Subgroups — #14574179

Order 2432.

380 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927097	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597334	C₂	1	1	yes	maximal, characteristic
3	#11926952	C₂	1	2	yes	maximal, complemented
4	#11926951	C₂	1	2	yes	maximal, complemented
5	#11926948	C₂	1	2	yes	maximal, complemented
6	#11926941	C₂	1	2	yes	maximal, complemented
7	#11926587	C₂	1	1	yes	maximal, characteristic
8	#11926586	C₂	1	1	yes	maximal, characteristic
9	#11926584	C₂	1	1	yes	maximal, characteristic
10	M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#428	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₃₈	—	2	1	no	—
13	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#117	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	#10597372	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂×Dic₁₉⋊C₄	—	2	1	no	—
19	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂×#64520	C₂²	1	1	yes	characteristic
21	#10597336	C₂²	1	1	yes	characteristic
22	#10597336	C₂²	1	1	yes	characteristic
23	#10597334	—	2	1	no	—
24	#10597334	—	2	1	no	—
25	#10597334	C₂²	1	2	yes	—
26	#10597334	C₂²	1	2	yes	—
27	#10597334	C₂²	1	1	yes	characteristic
28	#10597334	C₂²	1	1	yes	characteristic
29	#10597324	—	2	1	no	—
30	#10597324	—	2	1	no	—
31	C₄×Dic₃₈	—	2	1	no	—
32	C₄×Dic₃₈	—	2	1	no	—
33	C₁₉×#107	C₂²	1	2	yes	—
34	C₁₉×#106	C₂²	1	2	yes	—
35	#10597275	C₂²	1	2	yes	—
36	#10597274	C₂²	1	2	yes	—
37	#10597272	C₂²	1	2	yes	—
38	C₈×Dic₁₉	C₂²	1	2	yes	—
39	#10597265	C₂²	1	2	yes	—
40	#10597265	C₂²	1	2	yes	—
41	#10597264	C₂²	1	2	yes	—
42	#10597264	C₂²	1	2	yes	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₉	—	2	1	no	—
46	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
47	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
48	C₂×Dic₃₈	—	2	2	no	—
49	C₂×Dic₃₈	—	2	2	no	—
50	C₂×Dic₃₈	—	2	1	no	—
51	C₂×Dic₃₈	—	2	1	no	—
52	C₂×Dic₃₈	—	4	4	no	—
53	M₁₆×C₁₉	Q₈	1	4	yes	complemented
54	C₂×C₈×C₁₉	C₂³	1	2	yes	—
55	C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₄²×C₁₉	—	2	1	no	—
61	C₂²⋊Dic₁₉	—	2	1	no	—
62	C₄⋊Dic₁₉	—	2	1	no	—
63	C₄⋊Dic₁₉	—	2	1	no	—
64	C₄⋊Dic₁₉	—	2	1	no	—
65	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
66	C₄⋊Dic₁₉	C₂³	1	2	yes	—
67	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
68	Dic₁₉⋊C₄	—	2	1	no	—
69	Dic₁₉⋊C₄	—	2	1	no	—
70	Dic₁₉⋊C₄	—	2	1	no	—
71	Dic₁₉⋊C₄	—	2	1	no	—
72	Dic₁₉⋊C₄	—	2	2	no	—
73	Dic₁₉⋊C₄	—	2	2	no	—
74	C₄×Dic₁₉	—	2	1	no	—
75	C₄×Dic₁₉	D₄	1	1	yes	characteristic
76	C₄×Dic₁₉	D₄	1	1	yes	characteristic
77	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
78	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
79	#64520	Q₈	1	4	yes	complemented
80	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
