Subgroups — #25249733

Order 11008.

524 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143011	C₂	1	1	yes	maximal, characteristic
2	#19136409	C₂	1	4	yes	maximal, complemented
3	#19136405	C₂	1	4	yes	maximal, complemented
4	#19136360	C₂	1	2	yes	maximal, complemented
5	C₂×#14582680	C₂	1	2	yes	maximal
6	#19136200	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2110	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621872	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×D₄₃	C₄	1	1	yes	characteristic
10	#117×D₄₃	C₄	1	1	yes	characteristic
11	C₂×#13063265	C₂²	1	2	yes	—
12	#14582857	C₄	1	1	yes	characteristic
13	#14582856	C₂²	1	2	yes	—
14	#14582855	C₄	1	1	yes	characteristic
15	#14582854	C₂²	1	1	yes	characteristic
16	#14582853	C₄	1	2	yes	—
17	#14582851	C₂²	1	2	yes	—
18	C₄×#10621872	C₄	1	2	yes	—
19	#14582719	C₂²	1	8	yes	complemented
20	#14582680	C₂²	1	4	yes	—
21	#14582680	C₂²	1	4	yes	—
22	#14582677	C₂²	1	4	yes	complemented
23	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
24	C₄₃×#405	C₂²	1	1	yes	characteristic
25	C₄₃×#347	C₂²	1	4	yes	complemented
26	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
28	C₂×#10621872	—	2	2	no	—
29	C₂×#10621872	—	2	2	no	—
30	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
31	C₂×#10621872	C₂×C₄	1	2	yes	—
32	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
33	C₂×#10621872	C₂³	1	1	yes	characteristic
34	C₂×#10621872	C₂³	1	1	yes	characteristic
35	M₁₆×D₄₃	—	2	4	no	—
36	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
38	#13063284	C₂×C₄	1	1	yes	characteristic
39	#13063283	—	2	1	no	—
40	#13063282	C₂×C₄	1	2	yes	—
41	#13063281	—	2	1	no	—
42	C₄⋊C₄×D₄₃	—	2	1	no	—
43	C₂²⋊C₄×D₄₃	—	2	1	no	—
44	C₄²×D₄₃	C₂×C₄	1	2	yes	—
45	#13063265	—	2	2	no	—
46	#13063265	C₂³	1	4	yes	—
47	C₂×C₄₃⋊C₁₆	—	2	2	no	—
48	#13063236	C₂×C₄	1	2	yes	—
49	#13063235	C₂×C₄	1	2	yes	—
50	#13063235	C₂×C₄	1	2	yes	—
51	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
52	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
53	C₈×Dic₄₃	C₂³	1	2	yes	—
54	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
57	M₃₂×C₄₃	—	2	2	no	—
58	M₃₂×C₄₃	C₂³	1	4	yes	—
59	C₂×C₁₆×C₄₃	—	2	2	no	—
60	#97×C₄₃	C₂³	1	2	yes	—
61	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
62	C₂³×D₄₃	M₁₆	1	1	yes	characteristic
63	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×Dic₄₃	M₁₆	1	1	yes	characteristic
65	C₂×C₄×D₄₃	—	2	2	no	—
66	C₂×C₄×D₄₃	—	2	2	no	—
67	C₂×C₄×D₄₃	—	2	2	no	—
68	C₂×C₄×D₄₃	M₁₆	1	1	yes	characteristic
69	C₂×C₄×D₄₃	M₁₆	1	1	yes	characteristic
70	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
72	M₁₆×C₄₃	—	2	2	no	—
73	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
74	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₈×C₄₃	#41	1	2	yes	—
76	C₂×C₈×C₄₃	#41	1	2	yes	—
77	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
78	C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
81	C₂²⋊Dic₄₃	—	2	1	no	—
82	(C₂×D₄₃)⋊C₄	—	2	2	no	—
83	C₄⋊Dic₄₃	—	2	1	no	—
84	Dic₄₃⋊C₄	—	2	2	no	—
85	C₄×Dic₄₃	—	2	2	no	—
86	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
87	#10621877	M₁₆	1	4	yes	—
88	C₂×C₄₃⋊C₈	—	2	2	no	—
89	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
92	#10621872	—	2	1	no	—
93	#10621872	—	2	1	no	—
94	#10621872	—	2	1	no	—
95	#10621872	—	2	1	no	—
