Subgroups — #18078675

Order 4864.

578 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926831	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926609	C₂	1	1	yes	maximal, characteristic
3	#14564597	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563636	C₂	1	1	yes	maximal, characteristic
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₉	—	2	1	no	—
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	#11926831	—	2	2	no	—
11	#11926831	C₄	1	4	yes	complemented
12	#11926609	—	2	2	no	—
13	#11926609	—	2	2	no	—
14	C₂×#10597265	—	2	1	no	—
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#10597278	—	2	1	no	—
17	C₂×#10597266	—	2	1	no	—
18	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926414	C₂²	1	1	yes	characteristic
21	#11926307	—	2	1	no	—
22	#11926306	—	2	1	no	—
23	#11926306	—	2	1	no	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₉×#333	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×D₇₆	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	—	2	1	no	—
43	C₂×C₄⋊Dic₁₉	—	2	1	no	—
44	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
47	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
48	C₂×C₈×D₁₉	—	2	4	no	—
49	C₂×C₈×D₁₉	—	4	2	no	—
50	C₂×C₈×D₁₉	—	4	2	no	—
51	C₄×D₇₆	—	2	1	no	—
52	C₄×D₇₆	—	2	1	no	—
53	C₄×D₇₆	C₂×C₄	1	2	yes	—
54	C₄×D₇₆	D₄	1	2	yes	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
59	#10597278	—	4	2	no	—
60	(C₂×D₁₉)⋊C₈	—	2	4	no	—
61	#10597266	—	2	4	no	—
62	#10597265	—	2	4	no	—
63	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
65	C₄×C₁₉⋊C₈	—	2	1	no	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₂³×D₁₉	—	2	1	no	—
68	C₂×Q₈×C₁₉	—	2	2	no	—
69	C₂×Q₈×C₁₉	—	4	1	no	—
70	C₂×Q₈×C₁₉	—	8	1	no	—
71	C₂×Q₈×C₁₉	—	8	1	no	—
72	C₂²×C₄×C₁₉	—	4	1	no	—
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
76	C₂²×Dic₁₉	—	2	1	no	—
77	C₂²×Dic₁₉	—	4	1	no	—
78	C₂×D₇₆	—	2	1	no	—
79	C₂×D₇₆	—	2	1	no	—
80	C₂×D₇₆	—	2	1	no	—
81	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
82	C₂×D₇₆	SD₁₆	1	2	yes	—
83	C₂×D₇₆	Q₁₆	1	2	yes	—
84	C₂×C₄×D₁₉	—	2	2	no	—
85	C₂×C₄×D₁₉	—	2	2	no	—
86	C₂×C₄×D₁₉	—	4	1	no	—
87	C₂×C₄×D₁₉	—	4	1	no	—
88	C₂×C₄×D₁₉	—	4	1	no	—
89	C₂×C₄×D₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	—	2	2	no	—
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	2	2	no	—
97	C₄⋊C₄×C₁₉	—	2	2	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	(C₂×D₁₉)⋊C₄	—	2	2	no	—
105	(C₂×D₁₉)⋊C₄	—	2	2	no	—
106	C₄⋊Dic₁₉	—	2	1	no	—
107	C₄⋊Dic₁₉	—	4	1	no	—
108	C₄⋊Dic₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	1	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	8	1	no	—
112	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
113	C₂×C₁₉⋊C₈	—	2	1	no	—
114	C₂×C₁₉⋊C₈	—	2	1	no	—
115	C₂×C₁₉⋊C₈	—	2	2	no	—
116	C₂×C₁₉⋊C₈	—	2	1	no	—
117	C₂×C₁₉⋊C₈	—	2	1	no	—
