Subgroups — C₄₃×#11024 #24931041

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₄₃	C₂	1	2	yes	maximal
3	C₂×C₄₃×#391	C₂	1	2	yes	maximal
4	C₂×C₄₃×#340	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₄₃	C₂²	1	2	yes	—
7	C₂²×Q₁₆×C₄₃	—	2	4	no	—
8	C₂²×Q₁₆×C₄₃	—	2	4	no	—
9	C₂²×Q₁₆×C₄₃	—	2	2	no	—
10	C₂²×Q₁₆×C₄₃	—	2	2	no	—
11	C₂²×Q₁₆×C₄₃	C₄	1	4	yes	complemented
12	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#103×C₄₃	—	2	4	no	—
17	C₂×#103×C₄₃	—	2	4	no	—
18	C₂×#103×C₄₃	—	2	4	no	—
19	C₄₃×#391	—	2	4	no	—
20	C₄₃×#391	—	2	4	no	—
21	C₂×#95×C₄₃	—	2	4	no	—
22	C₄₃×#340	—	2	2	no	—
23	C₄₃×#336	—	2	2	no	—
24	C₂²×Q₈×C₄₃	—	2	2	no	—
25	C₂²×Q₈×C₄₃	—	2	2	no	—
26	C₂²×Q₈×C₄₃	—	2	2	no	—
27	C₂²×Q₈×C₄₃	—	2	2	no	—
28	C₂²×Q₈×C₄₃	—	2	2	no	—
29	C₂²×Q₈×C₄₃	—	2	2	no	—
30	C₂²×Q₈×C₄₃	—	2	2	no	—
31	C₂²×Q₈×C₄₃	—	2	2	no	—
32	C₂²×Q₈×C₄₃	—	2	2	no	—
33	C₂²×Q₈×C₄₃	—	2	2	no	—
34	C₂²×Q₈×C₄₃	—	2	2	no	—
35	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
37	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
38	C₂³×C₄×C₄₃	—	2	2	no	—
39	C₂³×C₄×C₄₃	—	2	2	no	—
40	C₂³×C₄×C₄₃	D₄	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂×Q₁₆×C₄₃	—	2	8	no	—
43	C₂×Q₁₆×C₄₃	—	2	8	no	—
44	C₂×Q₁₆×C₄₃	—	2	16	no	—
45	C₂×Q₁₆×C₄₃	—	2	16	no	—
46	C₂×Q₁₆×C₄₃	—	2	8	no	—
47	C₂²×C₈×C₄₃	—	2	2	no	—
48	C₂²×C₈×C₄₃	—	2	2	no	—
49	C₂²×C₈×C₄₃	—	2	1	no	—
50	C₂²×C₈×C₄₃	—	2	2	no	—
51	C₂²×C₈×C₄₃	—	2	2	no	—
52	C₂²×C₈×C₄₃	—	2	1	no	—
53	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₄₃	D₄	1	2	yes	—
55	C₂²×C₈×C₄₃	D₄	1	2	yes	—
56	C₂²×C₈×C₄₃	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
63	C₂×C₄²×C₄₃	—	2	1	no	—
64	C₂×C₄²×C₄₃	—	2	2	no	—
65	C₂×C₄²×C₄₃	—	2	2	no	—
66	C₂×C₄²×C₄₃	—	2	1	no	—
67	#103×C₄₃	—	2	16	no	—
68	#95×C₄₃	—	2	16	no	—
69	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂×Q₈×C₄₃	—	2	4	no	—
71	C₂×Q₈×C₄₃	—	2	4	no	—
72	C₂×Q₈×C₄₃	—	2	4	no	—
73	C₂×Q₈×C₄₃	—	2	4	no	—
74	C₂×Q₈×C₄₃	—	2	4	no	—
75	C₂×Q₈×C₄₃	—	2	4	no	—
76	C₂×Q₈×C₄₃	—	2	4	no	—
77	C₂×Q₈×C₄₃	—	2	4	no	—
78	C₂×Q₈×C₄₃	—	2	4	no	—
79	C₂×Q₈×C₄₃	—	2	4	no	—
80	C₂×Q₈×C₄₃	—	2	4	no	—
81	C₂×Q₈×C₄₃	—	2	4	no	—
82	C₂×Q₈×C₄₃	—	2	4	no	—
83	C₂×Q₈×C₄₃	—	2	4	no	—
84	C₂×Q₈×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	—	4	2	no	—
86	C₂×Q₈×C₄₃	—	4	2	no	—
87	C₂×Q₈×C₄₃	—	4	2	no	—
88	C₂×Q₈×C₄₃	—	4	2	no	—
89	C₂×Q₈×C₄₃	—	4	2	no	—
90	C₂×Q₈×C₄₃	—	4	2	no	—
91	C₂×Q₈×C₄₃	—	4	2	no	—
92	C₂×Q₈×C₄₃	—	4	2	no	—
93	C₂×Q₈×C₄₃	—	4	2	no	—
94	C₂×Q₈×C₄₃	—	4	2	no	—
95	C₂×Q₈×C₄₃	—	4	2	no	—
96	C₂×Q₈×C₄₃	—	4	2	no	—
97	C₂×Q₈×C₄₃	C₂²⋊C₄	1	8	yes	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	4	2	no	—
107	C₂²×C₄×C₄₃	—	4	2	no	—
108	C₂²×C₄×C₄₃	—	4	2	no	—
109	C₂²×C₄×C₄₃	—	4	2	no	—
110	C₂²×C₄×C₄₃	—	4	2	no	—
111	C₂²×C₄×C₄₃	—	4	2	no	—
