Subgroups — #14567154

Order 2432.

500 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597392	C₂	1	1	yes	maximal, characteristic
2	#11926479	C₂	1	2	yes	maximal
3	#11926475	C₂	1	2	yes	maximal, complemented
4	#11926451	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926435	C₂	1	2	yes	maximal
7	#11926428	C₂	1	2	yes	maximal, complemented
8	#11926413	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926401	C₂	1	1	yes	maximal, characteristic
10	C₄×(C₂×D₁₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₁₉	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
19	#10597392	—	2	4	no	—
20	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
22	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
23	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
27	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
28	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
29	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
30	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
31	C₁₉⋊#95	C₂²	1	1	yes	characteristic
32	C₁₉⋊#95	C₂²	1	1	yes	characteristic
33	C₁₉⋊#95	C₂²	1	2	yes	—
34	C₁₉⋊#95	C₂²	1	2	yes	—
35	C₁₉⋊#95	C₂²	1	2	yes	—
36	C₁₉⋊#95	C₂²	1	2	yes	—
37	C₂³×D₁₉	C₂³	1	1	yes	characteristic
38	C₂×Q₈×C₁₉	—	2	2	no	—
39	C₂×Q₈×C₁₉	—	2	2	no	—
40	C₂×Q₈×C₁₉	D₄	1	4	yes	—
41	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
47	C₂²×Dic₁₉	C₂³	1	2	yes	—
48	C₂²×Dic₁₉	C₂³	1	2	yes	—
49	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
50	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
51	C₂×C₄×D₁₉	—	2	2	no	—
52	C₂×C₄×D₁₉	—	2	2	no	—
53	C₂×C₄×D₁₉	—	2	2	no	—
54	C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₄²×C₁₉	—	2	4	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	(C₂×D₁₉)⋊C₄	—	2	4	no	—
59	(C₂×D₁₉)⋊C₄	—	2	2	no	—
60	(C₂×D₁₉)⋊C₄	—	4	2	no	—
61	(C₂×D₁₉)⋊C₄	Q₈	1	4	yes	complemented
62	C₄⋊Dic₁₉	—	2	2	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	Dic₁₉⋊C₄	—	2	4	no	—
65	Dic₁₉⋊C₄	—	2	4	no	—
66	Dic₁₉⋊C₄	—	4	2	no	—
67	Dic₁₉⋊C₄	—	4	2	no	—
68	C₄×Dic₁₉	—	2	2	no	—
69	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
70	C₂²×D₁₉	—	2	1	no	—
71	C₂²×D₁₉	—	2	1	no	—
72	C₂²×D₁₉	—	2	1	no	—
73	C₂²×D₁₉	—	2	1	no	—
74	C₂²×D₁₉	—	2	1	no	—
75	C₂²×D₁₉	—	2	1	no	—
76	C₂²×D₁₉	C₂×Q₈	1	2	yes	—
77	Q₈×C₁₉	—	2	8	no	—
78	C₂×C₄×C₁₉	—	2	1	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	1	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	2	1	no	—
86	C₂×C₄×C₁₉	—	2	1	no	—
87	C₂×C₄×C₁₉	—	2	2	no	—
88	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
89	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
90	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
91	C₂×C₄×C₁₉	#41	1	2	yes	—
92	C₂×C₄×C₁₉	#41	1	2	yes	—
93	C₂×Dic₁₉	—	2	1	no	—
94	C₂×Dic₁₉	—	2	1	no	—
95	C₂×Dic₁₉	—	2	1	no	—
96	C₂×Dic₁₉	—	2	1	no	—
97	C₂×Dic₁₉	—	2	1	no	—
98	C₂×Dic₁₉	—	2	2	no	—
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	—	2	2	no	—