118	C₂×C₁₉⋊C₈	—	2	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	—
122	C₈×D₁₉	—	4	8	no	—
123	#9215	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	#121	1	1	yes	characteristic
125	C₂²×D₁₉	—	2	2	no	—
126	C₂²×D₁₉	—	2	2	no	—
127	C₂²×D₁₉	—	2	2	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂²×D₁₉	—	4	1	no	—
130	C₂²×D₁₉	—	4	1	no	—
131	C₂²×D₁₉	—	4	1	no	—
132	Q₈×C₁₉	—	8	2	no	—
133	Q₈×C₁₉	—	8	2	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	4	2	no	—
137	C₂×C₄×C₁₉	—	8	1	no	—
138	C₂×C₄×C₁₉	—	8	1	no	—
139	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
143	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
144	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
151	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
153	C₂×Dic₁₉	—	2	2	no	—
154	C₂×Dic₁₉	—	4	1	no	—
155	C₂×Dic₁₉	—	4	1	no	—
156	C₂×Dic₁₉	—	8	1	no	—
157	C₂×Dic₁₉	—	8	1	no	—
158	C₂×Dic₁₉	—	8	1	no	—
159	D₇₆	—	2	2	no	—
160	D₇₆	—	2	2	no	—
161	D₇₆	—	2	2	no	—
162	D₇₆	#103	1	4	yes	—
163	C₄×D₁₉	—	4	2	no	—
164	C₄×D₁₉	—	4	2	no	—
165	C₄×D₁₉	—	4	2	no	—
166	C₄×D₁₉	—	4	2	no	—
167	C₈×C₁₉	—	4	2	no	—
168	C₈×C₁₉	—	8	1	no	—
169	C₁₉⋊C₈	—	2	2	no	—
170	C₁₉⋊C₈	—	4	2	no	—
171	C₁₉⋊C₈	—	4	1	no	—
172	C₂×#476	—	19	1	no	—
173	C₂×C₈×D₄	—	19	1	no	—
174	#1990	—	19	1	no	—
175	#1802	—	19	1	no	—
176	C₂×#333	D₁₉	1	1	yes	characteristic, complemented
177	#1296	—	19	1	no	—
178	#1277	—	19	1	no	—
179	C₂²×C₁₉	#386	1	1	yes	characteristic
180	C₂²×C₁₉	#461	1	1	yes	characteristic
181	C₂²×C₁₉	#463	1	1	yes	characteristic
182	C₂²×C₁₉	#465	1	1	yes	characteristic
183	C₂²×C₁₉	#467	1	1	yes	characteristic
184	C₂²×C₁₉	#471	1	1	yes	characteristic
185	C₂²×C₁₉	#472	1	1	yes	characteristic
186	C₂×D₁₉	—	2	4	no	—
187	C₂×D₁₉	—	4	2	no	—
188	C₂×D₁₉	—	4	2	no	—
189	C₂×D₁₉	—	4	2	no	—
190	C₂×D₁₉	—	4	2	no	—
191	C₂×D₁₉	—	4	2	no	—
192	C₂×D₁₉	—	4	2	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	8	2	no	—
196	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
197	C₄×C₁₉	#416	1	1	yes	characteristic
198	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
199	C₄×C₁₉	#440	1	1	yes	characteristic
200	C₄×C₁₉	#450	1	1	yes	characteristic
201	C₄×C₁₉	#452	1	1	yes	characteristic
202	C₄×C₁₉	#465	1	1	yes	characteristic
203	C₄×C₁₉	#467	1	1	yes	characteristic
204	Dic₁₉	—	4	2	no	—
205	Dic₁₉	—	16	1	no	—
206	C₂³×C₈	—	38	1	no	—
207	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
208	C₂×C₄×D₄	—	19	1	no	—
209	#476	—	19	4	no	—
210	#476	—	38	2	no	—
211	C₈×D₄	—	38	2	no	—
212	C₈×D₄	—	38	2	no	—
213	C₂×#106	—	38	1	no	—
214	C₂×C₄⋊C₈	—	19	1	no	—
215	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
217	C₂×#102	—	38	1	no	—
218	C₂×#102	—	38	1	no	—
219	C₂×C₂²⋊C₈	—	38	1	no	—
220	C₂×C₄×C₈	—	19	1	no	—
221	#384	—	19	1	no	—
222	#340	—	38	1	no	—
223	#340	—	38	1	no	—
224	#340	—	38	1	no	—
225	#333	—	2	2	no	—
