Subgroups — #18078441

Order 4864.

516 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572301	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562303	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926288	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562022	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561530	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561509	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3038	C₂	1	1	yes	maximal, characteristic
8	#11926605	—	2	2	no	—
9	#11926601	—	2	1	no	—
10	#11926597	—	2	1	no	—
11	#11926597	C₂²	1	1	yes	characteristic
12	#11926568	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	#11926511	—	2	1	no	—
16	#11926500	—	2	1	no	—
17	#11926288	—	2	1	no	—
18	#11926288	—	2	1	no	—
19	#11926288	—	2	2	no	—
20	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
21	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
22	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#460	—	2	1	no	—
26	C₁₉×#460	C₄	1	2	yes	—
27	C₁₉×#459	—	2	1	no	—
28	C₁₉×#459	C₄	1	2	yes	—
29	C₁₉×#423	C₂²	1	1	yes	characteristic
30	C₁₉×#418	—	2	1	no	—
31	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	—	2	1	no	—
35	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
36	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
37	C₂×SD₁₆×C₁₉	—	2	2	no	—
38	C₂×D₈×C₁₉	—	2	2	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	C₂×C₄	1	2	yes	—
44	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
45	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	—	2	1	no	—
48	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₉	—	2	1	no	—
53	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
54	C₂×#64520	—	2	1	no	—
55	C₂²×C₁₉⋊C₈	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₉×#102	—	2	2	no	—
60	C₁₉×#102	—	2	2	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
70	C₄⋊(C₁₉⋊C₈)	D₄	1	1	yes	characteristic
71	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
72	#10597260	—	2	2	no	—
73	C₄×C₁₉⋊C₈	—	2	2	no	—
74	C₄×C₁₉⋊C₈	—	2	1	no	—
75	C₂⁴×C₁₉	—	4	1	no	—
76	#41×C₁₉	—	2	1	no	—
77	#41×C₁₉	—	2	1	no	—
78	#41×C₁₉	—	2	1	no	—
79	#41×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	1	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	1	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	1	no	—
92	C₂×D₄×C₁₉	—	8	1	no	—
93	C₂×D₄×C₁₉	—	8	1	no	—
94	C₂×D₄×C₁₉	—	8	2	no	—
95	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	SD₁₆×C₁₉	—	4	4	no	—
103	D₈×C₁₉	—	4	4	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	1	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₉	—	2	1	no	—
112	C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₄²×C₁₉	—	2	1	no	—
115	C₄²×C₁₉	—	2	1	no	—
116	C₄²×C₁₉	—	2	1	no	—
117	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	#64520	—	4	1	no	—
122	#64520	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	2	1	no	—
124	C₂×C₁₉⋊C₈	—	2	2	no	—
125	C₂×C₁₉⋊C₈	—	2	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	8	1	no	—
131	#9174	—	19	1	no	maximal, Sylow
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	4	2	no	—
134	C₂³×C₁₉	—	8	2	no	—
135	C₂³×C₁₉	—	8	2	no	—
136	C₂³×C₁₉	—	8	1	no	—
137	C₂³×C₁₉	—	8	1	no	—
138	C₂³×C₁₉	#123	1	1	yes	characteristic
139	Q₈×C₁₉	—	2	1	no	—
140	Q₈×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	2	1	no	—
142	D₄×C₁₉	—	2	1	no	—
143	D₄×C₁₉	—	4	1	no	—
144	D₄×C₁₉	—	4	1	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	4	2	no	—
147	D₄×C₁₉	—	8	2	no	—
148	D₄×C₁₉	—	8	2	no	—
149	D₄×C₁₉	—	8	2	no	—
150	D₄×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	2	1	no	—
157	C₂×C₄×C₁₉	—	2	1	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	4	1	no	—
160	C₂×C₄×C₁₉	—	4	1	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	1	no	—
164	C₂×C₄×C₁₉	—	8	1	no	—
165	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
173	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₈×C₁₉	—	4	2	no	—
176	C₁₉⋊C₈	—	4	1	no	—
177	C₁₉⋊C₈	—	4	1	no	—
178	C₁₉⋊C₈	—	4	2	no	—
179	C₁₉⋊C₈	—	8	1	no	—
180	C₁₉⋊C₈	—	8	1	no	—
181	#3038	D₁₉	1	1	yes	characteristic
182	#2925	—	19	1	no	—
183	#1545	—	19	1	no	—
184	C₂×#331	—	19	1	no	—
185	#1477	—	19	1	no	—
186	#1301	—	19	1	no	—
187	#1292	—	19	1	no	—
188	C₂²×C₁₉	—	2	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	—	16	2	no	—
197	C₂²×C₁₉	—	16	2	no	—
198	C₂²×C₁₉	#386	1	1	yes	characteristic
199	C₂²×C₁₉	#482	1	1	yes	characteristic
200	C₂²×C₁₉	#482	1	1	yes	characteristic
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	—	4	1	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	#416	1	1	yes	characteristic
208	C₄×C₁₉	#418	1	1	yes	characteristic
209	C₄×C₁₉	#449	1	1	yes	characteristic
210	C₄×C₁₉	#449	1	1	yes	characteristic
211	C₄×C₁₉	#471	1	1	yes	characteristic
212	C₄×C₁₉	#472	1	1	yes	characteristic
213	C₂×AGL(1,ℤ/8)	—	2	1	no	—
214	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
215	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
