Subgroups — #19137202

Order 5504.

484 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×#13063284	C₂	1	1	yes	maximal, characteristic
2	#14582793	C₂	1	2	yes	maximal
3	#14582787	C₂	1	2	yes	maximal
4	#14582784	C₂	1	2	yes	maximal, complemented
5	#14582782	C₂	1	2	yes	maximal, complemented
6	#14582768	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582764	C₂	1	1	yes	maximal, characteristic, complemented
8	#14582759	C₂	1	1	yes	maximal, characteristic
9	C₄⋊C₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#380	C₂	1	1	yes	maximal, characteristic
12	#13063284	C₄	1	8	yes	complemented
13	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
18	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
19	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
20	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
23	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
24	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
26	C₄₃⋊#95	C₂²	1	2	yes	—
27	C₄₃⋊#95	C₂²	1	2	yes	—
28	C₄₃⋊#95	C₂²	1	2	yes	—
29	C₄₃⋊#95	C₂²	1	2	yes	—
30	C₄₃⋊#95	C₂²	1	2	yes	—
31	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
35	#95×C₄₃	C₂²	1	2	yes	—
36	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	—	2	2	no	—
39	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
40	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
41	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
42	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₃	C₂³	1	2	yes	—
45	C₂²×Dic₄₃	C₂³	1	2	yes	—
46	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
47	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
48	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
49	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
50	C₄⋊C₄×C₄₃	—	2	2	no	—
51	C₄⋊C₄×C₄₃	—	2	2	no	—
52	C₂²⋊C₄×C₄₃	—	4	2	no	—
53	C₂²⋊Dic₄₃	—	4	2	no	—
54	C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
55	C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
56	C₄⋊Dic₄₃	—	2	2	no	—
57	C₄⋊Dic₄₃	—	2	2	no	—
58	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
59	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
60	Dic₄₃⋊C₄	—	4	2	no	—
61	Dic₄₃⋊C₄	—	4	2	no	—
62	C₄×Dic₄₃	—	4	2	no	—
63	C₄×Dic₄₃	—	4	2	no	—
64	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
65	C₄×Dic₄₃	C₂×C₄	1	4	yes	—
66	C₂³×C₄₃	—	2	1	no	—
67	C₂³×C₄₃	—	2	1	no	—
68	C₂³×C₄₃	—	2	1	no	—
69	C₂³×C₄₃	—	2	1	no	—
70	C₂³×C₄₃	—	2	1	no	—
71	C₂³×C₄₃	—	2	1	no	—
72	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
73	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
74	C₂×C₄×C₄₃	—	2	1	no	—
75	C₂×C₄×C₄₃	—	2	1	no	—
76	C₂×C₄×C₄₃	—	2	8	no	—
77	C₂×C₄×C₄₃	—	2	2	no	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	—	2	2	no	—
81	C₂×C₄×C₄₃	—	2	2	no	—
82	C₂×C₄×C₄₃	—	2	2	no	—
83	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
85	C₂×C₄×C₄₃	#41	1	2	yes	—
86	C₂×C₄×C₄₃	#41	1	2	yes	—
