Subgroups — C₄₃×#17448 #24937465

Order 11008.

1646 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1490	C₂	1	4	yes	maximal, complemented
5	C₄₃×#1486	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1478	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₃	—	2	1	no	—
9	C₂×C₄×D₄×C₄₃	—	2	1	no	—
10	C₂×C₄×D₄×C₄₃	—	2	1	no	—
11	C₂×C₄×D₄×C₄₃	—	2	1	no	—
12	C₂×C₄×D₄×C₄₃	—	2	1	no	—
13	C₂×C₄×D₄×C₄₃	—	2	1	no	—
14	C₂×C₄×D₄×C₄₃	—	2	1	no	—
15	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
16	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
23	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#432	—	2	1	no	—
25	C₄₃×#432	—	2	1	no	—
26	C₄₃×#432	—	2	1	no	—
27	C₄₃×#432	C₂²	1	2	yes	complemented
28	C₄₃×#431	—	2	1	no	—
29	C₄₃×#431	C₂²	1	2	yes	complemented
30	C₄₃×#431	C₂²	1	2	yes	complemented
31	C₄₃×#431	C₂²	1	2	yes	complemented
32	C₄₃×#423	—	2	1	no	—
33	C₄₃×#423	C₂²	1	2	yes	complemented
34	C₄₃×#407	—	2	1	no	—
35	C₄₃×#407	—	2	1	no	—
36	C₄×M₁₆×C₄₃	—	2	1	no	—
37	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
38	C₄₃×D₄⋊C₈	C₂²	1	16	yes	complemented
39	C₂⁵×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	—	2	8	no	—
41	C₂²×D₄×C₄₃	—	2	1	no	—
42	C₂²×D₄×C₄₃	—	2	1	no	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
46	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	—	2	2	no	—
49	C₂³×C₄×C₄₃	—	2	2	no	—
50	C₂³×C₄×C₄₃	—	2	2	no	—
51	C₂³×C₄×C₄₃	—	2	2	no	—
52	C₂³×C₄×C₄₃	—	2	2	no	—
53	C₂³×C₄×C₄₃	—	2	2	no	—
54	C₂³×C₄×C₄₃	—	4	8	no	—
55	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₄₃	—	2	2	no	—
59	C₂×M₁₆×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₄×D₄×C₄₃	—	2	2	no	—
63	C₄×D₄×C₄₃	—	2	2	no	—
64	C₄×D₄×C₄₃	—	2	2	no	—
65	C₄×D₄×C₄₃	—	2	2	no	—
66	C₄×D₄×C₄₃	—	2	2	no	—
67	C₄×D₄×C₄₃	—	2	2	no	—
68	C₄×D₄×C₄₃	—	2	2	no	—
69	C₄×D₄×C₄₃	—	2	2	no	—
70	C₄×D₄×C₄₃	—	2	2	no	—
71	C₄×D₄×C₄₃	—	2	2	no	—
72	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
73	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
74	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₄₃	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₃	—	2	2	no	—
101	C₄⋊C₈×C₄₃	—	2	2	no	—
102	C₄⋊C₈×C₄₃	—	2	2	no	—
103	C₄⋊C₈×C₄₃	C₂³	1	4	yes	complemented
104	C₂²⋊C₈×C₄₃	—	2	2	no	—
105	C₂²⋊C₈×C₄₃	—	2	2	no	—
106	C₂²⋊C₈×C₄₃	—	2	2	no	—
107	C₂²⋊C₈×C₄₃	—	2	2	no	—
108	#97×C₄₃	—	2	2	no	—
109	#97×C₄₃	—	2	2	no	—
110	C₄×C₈×C₄₃	—	2	2	no	—
111	C₄×C₈×C₄₃	C₂³	1	4	yes	complemented
112	C₂⁴×C₄₃	—	2	8	no	—
113	C₂⁴×C₄₃	—	2	2	no	—
114	C₂⁴×C₄₃	—	2	2	no	—
115	C₂⁴×C₄₃	—	2	2	no	—
116	C₂⁴×C₄₃	—	4	4	no	—
117	C₂⁴×C₄₃	—	4	4	no	—
118	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×D₄×C₄₃	—	2	8	no	—
120	C₂×D₄×C₄₃	—	2	8	no	—
121	C₂×D₄×C₄₃	—	2	8	no	—
122	C₂×D₄×C₄₃	—	2	8	no	—
123	C₂×D₄×C₄₃	—	2	8	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	2	4	no	—
128	C₂×D₄×C₄₃	M₁₆	1	8	yes	complemented
129	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₄₃	—	2	4	no	—
131	C₂²×C₄×C₄₃	—	2	4	no	—
132	C₂²×C₄×C₄₃	—	2	4	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	4	no	—
135	C₂²×C₄×C₄₃	—	2	4	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	4	2	no	—
140	C₂²×C₄×C₄₃	—	4	4	no	—
141	C₂²×C₄×C₄₃	—	4	8	no	—
142	C₂²×C₄×C₄₃	—	4	8	no	—
143	C₂²×C₄×C₄₃	—	4	8	no	—
144	C₂²×C₄×C₄₃	—	4	8	no	—
145	C₂²×C₄×C₄₃	—	4	8	no	—
146	C₂²×C₄×C₄₃	—	4	8	no	—
147	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	M₁₆×C₄₃	—	4	4	no	—
166	M₁₆×C₄₃	—	4	4	no	—
167	C₂×C₈×C₄₃	—	2	4	no	—
168	C₂×C₈×C₄₃	—	2	4	no	—
169	C₄⋊C₄×C₄₃	—	2	2	no	—
170	C₄⋊C₄×C₄₃	—	2	2	no	—
