Subgroups — #14568071

Order 2432.

428 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11926483	C₂	1	2	yes	maximal, complemented
2	#11926466	C₂	1	2	yes	maximal
3	#11926443	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926442	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926434	C₂	1	2	yes	maximal
6	#11926425	C₂	1	2	yes	maximal, complemented
7	#11926401	C₂	1	1	yes	maximal, characteristic
8	#11926401	C₂	1	1	yes	maximal, characteristic
9	C₄⋊C₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×(C₂×D₁₉)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
20	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
21	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
25	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
26	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
28	C₁₉⋊#95	C₂²	1	1	yes	characteristic
29	C₁₉⋊#95	C₂²	1	1	yes	characteristic
30	C₁₉⋊#95	C₂²	1	2	yes	—
31	C₁₉⋊#95	C₂²	1	2	yes	—
32	C₁₉⋊#95	C₂²	1	2	yes	—
33	C₁₉⋊#95	C₂²	1	2	yes	—
34	C₁₉⋊#95	C₂²	1	2	yes	—
35	C₂³×D₁₉	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₉	C₂³	1	2	yes	—
43	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
44	C₂²×Dic₁₉	C₂³	1	2	yes	—
45	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
46	C₂×C₄×D₁₉	—	2	2	no	—
47	C₂×C₄×D₁₉	—	2	2	no	—
48	C₂×C₄×D₁₉	—	2	2	no	—
49	C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₄⋊C₄×C₁₉	—	4	2	no	—
52	C₄⋊C₄×C₁₉	—	4	2	no	—
53	C₄²×C₁₉	—	2	2	no	—
54	(C₂×D₁₉)⋊C₄	—	2	2	no	—
55	(C₂×D₁₉)⋊C₄	—	4	2	no	—
56	(C₂×D₁₉)⋊C₄	—	4	2	no	—
57	(C₂×D₁₉)⋊C₄	Q₈	1	4	yes	—
58	C₄⋊Dic₁₉	—	2	2	no	—
59	C₄⋊Dic₁₉	—	2	2	no	—
60	C₄⋊Dic₁₉	—	4	2	no	—
61	Dic₁₉⋊C₄	—	2	4	no	—
62	C₄×Dic₁₉	—	2	2	no	—
63	C₄×Dic₁₉	—	4	2	no	—
64	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
65	C₂²×D₁₉	—	2	1	no	—
66	C₂²×D₁₉	—	2	1	no	—
67	C₂²×D₁₉	—	2	1	no	—
68	C₂²×D₁₉	—	2	1	no	—
69	C₂²×D₁₉	—	2	1	no	—
70	C₂²×D₁₉	—	2	1	no	—
71	C₂²×D₁₉	C₂×Q₈	1	2	yes	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	1	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	2	no	—
77	C₂×C₄×C₁₉	—	2	2	no	—
78	C₂×C₄×C₁₉	—	2	2	no	—
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂×C₄×C₁₉	#41	1	2	yes	—
84	C₂×C₄×C₁₉	#41	1	2	yes	—
85	C₂×C₄×C₁₉	#41	1	2	yes	—
86	C₂×C₄×C₁₉	#41	1	2	yes	—
87	C₂×Dic₁₉	—	2	1	no	—
88	C₂×Dic₁₉	—	2	1	no	—
89	C₂×Dic₁₉	—	2	1	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	2	no	—
93	C₂×Dic₁₉	—	2	2	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	1	no	—
100	C₂×Dic₁₉	—	2	2	no	—
101	C₂×Dic₁₉	C₂×Q₈	1	2	yes	—
102	C₄×D₁₉	—	4	4	no	—
103	#2497	—	19	1	no	maximal, Sylow
104	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
105	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
106	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
107	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
108	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
109	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
110	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
111	C₂×D₁₉	—	2	2	no	—
112	C₂×D₁₉	—	2	2	no	—
113	C₂×D₁₉	—	2	2	no	—
114	C₂×D₁₉	—	4	1	no	—
115	C₂×D₁₉	—	4	1	no	—
116	C₂×D₁₉	—	4	1	no	—
117	C₂×D₁₉	—	4	1	no	—
118	C₄×C₁₉	—	2	2	no	—
119	C₄×C₁₉	—	2	2	no	—
120	C₄×C₁₉	—	4	2	no	—
121	C₄×C₁₉	—	4	2	no	—
122	C₄×C₁₉	#126	1	4	yes	—
123	Dic₁₉	—	2	2	no	—
124	Dic₁₉	—	4	1	no	—
125	Dic₁₉	—	4	2	no	—
126	Dic₁₉	—	4	1	no	—
127	Dic₁₉	—	4	2	no	—
128	#400	—	19	2	no	—
129	#396	—	19	2	no	—
130	#389	—	19	1	no	—
131	#389	—	19	1	no	—
132	#388	—	19	2	no	—
133	#387	—	19	2	no	—
134	#384	D₁₉	1	1	yes	characteristic, complemented
135	#380	—	19	1	no	—
136	#380	—	19	1	no	—
137	C₄×C₄⋊C₄	—	19	1	no	—
138	C₄×C₂²⋊C₄	—	19	1	no	—
139	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
140	C₂×C₁₉	#533	1	1	yes	characteristic
141	C₂×C₁₉	#540	1	1	yes	characteristic
142	C₂×C₁₉	#553	1	1	yes	characteristic
143	C₂×C₁₉	#554	1	1	yes	characteristic
144	C₂×C₁₉	#554	1	1	yes	characteristic
145	C₂×C₁₉	#555	1	1	yes	characteristic
