Subgroups — C₄₃×#17415 #24937432

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#553	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2924	C₂	1	2	yes	maximal, complemented
3	C₄₃×#1473	C₂	1	4	yes	maximal, complemented
4	C₄₃×#1471	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1466	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1465	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1460	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#553	—	2	2	no	—
10	C₄₃×#553	—	2	2	no	—
11	C₄₃×#553	—	2	4	no	—
12	C₂×#126×C₄₃	C₂²	1	2	yes	—
13	C₂×#125×C₄₃	C₄	1	1	yes	characteristic
14	C₂×#123×C₄₃	C₄	1	2	yes	—
15	C₂×#121×C₄₃	C₄	1	2	yes	—
16	C₂×#121×C₄₃	C₄	1	1	yes	characteristic
17	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
23	C₄₃×#433	—	2	4	no	—
24	C₄₃×#432	C₂²	1	4	yes	—
25	C₄₃×#431	C₂²	1	4	yes	—
26	C₄₃×#424	—	2	2	no	—
27	C₄₃×#407	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#405	—	2	2	no	—
30	C₄₃×#324	C₂²	1	2	yes	—
31	C₄₃×#324	C₂²	1	2	yes	—
32	C₄₃×#323	C₂²	1	1	yes	characteristic
33	C₄₃×#323	C₂²	1	1	yes	characteristic
34	C₄₃×#323	C₂²	1	2	yes	—
35	C₄₃×#323	C₂²	1	4	yes	—
36	C₄₃×#323	C₂²	1	4	yes	—
37	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₄₃	—	2	2	no	—
46	C₂²×C₈×C₄₃	—	2	2	no	—
47	#126×C₄₃	—	2	4	no	—
48	#126×C₄₃	—	2	4	no	—
49	#125×C₄₃	—	2	2	no	—
50	#125×C₄₃	—	2	2	no	—
51	#123×C₄₃	—	2	4	no	—
52	#123×C₄₃	—	2	4	no	—
53	#121×C₄₃	—	2	2	no	—
54	#121×C₄₃	—	2	2	no	—
55	#121×C₄₃	—	2	2	no	—
56	#121×C₄₃	—	2	2	no	—
57	#121×C₄₃	—	2	4	no	—
58	#121×C₄₃	—	2	4	no	—
59	C₄×D₄×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₄×D₄×C₄₃	—	2	1	no	—
63	C₄×D₄×C₄₃	—	2	1	no	—
64	C₄×D₄×C₄₃	—	2	4	no	—
65	C₄×D₄×C₄₃	—	2	4	no	—
66	#117×C₄₃	D₄	1	2	yes	—
67	#117×C₄₃	D₄	1	2	yes	—
68	#117×C₄₃	D₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
87	C₄⋊C₈×C₄₃	—	2	4	no	—
88	C₄⋊C₈×C₄₃	—	2	4	no	—
89	C₂²⋊C₈×C₄₃	—	2	2	no	—
90	C₂²⋊C₈×C₄₃	—	2	2	no	—
91	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
92	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
93	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
94	#97×C₄₃	—	2	4	no	—
95	C₄×C₈×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
97	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	2	1	no	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	2	4	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	4	no	—
106	C₂×D₄×C₄₃	—	4	1	no	—
107	C₂×D₄×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	4	2	no	—
109	C₂×D₄×C₄₃	—	8	2	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	—	8	2	no	—
119	C₂²×C₄×C₄₃	—	8	2	no	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₄₃	—	4	4	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	2	4	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	4	4	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	4	no	—
140	C₄⋊C₄×C₄₃	—	2	4	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
143	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
146	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
147	C₂²⋊C₄×C₄₃	—	2	2	no	—
148	C₂²⋊C₄×C₄₃	—	2	2	no	—
149	C₂²⋊C₄×C₄₃	—	2	4	no	—
150	C₂²⋊C₄×C₄₃	—	2	2	no	—
151	C₂²⋊C₄×C₄₃	—	2	4	no	—
152	C₂²⋊C₄×C₄₃	—	2	2	no	—
153	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
154	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₄²×C₄₃	—	2	1	no	—
157	C₄²×C₄₃	C₂×D₄	1	4	yes	—
158	C₄²×C₄₃	C₂×D₄	1	4	yes	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	2	1	no	—
162	C₂³×C₄₃	—	2	1	no	—
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	—	2	2	no	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	4	1	no	—
