Subgroups — #14573664

Order 2432.

428 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927091	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926864	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926861	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926828	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926827	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926743	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926742	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926684	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926681	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#64516	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#64527	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#64526	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926595	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic
17	C₂×#64541	—	2	1	no	—
18	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
22	C₂×#64527	C₂²	1	1	yes	characteristic
23	#10597386	C₂²	1	1	yes	characteristic
24	#10597384	C₂²	1	1	yes	characteristic
25	C₂×#64526	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₁₉	—	2	1	no	—
27	C₂×#64516	C₂²	1	1	yes	characteristic
28	#10597341	C₂²	1	1	yes	characteristic
29	C₄⋊C₄×D₁₉	—	2	1	no	—
30	C₄⋊C₄×D₁₉	C₂²	1	1	yes	characteristic
31	#10597334	C₂²	1	1	yes	characteristic
32	#10597333	—	2	1	no	—
33	#10597333	C₂²	1	1	yes	characteristic
34	#10597331	—	2	1	no	—
35	#10597330	—	2	1	no	—
36	C₄×D₇₆	C₂²	1	1	yes	characteristic
37	C₄²×D₁₉	—	2	1	no	—
38	C₄²×D₁₉	C₂²	1	1	yes	characteristic
39	C₄×Dic₃₈	—	2	1	no	—
40	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
41	C₁₉×#106	C₂²	1	1	yes	characteristic
42	C₁₉×#103	C₂²	1	1	yes	characteristic
43	C₁₉×#102	C₂²	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
45	#10597292	C₂²	1	1	yes	characteristic
46	#10597289	C₂²	1	1	yes	characteristic
47	#10597278	C₂²	1	1	yes	characteristic
48	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
50	#10597274	C₂²	1	1	yes	characteristic
51	#10597273	C₂²	1	1	yes	characteristic
52	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
53	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
54	#10597267	C₂²	1	1	yes	characteristic
55	#10597266	C₂²	1	1	yes	characteristic
56	#10597265	C₂²	1	1	yes	characteristic
57	#10597265	C₂²	1	1	yes	characteristic
58	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂×C₂²⋊D₁₉	—	2	1	no	—
63	C₂×C₂²⋊D₁₉	—	2	1	no	—
64	C₂×C₂²⋊D₁₉	—	2	1	no	—
65	Q₈×D₁₉	—	2	2	no	—
66	Q₈×D₁₉	—	2	2	no	—
67	#64541	—	4	4	no	—
68	C₂×D₇₆	—	2	1	no	—
69	C₂×D₇₆	C₂³	1	1	yes	characteristic
70	C₂×C₄×D₁₉	—	2	1	no	—
71	C₂×C₄×D₁₉	—	2	1	no	—
72	C₂×C₄×D₁₉	—	2	1	no	—
73	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
