Subgroups — #19143285

Order 5504.

520 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063333	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583410	C₂	1	1	yes	maximal, characteristic
4	#14582967	C₂	1	4	yes	maximal, complemented
5	(C₂²⋊D₄₃)⋊C₈	C₂	1	4	yes	maximal, complemented
6	#14582927	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582867	C₂	1	1	yes	maximal, characteristic, complemented
8	#14582857	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10621898	C₂²	1	1	yes	characteristic
11	#13063333	—	2	4	no	—
12	C₂×#10621872	C₂²	1	2	yes	complemented
13	C₂²×C₄₃⋊C₈	—	2	4	no	—
14	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
16	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
17	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₄₃	C₂²	1	2	yes	complemented
19	#13063308	C₄	1	2	yes	—
20	#13063304	C₄	1	2	yes	—
21	#13063299	C₄	1	2	yes	—
22	#13063294	C₄	1	2	yes	—
23	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
24	#13063284	C₂²	1	1	yes	characteristic
25	Dic₄₃⋊C₈	C₂²	1	4	yes	complemented
26	(C₂×D₄₃)⋊C₈	C₂²	1	4	yes	complemented
27	#13063235	C₂²	1	2	yes	complemented
28	C₈×Dic₄₃	C₂²	1	2	yes	complemented
29	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
32	C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
33	C₂⁴×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	—	2	2	no	—
35	C₂²×C₄×C₄₃	—	2	2	no	—
36	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
37	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
39	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂×C₂²⋊D₄₃	C₂×C₄	1	4	yes	—
41	C₂×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
42	#10621898	—	2	2	no	—
43	#10621898	—	2	2	no	—
44	C₂×D₁₇₂	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₄₃	C₂³	1	2	yes	—
46	C₂×Dic₈₆	C₂×C₄	1	1	yes	characteristic
47	M₁₆×C₄₃	—	2	2	no	—
48	M₁₆×C₄₃	—	2	2	no	—
49	C₂×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂×C₈×C₄₃	C₂³	1	2	yes	—
51	C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
52	C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
53	(C₂×D₄₃)⋊C₄	C₂×C₄	1	4	yes	—
54	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
55	Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
56	C₄×Dic₄₃	C₂³	1	2	yes	—
57	C₂×C₄₃⋊C₈	—	2	2	no	—
58	C₂×C₄₃⋊C₈	—	2	4	no	—
59	C₂×C₄₃⋊C₈	—	2	4	no	—
60	C₂×C₄₃⋊C₈	D₄	1	4	yes	complemented
61	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
62	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
64	#10621872	—	2	4	no	—
65	C₈×D₄₃	—	2	4	no	—
66	C₂³×C₄₃	—	2	2	no	—
67	C₂³×C₄₃	—	2	4	no	—
68	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
69	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
70	C₂²×D₄₃	C₂²×C₄	1	2	yes	—
71	C₂×C₄×C₄₃	—	2	2	no	—
72	C₂×C₄×C₄₃	—	2	4	no	—
73	C₂×C₄×C₄₃	—	2	2	no	—
74	C₂×C₄×C₄₃	—	2	2	no	—
75	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
76	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
78	C₂×C₄×C₄₃	#41	1	2	yes	—
79	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
80	C₂²⋊D₄₃	—	2	4	no	—
81	C₂²⋊D₄₃	—	2	8	no	—
82	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
83	C₂×Dic₄₃	C₂²×C₄	1	2	yes	—
84	D₁₇₂	—	2	2	no	—
85	C₄×D₄₃	—	2	2	no	—
86	C₄×D₄₃	—	2	2	no	—
87	Dic₈₆	—	2	2	no	—
88	C₈×C₄₃	—	2	2	no	—
89	C₈×C₄₃	—	2	2	no	—
90	C₄₃⋊C₈	—	2	2	no	—
91	C₄₃⋊C₈	C₂×D₄	1	2	yes	—
92	C₄₃⋊C₈	C₂×D₄	1	2	yes	—
93	C₂²×C₄₃	—	2	8	no	—
94	C₂²×C₄₃	—	2	2	no	—
95	C₂²×C₄₃	—	2	2	no	—
96	C₂²×C₄₃	—	2	2	no	—
97	C₂²×C₄₃	C₄×D₄	1	2	yes	—
98	C₂²×C₄₃	#131	1	4	yes	complemented
99	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
100	C₂×D₄₃	—	2	2	no	—
101	C₂×D₄₃	—	2	4	no	—
102	C₄×C₄₃	—	2	2	no	—
103	C₄×C₄₃	C₄×D₄	1	2	yes	—
104	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
105	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
106	Dic₄₃	—	2	2	no	—
107	Dic₄₃	—	2	4	no	—
108	#2929	—	43	1	no	maximal, Sylow
109	C₂×C₄₃	—	2	2	no	—
110	C₂×C₄₃	—	2	4	no	—
111	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
