Subgroups — #14573180

Order 2432.

472 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597361	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597362	C₂	1	1	yes	maximal, characteristic
3	#11927119	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927023	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926769	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926767	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926761	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926759	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926753	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926751	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926747	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926569	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926544	C₂	1	1	yes	maximal, characteristic, complemented
14	#103×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#461	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	C₂×#64543	C₂²	1	1	yes	characteristic
19	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	#10597393	C₂²	1	1	yes	characteristic
24	#10597390	C₂²	1	1	yes	characteristic
25	C₂×#64528	C₂²	1	1	yes	characteristic
26	C₂×#64528	C₂²	1	1	yes	characteristic
27	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
28	C₂×#64526	C₂²	1	1	yes	characteristic
29	C₂×#64525	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊D₁₉	—	2	1	no	—
31	C₂×Dic₁₉⋊C₄	—	2	1	no	—
32	#10597362	—	2	4	no	—
33	#10597361	—	2	4	no	—
34	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
35	C₂×#64516	C₂²	1	1	yes	characteristic
36	C₂×#64515	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
38	#10597342	—	2	1	no	—
39	#10597342	—	2	1	no	—
40	#10597340	—	2	1	no	—
41	#10597340	—	2	1	no	—
42	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
43	#10597333	C₂²	1	1	yes	characteristic
44	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
45	#10597323	—	2	1	no	—
46	#10597321	C₂²	1	1	yes	characteristic
47	#10597318	C₂²	1	1	yes	characteristic
48	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
49	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₉×#103	C₂²	1	1	yes	characteristic
51	C₁₉×#103	C₂²	1	1	yes	characteristic
52	#10597292	C₂²	1	1	yes	characteristic
53	#10597292	C₂²	1	1	yes	characteristic
54	#10597278	C₂²	1	1	yes	characteristic
55	#10597273	C₂²	1	1	yes	characteristic
56	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
57	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
58	#10597267	C₂²	1	1	yes	characteristic
59	#10597266	C₂²	1	1	yes	characteristic
60	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
61	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂×C₂²⋊D₁₉	—	2	1	no	—
66	C₂²×Dic₁₉	—	2	1	no	—
67	C₂²×Dic₁₉	—	2	1	no	—
68	#64545	—	2	2	no	—
69	#64545	—	2	2	no	—
70	Q₈×D₁₉	—	2	2	no	—
71	Q₈×D₁₉	—	2	2	no	—
72	#64543	—	2	2	no	—
