Subgroups — #18085351

Order 4864.

622 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926895	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926891	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926891	C₂	1	1	yes	maximal, characteristic
4	#14564596	C₂	1	1	yes	maximal, characteristic, complemented
5	#14564441	C₂	1	1	yes	maximal, characteristic
6	#14564437	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	C₂×#10597320	C₂²	1	1	yes	characteristic
11	#11926895	—	2	2	no	—
12	#11926895	—	2	2	no	—
13	#11926891	—	2	2	no	—
14	#11926891	—	2	2	no	—
15	#11926891	—	2	2	no	—
16	#11926891	—	2	2	no	—
17	C₂×#10597273	—	2	2	no	—
18	C₂×#10597273	—	2	2	no	—
19	C₂×#10597278	—	2	2	no	—
20	C₂×#10597278	—	2	2	no	—
21	C₂×#10597278	—	2	2	no	—
22	#11926414	C₂²	1	1	yes	characteristic
23	#11926307	—	2	2	no	—
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×D₇₆	—	2	1	no	—
28	C₂²×D₇₆	—	2	1	no	—
29	C₂²×D₇₆	—	2	1	no	—
30	C₂²×Dic₃₈	—	2	1	no	—
31	C₂²×Dic₃₈	—	2	1	no	—
32	C₂²×C₈×C₁₉	D₄	1	2	yes	—
33	C₂²×C₈×C₁₉	D₄	1	2	yes	—
34	C₂²×C₈×C₁₉	D₄	1	2	yes	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	—	2	1	no	—
40	C₂×C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	—	2	1	no	—
43	#10597320	—	2	1	no	—
44	#10597320	—	2	1	no	—
45	#10597320	—	2	1	no	—
46	#10597320	D₄	1	2	yes	—
47	#10597315	—	2	1	no	—
48	#10597315	—	2	1	no	—
49	#10597315	—	2	1	no	—
50	#10597315	—	2	1	no	—
51	#10597315	—	2	1	no	—
52	#10597315	—	2	1	no	—
53	#10597315	D₄	1	2	yes	—
54	#10597315	D₄	1	2	yes	—
55	C₄×C₈×C₁₉	—	2	1	no	—
56	C₄×C₈×C₁₉	—	2	1	no	—
57	C₄×C₈×C₁₉	—	2	1	no	—
58	C₄×C₈×C₁₉	—	2	1	no	—
59	C₄×C₈×C₁₉	—	2	1	no	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	#10597278	—	2	8	no	—
62	#10597278	—	2	8	no	—
63	#10597278	—	4	4	no	—
64	#10597273	—	2	8	no	—
65	#10597273	—	4	4	no	—
66	C₂³×D₁₉	—	4	1	no	—
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×Dic₁₉	—	4	1	no	—
71	C₂²×Dic₁₉	—	4	1	no	—
72	C₂²×Dic₁₉	—	4	1	no	—
73	C₂×D₇₆	—	2	2	no	—
74	C₂×D₇₆	—	2	2	no	—
75	C₂×D₇₆	—	2	2	no	—
76	C₂×D₇₆	—	4	2	no	—
77	C₂×D₇₆	—	4	2	no	—
78	C₂×D₇₆	—	4	2	no	—
79	C₂×D₇₆	—	4	2	no	—
80	C₂×D₇₆	—	4	2	no	—
81	C₂×D₇₆	—	4	2	no	—
82	C₂×D₇₆	—	4	1	no	—
83	C₂×D₇₆	—	4	1	no	—
84	C₂×D₇₆	—	4	1	no	—
85	C₂×Dic₃₈	—	2	2	no	—
86	C₂×Dic₃₈	—	2	2	no	—
87	C₂×Dic₃₈	—	4	2	no	—
88	C₂×Dic₃₈	—	4	2	no	—
89	C₂×Dic₃₈	—	4	2	no	—
90	C₂×Dic₃₈	—	4	2	no	—
91	C₂×Dic₃₈	—	4	1	no	—
92	C₂×Dic₃₈	—	4	1	no	—
93	C₂×C₈×C₁₉	—	2	2	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	2	2	no	—
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₁₉	#41	1	1	yes	characteristic