112	C₂²×C₄×C₄₃	—	4	4	no	—
113	C₂²×C₄×C₄₃	—	4	4	no	—
114	C₂²×C₄×C₄₃	Q₁₆	1	4	yes	complemented
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	2	yes	—
125	Q₁₆×C₄₃	—	2	32	no	—
126	C₂×C₈×C₄₃	—	2	4	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	4	no	—
130	C₂×C₈×C₄₃	—	2	4	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	4	1	no	—
133	C₂×C₈×C₄₃	—	4	2	no	—
134	C₂×C₈×C₄₃	—	4	1	no	—
135	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
136	C₄⋊C₄×C₄₃	—	2	4	no	—
137	C₄⋊C₄×C₄₃	—	2	4	no	—
138	C₄⋊C₄×C₄₃	—	4	2	no	—
139	C₄⋊C₄×C₄₃	—	4	2	no	—
140	C₄²×C₄₃	—	4	1	no	—
141	C₄²×C₄₃	—	4	2	no	—
142	C₄²×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
144	C₂³×C₄₃	#120	1	2	yes	—
145	C₂³×C₄₃	#121	1	2	yes	—
146	C₂³×C₄₃	#121	1	1	yes	characteristic
147	C₂³×C₄₃	#127	1	1	yes	characteristic
148	C₂³×C₄₃	C₂×Q₁₆	1	2	yes	—
149	C₂³×C₄₃	#135	1	2	yes	—
150	C₂³×C₄₃	#137	1	4	yes	—
151	Q₈×C₄₃	—	2	8	no	—
152	Q₈×C₄₃	—	2	8	no	—
153	Q₈×C₄₃	—	4	4	no	—
154	Q₈×C₄₃	—	4	4	no	—
155	Q₈×C₄₃	—	4	4	no	—
156	Q₈×C₄₃	—	4	4	no	—
157	Q₈×C₄₃	—	4	4	no	—
158	Q₈×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	2	8	no	—
160	C₂×C₄×C₄₃	—	2	8	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	4	4	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	4	no	—
167	C₂×C₄×C₄₃	—	4	4	no	—
168	C₂×C₄×C₄₃	—	4	4	no	—
169	C₂×C₄×C₄₃	—	4	4	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	4	no	—
172	C₂×C₄×C₄₃	—	4	8	no	—
173	C₂×C₄×C₄₃	—	8	4	no	—
174	C₂×C₄×C₄₃	—	8	2	no	—
175	C₂×C₄×C₄₃	—	8	2	no	—
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#120	1	2	yes	—
183	C₂×C₄×C₄₃	#120	1	2	yes	—
184	C₂×C₄×C₄₃	#121	1	2	yes	—
185	C₂×C₄×C₄₃	#121	1	2	yes	—
186	C₂×C₄×C₄₃	#121	1	2	yes	—
187	C₂×C₄×C₄₃	#121	1	2	yes	—
188	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#123	1	2	yes	—
190	C₂×C₄×C₄₃	#123	1	2	yes	—
191	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
192	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
193	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
194	C₈×C₄₃	—	2	4	no	—
195	C₈×C₄₃	—	4	2	no	—
196	#11024	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₃	#386	1	2	yes	—
198	C₂²×C₄₃	#390	1	1	yes	characteristic
199	C₂²×C₄₃	#392	1	1	yes	characteristic
200	C₂²×C₄₃	#392	1	2	yes	—
201	C₂²×C₄₃	#394	1	1	yes	characteristic
202	C₂²×C₄₃	C₄×Q₁₆	1	2	yes	—
203	C₂²×C₄₃	#441	1	2	yes	—
204	C₂²×C₄₃	#451	1	4	yes	—
205	C₂²×C₄₃	#452	1	4	yes	—
206	C₂²×C₄₃	#462	1	4	yes	—
207	C₂²×C₄₃	#464	1	4	yes	—
208	C₂²×C₄₃	#467	1	2	yes	—
209	C₂²×C₄₃	#470	1	2	yes	—
210	C₂²×C₄₃	#494	1	1	yes	characteristic
211	C₂²×C₄₃	#495	1	1	yes	characteristic
212	C₂²×C₄₃	#497	1	2	yes	—
213	C₄×C₄₃	—	4	8	no	—
214	C₄×C₄₃	—	4	4	no	—
215	C₄×C₄₃	—	8	4	no	—