226	C₂×C₁₉	#1671	1	1	yes	characteristic
227	C₂×C₁₉	#1675	1	1	yes	characteristic
228	C₂×C₁₉	#1677	1	1	yes	characteristic
229	C₂×C₁₉	#1683	1	1	yes	characteristic
230	C₂×C₁₉	#1877	1	1	yes	characteristic
231	C₂×C₁₉	#1892	1	1	yes	characteristic
232	C₂×C₁₉	#1907	1	1	yes	characteristic
233	D₁₉	—	4	4	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×D₄	—	19	1	no	—
236	C₂³×C₄	—	38	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	19	1	no	—
240	C₂²×C₈	—	19	1	no	—
241	C₂²×C₈	—	38	4	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₂²×C₈	—	76	2	no	—
244	C₂²×C₈	—	76	2	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	C₄×D₁₉	1	2	yes	—
249	C₄×D₄	—	19	2	no	—
250	C₄×D₄	—	19	2	no	—
251	C₄×D₄	—	38	1	no	—
252	C₄×D₄	—	38	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	19	1	no	—
256	C₂×C₄⋊C₄	—	38	1	no	—
257	C₂×C₄⋊C₄	—	38	1	no	—
258	C₂×C₄⋊C₄	—	38	1	no	—
259	C₂×C₂²⋊C₄	—	38	1	no	—
260	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
261	#106	—	38	4	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	19	2	no	—
266	C₄⋊C₈	—	38	1	no	—
267	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
268	#102	—	38	4	no	—
269	#102	—	76	2	no	—
270	C₂²⋊C₈	—	38	4	no	—
271	C₄×C₈	—	38	1	no	—
272	C₄×C₈	—	38	1	no	—
273	C₁₉	#9215	1	1	yes	characteristic, complemented, Sylow
274	C₂⁴	—	38	1	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	8	1	no	—
278	C₂×Q₈	—	8	1	no	—
279	C₂×D₄	—	19	2	no	—
280	C₂×D₄	—	19	2	no	—
281	C₂×D₄	—	19	2	no	—
282	C₂×D₄	—	38	1	no	—
283	C₂×D₄	—	38	1	no	—
284	C₂×D₄	—	38	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	38	1	no	—
287	C₂²×C₄	—	38	2	no	—
288	C₂²×C₄	—	38	2	no	—
289	C₂²×C₄	—	76	1	no	—
290	C₂²×C₄	—	76	1	no	—
291	C₂²×C₄	—	76	1	no	—
292	C₂²×C₄	—	76	1	no	—
293	C₂²×C₄	—	76	1	no	—
294	C₂²×C₄	#64541	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	19	2	no	—
304	C₂×C₈	—	38	1	no	—
305	C₂×C₈	—	38	1	no	—
306	C₂×C₈	—	38	1	no	—
307	C₂×C₈	—	38	2	no	—
308	C₂×C₈	—	38	1	no	—
309	C₂×C₈	—	38	1	no	—
310	C₂×C₈	—	76	8	no	—
311	C₂×C₈	—	76	1	no	—
312	C₂×C₈	—	76	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	19	2	no	—
318	C₄⋊C₄	—	38	1	no	—
319	C₄⋊C₄	—	76	1	no	—
320	C₄⋊C₄	—	76	1	no	—
321	C₄⋊C₄	—	76	1	no	—
322	C₄⋊C₄	—	76	1	no	—
323	C₄⋊C₄	—	152	1	no	—
324	C₂²⋊C₄	—	38	2	no	—
325	C₂²⋊C₄	—	38	2	no	—
326	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
327	C₄²	D₄×D₁₉	1	1	yes	characteristic
328	C₄²	#64543	1	1	yes	characteristic
329	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
330	C₂³	—	38	2	no	—
331	C₂³	—	38	2	no	—
332	C₂³	—	38	2	no	—
333	C₂³	—	76	1	no	—
334	C₂³	—	76	1	no	—
335	C₂³	—	76	1	no	—
336	C₂³	—	76	1	no	—
337	C₂³	#10597330	1	1	yes	characteristic
338	Q₈	—	8	2	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	19	4	no	—
341	D₄	—	38	2	no	—
342	D₄	—	38	2	no	—
343	D₄	—	38	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	1	no	—
