Subgroups — C₂×#19136396 #25249665

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#19136396	C₂	1	8	yes	maximal, direct product factor
3	C₂×Dic₄₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×(C₂×D₄₃)⋊C₁₆	C₂	1	2	yes	maximal
5	C₂×#14582675	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₃×#346	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₄₃	C₄	1	1	yes	characteristic
10	C₂²×C₄₃⋊C₁₆	C₂²	1	2	yes	—
11	C₂×C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₄₃	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×D₄₃	C₄	1	4	yes	—
15	C₄×C₈×D₄₃	C₂²	1	4	yes	—
16	Dic₄₃⋊C₁₆	C₂²	1	8	yes	complemented
17	(C₂×D₄₃)⋊C₁₆	C₂²	1	8	yes	—
18	#14582675	C₂²	1	4	yes	complemented
19	C₂²×C₁₆×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#346	C₂²	1	4	yes	complemented
22	C₂²×C₄×D₄₃	C₈	1	1	yes	characteristic
23	C₂²×C₄×D₄₃	C₈	1	1	yes	characteristic
24	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₄₃	—	2	4	no	—
28	C₂×C₈×D₄₃	—	2	4	no	—
29	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
30	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
31	C₂×C₈×D₄₃	C₂³	1	2	yes	—
32	C₂×C₄×Dic₄₃	C₈	1	1	yes	characteristic
33	C₂×C₄×Dic₄₃	C₈	1	1	yes	characteristic
34	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
35	C₄²×D₄₃	C₈	1	4	yes	—
36	C₄²×D₄₃	C₂×C₄	1	4	yes	—
37	C₂×C₄₃⋊C₁₆	—	2	4	no	—
38	C₂×C₄₃⋊C₁₆	C₂³	1	4	yes	—
39	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
40	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
41	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
42	C₈×Dic₄₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₁₆×C₄₃	—	2	4	no	—
47	C₂×C₁₆×C₄₃	C₂³	1	4	yes	—
48	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
49	C₄×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂³×D₄₃	C₂×C₈	1	1	yes	characteristic
51	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
53	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
56	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
57	C₂×C₄×D₄₃	—	2	2	no	—
58	C₂×C₄×D₄₃	—	2	2	no	—
59	C₂×C₄×D₄₃	—	2	4	no	—
60	C₂×C₄×D₄₃	—	2	4	no	—
61	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
62	C₂×C₄×D₄₃	C₂×C₈	1	4	yes	—
63	C₂×C₄×D₄₃	C₂×C₈	1	4	yes	—
64	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
65	C₂×C₈×C₄₃	M₁₆	1	4	yes	—
66	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
68	C₂×C₈×C₄₃	#41	1	4	yes	—
69	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
70	C₄²×C₄₃	C₂×C₈	1	2	yes	—
71	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
72	C₄×Dic₄₃	C₂×C₈	1	2	yes	—
73	C₄×Dic₄₃	C₂×C₈	1	4	yes	—
74	C₄×Dic₄₃	C₂×C₈	1	4	yes	—
75	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
76	C₂×C₄₃⋊C₈	—	2	2	no	—
77	C₂×C₄₃⋊C₈	—	2	2	no	—
78	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
79	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
80	C₈×D₄₃	—	2	4	no	—
81	C₈×D₄₃	—	2	8	no	—
82	C₈×D₄₃	—	2	4	no	—
83	C₁₆×C₄₃	—	2	4	no	—
84	C₄₃⋊C₁₆	—	2	4	no	—
85	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
86	C₂²×D₄₃	—	2	2	no	—
87	C₂²×D₄₃	—	2	2	no	—
88	C₂²×D₄₃	M₃₂	1	4	yes	—
89	C₂²×D₄₃	C₂²×C₈	1	2	yes	—