216	C₄×C₄₃	#379	1	1	yes	characteristic
217	C₄×C₄₃	#386	1	2	yes	—
218	C₄×C₄₃	#390	1	1	yes	characteristic
219	C₄×C₄₃	#392	1	1	yes	characteristic
220	C₄×C₄₃	#394	1	1	yes	characteristic
221	C₄×C₄₃	#394	1	2	yes	—
222	C₂³×Q₁₆	C₂×C₄₃	1	1	yes	characteristic
223	C₂²×#103	C₂×C₄₃	1	2	yes	—
224	C₂×#391	C₂×C₄₃	1	2	yes	—
225	C₂×#340	C₂×C₄₃	1	1	yes	characteristic
226	C₂×#336	C₂×C₄₃	1	1	yes	characteristic
227	C₂×C₄₃	#1438	1	1	yes	characteristic
228	C₂×C₄₃	#1878	1	4	yes	—
229	C₂×C₄₃	#1969	1	1	yes	characteristic
230	C₂×C₄₃	#1971	1	1	yes	characteristic
231	C₂×C₄₃	#2001	1	2	yes	—
232	C₂×C₄₃	#2015	1	2	yes	—
233	C₂×C₄₃	#2016	1	2	yes	—
234	C₂×C₄₃	#2056	1	2	yes	—
235	C₂³×Q₈	C₂²×C₄₃	1	2	yes	—
236	C₂²×Q₁₆	—	2	4	no	—
237	C₂²×Q₁₆	—	2	4	no	—
238	C₂²×Q₁₆	—	2	2	no	—
239	C₂²×Q₁₆	—	2	2	no	—
240	C₂²×Q₁₆	C₄×C₄₃	1	4	yes	complemented
241	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
242	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
244	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
245	C₂×#103	—	2	4	no	—
246	C₂×#103	—	2	4	no	—
247	C₂×#103	—	2	4	no	—
248	#391	—	2	4	no	—
249	#391	—	2	4	no	—
250	C₂×#95	—	2	4	no	—
251	#340	—	2	2	no	—
252	#336	—	2	2	no	—
253	C₄₃	#11024	1	1	yes	characteristic, direct product factor, Sylow
254	C₂²×Q₈	—	2	2	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	—	2	2	no	—
258	C₂²×Q₈	—	2	2	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	—	2	2	no	—
261	C₂²×Q₈	—	2	2	no	—
262	C₂²×Q₈	—	2	2	no	—
263	C₂²×Q₈	—	2	2	no	—
264	C₂²×Q₈	—	2	2	no	—
265	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
266	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
267	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	D₄×C₄₃	1	2	yes	—
271	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
272	C₂×Q₁₆	—	2	8	no	—
273	C₂×Q₁₆	—	2	8	no	—
274	C₂×Q₁₆	—	2	16	no	—
275	C₂×Q₁₆	—	2	16	no	—
276	C₂×Q₁₆	—	2	8	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	C₂×C₄×C₄₃	1	2	yes	—
284	C₂²×C₈	D₄×C₄₃	1	2	yes	—
285	C₂²×C₈	D₄×C₄₃	1	2	yes	—
286	C₂²×C₈	D₄×C₄₃	1	2	yes	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	#103	—	2	16	no	—
298	#95	—	2	16	no	—
299	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×Q₈	C₂²⋊C₄×C₄₃	1	8	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	Q₁₆×C₄₃	1	4	yes	complemented
345	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
352	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
353	C₂²×C₄	#41×C₄₃	1	2	yes	—
354	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
355	Q₁₆	—	2	32	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	C₂²⋊C₄×C₄₃	1	4	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	4	2	no	—
372	C₄²	—	4	1	no	—
373	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
