Subgroups — #14573446

Order 2432.

416 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597334	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926837	C₂	1	2	yes	maximal, complemented
4	#11926832	C₂	1	2	yes	maximal, complemented
5	#11926827	C₂	1	2	yes	maximal, complemented
6	#11926822	C₂	1	2	yes	maximal, complemented
7	#11926586	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926584	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926567	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926545	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#417	C₂	1	1	yes	maximal, characteristic
12	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×Dic₃₈	—	2	1	no	—
14	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
17	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
18	D₄×Dic₁₉	—	2	1	no	—
19	D₄×Dic₁₉	—	2	1	no	—
20	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
21	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
22	#10597372	—	2	1	no	—
23	#10597372	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×Dic₁₉⋊C₄	—	2	1	no	—
26	C₂×C₄×Dic₁₉	—	2	1	no	—
27	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
28	C₂×#64520	C₂²	1	1	yes	characteristic
29	#10597334	—	2	1	no	—
30	#10597334	—	2	1	no	—
31	#10597334	C₂²	1	2	yes	—
32	#10597334	C₂²	1	2	yes	—
33	C₁₉×#103	C₂²	1	2	yes	—
34	C₁₉×#102	C₂²	1	2	yes	—
35	#10597292	C₂²	1	2	yes	—
36	#10597289	C₂²	1	2	yes	—
37	#10597275	C₂²	1	2	yes	—
38	#10597274	C₂²	1	2	yes	—
39	Dic₁₉⋊C₈	C₂²	1	2	yes	—
40	Dic₁₉⋊C₈	C₂²	1	2	yes	—
41	#10597265	C₂²	1	2	yes	—
42	#10597264	C₂²	1	2	yes	—
43	#41×C₁₉	—	2	2	no	—
44	#41×C₁₉	Q₈	1	4	yes	complemented
45	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×D₄×C₁₉	—	2	1	no	—
47	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	—	2	1	no	—
49	C₂²×C₄×C₁₉	—	2	1	no	—
50	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×Dic₁₉	—	2	1	no	—
52	C₂²×Dic₁₉	—	2	1	no	—
53	C₂²×Dic₁₉	—	2	1	no	—
54	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
55	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
56	C₂×Dic₃₈	—	2	2	no	—
57	C₂×Dic₃₈	—	2	2	no	—
58	C₂×Dic₃₈	—	4	4	no	—
59	M₁₆×C₁₉	—	2	2	no	—
60	C₂×C₈×C₁₉	C₂³	1	2	yes	—
61	C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂²⋊Dic₁₉	—	2	1	no	—
64	C₂²⋊Dic₁₉	—	2	1	no	—
65	C₂²⋊Dic₁₉	—	2	1	no	—
66	C₄⋊Dic₁₉	—	2	1	no	—
67	C₄⋊Dic₁₉	—	2	1	no	—
68	C₄⋊Dic₁₉	—	2	1	no	—
69	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
70	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
71	C₄⋊Dic₁₉	C₂³	1	2	yes	—
72	Dic₁₉⋊C₄	—	2	2	no	—
73	Dic₁₉⋊C₄	—	2	2	no	—
74	C₄×Dic₁₉	—	2	1	no	—
75	C₄×Dic₁₉	—	2	1	no	—
76	C₄×Dic₁₉	—	2	1	no	—
77	C₄×Dic₁₉	D₄	1	1	yes	characteristic
78	C₄×Dic₁₉	D₄	1	1	yes	characteristic
79	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
80	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
81	#64520	—	2	2	no	—
82	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
