Subgroups — #19143391

Order 5504.

492 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063345	C₂	1	1	yes	maximal, characteristic
2	#41×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583367	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583008	C₂	1	2	yes	maximal, complemented
5	#14583003	C₂	1	2	yes	maximal, complemented
6	#14583002	C₂	1	2	yes	maximal, complemented
7	#14582996	C₂	1	2	yes	maximal, complemented
8	#14582935	C₂	1	1	yes	maximal, characteristic, complemented
9	#14582896	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10621898	C₂²	1	1	yes	characteristic
13	#13063345	C₄	1	8	yes	complemented
14	C₂×#10621885	C₂²	1	1	yes	characteristic
15	C₂×#10621883	C₂²	1	1	yes	characteristic
16	C₂×#10621884	C₂²	1	1	yes	characteristic
17	C₂×#10621882	C₂²	1	1	yes	characteristic
18	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×Dic₄₃	C₂²	1	2	yes	—
20	#13063290	C₂²	1	2	yes	—
21	D₄×Dic₄₃	—	2	2	no	—
22	D₄×Dic₄₃	C₂²	1	2	yes	—
23	#13063287	C₂²	1	2	yes	—
24	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
25	#13063284	—	2	1	no	—
26	#13063284	C₂²	1	1	yes	characteristic
27	#13063282	—	2	1	no	—
28	C₂×C₄×Dic₄₃	—	2	1	no	—
29	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
30	C₄²×D₄₃	—	2	1	no	—
31	#13063258	C₂²	1	2	yes	—
32	#13063256	C₂²	1	2	yes	—
33	#13063250	C₂²	1	2	yes	—
34	#13063247	C₂²	1	2	yes	—
35	#13063235	C₂²	1	2	yes	—
36	#13063235	C₂²	1	2	yes	—
37	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
38	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	#117×C₄₃	C₂²	1	1	yes	characteristic
40	#103×C₄₃	C₂²	1	2	yes	—
41	#102×C₄₃	C₂²	1	2	yes	—
42	#41×C₄₃	—	2	2	no	—
43	#41×C₄₃	C₂×C₄	1	4	yes	complemented
44	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×D₄×C₄₃	—	2	1	no	—
46	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×C₄×C₄₃	—	2	1	no	—
48	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×C₂²⋊D₄₃	—	2	1	no	—
50	C₂²×Dic₄₃	—	2	2	no	—
51	C₂²×Dic₄₃	D₄	1	2	yes	—
52	#10621898	—	2	2	no	—
53	#10621898	C₂×C₄	1	4	yes	complemented
54	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
55	C₂×C₄×D₄₃	—	2	1	no	—
56	C₂×C₄×D₄₃	—	2	2	no	—
57	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
58	C₂×C₈×C₄₃	—	2	2	no	—
59	C₂×C₈×C₄₃	C₂³	1	2	yes	—
60	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂²⋊C₄×C₄₃	—	2	1	no	—
62	C₄²×C₄₃	—	2	1	no	—
63	C₂²⋊Dic₄₃	—	2	2	no	—
64	C₂²⋊Dic₄₃	—	2	1	no	—
65	#10621885	C₂×C₄	1	4	yes	complemented
66	#10621884	C₂×C₄	1	4	yes	complemented
67	#10621883	C₂×C₄	1	4	yes	complemented
68	#10621882	C₂×C₄	1	4	yes	complemented
69	(C₂×D₄₃)⋊C₄	—	2	2	no	—
70	C₄⋊Dic₄₃	—	2	2	no	—
71	C₄⋊Dic₄₃	C₂³	1	2	yes	—
72	Dic₄₃⋊C₄	—	2	2	no	—
73	C₄×Dic₄₃	—	2	1	no	—
74	C₄×Dic₄₃	—	2	2	no	—
75	C₄×Dic₄₃	—	2	2	no	—
76	C₄×Dic₄₃	D₄	1	1	yes	characteristic
77	C₄×Dic₄₃	D₄	1	1	yes	characteristic
78	C₄×Dic₄₃	C₂³	1	2	yes	—
79	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	complemented
80	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂³×C₄₃	—	2	1	no	—
83	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×D₄₃	—	2	1	no	—
