Subgroups — #18081101

Order 4864.

378 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564353	C₂	1	2	yes	maximal
2	C₄×#10597275	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926297	C₂	1	1	yes	maximal, characteristic
4	#14561475	C₂	1	2	yes	maximal
5	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597275	C₄	1	2	yes	—
7	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
8	C₂×Dic₁₉⋊C₈	—	2	2	no	—
9	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	#11926307	C₄	1	1	yes	characteristic
11	#11926307	C₄	1	1	yes	characteristic
12	#11926298	—	2	2	no	—
13	#11926297	—	2	2	no	—
14	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#322	—	2	2	no	—
18	C₂²×C₈×C₁₉	—	2	1	no	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
26	C₂×C₄×Dic₁₉	—	2	2	no	—
27	C₂²×C₁₉⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₉	—	2	1	no	—
29	C₄×C₈×C₁₉	—	2	1	no	—
30	C₄×C₈×C₁₉	—	2	1	no	—
31	C₄×C₈×C₁₉	D₄	1	2	yes	—
32	C₄×C₈×C₁₉	Q₈	1	2	yes	—
33	C₄×C₈×C₁₉	Q₈	1	2	yes	—
34	C₁₉⋊#95	—	2	2	no	—
35	#10597275	—	2	4	no	—
36	Dic₁₉⋊C₈	—	4	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
42	C₂²×Dic₁₉	—	2	2	no	—
43	C₂²×Dic₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	1	no	—
45	C₂×C₈×C₁₉	—	2	1	no	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	—	2	1	no	—
49	C₂×C₈×C₁₉	—	2	1	no	—
50	C₂×C₈×C₁₉	—	2	2	no	—
51	C₂×C₈×C₁₉	—	4	2	no	—
52	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
53	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
54	C₂×C₈×C₁₉	D₈	1	2	yes	—
55	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
56	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
58	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₁₉	#41	1	1	yes	characteristic
60	C₄⋊Dic₁₉	—	2	2	no	—
61	C₄⋊Dic₁₉	—	2	2	no	—
62	C₄⋊Dic₁₉	—	2	2	no	—
63	C₄⋊Dic₁₉	M₁₆	1	4	yes	—
64	C₄×Dic₁₉	—	4	2	no	—
65	C₄×Dic₁₉	—	4	2	no	—
66	C₂×C₁₉⋊C₈	—	4	2	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	C₂×C₁₉⋊C₈	—	4	2	no	—
69	#9598	—	19	1	no	maximal, Sylow
70	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
77	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
79	C₂×C₄×C₁₉	#131	1	2	yes	—
80	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
83	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
84	C₂×Dic₁₉	—	2	4	no	—
85	C₂×Dic₁₉	—	4	2	no	—
86	C₂×Dic₁₉	—	4	2	no	—
87	C₂×Dic₁₉	—	4	2	no	—
88	C₂×Dic₁₉	—	4	2	no	—
89	C₂×Dic₁₉	—	4	2	no	—
90	C₈×C₁₉	—	2	2	no	—
91	C₈×C₁₉	—	2	2	no	—
92	C₈×C₁₉	—	2	2	no	—
93	C₈×C₁₉	—	2	2	no	—
94	C₈×C₁₉	—	4	2	no	—
95	C₁₉⋊C₈	—	8	2	no	—
96	#1939	—	19	2	no	—
97	C₄×#107	—	19	1	no	—
98	C₂×#335	—	19	1	no	—
99	C₂×#322	D₁₉	1	1	yes	characteristic
100	#1279	—	19	2	no	—
101	C₂²×C₁₉	#389	1	1	yes	characteristic
102	C₂²×C₁₉	#435	1	2	yes	—
103	C₂²×C₁₉	C₄×D₈	1	1	yes	characteristic
104	C₂²×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
105	C₂²×C₁₉	#444	1	2	yes	—
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	#423	1	1	yes	characteristic
109	C₄×C₁₉	#424	1	1	yes	characteristic
110	C₄×C₁₉	#446	1	2	yes	—
111	C₄×C₁₉	#466	1	1	yes	characteristic
112	C₄×C₁₉	#467	1	1	yes	characteristic
113	C₄×C₁₉	#499	1	1	yes	characteristic
114	C₄×C₁₉	#500	1	1	yes	characteristic
115	Dic₁₉	—	4	4	no	—
116	Dic₁₉	—	8	2	no	—
117	C₂×#107	—	19	2	no	—
118	C₂×C₄⋊C₈	—	19	2	no	—
119	C₂×C₄⋊C₈	—	38	2	no	—
120	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
121	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
123	C₄×C₄⋊C₄	—	19	2	no	—
124	#340	—	19	1	no	—
125	#340	—	19	1	no	—
126	#336	—	38	2	no	—
127	#335	—	38	2	no	—
128	#322	—	2	2	no	—
129	C₂×C₁₉	#1581	1	2	yes	—
130	C₂×C₁₉	#1584	1	2	yes	—
131	C₂×C₁₉	#1940	1	1	yes	characteristic
132	C₂×C₁₉	#1942	1	1	yes	characteristic
