Subgroups — #24987126

Order 11008.

506 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582853	C₂	1	1	yes	maximal, characteristic
2	#19132907	C₂	1	2	yes	maximal
3	#19132878	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132439	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10621872	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₂×#13063282	C₂²	1	1	yes	characteristic
9	#14582952	C₂²	1	2	yes	—
10	#14582853	—	2	1	no	—
11	#14582853	—	2	1	no	—
12	#14582853	—	2	1	no	—
13	#14582853	—	2	1	no	—
14	C₂×#13063236	C₂²	1	1	yes	characteristic
15	C₂×#13063235	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₄₃	C₄	1	1	yes	characteristic
17	#14582624	C₄	1	4	yes	—
18	#14582622	C₄	1	4	yes	—
19	#14582620	—	2	1	no	—
20	C₈×C₄₃⋊C₈	—	2	1	no	—
21	C₄₃×#431	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#322	—	2	1	no	—
24	C₈²×C₄₃	—	2	1	no	—
25	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
26	C₂×#10621872	—	2	1	no	—
27	C₂×#10621872	—	2	1	no	—
28	C₂×#10621872	—	2	2	no	—
29	C₂×#10621872	C₈	1	4	yes	complemented
30	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×D₄₃	—	2	1	no	—
33	C₂×C₈×D₄₃	—	2	1	no	—
34	C₂×C₈×D₄₃	—	2	2	no	—
35	C₂×C₈×D₄₃	C₈	1	4	yes	complemented
36	#13063282	—	2	1	no	—
37	#13063282	—	2	1	no	—
38	#13063282	—	2	2	no	—
39	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
40	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
41	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
42	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
43	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
44	#13063236	—	2	1	no	—
45	#13063236	—	2	1	no	—
46	#13063235	—	2	1	no	—
47	#13063235	—	2	1	no	—
48	C₄×C₄₃⋊C₈	—	2	2	no	—
49	C₈×Dic₄₃	—	2	1	no	—
50	C₈×Dic₄₃	—	2	1	no	—
51	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₄₃	—	2	2	no	—
55	C₂²⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
56	C₄×C₈×C₄₃	—	2	2	no	—
57	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
58	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
59	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
60	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
61	C₂³×D₄₃	C₄²	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
63	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×Dic₄₃	C₄²	1	1	yes	characteristic
65	C₂²×Dic₄₃	C₄²	1	2	yes	—
66	C₂×C₄×D₄₃	—	2	1	no	—
67	C₂×C₄×D₄₃	—	2	1	no	—
68	C₂×C₄×D₄₃	—	2	1	no	—
69	C₂×C₄×D₄₃	—	2	1	no	—
70	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
71	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
72	C₂×C₈×C₄₃	—	2	4	no	—
73	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
78	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
79	C₂×C₈×C₄₃	M₁₆	1	2	yes	—
80	C₂×C₈×C₄₃	M₁₆	1	2	yes	—
81	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₄₃	#41	1	2	yes	—
84	(C₂×D₄₃)⋊C₄	—	2	2	no	—
85	(C₂×D₄₃)⋊C₄	—	2	2	no	—
86	Dic₄₃⋊C₄	—	2	2	no	—
87	Dic₄₃⋊C₄	—	2	2	no	—
88	C₄×Dic₄₃	—	2	1	no	—
89	C₄×Dic₄₃	—	2	1	no	—
90	C₂×C₄₃⋊C₈	—	2	1	no	—
91	C₂×C₄₃⋊C₈	—	2	1	no	—
92	C₂×C₄₃⋊C₈	—	2	1	no	—
93	C₂×C₄₃⋊C₈	—	2	1	no	—
94	C₂×C₄₃⋊C₈	—	2	4	no	—
95	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
96	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
97	#10621872	—	2	4	no	—
98	#10621872	—	2	4	no	—
99	C₈×D₄₃	—	2	4	no	—
100	C₈×D₄₃	—	2	4	no	—
101	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
102	C₂²×D₄₃	—	2	1	no	—
103	C₂²×D₄₃	—	2	1	no	—
104	C₂²×D₄₃	—	4	2	no	—
