Subgroups — #25011445

Order 11008.

586 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₃	C₂	1	2	yes	maximal
2	C₂×#14582856	C₂	1	1	yes	maximal, characteristic
3	#19132675	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132674	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10621872	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	C₂×#13063282	C₄	1	1	yes	characteristic
9	C₂×#13063265	C₂²	1	2	yes	—
10	C₂×#13063264	C₄	1	4	yes	complemented
11	M₃₂×D₄₃	—	2	4	no	—
12	M₃₂×D₄₃	—	2	4	no	—
13	C₂×C₁₆×D₄₃	C₄	1	4	yes	complemented
14	#14582856	—	2	4	no	—
15	C₂×#13063235	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
17	C₂×C₈×Dic₄₃	C₄	1	1	yes	characteristic
18	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
19	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#10621872	—	2	2	no	—
22	C₂×#10621872	—	2	2	no	—
23	C₂×#10621872	C₈	1	4	yes	—
24	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
27	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
28	C₂×C₈×D₄₃	D₄	1	2	yes	—
29	C₂×C₈×D₄₃	D₄	1	4	yes	—
30	C₂×C₈×D₄₃	Q₈	1	2	yes	—
31	#13063282	—	2	2	no	—
32	#13063282	C₈	1	4	yes	—
33	C₂×Dic₄₃⋊C₄	—	2	1	no	—
34	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
35	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
36	#13063265	—	2	2	no	—
37	#13063265	—	2	2	no	—
38	#13063264	—	2	8	no	—
39	C₂×C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
40	C₁₆×D₄₃	—	2	8	no	—
41	#13063235	—	2	2	no	—
42	C₄×C₄₃⋊C₈	—	2	2	no	—
43	C₈×Dic₄₃	—	2	2	no	—
44	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
47	M₃₂×C₄₃	—	2	2	no	—
48	M₃₂×C₄₃	—	2	2	no	—
49	C₂×C₁₆×C₄₃	C₂×C₄	1	4	yes	—
50	#97×C₄₃	—	2	2	no	—
51	C₂³×D₄₃	M₁₆	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	—	2	1	no	—
53	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×Dic₄₃	—	2	1	no	—
55	C₂²×Dic₄₃	M₁₆	1	1	yes	characteristic
56	C₂×C₄×D₄₃	C₄²	1	2	yes	—
57	C₂×C₄×D₄₃	C₂²⋊C₄	1	2	yes	—
58	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
59	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
60	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
61	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
62	C₂×C₈×C₄₃	—	2	1	no	—
63	C₂×C₈×C₄₃	—	2	1	no	—
64	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
65	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
66	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
69	C₄²×C₄₃	—	2	1	no	—
70	C₄²×C₄₃	C₂×C₈	1	2	yes	—
71	(C₂×D₄₃)⋊C₄	—	2	4	no	—
72	Dic₄₃⋊C₄	—	2	4	no	—
73	C₄×Dic₄₃	—	2	1	no	—
74	C₄×Dic₄₃	C₂×C₈	1	2	yes	—
75	C₂×C₄₃⋊C₈	—	2	1	no	—
76	C₂×C₄₃⋊C₈	—	2	1	no	—
77	C₂×C₄₃⋊C₈	C₄²	1	1	yes	characteristic
78	C₂×C₄₃⋊C₈	C₄²	1	1	yes	characteristic
79	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
80	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
81	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
82	#10621872	—	2	8	no	—
83	C₈×D₄₃	C₂²⋊C₄	1	4	yes	—
84	C₈×D₄₃	C₂²⋊C₄	1	4	yes	—
85	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
86	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
87	C₁₆×C₄₃	—	2	4	no	—
88	C₄₃⋊C₁₆	—	2	4	no	—
89	C₂³×C₄₃	C₂×M₁₆	1	1	yes	characteristic
