Subgroups — #14574259

Order 2432.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927145	C₂	1	1	yes	maximal, characteristic
3	#11926944	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926915	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926911	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926907	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926793	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926789	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926774	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926770	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926644	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926642	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#64516	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926498	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	#10597392	C₂²	1	1	yes	characteristic
20	#10597390	C₂²	1	1	yes	characteristic
21	C₂×#64527	C₂²	1	1	yes	characteristic
22	#10597386	C₂²	1	1	yes	characteristic
23	#10597384	C₂²	1	1	yes	characteristic
24	C₂×#64526	C₂²	1	1	yes	characteristic
25	#10597376	—	2	1	no	—
26	#10597375	—	2	1	no	—
27	C₂×#64516	C₂²	1	1	yes	characteristic
28	C₂×#64515	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
30	#10597344	—	2	1	no	—
31	#10597343	C₂²	1	1	yes	characteristic
32	#10597341	C₂²	1	1	yes	characteristic
33	#10597336	C₂²	1	1	yes	characteristic
34	#10597336	C₂²	1	1	yes	characteristic
35	#10597335	—	2	1	no	—
36	#10597330	—	2	1	no	—
37	#10597329	—	2	1	no	—
38	#10597322	—	2	1	no	—
39	C₄×D₇₆	C₂²	1	1	yes	characteristic
40	#10597318	C₂²	1	1	yes	characteristic
41	#10597316	—	2	1	no	—
42	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
43	C₁₉×#106	C₂²	1	1	yes	characteristic
44	C₁₉×#103	C₂²	1	1	yes	characteristic
45	C₁₉×#102	C₂²	1	1	yes	characteristic
46	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
47	#10597292	C₂²	1	1	yes	characteristic
48	#10597289	C₂²	1	1	yes	characteristic
49	#10597278	C₂²	1	1	yes	characteristic
50	#10597274	C₂²	1	1	yes	characteristic
51	#10597273	C₂²	1	1	yes	characteristic
52	#10597272	C₂²	1	1	yes	characteristic
53	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
54	#10597267	C₂²	1	1	yes	characteristic
55	#10597266	C₂²	1	1	yes	characteristic
56	#10597264	C₂²	1	1	yes	characteristic
57	#10597264	C₂²	1	1	yes	characteristic
58	#10597260	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊D₁₉	—	2	1	no	—
63	C₂×C₂²⋊D₁₉	—	2	1	no	—
64	C₂×C₂²⋊D₁₉	—	2	1	no	—
65	C₂×D₇₆	—	2	1	no	—
66	C₂×D₇₆	C₂³	1	1	yes	characteristic
67	C₂×C₄×D₁₉	—	2	1	no	—
68	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
69	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
70	SD₁₆×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₄²×C₁₉	—	2	1	no	—
78	C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²⋊Dic₁₉	—	2	1	no	—
80	#64527	—	2	2	no	—
81	#64526	—	2	2	no	—
82	(C₂×D₁₉)⋊C₄	—	2	1	no	—
83	(C₂×D₁₉)⋊C₄	—	2	1	no	—
84	(C₂×D₁₉)⋊C₄	—	2	1	no	—
85	(C₂×D₁₉)⋊C₄	—	2	1	no	—
86	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
87	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
88	C₄⋊Dic₁₉	—	2	1	no	—
89	C₄⋊Dic₁₉	—	2	1	no	—
90	C₄⋊Dic₁₉	—	2	1	no	—
91	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
92	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
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	Dic₁₉⋊C₄	—	2	1	no	—
99	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
100	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
101	C₄×Dic₁₉	—	2	1	no	—
102	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
