Subgroups — #14574205

Order 2432.

380 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927078	C₂	1	2	yes	maximal, complemented
2	#11926946	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926928	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926899	C₂	1	2	yes	maximal, complemented
5	#11926785	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926780	C₂	1	1	yes	maximal, characteristic
7	#11926773	C₂	1	2	yes	maximal, complemented
8	C₄×Dic₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#64516	C₂	1	2	yes	maximal, complemented
10	C₄×D₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	#10597376	C₂²	1	2	yes	—
16	#10597375	—	2	2	no	—
17	C₄×C₂²⋊D₁₉	—	2	2	no	—
18	#10597370	C₂²	1	2	yes	—
19	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
20	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
21	C₂×#64516	C₂²	1	2	yes	—
22	#10597322	—	2	2	no	—
23	#10597321	C₂²	1	2	yes	—
24	C₄×D₇₆	C₂²	1	2	yes	—
25	#10597318	—	2	2	no	—
26	#10597316	C₂²	1	2	yes	—
27	C₄×Dic₃₈	C₂²	1	2	yes	—
28	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
29	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
32	#10597278	C₂²	1	2	yes	—
33	#10597278	C₂²	1	2	yes	—
34	#10597275	C₂²	1	1	yes	characteristic
35	#10597275	C₂²	1	1	yes	characteristic
36	#10597274	C₂²	1	2	yes	—
37	#10597273	C₂²	1	2	yes	—
38	#10597273	C₂²	1	2	yes	—
39	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂×C₂²⋊D₁₉	—	2	2	no	—
43	C₂×D₇₆	C₂³	1	2	yes	—
44	C₂×C₄×D₁₉	—	2	2	no	—
45	C₂×Dic₃₈	C₂³	1	2	yes	—
46	C₂×C₈×C₁₉	—	2	2	no	—
47	C₂×C₈×C₁₉	—	2	2	no	—
48	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
52	C₄²×C₁₉	D₄	1	1	yes	characteristic
53	C₄²×C₁₉	D₄	1	1	yes	characteristic
54	C₄²×C₁₉	C₂³	1	1	yes	characteristic
55	C₄²×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²⋊Dic₁₉	—	2	2	no	—
57	(C₂×D₁₉)⋊C₄	—	2	2	no	—
58	(C₂×D₁₉)⋊C₄	—	2	2	no	—
59	(C₂×D₁₉)⋊C₄	—	2	2	no	—
60	(C₂×D₁₉)⋊C₄	—	2	2	no	—
61	C₄⋊Dic₁₉	C₂³	1	2	yes	—
62	C₄⋊Dic₁₉	C₂³	1	2	yes	—
63	Dic₁₉⋊C₄	—	2	2	no	—
64	Dic₁₉⋊C₄	—	2	2	no	—
65	Dic₁₉⋊C₄	—	2	2	no	—
66	Dic₁₉⋊C₄	—	2	2	no	—
67	C₄×Dic₁₉	—	2	2	no	—
68	Dic₇₆	—	2	2	no	—
69	D₁₅₂	—	2	2	no	—
70	#64516	—	2	4	no	—
71	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×D₁₉	—	2	2	no	—
73	C₂×C₄×C₁₉	—	2	2	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	1	no	—
76	C₂×C₄×C₁₉	—	2	1	no	—
77	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
83	C₂²⋊D₁₉	—	4	4	no	—
84	C₂×Dic₁₉	—	2	2	no	—
85	C₂×Dic₁₉	—	2	2	no	—
86	C₂×Dic₁₉	—	2	2	no	—
87	D₇₆	—	2	2	no	—
88	D₇₆	—	2	2	no	—
89	C₄×D₁₉	—	4	4	no	—
90	Dic₃₈	—	2	2	no	—
91	Dic₃₈	—	2	2	no	—
92	C₈×C₁₉	—	2	1	no	—
93	C₈×C₁₉	—	2	1	no	—
94	C₈×C₁₉	#41	1	2	yes	—
95	C₈×C₁₉	#41	1	2	yes	—
96	#3168	—	19	1	no	maximal, Sylow
97	C₂²×C₁₉	—	2	1	no	—
98	C₂²×C₁₉	—	2	1	no	—
99	C₂²×C₁₉	#135	1	2	yes	—
100	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
101	C₂×D₁₉	—	4	2	no	—
102	C₂×D₁₉	—	4	2	no	—
103	C₂×D₁₉	—	4	2	no	—
104	C₄×C₁₉	—	2	1	no	—
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	#135	1	2	yes	—
109	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
110	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
111	Dic₁₉	—	4	2	no	—
112	Dic₁₉	—	4	2	no	—
113	Dic₁₉	—	4	2	no	—
114	#529	—	19	2	no	—
115	#499	—	19	1	no	—
116	#495	—	19	1	no	—
117	#488	—	19	2	no	—
118	#467	—	19	1	no	—
119	#466	—	19	1	no	—
120	#465	—	19	2	no	—
121	C₄×Q₁₆	—	19	1	no	—
122	C₄×SD₁₆	—	19	2	no	—
123	C₄×D₈	—	19	1	no	—
124	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic, complemented
125	C₂×C₁₉	—	2	2	no	—
126	C₂×C₁₉	#532	1	1	yes	characteristic
127	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
128	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
129	D₁₉	—	8	2	no	—
130	C₂×Q₁₆	—	19	1	no	—
131	C₂×SD₁₆	—	19	2	no	—
132	C₂×D₈	—	19	1	no	—