171	C₄⋊C₄×C₄₃	—	2	2	no	—
172	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
173	C₂²⋊C₄×C₄₃	—	2	4	no	—
174	C₂²⋊C₄×C₄₃	—	2	4	no	—
175	C₂²⋊C₄×C₄₃	—	2	4	no	—
176	C₂²⋊C₄×C₄₃	—	2	4	no	—
177	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	2	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	8	no	—
197	C₂³×C₄₃	—	2	8	no	—
198	C₂³×C₄₃	—	2	4	no	—
199	C₂³×C₄₃	—	2	8	no	—
200	C₂³×C₄₃	—	4	4	no	—
201	C₂³×C₄₃	—	4	4	no	—
202	C₂³×C₄₃	—	4	32	no	—
203	C₂³×C₄₃	—	4	4	no	—
204	C₂³×C₄₃	—	4	4	no	—
205	C₂³×C₄₃	—	4	4	no	—
206	C₂³×C₄₃	—	4	4	no	—
207	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	D₄×C₄₃	—	2	8	no	—
211	D₄×C₄₃	—	2	8	no	—
212	D₄×C₄₃	—	2	4	no	—
213	D₄×C₄₃	—	2	8	no	—
214	D₄×C₄₃	C₂×M₁₆	1	8	yes	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	2	2	no	—
226	C₂×C₄×C₄₃	—	2	2	no	—
227	C₂×C₄×C₄₃	—	2	4	no	—
228	C₂×C₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	1	no	—
232	C₂×C₄×C₄₃	—	4	8	no	—
233	C₂×C₄×C₄₃	—	4	8	no	—
234	C₂×C₄×C₄₃	—	4	4	no	—
235	C₂×C₄×C₄₃	—	4	4	no	—
236	C₂×C₄×C₄₃	—	4	4	no	—
237	C₂×C₄×C₄₃	—	4	8	no	—
238	C₂×C₄×C₄₃	—	4	8	no	—
239	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
249	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
250	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
253	C₈×C₄₃	—	4	4	no	—
254	C₈×C₄₃	—	4	4	no	—
255	#17448	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₃	—	2	8	no	—
257	C₂²×C₄₃	—	2	1	no	—
258	C₂²×C₄₃	—	2	1	no	—
259	C₂²×C₄₃	—	2	1	no	—
260	C₂²×C₄₃	—	2	1	no	—
261	C₂²×C₄₃	—	2	1	no	—
262	C₂²×C₄₃	—	2	1	no	—
263	C₂²×C₄₃	—	2	8	no	—
264	C₂²×C₄₃	—	4	16	no	—
265	C₂²×C₄₃	—	4	16	no	—
266	C₂²×C₄₃	—	4	16	no	—
267	C₂²×C₄₃	—	4	4	no	—
268	C₂²×C₄₃	—	4	4	no	—
269	C₂²×C₄₃	#407	1	2	yes	—
270	C₂²×C₄₃	#418	1	2	yes	—
271	C₂²×C₄₃	#421	1	2	yes	—
272	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₄×C₄₃	—	2	1	no	—
274	C₄×C₄₃	—	2	1	no	—
275	C₄×C₄₃	—	2	1	no	—
276	C₄×C₄₃	—	2	1	no	—
277	C₄×C₄₃	—	2	1	no	—
278	C₄×C₄₃	—	2	1	no	—
279	C₄×C₄₃	—	2	1	no	—
280	C₄×C₄₃	—	2	1	no	—
281	C₄×C₄₃	—	4	4	no	—
282	C₄×C₄₃	#407	1	2	yes	—
283	C₄×C₄₃	#418	1	2	yes	—
284	C₄×C₄₃	C₂²×M₁₆	1	2	yes	—
285	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
286	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
287	#2920	C₂×C₄₃	1	1	yes	characteristic, complemented
288	#2920	C₂×C₄₃	1	1	yes	characteristic, complemented
289	#1490	C₂×C₄₃	1	4	yes	complemented
290	#1486	C₂×C₄₃	1	4	yes	complemented
291	#1478	C₂×C₄₃	1	4	yes	complemented
292	C₂×C₄₃	—	2	2	no	—
293	C₂×C₄₃	—	2	2	no	—
294	C₂×C₄₃	—	2	2	no	—
295	C₂×C₄₃	—	4	8	no	—
296	C₂×C₄₃	C₂×#407	1	1	yes	characteristic
297	C₂×C₄₃	C₂×#418	1	1	yes	characteristic
298	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
299	C₂³×D₄	C₄×C₄₃	1	1	yes	characteristic
300	C₂⁴×C₄	—	2	1	no	—
301	C₂×C₄×D₄	—	2	1	no	—
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	—	2	1	no	—
305	C₂×C₄×D₄	—	2	1	no	—
306	C₂×C₄×D₄	—	2	1	no	—
307	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
308	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
309	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
311	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
312	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
313	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	—	2	1	no	—
315	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
316	#432	—	2	1	no	—
317	#432	—	2	1	no	—
318	#432	—	2	1	no	—
319	#432	C₂²×C₄₃	1	2	yes	complemented
320	#431	—	2	1	no	—
321	#431	C₂²×C₄₃	1	2	yes	complemented
322	#431	C₂²×C₄₃	1	2	yes	complemented
