Subgroups — #25093945

Order 11008.

1470 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582857	C₂	1	4	yes	maximal
2	C₂²×#13063236	C₂	1	1	yes	maximal, characteristic
3	C₄×#13063284	C₂	1	1	yes	maximal, characteristic
4	#19134281	C₂	1	4	yes	maximal, complemented
5	#97×Dic₄₃	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
8	C₂×#13063284	C₂²	1	2	yes	—
9	#14582857	C₄	1	32	yes	complemented
10	C₂×#13063236	C₄	1	8	yes	complemented
11	C₂×#13063236	C₂²	1	2	yes	—
12	C₂×#13063236	C₂²	1	2	yes	—
13	C₂×#13063235	C₂²	1	8	yes	—
14	C₂×C₈×Dic₄₃	C₂²	1	8	yes	—
15	C₄×C₄⋊Dic₄₃	C₄	1	4	yes	—
16	C₄×C₂²⋊Dic₄₃	C₄	1	4	yes	—
17	#14582745	C₂²	1	2	yes	—
18	C₄²×Dic₄₃	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄×M₁₆×C₄₃	C₄	1	8	yes	complemented
22	C₂×#97×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
24	C₂²×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	16	yes	—
26	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
27	#13063284	C₂×C₄	1	16	yes	—
28	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
29	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	4	yes	—
30	C₂×C₄×Dic₄₃	C₂×C₄	1	8	yes	—
31	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
32	#13063236	C₂×C₄	1	8	yes	—
33	#13063236	C₂×C₄	1	8	yes	—
34	#13063235	C₂×C₄	1	32	yes	complemented
35	C₈×Dic₄₃	C₂×C₄	1	32	yes	complemented
36	C₄₃⋊#95	C₂×C₄	1	8	yes	—
37	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₄₃	C₂×C₄	1	16	yes	—
40	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	—
41	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
42	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
47	#97×C₄₃	C₂×C₄	1	8	yes	—
48	C₄×C₈×C₄₃	C₂×C₄	1	8	yes	—
49	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₃	—	4	4	no	—
51	C₂²×C₄×C₄₃	C₄²	1	8	yes	—
52	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
53	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
54	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
56	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
57	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
59	C₂²×Dic₄₃	C₂²×C₄	1	8	yes	—
60	M₁₆×C₄₃	C₄²	1	32	yes	complemented
61	C₂×C₈×C₄₃	C₂²×C₄	1	16	yes	—
62	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	—
63	C₄²×C₄₃	C₄²	1	8	yes	—
64	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
65	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
66	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
67	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
68	C₂²⋊Dic₄₃	C₄²	1	16	yes	—
69	C₄⋊Dic₄₃	C₄²	1	16	yes	—
70	C₄×Dic₄₃	—	4	8	no	—
71	C₄×Dic₄₃	C₂²×C₄	1	16	yes	—
72	C₂×C₄₃⋊C₈	C₄²	1	32	yes	complemented
73	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
74	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
75	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
76	C₂³×C₄₃	—	2	4	no	—
77	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
78	C₂³×C₄₃	C₂×C₄²	1	2	yes	—
79	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
80	C₂×C₄×C₄₃	—	2	4	no	—
81	C₂×C₄×C₄₃	—	2	4	no	—
82	C₂×C₄×C₄₃	—	4	8	no	—
83	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
84	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
85	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
86	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
87	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
88	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
89	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
90	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
91	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
92	C₂×Dic₄₃	—	2	16	no	—
93	C₂×Dic₄₃	C₂×C₄²	1	16	yes	—
94	C₈×C₄₃	C₂×C₄²	1	16	yes	—
95	C₄₃⋊C₈	C₂×C₄²	1	16	yes	—
96	#20331	—	43	1	no	maximal, Sylow
97	C₂²×C₄₃	—	2	4	no	—
98	C₂²×C₄₃	—	2	8	no	—
99	C₂²×C₄₃	C₄³	1	4	yes	—
100	C₂²×C₄₃	C₂²×C₄²	1	2	yes	—
101	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
102	C₂²×C₄₃	#568	1	4	yes	—
103	C₄×C₄₃	—	2	4	no	—
104	C₄×C₄₃	—	2	4	no	—
105	C₄×C₄₃	C₄³	1	4	yes	—
106	C₄×C₄₃	C₂²×C₄²	1	2	yes	—
107	C₄×C₄₃	C₂²×C₄²	1	2	yes	—
108	Dic₄₃	—	2	16	no	—
109	C₂×#405	—	43	4	no	—
110	C₂×C₄×M₁₆	D₄₃	1	1	yes	characteristic
111	C₂²×#97	—	43	1	no	—
112	C₄×#117	—	43	1	no	—
113	#1726	—	43	4	no	—