167	C₂³×C₄₃	—	4	1	no	—
168	C₂³×C₄₃	—	4	1	no	—
169	C₂³×C₄₃	—	4	1	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	—	4	2	no	—
172	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂³×C₄₃	#131	1	2	yes	—
174	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	D₄×C₄₃	—	4	8	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	4	4	no	—
178	D₄×C₄₃	—	4	2	no	—
179	D₄×C₄₃	—	8	4	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	4	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	8	2	no	—
199	C₂×C₄×C₄₃	—	8	2	no	—
200	C₂×C₄×C₄₃	—	8	2	no	—
201	C₂×C₄×C₄₃	—	8	2	no	—
202	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
204	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	—	4	2	no	—
210	C₈×C₄₃	—	4	4	no	—
211	#17415	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	—	2	1	no	—
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	—	2	2	no	—
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	4	2	no	—
219	C₂²×C₄₃	—	4	2	no	—
220	C₂²×C₄₃	—	4	1	no	—
221	C₂²×C₄₃	—	4	1	no	—
222	C₂²×C₄₃	—	4	2	no	—
223	C₂²×C₄₃	—	4	2	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	8	1	no	—
226	C₂²×C₄₃	—	8	1	no	—
227	C₂²×C₄₃	—	8	2	no	—
228	C₂²×C₄₃	—	8	2	no	—
229	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
231	C₂²×C₄₃	#568	1	1	yes	characteristic
232	C₄×C₄₃	—	2	4	no	—
233	C₄×C₄₃	—	2	2	no	—
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	2	2	no	—
236	C₄×C₄₃	—	2	2	no	—
237	C₄×C₄₃	—	4	1	no	—
238	C₄×C₄₃	—	4	1	no	—
239	C₄×C₄₃	—	4	1	no	—
240	C₄×C₄₃	—	4	2	no	—
241	C₄×C₄₃	#410	1	2	yes	—
242	C₂×#553	C₂×C₄₃	1	1	yes	characteristic
243	#2924	C₂×C₄₃	1	2	yes	complemented
244	#1473	C₂×C₄₃	1	4	yes	complemented
245	#1471	C₂×C₄₃	1	2	yes	complemented
246	#1466	C₂×C₄₃	1	2	yes	complemented
247	#1465	C₂×C₄₃	1	1	yes	characteristic, complemented
248	#1460	C₂×C₄₃	1	2	yes	complemented
249	#1459	C₂×C₄₃	1	1	yes	characteristic, complemented
250	C₂×C₄₃	—	2	1	no	—
251	C₂×C₄₃	—	2	1	no	—
252	C₂×C₄₃	—	4	2	no	—
253	C₂×C₄₃	—	4	2	no	—
254	C₂×C₄₃	—	8	2	no	—
255	C₂×C₄₃	#2880	1	1	yes	characteristic
256	C₂×C₄₃	C₂×#410	1	1	yes	characteristic
257	C₂×C₄₃	#2888	1	1	yes	characteristic
258	#553	—	2	2	no	—
259	#553	—	2	2	no	—
260	#553	—	2	4	no	—
261	C₂×#126	C₂²×C₄₃	1	2	yes	—
262	C₂×#125	C₄×C₄₃	1	1	yes	characteristic
263	C₂×#123	C₄×C₄₃	1	2	yes	—
264	C₂×#121	C₄×C₄₃	1	2	yes	—
265	C₂×#121	C₄×C₄₃	1	1	yes	characteristic
266	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₄×C₄₃	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
269	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
272	#433	—	2	4	no	—
273	#432	C₂²×C₄₃	1	4	yes	—
274	#431	C₂²×C₄₃	1	4	yes	—
275	#424	—	2	2	no	—
276	#407	C₂²×C₄₃	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
278	#405	—	2	2	no	—
279	#324	C₂²×C₄₃	1	2	yes	—
280	#324	C₂²×C₄₃	1	2	yes	—
281	#323	C₂²×C₄₃	1	1	yes	characteristic
282	#323	C₂²×C₄₃	1	1	yes	characteristic
283	#323	C₂²×C₄₃	1	2	yes	—
284	#323	C₂²×C₄₃	1	4	yes	—
285	#323	C₂²×C₄₃	1	4	yes	—
286	C₄₃	#17415	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
288	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
289	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
290	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
291	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
293	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
294	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
295	C₂×M₁₆	—	2	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	#126	—	2	4	no	—
298	#126	—	2	4	no	—
299	#125	—	2	2	no	—
300	#125	—	2	2	no	—
301	#123	—	2	4	no	—
302	#123	—	2	4	no	—