96	#10621872	—	2	2	no	—
97	#10621872	—	2	2	no	—
98	#10621872	—	2	4	no	—
99	C₈×D₄₃	—	2	4	no	—
100	C₁₆×C₄₃	—	2	4	no	—
101	C₄₃⋊C₁₆	—	2	4	no	—
102	C₂³×C₄₃	C₂×M₁₆	1	1	yes	characteristic
103	C₂²×D₄₃	—	2	2	no	—
104	C₂²×D₄₃	—	8	1	no	—
105	C₂²×D₄₃	C₂×M₁₆	1	1	yes	characteristic
106	C₂²×D₄₃	C₂×M₁₆	1	1	yes	characteristic
107	C₂×C₄×C₄₃	—	2	2	no	—
108	C₂×C₄×C₄₃	#117	1	2	yes	—
109	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
110	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
111	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
112	C₂×Dic₄₃	—	2	2	no	—
113	C₂×Dic₄₃	—	2	2	no	—
114	C₂×Dic₄₃	C₂×M₁₆	1	1	yes	characteristic
115	C₂×Dic₄₃	C₂×M₁₆	1	1	yes	characteristic
116	C₄×D₄₃	—	2	1	no	—
117	C₄×D₄₃	—	2	1	no	—
118	C₄×D₄₃	—	2	1	no	—
119	C₄×D₄₃	—	2	1	no	—
120	C₄×D₄₃	—	2	2	no	—
121	C₄×D₄₃	—	2	2	no	—
122	C₄×D₄₃	—	8	2	no	—
123	C₈×C₄₃	—	2	2	no	—
124	C₈×C₄₃	#117	1	1	yes	characteristic
125	C₈×C₄₃	#117	1	1	yes	characteristic
126	C₈×C₄₃	C₂×#41	1	2	yes	—
127	C₄₃⋊C₈	—	2	1	no	—
128	C₄₃⋊C₈	—	2	1	no	—
129	C₄₃⋊C₈	C₂×M₁₆	1	4	yes	—
130	#33427	—	43	1	no	maximal, Sylow
131	C₂²×C₄₃	—	4	1	no	—
132	C₂²×C₄₃	#432	1	2	yes	—
133	C₂²×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
134	C₂×D₄₃	—	2	1	no	—
135	C₂×D₄₃	—	2	1	no	—
136	C₂×D₄₃	—	4	1	no	—
137	C₂×D₄₃	—	4	1	no	—
138	C₂×D₄₃	—	8	2	no	—
139	C₄×C₄₃	—	4	2	no	—
140	C₄×C₄₃	#432	1	2	yes	—
141	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
142	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
143	Dic₄₃	—	2	1	no	—
144	Dic₄₃	—	2	1	no	—
145	Dic₄₃	—	4	2	no	—
146	#2873	—	43	1	no	—
147	#2166	—	43	4	no	—
148	#2165	—	43	4	no	—
149	#2153	—	43	2	no	—
150	C₂×#349	—	43	2	no	—
151	#2110	—	43	1	no	—
152	#2110	D₄₃	1	1	yes	characteristic, complemented
153	C₂×C₄₃	—	2	1	no	—
154	C₂×C₄₃	—	2	2	no	—
155	C₂×C₄₃	C₂×#432	1	1	yes	characteristic
156	D₄₃	—	4	1	no	—
157	D₄₃	—	4	1	no	—
158	C₂²×M₁₆	—	43	1	no	—
159	C₂²×M₁₆	—	43	1	no	—
160	C₂×#117	—	43	1	no	—
161	C₂×M₃₂	—	43	2	no	—
162	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
163	#405	—	43	1	no	—
164	#405	—	43	1	no	—
165	#405	—	43	1	no	—
166	#405	—	43	2	no	—
167	#405	—	43	2	no	—
168	#405	C₂×D₄₃	1	1	yes	characteristic
169	C₄×M₁₆	—	43	2	no	—
170	C₄×M₁₆	—	43	2	no	—
171	#364	—	43	8	no	—
172	#349	—	43	4	no	—
173	#349	—	43	4	no	—
174	#347	—	43	4	no	—
175	#347	C₂×D₄₃	1	4	yes	complemented
176	C₄₃	#33427	1	1	yes	characteristic, complemented, Sylow
177	C₂³×C₄	—	43	1	no	—
178	C₂×M₁₆	—	43	1	no	—
179	C₂×M₁₆	—	43	2	no	—
180	C₂×M₁₆	—	43	1	no	—
181	C₂×M₁₆	—	43	1	no	—
182	C₂×M₁₆	—	43	1	no	—
183	C₂×M₁₆	—	43	1	no	—
184	C₂×M₁₆	—	86	4	no	—
185	C₂×M₁₆	—	86	2	no	—
186	C₂×M₁₆	—	86	2	no	—
187	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
188	C₂²×C₈	—	43	1	no	—
189	C₂²×C₈	—	43	2	no	—
190	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
191	#117	—	43	1	no	—
192	#117	—	43	2	no	—
193	#117	—	86	1	no	—
194	#117	—	86	1	no	—
195	#117	C₄×D₄₃	1	1	yes	characteristic
196	C₂×C₄⋊C₄	—	86	1	no	—
197	C₂×C₂²⋊C₄	—	86	1	no	—
198	C₂×C₄²	—	43	2	no	—
199	M₃₂	—	2	2	no	—
200	M₃₂	—	43	4	no	—
201	M₃₂	—	86	2	no	—
202	M₃₂	C₂²×D₄₃	1	4	yes	—
203	C₂×C₁₆	—	2	2	no	—
204	C₂×C₁₆	—	86	2	no	—
205	#97	—	43	2	no	—
206	#97	—	43	2	no	—
207	#97	—	43	2	no	—
208	#97	C₂²×D₄₃	1	2	yes	—
209	C₄×C₈	—	43	2	no	—
210	C₄×C₈	—	43	2	no	—
211	C₄×C₈	—	43	2	no	—