74	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
76	C₂×Dic₃₈	—	2	1	no	—
77	C₂×Dic₃₈	—	2	1	no	—
78	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
79	SD₁₆×C₁₉	—	2	2	no	—
80	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
82	C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₄²×C₁₉	—	2	1	no	—
87	C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²⋊Dic₁₉	—	2	1	no	—
89	#64527	—	2	2	no	—
90	#64526	—	2	2	no	—
91	(C₂×D₁₉)⋊C₄	—	2	1	no	—
92	(C₂×D₁₉)⋊C₄	—	2	1	no	—
93	C₄⋊Dic₁₉	—	2	1	no	—
94	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
96	Dic₁₉⋊C₄	—	2	1	no	—
97	Dic₁₉⋊C₄	—	2	1	no	—
98	Dic₁₉⋊C₄	—	2	1	no	—
99	Dic₁₉⋊C₄	—	2	1	no	—
100	C₄×Dic₁₉	—	2	1	no	—
101	C₄×Dic₁₉	—	2	1	no	—
102	C₄×Dic₁₉	—	2	1	no	—
103	C₄×Dic₁₉	D₄	1	1	yes	characteristic
104	C₄×Dic₁₉	D₄	1	1	yes	characteristic
105	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
108	#64516	—	2	2	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂²×D₁₉	—	2	1	no	—
111	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
112	Q₈×C₁₉	—	2	1	no	—
113	Q₈×C₁₉	#41	1	2	yes	complemented
114	D₄×C₁₉	—	2	1	no	—
115	D₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	4	2	no	—
120	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
123	C₂²⋊D₁₉	—	4	2	no	—
124	C₂²⋊D₁₉	—	4	2	no	—
125	C₂²⋊D₁₉	—	4	2	no	—
126	C₂×Dic₁₉	—	2	1	no	—
127	C₂×Dic₁₉	—	2	1	no	—
128	C₂×Dic₁₉	—	2	1	no	—
129	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
132	D₇₆	—	2	1	no	—
133	D₇₆	—	2	1	no	—
134	D₇₆	—	4	2	no	—
135	C₄×D₁₉	—	2	4	no	—
136	C₄×D₁₉	—	2	1	no	—
137	C₄×D₁₉	—	2	1	no	—
138	C₄×D₁₉	—	4	1	no	—
139	C₄×D₁₉	—	4	2	no	—
140	C₄×D₁₉	—	4	2	no	—
141	C₄×D₁₉	SD₁₆	1	4	yes	complemented
142	Dic₃₈	—	2	4	no	—
143	Dic₃₈	—	2	1	no	—
144	Dic₃₈	—	4	2	no	—
145	Dic₃₈	#41	1	2	yes	complemented
146	C₈×C₁₉	—	2	1	no	—
147	C₈×C₁₉	—	2	1	no	—
148	C₁₉⋊C₈	—	2	1	no	—
149	C₁₉⋊C₈	—	2	1	no	—
150	#3103	—	19	1	no	maximal, Sylow
151	C₂²×C₁₉	—	4	1	no	—
152	C₂²×C₁₉	—	4	1	no	—
153	C₂²×C₁₉	—	4	1	no	—
154	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
155	C₂×D₁₉	—	2	1	no	—
156	C₂×D₁₉	—	2	1	no	—
157	C₂×D₁₉	—	4	1	no	—
158	C₂×D₁₉	—	4	1	no	—
159	C₂×D₁₉	—	4	1	no	—
160	C₂×D₁₉	C₂×SD₁₆	1	2	yes	—
161	C₄×C₁₉	—	2	2	no	—
162	C₄×C₁₉	—	2	1	no	—
163	C₄×C₁₉	—	4	1	no	—
164	C₄×C₁₉	—	4	1	no	—
165	C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
166	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
167	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
168	Dic₁₉	—	2	1	no	—
169	Dic₁₉	—	2	2	no	—
170	Dic₁₉	—	2	1	no	—
171	Dic₁₉	—	4	1	no	—
172	Dic₁₉	—	4	1	no	—
173	Dic₁₉	C₂×SD₁₆	1	2	yes	—
174	#532	—	19	1	no	—
175	C₂×C₄×Q₈	—	19	1	no	—
176	#481	—	19	1	no	—
177	#481	—	19	1	no	—
178	#475	—	19	1	no	—
179	#475	—	19	1	no	—
180	#460	—	19	1	no	—
181	#460	—	19	1	no	—
182	#448	—	19	1	no	—