105	C₂²×D₄₃	C₄×C₈	1	2	yes	—
106	C₂×C₄×C₄₃	—	4	2	no	—
107	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
109	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
110	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
111	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
112	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
113	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
114	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
115	C₂×Dic₄₃	—	2	1	no	—
116	C₂×Dic₄₃	—	2	1	no	—
117	C₂×Dic₄₃	—	2	2	no	—
118	C₂×Dic₄₃	—	4	2	no	—
119	C₂×Dic₄₃	C₄×C₈	1	2	yes	—
120	C₄×D₄₃	—	2	2	no	—
121	C₄×D₄₃	—	2	2	no	—
122	C₄×D₄₃	—	2	2	no	—
123	C₄×D₄₃	—	2	2	no	—
124	C₈×C₄₃	—	4	4	no	—
125	C₈×C₄₃	C₂²⋊C₈	1	2	yes	—
126	C₈×C₄₃	C₂²⋊C₈	1	2	yes	—
127	C₈×C₄₃	C₂²⋊C₈	1	2	yes	—
128	C₈×C₄₃	C₂²⋊C₈	1	2	yes	—
129	C₄₃⋊C₈	—	2	2	no	—
130	C₄₃⋊C₈	—	2	2	no	—
131	C₄₃⋊C₈	—	4	4	no	—
132	#8156	—	43	1	no	maximal, Sylow
133	C₂²×C₄₃	—	2	2	no	—
134	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
136	C₂²×C₄₃	C₄×M₁₆	1	1	yes	characteristic
137	C₂×D₄₃	—	2	2	no	—
138	C₂×D₄₃	—	4	2	no	—
139	C₂×D₄₃	—	4	2	no	—
140	C₂×D₄₃	—	4	2	no	—
141	C₄×C₄₃	—	2	2	no	—
142	C₄×C₄₃	—	2	2	no	—
143	C₄×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
144	C₄×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
145	C₄×C₄₃	#431	1	1	yes	characteristic
146	C₄×C₄₃	#431	1	1	yes	characteristic
147	Dic₄₃	—	2	2	no	—
148	Dic₄₃	—	4	2	no	—
149	C₂×#405	—	43	1	no	—
150	#1458	—	43	2	no	—
151	#1450	—	43	1	no	—
152	#1450	D₄₃	1	1	yes	characteristic, complemented
153	#1281	—	43	2	no	—
154	C₂×C₄₃	—	2	1	no	—
155	C₂×C₄₃	—	2	1	no	—
156	C₂×C₄₃	C₄×C₂²⋊C₈	1	1	yes	characteristic
157	C₂×C₄₃	#1757	1	2	yes	—
158	D₄₃	—	4	2	no	—
159	C₂²×M₁₆	—	43	1	no	—
160	C₂³×C₈	—	43	1	no	—
161	C₂×#117	—	43	1	no	—
162	#431	—	43	2	no	—
163	#431	C₂×D₄₃	1	2	yes	—
164	#405	—	86	1	no	—
165	#405	—	86	1	no	—
166	#405	—	86	1	no	—
167	#405	—	86	1	no	—
168	C₂×#97	—	43	1	no	—
169	C₂×#97	—	43	1	no	—
170	C₂×C₄×C₈	—	43	1	no	—
171	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
172	#324	—	43	4	no	—
173	#323	—	43	4	no	—
174	#322	—	2	1	no	—
175	#322	—	86	1	no	—
176	C₈²	—	2	1	no	—
177	C₈²	—	86	1	no	—
178	C₄₃	#8156	1	1	yes	characteristic, complemented, Sylow
179	C₂³×C₄	—	43	1	no	—
180	C₂×M₁₆	—	43	4	no	—
181	C₂×M₁₆	—	86	2	no	—
182	C₂×M₁₆	—	86	1	no	—
183	C₂×M₁₆	—	86	1	no	—
184	C₂²×C₈	—	43	1	no	—
185	C₂²×C₈	—	43	1	no	—
186	C₂²×C₈	—	43	4	no	—
187	C₂²×C₈	—	86	2	no	—
188	C₂²×C₈	—	86	1	no	—
189	C₂²×C₈	—	86	1	no	—
190	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
191	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
192	#117	—	86	1	no	—
193	#117	—	86	2	no	—
194	#117	—	86	1	no	—
195	C₂×C₄⋊C₄	—	43	2	no	—
196	C₂×C₂²⋊C₄	—	43	2	no	—
197	C₂×C₄²	—	43	1	no	—
198	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
199	C₄⋊C₈	—	2	2	no	—
200	C₄⋊C₈	—	86	2	no	—
201	C₂²⋊C₈	—	43	4	no	—
202	C₂²⋊C₈	C₄×D₄₃	1	4	yes	—
203	#97	—	86	1	no	—
204	#97	—	86	1	no	—
205	#97	—	86	1	no	—
206	#97	—	86	1	no	—
207	C₄×C₈	—	2	2	no	—
208	C₄×C₈	—	86	1	no	—
209	C₄×C₈	—	86	1	no	—
210	C₄×C₈	—	86	2	no	—
211	C₄×C₈	D₁₇₂	1	1	yes	characteristic
212	C₄×C₈	D₁₇₂	1	1	yes	characteristic
213	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
214	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
215	C₂⁴	—	43	1	no	—
216	C₂²×C₄	—	43	1	no	—
217	C₂²×C₄	—	43	2	no	—
218	C₂²×C₄	—	43	2	no	—
219	C₂²×C₄	—	43	2	no	—
220	C₂²×C₄	—	86	1	no	—