90	C₂²×D₄₃	—	4	2	no	—
91	C₂²×D₄₃	#97	1	2	yes	—
92	C₂²×D₄₃	C₂²⋊C₈	1	2	yes	—
93	C₂²×D₄₃	C₄⋊C₈	1	2	yes	—
94	C₂×C₄×C₄₃	—	2	2	no	—
95	C₂×C₄×C₄₃	—	4	2	no	—
96	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
97	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
100	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
102	C₂×Dic₄₃	—	2	2	no	—
103	C₂×Dic₄₃	—	4	2	no	—
104	C₂×Dic₄₃	#97	1	2	yes	—
105	C₂×Dic₄₃	C₂²⋊C₈	1	2	yes	—
106	C₂×Dic₄₃	C₄⋊C₈	1	2	yes	—
107	C₄×D₄₃	#95	1	4	yes	—
108	C₄×D₄₃	C₄×C₈	1	4	yes	—
109	C₄×D₄₃	C₂²⋊C₈	1	4	yes	—
110	C₄×D₄₃	C₄⋊C₈	1	4	yes	—
111	C₈×C₄₃	—	2	2	no	—
112	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
113	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
114	C₄₃⋊C₈	—	2	2	no	—
115	C₄₃⋊C₈	#95	1	2	yes	—
116	C₄₃⋊C₈	#95	1	2	yes	—
117	#12547	—	43	1	no	maximal, Sylow
118	C₂²×C₄₃	—	2	2	no	—
119	C₂²×C₄₃	C₂×#97	1	1	yes	characteristic
120	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
121	C₂²×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
122	C₂×D₄₃	—	2	4	no	—
123	C₂×D₄₃	—	4	2	no	—
124	C₂×D₄₃	—	4	2	no	—
125	C₂×D₄₃	#336	1	4	yes	—
126	C₄×C₄₃	—	4	2	no	—
127	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
128	C₄×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
129	C₄×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
130	C₄×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
131	Dic₄₃	—	4	2	no	—
132	Dic₄₃	#336	1	4	yes	—
133	C₂²×M₃₂	—	43	2	no	—
134	C₂×#405	—	43	1	no	—
135	#1375	—	43	2	no	—
136	#1375	—	43	1	no	—
137	#1375	D₄₃	1	1	yes	characteristic, complemented
138	C₂×C₄₃	—	2	1	no	—
139	C₂×C₄₃	—	2	1	no	—
140	C₂×C₄₃	C₂×#336	1	1	yes	characteristic
141	C₂×C₄₃	#2110	1	2	yes	—
142	D₄₃	—	2	4	no	—
143	C₂²×M₁₆	—	43	1	no	—
144	C₂³×C₈	—	43	1	no	—
145	C₂×#117	—	43	1	no	—
146	C₂×M₃₂	—	43	2	no	—
147	C₂×M₃₂	—	43	4	no	—
148	C₂×M₃₂	—	86	4	no	—
149	C₂×M₃₂	—	86	4	no	—
150	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
151	C₂²×C₁₆	—	43	4	no	—
152	#405	—	86	4	no	—
153	C₂×#97	—	43	1	no	—
154	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
155	C₂×C₄×C₈	—	43	1	no	—
156	C₂×C₄×C₈	—	43	1	no	—
157	C₄₃	#12547	1	1	yes	characteristic, complemented, Sylow
158	C₂³×C₄	—	43	1	no	—
159	C₂×M₁₆	—	43	4	no	—
160	C₂×M₁₆	—	86	2	no	—
161	C₂×M₁₆	—	86	2	no	—
162	C₂²×C₈	—	43	1	no	—
163	C₂²×C₈	—	43	2	no	—
164	C₂²×C₈	—	43	2	no	—
165	C₂²×C₈	—	43	4	no	—
166	C₂²×C₈	—	43	2	no	—
167	C₂²×C₈	—	43	2	no	—
168	C₂²×C₈	—	43	1	no	—
169	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
170	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
171	#117	—	43	4	no	—
172	#117	—	86	2	no	—
173	C₂×C₄⋊C₄	—	86	1	no	—
174	C₂×C₂²⋊C₄	—	86	1	no	—
175	C₂×C₄²	—	43	1	no	—
176	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
177	M₃₂	—	2	2	no	—
178	M₃₂	—	2	2	no	—
179	M₃₂	—	86	8	no	—
180	M₃₂	—	86	2	no	—
181	M₃₂	—	86	2	no	—
182	C₂×C₁₆	—	43	4	no	—
183	C₂×C₁₆	—	86	8	no	—
184	C₂×C₁₆	C₄×D₄₃	1	4	yes	—
185	#97	—	2	2	no	—
186	#97	—	86	2	no	—
187	C₄×C₈	—	86	2	no	—
188	C₄×C₈	—	86	2	no	—
189	C₂⁴	—	43	1	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	43	1	no	—
192	C₂²×C₄	—	43	2	no	—
193	C₂²×C₄	—	43	2	no	—