83	C₂³×C₁₉	—	2	1	no	—
84	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
85	Q₈×C₁₉	—	2	1	no	—
86	Q₈×C₁₉	C₂×Q₈	1	2	yes	complemented
87	D₄×C₁₉	—	2	4	no	—
88	D₄×C₁₉	—	2	1	no	—
89	D₄×C₁₉	C₂×Q₈	1	2	yes	complemented
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	4	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
96	C₂×C₄×C₁₉	#41	1	2	yes	—
97	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
98	C₂×Dic₁₉	—	2	2	no	—
99	C₂×Dic₁₉	—	2	2	no	—
100	C₂×Dic₁₉	—	2	1	no	—
101	C₂×Dic₁₉	—	2	1	no	—
102	C₂×Dic₁₉	—	2	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	4	2	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
110	Dic₃₈	—	4	4	no	—
111	Dic₃₈	—	4	4	no	—
112	C₈×C₁₉	—	2	2	no	—
113	C₁₉⋊C₈	—	2	2	no	—
114	#3079	—	19	1	no	maximal, Sylow
115	C₂²×C₁₉	—	2	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	2	no	—
118	C₂²×C₁₉	—	4	1	no	—
119	C₂²×C₁₉	—	4	1	no	—
120	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
121	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	—	4	2	no	—
124	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
125	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
126	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
127	Dic₁₉	—	2	1	no	—
128	Dic₁₉	—	2	1	no	—
129	Dic₁₉	—	4	2	no	—
130	Dic₁₉	—	4	1	no	—
131	Dic₁₉	—	4	1	no	—
132	Dic₁₉	AGL(1,ℤ/8)	1	2	yes	—
133	Dic₁₉	#137	1	2	yes	—
134	C₂×C₄⋊Q₈	—	19	1	no	—
135	C₄×#41	—	19	1	no	—
136	#477	—	19	2	no	—
137	#476	—	19	2	no	—
138	#475	—	19	2	no	—
139	#474	—	19	2	no	—
140	#428	—	19	1	no	—
141	#428	—	19	1	no	—
142	#423	—	19	1	no	—
143	#417	—	19	1	no	—
144	#417	D₁₉	1	1	yes	characteristic
145	C₂×C₁₉	—	2	2	no	—
146	C₂×C₁₉	—	4	2	no	—
147	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
150	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
151	C₂²×Q₈	—	38	1	no	—
152	C₂×M₁₆	—	19	1	no	—
153	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
154	C₄⋊Q₈	—	19	2	no	—
155	C₄⋊Q₈	—	19	2	no	—
156	C₄⋊Q₈	—	38	1	no	—
157	C₄⋊Q₈	—	38	1	no	—
158	C₄×Q₈	—	19	1	no	—
159	C₄×Q₈	—	19	1	no	—
160	C₄×D₄	—	19	1	no	—
161	C₄×D₄	—	19	1	no	—
162	C₄×D₄	—	38	1	no	—
163	C₄×D₄	—	38	1	no	—
164	#117	—	19	1	no	—
165	#117	—	38	1	no	—
166	C₂×C₄⋊C₄	—	19	1	no	—
167	C₂×C₄⋊C₄	—	38	1	no	—
168	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
169	C₂×C₄²	—	19	1	no	—
170	C₂×C₄²	—	38	1	no	—
171	#107	—	19	2	no	—
172	#107	—	19	2	no	—
173	#106	—	19	2	no	—
174	#106	—	19	2	no	—
175	C₄⋊C₈	—	19	2	no	—
176	C₄⋊C₈	—	19	2	no	—
177	#103	—	19	2	no	—
178	#103	C₂×D₁₉	1	2	yes	—
179	#102	—	19	2	no	—
180	#102	C₂×D₁₉	1	2	yes	—
181	C₁₉	#3079	1	1	yes	characteristic, complemented, Sylow
182	#41	—	2	2	no	—
183	#41	Dic₃₈	1	4	yes	complemented
184	C₂×Q₈	—	38	2	no	—
185	C₂×Q₈	—	38	2	no	—
186	C₂×Q₈	—	76	4	no	—
187	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
188	C₂×D₄	—	2	1	no	—
189	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	19	1	no	—
193	C₂²×C₄	—	19	1	no	—
194	C₂²×C₄	—	38	1	no	—
195	C₂²×C₄	—	38	1	no	—
