Subgroups — #25014606

Order 11008.

298 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	C₂×#14582719	C₂	1	1	yes	maximal, characteristic
2	#19136355	C₂	1	1	yes	maximal, characteristic
3	#19136354	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
5	#19134475	C₂	1	1	yes	maximal, characteristic
6	#19132683	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1379	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063265	C₂²	1	1	yes	characteristic
9	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×#13063260	C₄	1	1	yes	characteristic
11	#14582935	C₄	1	1	yes	characteristic
12	#14582854	C₂²	1	1	yes	characteristic
13	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
14	#14582719	—	2	2	no	—
15	C₄⋊(C₄₃⋊C₁₆)	—	2	2	no	—
16	Dic₄₃⋊C₁₆	—	2	2	no	—
17	C₁₆×Dic₄₃	—	2	2	no	—
18	#14582660	C₄	1	1	yes	characteristic
19	#14582658	C₄	1	1	yes	characteristic
20	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#405	C₂²	1	1	yes	characteristic
23	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
25	#13063284	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
27	#13063265	—	2	1	no	—
28	#13063265	—	2	1	no	—
29	C₂×C₄₃⋊C₁₆	—	2	1	no	—
30	C₂×C₄₃⋊C₁₆	—	2	1	no	—
31	C₂×C₄₃⋊C₁₆	—	2	1	no	—
32	C₂×C₄₃⋊C₁₆	D₄	1	2	yes	—
33	#13063260	—	2	2	no	—
34	#13063258	C₈	1	2	yes	—
35	#13063256	C₈	1	2	yes	—
36	#13063235	—	2	1	no	—
37	C₈×Dic₄₃	—	2	1	no	—
38	C₈×Dic₄₃	D₄	1	2	yes	—
39	C₈×Dic₄₃	Q₈	1	2	yes	—
40	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
42	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
43	M₃₂×C₄₃	—	2	1	no	—
44	M₃₂×C₄₃	—	2	1	no	—
45	C₂×C₁₆×C₄₃	—	2	1	no	—
46	C₂×C₁₆×C₄₃	—	2	1	no	—
47	C₂×C₁₆×C₄₃	—	2	1	no	—
48	C₂×C₁₆×C₄₃	Q₈	1	2	yes	—
49	#97×C₄₃	—	2	1	no	—
50	C₄×C₈×C₄₃	—	2	1	no	—
51	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
52	C₂²×Dic₄₃	—	2	1	no	—
53	M₁₆×C₄₃	—	2	1	no	—
54	M₁₆×C₄₃	—	2	1	no	—
55	C₂×C₈×C₄₃	—	2	1	no	—
56	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
60	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
61	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
62	C₄⋊C₄×C₄₃	C₂×C₈	1	2	yes	—
63	C₂²⋊C₄×C₄₃	—	2	1	no	—
64	C₄²×C₄₃	—	2	1	no	—
65	C₂²⋊Dic₄₃	—	2	1	no	—
66	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	—
67	C₄×Dic₄₃	—	2	1	no	—
68	C₄×Dic₄₃	—	2	1	no	—
69	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
70	#10621877	—	2	1	no	—
71	#10621877	—	2	1	no	—
72	C₂×C₄₃⋊C₈	—	2	1	no	—
73	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
74	C₂×C₄₃⋊C₈	C₂×C₈	1	1	yes	characteristic
75	C₂×C₄₃⋊C₈	C₂×C₈	1	1	yes	characteristic
76	C₂×C₄₃⋊C₈	M₁₆	1	2	yes	—
77	C₁₆×C₄₃	—	2	2	no	—
78	C₁₆×C₄₃	—	4	1	no	—
79	C₄₃⋊C₁₆	—	2	2	no	—
80	C₄₃⋊C₁₆	—	4	1	no	—
81	C₂³×C₄₃	#131	1	1	yes	characteristic
82	C₂×C₄×C₄₃	—	2	2	no	—
83	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
87	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
88	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
89	C₂×Dic₄₃	—	2	4	no	—
90	C₂×Dic₄₃	—	2	2	no	—
91	C₂×Dic₄₃	—	2	2	no	—
92	C₈×C₄₃	—	4	1	no	—
93	C₈×C₄₃	#121	1	1	yes	characteristic
94	C₈×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
95	C₈×C₄₃	#125	1	1	yes	characteristic
96	C₈×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
97	C₄₃⋊C₈	—	4	1	no	—
98	C₄₃⋊C₈	C₄⋊C₈	1	2	yes	—
99	C₄₃⋊C₈	C₄⋊C₈	1	2	yes	—
100	#13161	—	43	1	no	maximal, Sylow
101	C₂²×C₄₃	—	2	2	no	—
102	C₂²×C₄₃	#424	1	1	yes	characteristic
103	C₂²×C₄₃	C₈×D₄	1	1	yes	characteristic
104	C₂²×C₄₃	#446	1	1	yes	characteristic
105	C₄×C₄₃	—	4	2	no	—
106	C₄×C₄₃	#389	1	1	yes	characteristic
107	C₄×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
108	C₄×C₄₃	#436	1	1	yes	characteristic
109	C₄×C₄₃	C₈×Q₈	1	1	yes	characteristic
110	Dic₄₃	—	2	4	no	—
111	Dic₄₃	—	4	2	no	—
112	C₂×#364	—	43	1	no	—
113	#2151	—	43	1	no	—
114	#2151	—	43	1	no	—
115	C₂×C₄×C₁₆	—	43	1	no	—
116	#1772	—	43	1	no	—
117	#1379	—	43	1	no	—
