Subgroups — C₂×#19134281 #25093923

Order 11008.

1614 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063236	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13063235	C₂	1	2	yes	maximal
3	C₂²×C₈×Dic₄₃	C₂	1	2	yes	maximal
4	C₂×#14582745	C₂	1	1	yes	maximal, characteristic
5	#19134281	C₂	1	8	yes	maximal, direct product factor
6	C₂²×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₃	C₂²	1	2	yes	—
9	C₂×#13063236	C₄	1	8	yes	complemented
10	C₂×#13063236	C₂²	1	4	yes	—
11	C₂×#13063235	C₄	1	16	yes	complemented
12	C₂×#13063235	C₂²	1	8	yes	—
13	C₂×C₈×Dic₄₃	C₄	1	16	yes	complemented
14	C₂×C₈×Dic₄₃	C₂²	1	8	yes	—
15	#14582745	C₄	1	4	yes	—
16	#14582745	C₂²	1	4	yes	—
17	C₂×C₄₃⋊#95	C₄	1	4	yes	—
18	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₄₃	C₄	1	8	yes	complemented
22	C₂×C₄×C₈×C₄₃	C₂²	1	4	yes	—
23	C₂³×Dic₄₃	C₂×C₄	1	4	yes	—
24	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
26	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
27	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
28	C₂×C₄×Dic₄₃	C₂×C₄	1	4	yes	—
29	C₂×C₄×Dic₄₃	C₂×C₄	1	8	yes	—
30	C₂×C₄×Dic₄₃	C₂×C₄	1	8	yes	—
31	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
32	#13063236	C₂×C₄	1	16	yes	complemented
33	#13063235	C₂×C₄	1	32	yes	complemented
34	C₈×Dic₄₃	C₂×C₄	1	32	yes	complemented
35	C₄₃⋊#95	C₂×C₄	1	16	yes	—
36	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	—
39	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	—
40	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
41	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
44	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
48	C₄×C₈×C₄₃	C₂×C₄	1	16	yes	complemented
49	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	—	2	8	no	—
51	C₂²×C₄×C₄₃	C₄²	1	8	yes	—
52	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
53	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
54	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
55	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
56	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
57	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
59	C₂²×Dic₄₃	—	2	16	no	—
60	C₂²×Dic₄₃	C₄²	1	16	yes	—
61	C₂²×Dic₄₃	C₂²×C₄	1	8	yes	—
62	C₂×C₈×C₄₃	C₄²	1	16	yes	—
63	C₂×C₈×C₄₃	C₄²	1	16	yes	—
64	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
65	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
66	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
67	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
68	C₄²×C₄₃	C₄²	1	8	yes	—
69	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
70	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
71	C₄×Dic₄₃	C₄²	1	16	yes	—
72	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
73	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
74	C₂×C₄₃⋊C₈	C₄²	1	32	yes	—
75	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
76	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
77	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
78	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
79	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
80	C₂³×C₄₃	#131	1	8	yes	—
81	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
82	C₂×C₄×C₄₃	—	2	8	no	—
83	C₂×C₄×C₄₃	—	2	16	no	—
84	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
85	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
86	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
87	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
88	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
89	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
90	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
91	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
92	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
93	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
94	C₂×Dic₄₃	—	2	16	no	—
95	C₂×Dic₄₃	—	2	32	no	—
96	C₂×Dic₄₃	C₂×C₄²	1	16	yes	—
97	C₈×C₄₃	C₂×C₄²	1	8	yes	—
98	C₈×C₄₃	C₂×C₄²	1	8	yes	—
99	C₄₃⋊C₈	C₂×C₄²	1	16	yes	—
100	C₂×#1726	—	43	1	no	maximal, Sylow
101	C₂²×C₄₃	C₄³	1	4	yes	—
102	C₂²×C₄₃	#405	1	16	yes	—
103	C₂²×C₄₃	#405	1	8	yes	—
104	C₂²×C₄₃	C₂²×C₄²	1	2	yes	—
105	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
106	C₂²×C₄₃	C₂×#131	1	4	yes	—
107	C₄×C₄₃	—	2	8	no	—
108	C₄×C₄₃	C₄³	1	4	yes	—
109	C₄×C₄₃	C₂²×C₄²	1	2	yes	—
110	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
111	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
112	Dic₄₃	—	2	16	no	—
113	C₂²×#97	—	43	1	no	—
114	C₂²×#97	—	43	2	no	—
115	C₂²×C₄×C₈	—	43	2	no	—
116	C₂²×C₄×C₈	D₄₃	1	1	yes	characteristic
117	C₂×#376	—	43	1	no	—
118	#1726	—	43	8	no	—
119	C₂×C₄₃	#1726	1	8	yes	complemented
120	C₂×C₄₃	C₂×C₄³	1	1	yes	characteristic
121	C₂×C₄₃	C₂×#405	1	4	yes	—
122	C₂×C₄₃	C₂×#405	1	2	yes	—
123	C₂³×C₈	—	43	2	no	—
124	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
125	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
126	C₂²×C₄²	—	43	2	no	—
127	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
128	C₂×#97	—	43	8	no	—
129	C₂×#97	—	43	16	no	—
130	C₂×#97	—	43	4	no	—
131	C₂×#97	—	43	8	no	—
132	C₂×C₄×C₈	—	43	8	no	—
133	C₂×C₄×C₈	—	43	16	no	—
134	C₂×C₄×C₈	Dic₄₃	1	8	yes	complemented
135	C₂×C₄×C₈	C₂×D₄₃	1	4	yes	—
136	#376	—	43	4	no	—
137	#376	—	43	4	no	—
138	C₂×#95	—	43	4	no	—
139	C₄₃	C₂×#1726	1	1	yes	characteristic, complemented, Sylow
140	C₂³×C₄	—	43	4	no	—
141	C₂³×C₄	C₄×D₄₃	1	2	yes	—
142	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
143	C₂²×C₈	—	43	8	no	—
144	C₂²×C₈	—	43	8	no	—
145	C₂²×C₈	—	43	8	no	—
146	C₂²×C₈	—	43	4	no	—
147	C₂²×C₈	C₄×D₄₃	1	8	yes	—
148	C₂²×C₈	C₄×D₄₃	1	8	yes	—
149	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
150	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
151	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
152	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
153	C₂×C₄²	—	43	4	no	—
154	C₂×C₄²	—	43	8	no	—
155	C₂×C₄²	—	43	8	no	—
156	C₂×C₄²	—	43	4	no	—
157	C₂×C₄²	C₄×D₄₃	1	2	yes	—
158	C₂×C₄²	C₄×D₄₃	1	4	yes	—
159	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
160	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
161	#97	—	43	32	no	—
162	#97	—	43	16	no	—
163	C₄×C₈	—	43	32	no	—
164	C₄×C₈	C₂×Dic₄₃	1	16	yes	complemented
165	#95	—	43	16	no	—
166	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
167	C₂²×C₄	—	2	8	no	—
168	C₂²×C₄	—	43	16	no	—
169	C₂²×C₄	—	43	8	no	—
170	C₂²×C₄	—	86	16	no	—
171	C₂²×C₄	C₄×Dic₄₃	1	8	yes	—
172	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
173	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
175	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
176	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
177	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
178	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
179	C₂×C₈	—	43	32	no	—
180	C₂×C₈	—	43	8	no	—
181	C₂×C₈	—	43	8	no	—
182	C₂×C₈	—	43	8	no	—
183	C₂×C₈	C₄×Dic₄₃	1	16	yes	—
184	C₂×C₈	C₄×Dic₄₃	1	16	yes	—
185	C₂×C₈	C₂×C₄×D₄₃	1	8	yes	—
186	C₂×C₈	C₂×C₄×D₄₃	1	8	yes	—
187	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
188	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
189	C₄²	—	43	16	no	—
190	C₄²	—	43	8	no	—
191	C₄²	—	43	8	no	—
192	C₄²	C₄×Dic₄₃	1	8	yes	—
193	C₄²	C₂×C₄×D₄₃	1	4	yes	—
194	C₄²	C₂²×Dic₄₃	1	4	yes	—
195	C₂³	C₄²×D₄₃	1	4	yes	—
196	C₂³	C₂×C₄×Dic₄₃	1	2	yes	—
197	C₂³	#13063331	1	8	yes	—
198	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
199	C₂×C₄	—	2	16	no	—
200	C₂×C₄	—	2	8	no	—
201	C₂×C₄	—	43	16	no	—
202	C₂×C₄	—	86	32	no	—
203	C₂×C₄	—	86	16	no	—
204	C₂×C₄	C₄²×D₄₃	1	8	yes	—
205	C₂×C₄	C₄²×D₄₃	1	4	yes	—
206	C₂×C₄	C₂×C₄×Dic₄₃	1	8	yes	—
207	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
208	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
209	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
210	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
211	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
212	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
213	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
214	C₈	—	43	16	no	—
215	C₈	C₂×C₄×Dic₄₃	1	8	yes	—
216	C₈	C₂×C₄×Dic₄₃	1	8	yes	—
217	C₂²	C₄²×Dic₄₃	1	4	yes	—
218	C₂²	#14582853	1	16	yes	—
219	C₂²	#14582854	1	8	yes	—
220	C₂²	C₂×C₄²×D₄₃	1	2	yes	—
221	C₂²	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
222	C₂²	C₂×#13063331	1	4	yes	—
223	C₄	—	2	8	no	—
224	C₄	—	86	16	no	—
225	C₄	C₄²×Dic₄₃	1	4	yes	—
226	C₄	C₂×C₄²×D₄₃	1	2	yes	—
227	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
228	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
229	C₂	#19134281	1	8	yes	direct product factor
230	C₂	C₂×C₄²×Dic₄₃	1	1	yes	characteristic
231	C₂	C₂×#14582853	1	4	yes	—
232	C₂	C₂×#14582854	1	2	yes	—