90	C₂×C₄×C₄₃	—	2	2	no	—
91	C₂×C₄×C₄₃	—	2	2	no	—
92	C₂×C₄×C₄₃	#117	1	2	yes	—
93	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
94	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
95	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
96	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
98	C₂×Dic₄₃	—	2	2	no	—
99	C₂×Dic₄₃	—	2	2	no	—
100	C₂×Dic₄₃	M₃₂	1	4	yes	—
101	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
102	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
103	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
104	C₄×D₄₃	—	2	8	no	—
105	C₄×D₄₃	—	2	2	no	—
106	C₄×D₄₃	—	2	2	no	—
107	C₄×D₄₃	—	2	4	no	—
108	C₄×D₄₃	—	2	8	no	—
109	C₈×C₄₃	#117	1	2	yes	—
110	C₈×C₄₃	C₂×M₁₆	1	4	yes	—
111	C₈×C₄₃	C₂×#41	1	2	yes	—
112	C₄₃⋊C₈	—	2	2	no	—
113	C₄₃⋊C₈	—	2	2	no	—
114	C₂×#2163	—	43	1	no	maximal, Sylow
115	C₂²×C₄₃	#431	1	2	yes	—
116	C₂²×C₄₃	C₂×M₃₂	1	2	yes	—
117	C₂²×C₄₃	C₂×M₃₂	1	2	yes	—
118	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
119	C₂×D₄₃	—	2	2	no	—
120	C₂×D₄₃	—	2	2	no	—
121	C₂×D₄₃	—	2	8	no	—
122	C₂×D₄₃	C₂×M₃₂	1	4	yes	—
123	C₄×C₄₃	—	2	2	no	—
124	C₄×C₄₃	—	2	2	no	—
125	C₄×C₄₃	#431	1	2	yes	—
126	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
127	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
128	Dic₄₃	—	2	2	no	—
129	Dic₄₃	—	2	2	no	—
130	Dic₄₃	C₂×M₃₂	1	4	yes	—
131	C₂²×C₄×C₈	—	43	1	no	—
132	#2163	—	43	8	no	—
133	C₂×C₄⋊C₁₆	—	43	2	no	—
134	C₂×C₂²⋊C₁₆	—	43	2	no	—
135	C₂×#346	—	43	1	no	—
136	C₂×#346	D₄₃	1	1	yes	characteristic, complemented
137	C₂×C₄₃	#2163	1	4	yes	complemented
138	C₂×C₄₃	C₂×#431	1	1	yes	characteristic
139	C₂×C₄₃	C₂²×M₃₂	1	1	yes	characteristic
140	C₂×C₄₃	C₂²×M₃₂	1	1	yes	characteristic
141	D₄₃	—	2	4	no	—
142	C₂³×C₈	—	43	1	no	—
143	C₂³×C₈	—	43	1	no	—
144	C₂²×C₄²	—	43	1	no	—
145	C₂²×C₁₆	—	43	2	no	—
146	C₂²×C₁₆	C₂×D₄₃	1	2	yes	—
147	C₂×C₄×C₈	—	43	1	no	—
148	C₂×C₄×C₈	—	43	1	no	—
149	C₂×C₄×C₈	—	43	1	no	—
150	C₂×C₄×C₈	—	43	4	no	—
151	C₂×C₄×C₈	—	43	4	no	—
152	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
153	C₄⋊C₁₆	—	43	8	no	—
154	C₂²⋊C₁₆	—	43	8	no	—
155	#346	—	43	4	no	—
156	#346	C₂×D₄₃	1	4	yes	complemented
157	C₄₃	C₂×#2163	1	1	yes	characteristic, complemented, Sylow
158	C₂³×C₄	—	43	1	no	—
159	C₂³×C₄	—	43	1	no	—
160	C₂³×C₄	—	43	1	no	—
161	C₂²×C₈	—	43	1	no	—
162	C₂²×C₈	—	43	1	no	—
163	C₂²×C₈	—	43	2	no	—
164	C₂²×C₈	—	43	4	no	—
165	C₂²×C₈	—	43	2	no	—
166	C₂²×C₈	—	86	4	no	—
167	C₂²×C₈	—	86	4	no	—
168	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
169	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
170	C₂×C₄²	—	43	1	no	—
171	C₂×C₄²	—	43	1	no	—
172	C₂×C₄²	—	43	1	no	—
173	C₂×C₄²	—	43	4	no	—
174	C₂×C₄²	—	43	4	no	—
175	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
176	C₂×C₁₆	—	2	4	no	—
177	C₂×C₁₆	—	43	4	no	—
178	C₂×C₁₆	—	86	4	no	—
179	C₂×C₁₆	C₂²×D₄₃	1	4	yes	—
180	C₄×C₈	—	43	2	no	—
181	C₄×C₈	—	43	4	no	—
182	C₄×C₈	—	43	2	no	—
183	C₄×C₈	—	43	4	no	—
184	C₄×C₈	C₄×D₄₃	1	2	yes	—
185	C₄×C₈	C₂²×D₄₃	1	2	yes	—
186	C₂⁴	—	43	1	no	—
187	C₂²×C₄	—	43	1	no	—
188	C₂²×C₄	—	43	1	no	—
189	C₂²×C₄	—	43	1	no	—
190	C₂²×C₄	—	43	4	no	—
191	C₂²×C₄	—	43	4	no	—