183	#448	—	19	1	no	—
184	C₄×SD₁₆	—	19	1	no	—
185	C₄×SD₁₆	—	19	1	no	—
186	C₄×SD₁₆	—	19	1	no	—
187	C₄×SD₁₆	D₁₉	1	1	yes	characteristic, complemented
188	#431	—	19	1	no	—
189	C₂×C₁₉	—	8	1	no	—
190	C₂×C₁₉	#525	1	1	yes	characteristic
191	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
192	C₂×C₁₉	#575	1	1	yes	characteristic
193	D₁₉	—	2	2	no	—
194	D₁₉	—	8	1	no	—
195	C₂×#41	—	38	1	no	—
196	C₂²×Q₈	—	19	1	no	—
197	C₂×SD₁₆	—	19	1	no	—
198	C₂×SD₁₆	—	19	1	no	—
199	C₂×SD₁₆	—	19	1	no	—
200	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
201	C₄⋊Q₈	—	19	1	no	—
202	#127	—	19	1	no	—
203	#124	—	38	1	no	—
204	#121	—	19	1	no	—
205	#121	—	19	1	no	—
206	#121	—	38	1	no	—
207	C₄×Q₈	—	19	1	no	—
208	C₄×Q₈	—	19	1	no	—
209	C₄×Q₈	—	19	1	no	—
210	C₄×Q₈	—	38	1	no	—
211	C₄×Q₈	—	38	1	no	—
212	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
213	C₄×D₄	—	19	1	no	—
214	C₄×D₄	—	38	1	no	—
215	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄⋊C₄	—	19	1	no	—
217	C₂×C₄⋊C₄	—	38	1	no	—
218	C₂×C₄²	—	19	1	no	—
219	C₂×C₄²	—	38	1	no	—
220	#106	—	19	1	no	—
221	#106	—	19	1	no	—
222	#106	—	19	1	no	—
223	#106	C₂×D₁₉	1	1	yes	characteristic
224	C₄⋊C₈	—	19	1	no	—
225	C₄⋊C₈	—	19	1	no	—
226	#103	—	19	1	no	—
227	#103	—	19	1	no	—
228	#103	—	19	1	no	—
229	#103	C₂×D₁₉	1	1	yes	characteristic
230	#102	—	19	1	no	—
231	#102	—	19	1	no	—
232	#102	—	19	1	no	—
233	#102	C₂×D₁₉	1	1	yes	characteristic
234	C₂²⋊C₈	—	19	1	no	—
235	C₂²⋊C₈	—	19	1	no	—
236	C₄×C₈	—	19	1	no	—
237	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
238	C₁₉	#3103	1	1	yes	characteristic, complemented, Sylow
239	#41	—	76	4	no	—
240	C₂×Q₈	—	19	1	no	—
241	C₂×Q₈	—	38	1	no	—
242	C₂×Q₈	—	38	1	no	—
243	C₂×Q₈	—	38	2	no	—
244	C₂×Q₈	—	38	2	no	—
245	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
246	C₂×D₄	—	19	1	no	—
247	C₂×D₄	—	38	1	no	—
248	C₂×D₄	—	38	1	no	—
249	C₂×D₄	—	38	1	no	—
250	C₂×D₄	—	38	1	no	—
251	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
252	C₂²×C₄	—	2	1	no	—
253	C₂²×C₄	—	19	1	no	—
254	C₂²×C₄	—	19	1	no	—
255	C₂²×C₄	—	19	1	no	—
256	C₂²×C₄	—	38	1	no	—
257	C₂²×C₄	—	38	1	no	—
258	C₂²×C₄	—	38	1	no	—
259	SD₁₆	—	2	2	no	—
260	SD₁₆	—	38	2	no	—
261	SD₁₆	—	38	2	no	—
262	SD₁₆	—	38	2	no	—
263	C₂×C₈	—	19	1	no	—
264	C₂×C₈	—	19	1	no	—
265	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
266	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
267	C₄⋊C₄	—	2	1	no	—
268	C₄⋊C₄	—	19	1	no	—
269	C₄⋊C₄	—	19	1	no	—
270	C₄⋊C₄	—	38	1	no	—
271	C₄⋊C₄	—	38	1	no	—
272	C₄⋊C₄	—	38	1	no	—
273	C₄⋊C₄	—	38	1	no	—
274	C₄⋊C₄	—	38	1	no	—
275	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
276	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	—	38	1	no	—
279	C₂²⋊C₄	—	38	1	no	—
280	C₂²⋊C₄	—	38	1	no	—
281	C₄²	—	2	1	no	—
282	C₄²	—	19	1	no	—
283	C₄²	—	19	1	no	—
