Subgroups — #18081470

Order 4864.

446 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	#14562383	C₂	1	1	yes	maximal, characteristic
3	#14562029	C₂	1	2	yes	maximal
4	#14561958	C₂	1	2	yes	maximal
5	C₁₉×#1450	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₇₆	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₃₈	C₂²	1	2	yes	—
8	C₄×Dic₇₆	—	2	1	no	—
9	C₄×Dic₇₆	—	2	1	no	—
10	C₄×Dic₇₆	—	2	1	no	—
11	C₄×Dic₇₆	—	2	1	no	—
12	#11926597	C₂²	1	2	yes	—
13	C₂×#10597275	C₄	1	1	yes	characteristic
14	C₂×#10597273	C₄	1	2	yes	—
15	#11926297	—	2	1	no	—
16	#11926295	—	2	1	no	—
17	#11926274	—	2	4	no	—
18	#11926269	—	2	4	no	—
19	C₁₉×#431	C₂²	1	1	yes	characteristic
20	C₁₉×#431	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#322	—	2	1	no	—
23	C₈²×C₁₉	—	2	1	no	—
24	C₂²×Dic₃₈	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₉⋊C₄	—	2	2	no	—
30	C₂×C₄×Dic₁₉	—	2	2	no	—
31	C₂×Dic₇₆	—	2	1	no	—
32	C₂×Dic₇₆	—	2	1	no	—
33	C₂×Dic₇₆	—	2	2	no	—
34	C₂×Dic₇₆	C₈	1	4	yes	complemented
35	C₄×Dic₃₈	—	2	2	no	—
36	C₄×Dic₃₈	—	2	2	no	—
37	C₄×Dic₃₈	—	2	2	no	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	—	2	1	no	—
40	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
41	C₁₉×C₂²⋊C₈	—	2	1	no	—
42	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₄×C₈×C₁₉	—	2	1	no	—
45	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
49	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
50	#10597275	—	2	1	no	—
51	#10597275	—	2	1	no	—
52	#10597273	—	2	2	no	—
53	#10597273	—	2	2	no	—
54	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
55	C₄×C₁₉⋊C₈	—	2	2	no	—
56	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂²×Dic₁₉	—	2	2	no	—
60	C₂²×Dic₁₉	—	2	2	no	—
61	C₂×Dic₃₈	—	2	2	no	—
62	C₂×Dic₃₈	—	2	2	no	—
63	C₂×Dic₃₈	—	2	2	no	—
64	C₂×Dic₃₈	—	2	2	no	—
65	C₂×Dic₃₈	—	2	2	no	—
66	C₂×Dic₃₈	C₂×C₈	1	4	yes	—
67	C₂×C₈×C₁₉	—	2	1	no	—
68	C₂×C₈×C₁₉	—	2	1	no	—
69	C₂×C₈×C₁₉	—	2	2	no	—
70	C₂×C₈×C₁₉	—	2	2	no	—
71	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
76	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
77	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₉	#41	1	1	yes	characteristic
81	C₄⋊Dic₁₉	—	2	2	no	—
82	C₄⋊Dic₁₉	—	2	2	no	—
83	Dic₁₉⋊C₄	—	4	2	no	—
84	Dic₁₉⋊C₄	—	4	2	no	—
85	C₄×Dic₁₉	—	4	2	no	—
86	C₄×Dic₁₉	—	4	2	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	Dic₇₆	—	2	4	no	—
89	Dic₇₆	—	2	4	no	—
90	#9669	—	19	1	no	maximal, Sylow
91	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
97	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
103	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
104	C₂×Dic₁₉	—	2	4	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	C₂×Dic₁₉	—	4	2	no	—
107	C₂×Dic₁₉	—	4	2	no	—
108	C₂×Dic₁₉	—	8	2	no	—
109	Dic₃₈	—	2	4	no	—
110	Dic₃₈	—	2	4	no	—
111	Dic₃₈	—	4	2	no	—
112	Dic₃₈	—	4	2	no	—
113	C₈×C₁₉	—	2	1	no	—