146	D₁₉	—	4	2	no	—
147	C₂³×C₄	—	19	1	no	—
148	C₂×C₄⋊C₄	—	19	1	no	—
149	C₂×C₄⋊C₄	—	19	1	no	—
150	C₂×C₄⋊C₄	—	19	2	no	—
151	C₂×C₄⋊C₄	—	19	2	no	—
152	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
153	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
154	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
155	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
156	C₂×C₂²⋊C₄	—	19	1	no	—
157	C₂×C₂²⋊C₄	—	19	1	no	—
158	C₂×C₂²⋊C₄	—	19	2	no	—
159	C₂×C₂²⋊C₄	—	19	2	no	—
160	C₂×C₄²	—	19	1	no	—
161	C₂×C₄²	—	19	2	no	—
162	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
163	#95	—	19	1	no	—
164	#95	—	19	1	no	—
165	#95	—	19	2	no	—
166	#95	—	19	2	no	—
167	#95	—	19	2	no	—
168	#95	—	19	2	no	—
169	#95	—	19	2	no	—
170	C₁₉	#2497	1	1	yes	characteristic, complemented, Sylow
171	C₂⁴	—	19	1	no	—
172	C₂²×C₄	—	19	1	no	—
173	C₂²×C₄	—	19	1	no	—
174	C₂²×C₄	—	19	2	no	—
175	C₂²×C₄	—	19	1	no	—
176	C₂²×C₄	—	19	2	no	—
177	C₂²×C₄	—	38	2	no	—
178	C₂²×C₄	—	38	2	no	—
179	C₂²×C₄	—	38	2	no	—
180	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
181	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
182	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
183	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
184	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄⋊C₄	—	38	2	no	—
190	C₄⋊C₄	—	38	4	no	—
191	C₄⋊C₄	—	38	2	no	—
192	C₄⋊C₄	—	76	2	no	—
193	C₂²⋊C₄	—	19	4	no	—
194	C₂²⋊C₄	—	38	2	no	—
195	C₂²⋊C₄	—	76	2	no	—
196	C₂²⋊C₄	—	76	2	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	38	2	no	—
199	C₄²	—	76	2	no	—
200	C₂³	—	19	2	no	—
201	C₂³	—	38	1	no	—
202	C₂³	—	38	1	no	—
203	C₂³	—	38	1	no	—
204	C₂³	—	38	1	no	—
205	C₂³	—	38	1	no	—
206	C₂³	—	38	1	no	—
207	C₂³	C₂³×D₁₉	1	1	yes	characteristic
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	19	2	no	—
219	C₂×C₄	—	38	1	no	—
220	C₂×C₄	—	38	1	no	—
221	C₂×C₄	—	38	2	no	—
222	C₂×C₄	—	38	1	no	—
223	C₂×C₄	—	38	1	no	—
224	C₂×C₄	—	38	2	no	—
225	C₂×C₄	—	38	2	no	—
226	C₂×C₄	—	38	1	no	—
227	C₂×C₄	—	38	1	no	—
228	C₂×C₄	—	38	1	no	—
229	C₂×C₄	—	38	2	no	—
230	C₂×C₄	—	38	2	no	—
231	C₂×C₄	—	38	2	no	—
232	C₂×C₄	—	38	1	no	—
233	C₂×C₄	—	76	4	no	—
234	C₂×C₄	#64541	1	2	yes	—
235	C₂×C₄	#64543	1	2	yes	—
236	C₂×C₄	Q₈×D₁₉	1	2	yes	—
237	C₂×C₄	#64545	1	2	yes	—
238	C₂×C₄	#64545	1	2	yes	—
239	C₂²	—	38	2	no	—
240	C₂²	—	38	2	no	—
241	C₂²	—	38	2	no	—
242	C₂²	—	76	1	no	—
243	C₂²	—	76	1	no	—
244	C₂²	—	76	1	no	—
245	C₂²	—	76	1	no	—
246	C₂²	C₂×#64541	1	1	yes	characteristic
247	C₂²	C₂×#64543	1	1	yes	characteristic
248	C₂²	#10597430	1	1	yes	characteristic
249	C₂²	#10597430	1	1	yes	characteristic
250	C₂²	C₂×Q₈×D₁₉	1	1	yes	characteristic
251	C₂²	C₂×#64545	1	1	yes	characteristic
252	C₂²	C₂×#64545	1	1	yes	characteristic
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	4	2	no	—
256	C₄	—	4	2	no	—
257	C₄	—	38	2	no	—
258	C₄	—	76	1	no	—
259	C₄	—	76	2	no	—
260	C₄	—	76	2	no	—
261	C₄	—	76	1	no	—
262	C₄	#10597344	1	4	yes	—
263	C₂	—	76	2	no	—
264	C₂	C₂×#10597344	1	1	yes	characteristic
265	C₂	#11927099	1	1	yes	characteristic
266	C₂	#11927148	1	1	yes	characteristic
267	C₂	#11927242	1	1	yes	characteristic
268	C₂	#11927249	1	1	yes	characteristic
269	C₂	#11927255	1	1	yes	characteristic
270	C₂	#11927260	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#384	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	#384	D₁₉
hypocenter	C₁₉	#2497
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #384

Complements

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

N	H ≅ G/N	type
1. #11926483	C₂	semidirect
3. #11926443	C₂	semidirect
4. #11926442	C₂	semidirect
6. #11926425	C₂	semidirect
9. C₄⋊C₄×Dic₁₉	C₂	semidirect
11. C₁₉×#384	C₂	semidirect
134. #384	D₁₉	semidirect
170. C₁₉	#2497	semidirect

Maximal subgroups

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

subgroup	index
#11926483	2
#11926466	2
#11926443	2
#11926442	2
#11926434	2
#11926425	2
#11926401	2
C₄⋊C₄×Dic₁₉	2
C₄×(C₂×D₁₉)⋊C₄	2
C₁₉×#384	2
#2497	19