284	C₄²	—	19	1	no	—
285	C₄²	—	38	1	no	—
286	C₄²	—	38	1	no	—
287	C₄²	—	38	1	no	—
288	C₄²	C₂²×D₁₉	1	1	yes	characteristic
289	C₂³	—	2	1	no	—
290	C₂³	—	19	1	no	—
291	C₂³	—	38	1	no	—
292	Q₈	—	2	1	no	—
293	Q₈	—	19	2	no	—
294	Q₈	—	38	4	no	—
295	Q₈	—	38	1	no	—
296	Q₈	—	76	2	no	—
297	Q₈	#64541	1	2	yes	complemented
298	D₄	—	2	1	no	—
299	D₄	—	2	1	no	—
300	D₄	—	38	1	no	—
301	D₄	—	38	1	no	—
302	D₄	—	76	2	no	—
303	D₄	—	76	2	no	—
304	D₄	—	76	2	no	—
305	D₄	—	76	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	19	1	no	—
311	C₂×C₄	—	19	4	no	—
312	C₂×C₄	—	19	1	no	—
313	C₂×C₄	—	19	1	no	—
314	C₂×C₄	—	38	4	no	—
315	C₂×C₄	—	38	1	no	—
316	C₂×C₄	—	38	1	no	—
317	C₂×C₄	—	38	1	no	—
318	C₂×C₄	—	38	1	no	—
319	C₂×C₄	—	38	1	no	—
320	C₂×C₄	—	76	1	no	—
321	C₂×C₄	—	76	2	no	—
322	C₂×C₄	—	76	2	no	—
323	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
325	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
326	C₈	—	2	1	no	—
327	C₈	—	2	1	no	—
328	C₈	—	38	1	no	—
329	C₈	—	38	1	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	4	1	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	19	2	no	—
334	C₂²	—	38	1	no	—
335	C₂²	—	38	1	no	—
336	C₂²	—	76	1	no	—
337	C₂²	—	76	1	no	—
338	C₂²	—	76	1	no	—
339	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	1	no	—
342	C₄	—	4	1	no	—
343	C₄	—	4	1	no	—
344	C₄	—	19	2	no	—
345	C₄	—	38	1	no	—
346	C₄	—	38	2	no	—
347	C₄	—	38	1	no	—
348	C₄	—	76	1	no	—
349	C₄	—	76	1	no	—
350	C₄	SD₁₆×D₁₉	1	2	yes	—
351	C₄	C₂×#64541	1	1	yes	characteristic
352	C₄	#41×D₁₉	1	1	yes	characteristic
353	C₂	—	8	1	no	—
354	C₂	—	38	2	no	—
355	C₂	—	152	1	no	—
356	C₂	#11927053	1	1	yes	characteristic
357	C₂	C₂×SD₁₆×D₁₉	1	1	yes	characteristic
358	C₂	#11927341	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₄×SD₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11927091	C₂
hypercenter	C₄×SD₁₆	D₁₉
hypocenter	C₁₉	#3103
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×D₁₉	C₂	semidirect
3. #11926864	C₂	semidirect
4. #11926861	C₂	semidirect
5. #11926828	C₂	semidirect
6. #11926827	C₂	semidirect
7. #11926743	C₂	semidirect
8. #11926742	C₂	semidirect
9. #11926684	C₂	semidirect
10. #11926681	C₂	semidirect
11. C₄×#64516	C₂	semidirect
12. C₄×#64527	C₂	semidirect
13. C₄×#64526	C₂	semidirect
14. #11926595	C₂	semidirect
15. C₄×SD₁₆×C₁₉	C₂	semidirect
113. Q₈×C₁₉	#41	semidirect
141. C₄×D₁₉	SD₁₆	semidirect
145. Dic₃₈	#41	semidirect
187. C₄×SD₁₆	D₁₉	semidirect
238. C₁₉	#3103	semidirect
297. Q₈	#64541	semidirect

Maximal subgroups

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

subgroup	index
#11927091	2
C₄×Q₈×D₁₉	2
#11926864	2
#11926861	2
#11926828	2
#11926827	2
#11926743	2
#11926742	2
#11926684	2
#11926681	2
C₄×#64516	2
C₄×#64527	2
C₄×#64526	2
#11926595	2
C₄×SD₁₆×C₁₉	2
#3103	19