Subgroups — #14573686

Order 2432.

454 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927081	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926878	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926864	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926843	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926842	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926762	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926761	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926693	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926679	C₂	1	1	yes	maximal, characteristic
11	C₄×#64527	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×D₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#64525	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926595	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₉	—	2	1	no	—
18	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	#10597393	C₂²	1	1	yes	characteristic, complemented
22	#10597392	C₂²	1	1	yes	characteristic
23	C₂×#64527	C₂²	1	1	yes	characteristic
24	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×#64525	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₁₉	—	2	1	no	—
27	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
28	#10597344	—	2	1	no	—
29	#10597341	C₂²	1	1	yes	characteristic
30	#10597340	—	2	1	no	—
31	#10597339	C₂²	1	1	yes	characteristic
32	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
33	#10597336	C₂²	1	1	yes	characteristic, complemented
34	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
35	C₂²⋊C₄×D₁₉	—	2	1	no	—
36	C₄×D₇₆	—	2	1	no	—
37	C₄×D₇₆	C₂²	1	1	yes	characteristic
38	C₄×D₇₆	C₂²	1	1	yes	characteristic, complemented
39	#10597318	—	2	1	no	—
40	C₄²×D₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#102	C₂²	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	#10597292	C₂²	1	1	yes	characteristic, complemented
46	#10597289	C₂²	1	1	yes	characteristic
47	#10597278	C₂²	1	1	yes	characteristic
48	#10597278	C₂²	1	1	yes	characteristic, complemented
49	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
51	#10597275	C₂²	1	1	yes	characteristic, complemented
52	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	#10597266	C₂²	1	1	yes	characteristic
55	#10597266	C₂²	1	1	yes	characteristic, complemented
56	#10597265	C₂²	1	1	yes	characteristic, complemented
57	#10597264	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊D₁₉	—	2	1	no	—
64	C₂²×Dic₁₉	—	2	1	no	—
65	D₄×D₁₉	—	2	2	no	—
66	D₄×D₁₉	—	2	2	no	—
67	C₂×D₇₆	—	2	1	no	—
68	C₂×D₇₆	C₂³	1	1	yes	characteristic
69	C₂×D₇₆	C₂³	1	1	yes	characteristic
70	C₂×C₄×D₁₉	—	2	1	no	—
71	C₂×C₄×D₁₉	—	2	1	no	—
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×C₄×D₁₉	—	2	1	no	—
74	C₂×C₄×D₁₉	—	4	4	no	—
75	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
76	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
77	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
