Subgroups — #14574236

Order 2432.

364 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927096	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927080	C₂	1	1	yes	maximal, characteristic
3	#11926951	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926937	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926911	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926905	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926800	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926792	C₂	1	1	yes	maximal, characteristic
9	#11926790	C₂	1	1	yes	maximal, characteristic
10	Q₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926636	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926631	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926629	C₂	1	1	yes	maximal, characteristic, complemented
14	M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	#10597393	C₂²	1	1	yes	characteristic
21	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
22	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
23	#10597390	C₂²	1	1	yes	characteristic
24	C₂×#64528	C₂²	1	1	yes	characteristic
25	C₂×#64527	C₂²	1	1	yes	characteristic
26	#10597376	C₂²	1	1	yes	characteristic
27	#10597370	C₂²	1	1	yes	characteristic
28	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×#64520	C₂²	1	1	yes	characteristic
30	C₂×#64516	C₂²	1	1	yes	characteristic
31	#10597344	—	2	1	no	—
32	#10597339	C₂²	1	1	yes	characteristic
33	#10597338	—	2	1	no	—
34	#10597336	C₂²	1	1	yes	characteristic
35	#10597335	—	2	1	no	—
36	#10597334	C₂²	1	1	yes	characteristic
37	#10597333	—	2	1	no	—
38	#10597333	C₂²	1	1	yes	characteristic
39	#10597332	—	2	1	no	—
40	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
41	#10597324	—	2	1	no	—
42	#10597323	—	2	1	no	—
43	C₁₉×#106	C₂²	1	1	yes	characteristic
44	C₁₉×#103	C₂²	1	1	yes	characteristic
45	C₁₉×#103	C₂²	1	1	yes	characteristic
46	#10597292	C₂²	1	1	yes	characteristic
47	#10597292	C₂²	1	1	yes	characteristic
48	#10597278	C₂²	1	1	yes	characteristic
49	#10597275	C₂²	1	1	yes	characteristic
50	#10597273	C₂²	1	1	yes	characteristic
51	#10597272	C₂²	1	1	yes	characteristic
52	#10597272	C₂²	1	1	yes	characteristic
53	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
54	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
55	#10597267	C₂²	1	1	yes	characteristic
56	#10597266	C₂²	1	1	yes	characteristic
57	#10597265	C₂²	1	1	yes	characteristic
58	#10597264	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊D₁₉	—	2	1	no	—
63	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
64	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
65	C₂×D₇₆	C₂³	1	1	yes	characteristic
66	C₂×C₄×D₁₉	—	2	1	no	—
67	C₂×Dic₃₈	—	2	1	no	—
68	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
69	Q₁₆×C₁₉	—	2	2	no	—
70	M₁₆×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	—	2	1	no	—
75	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂²⋊Dic₁₉	—	2	1	no	—
80	#64528	—	2	2	no	—
81	#64527	—	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	C₄⋊Dic₁₉	—	2	1	no	—
87	C₄⋊Dic₁₉	—	2	1	no	—
88	C₄⋊Dic₁₉	—	2	1	no	—
89	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
90	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
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	C₄×Dic₁₉	—	2	1	no	—
