Subgroups — #14573995

Order 2432.

372 conjugacy classes of subgroups.

The subgroup lattice has 342 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, complemented
2	#11927119	C₂	1	1	yes	maximal, characteristic
3	#11926912	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926911	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926906	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926905	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926900	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926899	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926893	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926551	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926544	C₂	1	1	yes	maximal, characteristic
12	#11926539	C₂	1	1	yes	maximal, characteristic
13	#103×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926498	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#64545	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	#10597393	C₂²	1	1	yes	characteristic
21	#10597392	—	2	1	no	—
22	#10597390	—	2	1	no	—
23	#10597390	C₂²	1	1	yes	characteristic
24	C₂×#64515	C₂²	1	1	yes	characteristic
25	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
26	#10597342	—	2	1	no	—
27	#10597342	—	2	1	no	—
28	#10597342	—	2	1	no	—
29	#10597340	—	2	1	no	—
30	#10597340	—	2	1	no	—
31	#10597338	C₂²	1	1	yes	characteristic
32	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
33	#10597336	C₂²	1	1	yes	characteristic
34	#10597335	—	2	1	no	—
35	#10597334	C₂²	1	1	yes	characteristic
36	#10597321	C₂²	1	1	yes	characteristic
37	#10597318	C₂²	1	1	yes	characteristic
38	#10597316	C₂²	1	1	yes	characteristic
39	C₁₉×#103	C₂²	1	1	yes	characteristic
40	C₁₉×#103	C₂²	1	1	yes	characteristic
41	C₁₉×#103	C₂²	1	1	yes	characteristic
42	C₁₉×#103	C₂²	1	1	yes	characteristic
43	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
44	#10597292	C₂²	1	1	yes	characteristic
45	#10597292	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	#10597278	C₂²	1	1	yes	characteristic
50	#10597273	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	#10597267	C₂²	1	1	yes	characteristic
56	#10597266	C₂²	1	1	yes	characteristic
57	#10597266	C₂²	1	1	yes	characteristic
58	#10597260	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	#64545	—	2	2	no	—
63	#64545	—	2	2	no	—
64	Q₈×D₁₉	—	2	2	no	—
65	Q₈×D₁₉	—	2	2	no	—
66	C₂×D₇₆	—	2	1	no	—
67	C₂×D₇₆	C₂³	1	1	yes	characteristic
68	C₂×C₄×D₁₉	—	2	1	no	—
69	C₂×C₄×D₁₉	—	2	1	no	—
70	C₂×C₄×D₁₉	—	2	1	no	—
71	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
72	C₂×Dic₃₈	—	2	1	no	—
73	C₂×Dic₃₈	—	2	1	no	—
74	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
75	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
87	(C₂×D₁₉)⋊C₄	—	2	1	no	—
88	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
89	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
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	—	2	1	no	—
100	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
101	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
102	C₄×Dic₁₉	—	2	1	no	—
103	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
106	#64515	—	2	2	no	—
107	C₈×D₁₉	—	2	2	no	—