106	C₄⋊Dic₁₉	—	2	2	no	—
107	C₄⋊Dic₁₉	—	2	2	no	—
108	C₄⋊Dic₁₉	—	2	2	no	—
109	C₄⋊Dic₁₉	—	2	2	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	—	4	1	no	—
113	C₄⋊Dic₁₉	—	4	1	no	—
114	C₄⋊Dic₁₉	—	4	2	no	—
115	C₄⋊Dic₁₉	—	4	2	no	—
116	C₄⋊Dic₁₉	—	4	2	no	—
117	#10311	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	#127	1	1	yes	characteristic
119	C₂²×D₁₉	—	4	2	no	—
120	C₂²×D₁₉	—	8	1	no	—
121	C₂²×D₁₉	—	8	1	no	—
122	C₂²×D₁₉	—	8	1	no	—
123	C₂²×D₁₉	—	8	1	no	—
124	C₂²×D₁₉	—	8	1	no	—
125	C₂²×D₁₉	—	8	1	no	—
126	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
128	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
129	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
130	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#135	1	2	yes	—
133	C₂×C₄×C₁₉	#135	1	2	yes	—
134	C₂×C₄×C₁₉	#135	1	2	yes	—
135	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
136	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
137	C₂×C₄×C₁₉	#137	1	2	yes	—
138	C₂×Dic₁₉	—	4	2	no	—
139	C₂×Dic₁₉	—	4	2	no	—
140	C₂×Dic₁₉	—	8	1	no	—
141	C₂×Dic₁₉	—	8	1	no	—
142	C₂×Dic₁₉	—	8	1	no	—
143	C₂×Dic₁₉	—	8	1	no	—
144	C₂×Dic₁₉	—	8	1	no	—
145	C₂×Dic₁₉	—	8	1	no	—
146	C₂×Dic₁₉	—	8	1	no	—
147	D₇₆	—	4	4	no	—
148	D₇₆	—	4	4	no	—
149	D₇₆	—	4	4	no	—
150	D₇₆	—	8	2	no	—
151	D₇₆	—	8	2	no	—
152	D₇₆	—	8	2	no	—
153	Dic₃₈	—	4	4	no	—
154	Dic₃₈	—	4	4	no	—
155	Dic₃₈	—	8	2	no	—
156	Dic₃₈	—	8	2	no	—
157	C₈×C₁₉	—	4	2	no	—
158	C₈×C₁₉	—	4	2	no	—
159	C₈×C₁₉	—	4	2	no	—
160	C₂×#487	—	19	1	no	—
161	C₂×#486	—	19	1	no	—
162	C₂×#486	—	19	1	no	—
163	#1990	—	19	1	no	—
164	#1957	—	19	1	no	—
165	#1956	—	19	1	no	—
166	#1273	D₁₉	1	1	yes	characteristic, complemented
167	C₂²×C₁₉	#392	1	1	yes	characteristic
168	C₂²×C₁₉	#495	1	1	yes	characteristic
169	C₂²×C₁₉	#495	1	1	yes	characteristic
170	C₂²×C₁₉	#495	1	1	yes	characteristic
171	C₂²×C₁₉	#496	1	1	yes	characteristic
172	C₂²×C₁₉	#496	1	1	yes	characteristic
173	C₂²×C₁₉	#497	1	1	yes	characteristic
174	C₂×D₁₉	—	8	2	no	—
175	C₂×D₁₉	—	8	2	no	—
176	C₂×D₁₉	—	8	2	no	—
177	C₂×D₁₉	—	16	1	no	—
178	C₂×D₁₉	—	16	1	no	—
179	C₂×D₁₉	—	16	1	no	—
180	C₂×D₁₉	—	16	1	no	—
181	C₄×C₁₉	#449	1	2	yes	—
182	C₄×C₁₉	#449	1	2	yes	—
183	C₄×C₁₉	#452	1	2	yes	—
184	C₄×C₁₉	#463	1	2	yes	—
185	C₄×C₁₉	#463	1	2	yes	—
186	C₄×C₁₉	#464	1	2	yes	—
187	Dic₁₉	—	8	2	no	—
188	Dic₁₉	—	8	2	no	—
189	Dic₁₉	—	16	1	no	—
190	C₂×C₄⋊Q₈	—	19	1	no	—
191	C₂×C₄⋊Q₈	—	19	1	no	—
192	C₂×#127	—	19	1	no	—
193	#487	—	38	2	no	—
194	#487	—	38	2	no	—
195	#486	—	38	2	no	—
196	#486	—	38	2	no	—
197	#486	—	38	2	no	—
198	#486	—	38	2	no	—
199	C₂×#103	—	38	2	no	—
200	C₂×#103	—	38	2	no	—
