Subgroups — #14573884

Order 2432.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927152	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927016	C₂	1	1	yes	maximal, characteristic
3	#11926888	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926883	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926846	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926843	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926748	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926747	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926696	C₂	1	1	yes	maximal, characteristic
10	#11926693	C₂	1	1	yes	maximal, characteristic
11	#11926644	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926642	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#64516	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926603	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
17	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
20	#10597392	C₂²	1	1	yes	characteristic
21	#10597390	C₂²	1	1	yes	characteristic, complemented
22	C₂×#64527	C₂²	1	1	yes	characteristic
23	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×#64526	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊D₁₉	—	2	1	no	—
26	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
27	C₂×#64516	C₂²	1	1	yes	characteristic
28	#10597344	—	2	1	no	—
29	#10597343	C₂²	1	1	yes	characteristic
30	#10597339	C₂²	1	1	yes	characteristic
31	#10597338	C₂²	1	1	yes	characteristic
32	#10597336	C₂²	1	1	yes	characteristic, complemented
33	#10597335	—	2	1	no	—
34	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
35	C₂²⋊C₄×D₁₉	—	2	1	no	—
36	#10597322	—	2	1	no	—
37	C₄×D₇₆	C₂²	1	1	yes	characteristic
38	#10597318	C₂²	1	1	yes	characteristic
39	#10597316	—	2	1	no	—
40	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₉×#106	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#103	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#102	C₂²	1	1	yes	characteristic
44	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
45	#10597292	C₂²	1	1	yes	characteristic, complemented
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, complemented
51	#10597273	C₂²	1	1	yes	characteristic, complemented
52	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	#10597267	C₂²	1	1	yes	characteristic, complemented
55	#10597266	C₂²	1	1	yes	characteristic
56	#10597264	C₂²	1	1	yes	characteristic, complemented
57	#10597264	C₂²	1	1	yes	characteristic, complemented
58	#10597260	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₉	—	2	1	no	—
60	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂×C₂²⋊D₁₉	—	2	1	no	—
64	C₂²×Dic₁₉	—	2	1	no	—
65	D₄×D₁₉	—	2	2	no	—
66	D₄×D₁₉	—	2	2	no	—
67	C₂×D₇₆	C₂³	1	1	yes	characteristic
68	C₂×C₄×D₁₉	—	2	1	no	—
69	C₂×C₄×D₁₉	—	2	1	no	—
70	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
71	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
