Subgroups — #14572553

Order 2432.

452 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597350	C₂	1	1	yes	maximal, characteristic
2	#11927310	C₂	1	2	yes	maximal, complemented
3	#11926667	C₂	1	4	yes	maximal, complemented
4	#11926662	C₂	1	4	yes	maximal, complemented
5	C₂×#10597276	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926562	C₂	1	2	yes	maximal, complemented
7	C₁₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64541	C₂²	1	2	yes	—
9	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	2	yes	—
13	#10597353	—	2	4	no	—
14	M₁₆×D₁₉	—	2	4	no	—
15	C₂×Dic₇₆	C₄	1	1	yes	characteristic, complemented
16	#10597350	C₄	1	2	yes	complemented
17	#10597350	C₄	1	2	yes	complemented
18	#10597350	C₂²	1	2	yes	—
19	#10597350	C₂²	1	2	yes	—
20	C₂×D₁₅₂	C₄	1	1	yes	characteristic, complemented
21	C₂×#64516	C₄	1	2	yes	complemented
22	#10597347	C₂²	1	8	yes	complemented
23	C₁₉×#97	C₂²	1	2	yes	complemented
24	C₄×C₈×C₁₉	C₂²	1	2	yes	complemented
25	#10597276	C₂²	1	2	yes	complemented
26	#10597276	C₂²	1	2	yes	complemented
27	#10597262	C₂²	1	8	yes	complemented
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊D₁₉	—	2	2	no	—
30	#64541	—	2	2	no	—
31	#64541	—	2	2	no	—
32	#64541	C₂×C₄	1	4	yes	—
33	#64541	C₂³	1	4	yes	—
34	C₂×D₇₆	C₂×C₄	1	2	yes	—
35	C₂×C₄×D₁₉	—	2	2	no	—
36	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
37	M₁₆×C₁₉	D₄	1	2	yes	—
38	M₁₆×C₁₉	D₄	1	2	yes	—
39	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×C₈×C₁₉	C₂³	1	2	yes	—
46	C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂²⋊C₄×C₁₉	—	2	1	no	—
48	C₄²×C₁₉	C₂³	1	2	yes	—
49	#64520	—	2	2	no	—
50	#64520	C₂³	1	4	yes	—
51	C₂×C₁₉⋊C₈	—	2	2	no	—
52	Dic₇₆	C₂×C₄	1	2	yes	—
53	Dic₇₆	C₂×C₄	1	2	yes	—
54	D₁₅₂	C₂×C₄	1	2	yes	—
55	D₁₅₂	C₂×C₄	1	2	yes	—
56	#64516	C₂×C₄	1	4	yes	—
57	#64516	C₂×C₄	1	4	yes	—
58	#64515	—	2	8	no	—
59	C₈×D₁₉	—	2	8	no	—
60	C₂³×C₁₉	#41	1	1	yes	characteristic
61	C₂²×D₁₉	—	2	2	no	—
62	C₂×C₄×C₁₉	—	2	2	no	—
63	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
68	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
69	C₂²⋊D₁₉	—	2	4	no	—
70	C₂²⋊D₁₉	—	2	4	no	—
71	C₂×Dic₁₉	—	2	2	no	—
72	D₇₆	—	2	2	no	—
73	D₇₆	C₂²×C₄	1	4	yes	—
74	C₄×D₁₉	—	2	4	no	—
75	C₄×D₁₉	—	2	4	no	—
76	Dic₃₈	—	2	2	no	—
77	Dic₃₈	C₂²×C₄	1	4	yes	—
78	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
79	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
80	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
81	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
82	C₈×C₁₉	C₂×D₄	1	4	yes	—
83	C₁₉⋊C₈	—	2	4	no	—
84	#2957	—	19	1	no	maximal, Sylow
85	C₂²×C₁₉	—	4	1	no	—
86	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
87	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
88	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
89	C₂×D₁₉	—	2	4	no	—
90	C₂×D₁₉	—	8	2	no	—
91	C₄×C₁₉	—	4	2	no	—
92	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
93	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
94	C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
95	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
96	Dic₁₉	—	2	4	no	—
97	C₂×#135	—	19	1	no	—
98	#568	—	19	2	no	—
99	#444	—	19	4	no	—
100	#443	—	19	4	no	—
101	C₂×#108	—	19	1	no	—
102	#421	—	19	2	no	—
103	#405	D₁₉	1	1	yes	characteristic, complemented
104	C₂×C₁₉	—	2	1	no	—
105	C₂×C₁₉	—	2	1	no	—
106	C₂×C₁₉	—	2	1	no	—
107	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
108	D₁₉	—	4	4	no	—
109	C₂×#41	—	19	2	no	—
110	#135	—	19	2	no	—
111	#135	—	19	2	no	—
112	#135	—	19	2	no	—
113	#135	—	19	2	no	—
114	C₂×Q₁₆	—	19	1	no	—
115	C₂×SD₁₆	—	19	2	no	—
116	C₂×D₈	—	19	1	no	—
117	#131	—	19	8	no	—
118	#131	—	38	4	no	—
119	C₂×M₁₆	—	19	2	no	—
120	C₂×M₁₆	—	38	4	no	—