323	#431	C₂²×C₄₃	1	2	yes	complemented
324	#423	—	2	1	no	—
325	#423	C₂²×C₄₃	1	2	yes	complemented
326	#407	—	2	1	no	—
327	#407	—	2	1	no	—
328	C₄×M₁₆	—	2	1	no	—
329	C₄×M₁₆	C₂²×C₄₃	1	2	yes	complemented
330	D₄⋊C₈	C₂²×C₄₃	1	16	yes	complemented
331	C₄₃	#17448	1	1	yes	characteristic, direct product factor, Sylow
332	C₂⁵	—	2	1	no	—
333	C₂²×D₄	—	2	8	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
338	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
339	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	—	2	2	no	—
342	C₂³×C₄	—	2	2	no	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	—	2	2	no	—
346	C₂³×C₄	—	2	2	no	—
347	C₂³×C₄	—	4	8	no	—
348	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
349	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
350	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
351	C₂×M₁₆	—	2	2	no	—
352	C₂×M₁₆	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
366	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
367	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
368	C₄×D₄	C₂³×C₄₃	1	4	yes	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
373	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
374	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
375	C₂×C₂²⋊C₄	—	2	2	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
382	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
383	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
384	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
385	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
386	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
387	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
388	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
389	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
393	C₄⋊C₈	—	2	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	2	2	no	—
396	C₄⋊C₈	C₂³×C₄₃	1	4	yes	complemented
397	C₂²⋊C₈	—	2	2	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	#97	—	2	2	no	—
402	#97	—	2	2	no	—
403	C₄×C₈	—	2	2	no	—
404	C₄×C₈	C₂³×C₄₃	1	4	yes	complemented
405	C₂⁴	—	2	8	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	4	4	no	—
410	C₂⁴	—	4	4	no	—
411	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	M₁₆×C₄₃	1	8	yes	complemented
422	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	8	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	—	4	8	no	—
437	C₂²×C₄	—	4	8	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	8	no	—
440	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
441	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
442	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
444	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
445	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
446	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
447	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
448	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
449	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
451	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
458	M₁₆	—	4	4	no	—
459	M₁₆	—	4	4	no	—
460	C₂×C₈	—	2	4	no	—
461	C₂×C₈	—	2	4	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
471	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
472	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
473	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
474	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
475	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