196	C₂²×C₄	—	38	1	no	—
197	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
198	M₁₆	—	2	2	no	—
199	M₁₆	—	38	2	no	—
200	C₂×C₈	—	19	2	no	—
201	C₂×C₈	C₂²×D₁₉	1	2	yes	—
202	C₄⋊C₄	—	2	1	no	—
203	C₄⋊C₄	—	19	2	no	—
204	C₄⋊C₄	—	19	1	no	—
205	C₄⋊C₄	—	19	1	no	—
206	C₄⋊C₄	—	38	2	no	—
207	C₄⋊C₄	—	38	2	no	—
208	C₄⋊C₄	—	38	1	no	—
209	C₄⋊C₄	—	38	1	no	—
210	C₄⋊C₄	—	38	1	no	—
211	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
212	C₂²⋊C₄	—	38	1	no	—
213	C₂²⋊C₄	—	38	1	no	—
214	C₂²⋊C₄	—	38	1	no	—
215	C₄²	—	19	1	no	—
216	C₄²	—	19	1	no	—
217	C₄²	—	19	1	no	—
218	C₄²	—	19	1	no	—
219	C₄²	—	38	1	no	—
220	C₄²	—	38	1	no	—
221	C₄²	—	38	1	no	—
222	C₂³	—	2	1	no	—
223	C₂³	D₄×D₁₉	1	1	yes	characteristic
224	Q₈	—	2	1	no	—
225	Q₈	—	76	4	no	—
226	Q₈	—	76	4	no	—
227	Q₈	C₂×Dic₃₈	1	2	yes	complemented
228	D₄	—	2	4	no	—
229	D₄	—	2	1	no	—
230	D₄	C₂×Dic₃₈	1	2	yes	complemented
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	19	1	no	—
236	C₂×C₄	—	19	1	no	—
237	C₂×C₄	—	19	1	no	—
238	C₂×C₄	—	19	1	no	—
239	C₂×C₄	—	38	2	no	—
240	C₂×C₄	—	38	2	no	—
241	C₂×C₄	—	38	1	no	—
242	C₂×C₄	—	38	1	no	—
243	C₂×C₄	—	38	2	no	—
244	C₂×C₄	—	76	2	no	—
245	C₂×C₄	—	76	2	no	—
246	C₂×C₄	—	76	2	no	—
247	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
248	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
249	C₂×C₄	#64543	1	2	yes	—
250	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
251	C₈	—	2	2	no	—
252	C₈	—	38	2	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	4	1	no	—
257	C₂²	—	4	1	no	—
258	C₂²	#10597324	1	2	yes	—
259	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
260	C₄	—	2	2	no	—
261	C₄	—	4	2	no	—
262	C₄	—	19	2	no	—
263	C₄	—	19	2	no	—
264	C₄	—	38	1	no	—
265	C₄	—	38	1	no	—
266	C₄	—	76	2	no	—
267	C₄	—	76	1	no	—
268	C₄	—	76	1	no	—
269	C₄	#10597324	1	2	yes	—
270	C₄	C₂²×Dic₃₈	1	1	yes	characteristic
271	C₄	C₂×#64543	1	1	yes	characteristic
272	C₂	—	2	2	no	—
273	C₂	—	4	2	no	—
274	C₂	C₂×#10597324	1	1	yes	characteristic
275	C₂	AGL(1,ℤ/8)×D₁₉	1	1	yes	characteristic
276	C₂	#137×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#417	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#41×C₁₉	C₂²
hypercenter	#417	D₁₉
hypocenter	C₁₉	#3079
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #417

Complements

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

N	H ≅ G/N	type
1. C₂×#10597334	C₂	semidirect
3. #11926837	C₂	semidirect
4. #11926832	C₂	semidirect
5. #11926827	C₂	semidirect
6. #11926822	C₂	semidirect
7. #11926586	C₂	semidirect
8. #11926584	C₂	semidirect
9. #11926567	C₂	semidirect
44. #41×C₁₉	Q₈	semidirect
86. Q₈×C₁₉	C₂×Q₈	semidirect
89. D₄×C₁₉	C₂×Q₈	semidirect
181. C₁₉	#3079	semidirect
183. #41	Dic₃₈	semidirect
227. Q₈	C₂×Dic₃₈	semidirect
230. D₄	C₂×Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597334	2
#41×Dic₁₉	2
#11926837	2
#11926832	2
#11926827	2
#11926822	2
#11926586	2
#11926584	2
#11926567	2
#11926545	2
C₁₉×#417	2
#3079	19