Subgroups — #18079238

Order 4864.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14574576	C₂	1	1	yes	maximal, characteristic
2	#14564616	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562303	C₂	1	1	yes	maximal, characteristic
4	#14562198	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561493	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561464	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2328	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926916	C₄	1	2	yes	complemented
10	#11926890	C₄	1	2	yes	complemented
11	#11926741	—	2	2	no	—
12	#11926695	—	2	2	no	—
13	#11926597	C₂²	1	1	yes	characteristic
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926568	C₂²	1	1	yes	characteristic
16	#11926304	—	2	1	no	—
17	#11926304	—	2	1	no	—
18	#11926288	—	2	2	no	—
19	#11926280	—	2	2	no	—
20	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₉	—	2	1	no	—
22	C₁₉×#390	—	2	1	no	—
23	C₁₉×#386	—	2	2	no	—
24	C₁₉×#386	—	2	2	no	—
25	C₁₉×#382	C₂²	1	1	yes	characteristic
26	C₁₉×#376	C₂²	1	1	yes	characteristic
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	2	1	no	—
29	C₂²×D₄×C₁₉	D₄	1	2	yes	—
30	C₂³×C₄×C₁₉	—	2	2	no	—
31	C₁₉×#127	—	2	1	no	—
32	C₁₉×#127	—	2	1	no	—
33	C₁₉×#127	C₂×C₄	1	2	yes	—
34	C₁₉×#127	D₄	1	2	yes	—
35	C₄×D₄×C₁₉	—	4	2	no	—
36	C₄×D₄×C₁₉	—	4	2	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
41	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×#64526	—	2	4	no	—
45	#10597372	—	2	1	no	—
46	#10597370	—	2	1	no	—
47	#10597370	—	2	1	no	—
48	C₂×#64520	—	2	1	no	—
49	#10597316	—	2	1	no	—
50	#10597315	C₂×C₄	1	1	yes	characteristic, complemented
51	#10597315	C₂×C₄	1	1	yes	characteristic, complemented
52	C₄×Dic₃₈	—	2	1	no	—
53	C₄×Dic₃₈	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉×#95	D₄	1	2	yes	—
58	#10597289	—	2	4	no	—
59	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄×C₁₉⋊C₈	—	2	1	no	—
66	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	complemented
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	—	2	2	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	4	1	no	—
75	C₂×D₄×C₁₉	—	4	1	no	—
76	C₂×D₄×C₁₉	—	4	1	no	—
77	C₂×D₄×C₁₉	—	8	2	no	—
78	C₂×D₄×C₁₉	—	8	2	no	—
79	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	2	1	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	4	4	no	—
84	C₂²×C₄×C₁₉	—	8	2	no	—
85	C₂²×C₄×C₁₉	—	8	2	no	—
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂×Dic₃₈	—	2	1	no	—
90	C₂×Dic₃₈	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₂²⋊C₄×C₁₉	—	4	4	no	—
94	C₂²⋊C₄×C₁₉	—	8	2	no	—
95	C₂²⋊C₄×C₁₉	—	8	2	no	—
96	C₄²×C₁₉	—	2	1	no	—
97	C₄²×C₁₉	—	2	1	no	—
98	C₄²×C₁₉	—	2	1	no	—
99	C₄²×C₁₉	SD₁₆	1	2	yes	complemented
100	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	#41	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	C₂²⋊Dic₁₉	—	4	1	no	—
105	#64526	—	8	4	no	—
106	C₄⋊Dic₁₉	—	2	1	no	—
107	C₄⋊Dic₁₉	—	2	1	no	—
108	C₄⋊Dic₁₉	—	2	1	no	—
109	C₄⋊Dic₁₉	—	2	1	no	—
110	Dic₁₉⋊C₄	—	4	1	no	—
111	Dic₁₉⋊C₄	—	4	1	no	—
112	C₄×Dic₁₉	—	4	1	no	—
113	#64520	—	4	1	no	—
114	#64520	—	4	1	no	—
115	C₂×C₁₉⋊C₈	—	2	2	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	#9295	—	19	1	no	maximal, Sylow