72	SD₁₆×C₁₉	—	2	2	no	—
73	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₄²×C₁₉	—	2	1	no	—
80	C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²⋊Dic₁₉	—	2	1	no	—
82	#64527	—	2	2	no	—
83	#64526	—	2	2	no	—
84	(C₂×D₁₉)⋊C₄	—	2	1	no	—
85	(C₂×D₁₉)⋊C₄	—	2	1	no	—
86	(C₂×D₁₉)⋊C₄	—	2	1	no	—
87	(C₂×D₁₉)⋊C₄	—	2	1	no	—
88	(C₂×D₁₉)⋊C₄	—	2	1	no	—
89	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
90	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
91	C₄⋊Dic₁₉	—	2	1	no	—
92	C₄⋊Dic₁₉	—	2	1	no	—
93	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
94	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
95	Dic₁₉⋊C₄	—	2	1	no	—
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	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
101	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
102	C₄×Dic₁₉	—	2	1	no	—
103	C₄×Dic₁₉	—	2	1	no	—
104	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
105	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
106	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
107	#64516	—	2	2	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂²×D₁₉	—	2	1	no	—
110	C₂²×D₁₉	—	2	4	no	—
111	C₂²×D₁₉	—	8	1	no	—
112	C₂²×D₁₉	—	8	1	no	—
113	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
114	Q₈×C₁₉	—	2	1	no	—
115	Q₈×C₁₉	—	2	1	no	—
116	D₄×C₁₉	—	2	1	no	—
117	D₄×C₁₉	#41	1	2	yes	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	8	1	no	—
122	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
125	C₂²⋊D₁₉	—	2	4	no	—
126	C₂×Dic₁₉	—	2	1	no	—
127	C₂×Dic₁₉	—	2	1	no	—
128	C₂×Dic₁₉	—	2	1	no	—
129	C₂×Dic₁₉	—	8	1	no	—
130	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
133	D₇₆	—	2	1	no	—
134	D₇₆	#41	1	2	yes	—
135	C₄×D₁₉	—	2	1	no	—
136	C₄×D₁₉	—	2	1	no	—
137	C₄×D₁₉	—	8	1	no	—
138	C₄×D₁₉	—	8	1	no	—
139	Dic₃₈	—	2	1	no	—
140	Dic₃₈	—	2	1	no	—
141	C₈×C₁₉	—	2	1	no	—
142	C₈×C₁₉	—	2	1	no	—
143	C₁₉⋊C₈	—	2	1	no	—
144	C₁₉⋊C₈	—	2	1	no	—
145	#3123	—	19	1	no	maximal, Sylow
146	C₂²×C₁₉	—	2	2	no	—
147	C₂²×C₁₉	—	4	1	no	—
148	C₂²×C₁₉	—	4	1	no	—
149	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
150	C₂×D₁₉	—	2	1	no	—
151	C₂×D₁₉	—	2	2	no	—
152	C₂×D₁₉	—	2	1	no	—
153	C₂×D₁₉	—	2	1	no	—
154	C₂×D₁₉	—	4	1	no	—
155	C₂×D₁₉	—	4	1	no	—
156	C₂×D₁₉	—	8	4	no	—
157	C₄×C₁₉	—	2	1	no	—
158	C₄×C₁₉	—	2	1	no	—
159	C₄×C₁₉	—	4	1	no	—
160	C₄×C₁₉	—	4	1	no	—
161	C₄×C₁₉	—	4	1	no	—
162	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
163	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
164	Dic₁₉	—	2	1	no	—
165	Dic₁₉	—	2	1	no	—
166	Dic₁₉	—	2	1	no	—
167	Dic₁₉	—	4	1	no	—
168	Dic₁₉	—	4	1	no	—
169	Dic₁₉	—	4	1	no	—
170	#541	—	19	1	no	—
171	#518	—	19	1	no	—
172	#485	—	19	1	no	—
173	#485	—	19	1	no	—
174	#478	—	19	1	no	—
175	#478	—	19	1	no	—
176	#461	—	19	1	no	—
177	#461	—	19	1	no	—
178	#450	—	19	1	no	—
179	#450	—	19	1	no	—
180	#440	—	19	1	no	—
181	#440	—	19	1	no	—
182	C₄×SD₁₆	—	19	1	no	—
183	C₄×SD₁₆	D₁₉	1	1	yes	characteristic, complemented
