Subgroups — #18081695

Order 4864.

430 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14574221	C₂	1	1	yes	maximal, characteristic
2	#14564579	C₂	1	2	yes	maximal
3	C₄×#10597275	C₂	1	1	yes	maximal, characteristic
4	#14562135	C₂	1	2	yes	maximal
5	C₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	2	yes	—
7	#11926949	C₄	1	1	yes	characteristic, complemented
8	#11926924	C₄	1	1	yes	characteristic, complemented
9	#11926895	C₄	1	2	yes	complemented
10	#11926785	—	2	1	no	—
11	#11926785	—	2	1	no	—
12	C₄×Dic₇₆	—	2	1	no	—
13	C₄×Dic₇₆	—	2	1	no	—
14	C₂×#10597275	—	2	1	no	—
15	C₄×C₄⋊Dic₁₉	C₂²	1	2	yes	—
16	#11926307	—	2	1	no	—
17	#11926305	—	2	4	no	—
18	#11926282	—	2	4	no	—
19	C₁₉×#431	C₂²	1	1	yes	characteristic
20	C₄×M₁₆×C₁₉	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	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
25	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	#10597372	—	2	2	no	—
29	C₂×C₄⋊Dic₁₉	—	2	2	no	—
30	#10597370	—	2	2	no	—
31	#10597370	—	2	2	no	—
32	C₂×C₄×Dic₁₉	—	2	2	no	—
33	C₂×Dic₇₆	—	2	1	no	—
34	C₂×Dic₇₆	—	2	1	no	—
35	#10597316	—	2	2	no	—
36	#10597315	C₂×C₄	1	2	yes	—
37	#10597315	C₂×C₄	1	2	yes	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₄×Dic₃₈	—	2	2	no	—
40	C₁₉×C₄⋊C₈	—	2	1	no	—
41	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
42	C₁₉×#97	—	2	1	no	—
43	C₄×C₈×C₁₉	—	2	1	no	—
44	C₄×C₈×C₁₉	—	2	1	no	—
45	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
49	C₁₉⋊#95	—	2	2	no	—
50	#10597275	—	2	4	no	—
51	#10597275	—	2	1	no	—
52	#10597275	—	2	1	no	—
53	#10597273	—	2	2	no	—
54	#10597273	—	2	2	no	—
55	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×Dic₁₉	—	4	2	no	—
59	C₂×Dic₃₈	—	2	2	no	—
60	C₂×Dic₃₈	—	2	2	no	—
61	M₁₆×C₁₉	—	2	2	no	—
62	M₁₆×C₁₉	Q₁₆	1	4	yes	complemented
63	C₂×C₈×C₁₉	—	2	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	1	no	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₉	#41	1	1	yes	characteristic
74	C₄²×C₁₉	#41	1	1	yes	characteristic
75	C₂²⋊Dic₁₉	—	4	2	no	—
76	C₄⋊Dic₁₉	—	2	4	no	—
77	C₄⋊Dic₁₉	—	2	2	no	—
78	C₄⋊Dic₁₉	—	2	2	no	—
79	C₄⋊Dic₁₉	—	2	2	no	—
80	C₄⋊Dic₁₉	—	2	2	no	—
81	C₄⋊Dic₁₉	—	4	2	no	—
82	Dic₁₉⋊C₄	—	4	2	no	—
83	Dic₁₉⋊C₄	—	4	2	no	—
84	C₄×Dic₁₉	—	4	2	no	—
85	C₄×Dic₁₉	—	4	4	no	—
86	Dic₇₆	—	4	2	no	—
87	Dic₇₆	—	4	2	no	—
88	#9718	—	19	1	no	maximal, Sylow
89	C₂³×C₁₉	#127	1	1	yes	characteristic
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	4	1	no	—
93	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₄×D₄	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	C₂×Q₁₆	1	2	yes	—
100	C₂×C₄×C₁₉	#135	1	2	yes	—
101	C₂×Dic₁₉	—	4	4	no	—
102	C₂×Dic₁₉	—	4	2	no	—
103	C₂×Dic₁₉	—	4	2	no	—
104	C₂×Dic₁₉	—	8	2	no	—
105	C₂×Dic₁₉	—	8	2	no	—
106	Dic₃₈	—	4	2	no	—
