	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
72	Q₁₆×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₄²×C₁₉	—	2	1	no	—
80	C₄²×C₁₉	—	2	1	no	—
81	C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	#64528	—	2	2	no	—
83	#64528	—	2	2	no	—
84	(C₂×D₁₉)⋊C₄	—	2	1	no	—
85	(C₂×D₁₉)⋊C₄	—	2	1	no	—
86	C₄⋊Dic₁₉	—	2	1	no	—
87	C₄⋊Dic₁₉	—	2	1	no	—
88	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
95	Dic₁₉⋊C₄	—	2	1	no	—
96	Dic₁₉⋊C₄	—	2	1	no	—
97	Dic₁₉⋊C₄	—	2	1	no	—
98	C₄×Dic₁₉	—	2	1	no	—
99	C₄×Dic₁₉	—	2	1	no	—
100	C₄×Dic₁₉	—	2	1	no	—
101	C₄×Dic₁₉	—	2	1	no	—
102	C₄×Dic₁₉	D₄	1	1	yes	characteristic
103	C₄×Dic₁₉	D₄	1	1	yes	characteristic
104	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
107	Dic₇₆	—	2	2	no	—
108	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
109	Q₈×C₁₉	—	2	1	no	—
110	Q₈×C₁₉	—	2	1	no	—
111	Q₈×C₁₉	—	2	1	no	—
112	Q₈×C₁₉	#41	1	2	yes	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
120	C₂×Dic₁₉	—	2	1	no	—
121	C₂×Dic₁₉	—	2	1	no	—
122	C₂×Dic₁₉	—	2	1	no	—
123	C₂×Dic₁₉	—	2	1	no	—
124	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
127	C₄×D₁₉	—	2	4	no	—
128	C₄×D₁₉	—	2	2	no	—
129	C₄×D₁₉	—	2	1	no	—
130	C₄×D₁₉	—	2	1	no	—
131	C₄×D₁₉	—	2	2	no	—
132	C₄×D₁₉	—	4	2	no	—
133	Dic₃₈	—	2	4	no	—
134	Dic₃₈	—	2	1	no	—
135	Dic₃₈	—	2	1	no	—
136	Dic₃₈	—	2	1	no	—
137	Dic₃₈	—	4	2	no	—
138	Dic₃₈	#41	1	2	yes	—
139	C₈×C₁₉	—	2	1	no	—
140	C₈×C₁₉	—	2	1	no	—
141	C₁₉⋊C₈	—	2	1	no	—
142	C₁₉⋊C₈	—	2	1	no	—
143	#3113	—	19	1	no	maximal, Sylow
144	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
145	C₂×D₁₉	—	2	1	no	—
146	C₂×D₁₉	—	2	1	no	—
147	C₂×D₁₉	#137	1	2	yes	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	1	no	—
150	C₄×C₁₉	—	2	1	no	—
151	C₄×C₁₉	—	4	1	no	—
152	C₄×C₁₉	—	4	1	no	—
153	C₄×C₁₉	—	4	1	no	—
154	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
155	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
156	Dic₁₉	—	2	1	no	—
157	Dic₁₉	—	2	2	no	—
158	Dic₁₉	—	2	1	no	—
159	Dic₁₉	—	4	1	no	—
160	Dic₁₉	—	4	1	no	—
161	Dic₁₉	—	4	1	no	—
162	Dic₁₉	#137	1	2	yes	—
163	#533	—	19	1	no	—
164	C₂×C₄×Q₈	—	19	1	no	—
165	#483	—	19	1	no	—
166	#483	—	19	1	no	—
167	#475	—	19	1	no	—
168	#475	—	19	1	no	—
169	#462	—	19	1	no	—
170	#462	—	19	1	no	—
171	#451	—	19	1	no	—
172	#451	—	19	1	no	—
173	#441	—	19	1	no	—
174	#441	—	19	1	no	—
175	#441	—	19	1	no	—
176	#441	D₁₉	1	1	yes	characteristic, complemented
177	#432	—	19	1	no	—
178	C₂×C₁₉	#525	1	1	yes	characteristic