184	#433	—	19	1	no	—
185	C₂×C₁₉	—	4	2	no	—
186	C₂×C₁₉	#525	1	1	yes	characteristic
187	C₂×C₁₉	#577	1	1	yes	characteristic
188	C₂×C₁₉	#577	1	1	yes	characteristic
189	D₁₉	—	4	1	no	—
190	D₁₉	—	4	2	no	—
191	C₂²×D₄	—	19	1	no	—
192	C₂×SD₁₆	—	19	1	no	—
193	C₂×SD₁₆	—	19	1	no	—
194	C₂×SD₁₆	—	19	1	no	—
195	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
196	C₄⋊Q₈	—	19	1	no	—
197	#126	—	38	1	no	—
198	#126	—	38	1	no	—
199	#125	—	19	1	no	—
200	#125	—	38	1	no	—
201	#125	—	38	1	no	—
202	C₂²⋊Q₈	—	19	1	no	—
203	C₂²⋊Q₈	—	19	1	no	—
204	C₄×Q₈	—	19	1	no	—
205	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
206	C₄×D₄	—	19	1	no	—
207	C₄×D₄	—	19	1	no	—
208	C₄×D₄	—	19	1	no	—
209	C₄×D₄	—	38	1	no	—
210	C₄×D₄	—	38	1	no	—
211	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
212	#117	—	19	1	no	—
213	#117	—	19	1	no	—
214	C₂×C₂²⋊C₄	—	38	1	no	—
215	C₂×C₂²⋊C₄	—	38	1	no	—
216	#107	—	19	1	no	—
217	#107	—	19	1	no	—
218	#106	—	19	1	no	—
219	#106	C₂×D₁₉	1	1	yes	characteristic, complemented
220	C₄⋊C₈	—	19	1	no	—
221	C₄⋊C₈	—	19	1	no	—
222	#103	—	19	1	no	—
223	#103	—	19	1	no	—
224	#103	—	19	1	no	—
225	#103	C₂×D₁₉	1	1	yes	characteristic, complemented
226	#102	—	19	1	no	—
227	#102	—	19	1	no	—
228	#102	—	19	1	no	—
229	#102	C₂×D₁₉	1	1	yes	characteristic
230	C₂²⋊C₈	—	19	1	no	—
231	C₂²⋊C₈	—	19	1	no	—
232	#97	—	19	1	no	—
233	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
234	C₁₉	#3123	1	1	yes	characteristic, complemented, Sylow
235	C₂⁴	—	38	1	no	—
236	C₂×Q₈	—	19	1	no	—
237	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
238	C₂×D₄	—	19	1	no	—
239	C₂×D₄	—	38	1	no	—
240	C₂×D₄	—	38	2	no	—
241	C₂×D₄	—	38	2	no	—
242	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
243	C₂²×C₄	—	2	1	no	—
244	C₂²×C₄	—	19	1	no	—
245	C₂²×C₄	—	38	1	no	—
246	C₂²×C₄	—	38	1	no	—
247	C₂²×C₄	—	38	1	no	—
248	SD₁₆	—	2	2	no	—
249	SD₁₆	—	38	2	no	—
250	SD₁₆	—	38	2	no	—
251	SD₁₆	—	38	2	no	—
252	C₂×C₈	—	19	1	no	—
253	C₂×C₈	—	19	1	no	—
254	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
255	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
256	C₄⋊C₄	—	2	1	no	—
257	C₄⋊C₄	—	19	1	no	—
258	C₄⋊C₄	—	19	1	no	—
259	C₄⋊C₄	—	19	1	no	—
260	C₄⋊C₄	—	19	1	no	—
261	C₄⋊C₄	—	38	1	no	—
262	C₄⋊C₄	—	38	1	no	—
263	C₄⋊C₄	—	38	1	no	—
264	C₄⋊C₄	—	38	1	no	—
265	C₄⋊C₄	—	38	1	no	—
266	C₄⋊C₄	—	38	1	no	—
267	C₄⋊C₄	—	38	1	no	—
268	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
269	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
270	C₂²⋊C₄	—	2	1	no	—
271	C₂²⋊C₄	—	19	1	no	—
272	C₂²⋊C₄	—	19	1	no	—
273	C₂²⋊C₄	—	38	1	no	—
274	C₂²⋊C₄	—	38	1	no	—
275	C₂²⋊C₄	—	38	1	no	—
276	C₂²⋊C₄	—	38	1	no	—
277	C₂²⋊C₄	—	38	1	no	—
278	C₂²⋊C₄	—	38	1	no	—
279	C₄²	—	2	1	no	—
280	C₄²	—	19	1	no	—
281	C₄²	—	38	1	no	—
282	C₄²	—	38	1	no	—
283	C₄²	C₂²×D₁₉	1	1	yes	characteristic
284	C₂³	—	2	1	no	—
285	C₂³	—	19	1	no	—
286	C₂³	—	38	4	no	—
287	C₂³	—	38	1	no	—
288	C₂³	—	152	1	no	—
289	C₂³	—	152	1	no	—
