Subgroups — #14572297

Order 2432.

392 conjugacy classes of subgroups.

The subgroup lattice has 254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	#11926602	C₂	1	2	yes	maximal, complemented
3	#11926602	C₂	1	2	yes	maximal, complemented
4	#11926598	C₂	1	2	yes	maximal, complemented
5	#11926594	C₂	1	2	yes	maximal, complemented
6	#11926567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926511	C₂	1	1	yes	maximal, characteristic
9	#11926502	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926499	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#408	C₂	1	1	yes	maximal, characteristic
12	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	Q₈×Dic₁₉	C₄	1	1	yes	characteristic
16	Q₈×Dic₁₉	C₄	1	1	yes	characteristic
17	D₄×Dic₁₉	C₄	1	2	yes	—
18	D₄×Dic₁₉	C₄	1	1	yes	characteristic
19	D₄×Dic₁₉	C₄	1	2	yes	—
20	D₄×Dic₁₉	C₄	1	1	yes	characteristic
21	#10597372	C₂²	1	2	yes	—
22	#10597372	C₂²	1	1	yes	characteristic
23	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
25	C₂×#64520	C₂²	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
30	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
31	#10597272	C₂²	1	2	yes	—
32	#10597272	C₂²	1	2	yes	—
33	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
34	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
35	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
36	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic
37	Dic₁₉⋊C₈	C₂²	1	2	yes	—
38	Dic₁₉⋊C₈	C₂²	1	2	yes	—
39	C₈×Dic₁₉	C₂²	1	2	yes	—
40	C₈×Dic₁₉	C₂²	1	2	yes	—
41	#41×C₁₉	—	2	2	no	—
42	#41×C₁₉	—	2	2	no	—
43	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
49	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
51	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
52	M₁₆×C₁₉	—	2	2	no	—
53	C₂×C₈×C₁₉	—	2	2	no	—
54	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
58	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
59	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
60	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
61	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
62	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
63	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
65	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
66	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
67	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₁₉	C₂³	1	2	yes	—
69	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
70	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
71	#64520	—	2	2	no	—
72	C₂×C₁₉⋊C₈	—	2	2	no	—
73	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
75	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
77	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	Q₈×C₁₉	—	2	2	no	—
79	D₄×C₁₉	—	2	4	no	—
80	D₄×C₁₉	—	2	2	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	#41	1	2	yes	—
86	C₂×C₄×C₁₉	#41	1	2	yes	—
87	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
88	C₂×Dic₁₉	—	2	2	no	—
89	C₂×Dic₁₉	—	2	4	no	—
90	C₂×Dic₁₉	—	4	1	no	—
91	C₂×Dic₁₉	—	4	2	no	—
92	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
94	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
96	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
98	C₈×C₁₉	—	2	1	no	—
99	C₈×C₁₉	—	2	1	no	—
100	C₈×C₁₉	—	2	2	no	—
101	C₁₉⋊C₈	—	2	1	no	—
102	C₁₉⋊C₈	—	2	1	no	—
103	C₁₉⋊C₈	—	2	2	no	—
104	#2925	—	19	1	no	maximal, Sylow
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	2	1	no	—
107	C₂²×C₁₉	—	2	2	no	—
108	C₂²×C₁₉	—	2	2	no	—
109	C₂²×C₁₉	—	2	2	no	—
110	C₂²×C₁₉	#117	1	2	yes	—
111	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	#117	1	2	yes	—
114	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
115	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
116	Dic₁₉	—	2	1	no	—
117	Dic₁₉	—	2	2	no	—
118	Dic₁₉	—	2	1	no	—
119	Dic₁₉	—	2	1	no	—
120	Dic₁₉	—	2	2	no	—
121	Dic₁₉	#131	1	2	yes	—
122	C₄×#41	—	19	1	no	—
123	#433	—	19	2	no	—
124	#433	—	19	2	no	—
125	#432	—	19	2	no	—
126	#431	—	19	2	no	—
127	#423	—	19	1	no	—
128	C₂×C₄⋊C₈	—	19	1	no	—
129	#408	—	19	1	no	—
130	#408	D₁₉	1	1	yes	characteristic
131	#405	—	19	1	no	—
132	#405	—	19	1	no	—
133	C₂×C₁₉	—	2	2	no	—
134	C₂×C₁₉	—	4	2	no	—
