Subgroups — #18081596

Order 4864.

498 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572013	C₂	1	1	yes	maximal, characteristic
2	#14563787	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926292	C₂	1	2	yes	maximal
4	C₂×#11926291	C₂	1	2	yes	maximal
5	C₄×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	1	yes	characteristic
7	C₂×#10597315	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	#11926450	—	2	1	no	—
11	#11926450	—	2	1	no	—
12	#11926450	C₄	1	4	yes	—
13	#11926410	—	2	2	no	—
14	#11926292	—	2	4	no	—
15	#11926291	—	2	4	no	—
16	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₉	—	2	1	no	—
18	C₄³×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	1	no	—
20	C₂²×Dic₃₈	—	2	1	no	—
21	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
22	C₂²×C₈×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	—	2	1	no	—
29	C₂×C₄⋊Dic₁₉	—	2	1	no	—
30	C₂×C₄⋊Dic₁₉	—	2	1	no	—
31	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
32	C₂²×C₁₉⋊C₈	—	2	2	no	—
33	#10597315	—	2	2	no	—
34	#10597315	—	2	2	no	—
35	#10597315	—	2	2	no	—
36	#10597315	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
39	C₄×C₈×C₁₉	—	4	2	no	—
40	C₁₉⋊#95	—	2	4	no	—
41	C₁₉⋊#95	—	2	4	no	—
42	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	4	4	no	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₉	—	2	2	no	—
51	C₂²×Dic₁₉	—	2	2	no	—
52	C₂×Dic₃₈	—	2	4	no	—
53	C₂×Dic₃₈	—	4	2	no	—
54	C₂×Dic₃₈	—	4	2	no	—
55	C₂×Dic₃₈	—	4	1	no	—
56	C₂×Dic₃₈	—	4	1	no	—
57	C₂×Dic₃₈	—	4	4	no	—
58	C₂×C₈×C₁₉	—	2	4	no	—
59	C₂×C₈×C₁₉	—	4	2	no	—
60	C₂×C₈×C₁₉	—	4	2	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	—	2	1	no	—
63	C₄²×C₁₉	—	2	1	no	—
64	C₄²×C₁₉	—	4	2	no	—
65	C₄²×C₁₉	SD₁₆	1	4	yes	—
66	C₄²×C₁₉	Q₁₆	1	4	yes	—
67	C₄²×C₁₉	C₂×D₄	1	2	yes	—
68	C₄²×C₁₉	#41	1	2	yes	—
69	C₄⋊Dic₁₉	—	2	4	no	—
70	C₄⋊Dic₁₉	—	4	2	no	—
71	C₄⋊Dic₁₉	—	4	1	no	—
72	C₄⋊Dic₁₉	—	4	1	no	—
73	C₄⋊Dic₁₉	—	4	1	no	—
74	C₄⋊Dic₁₉	—	4	1	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	4	no	—
77	#9697	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	#103	1	4	yes	—
85	C₂×C₄×C₁₉	#103	1	4	yes	—
86	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
90	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
92	C₂×C₄×C₁₉	#135	1	2	yes	—
93	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	2	no	—
97	C₂×Dic₁₉	—	4	4	no	—
98	C₂×Dic₁₉	—	4	2	no	—
99	C₂×Dic₁₉	—	4	2	no	—
100	Dic₃₈	—	8	2	no	—
101	Dic₃₈	—	8	2	no	—
102	Dic₃₈	—	8	4	no	—
103	C₈×C₁₉	—	4	4	no	—
104	C₁₉⋊C₈	—	8	2	no	—
105	#2862	—	19	1	no	—
106	#1842	—	19	1	no	—
107	C₄×C₄⋊C₈	D₁₉	1	1	yes	characteristic
108	C₂×#333	—	19	2	no	—
109	C₂×#332	—	19	2	no	—
110	C₂²×C₁₉	#390	1	1	yes	characteristic
111	C₂²×C₁₉	#413	1	2	yes	—
112	C₂²×C₁₉	C₂×#103	1	2	yes	—
113	C₂²×C₁₉	#416	1	1	yes	characteristic
114	C₂²×C₁₉	#417	1	1	yes	characteristic
115	C₄×C₁₉	—	2	4	no	—
116	C₄×C₁₉	—	2	4	no	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	#463	1	2	yes	—
119	C₄×C₁₉	#464	1	2	yes	—
120	C₄×C₁₉	#487	1	2	yes	—
121	C₄×C₁₉	#492	1	1	yes	characteristic
122	C₄×C₁₉	#494	1	1	yes	characteristic
123	Dic₁₉	—	8	2	no	—
124	Dic₁₉	—	8	2	no	—
125	C₂×C₄⋊Q₈	—	19	1	no	—
126	C₂×C₄⋊Q₈	—	19	1	no	—
127	C₂×C₄⋊C₈	—	19	2	no	—
128	C₂×C₄⋊C₈	—	38	2	no	—
129	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
130	C₂×C₄×C₈	—	2	1	no	—
131	#391	—	19	4	no	—
132	#391	—	38	1	no	—
133	#391	—	38	1	no	—
134	#382	—	38	2	no	—
135	C₄³	C₂×D₁₉	1	1	yes	characteristic
