Subgroups — #18078432

Order 4864.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573115	C₂	1	1	yes	maximal, characteristic
2	#14562304	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926287	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562022	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561532	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561509	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2906	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597395	—	2	1	no	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	#11926744	—	2	1	no	—
11	#11926744	C₄	1	2	yes	—
12	#11926739	—	2	1	no	—
13	#11926739	C₄	1	2	yes	—
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926568	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	#11926548	—	2	1	no	—
18	#11926287	—	2	2	no	—
19	#11926287	—	2	1	no	—
20	#11926287	—	2	1	no	—
21	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
22	D₄⋊(C₁₉⋊C₈)	—	2	1	no	—
23	C₂×C₁₉×#131	—	2	1	no	—
24	C₄×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#424	—	2	2	no	—
26	C₁₉×#424	—	2	1	no	—
27	C₁₉×#423	—	2	1	no	—
28	C₁₉×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
30	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₇₆	—	2	1	no	—
33	C₂²×D₇₆	—	2	1	no	—
34	C₂²×D₇₆	—	2	1	no	—
35	C₁₉×#131	—	4	2	no	—
36	C₁₉×#131	—	4	2	no	—
37	C₂×M₁₆×C₁₉	—	2	2	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂²×C₈×C₁₉	—	2	2	no	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
47	C₁₉×#117	—	2	1	no	—
48	C₁₉×#117	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
51	#10597395	—	4	2	no	—
52	#10597395	—	4	2	no	—
53	C₂×#64527	—	2	2	no	—
54	C₂×#64525	—	2	2	no	—
55	C₂×#64520	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	#10597320	—	2	1	no	—
58	#10597320	—	2	1	no	—
59	#10597320	—	2	1	no	—
60	#10597320	C₂×C₄	1	2	yes	—
61	C₁₉×C₄⋊C₈	—	2	2	no	—
62	C₁₉×C₄⋊C₈	—	2	2	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
66	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
67	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	#10597266	—	2	2	no	—
70	#10597266	—	2	2	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	—
76	C₄×C₁₉⋊C₈	—	2	1	no	—
77	C₂³×D₁₉	—	4	1	no	—
78	#41×C₁₉	—	2	1	no	—
79	#41×C₁₉	—	2	1	no	—
80	#41×C₁₉	D₈	1	2	yes	—
81	#41×C₁₉	SD₁₆	1	2	yes	—
82	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	1	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂×D₇₆	—	2	2	no	—
92	C₂×D₇₆	—	2	2	no	—
93	C₂×D₇₆	—	2	2	no	—
94	C₂×D₇₆	—	4	1	no	—
95	C₂×D₇₆	—	4	1	no	—
96	C₂×D₇₆	—	4	1	no	—
97	C₂×D₇₆	—	4	1	no	—
98	C₂×D₇₆	—	4	1	no	—
99	C₂×D₇₆	—	4	1	no	—
100	C₂×D₇₆	—	4	1	no	—
101	C₂×D₇₆	—	8	2	no	—
102	C₂×D₇₆	—	8	1	no	—
103	C₂×D₇₆	—	8	1	no	—
104	M₁₆×C₁₉	—	4	4	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	C₂×C₈×C₁₉	—	2	1	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	1	no	—
110	C₂×C₈×C₁₉	—	4	4	no	—
111	C₂×C₈×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂²⋊C₄×C₁₉	—	2	1	no	—
119	C₂²⋊C₄×C₁₉	—	2	1	no	—
120	C₄²×C₁₉	—	2	1	no	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
127	#64527	—	4	4	no	—
128	#64525	—	4	4	no	—
129	#64520	—	4	1	no	—
130	#64520	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	8	1	no	—
135	#9173	—	19	1	no	maximal, Sylow
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	#123	1	1	yes	characteristic
138	C₂²×D₁₉	—	4	2	no	—
139	C₂²×D₁₉	—	8	2	no	—
140	C₂²×D₁₉	—	8	2	no	—
141	C₂²×D₁₉	—	8	1	no	—
142	C₂²×D₁₉	—	8	1	no	—
143	Q₈×C₁₉	—	2	1	no	—
144	Q₈×C₁₉	#102	1	2	yes	—
145	D₄×C₁₉	—	2	2	no	—
146	D₄×C₁₉	—	2	2	no	—
147	D₄×C₁₉	—	2	1	no	—