114	C₈×C₁₉	—	2	1	no	—
115	C₈×C₁₉	—	4	2	no	—
116	C₈×C₁₉	—	4	2	no	—
117	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
118	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
119	C₁₉⋊C₈	—	8	2	no	—
120	C₂×C₄×Q₁₆	—	19	1	no	—
121	#1564	—	19	1	no	—
122	#1479	—	19	2	no	—
123	#1461	—	19	2	no	—
124	#1450	D₁₉	1	1	yes	characteristic
125	C₂²×C₁₉	—	2	1	no	—
126	C₂²×C₁₉	—	2	1	no	—
127	C₂²×C₁₉	#390	1	1	yes	characteristic
128	C₂²×C₁₉	C₈×D₄	1	1	yes	characteristic
129	C₂²×C₁₉	#436	1	1	yes	characteristic
130	C₄×C₁₉	—	2	1	no	—
131	C₄×C₁₉	—	2	1	no	—
132	C₄×C₁₉	—	2	1	no	—
133	C₄×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
134	C₄×C₁₉	#408	1	1	yes	characteristic
135	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
136	C₄×C₁₉	#436	1	1	yes	characteristic
137	C₄×C₁₉	#473	1	2	yes	—
138	Dic₁₉	—	4	4	no	—
139	Dic₁₉	—	8	2	no	—
140	C₂²×Q₁₆	—	19	1	no	—
141	C₂×C₄×Q₈	—	19	2	no	—
142	C₄×Q₁₆	—	38	1	no	—
143	C₄×Q₁₆	—	38	1	no	—
144	C₄×Q₁₆	—	38	1	no	—
145	C₄×Q₁₆	—	38	1	no	—
146	#431	—	19	2	no	—
147	#431	C₂×D₁₉	1	1	yes	characteristic
148	#431	C₂×D₁₉	1	1	yes	characteristic
149	C₂×#107	—	19	1	no	—
150	C₂×#103	—	19	2	no	—
151	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
152	#335	—	38	1	no	—
153	#334	—	38	1	no	—
154	Q₈⋊C₈	—	38	4	no	—
155	#324	—	38	4	no	—
156	#322	—	2	1	no	—
157	C₈²	—	2	1	no	—
158	C₂×C₁₉	—	2	1	no	—
159	C₂×C₁₉	—	2	1	no	—
160	C₂×C₁₉	#1954	1	1	yes	characteristic
161	C₂×C₁₉	#1976	1	1	yes	characteristic
162	C₂×C₁₉	#1979	1	1	yes	characteristic
163	C₂²×Q₈	—	19	2	no	—
164	C₂×Q₁₆	—	19	4	no	—
165	C₂×Q₁₆	—	38	2	no	—
166	C₂×Q₁₆	—	38	1	no	—
167	C₂×Q₁₆	—	38	1	no	—
168	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
169	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
170	C₄×Q₈	—	38	2	no	—
171	C₄×Q₈	—	38	2	no	—
172	C₄×Q₈	—	38	2	no	—
173	C₄×Q₈	—	38	2	no	—
174	C₂×C₄⋊C₄	—	19	2	no	—
175	C₂×C₄⋊C₄	—	38	2	no	—
176	C₂×C₄²	—	38	2	no	—
177	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
178	#107	—	38	1	no	—
179	#107	—	38	1	no	—
180	C₄⋊C₈	—	2	1	no	—
181	C₄⋊C₈	—	38	2	no	—
182	C₄⋊C₈	D₇₆	1	2	yes	—
183	#103	—	38	2	no	—
184	#103	—	38	2	no	—
185	C₂²⋊C₈	—	2	1	no	—
186	C₂²⋊C₈	—	38	2	no	—
187	C₂²⋊C₈	D₇₆	1	2	yes	—
188	C₄×C₈	—	2	1	no	—
189	C₄×C₈	—	2	1	no	—
190	C₄×C₈	—	38	2	no	—
191	C₄×C₈	D₇₆	1	1	yes	characteristic
192	C₄×C₈	D₇₆	1	1	yes	characteristic
193	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
194	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
195	C₁₉	#9669	1	1	yes	characteristic, complemented, Sylow
196	C₂×Q₈	—	19	4	no	—
197	C₂×Q₈	—	38	2	no	—
198	C₂×Q₈	—	38	2	no	—
199	C₂×Q₈	—	38	2	no	—
200	C₂×Q₈	—	38	2	no	—
201	C₂×Q₈	—	38	2	no	—
202	C₂²×C₄	—	38	2	no	—
203	C₂²×C₄	—	38	2	no	—
204	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
205	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
206	C₂²×C₄	#64541	1	1	yes	characteristic
