Subgroups — #18085550

Order 4864.

588 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	#14568661	C₂	1	1	yes	maximal, characteristic, complemented
2	#14564562	C₂	1	1	yes	maximal, characteristic
3	#14564561	C₂	1	1	yes	maximal, characteristic
4	#14564441	C₂	1	1	yes	maximal, characteristic
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597315	—	2	1	no	—
9	C₂×#10597334	—	2	1	no	—
10	C₂×#10597320	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#10597278	—	2	2	no	—
13	C₂×#10597278	—	2	1	no	—
14	C₂×#10597278	—	2	1	no	—
15	C₂×#10597266	—	2	1	no	—
16	C₂×#10597266	—	2	1	no	—
17	#11926465	—	2	2	no	—
18	#11926443	—	2	1	no	—
19	#11926442	—	2	1	no	—
20	#11926414	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×D₇₆	—	2	1	no	—
26	C₂²×D₇₆	—	2	1	no	—
27	C₂²×D₇₆	—	2	1	no	—
28	C₂²×Dic₃₈	—	2	2	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₉	—	2	2	no	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
41	C₂×Dic₁₉⋊C₄	—	2	2	no	—
42	C₂×C₄×Dic₁₉	—	2	1	no	—
43	C₂²×C₁₉⋊C₈	—	2	1	no	—
44	#10597334	—	4	2	no	—
45	#10597334	—	4	2	no	—
46	#10597320	—	2	1	no	—
47	#10597320	—	2	1	no	—
48	#10597320	—	2	1	no	—
49	#10597320	Q₈	1	2	yes	complemented
50	#10597315	—	4	2	no	—
51	#10597315	—	4	2	no	—
52	C₁₉×C₄⋊C₈	—	2	1	no	—
53	C₁₉×C₄⋊C₈	—	2	1	no	—
54	C₄×C₈×C₁₉	—	2	1	no	—
55	C₄×C₈×C₁₉	—	2	1	no	—
56	C₁₉×#95	—	2	1	no	—
57	C₁₉⋊#95	—	2	2	no	—
58	C₁₉⋊#95	—	2	1	no	—
59	#10597278	—	4	4	no	—
60	#10597278	—	4	2	no	—
61	#10597278	—	4	2	no	—
62	#10597266	—	4	2	no	—
63	#10597266	—	4	2	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₂³×D₁₉	—	4	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×Dic₁₉	—	2	1	no	—
73	C₂²×Dic₁₉	—	2	1	no	—
74	C₂²×Dic₁₉	—	2	2	no	—
75	C₂×D₇₆	—	2	2	no	—
76	C₂×D₇₆	—	2	2	no	—
77	C₂×D₇₆	—	2	2	no	—
78	C₂×D₇₆	—	4	2	no	—
79	C₂×D₇₆	—	4	2	no	—
80	C₂×D₇₆	—	4	1	no	—
81	C₂×D₇₆	—	4	1	no	—
82	C₂×D₇₆	—	4	1	no	—
83	C₂×D₇₆	—	4	1	no	—
84	C₂×D₇₆	—	4	1	no	—
85	C₂×D₇₆	—	4	1	no	—
86	C₂×D₇₆	—	4	1	no	—
87	C₂×D₇₆	—	4	1	no	—
88	C₂×D₇₆	—	4	1	no	—
89	C₂×D₇₆	—	4	1	no	—
90	C₂×D₇₆	—	4	1	no	—
91	C₂×Dic₃₈	—	4	4	no	—
92	C₂×Dic₃₈	—	4	4	no	—
93	C₂×Dic₃₈	—	8	2	no	—
94	C₂×C₈×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	2	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
103	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
104	C₄²×C₁₉	—	4	1	no	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	C₄²×C₁₉	#41	1	1	yes	characteristic
109	C₄²×C₁₉	#41	1	1	yes	characteristic
110	C₄⋊Dic₁₉	—	2	1	no	—
111	C₄⋊Dic₁₉	—	2	1	no	—
112	C₄⋊Dic₁₉	—	4	4	no	—
113	C₄⋊Dic₁₉	—	4	1	no	—
114	C₄⋊Dic₁₉	—	4	1	no	—
115	C₄⋊Dic₁₉	—	4	1	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₄⋊Dic₁₉	—	4	2	no	—
118	C₄⋊Dic₁₉	D₈	1	2	yes	—
119	C₄⋊Dic₁₉	SD₁₆	1	2	yes	—
120	Dic₁₉⋊C₄	—	4	4	no	—