107	Dic₃₈	—	4	2	no	—
108	Dic₃₈	—	8	2	no	—
109	C₈×C₁₉	—	2	1	no	—
110	C₈×C₁₉	—	2	1	no	—
111	C₈×C₁₉	—	2	1	no	—
112	C₈×C₁₉	—	2	4	no	—
113	C₈×C₁₉	—	4	2	no	—
114	C₈×C₁₉	#104	1	2	yes	—
115	#3170	—	19	1	no	—
116	#1986	—	19	2	no	—
117	C₄×#107	—	19	1	no	—
118	#1503	—	19	2	no	—
119	C₈×M₁₆	D₁₉	1	1	yes	characteristic
120	C₂²×C₁₉	—	2	1	no	—
121	C₂²×C₁₉	—	2	1	no	—
122	C₂²×C₁₉	#390	1	1	yes	characteristic
123	C₂²×C₁₉	#494	1	1	yes	characteristic
124	C₂²×C₁₉	#495	1	1	yes	characteristic
125	C₄×C₁₉	—	2	1	no	—
126	C₄×C₁₉	—	2	1	no	—
127	C₄×C₁₉	—	2	1	no	—
128	C₄×C₁₉	C₂×#104	1	1	yes	characteristic
129	C₄×C₁₉	#421	1	1	yes	characteristic
130	C₄×C₁₉	C₄×Q₁₆	1	2	yes	—
131	C₄×C₁₉	#467	1	2	yes	—
132	Dic₁₉	—	8	4	no	—
133	Dic₁₉	—	8	2	no	—
134	Dic₁₉	—	8	2	no	—
135	#533	—	19	2	no	—
136	#500	—	19	1	no	—
137	#494	—	19	1	no	—
138	#487	—	19	2	no	—
139	#467	—	38	1	no	—
140	#467	—	38	1	no	—
141	C₄×Q₁₆	—	38	1	no	—
142	C₄×Q₁₆	—	38	1	no	—
143	#431	C₂×D₁₉	1	1	yes	characteristic
144	C₂×#107	—	38	1	no	—
145	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
146	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
147	C₄×C₄⋊C₄	—	19	2	no	—
148	#340	—	38	1	no	—
149	#339	—	38	4	no	—
150	#328	—	38	4	no	—
151	#322	—	2	1	no	—
152	C₈²	—	2	1	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	—	2	1	no	—
155	C₂×C₁₉	#1969	1	1	yes	characteristic
156	C₂×C₁₉	#1976	1	1	yes	characteristic
157	C₂×C₁₉	#1980	1	1	yes	characteristic
158	C₂×Q₁₆	—	38	1	no	—
159	C₂×Q₁₆	—	38	1	no	—
160	C₂×M₁₆	D₇₆	1	2	yes	—
161	C₂²×C₈	D₇₆	1	1	yes	characteristic
162	C₂²×C₈	D₇₆	1	1	yes	characteristic
163	C₄⋊Q₈	—	19	2	no	—
164	C₄⋊Q₈	—	19	2	no	—
165	#125	—	38	2	no	—
166	C₂²⋊Q₈	—	38	2	no	—
167	C₂²⋊Q₈	—	38	2	no	—
168	C₄×Q₈	—	38	2	no	—
169	C₄×Q₈	—	38	2	no	—
170	#117	—	38	2	no	—
171	C₂×C₄⋊C₄	—	38	2	no	—
172	C₂×C₄²	—	38	2	no	—
173	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
174	#107	—	38	4	no	—
175	#107	—	38	1	no	—
176	#107	—	38	1	no	—
177	C₄⋊C₈	—	2	1	no	—
178	#103	—	38	2	no	—
179	#103	—	38	2	no	—
180	C₂²⋊C₈	D₇₆	1	2	yes	—
181	#97	—	2	1	no	—
182	C₄×C₈	—	2	1	no	—
183	C₄×C₈	—	2	1	no	—
184	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
185	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
186	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
187	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
188	#95	—	38	2	no	—
189	C₁₉	#9718	1	1	yes	characteristic, complemented, Sylow
190	C₂×Q₈	—	38	2	no	—
191	C₂×Q₈	—	38	2	no	—
192	C₂²×C₄	—	76	2	no	—
193	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
194	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
195	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
196	Q₁₆	—	76	2	no	—
197	Q₁₆	—	76	2	no	—
198	M₁₆	—	2	2	no	—