87	C₂×Dic₄₃	—	2	1	no	—
88	C₂×Dic₄₃	—	2	1	no	—
89	C₂×Dic₄₃	—	2	1	no	—
90	C₂×Dic₄₃	—	2	1	no	—
91	C₂×Dic₄₃	—	2	1	no	—
92	C₂×Dic₄₃	—	2	1	no	—
93	C₂×Dic₄₃	—	2	1	no	—
94	C₂×Dic₄₃	—	2	1	no	—
95	C₂×Dic₄₃	—	2	2	no	—
96	C₂×Dic₄₃	—	2	2	no	—
97	C₂×Dic₄₃	—	2	2	no	—
98	C₂×Dic₄₃	—	2	2	no	—
99	C₂×Dic₄₃	—	2	2	no	—
100	C₂×Dic₄₃	—	2	2	no	—
101	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
102	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
103	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
104	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄₃	—	2	2	no	—
106	C₂²×C₄₃	—	2	2	no	—
107	C₂²×C₄₃	—	2	2	no	—
108	C₂²×C₄₃	—	4	1	no	—
109	C₂²×C₄₃	—	4	1	no	—
110	C₂²×C₄₃	—	4	1	no	—
111	C₂²×C₄₃	—	4	1	no	—
112	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
113	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
114	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
115	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
116	C₂²×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
117	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
118	C₂²×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
119	C₄×C₄₃	—	2	2	no	—
120	C₄×C₄₃	—	4	2	no	—
121	C₄×C₄₃	—	4	2	no	—
122	C₄×C₄₃	#117	1	4	yes	—
123	Dic₄₃	—	2	2	no	—
124	Dic₄₃	—	2	2	no	—
125	Dic₄₃	—	2	2	no	—
126	Dic₄₃	—	2	2	no	—
127	Dic₄₃	—	4	2	no	—
128	Dic₄₃	—	4	2	no	—
129	#2314	—	43	1	no	maximal, Sylow
130	C₂×C₄₃	—	4	2	no	—
131	C₂×C₄₃	C₂×#117	1	1	yes	characteristic
132	C₂×C₄₃	#520	1	1	yes	characteristic
133	C₂×C₄₃	#520	1	1	yes	characteristic
134	C₂×C₄₃	#540	1	1	yes	characteristic
135	C₂×C₄₃	#541	1	1	yes	characteristic
136	C₂×C₄₃	#542	1	1	yes	characteristic
137	C₂×C₄₃	#542	1	1	yes	characteristic
138	C₂×#117	—	43	1	no	—
139	#388	—	43	2	no	—
140	#388	—	43	2	no	—
141	#387	—	43	2	no	—
142	#387	—	43	2	no	—
143	#384	—	43	1	no	—
144	#382	—	43	1	no	—
145	#380	—	43	1	no	—
146	#380	D₄₃	1	1	yes	characteristic
147	C₄×C₄⋊C₄	—	43	1	no	—
148	C₄×C₄⋊C₄	—	43	1	no	—
149	C₄₃	#2314	1	1	yes	characteristic, complemented, Sylow
150	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
151	#117	—	43	8	no	—
152	C₂×C₄⋊C₄	—	43	1	no	—
153	C₂×C₄⋊C₄	—	43	1	no	—
154	C₂×C₄⋊C₄	—	43	1	no	—
155	C₂×C₄⋊C₄	—	43	1	no	—
156	C₂×C₄⋊C₄	—	43	2	no	—
157	C₂×C₄⋊C₄	—	43	2	no	—
158	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
159	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
160	C₂×C₂²⋊C₄	—	43	1	no	—
161	C₂×C₂²⋊C₄	—	43	1	no	—
162	C₂×C₂²⋊C₄	—	43	2	no	—
163	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
164	C₂×C₄²	—	43	1	no	—
165	C₂×C₄²	—	43	1	no	—
166	C₂×C₄²	—	43	2	no	—
167	C₂×C₄²	—	43	2	no	—
168	#95	—	43	2	no	—
169	#95	—	43	2	no	—
170	#95	—	43	2	no	—
171	#95	—	43	2	no	—
172	#95	—	43	2	no	—
173	#95	C₂×D₄₃	1	2	yes	—
174	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	—	43	1	no	—
178	C₂²×C₄	—	43	1	no	—
179	C₂²×C₄	—	43	1	no	—
180	C₂²×C₄	—	43	1	no	—
181	C₂²×C₄	—	43	2	no	—