201	C₂×#102	—	38	2	no	—
202	C₂×#102	—	38	2	no	—
203	C₂×#102	—	38	2	no	—
204	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
207	#384	—	19	1	no	—
208	#340	—	38	2	no	—
209	C₂×C₁₉	#1711	1	1	yes	characteristic
210	C₂×C₁₉	#1717	1	1	yes	characteristic
211	C₂×C₁₉	#1719	1	1	yes	characteristic
212	C₂×C₁₉	#1720	1	1	yes	characteristic
213	C₂×C₁₉	#2012	1	1	yes	characteristic
214	C₂×C₁₉	#2012	1	1	yes	characteristic
215	C₂×C₁₉	#2015	1	1	yes	characteristic
216	D₁₉	—	16	2	no	—
217	C₂²×Q₈	—	38	1	no	—
218	C₂²×Q₈	—	38	1	no	—
219	C₂²×D₄	—	38	1	no	—
220	C₂²×D₄	—	38	1	no	—
221	C₂²×D₄	—	38	1	no	—
222	C₂²×C₈	D₇₆	1	2	yes	—
223	C₂²×C₈	D₇₆	1	2	yes	—
224	C₂²×C₈	D₇₆	1	2	yes	—
225	C₄⋊Q₈	—	19	2	no	—
226	C₄⋊Q₈	—	19	2	no	—
227	C₄⋊Q₈	—	38	1	no	—
228	C₄⋊Q₈	—	38	1	no	—
229	C₄⋊Q₈	—	38	1	no	—
230	C₄⋊Q₈	—	38	1	no	—
231	C₄⋊Q₈	—	38	1	no	—
232	C₄⋊Q₈	—	38	1	no	—
233	#127	—	19	2	no	—
234	#127	—	38	1	no	—
235	#127	—	38	1	no	—
236	#127	—	38	1	no	—
237	C₂×C₄⋊C₄	—	38	1	no	—
238	C₂×C₄⋊C₄	—	38	1	no	—
239	C₂×C₄⋊C₄	—	38	1	no	—
240	C₂×C₄⋊C₄	—	38	1	no	—
241	C₂×C₄⋊C₄	—	38	1	no	—
242	C₂×C₄⋊C₄	—	38	1	no	—
243	C₂×C₄⋊C₄	—	38	1	no	—
244	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
245	#103	—	38	8	no	—
246	#103	—	76	4	no	—
247	#102	—	38	8	no	—
248	#102	—	38	8	no	—
249	#102	—	76	4	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	2	1	no	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₁₉	#10311	1	1	yes	characteristic, complemented, Sylow
257	C₂⁴	—	76	1	no	—
258	C₂×Q₈	—	38	2	no	—
259	C₂×Q₈	—	38	2	no	—
260	C₂×Q₈	—	76	1	no	—
261	C₂×Q₈	—	76	1	no	—
262	C₂×Q₈	—	76	2	no	—
263	C₂×Q₈	—	76	2	no	—
264	C₂×Q₈	—	76	2	no	—
265	C₂×Q₈	—	76	2	no	—
266	C₂×D₄	—	38	2	no	—
267	C₂×D₄	—	38	2	no	—
268	C₂×D₄	—	38	2	no	—
269	C₂×D₄	—	76	1	no	—
270	C₂×D₄	—	76	1	no	—
271	C₂×D₄	—	76	1	no	—
272	C₂×D₄	—	76	2	no	—
273	C₂×D₄	—	76	2	no	—
274	C₂×D₄	—	76	2	no	—
275	C₂×D₄	—	76	2	no	—
276	C₂×D₄	—	76	2	no	—
277	C₂×D₄	—	76	2	no	—
278	C₂²×C₄	—	76	1	no	—
279	C₂²×C₄	—	76	1	no	—
280	C₂²×C₄	—	76	1	no	—
281	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₄⋊C₄	—	38	2	no	—
294	C₄⋊C₄	—	38	2	no	—
295	C₄⋊C₄	—	38	2	no	—
296	C₄⋊C₄	—	38	2	no	—
297	C₄⋊C₄	—	76	1	no	—
298	C₄⋊C₄	—	76	1	no	—
299	C₄⋊C₄	—	76	1	no	—
300	C₄⋊C₄	—	76	1	no	—
301	C₄⋊C₄	—	76	2	no	—
302	C₄⋊C₄	—	76	2	no	—
303	C₄⋊C₄	—	76	2	no	—
304	C₄²	D₄×D₁₉	1	1	yes	characteristic
305	C₄²	D₄×D₁₉	1	1	yes	characteristic
306	C₄²	D₄×D₁₉	1	1	yes	characteristic
307	C₄²	#64545	1	1	yes	characteristic
308	C₂³	—	76	2	no	—
309	C₂³	—	152	1	no	—
310	C₂³	—	152	1	no	—
311	C₂³	—	152	1	no	—
312	C₂³	—	152	1	no	—
313	C₂³	—	152	1	no	—