148	D₄×C₁₉	#102	1	2	yes	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	1	no	—
153	C₂×C₄×C₁₉	—	2	1	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	8	1	no	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
168	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
170	D₇₆	—	4	2	no	—
171	D₇₆	—	4	2	no	—
172	D₇₆	—	8	2	no	—
173	D₇₆	—	8	2	no	—
174	D₇₆	—	8	2	no	—
175	D₇₆	—	8	1	no	—
176	D₇₆	—	8	1	no	—
177	D₇₆	—	8	1	no	—
178	D₇₆	—	8	1	no	—
179	C₈×C₁₉	—	4	1	no	—
180	C₈×C₁₉	—	4	2	no	—
181	C₈×C₁₉	—	4	1	no	—
182	C₁₉⋊C₈	—	4	2	no	—
183	C₁₉⋊C₈	—	8	1	no	—
184	C₁₉⋊C₈	—	8	1	no	—
185	#3038	—	19	1	no	—
186	#2906	D₁₉	1	1	yes	characteristic, complemented
187	#1545	—	19	1	no	—
188	C₂×#331	—	19	1	no	—
189	#1477	—	19	1	no	—
190	#1301	—	19	1	no	—
191	#1292	—	19	1	no	—
192	C₂²×C₁₉	—	2	1	no	—
193	C₂²×C₁₉	—	2	1	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	#386	1	1	yes	characteristic
198	C₂²×C₁₉	#480	1	1	yes	characteristic
199	C₂²×C₁₉	#481	1	1	yes	characteristic
200	C₂×D₁₉	—	8	2	no	—
201	C₂×D₁₉	—	8	2	no	—
202	C₂×D₁₉	—	8	2	no	—
203	C₂×D₁₉	—	16	2	no	—
204	C₂×D₁₉	—	16	2	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	1	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	—	2	1	no	—
209	C₄×C₁₉	—	4	1	no	—
210	C₄×C₁₉	—	4	1	no	—
211	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
212	C₄×C₁₉	#417	1	1	yes	characteristic
213	C₄×C₁₉	#447	1	1	yes	characteristic
214	C₄×C₁₉	#448	1	1	yes	characteristic
215	C₄×C₁₉	#471	1	1	yes	characteristic
216	C₄×C₁₉	#472	1	1	yes	characteristic
217	C₂×AGL(1,ℤ/8)	—	38	1	no	—
218	C₂×#131	—	2	1	no	—
219	C₂×#127	—	19	1	no	—
220	C₄×#41	C₂×D₁₉	1	1	yes	characteristic
221	#460	—	19	2	no	—
222	#460	—	38	1	no	—
223	#459	—	19	2	no	—
224	#459	—	38	1	no	—
225	#431	—	19	1	no	—
226	#424	—	2	1	no	—
227	#424	—	2	2	no	—
228	#423	—	2	1	no	—
229	#423	—	19	1	no	—
230	#423	C₂×D₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₈	—	2	1	no	—
232	C₂×C₄⋊C₈	—	19	1	no	—
233	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
234	#418	—	38	1	no	—
235	#331	—	38	1	no	—
236	#331	—	38	1	no	—
237	#331	—	38	2	no	—
238	Q₈⋊C₈	—	38	1	no	—
239	D₄⋊C₈	—	38	1	no	—
240	C₂×C₁₉	—	2	1	no	—
241	C₂×C₁₉	—	2	1	no	—
242	C₂×C₁₉	—	4	2	no	—
243	C₂×C₁₉	#1874	1	1	yes	characteristic
244	C₂×C₁₉	#1903	1	1	yes	characteristic
245	C₂×C₁₉	#1907	1	1	yes	characteristic
246	D₁₉	—	16	2	no	—
247	C₂×#41	C₂²⋊D₁₉	1	1	yes	characteristic
248	C₂²×D₄	—	38	1	no	—
249	C₂²×D₄	—	38	1	no	—
250	C₂²×D₄	—	38	1	no	—
251	AGL(1,ℤ/8)	—	76	2	no	—
252	AGL(1,ℤ/8)	—	76	2	no	—
253	C₂×SD₁₆	—	38	2	no	—
254	C₂×D₈	—	38	2	no	—
255	#131	—	4	2	no	—
256	#131	—	4	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	38	1	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	38	1	no	—
263	#127	—	19	2	no	—
264	#127	—	38	1	no	—
265	#127	—	38	1	no	—
266	#127	—	38	1	no	—
267	C₄×Q₈	C₄×D₁₉	1	1	yes	characteristic
268	C₄×Q₈	D₇₆	1	1	yes	characteristic
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	C₄×D₁₉	1	1	yes	characteristic
272	C₄×D₄	D₇₆	1	1	yes	characteristic
273	#117	—	2	1	no	—
274	#117	C₂²⋊D₁₉	1	1	yes	characteristic
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	19	2	no	—
282	C₄⋊C₈	—	38	1	no	—
283	C₄⋊C₈	—	38	1	no	—
284	C₄⋊C₈	—	38	1	no	—
285	C₄⋊C₈	—	38	1	no	—
286	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
287	C₄⋊C₈	C₂²⋊D₁₉	1	1	yes	characteristic
288	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
289	#102	—	38	2	no	—
290	#102	—	38	2	no	—
291	C₂²⋊C₈	—	38	1	no	—
292	C₄×C₈	—	38	1	no	—
293	C₁₉	#9173	1	1	yes	characteristic, complemented, Sylow
294	C₂⁴	—	76	1	no	—
295	#41	—	2	1	no	—
296	#41	—	2	1	no	—
297	#41	#64525	1	2	yes	—