374	C₂³	#120×C₄₃	1	2	yes	—
375	C₂³	#121×C₄₃	1	2	yes	—
376	C₂³	#121×C₄₃	1	1	yes	characteristic
377	C₂³	#127×C₄₃	1	1	yes	characteristic
378	C₂³	C₂×Q₁₆×C₄₃	1	2	yes	—
379	C₂³	#135×C₄₃	1	2	yes	—
380	C₂³	#137×C₄₃	1	4	yes	—
381	Q₈	—	2	8	no	—
382	Q₈	—	2	8	no	—
383	Q₈	—	4	4	no	—
384	Q₈	—	4	4	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	4	4	no	—
387	Q₈	—	4	4	no	—
388	Q₈	—	4	4	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	4	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
408	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
409	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
410	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
411	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
412	C₂×C₄	#120×C₄₃	1	2	yes	—
413	C₂×C₄	#120×C₄₃	1	2	yes	—
414	C₂×C₄	#121×C₄₃	1	2	yes	—
415	C₂×C₄	#121×C₄₃	1	2	yes	—
416	C₂×C₄	#121×C₄₃	1	2	yes	—
417	C₂×C₄	#121×C₄₃	1	2	yes	—
418	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
419	C₂×C₄	#123×C₄₃	1	2	yes	—
420	C₂×C₄	#123×C₄₃	1	2	yes	—
421	C₂×C₄	#124×C₄₃	1	1	yes	characteristic
422	C₂×C₄	#124×C₄₃	1	1	yes	characteristic
423	C₂×C₄	#127×C₄₃	1	1	yes	characteristic
424	C₈	—	2	4	no	—
425	C₈	—	4	2	no	—
426	C₂²	C₄₃×#386	1	2	yes	—
427	C₂²	C₄₃×#390	1	1	yes	characteristic
428	C₂²	C₄₃×#392	1	1	yes	characteristic
429	C₂²	C₄₃×#392	1	2	yes	—
430	C₂²	C₄₃×#394	1	1	yes	characteristic
431	C₂²	C₄×Q₁₆×C₄₃	1	2	yes	—
432	C₂²	C₄₃×#441	1	2	yes	—
433	C₂²	C₄₃×#451	1	4	yes	—
434	C₂²	C₄₃×#452	1	4	yes	—
435	C₂²	C₄₃×#462	1	4	yes	—
436	C₂²	C₄₃×#464	1	4	yes	—
437	C₂²	C₄₃×#467	1	2	yes	—
438	C₂²	C₄₃×#470	1	2	yes	—
439	C₂²	C₄₃×#494	1	1	yes	characteristic
440	C₂²	C₄₃×#495	1	1	yes	characteristic
441	C₂²	C₄₃×#497	1	2	yes	—
442	C₄	—	4	8	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	4	no	—
445	C₄	C₄₃×#379	1	1	yes	characteristic
446	C₄	C₄₃×#386	1	2	yes	—
447	C₄	C₄₃×#390	1	1	yes	characteristic
448	C₄	C₄₃×#392	1	1	yes	characteristic
449	C₄	C₄₃×#394	1	1	yes	characteristic
450	C₄	C₄₃×#394	1	2	yes	—
451	C₂	C₄₃×#1438	1	1	yes	characteristic
452	C₂	C₄₃×#1878	1	4	yes	—
453	C₂	C₄₃×#1969	1	1	yes	characteristic
454	C₂	C₄₃×#1971	1	1	yes	characteristic
455	C₂	C₄₃×#2001	1	2	yes	—
456	C₂	C₄₃×#2015	1	2	yes	—
457	C₂	C₄₃×#2016	1	2	yes	—
458	C₂	C₄₃×#2056	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
11. C₂²×Q₁₆×C₄₃	C₄	semidirect
114. C₂²×C₄×C₄₃	Q₁₆	semidirect
196. #11024	C₄₃	direct (N × H)
240. C₂²×Q₁₆	C₄×C₄₃	semidirect
253. C₄₃	#11024	direct (N × H)
344. C₂²×C₄	Q₁₆×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₄₃	2
C₂²×#103×C₄₃	2
C₂×C₄₃×#391	2
C₂×C₄₃×#340	2
C₂×C₄₃×#336	2
#11024	43

Subgroups — C43×#11024 #24931041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#11024 #24931041