98	C₄×Dic₁₉	—	2	1	no	—
99	C₄×Dic₁₉	—	2	1	no	—
100	C₄×Dic₁₉	D₄	1	1	yes	characteristic
101	C₄×Dic₁₉	D₄	1	1	yes	characteristic
102	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
103	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
104	#64520	—	2	2	no	—
105	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
107	#64516	—	2	2	no	—
108	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×D₁₉	—	2	1	no	—
110	Q₈×C₁₉	—	2	1	no	—
111	Q₈×C₁₉	—	2	1	no	—
112	Q₈×C₁₉	—	2	1	no	—
113	Q₈×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	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₂²⋊D₁₉	—	4	2	no	—
123	C₂×Dic₁₉	—	2	2	no	—
124	C₂×Dic₁₉	—	2	1	no	—
125	C₂×Dic₁₉	—	2	1	no	—
126	C₂×Dic₁₉	—	2	1	no	—
127	C₂×Dic₁₉	—	4	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	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
132	D₇₆	—	2	1	no	—
133	D₇₆	—	2	1	no	—
134	C₄×D₁₉	—	4	2	no	—
135	Dic₃₈	—	2	1	no	—
136	Dic₃₈	—	2	1	no	—
137	Dic₃₈	—	4	2	no	—
138	C₈×C₁₉	—	2	1	no	—
139	C₈×C₁₉	#41	1	2	yes	—
140	C₁₉⋊C₈	—	2	1	no	—
141	C₁₉⋊C₈	#41	1	2	yes	—
142	#3172	—	19	1	no	maximal, Sylow
143	C₂²×C₁₉	—	2	1	no	—
144	C₂²×C₁₉	—	2	1	no	—
145	C₂²×C₁₉	—	2	1	no	—
146	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×D₁₉	—	4	1	no	—
148	C₂×D₁₉	—	4	1	no	—
149	C₂×D₁₉	—	4	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	—	4	1	no	—
155	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
156	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
157	Dic₁₉	—	2	1	no	—
158	Dic₁₉	—	2	1	no	—
159	Dic₁₉	—	2	1	no	—
160	Dic₁₉	—	4	1	no	—
161	Dic₁₉	—	4	1	no	—
162	Dic₁₉	—	4	1	no	—
163	Dic₁₉	#137	1	2	yes	—
164	#533	—	19	1	no	—
165	#529	—	19	1	no	—
166	#501	—	19	1	no	—
167	#497	—	19	1	no	—
168	#491	—	19	1	no	—
169	#489	—	19	1	no	—
170	#470	—	19	1	no	—
171	#470	D₁₉	1	1	yes	characteristic, complemented
172	#468	—	19	1	no	—
173	#468	—	19	1	no	—
174	C₄×Q₁₆	—	19	1	no	—
175	C₄×Q₁₆	—	19	1	no	—
176	C₄×SD₁₆	—	19	1	no	—
177	C₄×SD₁₆	—	19	1	no	—
178	C₄×M₁₆	—	19	1	no	—
179	C₂×C₁₉	—	4	1	no	—
180	C₂×C₁₉	#532	1	1	yes	characteristic
181	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
182	C₂×C₁₉	#575	1	1	yes	characteristic
183	D₁₉	—	8	1	no	—
184	C₂×Q₁₆	—	19	1	no	—
185	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
186	C₂×SD₁₆	—	19	1	no	—
187	C₂×SD₁₆	—	19	1	no	—
188	C₂×M₁₆	—	19	1	no	—
189	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
190	C₄⋊Q₈	—	19	1	no	—
191	C₄⋊Q₈	—	19	1	no	—
192	#126	—	38	1	no	—
193	#125	—	19	1	no	—
194	#125	—	38	1	no	—
195	#124	—	19	1	no	—
196	#123	—	38	1	no	—
197	C₂²⋊Q₈	—	19	1	no	—
198	C₂²⋊Q₈	—	38	1	no	—
199	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
200	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
201	#121	—	19	1	no	—
202	C₄×Q₈	—	19	1	no	—
203	C₄×Q₈	—	19	1	no	—
204	C₄×Q₈	—	19	1	no	—
205	C₄×Q₈	—	38	1	no	—
206	C₄×D₄	—	19	1	no	—
207	C₄×D₄	—	38	1	no	—
208	#117	—	38	1	no	—
209	#117	—	38	1	no	—
210	C₂×C₄²	—	19	1	no	—
211	#107	—	19	1	no	—
212	#107	—	19	1	no	—
213	#106	—	19	1	no	—
214	#106	C₂×D₁₉	1	1	yes	characteristic
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	#102	—	19	1	no	—
222	#102	—	19	1	no	—
223	#97	—	19	1	no	—
224	#97	—	19	1	no	—
225	C₄×C₈	—	19	1	no	—
226	C₄×C₈	—	19	1	no	—
227	C₁₉	#3172	1	1	yes	characteristic, complemented, Sylow
228	C₂×Q₈	—	19	1	no	—