298	#41	#64527	1	2	yes	—
299	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	38	2	no	—
302	C₂×D₄	—	38	2	no	—
303	C₂×D₄	—	38	2	no	—
304	C₂×D₄	—	76	1	no	—
305	C₂×D₄	—	76	1	no	—
306	C₂×D₄	—	76	1	no	—
307	C₂×D₄	—	76	1	no	—
308	C₂×D₄	—	76	1	no	—
309	C₂×D₄	—	76	1	no	—
310	C₂×D₄	—	76	1	no	—
311	C₂×D₄	—	152	1	no	—
312	C₂×D₄	—	152	1	no	—
313	C₂×D₄	—	152	2	no	—
314	C₂×D₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	#64541	1	1	yes	characteristic
319	C₂²×C₄	#64541	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
321	SD₁₆	—	76	4	no	—
322	D₈	—	76	4	no	—
323	M₁₆	—	4	4	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	76	1	no	—
327	M₁₆	—	76	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	4	4	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	38	2	no	—
335	C₂×C₈	—	76	1	no	—
336	C₂×C₈	—	76	1	no	—
337	C₂×C₈	—	152	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
341	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
349	C₄²	C₂×D₇₆	1	1	yes	characteristic
350	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
351	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
352	C₂³	—	2	1	no	—
353	C₂³	—	76	2	no	—
354	C₂³	—	152	2	no	—
355	C₂³	—	152	2	no	—
356	C₂³	—	152	1	no	—
357	C₂³	—	152	1	no	—
358	C₂³	#10597375	1	1	yes	characteristic
359	Q₈	—	2	1	no	—
360	Q₈	#10597266	1	2	yes	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	1	no	—
364	D₄	—	76	2	no	—
365	D₄	—	76	2	no	—
366	D₄	—	152	2	no	—
367	D₄	—	152	2	no	—
368	D₄	—	152	2	no	—
369	D₄	—	152	1	no	—
370	D₄	—	152	1	no	—
371	D₄	—	152	1	no	—
372	D₄	—	152	1	no	—
373	D₄	#10597266	1	2	yes	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	8	1	no	—
385	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
388	C₂×C₄	#10597376	1	1	yes	characteristic
389	C₂×C₄	#10597376	1	1	yes	characteristic
390	C₂×C₄	C₂×#64525	1	1	yes	characteristic
391	C₂×C₄	#10597378	1	1	yes	characteristic
392	C₂×C₄	C₂×#64527	1	1	yes	characteristic
393	C₂×C₄	#10597388	1	1	yes	characteristic
394	C₂×C₄	#10597399	1	1	yes	characteristic
395	C₈	—	4	1	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	76	2	no	—
399	C₈	—	152	1	no	—
400	C₈	—	152	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	304	2	no	—
407	C₂²	—	304	2	no	—
408	C₂²	—	152	2	no	—
409	C₂²	—	152	2	no	—
410	C₂²	—	152	2	no	—
411	C₂²	#11926423	1	1	yes	characteristic
412	C₂²	#11926857	1	1	yes	characteristic
413	C₂²	#11926862	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	C₂×#10597266	1	1	yes	characteristic
421	C₄	#11926543	1	1	yes	characteristic
422	C₄	#11926678	1	1	yes	characteristic
423	C₄	#11926683	1	1	yes	characteristic
424	C₄	#11926807	1	1	yes	characteristic
425	C₄	#11926814	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	4	2	no	—
429	C₂	—	304	2	no	—
430	C₂	#14563952	1	1	yes	characteristic
431	C₂	#14564115	1	1	yes	characteristic
432	C₂	#14564143	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2906	C₂
socle	C₂²×C₁₉	#386
prime radical	#14573115	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2906	D₁₉
hypocenter	C₁₉	#9173
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2906

Complements

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

N	H ≅ G/N	type
2. #14562304	C₂	semidirect
3. C₂×#11926287	C₂	semidirect
4. #14562022	C₂	semidirect
5. #14561532	C₂	semidirect
6. #14561509	C₂	semidirect
7. C₁₉×#2906	C₂	semidirect
186. #2906	D₁₉	semidirect
293. C₁₉	#9173	semidirect

Maximal subgroups

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

subgroup	index
#14573115	2
#14562304	2
C₂×#11926287	2
#14562022	2
#14561532	2
#14561509	2
C₁₉×#2906	2
#9173	19