73	#64543	D₄	1	4	yes	—
74	C₂×D₇₆	—	2	1	no	—
75	C₂×D₇₆	C₂³	1	1	yes	characteristic
76	C₂×C₄×D₁₉	—	2	1	no	—
77	C₂×C₄×D₁₉	—	2	1	no	—
78	C₂×C₄×D₁₉	—	2	1	no	—
79	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
80	C₂×Dic₃₈	—	2	1	no	—
81	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
82	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
83	SD₁₆×C₁₉	—	2	2	no	—
84	SD₁₆×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
90	C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₁₉	—	2	1	no	—
93	#64528	—	2	2	no	—
94	#64528	—	2	2	no	—
95	#64526	—	2	2	no	—
96	#64525	—	2	2	no	—
97	(C₂×D₁₉)⋊C₄	—	2	1	no	—
98	(C₂×D₁₉)⋊C₄	—	2	1	no	—
99	(C₂×D₁₉)⋊C₄	—	2	1	no	—
100	(C₂×D₁₉)⋊C₄	—	2	1	no	—
101	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
102	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
103	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
104	Dic₁₉⋊C₄	—	2	1	no	—
105	Dic₁₉⋊C₄	—	2	1	no	—
106	Dic₁₉⋊C₄	—	2	1	no	—
107	Dic₁₉⋊C₄	—	2	1	no	—
108	Dic₁₉⋊C₄	—	2	1	no	—
109	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
110	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
111	C₄×Dic₁₉	—	2	1	no	—
112	C₄×Dic₁₉	—	2	1	no	—
113	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
115	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
116	Dic₇₆	—	2	2	no	—
117	#64516	—	2	2	no	—
118	#64515	—	2	2	no	—
119	C₈×D₁₉	—	2	2	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂²×D₁₉	—	2	1	no	—
122	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
123	Q₈×C₁₉	—	2	1	no	—
124	Q₈×C₁₉	—	2	1	no	—
125	Q₈×C₁₉	—	2	1	no	—
126	Q₈×C₁₉	—	2	1	no	—
127	D₄×C₁₉	—	2	1	no	—
128	D₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	8	1	no	—
133	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	C₂²⋊D₁₉	—	2	4	no	—
137	C₂×Dic₁₉	—	2	1	no	—
138	C₂×Dic₁₉	—	2	4	no	—
139	C₂×Dic₁₉	—	2	1	no	—
140	C₂×Dic₁₉	—	2	1	no	—
141	C₂×Dic₁₉	—	8	1	no	—
142	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
145	D₇₆	—	2	1	no	—
146	D₇₆	—	2	1	no	—
147	D₇₆	—	4	2	no	—
148	C₄×D₁₉	—	4	2	no	—
149	C₄×D₁₉	—	4	2	no	—
150	C₄×D₁₉	—	8	1	no	—
151	C₄×D₁₉	C₂×D₄	1	2	yes	—
152	C₄×D₁₉	#41	1	2	yes	—
153	Dic₃₈	—	2	1	no	—
154	Dic₃₈	—	2	1	no	—
155	Dic₃₈	—	2	1	no	—
156	Dic₃₈	—	4	2	no	—
157	Dic₃₈	C₂×D₄	1	2	yes	—
158	C₈×C₁₉	—	2	1	no	—
159	C₈×C₁₉	—	2	1	no	—
160	C₁₉⋊C₈	—	2	1	no	—
161	C₁₉⋊C₈	—	2	1	no	—
162	#3046	—	19	1	no	maximal, Sylow
163	C₂²×C₁₉	—	2	2	no	—
164	C₂²×C₁₉	—	4	1	no	—
165	C₂²×C₁₉	—	4	1	no	—
166	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×D₁₉	—	2	1	no	—
168	C₂×D₁₉	—	2	1	no	—
169	C₂×D₁₉	—	4	1	no	—
170	C₂×D₁₉	—	4	1	no	—
171	C₂×D₁₉	—	4	1	no	—
172	C₂×D₁₉	#121	1	2	yes	—
173	C₄×C₁₉	—	2	1	no	—
174	C₄×C₁₉	—	2	1	no	—
175	C₄×C₁₉	—	4	1	no	—
176	C₄×C₁₉	—	4	1	no	—
177	C₄×C₁₉	—	4	1	no	—
178	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
180	Dic₁₉	—	2	2	no	—
181	Dic₁₉	—	2	1	no	—
182	Dic₁₉	—	2	1	no	—
183	Dic₁₉	—	4	1	no	—
