Subgroups — C₄₃×#29681 #24949698

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3461	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3039	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2546	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2028	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2007	C₂	1	2	yes	maximal
6	C₄₃×#2005	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1806	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#137×C₄₃	C₂²	1	4	yes	—
10	C₄₃×#544	C₂²	1	1	yes	characteristic
11	C₄₃×#542	—	2	2	no	—
12	C₄₃×#541	—	2	2	no	—
13	C₄₃×#539	—	2	2	no	—
14	C₄₃×#537	C₂²	1	1	yes	characteristic
15	C₄₃×#536	C₂²	1	2	yes	—
16	C₄₃×#533	—	2	2	no	—
17	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#529	—	2	2	no	—
20	C₄₃×#529	—	2	2	no	—
21	C₄×#41×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#462	—	2	2	no	—
24	C₄₃×#462	—	2	2	no	—
25	C₄₃×#461	—	2	2	no	—
26	C₄₃×#461	—	2	2	no	—
27	C₄₃×#423	C₂²	1	2	yes	—
28	C₂×#104×C₄₃	C₂²	1	4	yes	—
29	C₄₃×#419	C₂²	1	4	yes	—
30	C₂×#101×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#398	—	2	2	no	—
32	C₄₃×#391	C₂²	1	2	yes	—
33	C₄₃×#389	—	2	2	no	—
34	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#343	C₂²	1	2	yes	—
36	C₄₃×#339	C₂²	1	4	yes	—
37	C₂×#41×C₄₃	C₂³	1	2	yes	—
38	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
39	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
40	#137×C₄₃	—	4	4	no	—
41	#137×C₄₃	—	4	4	no	—
42	C₂×Q₁₆×C₄₃	—	2	4	no	—
43	C₂×SD₁₆×C₄₃	—	2	4	no	—
44	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₄₃	—	2	2	no	—
46	C₄⋊Q₈×C₄₃	—	2	2	no	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	—	2	2	no	—
49	C₄⋊Q₈×C₄₃	—	4	4	no	—
50	#126×C₄₃	—	2	4	no	—
51	#126×C₄₃	—	2	4	no	—
52	#125×C₄₃	—	2	2	no	—
53	#125×C₄₃	—	2	4	no	—
54	#125×C₄₃	—	2	2	no	—
55	#124×C₄₃	—	2	2	no	—
56	#124×C₄₃	—	2	2	no	—
57	#123×C₄₃	—	2	4	no	—
58	#123×C₄₃	—	2	4	no	—
59	C₂²⋊Q₈×C₄₃	—	2	4	no	—
60	C₂²⋊Q₈×C₄₃	—	2	2	no	—
61	C₂²⋊Q₈×C₄₃	—	2	2	no	—
62	C₂²⋊Q₈×C₄₃	—	2	2	no	—
63	C₂²⋊Q₈×C₄₃	—	2	2	no	—
64	#121×C₄₃	—	2	2	no	—
65	#121×C₄₃	—	2	2	no	—
66	C₄×Q₈×C₄₃	—	2	2	no	—
67	C₄×Q₈×C₄₃	—	2	2	no	—
68	C₄×Q₈×C₄₃	—	2	2	no	—
69	C₄×Q₈×C₄₃	D₄	1	2	yes	—
70	C₄×Q₈×C₄₃	D₄	1	2	yes	—
71	C₄×D₄×C₄₃	—	2	2	no	—
72	C₄×D₄×C₄₃	—	2	2	no	—
73	C₄×D₄×C₄₃	—	2	2	no	—
74	C₄×D₄×C₄₃	D₄	1	2	yes	—
75	C₄×D₄×C₄₃	D₄	1	2	yes	—
76	#117×C₄₃	—	2	4	no	—
77	#117×C₄₃	—	2	2	no	—
78	#117×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	—	2	2	no	—
86	C₂×C₄²×C₄₃	D₄	1	2	yes	—
87	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₃	—	2	2	no	—
90	C₄⋊C₈×C₄₃	—	2	2	no	—
91	#104×C₄₃	—	4	4	no	—
92	#103×C₄₃	—	2	4	no	—
93	#103×C₄₃	—	2	4	no	—
94	#101×C₄₃	—	4	2	no	—
95	#95×C₄₃	—	2	1	no	—
96	#95×C₄₃	—	2	4	no	—
97	#41×C₄₃	—	2	2	no	—