348	C₂×C₄	—	8	1	no	—
349	C₂×C₄	—	38	2	no	—
350	C₂×C₄	—	76	1	no	—
351	C₂×C₄	—	76	1	no	—
352	C₂×C₄	—	76	2	no	—
353	C₂×C₄	—	76	2	no	—
354	C₂×C₄	—	76	2	no	—
355	C₂×C₄	—	76	2	no	—
356	C₂×C₄	—	152	1	no	—
357	C₂×C₄	—	152	1	no	—
358	C₂×C₄	—	152	1	no	—
359	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
360	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
361	C₂×C₄	#10597329	1	1	yes	characteristic
362	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
363	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
364	C₂×C₄	#10597360	1	1	yes	characteristic
365	C₂×C₄	#10597362	1	1	yes	characteristic
366	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
367	C₂×C₄	#10597364	1	1	yes	characteristic
368	C₂×C₄	#10597365	1	1	yes	characteristic
369	C₂×C₄	#10597365	1	1	yes	characteristic
370	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
371	C₂×C₄	#10597383	1	1	yes	characteristic
372	C₂×C₄	#10597384	1	1	yes	characteristic
373	C₈	—	4	2	no	—
374	C₈	—	8	1	no	—
375	C₈	—	38	2	no	—
376	C₈	—	76	2	no	—
377	C₈	—	76	1	no	—
378	C₂²	—	38	4	no	—
379	C₂²	—	76	2	no	—
380	C₂²	—	76	2	no	—
381	C₂²	—	76	2	no	—
382	C₂²	—	76	2	no	—
383	C₂²	—	76	2	no	—
384	C₂²	—	76	2	no	—
385	C₂²	#11926420	1	1	yes	characteristic
386	C₂²	#11926748	1	1	yes	characteristic
387	C₂²	#11926762	1	1	yes	characteristic
388	C₂²	#11926776	1	1	yes	characteristic
389	C₂²	#11926784	1	1	yes	characteristic
390	C₂²	#11926806	1	1	yes	characteristic
391	C₂²	#11926813	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	304	1	no	—
396	C₄	—	76	2	no	—
397	C₄	#103×D₁₉	1	1	yes	characteristic
398	C₄	#11926539	1	1	yes	characteristic
399	C₄	#11926629	1	1	yes	characteristic
400	C₄	#11926647	1	1	yes	characteristic
401	C₄	#11926693	1	1	yes	characteristic
402	C₄	#11926705	1	1	yes	characteristic
403	C₄	#11926770	1	1	yes	characteristic
404	C₄	#11926782	1	1	yes	characteristic
405	C₂	—	76	4	no	—
406	C₂	#14563013	1	1	yes	characteristic
407	C₂	#14563033	1	1	yes	characteristic
408	C₂	#14563047	1	1	yes	characteristic
409	C₂	#14563089	1	1	yes	characteristic
410	C₂	#14563966	1	1	yes	characteristic
411	C₂	#14564055	1	1	yes	characteristic
412	C₂	#14564140	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#333	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#333	D₁₉
hypocenter	C₁₉	#9215
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

Complements

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

N	H ≅ G/N	type
3. #14564597	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561469	C₂	semidirect
7. C₂×C₁₉×#333	C₂	semidirect
11. #11926831	C₄	semidirect
176. C₂×#333	D₁₉	semidirect
273. C₁₉	#9215	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926831	2
C₂×#11926609	2
#14564597	2
#14563636	2
#14561519	2
#14561469	2
C₂×C₁₉×#333	2
#9215	19