192	C₂²×C₄	—	43	2	no	—
193	C₂²×C₄	—	43	2	no	—
194	C₂²×C₄	—	86	4	no	—
195	C₂²×C₄	—	86	4	no	—
196	C₂²×C₄	—	86	2	no	—
197	C₂²×C₄	—	86	2	no	—
198	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
199	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
201	C₂×C₈	—	43	2	no	—
202	C₂×C₈	—	43	2	no	—
203	C₂×C₈	—	86	2	no	—
204	C₂×C₈	—	86	2	no	—
205	C₂×C₈	—	86	4	no	—
206	C₂×C₈	—	86	8	no	—
207	C₂×C₈	—	86	4	no	—
208	C₂×C₈	#10621872	1	4	yes	—
209	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
210	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
211	C₂×C₈	#10621898	1	4	yes	—
212	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
213	C₄²	—	43	4	no	—
214	C₄²	—	43	2	no	—
215	C₄²	—	43	4	no	—
216	C₄²	—	43	2	no	—
217	C₄²	C₈×D₄₃	1	2	yes	—
218	C₄²	C₂×C₄×D₄₃	1	2	yes	—
219	C₁₆	—	2	4	no	—
220	C₁₆	—	86	4	no	—
221	C₂³	—	43	4	no	—
222	C₂³	—	43	2	no	—
223	C₂³	—	86	2	no	—
224	C₂³	—	86	2	no	—
225	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	43	4	no	—
229	C₂×C₄	—	43	2	no	—
230	C₂×C₄	—	43	2	no	—
231	C₂×C₄	—	43	2	no	—
232	C₂×C₄	—	86	8	no	—
233	C₂×C₄	—	86	8	no	—
234	C₂×C₄	—	86	2	no	—
235	C₂×C₄	—	86	2	no	—
236	C₂×C₄	—	86	2	no	—
237	C₂×C₄	—	86	2	no	—
238	C₂×C₄	—	86	4	no	—
239	C₂×C₄	#13063282	1	2	yes	—
240	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
241	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
242	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
243	C₂×C₄	C₂×#10621872	1	2	yes	—
244	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
245	C₈	—	86	2	no	—
246	C₈	—	86	2	no	—
247	C₈	#13063282	1	2	yes	—
248	C₈	C₂×#10621872	1	4	yes	—
249	C₈	C₂×#10621898	1	2	yes	—
250	C₂²	—	43	4	no	—
251	C₂²	—	86	2	no	—
252	C₂²	—	86	8	no	—
253	C₂²	—	86	2	no	—
254	C₂²	#14582950	1	2	yes	—
255	C₂²	M₃₂×D₄₃	1	2	yes	—
256	C₂²	M₃₂×D₄₃	1	2	yes	—
257	C₂²	C₂²×C₈×D₄₃	1	1	yes	characteristic
258	C₄	—	2	2	no	—
259	C₄	—	2	2	no	—
260	C₄	—	43	4	no	—
261	C₄	—	86	2	no	—
262	C₄	—	86	2	no	—
263	C₄	#14582950	1	2	yes	—
264	C₄	C₂×#13063282	1	1	yes	characteristic
265	C₄	C₂²×#10621872	1	1	yes	characteristic
266	C₂	—	86	4	no	—
267	C₂	#19136396	1	4	yes	direct product factor
268	C₂	C₂×#14582950	1	1	yes	characteristic
269	C₂	C₂×M₃₂×D₄₃	1	1	yes	characteristic
270	C₂	C₂×M₃₂×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂×C₄₃×#346	C₂
socle	C₂³×C₄₃	C₂²×C₈
prime radical	C₂³×D₄₃	C₂×C₈
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	C₂×#346	D₄₃
hypocenter	C₄₃	C₂×#2163
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. #19136396	C₂	direct (N × H)
3. C₂×Dic₄₃⋊C₁₆	C₂	semidirect
5. C₂×#14582675	C₂	semidirect
6. C₂×C₄₃×#346	C₂	semidirect
16. Dic₄₃⋊C₁₆	C₂²	semidirect
18. #14582675	C₂²	semidirect
21. C₄₃×#346	C₂²	semidirect
136. C₂×#346	D₄₃	semidirect
137. C₂×C₄₃	#2163	semidirect
156. #346	C₂×D₄₃	semidirect
157. C₄₃	C₂×#2163	semidirect
267. C₂	#19136396	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×C₄×C₈×D₄₃	2
#19136396	2
C₂×Dic₄₃⋊C₁₆	2
C₂×(C₂×D₄₃)⋊C₁₆	2
C₂×#14582675	2
C₂×C₄₃×#346	2
C₂×#2163	43

Subgroups — C2×#19136396 #25249665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19136396 #25249665