78	SD₁₆×C₁₉	—	2	2	no	—
79	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂²⋊C₄×C₁₉	—	2	1	no	—
85	C₄²×C₁₉	—	2	1	no	—
86	C₄²×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²⋊Dic₁₉	—	2	1	no	—
88	#64527	—	2	2	no	—
89	#64525	—	2	2	no	—
90	(C₂×D₁₉)⋊C₄	—	2	1	no	—
91	(C₂×D₁₉)⋊C₄	—	2	1	no	—
92	(C₂×D₁₉)⋊C₄	—	2	1	no	—
93	(C₂×D₁₉)⋊C₄	—	2	1	no	—
94	(C₂×D₁₉)⋊C₄	—	2	1	no	—
95	(C₂×D₁₉)⋊C₄	—	2	1	no	—
96	(C₂×D₁₉)⋊C₄	—	2	1	no	—
97	C₄⋊Dic₁₉	—	2	1	no	—
98	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
100	Dic₁₉⋊C₄	—	2	1	no	—
101	Dic₁₉⋊C₄	—	2	1	no	—
102	Dic₁₉⋊C₄	—	2	1	no	—
103	C₄×Dic₁₉	D₄	1	1	yes	characteristic
104	C₄×Dic₁₉	D₄	1	1	yes	characteristic
105	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
108	D₁₅₂	—	2	2	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂²×D₁₉	—	2	4	no	—
111	C₂²×D₁₉	—	2	1	no	—
112	C₂²×D₁₉	—	2	1	no	—
113	C₂²×D₁₉	—	4	2	no	—
114	C₂²×D₁₉	—	4	2	no	—
115	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
116	Q₈×C₁₉	—	2	1	no	—
117	Q₈×C₁₉	—	2	1	no	—
118	D₄×C₁₉	—	2	1	no	—
119	D₄×C₁₉	#41	1	2	yes	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	4	2	no	—
124	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
127	C₂²⋊D₁₉	—	2	4	no	—
128	C₂×Dic₁₉	—	2	1	no	—
129	C₂×Dic₁₉	—	2	1	no	—
130	C₂×Dic₁₉	—	4	2	no	—
131	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
134	D₇₆	—	2	1	no	—
135	D₇₆	—	2	1	no	—
136	D₇₆	—	2	1	no	—
137	D₇₆	—	4	2	no	—
138	D₇₆	#41	1	2	yes	—
139	C₄×D₁₉	—	2	2	no	—
140	C₄×D₁₉	—	2	2	no	—
141	C₄×D₁₉	—	2	1	no	—
142	C₄×D₁₉	—	2	1	no	—
143	C₄×D₁₉	—	4	2	no	—
144	C₄×D₁₉	—	4	2	no	—
145	C₄×D₁₉	—	4	2	no	—
146	C₄×D₁₉	—	4	2	no	—
147	C₈×C₁₉	—	2	1	no	—
148	C₈×C₁₉	—	2	1	no	—
149	C₁₉⋊C₈	—	2	1	no	—
150	C₁₉⋊C₈	—	2	1	no	—
151	#3105	—	19	1	no	maximal, Sylow
152	C₂²×C₁₉	—	2	2	no	—
153	C₂²×C₁₉	—	4	1	no	—
154	C₂²×C₁₉	—	4	1	no	—
155	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×D₁₉	—	2	1	no	—
157	C₂×D₁₉	—	2	1	no	—
158	C₂×D₁₉	—	2	2	no	—
159	C₂×D₁₉	—	4	8	no	—
160	C₂×D₁₉	—	4	1	no	—
161	C₂×D₁₉	—	4	1	no	—
162	C₂×D₁₉	—	4	1	no	—
163	C₂×D₁₉	—	4	1	no	—
164	C₂×D₁₉	—	4	1	no	—
165	C₂×D₁₉	#135	1	2	yes	—
166	C₄×C₁₉	—	2	1	no	—
167	C₄×C₁₉	—	4	1	no	—
168	C₄×C₁₉	—	4	1	no	—
169	C₄×C₁₉	—	4	1	no	—
170	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
172	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
173	Dic₁₉	—	2	1	no	—
174	Dic₁₉	—	2	1	no	—
175	Dic₁₉	—	2	1	no	—
176	Dic₁₉	—	4	1	no	—
177	Dic₁₉	—	4	1	no	—
178	#529	—	19	1	no	—
179	C₂×C₄×D₄	—	19	1	no	—
180	#484	—	19	1	no	—
181	#481	—	19	1	no	—
182	#478	—	19	1	no	—
183	#478	—	19	1	no	—
184	#463	—	19	1	no	—
185	#463	—	19	1	no	—
186	#450	—	19	1	no	—
187	#447	—	19	1	no	—
188	C₄×SD₁₆	—	19	1	no	—
189	C₄×SD₁₆	D₁₉	1	1	yes	characteristic, complemented
190	C₄×D₈	—	19	1	no	—
191	C₄×D₈	—	19	1	no	—
192	#431	—	19	1	no	—
193	C₂×C₁₉	—	4	2	no	—
194	C₂×C₁₉	#525	1	1	yes	characteristic
195	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
196	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	D₁₉	—	2	2	no	—