221	C₂²×C₄	—	86	1	no	—
222	C₂²×C₄	—	86	1	no	—
223	C₂²×C₄	—	86	1	no	—
224	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
225	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
226	M₁₆	—	86	4	no	—
227	M₁₆	—	86	4	no	—
228	C₂×C₈	—	2	4	no	—
229	C₂×C₈	—	43	2	no	—
230	C₂×C₈	—	43	2	no	—
231	C₂×C₈	—	86	1	no	—
232	C₂×C₈	—	86	1	no	—
233	C₂×C₈	—	86	1	no	—
234	C₂×C₈	—	86	1	no	—
235	C₂×C₈	—	86	4	no	—
236	C₂×C₈	—	86	4	no	—
237	C₂×C₈	—	86	4	no	—
238	C₂×C₈	C₈×D₄₃	1	2	yes	—
239	C₂×C₈	C₈×D₄₃	1	2	yes	—
240	C₂×C₈	#10621872	1	2	yes	—
241	C₂×C₈	#10621872	1	2	yes	—
242	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
243	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
244	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
245	C₂×C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
246	C₄⋊C₄	—	86	2	no	—
247	C₄⋊C₄	—	86	2	no	—
248	C₂²⋊C₄	—	86	2	no	—
249	C₂²⋊C₄	—	86	2	no	—
250	C₄²	—	86	1	no	—
251	C₄²	—	86	1	no	—
252	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
253	C₄²	#10621898	1	2	yes	—
254	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
255	C₂³	—	43	2	no	—
256	C₂³	—	86	1	no	—
257	C₂³	—	86	1	no	—
258	C₂³	—	172	2	no	—
259	C₂³	C₄²×D₄₃	1	1	yes	characteristic
260	C₂×C₄	—	4	2	no	—
261	C₂×C₄	—	43	2	no	—
262	C₂×C₄	—	86	1	no	—
263	C₂×C₄	—	86	1	no	—
264	C₂×C₄	—	86	2	no	—
265	C₂×C₄	—	86	2	no	—
266	C₂×C₄	—	86	2	no	—
267	C₂×C₄	—	86	2	no	—
268	C₂×C₄	—	86	2	no	—
269	C₂×C₄	—	172	2	no	—
270	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
271	C₂×C₄	#13063282	1	1	yes	characteristic
272	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
273	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
274	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
275	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
276	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
277	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
278	C₈	—	4	4	no	—
279	C₈	—	86	2	no	—
280	C₈	—	86	2	no	—
281	C₈	—	172	4	no	—
282	C₈	(C₂×D₄₃)⋊C₈	1	2	yes	—
283	C₈	(C₂×D₄₃)⋊C₈	1	2	yes	—
284	C₈	(C₂×D₄₃)⋊C₈	1	2	yes	—
285	C₈	(C₂×D₄₃)⋊C₈	1	2	yes	—
286	C₂²	—	2	2	no	—
287	C₂²	—	86	2	no	—
288	C₂²	—	172	2	no	—
289	C₂²	—	172	2	no	—
290	C₂²	—	172	2	no	—
291	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
292	C₂²	C₄×C₈×D₄₃	1	1	yes	characteristic
293	C₂²	C₄×#10621872	1	1	yes	characteristic
294	C₄	—	2	2	no	—
295	C₄	—	2	2	no	—
296	C₄	—	86	2	no	—
297	C₄	—	172	2	no	—
298	C₄	C₂×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
299	C₄	C₂×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
300	C₄	#14582950	1	1	yes	characteristic
301	C₄	#14582950	1	1	yes	characteristic
302	C₂	—	2	1	no	—
303	C₂	—	2	1	no	—
304	C₂	—	172	2	no	—
305	C₂	C₄×(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
306	C₂	#19134396	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄₃	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1450	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1450	D₄₃
hypocenter	C₄₃	#8156
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1450

Complements

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

N	H ≅ G/N	type
3. #19132878	C₂	semidirect
4. #19132439	C₂	semidirect
5. C₄₃×#1450	C₂	semidirect
29. C₂×#10621872	C₈	semidirect
35. C₂×C₈×D₄₃	C₈	semidirect
152. #1450	D₄₃	semidirect
178. C₄₃	#8156	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582853	2
#19132907	2
#19132878	2
#19132439	2
C₄₃×#1450	2
#8156	43