Subgroups — C₂×#11927359 #14578400

Order 2432.

1408 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	C₂×#10597436	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927359	C₂	1	16	yes	maximal, direct product factor
3	C₂×#10597388	C₂	1	3	yes	maximal, complemented
4	C₂×#10597397	C₂	1	3	yes	maximal, complemented
5	C₂×#10597396	C₂	1	3	yes	maximal, complemented
6	C₂²×#64528	C₂	1	3	yes	maximal, complemented
7	C₂×#10597394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×2₋¹⁺⁴	—	2	4	no	—
10	C₁₉×2₋¹⁺⁴	C₂²	1	8	yes	complemented
11	C₂×#41×C₁₉	—	2	3	no	—
12	C₂×#41×C₁₉	C₂²	1	3	yes	—
13	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₁₉	—	2	1	no	—
15	C₂²×Q₈×C₁₉	C₂²	1	3	yes	—
16	#10597436	—	2	4	no	—
17	#10597436	C₂²	1	8	yes	complemented
18	C₂×Q₈×D₁₉	—	2	1	no	—
19	C₂×#64543	—	2	3	no	—
20	C₂×#64541	C₂²	1	3	yes	—
21	C₂²×Dic₃₈	C₂²	1	3	yes	—
22	#10597397	C₂²	1	24	yes	complemented
23	#10597396	C₂²	1	24	yes	complemented
24	#10597394	C₂²	1	8	yes	complemented
25	C₂×#64528	C₂²	1	3	yes	—
26	C₂×#64528	C₂²	1	6	yes	—
27	C₂×#64528	C₂²	1	24	yes	complemented
28	#10597388	C₂²	1	24	yes	complemented
29	C₂×#64527	C₂²	1	3	yes	—
30	C₂×#64526	C₂²	1	3	yes	—
31	C₂×#64525	C₂²	1	1	yes	characteristic
32	C₂×#64520	C₂²	1	3	yes	—
33	C₂²×C₁₉⋊C₈	C₂²	1	3	yes	—
34	#41×C₁₉	—	2	24	no	—
35	#41×C₁₉	—	2	6	no	—
36	#41×C₁₉	D₄	1	4	yes	—
37	#41×C₁₉	C₂³	1	12	yes	—
38	#41×C₁₉	C₂³	1	4	yes	—
39	C₂×Q₈×C₁₉	—	2	8	no	—
40	C₂×Q₈×C₁₉	—	2	3	no	—
41	C₂×Q₈×C₁₉	—	2	6	no	—
42	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
44	C₂×Q₈×C₁₉	C₂³	1	12	yes	—
45	C₂×D₄×C₁₉	—	2	3	no	—
46	C₂×D₄×C₁₉	D₄	1	3	yes	—
47	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	—	2	3	no	—
49	C₂²×C₄×C₁₉	—	2	3	no	—
50	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
51	C₂×C₂²⋊D₁₉	—	2	3	no	—
52	C₂²×Dic₁₉	—	2	3	no	—
53	Q₈×D₁₉	—	2	8	no	—
54	#64543	—	2	24	no	—
55	#64541	—	2	6	no	—
56	#64541	C₂³	1	12	yes	—
57	C₂×D₇₆	C₂³	1	1	yes	characteristic
58	C₂×C₄×D₁₉	—	2	3	no	—
59	C₂×Dic₃₈	—	2	3	no	—
60	C₂×Dic₃₈	—	2	6	no	—
61	C₂×Dic₃₈	C₂³	1	3	yes	—
62	C₂×Dic₃₈	C₂³	1	12	yes	—
63	#64528	C₂³	1	24	yes	—
64	#64528	C₂³	1	12	yes	—
65	#64527	C₂³	1	12	yes	—
66	#64526	C₂³	1	12	yes	—
67	#64525	C₂³	1	4	yes	—
68	#64520	C₂³	1	12	yes	—
69	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₁₉⋊C₈	C₂³	1	3	yes	—
71	C₂×C₁₉⋊C₈	C₂³	1	12	yes	—
72	C₂³×C₁₉	—	2	1	no	—
73	C₂³×C₁₉	C₂×D₄	1	3	yes	—
74	C₂²×D₁₉	—	2	1	no	—
75	Q₈×C₁₉	—	2	3	no	—
76	Q₈×C₁₉	—	2	12	no	—
77	Q₈×C₁₉	C₂×D₄	1	4	yes	—
78	Q₈×C₁₉	C₂⁴	1	6	yes	—
79	D₄×C₁₉	—	2	12	no	—
80	D₄×C₁₉	—	2	1	no	—
81	D₄×C₁₉	C₂×D₄	1	12	yes	—
82	D₄×C₁₉	C₂⁴	1	2	yes	—
83	C₂×C₄×C₁₉	—	2	3	no	—
84	C₂×C₄×C₁₉	—	2	12	no	—
85	C₂×C₄×C₁₉	—	2	12	no	—