476	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
477	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
478	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
480	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
481	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
482	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
485	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	8	no	—
490	C₂³	—	2	8	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	8	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	32	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
501	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
502	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
503	D₄	—	2	8	no	—
504	D₄	—	2	8	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	8	no	—
507	D₄	C₂×M₁₆×C₄₃	1	8	yes	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	8	no	—
526	C₂×C₄	—	4	8	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
534	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
535	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
536	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
537	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
538	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
539	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
540	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
541	C₂×C₄	C₂×M₁₆×C₄₃	1	4	yes	—
542	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
543	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
546	C₈	—	4	4	no	—
547	C₈	—	4	4	no	—
548	C₂²	—	2	8	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	8	no	—
556	C₂²	—	4	16	no	—
557	C₂²	—	4	16	no	—
558	C₂²	—	4	16	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	C₄₃×#407	1	2	yes	—
562	C₂²	C₄₃×#418	1	2	yes	—
563	C₂²	C₄₃×#421	1	2	yes	—
564	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	4	4	no	—
574	C₄	C₄₃×#407	1	2	yes	—
575	C₄	C₄₃×#418	1	2	yes	—
576	C₄	C₂²×M₁₆×C₄₃	1	2	yes	—
577	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
578	C₂	—	2	2	no	—
579	C₂	—	2	2	no	—
580	C₂	—	2	2	no	—
581	C₂	—	4	8	no	—
582	C₂	C₂×C₄₃×#407	1	1	yes	characteristic
583	C₂	C₂×C₄₃×#418	1	1	yes	characteristic
584	C₂	C₂×C₄₃×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₄²	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂³×D₄×C₄₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2920	C₂	semidirect
3. C₄₃×#2920	C₂	semidirect
4. C₄₃×#1490	C₂	semidirect
5. C₄₃×#1486	C₂	semidirect
6. C₄₃×#1478	C₂	semidirect
27. C₄₃×#432	C₂²	semidirect
29. C₄₃×#431	C₂²	semidirect
30. C₄₃×#431	C₂²	semidirect
31. C₄₃×#431	C₂²	semidirect
33. C₄₃×#423	C₂²	semidirect
37. C₄×M₁₆×C₄₃	C₂²	semidirect
38. C₄₃×D₄⋊C₈	C₂²	semidirect
103. C₄⋊C₈×C₄₃	C₂³	semidirect
111. C₄×C₈×C₄₃	C₂³	semidirect
128. C₂×D₄×C₄₃	M₁₆	semidirect
255. #17448	C₄₃	direct (N × H)
287. #2920	C₂×C₄₃	semidirect
288. #2920	C₂×C₄₃	semidirect
289. #1490	C₂×C₄₃	semidirect
290. #1486	C₂×C₄₃	semidirect
291. #1478	C₂×C₄₃	semidirect
319. #432	C₂²×C₄₃	semidirect
321. #431	C₂²×C₄₃	semidirect
322. #431	C₂²×C₄₃	semidirect
323. #431	C₂²×C₄₃	semidirect
325. #423	C₂²×C₄₃	semidirect
329. C₄×M₁₆	C₂²×C₄₃	semidirect
330. D₄⋊C₈	C₂²×C₄₃	semidirect
331. C₄₃	#17448	direct (N × H)
396. C₄⋊C₈	C₂³×C₄₃	semidirect
404. C₄×C₈	C₂³×C₄₃	semidirect
421. C₂×D₄	M₁₆×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₄₃×#2920	2
C₄₃×#1490	2
C₄₃×#1486	2
C₄₃×#1478	2
#17448	43

Subgroups — C43×#17448 #24937465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17448 #24937465