184	Dic₁₉	—	4	1	no	—
185	Dic₁₉	#121	1	2	yes	—
186	C₂×#137	—	19	1	no	—
187	C₂×#135	—	19	1	no	—
188	#536	—	19	1	no	—
189	#520	—	19	1	no	—
190	#464	—	19	1	no	—
191	#464	—	19	1	no	—
192	#463	—	19	1	no	—
193	#463	—	19	1	no	—
194	#462	—	19	1	no	—
195	#462	—	19	1	no	—
196	#461	—	19	1	no	—
197	#461	D₁₉	1	1	yes	characteristic, complemented
198	#424	—	19	1	no	—
199	#417	—	19	1	no	—
200	C₂×#103	—	19	1	no	—
201	C₂×C₁₉	—	4	2	no	—
202	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
203	C₂×C₁₉	#577	1	1	yes	characteristic
204	C₂×C₁₉	#578	1	1	yes	characteristic
205	D₁₉	—	2	2	no	—
206	D₁₉	—	8	1	no	—
207	C₂×#41	—	19	1	no	—
208	C₂×#41	—	19	1	no	—
209	C₂²×Q₈	—	19	1	no	—
210	#137	—	38	4	no	—
211	#135	—	38	4	no	—
212	C₂×Q₁₆	—	19	1	no	—
213	C₂×Q₁₆	—	19	1	no	—
214	C₂×Q₁₆	—	19	1	no	—
215	C₂×SD₁₆	—	19	1	no	—
216	C₂×SD₁₆	—	19	1	no	—
217	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
218	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
219	C₂×D₈	—	19	1	no	—
220	C₂×M₁₆	—	19	1	no	—
221	C₂²×C₈	—	19	1	no	—
222	C₄⋊Q₈	—	19	1	no	—
223	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
224	#124	—	19	1	no	—
225	#124	—	19	1	no	—
226	#123	—	38	1	no	—
227	#123	—	38	1	no	—
228	C₂²⋊Q₈	—	38	1	no	—
229	C₂²⋊Q₈	—	38	1	no	—
230	C₄×Q₈	—	19	1	no	—
231	C₄×Q₈	—	19	1	no	—
232	C₄×D₄	—	19	1	no	—
233	C₄×D₄	—	38	1	no	—
234	C₄×D₄	—	38	1	no	—
235	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
236	#117	—	19	1	no	—
237	#117	—	38	1	no	—
238	C₂×C₄⋊C₄	—	19	1	no	—
239	C₂×C₄⋊C₄	—	38	1	no	—
240	C₄⋊C₈	—	19	1	no	—
241	C₄⋊C₈	—	19	1	no	—
242	C₄⋊C₈	—	19	1	no	—
243	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
244	#103	—	19	1	no	—
245	#103	—	19	1	no	—
246	#103	—	19	1	no	—
247	#103	—	19	1	no	—
248	#103	C₂×D₁₉	1	1	yes	characteristic
249	#103	C₂×D₁₉	1	1	yes	characteristic
250	#102	—	19	1	no	—
251	#102	—	19	1	no	—
252	C₁₉	#3046	1	1	yes	characteristic, complemented, Sylow
253	#41	—	19	4	no	—
254	#41	—	38	2	no	—
255	#41	—	38	2	no	—
256	#41	—	38	2	no	—
257	C₂×Q₈	—	19	1	no	—
258	C₂×Q₈	—	19	1	no	—
259	C₂×Q₈	—	38	1	no	—
260	C₂×Q₈	—	38	2	no	—
261	C₂×Q₈	—	38	2	no	—
262	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
263	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
264	C₂×D₄	—	19	1	no	—
265	C₂×D₄	—	38	1	no	—
266	C₂×D₄	—	38	1	no	—
267	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	19	1	no	—
270	C₂²×C₄	—	38	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	Q₁₆	—	38	2	no	—
276	Q₁₆	—	38	2	no	—
277	Q₁₆	—	38	2	no	—
278	SD₁₆	—	2	2	no	—
279	SD₁₆	—	2	2	no	—
280	SD₁₆	—	38	2	no	—
281	SD₁₆	—	38	2	no	—
282	D₈	—	38	2	no	—
283	M₁₆	—	38	2	no	—
284	C₂×C₈	—	19	1	no	—
285	C₂×C₈	—	19	1	no	—
286	C₂×C₈	—	38	2	no	—
287	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
288	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	19	1	no	—
292	C₄⋊C₄	—	19	1	no	—
293	C₄⋊C₄	—	19	1	no	—
294	C₄⋊C₄	—	38	1	no	—