98	#41×C₄₃	—	2	2	no	—
99	#41×C₄₃	—	2	2	no	—
100	#41×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	2	4	no	—
107	C₂×Q₈×C₄₃	—	2	4	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₄₃	—	4	8	no	—
125	SD₁₆×C₄₃	—	4	8	no	—
126	M₁₆×C₄₃	—	2	4	no	—
127	M₁₆×C₄₃	—	2	4	no	—
128	C₂×C₈×C₄₃	—	2	4	no	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	2	4	no	—
131	C₄⋊C₄×C₄₃	—	2	4	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	4	no	—
135	C₄⋊C₄×C₄₃	—	2	4	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	4	8	no	—
140	C₄⋊C₄×C₄₃	—	4	1	no	—
141	C₄⋊C₄×C₄₃	—	4	2	no	—
142	C₄⋊C₄×C₄₃	—	4	1	no	—
143	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
145	C₂²⋊C₄×C₄₃	—	2	4	no	—
146	C₂²⋊C₄×C₄₃	—	2	4	no	—
147	C₂²⋊C₄×C₄₃	—	2	4	no	—
148	C₂²⋊C₄×C₄₃	—	2	2	no	—
149	C₂²⋊C₄×C₄₃	—	2	2	no	—
150	C₂²⋊C₄×C₄₃	—	2	2	no	—
151	C₄²×C₄₃	—	2	2	no	—
152	C₄²×C₄₃	—	2	2	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₄²×C₄₃	—	2	4	no	—
157	C₄²×C₄₃	C₂×D₄	1	2	yes	—
158	C₄²×C₄₃	C₂×D₄	1	2	yes	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₄₃	—	2	2	no	—
162	Q₈×C₄₃	—	2	2	no	—
163	Q₈×C₄₃	—	4	2	no	—
164	Q₈×C₄₃	—	4	2	no	—
165	Q₈×C₄₃	—	4	4	no	—
166	Q₈×C₄₃	—	4	4	no	—
167	Q₈×C₄₃	—	8	2	no	—
168	D₄×C₄₃	—	2	2	no	—
169	D₄×C₄₃	—	2	2	no	—
170	D₄×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	8	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	8	2	no	—
193	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
194	C₂×C₄×C₄₃	#120	1	2	yes	—
195	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₄₃	—	4	4	no	—
201	#29681	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
208	C₂²×C₄₃	#535	1	1	yes	characteristic
209	C₂²×C₄₃	#537	1	1	yes	characteristic
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	2	no	—
212	C₄×C₄₃	—	4	4	no	—
213	C₄×C₄₃	—	4	2	no	—
214	C₄×C₄₃	—	4	2	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	—	4	2	no	—
218	C₄×C₄₃	—	8	2	no	—
219	C₄×C₄₃	#456	1	2	yes	—
220	C₄×C₄₃	#535	1	2	yes	—
221	C₄×C₄₃	#537	1	2	yes	—
222	#3461	C₂×C₄₃	1	1	yes	characteristic
223	#3039	C₂×C₄₃	1	2	yes	complemented
224	#2546	C₂×C₄₃	1	1	yes	characteristic, complemented
225	#2028	C₂×C₄₃	1	2	yes	complemented
226	#2007	C₂×C₄₃	1	2	yes	—
227	#2005	C₂×C₄₃	1	4	yes	complemented
228	#1806	C₂×C₄₃	1	2	yes	complemented
229	#1801	C₂×C₄₃	1	1	yes	characteristic, complemented
230	C₂×C₄₃	—	2	1	no	—
231	C₂×C₄₃	—	2	1	no	—
232	C₂×C₄₃	—	8	2	no	—
233	C₂×C₄₃	#2615	1	1	yes	characteristic
234	C₂×C₄₃	C₂×#456	1	1	yes	characteristic
235	C₂×C₄₃	#3022	1	1	yes	characteristic
236	C₂×#137	C₂²×C₄₃	1	4	yes	—
237	#544	C₂²×C₄₃	1	1	yes	characteristic
238	#542	—	2	2	no	—
239	#541	—	2	2	no	—
240	#539	—	2	2	no	—
241	#537	C₂²×C₄₃	1	1	yes	characteristic
242	#536	C₂²×C₄₃	1	2	yes	—
243	#533	—	2	2	no	—