118	#1379	D₄₃	1	1	yes	characteristic
119	C₂×C₄₃	—	2	1	no	—
120	C₂×C₄₃	—	2	1	no	—
121	C₂×C₄₃	#1939	1	1	yes	characteristic
122	C₂×C₄₃	#2170	1	2	yes	—
123	C₂×M₃₂	—	43	1	no	—
124	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
125	C₂²×C₁₆	—	43	1	no	—
126	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
127	C₂×#108	—	43	1	no	—
128	#427	—	43	1	no	—
129	#405	—	43	1	no	—
130	#405	C₂×D₄₃	1	1	yes	characteristic
131	C₂×C₄×C₈	—	43	1	no	—
132	#364	—	86	2	no	—
133	C₄⋊C₁₆	—	86	2	no	—
134	C₄⋊C₁₆	—	86	2	no	—
135	C₄×C₁₆	—	86	2	no	—
136	#339	—	43	1	no	—
137	#339	—	43	1	no	—
138	C₄₃	#13161	1	1	yes	characteristic, complemented, Sylow
139	C₂×M₁₆	—	43	1	no	—
140	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
141	C₂²×C₈	—	43	1	no	—
142	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
143	#117	—	43	1	no	—
144	#117	C₄×D₄₃	1	1	yes	characteristic
145	C₂×C₄²	—	43	1	no	—
146	M₃₂	—	2	1	no	—
147	M₃₂	—	2	1	no	—
148	M₃₂	—	86	1	no	—
149	M₃₂	—	86	1	no	—
150	C₂×C₁₆	—	2	1	no	—
151	C₂×C₁₆	—	2	1	no	—
152	C₂×C₁₆	—	2	1	no	—
153	C₂×C₁₆	—	43	2	no	—
154	C₂×C₁₆	—	86	1	no	—
155	C₂×C₁₆	—	86	1	no	—
156	C₂×C₁₆	—	86	1	no	—
157	C₂×C₁₆	Dic₈₆	1	2	yes	—
158	#108	—	86	2	no	—
159	#107	—	43	2	no	—
160	#106	—	43	2	no	—
161	#97	—	2	1	no	—
162	#97	—	86	1	no	—
163	C₄×C₈	—	2	1	no	—
164	C₄×C₈	—	43	2	no	—
165	C₄×C₈	—	43	2	no	—
166	C₄×C₈	—	86	1	no	—
167	C₂²×C₄	—	86	1	no	—
168	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
169	M₁₆	—	2	1	no	—
170	M₁₆	—	2	1	no	—
171	M₁₆	—	86	1	no	—
172	M₁₆	—	86	1	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	43	2	no	—
175	C₂×C₈	—	43	1	no	—
176	C₂×C₈	—	43	1	no	—
177	C₂×C₈	—	43	2	no	—
178	C₂×C₈	—	86	1	no	—
179	C₂×C₈	C₂×Dic₈₆	1	1	yes	characteristic
180	C₂×C₈	#10621898	1	1	yes	characteristic
181	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
182	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
183	C₂×C₈	#10621900	1	1	yes	characteristic
184	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
185	C₄⋊C₄	—	43	2	no	—
186	C₄⋊C₄	C₈×D₄₃	1	2	yes	—
187	C₂²⋊C₄	—	2	1	no	—
188	C₂²⋊C₄	—	86	1	no	—
189	C₄²	—	2	1	no	—
190	C₄²	—	43	2	no	—
191	C₄²	—	86	1	no	—
192	C₄²	—	86	1	no	—
193	C₁₆	—	2	2	no	—
194	C₁₆	—	4	1	no	—
195	C₁₆	—	86	2	no	—
196	C₁₆	—	172	1	no	—
197	C₂³	#13063333	1	1	yes	characteristic
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	86	4	no	—
200	C₂×C₄	—	86	2	no	—
201	C₂×C₄	—	86	2	no	—
202	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
203	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
205	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
206	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
207	C₂×C₄	#13063331	1	1	yes	characteristic
208	C₈	—	4	1	no	—
209	C₈	—	43	2	no	—
210	C₈	—	43	2	no	—
211	C₈	—	172	1	no	—
212	C₈	#13063298	1	1	yes	characteristic
213	C₈	#13063302	1	1	yes	characteristic
214	C₈	#13063315	1	1	yes	characteristic
215	C₈	#13063324	1	1	yes	characteristic
216	C₂²	—	2	2	no	—
217	C₂²	#14582924	1	1	yes	characteristic
218	C₂²	(C₂²⋊D₄₃)⋊C₈	1	1	yes	characteristic
219	C₂²	#14583027	1	1	yes	characteristic
220	C₄	—	4	2	no	—
221	C₄	—	86	4	no	—
222	C₄	—	172	2	no	—
223	C₄	#14582796	1	1	yes	characteristic
224	C₄	C₄⋊C₈×D₄₃	1	1	yes	characteristic
225	C₄	#14582974	1	1	yes	characteristic
226	C₄	C₈×Dic₈₆	1	1	yes	characteristic
227	C₂	—	2	1	no	—
228	C₂	—	2	1	no	—
229	C₂	#19135312	1	1	yes	characteristic
230	C₂	#19136429	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1379	C₂
socle	C₂²×C₄₃	C₈×D₄
prime radical	C₂³×C₄₃	#131
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1379	D₄₃
hypocenter	C₄₃	#13161
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1379

Complements

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

N	H ≅ G/N	type
138. C₄₃	#13161	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582719	2
#19136355	2
#19136354	2
C₂×C₁₆×Dic₄₃	2
#19134475	2
#19132683	2
C₄₃×#1379	2
#13161	43