207	Q₁₆	—	38	4	no	—
208	Q₁₆	—	38	4	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	76	2	no	—
214	C₂×C₈	C₈×D₁₉	1	2	yes	—
215	C₂×C₈	#64515	1	2	yes	—
216	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
217	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
218	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
219	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
220	C₄⋊C₄	—	38	2	no	—
221	C₄⋊C₄	—	38	2	no	—
222	C₄⋊C₄	—	76	2	no	—
223	C₄⋊C₄	—	76	2	no	—
224	C₄²	—	76	2	no	—
225	C₄²	—	76	2	no	—
226	C₄²	C₂×D₇₆	1	1	yes	characteristic
227	C₄²	C₂×D₇₆	1	1	yes	characteristic
228	C₄²	#64541	1	1	yes	characteristic
229	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
230	C₂³	C₄×D₇₆	1	1	yes	characteristic
231	Q₈	—	38	4	no	—
232	Q₈	—	38	4	no	—
233	Q₈	—	76	2	no	—
234	Q₈	—	76	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	38	4	no	—
238	C₂×C₄	—	76	2	no	—
239	C₂×C₄	—	76	2	no	—
240	C₂×C₄	—	76	2	no	—
241	C₂×C₄	—	152	2	no	—
242	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
243	C₂×C₄	#10597320	1	1	yes	characteristic
244	C₂×C₄	#10597321	1	1	yes	characteristic
245	C₂×C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
246	C₂×C₄	C₂×#64515	1	1	yes	characteristic
247	C₂×C₄	#10597347	1	1	yes	characteristic
248	C₂×C₄	#10597347	1	1	yes	characteristic
249	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
250	C₂×C₄	#10597376	1	1	yes	characteristic
251	C₂×C₄	#10597376	1	1	yes	characteristic
252	C₈	—	2	1	no	—
253	C₈	—	2	1	no	—
254	C₈	—	4	2	no	—
255	C₈	—	4	2	no	—
256	C₈	—	152	2	no	—
257	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
258	C₈	(C₂×D₁₉)⋊C₈	1	2	yes	—
259	C₂²	—	2	1	no	—
260	C₂²	—	2	1	no	—
261	C₂²	#11926446	1	1	yes	characteristic
262	C₂²	C₈×D₇₆	1	1	yes	characteristic
263	C₂²	#11926623	1	1	yes	characteristic
264	C₄	—	2	1	no	—
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	—	76	4	no	—
268	C₄	—	152	2	no	—
269	C₄	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
270	C₄	#11926510	1	1	yes	characteristic
271	C₄	C₈×D₇₆	1	1	yes	characteristic
272	C₄	#11926623	1	1	yes	characteristic
273	C₄	#11926819	1	2	yes	—
274	C₂	—	2	1	no	—
275	C₂	—	2	1	no	—
276	C₂	#14564429	1	1	yes	characteristic
277	C₂	#14564533	1	1	yes	characteristic
278	C₂	#14564550	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₂×C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1450	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	C₄×D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1450	D₁₉
hypocenter	C₁₉	#9669
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1450

Complements

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

N	H ≅ G/N	type
34. C₂×Dic₇₆	C₈	semidirect
195. C₁₉	#9669	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₇₆	2
#14562383	2
#14562029	2
#14561958	2
C₁₉×#1450	2
#9669	19