86	C₂×C₄×C₁₉	C₂×D₄	1	3	yes	—
87	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
88	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
89	C₂×C₄×C₁₉	C₂⁴	1	6	yes	—
90	C₂²⋊D₁₉	—	2	12	no	—
91	C₂×Dic₁₉	—	2	3	no	—
92	C₂×Dic₁₉	—	2	12	no	—
93	D₇₆	—	2	1	no	—
94	D₇₆	C₂⁴	1	2	yes	—
95	C₄×D₁₉	—	2	12	no	—
96	Dic₃₈	—	2	3	no	—
97	Dic₃₈	—	2	12	no	—
98	Dic₃₈	C₂⁴	1	6	yes	—
99	C₁₉⋊C₈	C₂⁴	1	2	yes	—
100	C₁₉⋊C₈	C₂⁴	1	6	yes	—
101	C₂×#578	—	19	1	no	maximal, Sylow
102	C₂²×C₁₉	—	2	6	no	—
103	C₂²×C₁₉	—	2	2	no	—
104	C₂²×C₁₉	—	4	2	no	—
105	C₂²×C₁₉	C₂²×D₄	1	6	yes	—
106	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
107	C₂×D₁₉	—	2	2	no	—
108	C₂×D₁₉	—	4	2	no	—
109	C₄×C₁₉	—	2	6	no	—
110	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
111	C₄×C₁₉	C₂²×D₄	1	6	yes	—
112	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
113	Dic₁₉	—	2	6	no	—
114	C₂×2₋¹⁺⁴	—	19	1	no	—
115	C₂×2₋¹⁺⁴	D₁₉	1	1	yes	characteristic, complemented
116	#578	—	19	16	no	—
117	C₂×#137	—	19	3	no	—
118	C₂×#137	—	19	3	no	—
119	C₂×#135	—	19	3	no	—
120	C₂²×Q₁₆	—	19	3	no	—
121	C₂×#131	—	19	1	no	—
122	C₂×C₁₉	—	2	6	no	—
123	C₂×C₁₉	—	4	2	no	—
124	C₂×C₁₉	#578	1	2	yes	complemented
125	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
126	D₁₉	—	4	2	no	—
127	2₋¹⁺⁴	—	2	4	no	—
128	2₋¹⁺⁴	—	19	8	no	—
129	2₋¹⁺⁴	—	38	4	no	—
130	2₋¹⁺⁴	C₂×D₁₉	1	8	yes	complemented
131	C₂×#41	—	2	3	no	—
132	C₂×#41	—	19	3	no	—
133	C₂×#41	—	38	3	no	—
134	C₂×#41	C₂×D₁₉	1	3	yes	—
135	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
136	C₂²×Q₈	—	2	1	no	—
137	C₂²×Q₈	—	19	3	no	—
138	C₂²×Q₈	—	38	1	no	—
139	C₂²×Q₈	C₂×D₁₉	1	3	yes	—
140	#137	—	19	24	no	—
141	#137	—	19	24	no	—
142	#135	—	19	24	no	—
143	C₂×Q₁₆	—	19	3	no	—
144	C₂×Q₁₆	—	19	6	no	—
145	C₂×Q₁₆	—	19	24	no	—
146	C₂×SD₁₆	—	19	3	no	—
147	C₂×SD₁₆	—	19	3	no	—
148	C₂×D₈	—	19	1	no	—
149	#131	—	19	8	no	—
150	C₂×M₁₆	—	19	3	no	—
151	C₂²×C₈	—	19	3	no	—
152	C₁₉	C₂×#578	1	1	yes	characteristic, complemented, Sylow
153	#41	—	2	24	no	—
154	#41	—	2	6	no	—
155	#41	—	19	12	no	—
156	#41	—	38	24	no	—
157	#41	—	38	6	no	—
158	#41	C₂²⋊D₁₉	1	4	yes	—
159	#41	C₂²×D₁₉	1	12	yes	—
160	#41	C₂²×D₁₉	1	4	yes	—
161	C₂×Q₈	—	2	8	no	—
162	C₂×Q₈	—	2	3	no	—
163	C₂×Q₈	—	2	6	no	—
164	C₂×Q₈	—	19	3	no	—
165	C₂×Q₈	—	19	12	no	—
166	C₂×Q₈	—	38	8	no	—
167	C₂×Q₈	—	38	3	no	—
168	C₂×Q₈	—	38	6	no	—
169	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
170	C₂×Q₈	C₂²×D₁₉	1	3	yes	—
171	C₂×Q₈	C₂²×D₁₉	1	12	yes	—
172	C₂×D₄	—	2	3	no	—
173	C₂×D₄	—	19	1	no	—
174	C₂×D₄	—	38	3	no	—
175	C₂×D₄	C₂²⋊D₁₉	1	3	yes	—
176	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
177	C₂²×C₄	—	2	3	no	—
178	C₂²×C₄	—	2	3	no	—
179	C₂²×C₄	—	38	3	no	—
