Subgroups — #19143229

Order 5504.

392 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#117×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#14582961	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582960	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582959	C₂	1	2	yes	maximal, complemented
5	#14582958	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582957	C₂	1	2	yes	maximal, complemented
7	#14582921	C₂	1	2	yes	maximal, complemented
8	#14582861	C₂	1	2	yes	maximal
9	#14582851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#10621872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
13	C₂×#10621872	C₂²	1	2	yes	—
14	C₂×#10621872	C₂²	1	2	yes	—
15	#13063284	C₂²	1	1	yes	characteristic
16	#13063283	C₄	1	2	yes	—
17	#13063282	C₂²	1	1	yes	characteristic
18	#13063282	C₂²	1	1	yes	characteristic
19	#13063281	C₄	1	2	yes	—
20	C₄⋊C₄×D₄₃	C₄	1	2	yes	—
21	C₂²⋊C₄×D₄₃	C₄	1	2	yes	—
22	C₄²×D₄₃	C₂²	1	1	yes	characteristic
23	C₄²×D₄₃	C₂²	1	1	yes	characteristic
24	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
25	Dic₄₃⋊C₈	C₂²	1	2	yes	complemented
26	Dic₄₃⋊C₈	C₂²	1	2	yes	complemented
27	C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
28	(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
29	(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
30	#13063236	C₂²	1	1	yes	characteristic, complemented
31	#13063235	C₂²	1	2	yes	complemented
32	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₈×Dic₄₃	C₂²	1	2	yes	complemented
34	#117×C₄₃	C₂²	1	1	yes	characteristic
35	C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
36	C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
37	#97×C₄₃	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
39	C₂³×D₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²×Dic₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×D₄₃	—	2	4	no	—
43	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
46	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
47	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
48	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
49	C₂×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂×C₈×C₄₃	C₂³	1	2	yes	—
51	C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
52	C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
53	C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄²×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
56	(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
57	(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
58	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
59	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
60	Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
61	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
62	C₄×Dic₄₃	C₂×C₄	1	2	yes	—
63	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
64	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
66	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
67	#10621872	—	2	4	no	—
68	#10621872	—	2	4	no	—
69	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
70	C₂²×D₄₃	—	2	2	no	—
71	C₂²×D₄₃	—	4	2	no	—
72	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×D₄₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₄₃	—	2	2	no	—
75	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
76	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
79	C₂×Dic₄₃	—	2	2	no	—
80	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
81	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
82	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
84	C₄×D₄₃	—	2	2	no	—
85	C₄×D₄₃	—	2	2	no	—
86	C₄×D₄₃	—	2	2	no	—
87	C₄×D₄₃	—	4	2	no	—
88	C₄×D₄₃	—	4	2	no	—
89	C₄×D₄₃	#41	1	4	yes	—
90	C₈×C₄₃	—	2	2	no	—
91	C₈×C₄₃	—	2	2	no	—
92	C₄₃⋊C₈	—	2	2	no	—
93	C₄₃⋊C₈	—	2	2	no	—
94	C₂²×C₄₃	—	2	1	no	—
95	C₂²×C₄₃	—	2	2	no	—
96	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
97	C₂×D₄₃	—	2	2	no	—
98	C₂×D₄₃	—	2	1	no	—
99	C₂×D₄₃	—	2	2	no	—
100	C₂×D₄₃	—	4	4	no	—
101	C₂×D₄₃	#117	1	2	yes	—
102	C₄×C₄₃	—	2	1	no	—
103	C₄×C₄₃	—	2	2	no	—
104	C₄×C₄₃	—	2	2	no	—
105	C₄×C₄₃	C₂×#41	1	2	yes	—
106	Dic₄₃	—	2	1	no	—