198	D₁₉	—	4	2	no	—
199	D₁₉	—	8	1	no	—
200	C₂²×D₄	—	19	1	no	—
201	C₂³×C₄	—	38	1	no	—
202	C₂×SD₁₆	—	19	1	no	—
203	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
204	C₂×D₈	—	19	1	no	—
205	C₂×D₈	—	19	1	no	—
206	#126	—	38	1	no	—
207	#125	—	19	1	no	—
208	#124	—	19	1	no	—
209	#123	—	38	1	no	—
210	C₂²⋊Q₈	—	19	1	no	—
211	#121	—	19	1	no	—
212	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
213	C₄×D₄	—	19	1	no	—
214	C₄×D₄	—	19	1	no	—
215	C₄×D₄	—	19	1	no	—
216	C₄×D₄	—	19	1	no	—
217	C₄×D₄	—	38	1	no	—
218	C₄×D₄	—	38	1	no	—
219	C₄×D₄	—	38	1	no	—
220	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
221	#117	—	38	1	no	—
222	C₂×C₄⋊C₄	—	19	1	no	—
223	C₂×C₂²⋊C₄	—	38	1	no	—
224	C₂×C₄²	—	19	1	no	—
225	#107	—	19	1	no	—
226	#107	—	19	1	no	—
227	#106	—	19	1	no	—
228	#106	C₂×D₁₉	1	1	yes	characteristic, complemented
229	C₄⋊C₈	—	19	1	no	—
230	C₄⋊C₈	—	19	1	no	—
231	#103	—	19	1	no	—
232	#103	C₂×D₁₉	1	1	yes	characteristic, complemented
233	#102	—	19	1	no	—
234	#102	—	19	1	no	—
235	#102	—	19	1	no	—
236	#102	—	19	1	no	—
237	#102	—	19	1	no	—
238	#102	C₂×D₁₉	1	1	yes	characteristic
239	C₂²⋊C₈	—	19	1	no	—
240	C₂²⋊C₈	—	19	1	no	—
241	C₄×C₈	—	19	1	no	—
242	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
243	C₁₉	#3105	1	1	yes	characteristic, complemented, Sylow
244	C₂⁴	—	38	1	no	—
245	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
246	C₂×D₄	—	19	1	no	—
247	C₂×D₄	—	19	1	no	—
248	C₂×D₄	—	38	1	no	—
249	C₂×D₄	—	38	1	no	—
250	C₂×D₄	—	38	2	no	—
251	C₂×D₄	—	38	2	no	—
252	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	19	1	no	—
255	C₂²×C₄	—	19	1	no	—
256	C₂²×C₄	—	19	1	no	—
257	C₂²×C₄	—	38	1	no	—
258	C₂²×C₄	—	38	1	no	—
259	C₂²×C₄	—	38	1	no	—
260	C₂²×C₄	—	38	1	no	—
261	C₂²×C₄	—	38	1	no	—
262	C₂²×C₄	—	76	4	no	—
263	SD₁₆	—	2	2	no	—
264	SD₁₆	—	38	2	no	—
265	D₈	—	38	2	no	—
266	D₈	—	38	2	no	—
267	C₂×C₈	—	19	1	no	—
268	C₂×C₈	—	19	1	no	—
269	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
270	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
271	C₄⋊C₄	—	2	1	no	—
272	C₄⋊C₄	—	19	1	no	—
273	C₄⋊C₄	—	19	1	no	—
274	C₄⋊C₄	—	38	1	no	—
275	C₄⋊C₄	—	38	1	no	—
276	C₄⋊C₄	—	38	1	no	—
277	C₄⋊C₄	—	38	1	no	—
278	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
279	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
280	C₂²⋊C₄	—	2	1	no	—
281	C₂²⋊C₄	—	38	1	no	—
282	C₂²⋊C₄	—	38	1	no	—
283	C₂²⋊C₄	—	38	1	no	—
284	C₂²⋊C₄	—	38	1	no	—
285	C₂²⋊C₄	—	38	1	no	—
286	C₂²⋊C₄	—	38	1	no	—
287	C₂²⋊C₄	—	38	1	no	—
288	C₂²⋊C₄	—	38	1	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	19	1	no	—
291	C₄²	—	19	1	no	—
292	C₄²	—	19	1	no	—
293	C₄²	C₂²×D₁₉	1	1	yes	characteristic
294	C₂³	—	2	1	no	—
295	C₂³	—	19	1	no	—
296	C₂³	—	38	4	no	—
297	C₂³	—	38	1	no	—
298	C₂³	—	38	1	no	—
299	C₂³	—	76	2	no	—
300	C₂³	—	76	2	no	—
301	Q₈	—	2	1	no	—
302	Q₈	—	2	1	no	—
303	D₄	—	2	1	no	—
304	D₄	—	19	2	no	—
305	D₄	—	38	4	no	—
306	D₄	—	38	1	no	—
307	D₄	—	38	1	no	—
308	D₄	—	38	1	no	—
309	D₄	—	76	2	no	—