135	C₂×C₁₉	C₂×#117	1	1	yes	characteristic
136	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
137	C₂×C₁₉	#568	1	1	yes	characteristic
138	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
139	C₂×M₁₆	—	19	1	no	—
140	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
141	C₂²×C₈	—	19	1	no	—
142	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
143	C₄×Q₈	—	19	1	no	—
144	C₄×Q₈	—	19	1	no	—
145	C₄×D₄	—	19	2	no	—
146	C₄×D₄	—	19	1	no	—
147	C₄×D₄	—	19	2	no	—
148	C₄×D₄	—	19	1	no	—
149	#117	—	19	1	no	—
150	#117	—	19	2	no	—
151	C₂×C₄²	—	19	1	no	—
152	C₂×C₄²	—	19	2	no	—
153	C₄⋊C₈	—	19	1	no	—
154	C₄⋊C₈	—	19	1	no	—
155	C₄⋊C₈	—	19	1	no	—
156	C₄⋊C₈	—	19	1	no	—
157	C₄⋊C₈	—	19	2	no	—
158	C₄⋊C₈	—	19	2	no	—
159	C₂²⋊C₈	—	19	2	no	—
160	C₂²⋊C₈	—	19	2	no	—
161	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
162	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
163	#97	—	19	2	no	—
164	#97	—	19	2	no	—
165	C₄×C₈	—	19	2	no	—
166	C₄×C₈	—	19	2	no	—
167	C₁₉	#2925	1	1	yes	characteristic, complemented, Sylow
168	#41	—	2	2	no	—
169	#41	—	2	2	no	—
170	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
171	C₂×D₄	C₄×D₁₉	1	2	yes	—
172	C₂×D₄	C₄×D₁₉	1	1	yes	characteristic
173	C₂²×C₄	—	19	2	no	—
174	C₂²×C₄	—	19	1	no	—
175	C₂²×C₄	—	19	2	no	—
176	C₂²×C₄	—	19	1	no	—
177	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
178	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
179	M₁₆	—	2	2	no	—
180	M₁₆	—	38	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	19	1	no	—
183	C₂×C₈	—	19	2	no	—
184	C₂×C₈	—	19	1	no	—
185	C₂×C₈	—	38	2	no	—
186	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
187	C₂×C₈	C₂²×D₁₉	1	2	yes	—
188	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
189	C₄⋊C₄	—	19	2	no	—
190	C₄⋊C₄	—	19	2	no	—
191	C₄⋊C₄	—	19	1	no	—
192	C₄⋊C₄	—	19	1	no	—
193	C₂²⋊C₄	—	19	2	no	—
194	C₂²⋊C₄	—	19	2	no	—
195	C₂²⋊C₄	—	19	2	no	—
196	C₄²	—	19	2	no	—
197	C₄²	—	19	1	no	—
198	C₄²	—	19	2	no	—
199	C₄²	—	19	1	no	—
200	C₄²	—	19	2	no	—
201	C₄²	—	19	1	no	—
202	C₄²	—	19	1	no	—
203	C₂³	C₂×C₄×D₁₉	1	2	yes	—
204	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
205	Q₈	—	2	2	no	—
206	D₄	—	2	4	no	—
207	D₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	19	1	no	—
211	C₂×C₄	—	19	1	no	—
212	C₂×C₄	—	19	2	no	—
213	C₂×C₄	—	19	1	no	—
214	C₂×C₄	—	19	2	no	—
215	C₂×C₄	—	19	1	no	—
216	C₂×C₄	—	38	2	no	—
217	C₂×C₄	—	38	4	no	—
218	C₂×C₄	—	76	1	no	—
219	C₂×C₄	—	76	2	no	—
220	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
221	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
222	C₂×C₄	#64543	1	2	yes	—
223	C₂×C₄	#64543	1	2	yes	—
224	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
225	C₈	—	2	1	no	—
226	C₈	—	2	1	no	—
227	C₈	—	2	2	no	—
228	C₈	—	38	1	no	—
229	C₈	—	38	1	no	—
230	C₈	—	38	2	no	—
231	C₂²	—	2	1	no	—
232	C₂²	—	2	1	no	—
233	C₂²	—	2	2	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	2	no	—
236	C₂²	#10597323	1	2	yes	—
237	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
238	C₄	—	2	2	no	—
239	C₄	—	19	2	no	—
240	C₄	—	38	2	no	—
241	C₄	—	38	1	no	—
242	C₄	—	38	1	no	—
243	C₄	—	38	2	no	—
244	C₄	—	38	1	no	—
245	C₄	#10597323	1	2	yes	—
246	C₄	C₂×#64543	1	1	yes	characteristic
247	C₄	C₂×#64543	1	1	yes	characteristic
248	C₂	—	2	2	no	—
249	C₂	—	4	2	no	—
250	C₂	C₂×#10597323	1	1	yes	characteristic
251	C₂	#131×D₁₉	1	1	yes	characteristic
252	C₂	#11927309	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#408	C₂
prime radical	C₂×#41×C₁₉	C₂²
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#408	D₁₉
hypocenter	C₁₉	#2925
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #408

Complements

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

N	H ≅ G/N	type
2. #11926602	C₂	semidirect
3. #11926602	C₂	semidirect
4. #11926598	C₂	semidirect
5. #11926594	C₂	semidirect
6. #11926567	C₂	semidirect
7. C₂×Dic₁₉⋊C₈	C₂	semidirect
9. #11926502	C₂	semidirect
10. #11926499	C₂	semidirect
167. C₁₉	#2925	semidirect

Maximal subgroups

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

subgroup	index
#41×Dic₁₉	2
#11926602	2
#11926598	2
#11926594	2
#11926567	2
C₂×Dic₁₉⋊C₈	2
#11926511	2
#11926502	2
#11926499	2
C₁₉×#408	2
#2925	19