	subgroup	G/H
center	C₂³×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₂×C₄³
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂²×C₄×C₈×C₄₃	C₂
socle, prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂²×C₄×C₈	D₄₃
hypocenter	C₄₃	C₂×#1726
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₈ ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
5. #19134281	C₂	direct (N × H)
9. C₂×#13063236	C₄	semidirect
11. C₂×#13063235	C₄	semidirect
13. C₂×C₈×Dic₄₃	C₄	semidirect
21. C₂×C₄×C₈×C₄₃	C₄	semidirect
32. #13063236	C₂×C₄	semidirect
33. #13063235	C₂×C₄	semidirect
34. C₈×Dic₄₃	C₂×C₄	semidirect
48. C₄×C₈×C₄₃	C₂×C₄	semidirect
119. C₂×C₄₃	#1726	semidirect
134. C₂×C₄×C₈	Dic₄₃	semidirect
139. C₄₃	C₂×#1726	semidirect
164. C₄×C₈	C₂×Dic₄₃	semidirect
229. C₂	#19134281	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×#13063236	2
C₂²×#13063235	2
C₂²×C₈×Dic₄₃	2
C₂×#14582745	2
#19134281	2
C₂²×C₄×C₈×C₄₃	2
C₂×#1726	43

Subgroups — C2×#19134281 #25093923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19134281 #25093923