112	C₂×C₄₃	C₂×#131	1	2	yes	—
113	D₄₃	—	4	2	no	—
114	C₂×#131	—	43	1	no	—
115	C₂³×C₈	—	43	1	no	—
116	#525	—	43	1	no	—
117	#435	—	43	4	no	—
118	C₈×D₄	—	43	4	no	—
119	#424	—	43	1	no	—
120	#408	—	43	1	no	—
121	#407	D₄₃	1	1	yes	characteristic, complemented
122	#405	—	43	1	no	—
123	C₄₃	#2929	1	1	yes	characteristic, complemented, Sylow
124	C₂×#41	—	43	1	no	—
125	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
126	#131	—	86	4	no	—
127	C₂×M₁₆	—	43	2	no	—
128	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
129	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
130	C₂²×C₈	—	43	1	no	—
131	C₂²×C₈	—	43	1	no	—
132	C₂²×C₈	—	43	2	no	—
133	C₂²×C₈	—	43	2	no	—
134	C₂²×C₈	—	43	2	no	—
135	C₂²×C₈	—	86	4	no	—
136	#123	—	43	2	no	—
137	C₂²⋊Q₈	—	43	2	no	—
138	#121	—	43	2	no	—
139	#120	—	43	2	no	—
140	C₄×D₄	—	43	4	no	—
141	#117	—	43	1	no	—
142	C₄⋊C₈	—	43	4	no	—
143	C₂²⋊C₈	—	43	4	no	—
144	C₂²⋊C₈	C₂×D₄₃	1	4	yes	—
145	#97	—	43	2	no	—
146	C₄×C₈	—	43	2	no	—
147	C₂⁴	C₄×D₄₃	1	1	yes	characteristic
148	#41	—	86	2	no	—
149	#41	—	86	2	no	—
150	C₂×Q₈	—	43	1	no	—
151	C₂×D₄	—	43	4	no	—
152	C₂×D₄	—	43	2	no	—
153	C₂×D₄	—	43	1	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	43	2	no	—
157	C₂²×C₄	C₄×D₄₃	1	2	yes	—
158	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
159	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
160	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
161	M₁₆	—	2	2	no	—
162	M₁₆	—	2	2	no	—
163	M₁₆	—	86	4	no	—
164	C₂×C₈	—	43	4	no	—
165	C₂×C₈	—	43	1	no	—
166	C₂×C₈	—	43	1	no	—
167	C₂×C₈	—	43	2	no	—
168	C₂×C₈	—	86	4	no	—
169	C₂×C₈	—	86	4	no	—
170	C₂×C₈	—	86	4	no	—
171	C₂×C₈	—	86	2	no	—
172	C₂×C₈	C₂²×D₄₃	1	2	yes	—
173	C₂×C₈	C₂²×D₄₃	1	2	yes	—
174	C₄⋊C₄	—	43	2	no	—
175	C₄⋊C₄	—	43	4	no	—
176	C₂²⋊C₄	—	43	2	no	—
177	C₂²⋊C₄	—	43	4	no	—
178	C₂²⋊C₄	—	43	4	no	—
179	C₄²	—	43	2	no	—
180	C₂³	—	2	2	no	—
181	C₂³	—	2	4	no	—
182	C₂³	—	43	2	no	—
183	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
184	C₂³	C₂×C₄×D₄₃	1	2	yes	—
185	Q₈	—	86	2	no	—
186	D₄	—	86	4	no	—
187	D₄	—	86	8	no	—
188	D₄	—	86	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	43	4	no	—
194	C₂×C₄	—	43	2	no	—
195	C₂×C₄	—	86	2	no	—
196	C₂×C₄	—	86	2	no	—
197	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
198	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
199	C₂×C₄	D₄×D₄₃	1	2	yes	—
200	C₂×C₄	#10621900	1	2	yes	—
201	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	—	2	2	no	—
204	C₈	—	43	2	no	—
205	C₈	—	43	2	no	—
206	C₈	—	86	2	no	—
207	C₂²	—	2	8	no	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	86	2	no	—
212	C₂²	—	86	4	no	—
213	C₂²	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
214	C₂²	#13063333	1	4	yes	complemented
215	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	86	2	no	—
218	C₄	—	86	4	no	—
219	C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
220	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
221	C₄	C₂×#10621900	1	1	yes	characteristic
222	C₂	—	2	2	no	—
223	C₂	—	2	4	no	—
224	C₂	—	172	2	no	—
225	C₂	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
226	C₂	C₂×#13063333	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₄
Fitting	C₄₃×#407	C₂
hypercenter	#407	D₄₃
hypocenter	C₄₃	#2929
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #407

Complements

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

N	H ≅ G/N	type
1. C₂×#13063333	C₂	semidirect
2. C₂³×C₄₃⋊C₈	C₂	semidirect
4. #14582967	C₂	semidirect
5. (C₂²⋊D₄₃)⋊C₈	C₂	semidirect
6. #14582927	C₂	semidirect
7. #14582867	C₂	semidirect
8. #14582857	C₂	semidirect
9. C₄₃×#407	C₂	semidirect
12. C₂×#10621872	C₂²	semidirect
18. C₂×C₈×D₄₃	C₂²	semidirect
25. Dic₄₃⋊C₈	C₂²	semidirect
26. (C₂×D₄₃)⋊C₈	C₂²	semidirect
27. #13063235	C₂²	semidirect
28. C₈×Dic₄₃	C₂²	semidirect
60. C₂×C₄₃⋊C₈	D₄	semidirect
98. C₂²×C₄₃	#131	semidirect
121. #407	D₄₃	semidirect
123. C₄₃	#2929	semidirect
214. C₂²	#13063333	semidirect