121	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
122	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
123	#117	C₂×D₁₉	1	1	yes	characteristic
124	#108	—	19	2	no	—
125	#108	—	19	2	no	—
126	#104	—	19	8	no	—
127	#97	C₂×D₁₉	1	2	yes	complemented
128	C₄×C₈	C₂×D₁₉	1	2	yes	complemented
129	C₁₉	#2957	1	1	yes	characteristic, complemented, Sylow
130	#41	—	19	4	no	—
131	#41	—	19	4	no	—
132	#41	—	38	2	no	—
133	#41	—	38	2	no	—
134	C₂×Q₈	—	19	2	no	—
135	C₂×D₄	—	19	2	no	—
136	C₂×D₄	—	38	2	no	—
137	C₂²×C₄	—	38	2	no	—
138	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
139	Q₁₆	—	19	2	no	—
140	Q₁₆	—	19	2	no	—
141	SD₁₆	—	19	4	no	—
142	SD₁₆	—	19	4	no	—
143	D₈	—	19	2	no	—
144	D₈	—	19	2	no	—
145	M₁₆	—	19	4	no	—
146	M₁₆	—	38	2	no	—
147	M₁₆	—	38	8	no	—
148	M₁₆	D₇₆	1	2	yes	—
149	M₁₆	D₇₆	1	2	yes	—
150	C₂×C₈	—	38	2	no	—
151	C₂×C₈	—	38	8	no	—
152	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
153	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
154	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
155	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
156	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
157	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
158	C₂×C₈	C₂²×D₁₉	1	2	yes	—
159	C₄⋊C₄	—	2	1	no	—
160	C₂²⋊C₄	—	2	1	no	—
161	C₄²	C₂²×D₁₉	1	2	yes	—
162	C₂³	—	38	2	no	—
163	C₂³	#64541	1	1	yes	characteristic
164	Q₈	—	19	4	no	—
165	Q₈	—	38	2	no	—
166	D₄	—	19	4	no	—
167	D₄	—	38	4	no	—
168	D₄	—	38	4	no	—
169	D₄	—	38	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	38	2	no	—
172	C₂×C₄	—	38	4	no	—
173	C₂×C₄	—	38	4	no	—
174	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
175	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
176	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
177	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
178	C₂×C₄	#64541	1	1	yes	characteristic
179	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
180	C₈	—	38	4	no	—
181	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
182	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
183	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
184	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
185	C₈	C₂×D₇₆	1	4	yes	—
186	C₂²	—	4	1	no	—
187	C₂²	—	38	4	no	—
188	C₂²	—	152	2	no	—
189	C₂²	C₄×D₇₆	1	1	yes	characteristic
190	C₂²	C₄×D₇₆	1	1	yes	characteristic
191	C₂²	C₂×#64541	1	1	yes	characteristic
192	C₄	—	4	2	no	—
193	C₄	—	38	4	no	—
194	C₄	C₄×D₇₆	1	1	yes	characteristic
195	C₄	C₄×D₇₆	1	1	yes	characteristic
196	C₄	C₂²×C₄×D₁₉	1	1	yes	characteristic
197	C₄	C₂²×D₇₆	1	1	yes	characteristic
198	C₂	—	2	1	no	—
199	C₂	—	2	1	no	—
200	C₂	—	2	1	no	—
201	C₂	—	76	4	no	—
202	C₂	C₂×C₄×D₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₇₆
commutator	C₄×C₁₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#405	C₂
socle	C₂×C₁₉	C₂×C₄×D₄
prime radical	C₂×#10597350	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#405	D₁₉
hypocenter	C₁₉	#2957
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #11927310	C₂	semidirect
3. #11926667	C₂	semidirect
4. #11926662	C₂	semidirect
5. C₂×#10597276	C₂	semidirect
6. #11926562	C₂	semidirect
7. C₁₉×#405	C₂	semidirect
15. C₂×Dic₇₆	C₄	semidirect
16. #10597350	C₄	semidirect
17. #10597350	C₄	semidirect
20. C₂×D₁₅₂	C₄	semidirect
21. C₂×#64516	C₄	semidirect
22. #10597347	C₂²	semidirect
23. C₁₉×#97	C₂²	semidirect
24. C₄×C₈×C₁₉	C₂²	semidirect
25. #10597276	C₂²	semidirect
26. #10597276	C₂²	semidirect
27. #10597262	C₂²	semidirect
103. #405	D₁₉	semidirect
127. #97	C₂×D₁₉	semidirect
128. C₄×C₈	C₂×D₁₉	semidirect
129. C₁₉	#2957	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597350	2
#11927310	2
#11926667	2
#11926662	2
C₂×#10597276	2
#11926562	2
C₁₉×#405	2
#2957	19