310	D₄	#64541	1	2	yes	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	19	1	no	—
316	C₂×C₄	—	19	1	no	—
317	C₂×C₄	—	19	1	no	—
318	C₂×C₄	—	38	2	no	—
319	C₂×C₄	—	38	1	no	—
320	C₂×C₄	—	38	1	no	—
321	C₂×C₄	—	38	2	no	—
322	C₂×C₄	—	38	1	no	—
323	C₂×C₄	—	38	1	no	—
324	C₂×C₄	—	76	2	no	—
325	C₂×C₄	—	76	2	no	—
326	C₂×C₄	—	76	2	no	—
327	C₂×C₄	—	76	2	no	—
328	C₂×C₄	—	76	2	no	—
329	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
330	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
331	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
332	C₈	—	2	1	no	—
333	C₈	—	2	1	no	—
334	C₈	—	38	1	no	—
335	C₈	—	38	1	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	1	no	—
339	C₂²	—	19	2	no	—
340	C₂²	—	38	1	no	—
341	C₂²	—	38	1	no	—
342	C₂²	—	38	2	no	—
343	C₂²	—	76	8	no	—
344	C₂²	—	76	1	no	—
345	C₂²	—	76	1	no	—
346	C₂²	—	76	1	no	—
347	C₂²	—	76	1	no	—
348	C₂²	—	76	1	no	—
349	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
350	C₄	—	2	1	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	—	4	1	no	—
354	C₄	—	38	1	no	—
355	C₄	—	38	1	no	—
356	C₄	—	38	1	no	—
357	C₄	—	76	1	no	—
358	C₄	—	76	1	no	—
359	C₄	#10597360	1	2	yes	—
360	C₄	C₂×#64541	1	1	yes	characteristic
361	C₄	#41×D₁₉	1	1	yes	characteristic
362	C₂	—	4	2	no	—
363	C₂	—	38	2	no	—
364	C₂	—	76	2	no	—
365	C₂	—	152	1	no	—
366	C₂	#11927053	1	1	yes	characteristic
367	C₂	#135×D₁₉	1	1	yes	characteristic
368	C₂	C₂×#10597360	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	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	#11926679	C₂
hypercenter	C₄×SD₁₆	D₁₉
hypocenter	C₁₉	#3105
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #11927081	C₂	semidirect
2. C₄×D₄×D₁₉	C₂	semidirect
3. #11926878	C₂	semidirect
4. #11926864	C₂	semidirect
5. #11926843	C₂	semidirect
6. #11926842	C₂	semidirect
7. #11926762	C₂	semidirect
8. #11926761	C₂	semidirect
9. #11926693	C₂	semidirect
11. C₄×#64527	C₂	semidirect
12. C₄×D₁₅₂	C₂	semidirect
13. C₄×#64525	C₂	semidirect
14. #11926595	C₂	semidirect
15. C₄×SD₁₆×C₁₉	C₂	semidirect
19. C₄×Q₈×C₁₉	C₂²	semidirect
21. #10597393	C₂²	semidirect
33. #10597336	C₂²	semidirect
38. C₄×D₇₆	C₂²	semidirect
41. C₁₉×#106	C₂²	semidirect
42. C₁₉×#103	C₂²	semidirect
44. C₄×C₈×C₁₉	C₂²	semidirect
45. #10597292	C₂²	semidirect
48. #10597278	C₂²	semidirect
51. #10597275	C₂²	semidirect
52. Dic₁₉⋊C₈	C₂²	semidirect
53. Dic₁₉⋊C₈	C₂²	semidirect
55. #10597266	C₂²	semidirect
56. #10597265	C₂²	semidirect
57. #10597264	C₂²	semidirect
58. C₄×C₁₉⋊C₈	C₂²	semidirect
189. C₄×SD₁₆	D₁₉	semidirect
212. C₄×Q₈	C₂×D₁₉	semidirect
228. #106	C₂×D₁₉	semidirect
232. #103	C₂×D₁₉	semidirect
242. C₄×C₈	C₂×D₁₉	semidirect
243. C₁₉	#3105	semidirect

Maximal subgroups

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

subgroup	index
#11927081	2
C₄×D₄×D₁₉	2
#11926878	2
#11926864	2
#11926843	2
#11926842	2
#11926762	2
#11926761	2
#11926693	2
#11926679	2
C₄×#64527	2
C₄×D₁₅₂	2
C₄×#64525	2
#11926595	2
C₄×SD₁₆×C₁₉	2
#3105	19