303	#121	—	2	2	no	—
304	#121	—	2	2	no	—
305	#121	—	2	2	no	—
306	#121	—	2	2	no	—
307	#121	—	2	4	no	—
308	#121	—	2	4	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	#117	D₄×C₄₃	1	2	yes	—
317	#117	D₄×C₄₃	1	2	yes	—
318	#117	D₄×C₄₃	1	4	yes	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
326	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
332	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
335	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
337	C₄⋊C₈	—	2	4	no	—
338	C₄⋊C₈	—	2	4	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
342	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
343	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
344	#97	—	2	4	no	—
345	C₄×C₈	—	2	4	no	—
346	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
347	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
348	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	8	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	8	2	no	—
369	C₂²×C₄	—	8	2	no	—
370	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
372	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
375	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
376	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
380	M₁₆	—	4	4	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	4	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	4	4	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
393	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
394	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
395	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
396	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
404	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	C₂×D₄×C₄₃	1	4	yes	—
408	C₄²	C₂×D₄×C₄₃	1	4	yes	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
423	C₂³	#131×C₄₃	1	2	yes	—
424	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
425	D₄	—	4	8	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	8	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	—	8	2	no	—
450	C₂×C₄	—	8	2	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
454	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
455	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
456	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	4	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
479	C₂²	C₂×#131×C₄₃	1	1	yes	characteristic
480	C₂²	C₄₃×#568	1	1	yes	characteristic
481	C₄	—	2	4	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	2	no	—
490	C₄	C₄₃×#410	1	2	yes	—
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	4	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	8	2	no	—
496	C₂	C₄₃×#2880	1	1	yes	characteristic
497	C₂	C₂×C₄₃×#410	1	1	yes	characteristic
498	C₂	C₄₃×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#553	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2924	C₂	semidirect
3. C₄₃×#1473	C₂	semidirect
4. C₄₃×#1471	C₂	semidirect
5. C₄₃×#1466	C₂	semidirect
6. C₄₃×#1465	C₂	semidirect
7. C₄₃×#1460	C₂	semidirect
8. C₄₃×#1459	C₂	semidirect
211. #17415	C₄₃	direct (N × H)
243. #2924	C₂×C₄₃	semidirect
244. #1473	C₂×C₄₃	semidirect
245. #1471	C₂×C₄₃	semidirect
246. #1466	C₂×C₄₃	semidirect
247. #1465	C₂×C₄₃	semidirect
248. #1460	C₂×C₄₃	semidirect
249. #1459	C₂×C₄₃	semidirect
286. C₄₃	#17415	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#553	2
C₄₃×#2924	2
C₄₃×#1473	2
C₄₃×#1471	2
C₄₃×#1466	2
C₄₃×#1465	2
C₄₃×#1460	2
C₄₃×#1459	2
#17415	43

Subgroups — C43×#17415 #24937432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17415 #24937432