119	C₂³×C₁₉	—	2	4	no	—
120	C₂³×C₁₉	—	4	2	no	—
121	C₂³×C₁₉	—	4	2	no	—
122	C₂³×C₁₉	—	4	2	no	—
123	C₂³×C₁₉	—	4	2	no	—
124	C₂³×C₁₉	—	4	2	no	—
125	C₂³×C₁₉	—	4	2	no	—
126	C₂³×C₁₉	#120	1	1	yes	characteristic
127	D₄×C₁₉	—	4	4	no	—
128	D₄×C₁₉	—	4	2	no	—
129	D₄×C₁₉	—	4	2	no	—
130	D₄×C₁₉	—	4	2	no	—
131	D₄×C₁₉	—	4	2	no	—
132	D₄×C₁₉	—	8	2	no	—
133	D₄×C₁₉	—	8	2	no	—
134	D₄×C₁₉	—	8	2	no	—
135	C₂×C₄×C₁₉	—	2	2	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	2	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	8	8	no	—
147	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
157	C₂×Dic₁₉	—	4	1	no	—
158	C₂×Dic₁₉	—	4	1	no	—
159	Dic₃₈	—	4	2	no	—
160	Dic₃₈	—	8	1	no	—
161	C₁₉⋊C₈	—	4	2	no	—
162	C₁₉⋊C₈	—	8	1	no	—
163	C₁₉⋊C₈	—	8	1	no	—
164	#3208	—	19	1	no	—
165	#2328	D₁₉	1	1	yes	characteristic
166	#1995	—	19	1	no	—
167	#1545	—	19	1	no	—
168	#1518	—	19	1	no	—
169	#1286	—	19	1	no	—
170	#1274	—	19	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	—	4	4	no	—
174	C₂²×C₁₉	—	4	4	no	—
175	C₂²×C₁₉	—	4	4	no	—
176	C₂²×C₁₉	—	8	2	no	—
177	C₂²×C₁₉	—	8	2	no	—
178	C₂²×C₁₉	—	8	2	no	—
179	C₂²×C₁₉	—	8	2	no	—
180	C₂²×C₁₉	#386	1	1	yes	characteristic
181	C₂²×C₁₉	#450	1	1	yes	characteristic
182	C₂²×C₁₉	#452	1	1	yes	characteristic
183	C₄×C₁₉	—	2	1	no	—
184	C₄×C₁₉	—	2	1	no	—
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	4	2	no	—
188	C₄×C₁₉	—	8	1	no	—
189	C₄×C₁₉	—	8	2	no	—
190	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
191	C₄×C₁₉	#440	1	1	yes	characteristic
192	C₄×C₁₉	#461	1	1	yes	characteristic
193	C₄×C₁₉	#463	1	1	yes	characteristic
194	Dic₁₉	—	8	1	no	—
195	Dic₁₉	—	8	1	no	—
196	#533	—	19	1	no	—
197	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
198	C₂×C₄×D₄	—	2	1	no	—
199	#492	—	19	2	no	—
200	#486	—	19	2	no	—
201	#460	—	38	2	no	—
202	#450	—	38	2	no	—
203	#431	—	19	1	no	—
204	#431	—	19	1	no	—
205	#423	—	19	1	no	—
206	#390	—	2	1	no	—
207	#386	—	2	2	no	—
208	#386	—	2	2	no	—
209	#382	C₂×D₁₉	1	1	yes	characteristic
210	#376	C₂×D₁₉	1	1	yes	characteristic
211	#339	—	38	1	no	—
212	#339	—	38	1	no	—
213	#331	—	38	2	no	—
214	#328	—	38	2	no	—
215	C₂×C₁₉	—	2	1	no	—
216	C₂×C₁₉	—	2	1	no	—
217	C₂×C₁₉	—	8	4	no	—
218	C₂×C₁₉	#1877	1	1	yes	characteristic
219	C₂×C₁₉	#1904	1	1	yes	characteristic
220	C₂×C₁₉	#1911	1	1	yes	characteristic
221	C₂²×D₄	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
224	C₂³×C₄	—	2	2	no	—
225	C₂×SD₁₆	—	38	4	no	—
226	C₂×M₁₆	—	38	1	no	—
227	C₄⋊Q₈	—	19	1	no	—
228	C₄⋊Q₈	—	19	1	no	—
229	#127	—	2	1	no	—
230	#127	—	2	1	no	—
231	#127	C₄×D₁₉	1	2	yes	—
232	#127	D₇₆	1	2	yes	—
233	#125	—	38	1	no	—
234	C₂²⋊Q₈	—	38	1	no	—
235	C₂²⋊Q₈	—	38	1	no	—
236	C₄×Q₈	—	38	1	no	—
237	C₄×Q₈	—	38	1	no	—
238	C₄×D₄	—	4	2	no	—
239	C₄×D₄	—	4	2	no	—
240	#117	—	38	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
248	C₄⋊C₈	—	38	1	no	—
249	C₄⋊C₈	—	38	1	no	—
250	C₄⋊C₈	—	38	1	no	—
251	C₄⋊C₈	—	38	1	no	—
252	#102	—	38	4	no	—
253	C₂²⋊C₈	—	38	1	no	—
254	C₂²⋊C₈	—	38	1	no	—
255	C₄×C₈	—	19	2	no	—
256	C₄×C₈	—	38	1	no	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	#95	—	2	1	no	—
260	#95	C₂²⋊D₁₉	1	2	yes	—
261	C₁₉	#9295	1	1	yes	characteristic, complemented, Sylow