216	#460	—	2	1	no	—
217	#460	Dic₁₉	1	2	yes	—
218	#459	—	2	1	no	—
219	#459	Dic₁₉	1	2	yes	—
220	#433	—	38	2	no	—
221	#432	—	38	1	no	—
222	#431	—	19	1	no	—
223	#431	—	38	1	no	—
224	#423	—	19	1	no	—
225	#423	C₂×D₁₉	1	1	yes	characteristic
226	C₂×C₄⋊C₈	—	19	1	no	—
227	C₂×C₄⋊C₈	—	19	1	no	—
228	#418	—	2	1	no	—
229	#408	—	38	1	no	—
230	#405	—	38	1	no	—
231	#331	—	38	1	no	—
232	#331	—	38	1	no	—
233	#331	—	38	2	no	—
234	Q₈⋊C₈	—	38	1	no	—
235	D₄⋊C₈	—	38	1	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	8	1	no	—
239	C₂×C₁₉	—	16	2	no	—
240	C₂×C₁₉	#1875	1	1	yes	characteristic
241	C₂×C₁₉	#1903	1	1	yes	characteristic
242	C₂×C₁₉	#1907	1	1	yes	characteristic
243	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	AGL(1,ℤ/8)	—	4	2	no	—
248	AGL(1,ℤ/8)	—	4	2	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×D₈	—	2	2	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂×M₁₆	—	38	1	no	—
253	C₂²×C₈	—	38	1	no	—
254	C₂²×C₈	—	38	1	no	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	C₂×Dic₁₉	1	2	yes	—
259	C₄×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
260	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	C₂×Dic₁₉	1	1	yes	characteristic
264	C₄×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
265	#117	—	2	1	no	—
266	#117	C₂²⋊D₁₉	1	1	yes	characteristic
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	19	1	no	—
271	C₄⋊C₈	—	19	1	no	—
272	C₄⋊C₈	—	19	2	no	—
273	C₄⋊C₈	—	38	1	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	—	38	1	no	—
276	C₄⋊C₈	—	38	1	no	—
277	C₄⋊C₈	—	38	1	no	—
278	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	C₂²⋊C₈	—	38	2	no	—
282	C₂²⋊C₈	—	38	2	no	—
283	C₂²⋊C₈	—	38	1	no	—
284	#97	—	38	2	no	—
285	C₄×C₈	—	38	2	no	—
286	C₄×C₈	—	38	1	no	—
287	C₁₉	#9174	1	1	yes	characteristic, complemented, Sylow
288	C₂⁴	—	4	1	no	—
289	#41	—	2	1	no	—
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	C₂×Q₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	8	1	no	—
306	C₂×D₄	—	8	1	no	—
307	C₂×D₄	—	8	2	no	—
308	C₂×D₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	#64543	1	1	yes	characteristic
313	C₂²×C₄	#64543	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
315	SD₁₆	—	4	4	no	—
316	D₈	—	4	4	no	—
317	M₁₆	—	4	1	no	—
318	M₁₆	—	4	1	no	—
319	M₁₆	—	76	1	no	—
320	M₁₆	—	76	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	38	1	no	—
323	C₂×C₈	—	38	2	no	—
324	C₂×C₈	—	38	1	no	—
325	C₂×C₈	—	76	1	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₂×C₈	—	76	1	no	—
329	C₂×C₈	—	152	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
333	C₄⋊C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	D₄×D₁₉	1	1	yes	characteristic
341	C₄²	D₄×D₁₉	1	1	yes	characteristic
342	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
343	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	#10597381	1	1	yes	characteristic
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	D₄	—	2	1	no	—
354	D₄	—	2	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	1	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	8	1	no	—
377	C₂×C₄	#10597378	1	1	yes	characteristic
378	C₂×C₄	#10597378	1	1	yes	characteristic
379	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
380	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
381	C₂×C₄	#10597383	1	1	yes	characteristic
382	C₂×C₄	#10597385	1	1	yes	characteristic
383	C₂×C₄	#10597385	1	1	yes	characteristic
384	C₂×C₄	#10597396	1	1	yes	characteristic
385	C₂×C₄	#10597396	1	1	yes	characteristic
386	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
387	C₈	—	4	2	no	—
388	C₈	—	76	1	no	—
389	C₈	—	76	1	no	—
390	C₈	—	76	2	no	—
391	C₈	—	152	1	no	—
392	C₈	—	152	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	—	16	2	no	—
403	C₂²	#11926424	1	1	yes	characteristic
404	C₂²	#11926865	1	1	yes	characteristic
405	C₂²	#11926865	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	#11926540	1	1	yes	characteristic
413	C₄	#11926549	1	1	yes	characteristic
414	C₄	#11926687	1	1	yes	characteristic
415	C₄	#11926687	1	1	yes	characteristic
416	C₄	#11926805	1	1	yes	characteristic
417	C₄	#11926812	1	1	yes	characteristic
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	8	1	no	—
421	C₂	—	16	2	no	—
422	C₂	#14563958	1	1	yes	characteristic
423	C₂	#14564117	1	1	yes	characteristic
424	C₂	#14564145	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3038	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3038	D₁₉
hypocenter	C₁₉	#9174
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3038

Complements

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

N	H ≅ G/N	type
1. #14572301	C₂	semidirect
2. #14562303	C₂	semidirect
3. C₂×#11926288	C₂	semidirect
4. #14562022	C₂	semidirect
5. #14561530	C₂	semidirect
6. #14561509	C₂	semidirect
287. C₁₉	#9174	semidirect

Maximal subgroups

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

subgroup	index
#14572301	2
#14562303	2
C₂×#11926288	2
#14562022	2
#14561530	2
#14561509	2
C₁₉×#3038	2
#9174	19