Subgroups — C₂×#11927344 #14578382

Order 2432.

1484 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#64541	C₂	1	2	yes	maximal, complemented
2	#11927344	C₂	1	16	yes	maximal, direct product factor
3	C₂×#10597355	C₂	1	4	yes	maximal, complemented
4	C₂×#10597354	C₂	1	4	yes	maximal, complemented
5	C₂×#10597350	C₂	1	4	yes	maximal, complemented
6	C₂²×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₂²⋊D₁₉	—	2	2	no	—
9	C₂×#64541	—	2	2	no	—
10	C₂×#64541	—	2	8	no	—
11	C₂×#64541	—	2	2	no	—
12	C₂×#64541	C₂²	1	4	yes	—
13	C₂×#64541	C₂²	1	4	yes	complemented
14	C₂×#64541	C₂²	1	16	yes	complemented
15	C₂²×D₇₆	C₂²	1	2	yes	complemented
16	C₂²×C₄×D₁₉	—	2	2	no	—
17	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
18	C₂×M₁₆×C₁₉	C₂²	1	4	yes	complemented
19	C₂×M₁₆×C₁₉	C₂²	1	8	yes	complemented
20	C₂²×C₈×C₁₉	C₂²	1	2	yes	complemented
21	#10597355	C₂²	1	32	yes	complemented
22	#10597354	C₂²	1	32	yes	complemented
23	C₂×Dic₇₆	C₂²	1	4	yes	complemented
24	#10597350	C₂²	1	32	yes	complemented
25	C₂×D₁₅₂	C₂²	1	4	yes	complemented
26	C₂×#64516	C₂²	1	8	yes	complemented
27	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
28	C₂³×D₁₉	—	2	2	no	—
29	C₂²×C₄×C₁₉	D₄	1	2	yes	—
30	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	D₄	1	4	yes	—
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
35	C₂×C₂²⋊D₁₉	—	2	4	no	—
36	C₂×C₂²⋊D₁₉	—	2	4	no	—
37	C₂×C₂²⋊D₁₉	—	2	16	no	—
38	C₂²×Dic₁₉	—	2	2	no	—
39	#64541	—	2	8	no	—
40	#64541	—	2	8	no	—
41	#64541	—	2	16	no	—
42	#64541	—	2	16	no	—
43	#64541	C₂³	1	16	yes	—
44	#64541	C₂³	1	16	yes	complemented
45	C₂×D₇₆	—	2	4	no	—
46	C₂×D₇₆	—	2	2	no	—
47	C₂×D₇₆	C₂³	1	4	yes	—
48	C₂×D₇₆	C₂³	1	8	yes	complemented
49	C₂×C₄×D₁₉	—	2	4	no	—
50	C₂×C₄×D₁₉	—	2	16	no	—
51	C₂×C₄×D₁₉	—	2	4	no	—
52	C₂×Dic₃₈	—	2	4	no	—
53	C₂×Dic₃₈	—	2	2	no	—
54	C₂×Dic₃₈	C₂³	1	4	yes	—
55	C₂×Dic₃₈	C₂³	1	8	yes	complemented
56	M₁₆×C₁₉	C₂³	1	16	yes	complemented
57	C₂×C₈×C₁₉	C₂³	1	4	yes	—
58	C₂×C₈×C₁₉	C₂³	1	8	yes	complemented
59	Dic₇₆	C₂³	1	16	yes	complemented
60	D₁₅₂	C₂³	1	16	yes	complemented
61	#64516	C₂³	1	32	yes	complemented
62	C₂³×C₁₉	—	4	2	no	—
63	C₂³×C₁₉	C₂×D₄	1	2	yes	—
64	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
65	C₂³×C₁₉	C₂×D₄	1	4	yes	—
66	C₂²×D₁₉	—	2	4	no	—
67	C₂²×D₁₉	—	2	8	no	—
68	C₂²×D₁₉	—	4	8	no	—
69	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
71	C₂×C₄×C₁₉	C₂×D₄	1	8	yes	—
72	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
73	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
74	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
76	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
77	C₂×C₄×C₁₉	C₂⁴	1	4	yes	—
78	C₂²⋊D₁₉	—	2	16	no	—
79	C₂²⋊D₁₉	—	2	16	no	—
80	C₂×Dic₁₉	—	2	4	no	—
81	C₂×Dic₁₉	—	2	8	no	—