295	C₄⋊C₄	—	38	1	no	—
296	C₄⋊C₄	—	38	1	no	—
297	C₄⋊C₄	—	38	1	no	—
298	C₄⋊C₄	—	38	1	no	—
299	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	19	1	no	—
302	C₂²⋊C₄	—	19	1	no	—
303	C₂²⋊C₄	—	38	1	no	—
304	C₂²⋊C₄	—	38	1	no	—
305	C₂²⋊C₄	—	38	1	no	—
306	C₂²⋊C₄	—	38	1	no	—
307	C₂²⋊C₄	—	38	1	no	—
308	C₄²	—	19	1	no	—
309	C₄²	—	38	1	no	—
310	C₄²	—	38	1	no	—
311	C₄²	C₂²×D₁₉	1	1	yes	characteristic
312	C₂³	—	2	1	no	—
313	C₂³	—	19	1	no	—
314	C₂³	—	38	1	no	—
315	Q₈	—	2	1	no	—
316	Q₈	—	2	1	no	—
317	Q₈	—	2	1	no	—
318	Q₈	—	2	1	no	—
319	Q₈	—	19	2	no	—
320	Q₈	—	38	1	no	—
321	Q₈	—	38	1	no	—
322	Q₈	—	38	1	no	—
323	Q₈	—	76	2	no	—
324	D₄	—	2	1	no	—
325	D₄	—	38	4	no	—
326	D₄	—	38	1	no	—
327	D₄	—	38	1	no	—
328	D₄	—	76	2	no	—
329	D₄	D₄×D₁₉	1	2	yes	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	8	1	no	—
334	C₂×C₄	—	19	1	no	—
335	C₂×C₄	—	19	2	no	—
336	C₂×C₄	—	19	2	no	—
337	C₂×C₄	—	19	1	no	—
338	C₂×C₄	—	19	1	no	—
339	C₂×C₄	—	38	4	no	—
340	C₂×C₄	—	38	1	no	—
341	C₂×C₄	—	38	1	no	—
342	C₂×C₄	—	38	1	no	—
343	C₂×C₄	—	76	2	no	—
344	C₂×C₄	—	76	2	no	—
345	C₂×C₄	—	152	1	no	—
346	C₂×C₄	—	152	1	no	—
347	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
348	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
349	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	38	1	no	—
353	C₈	—	38	1	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	19	2	no	—
358	C₂²	—	38	1	no	—
359	C₂²	—	38	1	no	—
360	C₂²	—	76	1	no	—
361	C₂²	—	76	1	no	—
362	C₂²	—	76	1	no	—
363	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	19	2	no	—
370	C₄	—	38	1	no	—
371	C₄	—	38	1	no	—
372	C₄	—	38	2	no	—
373	C₄	—	76	1	no	—
374	C₄	—	76	1	no	—
375	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
376	C₄	#41×D₁₉	1	1	yes	characteristic
377	C₂	—	4	2	no	—
378	C₂	—	38	2	no	—
379	C₂	—	152	1	no	—
380	C₂	#121×D₁₉	1	1	yes	characteristic
381	C₂	#11927350	1	1	yes	characteristic
382	C₂	#11927360	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×#461	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#10597362	C₂
hypercenter	#461	D₁₉
hypocenter	C₁₉	#3046
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #461

Complements

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

N	H ≅ G/N	type
1. C₂×#10597361	C₂	semidirect
3. #11927119	C₂	semidirect
4. #11927023	C₂	semidirect
5. #11926769	C₂	semidirect
6. #11926767	C₂	semidirect
7. #11926761	C₂	semidirect
8. #11926759	C₂	semidirect
9. #11926753	C₂	semidirect
10. #11926751	C₂	semidirect
11. #11926747	C₂	semidirect
12. #11926569	C₂	semidirect
13. #11926544	C₂	semidirect
14. #103×D₁₉	C₂	semidirect
15. C₁₉×#461	C₂	semidirect
197. #461	D₁₉	semidirect
252. C₁₉	#3046	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597361	2
C₂×#10597362	2
#11927119	2
#11927023	2
#11926769	2
#11926767	2
#11926761	2
#11926759	2
#11926753	2
#11926751	2
#11926747	2
#11926569	2
#11926544	2
#103×D₁₉	2
C₁₉×#461	2
#3046	19