121	C₄×Dic₁₉	—	4	1	no	—
122	C₄×Dic₁₉	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	#10348	—	19	1	no	maximal, Sylow
127	C₂³×C₁₉	#120	1	1	yes	characteristic
128	C₂²×D₁₉	—	4	2	no	—
129	C₂²×D₁₉	—	8	1	no	—
130	C₂²×D₁₉	—	8	1	no	—
131	C₂²×D₁₉	—	8	1	no	—
132	C₂²×D₁₉	—	8	1	no	—
133	C₂²×D₁₉	—	8	1	no	—
134	C₂²×D₁₉	—	8	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	2	2	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	1	no	—
143	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
147	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
148	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
157	C₂×Dic₁₉	—	2	2	no	—
158	C₂×Dic₁₉	—	2	2	no	—
159	C₂×Dic₁₉	—	4	1	no	—
160	C₂×Dic₁₉	—	4	1	no	—
161	C₂×Dic₁₉	—	4	1	no	—
162	C₂×Dic₁₉	—	4	1	no	—
163	C₂×Dic₁₉	—	4	2	no	—
164	C₂×Dic₁₉	—	4	2	no	—
165	C₂×Dic₁₉	—	4	2	no	—
166	D₇₆	—	4	4	no	—
167	D₇₆	—	4	2	no	—
168	D₇₆	—	4	2	no	—
169	D₇₆	—	4	2	no	—
170	D₇₆	—	4	2	no	—
171	D₇₆	—	8	2	no	—
172	D₇₆	—	8	1	no	—
173	D₇₆	—	8	1	no	—
174	D₇₆	—	8	1	no	—
175	D₇₆	—	8	1	no	—
176	Dic₃₈	—	8	8	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₈×C₁₉	—	8	1	no	—
179	C₁₉⋊C₈	—	8	1	no	—
180	#2551	—	19	1	no	—
181	#1982	—	19	1	no	—
182	#1982	—	19	1	no	—
183	#1957	—	19	1	no	—
184	#1296	—	19	1	no	—
185	#1279	—	19	1	no	—
186	#1279	D₁₉	1	1	yes	characteristic, complemented
187	C₂²×C₁₉	#393	1	1	yes	characteristic
188	C₂²×C₁₉	#447	1	1	yes	characteristic
189	C₂²×C₁₉	#447	1	1	yes	characteristic
190	C₂²×C₁₉	#448	1	1	yes	characteristic
191	C₂²×C₁₉	#448	1	1	yes	characteristic
192	C₂²×C₁₉	#453	1	1	yes	characteristic
193	C₂²×C₁₉	#454	1	1	yes	characteristic
194	C₂×D₁₉	—	8	2	no	—
195	C₂×D₁₉	—	8	2	no	—
196	C₂×D₁₉	—	8	2	no	—
197	C₂×D₁₉	—	16	1	no	—
198	C₂×D₁₉	—	16	1	no	—
199	C₂×D₁₉	—	16	1	no	—
200	C₂×D₁₉	—	16	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	#474	1	1	yes	characteristic
206	C₄×C₁₉	#474	1	1	yes	characteristic
207	C₄×C₁₉	#476	1	1	yes	characteristic
208	C₄×C₁₉	#476	1	1	yes	characteristic
209	C₄×C₁₉	#486	1	1	yes	characteristic
210	C₄×C₁₉	#486	1	1	yes	characteristic
211	C₄×C₁₉	#489	1	1	yes	characteristic
212	C₄×C₁₉	#489	1	1	yes	characteristic
213	Dic₁₉	—	4	2	no	—
214	Dic₁₉	—	4	2	no	—
215	Dic₁₉	—	8	2	no	—
216	C₂×C₄⋊Q₈	—	38	1	no	—
217	C₂×C₄⋊Q₈	—	38	1	no	—
218	C₂×#127	—	19	1	no	—
219	C₂×C₄⋊C₈	—	19	1	no	—
220	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
221	C₂×#102	—	38	2	no	—
222	C₂×#102	—	38	1	no	—
223	C₂×#102	—	38	1	no	—
224	C₂×#102	—	38	1	no	—
225	C₂×#102	—	38	1	no	—
226	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
227	#395	—	38	2	no	—
228	#389	—	38	1	no	—
229	#389	—	38	1	no	—
230	#384	—	19	1	no	—
231	C₄×C₄⋊C₄	—	19	1	no	—
232	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
233	C₂×C₁₉	#1619	1	1	yes	characteristic