262	C₂⁴	—	2	2	no	—
263	C₂×Q₈	—	38	1	no	—
264	C₂×Q₈	—	38	1	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂×D₄	—	4	1	no	—
274	C₂×D₄	—	8	2	no	—
275	C₂×D₄	—	8	2	no	—
276	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	8	2	no	—
282	C₂²×C₄	—	8	2	no	—
283	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
286	SD₁₆	—	152	4	no	—
287	M₁₆	—	76	1	no	—
288	M₁₆	—	76	1	no	—
289	C₂×C₈	—	38	2	no	—
290	C₂×C₈	—	76	1	no	—
291	C₂×C₈	—	76	1	no	—
292	C₄⋊C₄	—	4	1	no	—
293	C₄⋊C₄	—	4	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	—	76	1	no	—
299	C₄⋊C₄	—	76	1	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	8	2	no	—
302	C₂²⋊C₄	—	8	2	no	—
303	C₂²⋊C₄	—	76	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	76	1	no	—
308	C₄²	#64526	1	2	yes	complemented
309	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
310	C₄²	C₂×D₇₆	1	1	yes	characteristic
311	C₄²	#64541	1	1	yes	characteristic
312	C₄²	#64541	1	1	yes	characteristic
313	C₂³	—	2	4	no	—
314	C₂³	—	4	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	#10597399	1	1	yes	characteristic
321	Q₈	—	76	2	no	—
322	Q₈	—	152	1	no	—
323	D₄	—	4	4	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	8	8	no	—
343	C₂×C₄	—	76	1	no	—
344	C₂×C₄	—	76	1	no	—
345	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
347	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
348	C₂×C₄	#10597375	1	1	yes	characteristic
349	C₂×C₄	#10597376	1	1	yes	characteristic
350	C₂×C₄	#10597376	1	1	yes	characteristic
351	C₂×C₄	#10597378	1	1	yes	characteristic
352	C₂×C₄	C₂×#64526	1	1	yes	characteristic
353	C₂×C₄	#10597396	1	1	yes	characteristic
354	C₂×C₄	#10597397	1	1	yes	characteristic
355	C₈	—	76	2	no	—
356	C₈	—	152	1	no	—
357	C₈	—	152	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	#11926423	1	1	yes	characteristic
368	C₂²	#11926695	1	1	yes	characteristic
369	C₂²	#11926706	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	4	2	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	152	1	no	—
378	C₄	—	152	1	no	—
379	C₄	C₄×#64526	1	1	yes	characteristic
380	C₄	#11926644	1	1	yes	characteristic
381	C₄	#11926749	1	1	yes	characteristic
382	C₄	#11926759	1	1	yes	characteristic
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	—	8	4	no	—
386	C₂	#14563969	1	1	yes	characteristic
387	C₂	#14564122	1	1	yes	characteristic
388	C₂	#14564167	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2328	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2328	D₁₉
hypocenter	C₁₉	#9295
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2328

Complements

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

N	H ≅ G/N	type
2. #14564616	C₂	semidirect
4. #14562198	C₂	semidirect
5. #14561493	C₂	semidirect
6. #14561464	C₂	semidirect
9. #11926916	C₄	semidirect
10. #11926890	C₄	semidirect
50. #10597315	C₂×C₄	semidirect
51. #10597315	C₂×C₄	semidirect
66. C₄×C₁₉⋊C₈	C₂×C₄	semidirect
99. C₄²×C₁₉	SD₁₆	semidirect
261. C₁₉	#9295	semidirect
308. C₄²	#64526	semidirect

Maximal subgroups

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

subgroup	index
#14574576	2
#14564616	2
#14562303	2
#14562198	2
#14561493	2
#14561464	2
C₁₉×#2328	2
#9295	19