108	C₂²×D₁₉	—	2	1	no	—
109	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
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	Q₈×C₁₉	—	8	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	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	C₂×Dic₁₉	—	2	1	no	—
123	C₂×Dic₁₉	—	2	1	no	—
124	C₂×Dic₁₉	—	2	1	no	—
125	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
128	D₇₆	—	2	1	no	—
129	D₇₆	—	2	1	no	—
130	D₇₆	—	4	2	no	—
131	C₄×D₁₉	—	4	2	no	—
132	C₄×D₁₉	—	4	2	no	—
133	C₄×D₁₉	—	8	1	no	—
134	C₄×D₁₉	#41	1	2	yes	—
135	C₄×D₁₉	#41	1	2	yes	—
136	Dic₃₈	—	2	1	no	—
137	Dic₃₈	—	2	1	no	—
138	Dic₃₈	—	4	2	no	—
139	Dic₃₈	—	8	1	no	—
140	C₈×C₁₉	—	2	1	no	—
141	C₈×C₁₉	—	2	1	no	—
142	C₁₉⋊C₈	—	2	1	no	—
143	C₁₉⋊C₈	—	2	1	no	—
144	#3137	—	19	1	no	maximal, Sylow
145	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
146	C₂×D₁₉	—	2	1	no	—
147	C₂×D₁₉	—	2	1	no	—
148	C₂×D₁₉	—	4	1	no	—
149	C₂×D₁₉	—	4	1	no	—
150	C₂×D₁₉	—	4	1	no	—
151	C₂×D₁₉	#124	1	2	yes	—
152	C₄×C₁₉	—	2	1	no	—
153	C₄×C₁₉	—	2	1	no	—
154	C₄×C₁₉	—	4	1	no	—
155	C₄×C₁₉	—	4	1	no	—
156	C₄×C₁₉	—	4	1	no	—
157	C₄×C₁₉	—	4	1	no	—
158	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
159	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
160	Dic₁₉	—	2	1	no	—
161	Dic₁₉	—	2	1	no	—
162	Dic₁₉	—	4	1	no	—
163	Dic₁₉	—	4	1	no	—
164	Dic₁₉	—	4	1	no	—
165	Dic₁₉	#124	1	2	yes	—
166	#544	—	19	1	no	—
167	#536	—	19	1	no	—
168	#491	—	19	1	no	—
169	#491	—	19	1	no	—
170	#489	—	19	1	no	—
171	#489	—	19	1	no	—
172	#488	—	19	1	no	—
173	#488	—	19	1	no	—
174	#487	—	19	1	no	—
175	#487	D₁₉	1	1	yes	characteristic, complemented
176	#419	—	19	1	no	—
177	#417	—	19	1	no	—
178	#416	—	19	1	no	—
179	C₂×#103	—	19	1	no	—
180	#405	—	19	1	no	—
181	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
182	C₂×C₁₉	#577	1	1	yes	characteristic
183	C₂×C₁₉	#578	1	1	yes	characteristic
184	D₁₉	—	2	2	no	—
185	D₁₉	—	8	1	no	—
186	C₂×#41	—	19	1	no	—
187	C₂²×Q₈	—	19	1	no	—
188	C₂×M₁₆	—	19	1	no	—
189	C₂²×C₈	—	19	1	no	—
190	C₄⋊Q₈	—	19	1	no	—
191	C₄⋊Q₈	—	19	1	no	—
192	C₄⋊Q₈	—	38	1	no	—
193	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
194	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
195	#125	—	19	1	no	—
196	#125	—	19	1	no	—
197	#125	—	38	1	no	—
198	#124	—	19	1	no	—
199	#124	—	19	1	no	—
200	#123	—	38	1	no	—
201	#123	—	38	1	no	—
202	C₂²⋊Q₈	—	38	1	no	—
203	C₂²⋊Q₈	—	38	1	no	—
204	C₂²⋊Q₈	—	38	1	no	—
205	C₂²⋊Q₈	—	38	1	no	—
206	#117	—	19	1	no	—
207	#117	—	19	1	no	—
208	C₂×C₄⋊C₄	—	19	1	no	—
209	#103	—	19	1	no	—
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	—	19	1	no	—
217	#103	C₂×D₁₉	1	1	yes	characteristic
218	#103	C₂×D₁₉	1	1	yes	characteristic
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	#102	—	19	1	no	—
224	#102	—	19	1	no	—
225	#97	—	19	1	no	—
226	#97	—	19	1	no	—
227	C₄×C₈	—	19	1	no	—
228	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
229	C₁₉	#3137	1	1	yes	characteristic, complemented, Sylow
230	#41	—	38	2	no	—
231	#41	—	38	2	no	—
232	C₂×Q₈	—	2	1	no	—
233	C₂×Q₈	—	19	1	no	—
234	C₂×Q₈	—	38	1	no	—
235	C₂×Q₈	—	38	1	no	—
236	C₂×Q₈	—	38	2	no	—
237	C₂×Q₈	—	38	2	no	—
238	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