133	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
134	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
135	#126	—	38	2	no	—
136	#125	—	19	2	no	—
137	#124	—	19	2	no	—
138	#123	—	38	2	no	—
139	C₂²⋊Q₈	—	19	2	no	—
140	#121	—	19	2	no	—
141	C₄×Q₈	—	19	2	no	—
142	C₄×D₄	—	19	2	no	—
143	C₄×D₄	—	38	2	no	—
144	#117	—	38	2	no	—
145	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
146	#107	—	19	1	no	—
147	#107	—	19	1	no	—
148	#106	—	19	2	no	—
149	#103	—	19	2	no	—
150	#103	—	19	2	no	—
151	#102	—	19	2	no	—
152	#102	—	19	2	no	—
153	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
154	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
155	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
156	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
157	C₁₉	#3168	1	1	yes	characteristic, complemented, Sylow
158	C₂×Q₈	—	19	2	no	—
159	C₂×D₄	—	19	2	no	—
160	C₂×D₄	—	38	2	no	—
161	C₂²×C₄	—	38	2	no	—
162	C₂²×C₄	D₇₆	1	1	yes	characteristic
163	C₂²×C₄	D₇₆	1	1	yes	characteristic
164	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
165	Q₁₆	—	38	2	no	—
166	SD₁₆	—	38	4	no	—
167	D₈	—	38	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
171	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
172	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
173	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
174	C₄⋊C₄	—	19	2	no	—
175	C₄⋊C₄	—	19	2	no	—
176	C₄⋊C₄	—	38	2	no	—
177	C₄⋊C₄	—	38	2	no	—
178	C₄⋊C₄	—	38	2	no	—
179	C₄⋊C₄	—	38	2	no	—
180	C₂²⋊C₄	—	38	2	no	—
181	C₂²⋊C₄	—	38	2	no	—
182	C₂²⋊C₄	—	38	2	no	—
183	C₂²⋊C₄	—	38	2	no	—
184	C₂²⋊C₄	—	38	2	no	—
185	C₄²	—	38	2	no	—
186	C₄²	D₇₆	1	1	yes	characteristic
187	C₄²	D₇₆	1	1	yes	characteristic
188	C₄²	C₂²×D₁₉	1	1	yes	characteristic
189	C₄²	C₂²×D₁₉	1	1	yes	characteristic
190	C₂³	—	38	2	no	—
191	C₂³	C₂×D₇₆	1	1	yes	characteristic
192	Q₈	—	38	2	no	—
193	Q₈	—	38	2	no	—
194	D₄	—	38	2	no	—
195	D₄	—	38	2	no	—
196	D₄	—	76	4	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	38	2	no	—
202	C₂×C₄	—	38	2	no	—
203	C₂×C₄	—	38	2	no	—
204	C₂×C₄	—	76	4	no	—
205	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
206	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
207	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
208	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
209	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
210	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
211	C₈	—	2	1	no	—
212	C₈	—	2	1	no	—
213	C₈	#64541	1	2	yes	—
214	C₈	#64541	1	2	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	—	76	2	no	—
218	C₂²	—	76	2	no	—
219	C₂²	—	76	2	no	—
220	C₂²	#10597350	1	2	yes	—
221	C₂²	C₂²×D₇₆	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	76	2	no	—
227	C₄	—	76	2	no	—
228	C₄	—	76	2	no	—
229	C₄	#10597350	1	2	yes	—
230	C₄	C₂×#64541	1	1	yes	characteristic
231	C₄	C₂×#64541	1	1	yes	characteristic
232	C₂	—	2	2	no	—
233	C₂	—	152	2	no	—
234	C₂	#11927094	1	1	yes	characteristic
235	C₂	C₂×#10597350	1	1	yes	characteristic
236	C₂	C₂×#10597350	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#11926780	C₂
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	#3168
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #11927078	C₂	semidirect
2. #11926946	C₂	semidirect
3. #11926928	C₂	semidirect
4. #11926899	C₂	semidirect
5. #11926785	C₂	semidirect
7. #11926773	C₂	semidirect
8. C₄×Dic₇₆	C₂	semidirect
9. C₄×#64516	C₂	semidirect
10. C₄×D₁₅₂	C₂	semidirect
11. C₂×C₄×C₈×C₁₉	C₂	semidirect
124. C₂×C₄×C₈	D₁₉	semidirect
157. C₁₉	#3168	semidirect

Maximal subgroups

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

subgroup	index
#11927078	2
#11926946	2
#11926928	2
#11926899	2
#11926785	2
#11926780	2
#11926773	2
C₄×Dic₇₆	2
C₄×#64516	2
C₄×D₁₅₂	2
C₂×C₄×C₈×C₁₉	2
#3168	19