85	Q₈×C₄₃	—	2	1	no	—
86	Q₈×C₄₃	C₂²×C₄	1	2	yes	—
87	D₄×C₄₃	—	2	4	no	—
88	D₄×C₄₃	—	2	1	no	—
89	D₄×C₄₃	C₂²×C₄	1	2	yes	—
90	C₂×C₄×C₄₃	—	2	1	no	—
91	C₂×C₄×C₄₃	—	2	4	no	—
92	C₂×C₄×C₄₃	—	2	2	no	—
93	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
94	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×C₄₃	#41	1	2	yes	—
96	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
97	C₂²⋊D₄₃	—	2	4	no	—
98	C₂×Dic₄₃	—	2	1	no	—
99	C₂×Dic₄₃	—	2	2	no	—
100	C₂×Dic₄₃	—	4	2	no	—
101	C₂×Dic₄₃	—	4	4	no	—
102	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
103	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
104	D₁₇₂	—	2	1	no	—
105	D₁₇₂	C₂²×C₄	1	2	yes	—
106	C₄×D₄₃	—	2	4	no	—
107	C₄×D₄₃	—	4	4	no	—
108	Dic₈₆	—	2	1	no	—
109	Dic₈₆	C₂²×C₄	1	2	yes	—
110	C₈×C₄₃	—	2	2	no	—
111	C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
112	C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
113	C₂²×C₄₃	—	2	2	no	—
114	C₂²×C₄₃	—	2	2	no	—
115	C₂²×C₄₃	—	4	2	no	—
116	C₂²×C₄₃	C₄×D₄	1	2	yes	—
117	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
118	C₂×D₄₃	—	2	2	no	—
119	C₂×D₄₃	—	4	2	no	—
120	C₄×C₄₃	—	2	2	no	—
121	C₄×C₄₃	—	4	2	no	—
122	C₄×C₄₃	C₄×D₄	1	2	yes	—
123	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
124	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
125	Dic₄₃	—	2	2	no	—
126	Dic₄₃	—	2	2	no	—
127	Dic₄₃	—	2	2	no	—
128	Dic₄₃	—	4	2	no	—
129	#2943	—	43	1	no	maximal, Sylow
130	C₂×C₄₃	—	2	2	no	—
131	C₂×C₄₃	—	4	2	no	—
132	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
133	C₂×C₄₃	#575	1	2	yes	—
134	D₄₃	—	4	2	no	—
135	C₂×#135	—	43	1	no	—
136	C₄×#41	—	43	1	no	—
137	C₄×#41	—	43	1	no	—
138	#442	—	43	2	no	—
139	#441	—	43	2	no	—
140	#440	—	43	2	no	—
141	#440	—	43	2	no	—
142	#427	—	43	1	no	—
143	#416	—	43	1	no	—
144	#416	D₄₃	1	1	yes	characteristic, complemented
145	C₂×#97	—	43	1	no	—
146	C₄₃	#2943	1	1	yes	characteristic, complemented, Sylow
147	C₂×#41	—	43	1	no	—
148	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
149	#135	—	43	8	no	—
150	C₂×Q₁₆	—	43	1	no	—
151	C₂×SD₁₆	—	43	1	no	—
152	C₂×SD₁₆	—	43	1	no	—
153	C₂×D₈	—	43	1	no	—
154	C₂²×C₈	—	43	1	no	—
155	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
156	C₄×Q₈	—	43	2	no	—
157	C₄×Q₈	—	43	2	no	—
158	C₄×D₄	—	43	2	no	—
159	C₄×D₄	—	43	2	no	—
160	C₄×D₄	—	86	2	no	—
161	C₄×D₄	—	86	2	no	—
162	#117	—	43	1	no	—
163	#117	—	86	1	no	—
164	#117	—	86	1	no	—
165	#117	C₂×D₄₃	1	1	yes	characteristic
166	C₂×C₄²	—	43	1	no	—
167	C₂×C₄²	—	86	1	no	—
168	C₂×C₄²	—	86	1	no	—
169	#107	—	43	2	no	—
170	#106	—	43	2	no	—
171	#103	—	43	2	no	—
172	#103	C₂×D₄₃	1	2	yes	—
173	#102	—	43	2	no	—
174	#102	C₂×D₄₃	1	2	yes	—
175	#97	—	43	2	no	—
176	#97	—	43	2	no	—
177	#41	—	2	2	no	—
178	#41	—	43	4	no	—
179	#41	—	86	2	no	—
180	#41	C₄×D₄₃	1	4	yes	complemented
181	C₂×Q₈	—	43	1	no	—
182	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
183	C₂×D₄	—	2	1	no	—
184	C₂×D₄	—	43	1	no	—
185	C₂×D₄	—	86	1	no	—
186	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	43	2	no	—
189	C₂²×C₄	—	86	2	no	—