101	C₂×Dic₁₉	—	2	1	no	—
102	C₂×Dic₁₉	—	2	1	no	—
103	C₂×Dic₁₉	—	2	2	no	—
104	C₂×Dic₁₉	—	2	2	no	—
105	C₂×Dic₁₉	—	2	2	no	—
106	C₂×Dic₁₉	C₂×Q₈	1	2	yes	—
107	C₂×Dic₁₉	#41	1	2	yes	—
108	C₄×D₁₉	—	4	4	no	—
109	#2423	—	19	1	no	maximal, Sylow
110	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
111	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
112	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
113	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
114	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
115	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
116	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
117	C₂×D₁₉	—	2	2	no	—
118	C₂×D₁₉	—	2	2	no	—
119	C₂×D₁₉	—	2	2	no	—
120	C₂×D₁₉	—	4	1	no	—
121	C₂×D₁₉	—	4	1	no	—
122	C₂×D₁₉	—	4	1	no	—
123	C₂×D₁₉	—	4	1	no	—
124	C₄×C₁₉	—	2	4	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	4	2	no	—
127	C₄×C₁₉	—	4	1	no	—
128	C₄×C₁₉	#123	1	4	yes	—
129	Dic₁₉	—	2	2	no	—
130	Dic₁₉	—	2	2	no	—
131	Dic₁₉	—	4	1	no	—
132	Dic₁₉	—	4	2	no	—
133	Dic₁₉	—	4	2	no	—
134	C₂×C₂²⋊Q₈	—	19	1	no	—
135	C₂×C₄×Q₈	D₁₉	1	1	yes	characteristic, complemented
136	#399	—	19	2	no	—
137	#398	—	19	2	no	—
138	#391	—	19	1	no	—
139	#389	—	19	1	no	—
140	#388	—	19	2	no	—
141	#387	—	19	2	no	—
142	#384	—	19	1	no	—
143	#380	—	19	1	no	—
144	C₄×C₂²⋊C₄	—	19	1	no	—
145	C₂×C₁₉	C₂×#123	1	1	yes	characteristic
146	C₂×C₁₉	#533	1	1	yes	characteristic
147	C₂×C₁₉	#542	1	1	yes	characteristic
148	C₂×C₁₉	D₄×Q₈	1	1	yes	characteristic
149	C₂×C₁₉	#550	1	1	yes	characteristic
150	C₂×C₁₉	#552	1	1	yes	characteristic
151	C₂×C₁₉	#554	1	1	yes	characteristic
152	D₁₉	—	4	2	no	—
153	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
154	C₂³×C₄	—	19	1	no	—
155	C₂²⋊Q₈	—	38	4	no	—
156	C₄×Q₈	—	2	4	no	—
157	C₂×C₄⋊C₄	—	19	1	no	—
158	C₂×C₄⋊C₄	—	19	2	no	—
159	C₂×C₄⋊C₄	—	19	1	no	—
160	C₂×C₄⋊C₄	—	19	2	no	—
161	C₂×C₄⋊C₄	—	19	2	no	—
162	C₂×C₄⋊C₄	—	19	2	no	—
163	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
164	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
165	C₂×C₂²⋊C₄	—	19	1	no	—
166	C₂×C₂²⋊C₄	—	19	2	no	—
167	C₂×C₂²⋊C₄	—	19	1	no	—
168	C₂×C₂²⋊C₄	—	19	2	no	—
169	C₂×C₄²	—	19	1	no	—
170	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
171	C₂×C₄²	C₂×D₁₉	1	2	yes	—
172	#95	—	19	1	no	—
173	#95	—	19	1	no	—
174	#95	—	19	2	no	—
175	#95	—	19	2	no	—
176	#95	—	19	2	no	—
177	#95	—	19	2	no	—
178	C₁₉	#2423	1	1	yes	characteristic, complemented, Sylow
179	C₂⁴	—	19	1	no	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	C₂²⋊D₁₉	1	4	yes	—
183	C₂²×C₄	—	19	1	no	—
184	C₂²×C₄	—	19	1	no	—
185	C₂²×C₄	—	19	2	no	—
186	C₂²×C₄	—	19	1	no	—
187	C₂²×C₄	—	19	2	no	—
188	C₂²×C₄	—	38	2	no	—
189	C₂²×C₄	—	38	2	no	—
190	C₂²×C₄	—	38	2	no	—
191	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
192	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
193	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