180	C₂²×C₄	—	38	3	no	—
181	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
182	Q₁₆	—	19	12	no	—
183	Q₁₆	—	19	24	no	—
184	SD₁₆	—	19	12	no	—
185	SD₁₆	—	19	12	no	—
186	D₈	—	19	4	no	—
187	M₁₆	—	19	12	no	—
188	C₂×C₈	—	19	1	no	—
189	C₂×C₈	—	19	3	no	—
190	C₂×C₈	—	19	12	no	—
191	C₂³	—	2	1	no	—
192	C₂³	—	38	1	no	—
193	C₂³	C₂×C₂²⋊D₁₉	1	3	yes	—
194	Q₈	—	2	12	no	—
195	Q₈	—	2	3	no	—
196	Q₈	—	19	6	no	—
197	Q₈	—	38	12	no	—
198	Q₈	—	38	3	no	—
199	Q₈	C₂×C₂²⋊D₁₉	1	4	yes	—
200	Q₈	C₂³×D₁₉	1	6	yes	—
201	D₄	—	2	12	no	—
202	D₄	—	2	1	no	—
203	D₄	—	19	2	no	—
204	D₄	—	38	12	no	—
205	D₄	—	38	1	no	—
206	D₄	C₂×C₂²⋊D₁₉	1	12	yes	—
207	D₄	C₂³×D₁₉	1	2	yes	—
208	C₂×C₄	—	2	12	no	—
209	C₂×C₄	—	2	3	no	—
210	C₂×C₄	—	2	12	no	—
211	C₂×C₄	—	38	12	no	—
212	C₂×C₄	—	38	3	no	—
213	C₂×C₄	—	38	12	no	—
214	C₂×C₄	C₂×C₂²⋊D₁₉	1	6	yes	—
215	C₂×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
216	C₂×C₄	C₂³×D₁₉	1	6	yes	—
217	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
218	C₈	—	19	2	no	—
219	C₈	—	19	6	no	—
220	C₂²	—	2	6	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	4	2	no	—
223	C₂²	—	38	2	no	—
224	C₂²	—	76	2	no	—
225	C₂²	C₂²×C₂²⋊D₁₉	1	6	yes	—
226	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
227	C₄	—	2	6	no	—
228	C₄	—	38	6	no	—
229	C₄	C₂²×C₂²⋊D₁₉	1	6	yes	—
230	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
231	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
232	C₂	—	2	6	no	—
233	C₂	—	4	2	no	—
234	C₂	—	76	2	no	—
235	C₂	#11927359	1	2	yes	direct product factor
236	C₂	C₂³×C₂²⋊D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×2₋¹⁺⁴	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×2₋¹⁺⁴	D₁₉
hypocenter	C₁₉	C₂×#578
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ C₂×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂×#10597436	C₂	semidirect
2. #11927359	C₂	direct (N × H)
3. C₂×#10597388	C₂	semidirect
4. C₂×#10597397	C₂	semidirect
5. C₂×#10597396	C₂	semidirect
6. C₂²×#64528	C₂	semidirect
7. C₂×#10597394	C₂	semidirect
8. C₂×C₁₉×2₋¹⁺⁴	C₂	semidirect
10. C₁₉×2₋¹⁺⁴	C₂²	semidirect
17. #10597436	C₂²	semidirect
22. #10597397	C₂²	semidirect
23. #10597396	C₂²	semidirect
24. #10597394	C₂²	semidirect
27. C₂×#64528	C₂²	semidirect
28. #10597388	C₂²	semidirect
115. C₂×2₋¹⁺⁴	D₁₉	semidirect
124. C₂×C₁₉	#578	semidirect
130. 2₋¹⁺⁴	C₂×D₁₉	semidirect
152. C₁₉	C₂×#578	semidirect
235. C₂	#11927359	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10597436	2
#11927359	2
C₂×#10597388	2
C₂×#10597397	2
C₂×#10597396	2
C₂²×#64528	2
C₂×#10597394	2
C₂×C₁₉×2₋¹⁺⁴	2
C₂×#578	19

Subgroups — C2×#11927359 #14578400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927359 #14578400