107	Dic₄₃	—	2	2	no	—
108	Dic₄₃	—	2	2	no	—
109	Dic₄₃	#117	1	2	yes	—
110	#2921	—	43	1	no	maximal, Sylow
111	C₂×C₄₃	—	4	1	no	—
112	C₂×C₄₃	C₂×#117	1	1	yes	characteristic
113	C₂×C₄₃	#568	1	2	yes	—
114	D₄₃	—	2	2	no	—
115	D₄₃	—	4	1	no	—
116	C₂×#117	—	43	1	no	—
117	#433	—	43	1	no	—
118	#433	—	43	2	no	—
119	#433	—	43	2	no	—
120	#433	—	43	1	no	—
121	#433	—	43	1	no	—
122	#433	D₄₃	1	1	yes	characteristic, complemented
123	#423	—	43	2	no	—
124	#407	—	43	2	no	—
125	C₄×M₁₆	—	43	1	no	—
126	C₄×M₁₆	—	43	1	no	—
127	C₄₃	#2921	1	1	yes	characteristic, complemented, Sylow
128	C₂³×C₄	—	43	1	no	—
129	C₂×M₁₆	—	43	2	no	—
130	C₂×M₁₆	—	43	2	no	—
131	#117	—	43	1	no	—
132	#117	—	43	2	no	—
133	#117	—	43	2	no	—
134	#117	—	43	1	no	—
135	#117	—	43	1	no	—
136	#117	C₂×D₄₃	1	1	yes	characteristic
137	C₂×C₄⋊C₄	—	43	2	no	—
138	C₂×C₂²⋊C₄	—	43	2	no	—
139	C₂×C₄²	—	43	1	no	—
140	C₂×C₄²	—	43	1	no	—
141	C₄⋊C₈	—	43	2	no	—
142	C₄⋊C₈	—	43	2	no	—
143	C₄⋊C₈	—	43	2	no	—
144	C₄⋊C₈	C₂×D₄₃	1	2	yes	complemented
145	C₂²⋊C₈	—	43	2	no	—
146	C₂²⋊C₈	—	43	2	no	—
147	C₂²⋊C₈	—	43	2	no	—
148	C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
149	#97	—	43	2	no	—
150	#97	—	43	1	no	—
151	#97	C₂×D₄₃	1	1	yes	characteristic, complemented
152	C₄×C₈	—	43	2	no	—
153	C₄×C₈	—	43	1	no	—
154	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
155	C₂⁴	—	43	1	no	—
156	C₂²×C₄	—	43	1	no	—
157	C₂²×C₄	—	43	1	no	—
158	C₂²×C₄	—	43	1	no	—
159	C₂²×C₄	—	43	1	no	—
160	C₂²×C₄	—	43	1	no	—
161	C₂²×C₄	—	43	2	no	—
162	C₂²×C₄	—	43	2	no	—
163	C₂²×C₄	—	86	4	no	—
164	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
165	M₁₆	—	86	4	no	—
166	M₁₆	—	86	4	no	—
167	C₂×C₈	—	43	2	no	—
168	C₂×C₈	—	43	2	no	—
169	C₂×C₈	C₂²×D₄₃	1	2	yes	—
170	C₂×C₈	C₂²×D₄₃	1	2	yes	—
171	C₄⋊C₄	—	43	2	no	—
172	C₄⋊C₄	—	43	2	no	—
173	C₄⋊C₄	—	43	2	no	—
174	C₄⋊C₄	C₄×D₄₃	1	2	yes	—
175	C₂²⋊C₄	—	43	2	no	—
176	C₂²⋊C₄	—	43	2	no	—
177	C₂²⋊C₄	—	43	2	no	—
178	C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
179	C₄²	—	43	2	no	—
180	C₄²	—	43	2	no	—
181	C₄²	—	43	1	no	—
182	C₄²	—	43	1	no	—
183	C₄²	C₂²×D₄₃	1	1	yes	characteristic
184	C₄²	C₂²×D₄₃	1	1	yes	characteristic
185	C₂³	—	43	1	no	—
186	C₂³	—	43	1	no	—
187	C₂³	—	86	2	no	—
188	C₂³	—	172	2	no	—
189	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	43	1	no	—
192	C₂×C₄	—	43	4	no	—
193	C₂×C₄	—	43	2	no	—
194	C₂×C₄	—	43	2	no	—
195	C₂×C₄	—	43	1	no	—
196	C₂×C₄	—	86	2	no	—
197	C₂×C₄	—	86	2	no	—
198	C₂×C₄	—	86	2	no	—
199	C₂×C₄	—	86	2	no	—
200	C₂×C₄	—	172	2	no	—
201	C₂×C₄	—	172	2	no	—
202	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
203	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
204	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
205	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
206	C₈	—	2	2	no	—
207	C₈	—	2	2	no	—
208	C₈	—	86	2	no	—
209	C₈	—	86	2	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	43	2	no	—
213	C₂²	—	86	2	no	—
214	C₂²	—	86	1	no	—
215	C₂²	—	86	2	no	—
216	C₂²	—	172	4	no	—
217	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	2	2	no	—
220	C₄	—	2	2	no	—
221	C₄	—	43	2	no	—
222	C₄	—	86	1	no	—
223	C₄	—	86	2	no	—
224	C₄	—	86	2	no	—
225	C₄	#41×D₄₃	1	2	yes	—
226	C₂	—	4	1	no	—
227	C₂	—	86	2	no	—
228	C₂	—	172	1	no	—
229	C₂	#117×D₄₃	1	1	yes	characteristic
230	C₂	#14583664	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#433	C₂
hypercenter	#433	D₄₃
hypocenter	C₄₃	#2921
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
2. #14582961	C₂	semidirect
3. #14582960	C₂	semidirect
4. #14582959	C₂	semidirect
5. #14582958	C₂	semidirect
6. #14582957	C₂	semidirect
7. #14582921	C₂	semidirect
9. #14582851	C₂	semidirect
10. C₄×#10621872	C₂	semidirect
11. C₄₃×#433	C₂	semidirect
24. C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
25. Dic₄₃⋊C₈	C₂²	semidirect
26. Dic₄₃⋊C₈	C₂²	semidirect
30. #13063236	C₂²	semidirect
31. #13063235	C₂²	semidirect
32. C₄×C₄₃⋊C₈	C₂²	semidirect
33. C₈×Dic₄₃	C₂²	semidirect
35. C₄⋊C₈×C₄₃	C₂²	semidirect
37. #97×C₄₃	C₂²	semidirect
38. C₄×C₈×C₄₃	C₂²	semidirect
122. #433	D₄₃	semidirect
127. C₄₃	#2921	semidirect
144. C₄⋊C₈	C₂×D₄₃	semidirect
151. #97	C₂×D₄₃	semidirect
154. C₄×C₈	C₂×D₄₃	semidirect