234	C₂×C₁₉	#1623	1	1	yes	characteristic
235	C₂×C₁₉	#1627	1	1	yes	characteristic
236	C₂×C₁₉	#1627	1	1	yes	characteristic
237	C₂×C₁₉	#2023	1	1	yes	characteristic
238	C₂×C₁₉	#2023	1	1	yes	characteristic
239	C₂×C₁₉	#2027	1	1	yes	characteristic
240	D₁₉	—	16	2	no	—
241	C₂²×Q₈	—	38	2	no	—
242	C₂²×D₄	—	38	1	no	—
243	C₂²×D₄	—	38	1	no	—
244	C₂²×D₄	—	38	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	38	1	no	—
248	C₄⋊Q₈	—	76	2	no	—
249	C₄⋊Q₈	—	76	2	no	—
250	C₄⋊Q₈	—	76	2	no	—
251	C₄⋊Q₈	—	76	2	no	—
252	#127	—	19	2	no	—
253	#127	—	38	1	no	—
254	#127	—	38	1	no	—
255	#127	—	38	1	no	—
256	C₂×C₄⋊C₄	—	19	1	no	—
257	C₂×C₄⋊C₄	—	19	1	no	—
258	C₂×C₄⋊C₄	—	19	2	no	—
259	C₂×C₄⋊C₄	—	38	2	no	—
260	C₂×C₄⋊C₄	—	38	2	no	—
261	C₂×C₄⋊C₄	—	38	1	no	—
262	C₂×C₄⋊C₄	—	38	1	no	—
263	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	38	1	no	—
267	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	38	1	no	—
271	C₄⋊C₈	—	38	1	no	—
272	#102	—	76	2	no	—
273	#102	—	76	2	no	—
274	#102	—	76	4	no	—
275	#102	—	76	2	no	—
276	#102	—	76	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	#95	—	2	1	no	—
280	#95	—	38	2	no	—
281	#95	—	38	1	no	—
282	C₁₉	#10348	1	1	yes	characteristic, complemented, Sylow
283	C₂⁴	—	76	1	no	—
284	C₂×Q₈	—	76	4	no	—
285	C₂×Q₈	—	76	4	no	—
286	C₂×Q₈	—	152	2	no	—
287	C₂×D₄	—	38	2	no	—
288	C₂×D₄	—	38	2	no	—
289	C₂×D₄	—	38	2	no	—
290	C₂×D₄	—	76	2	no	—
291	C₂×D₄	—	76	2	no	—
292	C₂×D₄	—	76	1	no	—
293	C₂×D₄	—	76	1	no	—
294	C₂×D₄	—	76	1	no	—
295	C₂×D₄	—	76	1	no	—
296	C₂×D₄	—	76	1	no	—
297	C₂×D₄	—	76	1	no	—
298	C₂×D₄	—	76	1	no	—
299	C₂×D₄	—	76	1	no	—
300	C₂×D₄	—	76	1	no	—
301	C₂×D₄	—	76	1	no	—
302	C₂×D₄	—	76	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	38	1	no	—
306	C₂²×C₄	—	38	1	no	—
307	C₂²×C₄	—	38	2	no	—
308	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	76	1	no	—
318	C₂×C₈	—	76	1	no	—
319	C₂×C₈	—	76	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	19	2	no	—
323	C₄⋊C₄	—	19	2	no	—
324	C₄⋊C₄	—	38	1	no	—
325	C₄⋊C₄	—	38	1	no	—
326	C₄⋊C₄	—	76	2	no	—
327	C₄⋊C₄	—	76	4	no	—
328	C₄⋊C₄	—	76	4	no	—
329	C₄⋊C₄	—	76	1	no	—
330	C₄⋊C₄	—	76	1	no	—
331	C₄⋊C₄	—	76	1	no	—
332	C₄⋊C₄	—	76	1	no	—
333	C₄⋊C₄	#64516	1	2	yes	—
334	C₄⋊C₄	D₁₅₂	1	2	yes	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	76	1	no	—
338	C₄²	—	76	1	no	—
339	C₄²	#64541	1	1	yes	characteristic
340	C₄²	#64541	1	1	yes	characteristic
341	C₄²	#64543	1	1	yes	characteristic
342	C₄²	Q₈×D₁₉	1	1	yes	characteristic
343	C₂³	—	76	2	no	—
344	C₂³	—	152	1	no	—
345	C₂³	—	152	1	no	—
346	C₂³	—	152	1	no	—
347	C₂³	—	152	1	no	—
348	C₂³	—	152	1	no	—
349	C₂³	—	152	1	no	—
350	C₂³	#10597328	1	1	yes	characteristic
351	Q₈	—	152	8	no	—
352	D₄	—	76	4	no	—
353	D₄	—	76	2	no	—
354	D₄	—	76	2	no	—