133	C₂×C₁₉	#1946	1	1	yes	characteristic
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	—	38	2	no	—
136	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
137	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
138	C₂²×C₈	D₇₆	1	1	yes	characteristic
139	C₂²×C₈	D₇₆	1	1	yes	characteristic
140	C₂×C₄⋊C₄	—	19	2	no	—
141	C₂×C₄⋊C₄	—	19	2	no	—
142	C₂×C₄²	—	38	2	no	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	#107	—	38	4	no	—
145	C₄⋊C₈	—	38	2	no	—
146	C₄⋊C₈	—	38	2	no	—
147	C₄⋊C₈	—	76	4	no	—
148	C₄×C₈	—	2	1	no	—
149	C₄×C₈	—	2	1	no	—
150	C₄×C₈	—	2	1	no	—
151	C₄×C₈	Dic₃₈	1	2	yes	—
152	C₄×C₈	Dic₃₈	1	2	yes	—
153	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
154	#95	—	38	2	no	—
155	C₁₉	#9598	1	1	yes	characteristic, complemented, Sylow
156	C₂²×C₄	—	38	2	no	—
157	C₂²×C₄	—	38	2	no	—
158	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
159	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
160	C₂²×C₄	#64541	1	1	yes	characteristic
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	2	1	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	76	2	no	—
170	C₂×C₈	—	76	2	no	—
171	C₂×C₈	—	76	2	no	—
172	C₂×C₈	D₁₅₂	1	2	yes	—
173	C₂×C₈	Dic₇₆	1	2	yes	—
174	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
175	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
176	C₄⋊C₄	—	19	4	no	—
177	C₄⋊C₄	—	38	2	no	—
178	C₄⋊C₄	—	38	2	no	—
179	C₄⋊C₄	—	38	2	no	—
180	C₄²	—	76	2	no	—
181	C₄²	—	76	2	no	—
182	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
183	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
184	C₄²	#64541	1	1	yes	characteristic
185	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
186	C₂³	C₄×D₇₆	1	1	yes	characteristic
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	38	4	no	—
189	C₂×C₄	—	76	2	no	—
190	C₂×C₄	—	76	2	no	—
191	C₂×C₄	—	76	2	no	—
192	C₂×C₄	—	76	2	no	—
193	C₂×C₄	—	76	2	no	—
194	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
195	C₂×C₄	#10597315	1	1	yes	characteristic
196	C₂×C₄	#10597316	1	1	yes	characteristic
197	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
198	C₂×C₄	#10597350	1	1	yes	characteristic
199	C₂×C₄	#10597350	1	1	yes	characteristic
200	C₂×C₄	C₂×Dic₇₆	1	1	yes	characteristic
201	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
202	C₂×C₄	#10597353	1	2	yes	—
203	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
204	C₂×C₄	#10597370	1	1	yes	characteristic
205	C₂×C₄	#10597376	1	1	yes	characteristic
206	C₈	—	2	2	no	—
207	C₈	—	2	2	no	—
208	C₈	—	2	2	no	—
209	C₈	—	2	2	no	—
210	C₈	—	4	2	no	—
211	C₈	—	152	2	no	—
212	C₂²	#11926442	1	1	yes	characteristic
213	C₂²	#11926617	1	2	yes	—
214	C₂²	C₄×D₁₅₂	1	1	yes	characteristic
215	C₂²	C₄×Dic₇₆	1	1	yes	characteristic
216	C₂²	#11926667	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	76	4	no	—
220	C₄	—	152	2	no	—
221	C₄	#11926567	1	1	yes	characteristic
222	C₄	#11926572	1	1	yes	characteristic
223	C₄	#11926672	1	2	yes	—
224	C₄	#11926780	1	1	yes	characteristic
225	C₄	#11926785	1	1	yes	characteristic
226	C₄	#11926946	1	1	yes	characteristic
227	C₄	#11926949	1	1	yes	characteristic
228	C₂	#14562466	1	2	yes	—
229	C₂	#14562487	1	2	yes	—
230	C₂	#14564358	1	1	yes	characteristic
231	C₂	#14564368	1	1	yes	characteristic
232	C₂	#14564388	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇₆
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle, prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#9598
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
155. C₁₉	#9598	semidirect

Maximal subgroups

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

subgroup	index
#14564353	2
C₄×#10597275	2
C₂×#11926297	2
#14561475	2
C₂×C₁₉×#322	2
#9598	19