190	C₂²×C₄	—	86	2	no	—
191	C₂²×C₄	—	86	1	no	—
192	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
193	Q₁₆	—	43	4	no	—
194	SD₁₆	—	43	4	no	—
195	SD₁₆	—	43	4	no	—
196	D₈	—	43	4	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	43	4	no	—
199	C₂×C₈	—	43	1	no	—
200	C₂×C₈	—	43	1	no	—
201	C₂×C₈	C₂²×D₄₃	1	2	yes	—
202	C₄⋊C₄	—	43	2	no	—
203	C₄⋊C₄	—	86	2	no	—
204	C₄⋊C₄	—	86	2	no	—
205	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
206	C₂²⋊C₄	—	2	1	no	—
207	C₂²⋊C₄	—	86	2	no	—
208	C₂²⋊C₄	—	86	2	no	—
209	C₂²⋊C₄	—	86	1	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	43	1	no	—
212	C₄²	—	43	1	no	—
213	C₄²	—	43	2	no	—
214	C₄²	—	86	2	no	—
215	C₄²	—	86	2	no	—
216	C₄²	—	86	1	no	—
217	C₂³	—	2	1	no	—
218	C₂³	—	86	1	no	—
219	C₂³	D₄×D₄₃	1	1	yes	characteristic
220	Q₈	—	2	1	no	—
221	Q₈	—	43	2	no	—
222	Q₈	—	86	1	no	—
223	Q₈	C₂×C₄×D₄₃	1	2	yes	—
224	D₄	—	2	4	no	—
225	D₄	—	2	1	no	—
226	D₄	—	43	2	no	—
227	D₄	—	86	4	no	—
228	D₄	—	86	1	no	—
229	D₄	C₂×C₄×D₄₃	1	2	yes	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	43	2	no	—
234	C₂×C₄	—	43	2	no	—
235	C₂×C₄	—	86	1	no	—
236	C₂×C₄	—	86	4	no	—
237	C₂×C₄	—	86	2	no	—
238	C₂×C₄	—	172	4	no	—
239	C₂×C₄	—	172	2	no	—
240	C₂×C₄	—	172	4	no	—
241	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
242	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
243	C₂×C₄	#10621900	1	2	yes	—
244	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
245	C₈	—	2	2	no	—
246	C₈	—	43	2	no	—
247	C₈	—	43	2	no	—
248	C₂²	—	2	2	no	—
249	C₂²	—	2	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	86	2	no	—
252	C₂²	—	172	2	no	—
253	C₂²	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
254	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
255	C₄	—	2	2	no	—
256	C₄	—	4	2	no	—
257	C₄	—	86	2	no	—
258	C₄	—	86	2	no	—
259	C₄	—	86	2	no	—
260	C₄	—	172	2	no	—
261	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
262	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
263	C₄	C₂×#10621900	1	1	yes	characteristic
264	C₂	—	2	2	no	—
265	C₂	—	4	2	no	—
266	C₂	—	172	2	no	—
267	C₂	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
268	C₂	#14583696	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#416	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#416	D₄₃
hypocenter	C₄₃	#2943
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #416

Complements

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

N	H ≅ G/N	type
2. #41×Dic₄₃	C₂	semidirect
3. #14583367	C₂	semidirect
4. #14583008	C₂	semidirect
5. #14583003	C₂	semidirect
6. #14583002	C₂	semidirect
7. #14582996	C₂	semidirect
8. #14582935	C₂	semidirect
9. #14582896	C₂	semidirect
10. C₂×#13063235	C₂	semidirect
11. C₄₃×#416	C₂	semidirect
13. #13063345	C₄	semidirect
43. #41×C₄₃	C₂×C₄	semidirect
53. #10621898	C₂×C₄	semidirect
65. #10621885	C₂×C₄	semidirect
66. #10621884	C₂×C₄	semidirect
67. #10621883	C₂×C₄	semidirect
68. #10621882	C₂×C₄	semidirect
79. C₂×C₄₃⋊C₈	C₂×C₄	semidirect
144. #416	D₄₃	semidirect
146. C₄₃	#2943	semidirect
180. #41	C₄×D₄₃	semidirect