290	Q₈	—	2	1	no	—
291	Q₈	—	2	1	no	—
292	Q₈	—	38	1	no	—
293	Q₈	—	38	1	no	—
294	D₄	—	2	1	no	—
295	D₄	—	19	2	no	—
296	D₄	—	38	4	no	—
297	D₄	—	38	1	no	—
298	D₄	#64541	1	2	yes	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	8	1	no	—
303	C₂×C₄	—	19	1	no	—
304	C₂×C₄	—	19	1	no	—
305	C₂×C₄	—	19	1	no	—
306	C₂×C₄	—	38	1	no	—
307	C₂×C₄	—	38	1	no	—
308	C₂×C₄	—	38	1	no	—
309	C₂×C₄	—	38	1	no	—
310	C₂×C₄	—	38	1	no	—
311	C₂×C₄	—	152	1	no	—
312	C₂×C₄	—	152	1	no	—
313	C₂×C₄	—	152	1	no	—
314	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
315	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
316	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
317	C₈	—	2	1	no	—
318	C₈	—	2	1	no	—
319	C₈	—	38	1	no	—
320	C₈	—	38	1	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	4	1	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	38	1	no	—
325	C₂²	—	38	2	no	—
326	C₂²	—	38	1	no	—
327	C₂²	—	38	1	no	—
328	C₂²	—	76	1	no	—
329	C₂²	—	76	1	no	—
330	C₂²	—	152	4	no	—
331	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	4	1	no	—
335	C₄	—	4	1	no	—
336	C₄	—	4	1	no	—
337	C₄	—	38	1	no	—
338	C₄	—	38	1	no	—
339	C₄	—	38	1	no	—
340	C₄	—	76	1	no	—
341	C₄	—	76	1	no	—
342	C₄	—	76	1	no	—
343	C₄	C₂×#64541	1	1	yes	characteristic
344	C₄	#41×D₁₉	1	1	yes	characteristic
345	C₂	—	4	2	no	—
346	C₂	—	76	1	no	—
347	C₂	—	76	2	no	—
348	C₂	#11927053	1	1	yes	characteristic
349	C₂	#11927350	1	1	yes	characteristic
350	C₂	#11927351	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×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	C₂×D₄×D₁₉	C₂²
hypercenter	C₄×SD₁₆	D₁₉
hypocenter	C₁₉	#3123
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #11927152	C₂	semidirect
3. #11926888	C₂	semidirect
4. #11926883	C₂	semidirect
5. #11926846	C₂	semidirect
6. #11926843	C₂	semidirect
7. #11926748	C₂	semidirect
8. #11926747	C₂	semidirect
11. #11926644	C₂	semidirect
12. #11926642	C₂	semidirect
13. C₄×#64516	C₂	semidirect
14. #11926603	C₂	semidirect
15. C₄×SD₁₆×C₁₉	C₂	semidirect
18. C₄×Q₈×C₁₉	C₂²	semidirect
21. #10597390	C₂²	semidirect
32. #10597336	C₂²	semidirect
40. C₄×Dic₃₈	C₂²	semidirect
41. C₁₉×#106	C₂²	semidirect
42. C₁₉×#103	C₂²	semidirect
44. C₄×C₈×C₁₉	C₂²	semidirect
45. #10597292	C₂²	semidirect
50. #10597274	C₂²	semidirect
51. #10597273	C₂²	semidirect
52. Dic₁₉⋊C₈	C₂²	semidirect
53. Dic₁₉⋊C₈	C₂²	semidirect
54. #10597267	C₂²	semidirect
56. #10597264	C₂²	semidirect
57. #10597264	C₂²	semidirect
58. #10597260	C₂²	semidirect
183. C₄×SD₁₆	D₁₉	semidirect
205. C₄×Q₈	C₂×D₁₉	semidirect
219. #106	C₂×D₁₉	semidirect
225. #103	C₂×D₁₉	semidirect
233. C₄×C₈	C₂×D₁₉	semidirect
234. C₁₉	#3123	semidirect

Maximal subgroups

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

subgroup	index
#11927152	2
#11927016	2
#11926888	2
#11926883	2
#11926846	2
#11926843	2
#11926748	2
#11926747	2
#11926696	2
#11926693	2
#11926644	2
#11926642	2
C₄×#64516	2
#11926603	2
C₄×SD₁₆×C₁₉	2
#3123	19