314	C₂³	—	152	1	no	—
315	C₂³	#10597320	1	1	yes	characteristic
316	Q₈	—	76	4	no	—
317	Q₈	—	76	4	no	—
318	Q₈	—	152	2	no	—
319	Q₈	—	152	2	no	—
320	D₄	—	76	4	no	—
321	D₄	—	76	4	no	—
322	D₄	—	76	4	no	—
323	D₄	—	152	2	no	—
324	D₄	—	152	2	no	—
325	D₄	—	152	2	no	—
326	C₂×C₄	—	76	2	no	—
327	C₂×C₄	—	76	2	no	—
328	C₂×C₄	—	152	1	no	—
329	C₂×C₄	—	152	1	no	—
330	C₂×C₄	—	152	1	no	—
331	C₂×C₄	—	152	1	no	—
332	C₂×C₄	—	152	1	no	—
333	C₂×C₄	—	152	1	no	—
334	C₂×C₄	—	152	1	no	—
335	C₂×C₄	#10597328	1	1	yes	characteristic
336	C₂×C₄	#10597328	1	1	yes	characteristic
337	C₂×C₄	#10597328	1	1	yes	characteristic
338	C₂×C₄	#10597341	1	1	yes	characteristic
339	C₂×C₄	#10597341	1	1	yes	characteristic
340	C₂×C₄	#10597341	1	1	yes	characteristic
341	C₂×C₄	#10597350	1	2	yes	—
342	C₂×C₄	#10597350	1	2	yes	—
343	C₂×C₄	#10597350	1	2	yes	—
344	C₂×C₄	#10597354	1	2	yes	—
345	C₂×C₄	#10597354	1	2	yes	—
346	C₂×C₄	#10597355	1	2	yes	—
347	C₈	—	4	2	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₂²	—	304	1	no	—
351	C₂²	—	304	1	no	—
352	C₂²	—	304	1	no	—
353	C₂²	—	304	1	no	—
354	C₂²	—	152	2	no	—
355	C₂²	—	152	2	no	—
356	C₂²	—	152	2	no	—
357	C₂²	#11926454	1	1	yes	characteristic
358	C₂²	#11926928	1	1	yes	characteristic
359	C₂²	#11926928	1	1	yes	characteristic
360	C₂²	#11926928	1	1	yes	characteristic
361	C₂²	#11926933	1	1	yes	characteristic
362	C₂²	#11926933	1	1	yes	characteristic
363	C₂²	#11926938	1	1	yes	characteristic
364	C₄	—	304	1	no	—
365	C₄	—	152	2	no	—
366	C₄	—	152	2	no	—
367	C₄	#11926691	1	2	yes	—
368	C₄	#11926691	1	2	yes	—
369	C₄	#11926708	1	2	yes	—
370	C₄	#11926760	1	2	yes	—
371	C₄	#11926760	1	2	yes	—
372	C₄	#11926767	1	2	yes	—
373	C₂	—	304	2	no	—
374	C₂	#14563247	1	1	yes	characteristic
375	C₂	#14563274	1	1	yes	characteristic
376	C₂	#14563288	1	1	yes	characteristic
377	C₂	#14563295	1	1	yes	characteristic
378	C₂	#14564715	1	1	yes	characteristic
379	C₂	#14564715	1	1	yes	characteristic
380	C₂	#14564732	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597320
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1273	C₂
socle	C₂³×C₁₉	#127
prime radical	C₂×#10597320	C₂²
hypercenter	#1273	D₁₉
hypocenter	C₁₉	#10311
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

Complements

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

N	H ≅ G/N	type
1. C₂×#11926895	C₂	semidirect
4. #14564596	C₂	semidirect
6. #14564437	C₂	semidirect
7. C₁₉×#1273	C₂	semidirect
166. #1273	D₁₉	semidirect
256. C₁₉	#10311	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926895	2
C₂×#11926891	2
#14564596	2
#14564441	2
#14564437	2
C₁₉×#1273	2
#10311	19