229	C₂×Q₈	—	38	1	no	—
230	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
231	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
232	C₂×D₄	—	19	1	no	—
233	C₂×D₄	—	38	1	no	—
234	C₂²×C₄	—	19	1	no	—
235	C₂²×C₄	—	19	1	no	—
236	C₂²×C₄	—	38	1	no	—
237	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
238	Q₁₆	—	2	2	no	—
239	Q₁₆	—	38	2	no	—
240	SD₁₆	—	38	2	no	—
241	SD₁₆	—	38	2	no	—
242	M₁₆	—	2	2	no	—
243	M₁₆	—	38	2	no	—
244	C₂×C₈	—	19	1	no	—
245	C₂×C₈	—	19	1	no	—
246	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
247	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	2	1	no	—
250	C₄⋊C₄	—	19	1	no	—
251	C₄⋊C₄	—	19	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	—	2	1	no	—
264	C₂²⋊C₄	—	2	1	no	—
265	C₂²⋊C₄	—	38	1	no	—
266	C₂²⋊C₄	—	38	1	no	—
267	C₂²⋊C₄	—	38	1	no	—
268	C₂²⋊C₄	—	38	1	no	—
269	C₂²⋊C₄	—	38	1	no	—
270	C₄²	—	19	1	no	—
271	C₄²	—	19	1	no	—
272	C₄²	—	19	1	no	—
273	C₄²	—	19	1	no	—
274	C₄²	—	38	1	no	—
275	C₄²	—	38	1	no	—
276	C₄²	—	38	1	no	—
277	C₂³	—	38	1	no	—
278	C₂³	D₄×D₁₉	1	1	yes	characteristic
279	Q₈	—	2	1	no	—
280	Q₈	—	2	1	no	—
281	Q₈	—	2	1	no	—
282	Q₈	—	2	1	no	—
283	Q₈	—	38	1	no	—
284	Q₈	—	38	1	no	—
285	Q₈	—	76	2	no	—
286	D₄	—	38	1	no	—
287	D₄	—	38	1	no	—
288	D₄	—	76	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	19	1	no	—
296	C₂×C₄	—	19	1	no	—
297	C₂×C₄	—	19	1	no	—
298	C₂×C₄	—	19	1	no	—
299	C₂×C₄	—	38	2	no	—
300	C₂×C₄	—	38	1	no	—
301	C₂×C₄	—	38	1	no	—
302	C₂×C₄	—	38	1	no	—
303	C₂×C₄	—	76	2	no	—
304	C₂×C₄	—	76	1	no	—
305	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
306	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
307	C₈	—	2	1	no	—
308	C₈	—	19	2	no	—
309	C₈	—	38	1	no	—
310	C₈	#64543	1	2	yes	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	76	1	no	—
315	C₂²	—	76	1	no	—
316	C₂²	—	76	1	no	—
317	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
318	C₄	—	2	1	no	—
319	C₄	—	4	1	no	—
320	C₄	—	4	1	no	—
321	C₄	—	4	1	no	—
322	C₄	—	4	1	no	—
323	C₄	—	19	2	no	—
324	C₄	—	38	1	no	—
325	C₄	—	38	1	no	—
326	C₄	—	38	1	no	—
327	C₄	—	76	1	no	—
328	C₄	—	76	1	no	—
329	C₄	—	76	1	no	—
330	C₄	C₂×#64543	1	1	yes	characteristic
331	C₄	#41×D₁₉	1	1	yes	characteristic
332	C₂	—	4	1	no	—
333	C₂	—	152	1	no	—
334	C₂	#11927089	1	1	yes	characteristic
335	C₂	#137×D₁₉	1	1	yes	characteristic
336	C₂	#11927343	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×#470	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#10597376	C₂²
hypercenter	#470	D₁₉
hypocenter	C₁₉	#3172
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #470

Complements

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

N	H ≅ G/N	type
1. #11927096	C₂	semidirect
3. #11926951	C₂	semidirect
4. #11926937	C₂	semidirect
5. #11926911	C₂	semidirect
6. #11926905	C₂	semidirect
7. #11926800	C₂	semidirect
10. Q₁₆×Dic₁₉	C₂	semidirect
11. #11926636	C₂	semidirect
12. #11926631	C₂	semidirect
13. #11926629	C₂	semidirect
14. M₁₆×Dic₁₉	C₂	semidirect
15. C₁₉×#470	C₂	semidirect
171. #470	D₁₉	semidirect
227. C₁₉	#3172	semidirect

Maximal subgroups

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

subgroup	index
#11927096	2
#11927080	2
#11926951	2
#11926937	2
#11926911	2
#11926905	2
#11926800	2
#11926792	2
#11926790	2
Q₁₆×Dic₁₉	2
#11926636	2
#11926631	2
#11926629	2
M₁₆×Dic₁₉	2
C₁₉×#470	2
#3172	19