179	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
180	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
181	D₁₉	—	2	2	no	—
182	C₂²×Q₈	—	19	1	no	—
183	C₂×Q₁₆	—	19	1	no	—
184	C₂×Q₁₆	—	19	1	no	—
185	C₂×Q₁₆	—	19	1	no	—
186	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
187	C₄⋊Q₈	—	19	1	no	—
188	C₄⋊Q₈	—	19	1	no	—
189	#125	—	38	1	no	—
190	C₂²⋊Q₈	—	19	1	no	—
191	C₂²⋊Q₈	—	19	1	no	—
192	C₂²⋊Q₈	—	38	1	no	—
193	C₄×Q₈	—	19	1	no	—
194	C₄×Q₈	—	19	1	no	—
195	C₄×Q₈	—	19	1	no	—
196	C₄×Q₈	—	19	1	no	—
197	C₄×Q₈	—	38	1	no	—
198	C₄×Q₈	—	38	1	no	—
199	C₄×Q₈	—	38	1	no	—
200	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
201	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
202	#117	—	38	1	no	—
203	C₂×C₄⋊C₄	—	19	1	no	—
204	C₂×C₄⋊C₄	—	38	1	no	—
205	C₂×C₄²	—	19	1	no	—
206	C₂×C₄²	—	38	1	no	—
207	#106	—	19	1	no	—
208	#106	—	19	1	no	—
209	#106	—	19	1	no	—
210	#106	C₂×D₁₉	1	1	yes	characteristic
211	C₄⋊C₈	—	19	1	no	—
212	C₄⋊C₈	—	19	1	no	—
213	#103	—	19	1	no	—
214	#103	—	19	1	no	—
215	#103	—	19	1	no	—
216	#103	—	19	1	no	—
217	#103	—	19	1	no	—
218	#103	—	19	1	no	—
219	#103	C₂×D₁₉	1	1	yes	characteristic
220	#103	C₂×D₁₉	1	1	yes	characteristic
221	C₂²⋊C₈	—	19	1	no	—
222	C₂²⋊C₈	—	19	1	no	—
223	#97	—	19	1	no	—
224	#97	C₂×D₁₉	1	1	yes	characteristic
225	C₁₉	#3113	1	1	yes	characteristic, complemented, Sylow
226	C₂×Q₈	—	19	1	no	—
227	C₂×Q₈	—	19	1	no	—
228	C₂×Q₈	—	38	1	no	—
229	C₂×Q₈	—	38	1	no	—
230	C₂×Q₈	—	38	2	no	—
231	C₂×Q₈	—	38	2	no	—
232	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
233	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
234	C₂²×C₄	—	19	1	no	—
235	C₂²×C₄	—	19	1	no	—
236	C₂²×C₄	—	19	1	no	—
237	C₂²×C₄	—	38	1	no	—
238	C₂²×C₄	—	38	1	no	—
239	Q₁₆	—	2	2	no	—
240	Q₁₆	—	38	2	no	—
241	Q₁₆	—	38	2	no	—
242	Q₁₆	—	38	2	no	—
243	C₂×C₈	—	19	1	no	—
244	C₂×C₈	—	19	1	no	—
245	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
246	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
247	C₄⋊C₄	—	2	1	no	—
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	19	1	no	—
250	C₄⋊C₄	—	19	1	no	—
251	C₄⋊C₄	—	38	1	no	—
252	C₄⋊C₄	—	38	1	no	—
253	C₄⋊C₄	—	38	1	no	—
254	C₄⋊C₄	—	38	1	no	—
255	C₄⋊C₄	—	38	1	no	—
256	C₄⋊C₄	—	38	1	no	—
257	C₄⋊C₄	—	38	1	no	—
258	C₄⋊C₄	—	38	1	no	—
259	C₄⋊C₄	—	38	1	no	—
260	C₄⋊C₄	—	38	1	no	—
261	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
262	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
263	C₂²⋊C₄	—	38	1	no	—
264	C₂²⋊C₄	—	38	1	no	—