114	C₄×#97	—	43	4	no	—
115	C₂×C₄₃	—	2	4	no	—
116	C₂×C₄₃	C₂×C₄³	1	1	yes	characteristic
117	C₂×C₄₃	#2873	1	2	yes	—
118	C₂×C₄₃	#2875	1	4	yes	—
119	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
120	C₂³×C₈	—	43	2	no	—
121	C₂×#117	—	43	2	no	—
122	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
123	#405	—	43	32	no	—
124	C₄×M₁₆	Dic₄₃	1	8	yes	complemented
125	C₂×#97	—	43	8	no	—
126	C₂×#97	—	43	2	no	—
127	C₂×#97	—	43	2	no	—
128	C₂×#97	—	43	8	no	—
129	C₂×#97	C₂×D₄₃	1	2	yes	—
130	C₂×C₄×C₈	—	43	8	no	—
131	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
132	C₄×C₄⋊C₄	—	43	4	no	—
133	C₄×C₂²⋊C₄	—	43	4	no	—
134	#376	—	43	2	no	—
135	C₄³	—	43	2	no	—
136	C₄₃	#20331	1	1	yes	characteristic, complemented, Sylow
137	C₂³×C₄	C₄×D₄₃	1	2	yes	—
138	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
139	C₂×M₁₆	C₄×D₄₃	1	16	yes	—
140	C₂×M₁₆	C₂×Dic₄₃	1	8	yes	—
141	C₂²×C₈	—	43	8	no	—
142	C₂²×C₈	—	43	16	no	—
143	C₂²×C₈	—	43	4	no	—
144	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
145	#117	—	43	16	no	—
146	C₂×C₄⋊C₄	—	43	4	no	—
147	C₂×C₂²⋊C₄	—	43	4	no	—
148	C₂×C₄²	—	43	4	no	—
149	C₂×C₄²	—	43	8	no	—
150	C₂×C₄²	C₄×D₄₃	1	2	yes	—
151	C₂×C₄²	C₄×D₄₃	1	4	yes	—
152	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
153	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
154	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
155	#97	—	43	32	no	—
156	#97	—	43	8	no	—
157	#97	—	43	8	no	—
158	#97	C₂×Dic₄₃	1	8	yes	—
159	C₄×C₈	—	43	32	no	—
160	C₄×C₈	C₂×Dic₄₃	1	8	yes	—
161	#95	—	43	8	no	—
162	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
163	C₂²×C₄	—	4	4	no	—
164	C₂²×C₄	—	43	8	no	—
165	C₂²×C₄	C₄×Dic₄₃	1	8	yes	—
166	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
167	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
168	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
170	C₂²×C₄	C₂×C₄×D₄₃	1	8	yes	—
171	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
172	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
173	M₁₆	C₄×Dic₄₃	1	32	yes	complemented
174	C₂×C₈	—	43	32	no	—
175	C₂×C₈	—	43	8	no	—
176	C₂×C₈	—	43	8	no	—
177	C₂×C₈	—	43	8	no	—
178	C₂×C₈	C₂×C₄×D₄₃	1	16	yes	—
179	C₂×C₈	C₂²×Dic₄₃	1	8	yes	—
180	C₄⋊C₄	—	43	16	no	—
181	C₂²⋊C₄	—	43	16	no	—
182	C₄²	—	43	16	no	—
183	C₄²	—	172	8	no	—
184	C₄²	C₄×Dic₄₃	1	8	yes	—
185	C₄²	C₂×C₄×D₄₃	1	2	yes	—
186	C₄²	C₂×C₄×D₄₃	1	2	yes	—
187	C₄²	C₂²×Dic₄₃	1	2	yes	—
188	C₄²	C₂²×Dic₄₃	1	2	yes	—
189	C₂³	—	2	4	no	—
190	C₂³	C₄²×D₄₃	1	4	yes	—
191	C₂³	C₂×C₄×Dic₄₃	1	2	yes	—
192	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	4	8	no	—
196	C₂×C₄	—	43	16	no	—
197	C₂×C₄	—	86	16	no	—
198	C₂×C₄	C₄²×D₄₃	1	8	yes	—
199	C₂×C₄	C₄²×D₄₃	1	4	yes	—
200	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
201	C₂×C₄	C₂×C₄×Dic₄₃	1	4	yes	—
202	C₂×C₄	C₂×C₄×Dic₄₃	1	8	yes	—
203	C₂×C₄	C₂×C₄×Dic₄₃	1	2	yes	—
204	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
205	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
206	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
207	C₈	—	43	16	no	—
208	C₈	C₂×C₄×Dic₄₃	1	16	yes	—
209	C₂²	—	2	4	no	—
210	C₂²	—	2	8	no	—
211	C₂²	C₄²×Dic₄₃	1	4	yes	—
212	C₂²	C₂×C₄²×D₄₃	1	2	yes	—
213	C₂²	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
214	C₂²	#14583665	1	4	yes	—
215	C₄	—	2	4	no	—
216	C₄	—	2	4	no	—
217	C₄	—	86	16	no	—
218	C₄	C₄²×Dic₄₃	1	4	yes	—
219	C₄	C₂×C₄²×D₄₃	1	2	yes	—
220	C₄	C₂²×C₄×Dic₄₃	1	2	yes	—
221	C₂	—	2	4	no	—
222	C₂	C₂×C₄²×Dic₄₃	1	1	yes	characteristic
223	C₂	#19143013	1	2	yes	—
224	C₂	#19143024	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂×C₄₃	C₂×C₄³
Fitting	C₂×C₄×M₁₆×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₄₃
hypocenter	C₄₃	#20331
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #19134281	C₂	semidirect
5. #97×Dic₄₃	C₂	semidirect
9. #14582857	C₄	semidirect
10. C₂×#13063236	C₄	semidirect
21. C₄×M₁₆×C₄₃	C₄	semidirect
34. #13063235	C₂×C₄	semidirect
35. C₈×Dic₄₃	C₂×C₄	semidirect
60. M₁₆×C₄₃	C₄²	semidirect
72. C₂×C₄₃⋊C₈	C₄²	semidirect
124. C₄×M₁₆	Dic₄₃	semidirect
136. C₄₃	#20331	semidirect
173. M₁₆	C₄×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582857	2
C₂²×#13063236	2
C₄×#13063284	2
#19134281	2
#97×Dic₄₃	2
C₂×C₄×M₁₆×C₄₃	2
#20331	43