355	D₄	—	76	2	no	—
356	D₄	—	76	2	no	—
357	D₄	—	152	2	no	—
358	D₄	—	152	1	no	—
359	D₄	—	152	1	no	—
360	D₄	—	152	1	no	—
361	D₄	—	152	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	38	2	no	—
371	C₂×C₄	—	38	2	no	—
372	C₂×C₄	—	76	1	no	—
373	C₂×C₄	—	76	1	no	—
374	C₂×C₄	—	76	1	no	—
375	C₂×C₄	—	76	1	no	—
376	C₂×C₄	—	76	2	no	—
377	C₂×C₄	—	76	2	no	—
378	C₂×C₄	—	76	2	no	—
379	C₂×C₄	#10597321	1	1	yes	characteristic
380	C₂×C₄	#10597331	1	1	yes	characteristic
381	C₂×C₄	#10597331	1	1	yes	characteristic
382	C₂×C₄	#10597342	1	1	yes	characteristic
383	C₂×C₄	#10597342	1	1	yes	characteristic
384	C₂×C₄	#10597343	1	1	yes	characteristic
385	C₂×C₄	C₂×#64516	1	1	yes	characteristic
386	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
387	C₂×C₄	#10597354	1	1	yes	characteristic
388	C₂×C₄	#10597355	1	1	yes	characteristic
389	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
390	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
391	C₂×C₄	#10597360	1	1	yes	characteristic
392	C₂×C₄	#10597364	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	8	1	no	—
395	C₈	—	152	1	no	—
396	C₂²	—	304	1	no	—
397	C₂²	—	304	1	no	—
398	C₂²	—	304	1	no	—
399	C₂²	—	304	1	no	—
400	C₂²	—	152	2	no	—
401	C₂²	—	152	2	no	—
402	C₂²	—	152	2	no	—
403	C₂²	#11926457	1	1	yes	characteristic
404	C₂²	#11926679	1	1	yes	characteristic
405	C₂²	#11926680	1	1	yes	characteristic
406	C₂²	#11926684	1	1	yes	characteristic
407	C₂²	#11926685	1	1	yes	characteristic
408	C₂²	#11926713	1	1	yes	characteristic
409	C₂²	#11926718	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	76	2	no	—
415	C₄	—	76	2	no	—
416	C₄	—	152	2	no	—
417	C₄	#11926823	1	1	yes	characteristic
418	C₄	#11926825	1	1	yes	characteristic
419	C₄	#11926833	1	1	yes	characteristic
420	C₄	#11926835	1	1	yes	characteristic
421	C₄	#11926889	1	1	yes	characteristic
422	C₄	#11926891	1	1	yes	characteristic
423	C₄	#11926904	1	1	yes	characteristic
424	C₄	#11926905	1	1	yes	characteristic
425	C₂	—	304	2	no	—
426	C₂	#14562691	1	1	yes	characteristic
427	C₂	#14562715	1	1	yes	characteristic
428	C₂	#14562740	1	1	yes	characteristic
429	C₂	#14562741	1	1	yes	characteristic
430	C₂	#14564770	1	1	yes	characteristic
431	C₂	#14564772	1	1	yes	characteristic
432	C₂	#14564790	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#10348
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
1. #14568661	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561475	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
49. #10597320	Q₈	semidirect
186. #1279	D₁₉	semidirect
282. C₁₉	#10348	semidirect

Maximal subgroups

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

subgroup	index
#14568661	2
#14564562	2
#14564561	2
#14564441	2
#14561519	2
#14561475	2
C₁₉×#1279	2
#10348	19