194	C₂²×C₄	—	43	2	no	—
195	C₂²×C₄	—	43	2	no	—
196	C₂²×C₄	—	43	2	no	—
197	C₂²×C₄	—	43	2	no	—
198	C₂²×C₄	—	86	1	no	—
199	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
200	M₁₆	—	86	8	no	—
201	C₂×C₈	—	2	1	no	—
202	C₂×C₈	—	2	1	no	—
203	C₂×C₈	—	43	1	no	—
204	C₂×C₈	—	43	1	no	—
205	C₂×C₈	—	43	2	no	—
206	C₂×C₈	—	43	2	no	—
207	C₂×C₈	—	43	4	no	—
208	C₂×C₈	—	43	4	no	—
209	C₂×C₈	—	43	4	no	—
210	C₂×C₈	—	43	4	no	—
211	C₂×C₈	—	43	2	no	—
212	C₂×C₈	—	86	1	no	—
213	C₂×C₈	—	86	1	no	—
214	C₂×C₈	C₈×D₄₃	1	2	yes	—
215	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
216	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
217	C₂×C₈	D₄×D₄₃	1	2	yes	—
218	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
219	C₄⋊C₄	—	86	4	no	—
220	C₂²⋊C₄	—	86	4	no	—
221	C₄²	—	2	1	no	—
222	C₄²	—	43	2	no	—
223	C₄²	—	86	1	no	—
224	C₄²	C₈×D₄₃	1	2	yes	—
225	C₁₆	—	2	4	no	—
226	C₁₆	—	86	4	no	—
227	C₂³	—	43	2	no	—
228	C₂³	—	43	2	no	—
229	C₂³	—	43	2	no	—
230	C₂³	—	172	2	no	—
231	C₂³	M₁₆×D₄₃	1	1	yes	characteristic
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	43	2	no	—
235	C₂×C₄	—	43	2	no	—
236	C₂×C₄	—	43	2	no	—
237	C₂×C₄	—	43	4	no	—
238	C₂×C₄	—	43	4	no	—
239	C₂×C₄	—	43	4	no	—
240	C₂×C₄	—	43	4	no	—
241	C₂×C₄	—	86	2	no	—
242	C₂×C₄	—	172	2	no	—
243	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
244	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
245	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
246	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
247	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
248	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
249	C₈	—	2	2	no	—
250	C₈	—	43	2	no	—
251	C₈	—	43	2	no	—
252	C₈	—	86	2	no	—
253	C₈	C₂²⋊C₄×D₄₃	1	2	yes	—
254	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
255	C₂²	—	2	2	no	—
256	C₂²	—	43	4	no	—
257	C₂²	—	86	4	no	—
258	C₂²	—	172	2	no	—
259	C₂²	—	172	2	no	—
260	C₂²	#97×D₄₃	1	1	yes	characteristic
261	C₂²	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
262	C₂²	C₄⋊C₈×D₄₃	1	1	yes	characteristic
263	C₄	—	4	2	no	—
264	C₄	—	43	4	no	—
265	C₄	—	172	2	no	—
266	C₄	#95×D₄₃	1	1	yes	characteristic
267	C₄	C₄×C₈×D₄₃	1	1	yes	characteristic
268	C₄	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
269	C₄	C₄⋊C₈×D₄₃	1	1	yes	characteristic
270	C₂	—	2	1	no	—
271	C₂	—	2	1	no	—
272	C₂	—	86	4	no	—
273	C₂	#336×D₄₃	1	1	yes	characteristic
274	C₂	#19136198	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄²×D₄₃
commutator	C₄×C₄₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1375	C₂
socle	C₂²×C₄₃	C₂×#97
prime radical	C₂³×D₄₃	M₁₆
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1375	D₄₃
hypocenter	C₄₃	#12547
LCS	G ▷ C₄×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #1375

Complements

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

N	H ≅ G/N	type
3. #19132675	C₂	semidirect
4. #19132674	C₂	semidirect
5. C₄₃×#1375	C₂	semidirect
10. C₂×#13063264	C₄	semidirect
13. C₂×C₁₆×D₄₃	C₄	semidirect
137. #1375	D₄₃	semidirect
157. C₄₃	#12547	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₃	2
C₂×#14582856	2
#19132675	2
#19132674	2
C₄₃×#1375	2
#12547	43