199	M₁₆	Dic₇₆	1	4	yes	complemented
200	C₂×C₈	—	2	2	no	—
201	C₂×C₈	—	2	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	4	1	no	—
204	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
205	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
206	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
208	C₄⋊C₄	—	38	4	no	—
209	C₄⋊C₄	—	38	2	no	—
210	C₄⋊C₄	—	38	2	no	—
211	C₄⋊C₄	—	38	2	no	—
212	C₄⋊C₄	—	38	2	no	—
213	C₄⋊C₄	—	76	2	no	—
214	C₄⋊C₄	—	76	2	no	—
215	C₄⋊C₄	—	76	2	no	—
216	C₂²⋊C₄	—	76	2	no	—
217	C₄²	—	76	2	no	—
218	C₄²	—	76	4	no	—
219	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
220	C₄²	#64541	1	1	yes	characteristic
221	C₄²	#64541	1	1	yes	characteristic
222	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂³	#10597320	1	1	yes	characteristic
224	Q₈	—	76	2	no	—
225	Q₈	—	76	2	no	—
226	Q₈	—	152	2	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	76	4	no	—
231	C₂×C₄	—	76	2	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	152	2	no	—
234	C₂×C₄	—	152	2	no	—
235	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
236	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
237	C₂×C₄	#10597321	1	1	yes	characteristic
238	C₂×C₄	#10597350	1	2	yes	—
239	C₂×C₄	C₂×Dic₇₆	1	2	yes	—
240	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
241	C₂×C₄	#10597376	1	1	yes	characteristic
242	C₂×C₄	#10597376	1	1	yes	characteristic
243	C₈	—	2	4	no	—
244	C₈	—	2	1	no	—
245	C₈	—	2	1	no	—
246	C₈	—	2	1	no	—
247	C₈	—	4	2	no	—
248	C₈	#10597282	1	2	yes	—
249	C₂²	—	2	1	no	—
250	C₂²	—	2	1	no	—
251	C₂²	#11926446	1	1	yes	characteristic
252	C₂²	#11926924	1	1	yes	characteristic
253	C₂²	#11926928	1	1	yes	characteristic
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	—	2	1	no	—
257	C₄	—	152	4	no	—
258	C₄	—	152	2	no	—
259	C₄	—	152	2	no	—
260	C₄	C₂×#10597282	1	1	yes	characteristic
261	C₄	#11926560	1	1	yes	characteristic
262	C₄	C₄×Dic₇₆	1	2	yes	—
263	C₄	#11926785	1	2	yes	—
264	C₂	—	2	1	no	—
265	C₂	—	2	1	no	—
266	C₂	#14564496	1	1	yes	characteristic
267	C₂	#14564533	1	1	yes	characteristic
268	C₂	#14564554	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10597376
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₈×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#390
prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₈×M₁₆	D₁₉
hypocenter	C₁₉	#9718
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
7. #11926949	C₄	semidirect
8. #11926924	C₄	semidirect
9. #11926895	C₄	semidirect
62. M₁₆×C₁₉	Q₁₆	semidirect
189. C₁₉	#9718	semidirect
199. M₁₆	Dic₇₆	semidirect

Maximal subgroups

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

subgroup	index
#14574221	2
#14564579	2
C₄×#10597275	2
#14562135	2
C₈×M₁₆×C₁₉	2
#9718	19