265	C₄²	—	2	1	no	—
266	C₄²	—	2	1	no	—
267	C₄²	—	19	1	no	—
268	C₄²	—	19	1	no	—
269	C₄²	—	19	1	no	—
270	C₄²	—	38	1	no	—
271	C₄²	—	38	1	no	—
272	C₄²	—	38	1	no	—
273	C₄²	—	38	1	no	—
274	C₄²	C₂²×D₁₉	1	1	yes	characteristic
275	C₂³	—	19	1	no	—
276	Q₈	—	2	1	no	—
277	Q₈	—	2	1	no	—
278	Q₈	—	2	1	no	—
279	Q₈	—	19	2	no	—
280	Q₈	—	38	4	no	—
281	Q₈	—	38	1	no	—
282	Q₈	—	38	1	no	—
283	Q₈	—	38	1	no	—
284	Q₈	—	76	2	no	—
285	Q₈	#64541	1	2	yes	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	19	1	no	—
291	C₂×C₄	—	19	1	no	—
292	C₂×C₄	—	19	1	no	—
293	C₂×C₄	—	38	2	no	—
294	C₂×C₄	—	38	2	no	—
295	C₂×C₄	—	38	4	no	—
296	C₂×C₄	—	38	1	no	—
297	C₂×C₄	—	38	1	no	—
298	C₂×C₄	—	38	1	no	—
299	C₂×C₄	—	38	1	no	—
300	C₂×C₄	—	38	1	no	—
301	C₂×C₄	—	38	1	no	—
302	C₂×C₄	—	76	2	no	—
303	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
304	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
305	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
306	C₈	—	2	1	no	—
307	C₈	—	2	1	no	—
308	C₈	—	38	1	no	—
309	C₈	—	38	1	no	—
310	C₂²	—	19	2	no	—
311	C₂²	—	38	1	no	—
312	C₂²	—	38	1	no	—
313	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
314	C₄	—	2	2	no	—
315	C₄	—	2	1	no	—
316	C₄	—	2	1	no	—
317	C₄	—	4	1	no	—
318	C₄	—	4	1	no	—
319	C₄	—	4	1	no	—
320	C₄	—	19	2	no	—
321	C₄	—	38	1	no	—
322	C₄	—	38	2	no	—
323	C₄	—	38	1	no	—
324	C₄	—	76	1	no	—
325	C₄	—	76	1	no	—
326	C₄	—	76	1	no	—
327	C₄	C₂×#64541	1	1	yes	characteristic
328	C₄	#41×D₁₉	1	1	yes	characteristic
329	C₂	—	38	2	no	—
330	C₂	#11927053	1	1	yes	characteristic
331	C₂	#137×D₁₉	1	1	yes	characteristic
332	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×#441	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂²×D₁₉	C₂×D₄
hypercenter	#441	D₁₉
hypocenter	C₁₉	#3113
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #441

Complements

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

N	H ≅ G/N	type
5. #11926828	C₂	semidirect
6. #11926827	C₂	semidirect
7. #11926753	C₂	semidirect
8. #11926752	C₂	semidirect
11. #11926652	C₂	semidirect
12. #11926649	C₂	semidirect
13. #11926649	C₂	semidirect
15. C₁₉×#441	C₂	semidirect
176. #441	D₁₉	semidirect
225. C₁₉	#3113	semidirect

Maximal subgroups

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

subgroup	index
#11927098	2
C₄×Q₈×D₁₉	2
#11926876	2
#11926873	2
#11926828	2
#11926827	2
#11926753	2
#11926752	2
#11926701	2
#11926698	2
#11926652	2
#11926649	2
#11926599	2
C₁₉×#441	2
#3113	19