82	D₇₆	—	2	4	no	—
83	D₇₆	—	2	8	no	—
84	D₇₆	C₂⁴	1	8	yes	—
85	C₄×D₁₉	—	2	16	no	—
86	C₄×D₁₉	—	2	16	no	—
87	Dic₃₈	—	2	4	no	—
88	Dic₃₈	—	2	8	no	—
89	Dic₃₈	C₂⁴	1	8	yes	—
90	C₈×C₁₉	C₂⁴	1	8	yes	—
91	C₂×#575	—	19	1	no	maximal, Sylow
92	C₂²×C₁₉	—	2	4	no	—
93	C₂²×C₁₉	—	2	2	no	—
94	C₂²×C₁₉	—	4	4	no	—
95	C₂²×C₁₉	C₂²×D₄	1	4	yes	—
96	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
97	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
98	C₂×D₁₉	—	2	8	no	—
99	C₂×D₁₉	—	4	16	no	—
100	C₂×D₁₉	—	4	8	no	—
101	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
102	C₄×C₁₉	C₂²×D₄	1	4	yes	—
103	C₄×C₁₉	C₂²×D₄	1	2	yes	—
104	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
105	Dic₁₉	—	2	8	no	—
106	C₂²×#41	—	19	2	no	—
107	#575	—	19	16	no	—
108	C₂×#137	—	19	4	no	—
109	C₂×AGL(1,ℤ/8)	—	19	4	no	—
110	C₂×#135	—	19	4	no	—
111	C₂²×M₁₆	D₁₉	1	1	yes	characteristic, complemented
112	C₂×C₁₉	—	2	4	no	—
113	C₂×C₁₉	—	2	2	no	—
114	C₂×C₁₉	#575	1	2	yes	complemented
115	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
116	D₁₉	—	4	8	no	—
117	C₂×#41	—	19	4	no	—
118	C₂×#41	—	19	4	no	—
119	C₂×#41	—	19	16	no	—
120	C₂×#41	—	38	2	no	—
121	C₂×#41	—	38	8	no	—
122	C₂×#41	—	38	2	no	—
123	C₂²×Q₈	—	19	2	no	—
124	C₂²×D₄	—	19	2	no	—
125	C₂²×D₄	—	38	2	no	—
126	C₂³×C₄	—	38	2	no	—
127	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
128	#137	—	19	32	no	—
129	AGL(1,ℤ/8)	—	19	32	no	—
130	#135	—	19	32	no	—
131	C₂×Q₁₆	—	19	4	no	—
132	C₂×SD₁₆	—	19	8	no	—
133	C₂×D₈	—	19	4	no	—
134	C₂×M₁₆	C₂×D₁₉	1	4	yes	complemented
135	C₂×M₁₆	C₂×D₁₉	1	8	yes	complemented
136	C₂²×C₈	C₂×D₁₉	1	2	yes	complemented
137	C₁₉	C₂×#575	1	1	yes	characteristic, complemented, Sylow
138	C₂⁴	—	38	2	no	—
139	C₂⁴	D₇₆	1	1	yes	characteristic
140	#41	—	19	16	no	—
141	#41	—	19	16	no	—
142	#41	—	38	16	no	—
143	#41	—	38	8	no	—
144	#41	—	38	8	no	—
145	#41	—	38	16	no	—
146	C₂×Q₈	—	19	4	no	—
147	C₂×Q₈	—	19	8	no	—
148	C₂×Q₈	—	38	2	no	—
149	C₂×Q₈	—	38	4	no	—
150	C₂×D₄	—	19	4	no	—
151	C₂×D₄	—	19	8	no	—
152	C₂×D₄	—	38	4	no	—
153	C₂×D₄	—	38	4	no	—
154	C₂×D₄	—	38	16	no	—
155	C₂×D₄	—	38	2	no	—
156	C₂×D₄	—	38	4	no	—
157	C₂²×C₄	—	38	2	no	—
158	C₂²×C₄	—	38	4	no	—
159	C₂²×C₄	—	38	16	no	—
160	C₂²×C₄	—	38	4	no	—
161	C₂²×C₄	D₇₆	1	1	yes	characteristic
162	C₂²×C₄	D₇₆	1	4	yes	—
163	C₂²×C₄	D₇₆	1	2	yes	—
164	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
165	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
166	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
167	Q₁₆	—	19	16	no	—
168	SD₁₆	—	19	32	no	—
169	D₈	—	19	16	no	—
170	M₁₆	C₂²×D₁₉	1	16	yes	complemented
171	C₂×C₈	C₂²×D₁₉	1	4	yes	—
172	C₂×C₈	C₂²×D₁₉	1	8	yes	complemented
173	C₂³	—	4	2	no	—
174	C₂³	—	38	8	no	—
175	C₂³	—	38	4	no	—
176	C₂³	—	76	8	no	—