239	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
240	C₂×D₄	—	19	1	no	—
241	C₂×D₄	—	38	1	no	—
242	C₂²×C₄	—	19	1	no	—
243	C₂²×C₄	—	38	1	no	—
244	C₂²×C₄	—	38	1	no	—
245	C₂²×C₄	—	38	1	no	—
246	M₁₆	—	38	2	no	—
247	C₂×C₈	—	19	1	no	—
248	C₂×C₈	—	19	1	no	—
249	C₂×C₈	—	38	2	no	—
250	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
251	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
252	C₄⋊C₄	—	2	1	no	—
253	C₄⋊C₄	—	2	1	no	—
254	C₄⋊C₄	—	2	1	no	—
255	C₄⋊C₄	—	19	1	no	—
256	C₄⋊C₄	—	19	1	no	—
257	C₄⋊C₄	—	19	1	no	—
258	C₄⋊C₄	—	19	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	—	19	1	no	—
270	C₂²⋊C₄	—	19	1	no	—
271	C₂²⋊C₄	—	38	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	C₄²	—	19	1	no	—
277	C₄²	—	38	1	no	—
278	C₄²	C₂²×D₁₉	1	1	yes	characteristic
279	C₂³	—	19	1	no	—
280	C₂³	—	38	1	no	—
281	Q₈	—	2	1	no	—
282	Q₈	—	2	1	no	—
283	Q₈	—	2	1	no	—
284	Q₈	—	2	1	no	—
285	Q₈	—	8	1	no	—
286	Q₈	—	38	1	no	—
287	Q₈	—	38	1	no	—
288	Q₈	—	76	2	no	—
289	Q₈	—	152	1	no	—
290	D₄	—	38	1	no	—
291	D₄	—	38	1	no	—
292	D₄	—	76	2	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	19	1	no	—
298	C₂×C₄	—	19	2	no	—
299	C₂×C₄	—	19	2	no	—
300	C₂×C₄	—	19	1	no	—
301	C₂×C₄	—	19	1	no	—
302	C₂×C₄	—	38	1	no	—
303	C₂×C₄	—	38	1	no	—
304	C₂×C₄	—	38	1	no	—
305	C₂×C₄	—	76	2	no	—
306	C₂×C₄	—	76	2	no	—
307	C₂×C₄	—	152	1	no	—
308	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
309	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
310	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
311	C₈	—	2	1	no	—
312	C₈	—	2	1	no	—
313	C₈	—	38	1	no	—
314	C₈	—	38	1	no	—
315	C₂²	—	19	2	no	—
316	C₂²	—	38	1	no	—
317	C₂²	—	38	1	no	—
318	C₂²	—	76	1	no	—
319	C₂²	—	76	1	no	—
320	C₂²	—	76	1	no	—
321	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
322	C₄	—	2	1	no	—
323	C₄	—	2	1	no	—
324	C₄	—	4	1	no	—
325	C₄	—	4	1	no	—
326	C₄	—	4	1	no	—
327	C₄	—	4	1	no	—
328	C₄	—	19	2	no	—
329	C₄	—	38	1	no	—
330	C₄	—	38	1	no	—
331	C₄	—	76	1	no	—
332	C₄	—	76	1	no	—
333	C₄	—	76	1	no	—
334	C₄	#41×D₁₉	1	1	yes	characteristic
335	C₄	#41×D₁₉	1	1	yes	characteristic
336	C₂	—	38	2	no	—
337	C₂	—	152	1	no	—
338	C₂	#124×D₁₉	1	1	yes	characteristic
339	C₂	#11927350	1	1	yes	characteristic
340	C₂	#11927357	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×#487	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#64545	C₂²
hypercenter	#487	D₁₉
hypocenter	C₁₉	#3137
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

Complements

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

N	H ≅ G/N	type
1. #11927171	C₂	semidirect
3. #11926912	C₂	semidirect
4. #11926911	C₂	semidirect
5. #11926906	C₂	semidirect
6. #11926905	C₂	semidirect
7. #11926900	C₂	semidirect
8. #11926899	C₂	semidirect
9. #11926893	C₂	semidirect
10. #11926551	C₂	semidirect
13. #103×D₁₉	C₂	semidirect
14. #11926498	C₂	semidirect
15. C₁₉×#487	C₂	semidirect
175. #487	D₁₉	semidirect
229. C₁₉	#3137	semidirect

Maximal subgroups

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

subgroup	index
#11927171	2
#11927119	2
#11926912	2
#11926911	2
#11926906	2
#11926905	2
#11926900	2
#11926899	2
#11926893	2
#11926551	2
#11926544	2
#11926539	2
#103×D₁₉	2
#11926498	2
C₁₉×#487	2
#3137	19