81	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	—	2	1	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
88	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
89	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	2	no	—
92	C₂×Dic₁₉	—	2	1	no	—
93	C₂×Dic₁₉	—	2	1	no	—
94	C₂×Dic₁₉	—	2	2	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
100	Dic₃₈	—	4	4	no	—
101	Dic₃₈	—	4	2	no	—
102	Dic₃₈	—	4	4	no	—
103	Dic₃₈	—	4	2	no	—
104	C₈×C₁₉	C₂×Q₈	1	4	yes	complemented
105	C₁₉⋊C₈	C₂×Q₈	1	4	yes	complemented
106	#3165	—	19	1	no	maximal, Sylow
107	C₂²×C₁₉	—	2	1	no	—
108	C₂²×C₁₉	—	2	1	no	—
109	C₂²×C₁₉	C₄⋊Q₈	1	2	yes	—
110	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
111	C₄×C₁₉	—	4	2	no	—
112	C₄×C₁₉	—	4	1	no	—
113	C₄×C₁₉	—	4	1	no	—
114	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
115	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
116	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
117	Dic₁₉	—	2	1	no	—
118	Dic₁₉	—	2	1	no	—
119	Dic₁₉	—	4	2	no	—
120	Dic₁₉	—	4	1	no	—
121	Dic₁₉	—	4	1	no	—
122	Dic₁₉	AGL(1,ℤ/8)	1	2	yes	—
123	Dic₁₉	#137	1	2	yes	—
124	#533	—	19	1	no	—
125	C₂×C₄⋊Q₈	—	19	1	no	—
126	#501	—	19	2	no	—
127	#501	—	19	2	no	—
128	#500	—	19	2	no	—
129	#498	—	19	2	no	—
130	#428	—	19	1	no	—
131	#428	—	19	1	no	—
132	#428	—	19	1	no	—
133	#428	D₁₉	1	1	yes	characteristic
134	C₄×M₁₆	—	19	1	no	—
135	C₂×C₁₉	—	2	2	no	—
136	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
137	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
139	C₂²×Q₈	—	38	1	no	—
140	C₂×M₁₆	—	19	1	no	—
141	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
142	C₄⋊Q₈	—	19	2	no	—
143	C₄⋊Q₈	—	19	2	no	—
144	C₄⋊Q₈	—	19	1	no	—
145	C₄⋊Q₈	—	19	1	no	—
146	C₄⋊Q₈	—	38	1	no	—
147	C₄⋊Q₈	—	38	1	no	—
148	#125	—	19	1	no	—
149	#125	—	19	1	no	—
150	C₂²⋊Q₈	—	38	1	no	—
151	C₂²⋊Q₈	—	38	1	no	—
152	C₄×Q₈	—	38	1	no	—
153	C₄×Q₈	—	38	1	no	—
154	#117	—	19	1	no	—
155	#117	C₂×D₁₉	1	1	yes	characteristic
156	C₂×C₄⋊C₄	—	19	1	no	—
157	C₂×C₄⋊C₄	—	38	1	no	—
158	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
159	C₂×C₄²	—	19	1	no	—
160	#107	—	19	2	no	—
161	#107	—	19	2	no	—
162	#107	—	19	2	no	—
163	#107	C₂×D₁₉	1	2	yes	—
164	#106	—	19	2	no	—
165	#106	—	19	2	no	—
166	#106	—	19	2	no	—
167	#106	C₂×D₁₉	1	2	yes	—
168	#97	—	19	2	no	—
169	C₄×C₈	—	19	2	no	—
170	C₁₉	#3165	1	1	yes	characteristic, complemented, Sylow
171	C₂×Q₈	—	38	1	no	—
172	C₂×Q₈	—	38	1	no	—
173	C₂×Q₈	—	38	2	no	—
174	C₂×Q₈	—	38	2	no	—
175	C₂×Q₈	—	76	4	no	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	19	1	no	—
178	C₂²×C₄	—	19	1	no	—
179	C₂²×C₄	—	38	1	no	—
180	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
181	M₁₆	—	19	4	no	—
182	M₁₆	Dic₃₈	1	4	yes	complemented