104	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
105	#64516	—	2	2	no	—
106	#64515	—	2	2	no	—
107	C₈×D₁₉	—	2	2	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂²×D₁₉	—	2	1	no	—
110	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
111	Q₈×C₁₉	—	2	1	no	—
112	Q₈×C₁₉	—	2	1	no	—
113	D₄×C₁₉	—	2	1	no	—
114	D₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	8	1	no	—
119	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂²⋊D₁₉	—	8	1	no	—
123	C₂²⋊D₁₉	—	8	1	no	—
124	C₂²⋊D₁₉	—	8	1	no	—
125	C₂×Dic₁₉	—	2	1	no	—
126	C₂×Dic₁₉	—	2	1	no	—
127	C₂×Dic₁₉	—	2	1	no	—
128	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
129	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
131	D₇₆	—	2	1	no	—
132	D₇₆	—	2	1	no	—
133	D₇₆	—	8	1	no	—
134	C₄×D₁₉	—	2	1	no	—
135	C₄×D₁₉	—	2	1	no	—
136	C₄×D₁₉	—	8	1	no	—
137	Dic₃₈	—	2	1	no	—
138	Dic₃₈	—	2	1	no	—
139	C₈×C₁₉	—	2	1	no	—
140	C₈×C₁₉	#41	1	2	yes	—
141	C₁₉⋊C₈	—	2	1	no	—
142	C₁₉⋊C₈	#41	1	2	yes	—
143	#3174	—	19	1	no	maximal, Sylow
144	C₂²×C₁₉	—	4	1	no	—
145	C₂²×C₁₉	—	4	1	no	—
146	C₂²×C₁₉	—	4	1	no	—
147	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
148	C₂×D₁₉	—	2	1	no	—
149	C₂×D₁₉	—	2	1	no	—
150	C₂×D₁₉	—	2	1	no	—
151	C₂×D₁₉	—	4	1	no	—
152	C₂×D₁₉	—	4	1	no	—
153	C₂×D₁₉	—	4	1	no	—
154	C₄×C₁₉	—	2	1	no	—
155	C₄×C₁₉	—	2	1	no	—
156	C₄×C₁₉	—	4	1	no	—
157	C₄×C₁₉	—	4	1	no	—
158	C₄×C₁₉	—	4	1	no	—
159	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
160	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
161	Dic₁₉	—	2	1	no	—
162	Dic₁₉	—	2	1	no	—
163	Dic₁₉	—	2	1	no	—
164	Dic₁₉	—	4	1	no	—
165	Dic₁₉	—	4	1	no	—
166	Dic₁₉	—	4	1	no	—
167	#541	—	19	1	no	—
168	#540	—	19	1	no	—
169	#499	—	19	1	no	—
170	#492	—	19	1	no	—
171	#491	—	19	1	no	—
172	#490	—	19	1	no	—
173	#468	—	19	1	no	—
174	#468	—	19	1	no	—
175	#465	—	19	1	no	—
176	#465	—	19	1	no	—
177	#440	—	19	1	no	—
178	#440	—	19	1	no	—
179	C₄×SD₁₆	—	19	1	no	—
180	C₄×SD₁₆	D₁₉	1	1	yes	characteristic, complemented
181	#405	—	19	1	no	—
182	C₂×C₁₉	—	8	1	no	—
183	C₂×C₁₉	#532	1	1	yes	characteristic
184	C₂×C₁₉	#577	1	1	yes	characteristic
185	C₂×C₁₉	#577	1	1	yes	characteristic
186	D₁₉	—	4	1	no	—
187	D₁₉	—	8	1	no	—
188	C₂×SD₁₆	—	19	1	no	—
189	C₂×SD₁₆	—	19	1	no	—
190	C₂×SD₁₆	—	19	1	no	—
191	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
192	C₂×M₁₆	—	19	1	no	—
193	C₂²×C₈	—	19	1	no	—
194	C₄⋊Q₈	—	19	1	no	—
195	#127	—	19	1	no	—
196	#126	—	38	1	no	—
197	#126	—	38	1	no	—
198	#125	—	19	1	no	—
199	#125	—	19	1	no	—
200	#125	—	38	1	no	—
201	#125	—	38	1	no	—
202	#123	—	38	1	no	—
203	#123	—	38	1	no	—
204	C₂²⋊Q₈	—	19	1	no	—
205	C₂²⋊Q₈	—	19	1	no	—
206	#121	—	19	1	no	—
207	#121	—	19	1	no	—
208	#121	—	38	1	no	—
209	#121	—	38	1	no	—
210	C₄×Q₈	—	19	1	no	—
211	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
212	C₄×D₄	—	19	1	no	—
213	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
214	#117	—	19	1	no	—
215	#107	—	19	1	no	—
216	#107	—	19	1	no	—
217	#106	—	19	1	no	—
218	#106	C₂×D₁₉	1	1	yes	characteristic
219	#103	—	19	1	no	—
220	#103	—	19	1	no	—
221	#103	—	19	1	no	—
222	#103	C₂×D₁₉	1	1	yes	characteristic
223	#102	—	19	1	no	—
224	#102	—	19	1	no	—
225	#102	—	19	1	no	—
226	#102	C₂×D₁₉	1	1	yes	characteristic
227	#97	—	19	1	no	—
228	#97	—	19	1	no	—
229	C₄×C₈	—	19	1	no	—
230	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
231	C₁₉	#3174	1	1	yes	characteristic, complemented, Sylow
232	C₂×Q₈	—	19	1	no	—
233	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
234	C₂×D₄	—	19	1	no	—
235	C₂×D₄	—	38	1	no	—
236	C₂×D₄	—	38	1	no	—
237	C₂×D₄	—	38	1	no	—
238	C₂×D₄	—	38	1	no	—
