Subgroups — #18081768

Order 4864.

486 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	C₂×#11926949	C₂	1	1	yes	maximal, characteristic
2	#14564558	C₂	1	2	yes	maximal
3	C₂×#11926297	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926289	C₂	1	2	yes	maximal
5	C₈×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597315	C₂²	1	2	yes	—
7	#11926949	—	2	2	no	—
8	#11926949	C₄	1	4	yes	complemented
9	C₂×#10597275	—	2	1	no	—
10	C₂×#10597275	—	2	1	no	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
12	C₂×#10597267	—	2	4	no	—
13	#11926297	—	2	2	no	—
14	#11926289	—	2	4	no	—
15	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₉	—	2	1	no	—
17	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#336	—	2	1	no	—
20	C₂²×Dic₃₈	—	2	2	no	—
21	C₂²×C₈×C₁₉	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
25	C₂×C₄²×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₄⋊Dic₁₉	—	2	2	no	—
29	C₂²×C₁₉⋊C₈	—	2	2	no	—
30	#10597315	—	2	2	no	—
31	#10597315	—	2	2	no	—
32	#10597315	—	2	2	no	—
33	#10597315	C₂×C₄	1	4	yes	—
34	C₁₉×C₄⋊C₈	—	2	1	no	—
35	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
36	C₄×C₈×C₁₉	—	4	2	no	—
37	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
38	C₄×C₈×C₁₉	D₄	1	2	yes	—
39	C₁₉×#95	—	2	1	no	—
40	#10597275	—	2	4	no	—
41	#10597275	—	2	4	no	—
42	#10597267	—	4	8	no	—
43	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
45	C₂²×C₄×C₁₉	—	2	2	no	—
46	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
49	C₂²×Dic₁₉	—	4	2	no	—
50	C₂×Dic₃₈	—	2	4	no	—
51	C₂×Dic₃₈	—	4	4	no	—
52	C₂×Dic₃₈	—	4	4	no	—
53	C₂×Dic₃₈	—	4	2	no	—
54	C₂×C₈×C₁₉	—	2	1	no	—
55	C₂×C₈×C₁₉	—	2	1	no	—
56	C₂×C₈×C₁₉	—	2	2	no	—
57	C₂×C₈×C₁₉	—	4	1	no	—
58	C₂×C₈×C₁₉	—	4	1	no	—
59	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₈×C₁₉	SD₁₆	1	2	yes	—
62	C₂×C₈×C₁₉	Q₁₆	1	2	yes	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	D₈	1	4	yes	—
65	C₄²×C₁₉	—	4	1	no	—
66	C₄²×C₁₉	—	4	1	no	—
67	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₉	#41	1	1	yes	characteristic
71	C₄⋊Dic₁₉	—	2	4	no	—
72	C₄⋊Dic₁₉	—	2	4	no	—
73	C₄⋊Dic₁₉	—	4	2	no	—
74	C₄⋊Dic₁₉	—	4	2	no	—
75	C₂×C₁₉⋊C₈	—	4	2	no	—
76	C₂×C₁₉⋊C₈	—	4	4	no	—
77	#9731	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	#121	1	1	yes	characteristic
79	C₂×C₄×C₁₉	—	2	2	no	—
80	C₂×C₄×C₁₉	—	2	4	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
87	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
90	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#135	1	2	yes	—
93	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
94	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
95	C₂×Dic₁₉	—	4	4	no	—
96	C₂×Dic₁₉	—	8	4	no	—
97	Dic₃₈	—	4	8	no	—
98	Dic₃₈	—	8	2	no	—
99	Dic₃₈	—	8	2	no	—
100	C₈×C₁₉	—	2	2	no	—
101	C₈×C₁₉	—	4	2	no	—
102	C₈×C₁₉	#103	1	4	yes	complemented
103	C₁₉⋊C₈	—	8	2	no	—
104	C₂×#500	—	19	1	no	—
105	#1981	—	19	2	no	—
106	C₈×C₄⋊C₄	D₁₉	1	1	yes	characteristic
107	C₂×#335	—	19	1	no	—
108	C₂×#332	—	19	2	no	—
109	C₂²×C₁₉	#390	1	1	yes	characteristic
110	C₂²×C₁₉	#461	1	1	yes	characteristic
111	C₂²×C₁₉	#462	1	1	yes	characteristic
112	C₂²×C₁₉	#466	1	2	yes	—
113	C₂²×C₁₉	#473	1	2	yes	—
114	C₄×C₁₉	—	2	1	no	—
115	C₄×C₁₉	—	2	1	no	—
116	C₄×C₁₉	—	4	4	no	—
117	C₄×C₁₉	C₂×#103	1	1	yes	characteristic
118	C₄×C₁₉	#419	1	1	yes	characteristic
119	C₄×C₁₉	C₄×D₈	1	2	yes	—
120	C₄×C₁₉	#461	1	1	yes	characteristic
121	C₄×C₁₉	#462	1	1	yes	characteristic
122	C₄×C₁₉	#493	1	1	yes	characteristic
123	C₄×C₁₉	#495	1	1	yes	characteristic
124	Dic₁₉	—	8	4	no	—
125	C₂×C₄⋊Q₈	—	19	2	no	—
126	#500	—	19	4	no	—
127	#500	—	38	2	no	—
128	C₂×#107	—	38	1	no	—
129	C₂×#107	—	38	1	no	—
130	C₂×C₄⋊C₈	—	19	2	no	—
131	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
132	C₂×#103	—	38	4	no	—
133	C₂×C₄×C₈	—	2	1	no	—
134	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
135	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
136	#336	—	2	1	no	—
137	#335	—	38	2	no	—
138	#332	—	38	4	no	—