183	C₂×C₈	—	19	2	no	—
184	C₂×C₈	C₂²×D₁₉	1	2	yes	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	19	1	no	—
187	C₄⋊C₄	—	19	2	no	—
188	C₄⋊C₄	—	19	1	no	—
189	C₄⋊C₄	—	38	2	no	—
190	C₄⋊C₄	—	38	2	no	—
191	C₄⋊C₄	—	38	1	no	—
192	C₄⋊C₄	—	38	1	no	—
193	C₄⋊C₄	—	38	1	no	—
194	C₄⋊C₄	—	38	1	no	—
195	C₄⋊C₄	—	38	1	no	—
196	C₄⋊C₄	—	38	1	no	—
197	C₄⋊C₄	—	38	1	no	—
198	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
199	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
200	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
201	C₂²⋊C₄	—	2	1	no	—
202	C₂²⋊C₄	—	38	1	no	—
203	C₄²	—	2	1	no	—
204	C₄²	—	19	1	no	—
205	C₄²	—	19	1	no	—
206	C₄²	—	19	1	no	—
207	C₄²	—	19	1	no	—
208	C₄²	—	38	1	no	—
209	C₂³	D₄×D₁₉	1	1	yes	characteristic
210	Q₈	—	76	4	no	—
211	Q₈	—	76	2	no	—
212	Q₈	—	76	2	no	—
213	Q₈	—	76	4	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	19	1	no	—
219	C₂×C₄	—	19	1	no	—
220	C₂×C₄	—	19	1	no	—
221	C₂×C₄	—	19	1	no	—
222	C₂×C₄	—	38	2	no	—
223	C₂×C₄	—	38	2	no	—
224	C₂×C₄	—	38	1	no	—
225	C₂×C₄	—	38	1	no	—
226	C₂×C₄	—	38	2	no	—
227	C₂×C₄	—	76	2	no	—
228	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
229	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
230	C₂×C₄	Q₈×D₁₉	1	2	yes	—
231	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
232	C₈	—	19	4	no	—
233	C₈	C₂×Dic₃₈	1	4	yes	complemented
234	C₂²	—	2	1	no	—
235	C₂²	—	2	1	no	—
236	C₂²	#10597334	1	2	yes	—
237	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
238	C₄	—	4	2	no	—
239	C₄	—	4	1	no	—
240	C₄	—	4	1	no	—
241	C₄	—	19	2	no	—
242	C₄	—	19	2	no	—
243	C₄	—	38	1	no	—
244	C₄	—	38	1	no	—
245	C₄	—	76	2	no	—
246	C₄	—	76	1	no	—
247	C₄	—	76	1	no	—
248	C₄	#10597334	1	2	yes	—
249	C₄	C₂²×Dic₃₈	1	1	yes	characteristic
250	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
251	C₂	—	2	2	no	—
252	C₂	C₂×#10597334	1	1	yes	characteristic
253	C₂	AGL(1,ℤ/8)×D₁₉	1	1	yes	characteristic
254	C₂	#137×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#428	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#428	D₁₉
hypocenter	C₁₉	#3165
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #428

Complements

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

N	H ≅ G/N	type
3. #11926952	C₂	semidirect
4. #11926951	C₂	semidirect
5. #11926948	C₂	semidirect
6. #11926941	C₂	semidirect
53. M₁₆×C₁₉	Q₈	semidirect
79. #64520	Q₈	semidirect
104. C₈×C₁₉	C₂×Q₈	semidirect
105. C₁₉⋊C₈	C₂×Q₈	semidirect
170. C₁₉	#3165	semidirect
182. M₁₆	Dic₃₈	semidirect
233. C₈	C₂×Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
#11927097	2
C₂×#10597334	2
#11926952	2
#11926951	2
#11926948	2
#11926941	2
#11926587	2
#11926586	2
#11926584	2
M₁₆×Dic₁₉	2
C₁₉×#428	2
#3165	19