212	C₄×C₈	C₄×D₄₃	1	2	yes	—
213	C₂⁴	—	43	1	no	—
214	C₂²×C₄	—	43	1	no	—
215	C₂²×C₄	—	43	1	no	—
216	C₂²×C₄	—	43	1	no	—
217	C₂²×C₄	—	43	1	no	—
218	C₂²×C₄	—	43	1	no	—
219	C₂²×C₄	—	86	2	no	—
220	C₂²×C₄	—	86	2	no	—
221	C₂²×C₄	—	86	2	no	—
222	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
223	M₁₆	—	2	2	no	—
224	M₁₆	—	43	4	no	—
225	M₁₆	—	86	4	no	—
226	M₁₆	—	86	1	no	—
227	M₁₆	—	86	1	no	—
228	M₁₆	—	86	1	no	—
229	M₁₆	—	86	1	no	—
230	M₁₆	—	86	2	no	—
231	M₁₆	—	86	2	no	—
232	C₂×C₈	—	43	2	no	—
233	C₂×C₈	—	43	1	no	—
234	C₂×C₈	—	43	1	no	—
235	C₂×C₈	—	86	4	no	—
236	C₂×C₈	—	86	2	no	—
237	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
238	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
239	C₂×C₈	#10621898	1	2	yes	—
240	C₂×C₈	#10621898	1	2	yes	—
241	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
242	C₄⋊C₄	—	2	1	no	—
243	C₄⋊C₄	—	86	2	no	—
244	C₄⋊C₄	—	86	1	no	—
245	C₂²⋊C₄	—	2	1	no	—
246	C₂²⋊C₄	—	86	2	no	—
247	C₂²⋊C₄	—	86	1	no	—
248	C₄²	—	43	2	no	—
249	C₄²	—	86	2	no	—
250	C₄²	C₂×C₄×D₄₃	1	2	yes	—
251	C₁₆	—	2	4	no	—
252	C₁₆	—	86	4	no	—
253	C₂³	—	43	1	no	—
254	C₂³	—	43	1	no	—
255	C₂³	—	86	2	no	—
256	C₂³	—	344	1	no	—
257	C₂³	M₁₆×D₄₃	1	1	yes	characteristic
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	43	1	no	—
260	C₂×C₄	—	43	1	no	—
261	C₂×C₄	—	86	2	no	—
262	C₂×C₄	—	86	1	no	—
263	C₂×C₄	—	86	1	no	—
264	C₂×C₄	—	86	1	no	—
265	C₂×C₄	—	86	1	no	—
266	C₂×C₄	—	86	2	no	—
267	C₂×C₄	—	86	2	no	—
268	C₂×C₄	—	86	2	no	—
269	C₂×C₄	—	344	2	no	—
270	C₂×C₄	#13063282	1	2	yes	—
271	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
272	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
273	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
274	C₈	—	2	2	no	—
275	C₈	—	43	4	no	—
276	C₈	—	86	1	no	—
277	C₈	—	86	1	no	—
278	C₈	#13063282	1	1	yes	characteristic
279	C₈	#13063282	1	1	yes	characteristic
280	C₈	C₂×#10621898	1	2	yes	—
281	C₂²	—	4	1	no	—
282	C₂²	—	86	1	no	—
283	C₂²	—	86	1	no	—
284	C₂²	—	344	2	no	—
285	C₂²	—	172	1	no	—
286	C₂²	—	172	1	no	—
287	C₂²	#14582954	1	2	yes	—
288	C₂²	C₂×M₁₆×D₄₃	1	1	yes	characteristic
289	C₄	—	4	2	no	—
290	C₄	—	86	1	no	—
291	C₄	—	86	1	no	—
292	C₄	—	172	2	no	—
293	C₄	#14582954	1	2	yes	—
294	C₄	C₂×#13063282	1	1	yes	characteristic
295	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
296	C₂	—	2	1	no	—
297	C₂	—	2	2	no	—
298	C₂	—	172	1	no	—
299	C₂	—	172	1	no	—
300	C₂	C₂×#14582954	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13063282
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2110	C₂
socle	C₂×C₄₃	C₂×#432
prime radical	C₂³×D₄₃	M₁₆
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	#2110	D₄₃
hypocenter	C₄₃	#33427
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ #405 ◁ #2110

Complements

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

N	H ≅ G/N	type
2. #19136409	C₂	semidirect
3. #19136405	C₂	semidirect
4. #19136360	C₂	semidirect
6. #19136200	C₂	semidirect
7. C₄₃×#2110	C₂	semidirect
19. #14582719	C₂²	semidirect
22. #14582677	C₂²	semidirect
25. C₄₃×#347	C₂²	semidirect
152. #2110	D₄₃	semidirect
175. #347	C₂×D₄₃	semidirect
176. C₄₃	#33427	semidirect

Maximal subgroups

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

subgroup	index
#19143011	2
#19136409	2
#19136405	2
#19136360	2
C₂×#14582680	2
#19136200	2
C₄₃×#2110	2
#33427	43