139	C₂×C₁₉	#1673	1	2	yes	—
140	C₂×C₁₉	#1674	1	2	yes	—
141	C₂×C₁₉	#1970	1	1	yes	characteristic
142	C₂×C₁₉	#1979	1	1	yes	characteristic
143	C₂×C₁₉	#1981	1	1	yes	characteristic
144	C₂²×Q₈	—	38	2	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	38	2	no	—
147	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
148	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
149	C₄⋊Q₈	—	19	4	no	—
150	C₄⋊Q₈	—	38	2	no	—
151	C₄⋊Q₈	—	38	2	no	—
152	C₄⋊Q₈	—	38	2	no	—
153	C₂×C₄⋊C₄	—	38	2	no	—
154	C₂×C₄⋊C₄	—	38	2	no	—
155	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
156	C₂×C₄²	—	2	1	no	—
157	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
158	#107	—	38	4	no	—
159	#107	—	38	4	no	—
160	C₄⋊C₈	—	2	1	no	—
161	C₄⋊C₈	—	38	2	no	—
162	C₄⋊C₈	—	38	2	no	—
163	C₄⋊C₈	D₇₆	1	2	yes	—
164	#103	—	76	8	no	—
165	C₄×C₈	—	4	2	no	—
166	C₄×C₈	C₄×D₁₉	1	2	yes	—
167	C₄×C₈	D₇₆	1	2	yes	—
168	#95	—	2	1	no	—
169	C₁₉	#9731	1	1	yes	characteristic, complemented, Sylow
170	C₂×Q₈	—	38	4	no	—
171	C₂×Q₈	—	76	2	no	—
172	C₂×Q₈	—	76	4	no	—
173	C₂×Q₈	—	76	4	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	—	76	2	no	—
176	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
177	C₂²×C₄	#64541	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	4	1	no	—
183	C₂×C₈	—	4	1	no	—
184	C₂×C₈	—	76	2	no	—
185	C₂×C₈	—	76	4	no	—
186	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
187	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
188	C₂×C₈	#64526	1	2	yes	—
189	C₂×C₈	#64528	1	2	yes	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	38	4	no	—
192	C₄⋊C₄	—	38	4	no	—
193	C₄⋊C₄	—	76	2	no	—
194	C₄⋊C₄	—	76	2	no	—
195	C₄⋊C₄	D₁₅₂	1	4	yes	—
196	C₄²	—	4	1	no	—
197	C₄²	—	4	1	no	—
198	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
199	C₄²	C₂×D₇₆	1	1	yes	characteristic
200	C₄²	C₂×D₇₆	1	1	yes	characteristic
201	C₄²	#64541	1	1	yes	characteristic
202	C₂³	#10597376	1	1	yes	characteristic
203	Q₈	—	76	8	no	—
204	Q₈	—	152	2	no	—
205	Q₈	—	152	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	76	4	no	—
211	C₂×C₄	—	152	4	no	—
212	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
213	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
214	C₂×C₄	#10597320	1	1	yes	characteristic
215	C₂×C₄	#10597321	1	1	yes	characteristic
216	C₂×C₄	C₂×D₁₅₂	1	2	yes	—
217	C₂×C₄	#10597350	1	2	yes	—
218	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
219	C₂×C₄	#10597376	1	1	yes	characteristic
220	C₂×C₄	C₂×#64526	1	1	yes	characteristic
221	C₂×C₄	C₂×#64528	1	1	yes	characteristic
222	C₂×C₄	#10597397	1	1	yes	characteristic
223	C₂×C₄	#10597397	1	1	yes	characteristic
224	C₈	—	2	2	no	—
225	C₈	—	4	2	no	—
226	C₈	—	152	2	no	—
227	C₈	#10597267	1	4	yes	complemented
228	C₂²	#11926446	1	1	yes	characteristic
229	C₂²	#11926749	1	1	yes	characteristic
230	C₂²	#11926754	1	1	yes	characteristic
231	C₂²	#11926780	1	2	yes	—
232	C₂²	#11926819	1	2	yes	—
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	4	no	—
236	C₄	—	152	4	no	—
237	C₄	C₂×#10597267	1	1	yes	characteristic
238	C₄	#11926552	1	1	yes	characteristic
239	C₄	C₄×D₁₅₂	1	2	yes	—
240	C₄	#11926749	1	1	yes	characteristic
241	C₄	#11926754	1	1	yes	characteristic
242	C₄	#11926921	1	1	yes	characteristic
243	C₄	#11926928	1	1	yes	characteristic
244	C₂	#14563024	1	2	yes	—
245	C₂	#14563029	1	2	yes	—
246	C₂	#14564501	1	1	yes	characteristic
247	C₂	#14564550	1	1	yes	characteristic
248	C₂	#14564558	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₈×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	#121
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₈×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#9731
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
8. #11926949	C₄	semidirect
102. C₈×C₁₉	#103	semidirect
169. C₁₉	#9731	semidirect
227. C₈	#10597267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926949	2
#14564558	2
C₂×#11926297	2
C₂×#11926289	2
C₈×C₄⋊C₄×C₁₉	2
#9731	19