136	#336	—	2	1	no	—
137	#333	—	38	4	no	—
138	#332	—	38	4	no	—
139	C₂×C₁₉	#1542	1	2	yes	—
140	C₂×C₁₉	#1550	1	2	yes	—
141	C₂×C₁₉	#1956	1	1	yes	characteristic
142	C₂×C₁₉	#1967	1	1	yes	characteristic
143	C₂×C₁₉	#1983	1	1	yes	characteristic
144	C₂²×Q₈	—	19	2	no	—
145	C₂²×Q₈	—	38	1	no	—
146	C₂²×C₈	—	2	2	no	—
147	C₂²×C₈	—	38	2	no	—
148	C₄⋊Q₈	—	38	2	no	—
149	C₄⋊Q₈	—	38	2	no	—
150	C₄⋊Q₈	—	38	2	no	—
151	C₄⋊Q₈	—	38	2	no	—
152	C₂×C₄⋊C₄	—	19	2	no	—
153	C₂×C₄⋊C₄	—	38	1	no	—
154	C₂×C₄⋊C₄	—	38	1	no	—
155	C₂×C₄⋊C₄	—	38	1	no	—
156	C₂×C₄²	C₄×D₁₉	1	2	yes	—
157	C₂×C₄²	D₇₆	1	2	yes	—
158	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
159	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
160	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
161	C₄⋊C₈	—	2	2	no	—
162	C₄⋊C₈	—	38	2	no	—
163	C₄⋊C₈	—	38	2	no	—
164	C₄⋊C₈	—	76	4	no	—
165	C₄⋊C₈	D₇₆	1	4	yes	—
166	C₄×C₈	—	4	2	no	—
167	#95	—	38	4	no	—
168	#95	—	38	4	no	—
169	C₁₉	#9697	1	1	yes	characteristic, complemented, Sylow
170	C₂×Q₈	—	38	4	no	—
171	C₂×Q₈	—	76	4	no	—
172	C₂×Q₈	—	76	2	no	—
173	C₂×Q₈	—	76	1	no	—
174	C₂×Q₈	—	76	1	no	—
175	C₂×Q₈	—	76	2	no	—
176	C₂²×C₄	—	38	2	no	—
177	C₂²×C₄	—	38	2	no	—
178	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
179	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
180	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
181	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	76	2	no	—
187	C₂×C₈	—	76	4	no	—
188	C₄⋊C₄	—	38	4	no	—
189	C₄⋊C₄	—	76	2	no	—
190	C₄⋊C₄	—	76	1	no	—
191	C₄⋊C₄	—	76	1	no	—
192	C₄⋊C₄	—	76	1	no	—
193	C₄⋊C₄	—	76	1	no	—
194	C₄²	—	2	1	no	—
195	C₄²	—	2	1	no	—
196	C₄²	—	2	2	no	—
197	C₄²	—	4	2	no	—
198	C₄²	#64516	1	4	yes	—
199	C₄²	Dic₇₆	1	4	yes	—
200	C₄²	C₂×D₇₆	1	2	yes	—
201	C₄²	#64541	1	2	yes	—
202	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
203	Q₈	—	152	4	no	—
204	Q₈	—	152	2	no	—
205	Q₈	—	152	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	76	2	no	—
212	C₂×C₄	—	76	2	no	—
213	C₂×C₄	—	76	2	no	—
214	C₂×C₄	—	76	2	no	—
215	C₂×C₄	—	76	4	no	—
216	C₂×C₄	#10597273	1	4	yes	—
217	C₂×C₄	#10597273	1	4	yes	—
218	C₂×C₄	C₄×D₇₆	1	2	yes	—
219	C₂×C₄	#10597320	1	1	yes	characteristic
220	C₂×C₄	#10597321	1	1	yes	characteristic
221	C₂×C₄	C₂×#64516	1	2	yes	—
222	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
223	C₂×C₄	#10597376	1	2	yes	—
224	C₂×C₄	#10597378	1	1	yes	characteristic
225	C₂×C₄	#10597388	1	1	yes	characteristic
226	C₂×C₄	#10597396	1	2	yes	—
227	C₈	—	4	4	no	—
228	C₈	—	152	2	no	—
229	C₂²	#11926446	1	1	yes	characteristic
230	C₂²	#11926526	1	2	yes	—
231	C₂²	C₂×#10597273	1	2	yes	—
232	C₂²	#11926538	1	1	yes	characteristic
233	C₂²	#11926543	1	1	yes	characteristic
234	C₄	—	2	4	no	—
235	C₄	—	2	2	no	—
236	C₄	—	2	4	no	—
237	C₄	—	152	2	no	—
238	C₄	—	152	2	no	—
239	C₄	#11926759	1	2	yes	—
240	C₄	#11926766	1	2	yes	—
241	C₄	#11926895	1	2	yes	—
242	C₄	#11926917	1	1	yes	characteristic
243	C₄	#11926924	1	1	yes	characteristic
244	C₂	#14562290	1	2	yes	—
245	C₂	#14562323	1	2	yes	—
246	C₂	#14564437	1	1	yes	characteristic
247	C₂	#14564484	1	1	yes	characteristic
248	C₂	#14564567	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₄⋊C₈	D₁₉
hypocenter	C₁₉	#9697
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
169. C₁₉	#9697	semidirect

Maximal subgroups

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

subgroup	index
#14572013	2
#14563787	2
C₂×#11926292	2
C₂×#11926291	2
C₄×C₁₉×C₄⋊C₈	2
#9697	19