239	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
240	C₂²×C₄	—	2	1	no	—
241	C₂²×C₄	—	19	1	no	—
242	C₂²×C₄	—	38	1	no	—
243	SD₁₆	—	2	2	no	—
244	SD₁₆	—	38	2	no	—
245	SD₁₆	—	38	2	no	—
246	SD₁₆	—	38	2	no	—
247	M₁₆	—	38	2	no	—
248	C₂×C₈	—	19	1	no	—
249	C₂×C₈	—	19	1	no	—
250	C₂×C₈	—	38	2	no	—
251	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
252	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
253	C₄⋊C₄	—	2	1	no	—
254	C₄⋊C₄	—	19	1	no	—
255	C₄⋊C₄	—	19	1	no	—
256	C₄⋊C₄	—	19	1	no	—
257	C₄⋊C₄	—	19	1	no	—
258	C₄⋊C₄	—	38	1	no	—
259	C₄⋊C₄	—	38	1	no	—
260	C₄⋊C₄	—	38	1	no	—
261	C₄⋊C₄	—	38	1	no	—
262	C₄⋊C₄	—	38	1	no	—
263	C₄⋊C₄	—	38	1	no	—
264	C₄⋊C₄	—	38	1	no	—
265	C₄⋊C₄	—	38	1	no	—
266	C₄⋊C₄	—	38	1	no	—
267	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
268	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
269	C₂²⋊C₄	—	2	1	no	—
270	C₂²⋊C₄	—	19	1	no	—
271	C₂²⋊C₄	—	19	1	no	—
272	C₂²⋊C₄	—	38	1	no	—
273	C₂²⋊C₄	—	38	1	no	—
274	C₂²⋊C₄	—	38	1	no	—
275	C₂²⋊C₄	—	38	1	no	—
276	C₂²⋊C₄	—	38	1	no	—
277	C₄²	—	2	1	no	—
278	C₄²	—	19	1	no	—
279	C₄²	—	38	1	no	—
280	C₄²	C₂²×D₁₉	1	1	yes	characteristic
281	C₂³	—	2	1	no	—
282	C₂³	—	19	1	no	—
283	C₂³	—	38	1	no	—
284	Q₈	—	2	1	no	—
285	Q₈	—	2	1	no	—
286	Q₈	—	38	1	no	—
287	Q₈	—	38	1	no	—
288	D₄	—	2	1	no	—
289	D₄	—	2	1	no	—
290	D₄	—	38	1	no	—
291	D₄	—	38	1	no	—
292	D₄	—	152	1	no	—
293	D₄	—	152	1	no	—
294	D₄	—	152	1	no	—
295	D₄	—	152	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	8	1	no	—
300	C₂×C₄	—	19	1	no	—
301	C₂×C₄	—	19	1	no	—
302	C₂×C₄	—	19	1	no	—
303	C₂×C₄	—	38	1	no	—
304	C₂×C₄	—	38	1	no	—
305	C₂×C₄	—	38	1	no	—
306	C₂×C₄	—	38	1	no	—
307	C₂×C₄	—	38	1	no	—
308	C₂×C₄	—	152	1	no	—
309	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
310	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
311	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
312	C₈	—	2	1	no	—
313	C₈	—	19	2	no	—
314	C₈	—	38	1	no	—
315	C₈	#64541	1	2	yes	—
316	C₂²	—	4	1	no	—
317	C₂²	—	4	1	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	38	1	no	—
320	C₂²	—	38	1	no	—
321	C₂²	—	38	1	no	—
322	C₂²	—	76	1	no	—
323	C₂²	—	76	1	no	—
324	C₂²	—	76	1	no	—
325	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	4	1	no	—
329	C₄	—	4	1	no	—
330	C₄	—	4	1	no	—
331	C₄	—	38	1	no	—
332	C₄	—	38	1	no	—
333	C₄	—	38	1	no	—
334	C₄	—	76	1	no	—
335	C₄	—	76	1	no	—
336	C₄	—	76	1	no	—
337	C₄	C₂×#64541	1	1	yes	characteristic
338	C₄	#41×D₁₉	1	1	yes	characteristic
339	C₂	—	8	1	no	—
340	C₂	—	76	1	no	—
341	C₂	—	152	1	no	—
342	C₂	#11927091	1	1	yes	characteristic
343	C₂	#11927350	1	1	yes	characteristic
344	C₂	#11927351	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₄×SD₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11927145	C₂
hypercenter	C₄×SD₁₆	D₁₉
hypocenter	C₁₉	#3174
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #11927152	C₂	semidirect
3. #11926944	C₂	semidirect
4. #11926915	C₂	semidirect
5. #11926911	C₂	semidirect
6. #11926907	C₂	semidirect
7. #11926793	C₂	semidirect
8. #11926789	C₂	semidirect
9. #11926774	C₂	semidirect
10. #11926770	C₂	semidirect
11. #11926644	C₂	semidirect
12. #11926642	C₂	semidirect
13. C₄×#64516	C₂	semidirect
14. #11926498	C₂	semidirect
15. C₄×SD₁₆×C₁₉	C₂	semidirect
180. C₄×SD₁₆	D₁₉	semidirect
231. C₁₉	#3174	semidirect

Maximal subgroups

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

subgroup	index
#11927152	2
#11927145	2
#11926944	2
#11926915	2
#11926911	2
#11926907	2
#11926793	2
#11926789	2
#11926774	2
#11926770	2
#11926644	2
#11926642	2
C₄×#64516	2
#11926498	2
C₄×SD₁₆×C₁₉	2
#3174	19