177	C₂³	C₂×D₇₆	1	2	yes	—
178	C₂³	C₂×D₇₆	1	1	yes	characteristic
179	C₂³	C₂×D₇₆	1	4	yes	—
180	Q₈	—	19	8	no	—
181	Q₈	—	38	8	no	—
182	Q₈	—	38	4	no	—
183	D₄	—	19	8	no	—
184	D₄	—	38	16	no	—
185	D₄	—	38	16	no	—
186	D₄	—	38	8	no	—
187	D₄	—	38	4	no	—
188	C₂×C₄	—	38	8	no	—
189	C₂×C₄	—	38	4	no	—
190	C₂×C₄	—	38	16	no	—
191	C₂×C₄	—	38	16	no	—
192	C₂×C₄	C₂×D₇₆	1	2	yes	—
193	C₂×C₄	C₂×D₇₆	1	8	yes	—
194	C₂×C₄	C₂×D₇₆	1	4	yes	—
195	C₂×C₄	C₂×D₇₆	1	2	yes	—
196	C₂×C₄	C₂×D₇₆	1	4	yes	—
197	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
198	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
199	C₂×C₄	C₂³×D₁₉	1	2	yes	—
200	C₂×C₄	C₂³×D₁₉	1	4	yes	—
201	C₈	C₂³×D₁₉	1	8	yes	—
202	C₂²	—	2	4	no	—
203	C₂²	—	2	2	no	—
204	C₂²	—	4	4	no	—
205	C₂²	—	38	8	no	—
206	C₂²	—	76	16	no	—
207	C₂²	—	76	8	no	—
208	C₂²	C₂²×D₇₆	1	4	yes	—
209	C₂²	C₂²×D₇₆	1	2	yes	—
210	C₂²	C₂²×D₇₆	1	1	yes	characteristic
211	C₄	—	38	8	no	—
212	C₄	C₂²×D₇₆	1	2	yes	—
213	C₄	C₂²×D₇₆	1	4	yes	—
214	C₄	C₂²×D₇₆	1	1	yes	characteristic
215	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
216	C₂	—	2	4	no	—
217	C₂	—	2	2	no	—
218	C₂	—	76	8	no	—
219	C₂	#11927344	1	2	yes	direct product factor
220	C₂	C₂³×D₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₇₆
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂²×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂²×M₁₆	D₁₉
hypocenter	C₁₉	C₂×#575
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×#64541	C₂	semidirect
2. #11927344	C₂	direct (N × H)
3. C₂×#10597355	C₂	semidirect
4. C₂×#10597354	C₂	semidirect
5. C₂×#10597350	C₂	semidirect
6. C₂²×M₁₆×C₁₉	C₂	semidirect
13. C₂×#64541	C₂²	semidirect
14. C₂×#64541	C₂²	semidirect
15. C₂²×D₇₆	C₂²	semidirect
17. C₂²×Dic₃₈	C₂²	semidirect
18. C₂×M₁₆×C₁₉	C₂²	semidirect
19. C₂×M₁₆×C₁₉	C₂²	semidirect
20. C₂²×C₈×C₁₉	C₂²	semidirect
21. #10597355	C₂²	semidirect
22. #10597354	C₂²	semidirect
23. C₂×Dic₇₆	C₂²	semidirect
24. #10597350	C₂²	semidirect
25. C₂×D₁₅₂	C₂²	semidirect
26. C₂×#64516	C₂²	semidirect
44. #64541	C₂³	semidirect
48. C₂×D₇₆	C₂³	semidirect
55. C₂×Dic₃₈	C₂³	semidirect
56. M₁₆×C₁₉	C₂³	semidirect
58. C₂×C₈×C₁₉	C₂³	semidirect
59. Dic₇₆	C₂³	semidirect
60. D₁₅₂	C₂³	semidirect
61. #64516	C₂³	semidirect
111. C₂²×M₁₆	D₁₉	semidirect
114. C₂×C₁₉	#575	semidirect
134. C₂×M₁₆	C₂×D₁₉	semidirect
135. C₂×M₁₆	C₂×D₁₉	semidirect
136. C₂²×C₈	C₂×D₁₉	semidirect
137. C₁₉	C₂×#575	semidirect
170. M₁₆	C₂²×D₁₉	semidirect
172. C₂×C₈	C₂²×D₁₉	semidirect
219. C₂	#11927344	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#64541	2
#11927344	2
C₂×#10597355	2
C₂×#10597354	2
C₂×#10597350	2
C₂²×M₁₆×C₁₉	2
C₂×#575	19

Subgroups — C2×#11927344 #14578382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927344 #14578382