194	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
195	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
196	C₄⋊C₄	—	2	4	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	38	4	no	—
199	C₄⋊C₄	—	38	2	no	—
200	C₄⋊C₄	—	38	4	no	—
201	C₄⋊C₄	—	38	2	no	—
202	C₄⋊C₄	—	76	2	no	—
203	C₄⋊C₄	—	76	2	no	—
204	C₂²⋊C₄	—	19	4	no	—
205	C₂²⋊C₄	—	38	2	no	—
206	C₂²⋊C₄	—	38	4	no	—
207	C₂²⋊C₄	—	76	2	no	—
208	C₄²	—	2	4	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	38	2	no	—
211	C₂³	—	19	2	no	—
212	C₂³	—	38	1	no	—
213	C₂³	—	38	1	no	—
214	C₂³	—	38	1	no	—
215	C₂³	—	38	1	no	—
216	C₂³	—	38	1	no	—
217	C₂³	—	38	1	no	—
218	C₂³	C₂³×D₁₉	1	1	yes	characteristic
219	Q₈	—	2	8	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	19	2	no	—
231	C₂×C₄	—	19	2	no	—
232	C₂×C₄	—	38	1	no	—
233	C₂×C₄	—	38	1	no	—
234	C₂×C₄	—	38	1	no	—
235	C₂×C₄	—	38	1	no	—
236	C₂×C₄	—	38	2	no	—
237	C₂×C₄	—	38	1	no	—
238	C₂×C₄	—	38	1	no	—
239	C₂×C₄	—	38	2	no	—
240	C₂×C₄	—	38	2	no	—
241	C₂×C₄	—	38	2	no	—
242	C₂×C₄	—	38	2	no	—
243	C₂×C₄	—	38	2	no	—
244	C₂×C₄	—	38	1	no	—
245	C₂×C₄	—	76	4	no	—
246	C₂×C₄	#64541	1	2	yes	—
247	C₂×C₄	#64541	1	2	yes	—
248	C₂×C₄	Q₈×D₁₉	1	2	yes	—
249	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
250	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
251	C₂²	—	38	2	no	—
252	C₂²	—	38	2	no	—
253	C₂²	—	38	2	no	—
254	C₂²	—	76	1	no	—
255	C₂²	—	76	1	no	—
256	C₂²	—	76	1	no	—
257	C₂²	—	76	1	no	—
258	C₂²	C₂×#64541	1	1	yes	characteristic
259	C₂²	C₂×#64541	1	1	yes	characteristic
260	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
261	C₂²	#10597433	1	1	yes	characteristic
262	C₂²	#41×D₁₉	1	1	yes	characteristic
263	C₂²	#10597435	1	1	yes	characteristic
264	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
265	C₄	—	2	4	no	—
266	C₄	—	2	2	no	—
267	C₄	—	4	1	no	—
268	C₄	—	4	2	no	—
269	C₄	—	38	2	no	—
270	C₄	—	38	2	no	—
271	C₄	—	76	1	no	—
272	C₄	—	76	2	no	—
273	C₄	—	76	2	no	—
274	C₄	#10597375	1	4	yes	—
275	C₂	—	76	2	no	—
276	C₂	C₂×#10597375	1	1	yes	characteristic
277	C₂	#11927098	1	1	yes	characteristic
278	C₂	#11927166	1	1	yes	characteristic
279	C₂	Q₈×C₂²⋊D₁₉	1	1	yes	characteristic
280	C₂	#11927213	1	1	yes	characteristic
281	C₂	#11927235	1	1	yes	characteristic
282	C₂	#11927254	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₄×Q₈×C₁₉	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	C₂×C₄×Q₈	D₁₉
hypocenter	C₁₉	#2423
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. #11926475	C₂	semidirect
4. #11926451	C₂	semidirect
5. #11926442	C₂	semidirect
7. #11926428	C₂	semidirect
8. #11926413	C₂	semidirect
11. C₂×C₄×Q₈×C₁₉	C₂	semidirect
61. (C₂×D₁₉)⋊C₄	Q₈	semidirect
135. C₂×C₄×Q₈	D₁₉	semidirect
178. C₁₉	#2423	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597392	2
#11926479	2
#11926475	2
#11926451	2
#11926442	2
#11926435	2
#11926428	2
#11926413	2
#11926401	2
C₄×(C₂×D₁₉)⋊C₄	2
C₂×C₄×Q₈×C₁₉	2
#2423	19