182	C₂²×C₄	—	43	2	no	—
183	C₂²×C₄	C₄×D₄₃	1	4	yes	—
184	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
185	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
186	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
187	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	43	4	no	—
191	C₄⋊C₄	—	43	4	no	—
192	C₄⋊C₄	—	86	2	no	—
193	C₄⋊C₄	—	86	2	no	—
194	C₄⋊C₄	—	172	2	no	—
195	C₄⋊C₄	—	172	2	no	—
196	C₂²⋊C₄	—	4	2	no	—
197	C₂²⋊C₄	—	43	4	no	—
198	C₂²⋊C₄	—	43	4	no	—
199	C₂²⋊C₄	—	172	2	no	—
200	C₄²	—	43	4	no	—
201	C₄²	—	43	4	no	—
202	C₄²	—	172	2	no	—
203	C₄²	—	172	2	no	—
204	C₂³	—	2	1	no	—
205	C₂³	—	2	1	no	—
206	C₂³	—	2	1	no	—
207	C₂³	—	2	1	no	—
208	C₂³	—	2	1	no	—
209	C₂³	—	2	1	no	—
210	C₂³	C₂×C₄×D₄₃	1	2	yes	—
211	C₂³	C₂³×D₄₃	1	1	yes	characteristic
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	8	no	—
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	43	2	no	—
222	C₂×C₄	—	43	2	no	—
223	C₂×C₄	—	43	2	no	—
224	C₂×C₄	—	43	2	no	—
225	C₂×C₄	—	86	1	no	—
226	C₂×C₄	—	86	1	no	—
227	C₂×C₄	—	86	1	no	—
228	C₂×C₄	—	86	1	no	—
229	C₂×C₄	—	86	1	no	—
230	C₂×C₄	—	86	1	no	—
231	C₂×C₄	—	86	1	no	—
232	C₂×C₄	—	86	1	no	—
233	C₂×C₄	—	86	2	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	2	no	—
239	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
240	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
241	C₂×C₄	#10621900	1	2	yes	—
242	C₂×C₄	#10621900	1	2	yes	—
243	C₂²	—	2	2	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	2	2	no	—
246	C₂²	—	4	1	no	—
247	C₂²	—	4	1	no	—
248	C₂²	—	4	1	no	—
249	C₂²	—	4	1	no	—
250	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
251	C₂²	C₂×#10621900	1	1	yes	characteristic
252	C₂²	C₂×#10621900	1	1	yes	characteristic
253	C₂²	#13063370	1	1	yes	characteristic
254	C₂²	#13063371	1	1	yes	characteristic
255	C₂²	#13063372	1	1	yes	characteristic
256	C₂²	#13063373	1	1	yes	characteristic
257	C₄	—	2	2	no	—
258	C₄	—	4	2	no	—
259	C₄	—	4	2	no	—
260	C₄	—	86	2	no	—
261	C₄	—	86	2	no	—
262	C₄	—	86	2	no	—
263	C₄	—	86	2	no	—
264	C₄	—	172	2	no	—
265	C₄	—	172	2	no	—
266	C₄	#13063281	1	4	yes	—
267	C₂	—	4	2	no	—
268	C₂	C₂×#13063281	1	1	yes	characteristic
269	C₂	#14583379	1	1	yes	characteristic
270	C₂	#14583380	1	1	yes	characteristic
271	C₂	#14583502	1	1	yes	characteristic
272	C₂	#14583509	1	1	yes	characteristic
273	C₂	#14583516	1	1	yes	characteristic
274	C₂	#14583522	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#380	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	#380	D₄₃
hypocenter	C₄₃	#2314
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #380

Complements

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

N	H ≅ G/N	type
4. #14582784	C₂	semidirect
5. #14582782	C₂	semidirect
6. #14582768	C₂	semidirect
7. #14582764	C₂	semidirect
9. C₄⋊C₄×Dic₄₃	C₂	semidirect
10. C₄⋊C₄×Dic₄₃	C₂	semidirect
12. #13063284	C₄	semidirect
149. C₄₃	#2314	semidirect