244	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
246	#529	—	2	2	no	—
247	#529	—	2	2	no	—
248	C₄×#41	C₂²×C₄₃	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
250	#462	—	2	2	no	—
251	#462	—	2	2	no	—
252	#461	—	2	2	no	—
253	#461	—	2	2	no	—
254	#423	C₂²×C₄₃	1	2	yes	—
255	C₂×#104	C₂²×C₄₃	1	4	yes	—
256	#419	C₂²×C₄₃	1	4	yes	—
257	C₂×#101	C₂²×C₄₃	1	2	yes	—
258	#398	—	2	2	no	—
259	#391	C₂²×C₄₃	1	2	yes	—
260	#389	—	2	2	no	—
261	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
262	#343	C₂²×C₄₃	1	2	yes	—
263	#339	C₂²×C₄₃	1	4	yes	—
264	C₄₃	#29681	1	1	yes	characteristic, direct product factor, Sylow
265	C₂×#41	C₂³×C₄₃	1	2	yes	—
266	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
267	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
268	#137	—	4	4	no	—
269	#137	—	4	4	no	—
270	C₂×Q₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	—	2	2	no	—
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	4	4	no	—
278	#126	—	2	4	no	—
279	#126	—	2	4	no	—
280	#125	—	2	2	no	—
281	#125	—	2	4	no	—
282	#125	—	2	2	no	—
283	#124	—	2	2	no	—
284	#124	—	2	2	no	—
285	#123	—	2	4	no	—
286	#123	—	2	4	no	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×Q₈	D₄×C₄₃	1	2	yes	—
298	C₄×Q₈	D₄×C₄₃	1	2	yes	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	D₄×C₄₃	1	2	yes	—
303	C₄×D₄	D₄×C₄₃	1	2	yes	—
304	#117	—	2	4	no	—
305	#117	—	2	2	no	—
306	#117	C₂³×C₄₃	1	2	yes	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	D₄×C₄₃	1	2	yes	—
315	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
316	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
317	C₄⋊C₈	—	2	2	no	—
318	C₄⋊C₈	—	2	2	no	—
319	#104	—	4	4	no	—
320	#103	—	2	4	no	—
321	#103	—	2	4	no	—
322	#101	—	4	2	no	—
323	#95	—	2	1	no	—
324	#95	—	2	4	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
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	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
352	Q₁₆	—	4	8	no	—
353	SD₁₆	—	4	8	no	—
354	M₁₆	—	2	4	no	—
355	M₁₆	—	2	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	8	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
372	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	4	no	—
385	C₄²	C₂×D₄×C₄₃	1	2	yes	—
386	C₄²	C₂×D₄×C₄₃	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	4	no	—
394	Q₈	—	4	4	no	—
395	Q₈	—	8	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
422	C₂×C₄	#120×C₄₃	1	2	yes	—
423	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
425	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
426	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
427	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
428	C₈	—	4	4	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
435	C₂²	C₄₃×#535	1	1	yes	characteristic
436	C₂²	C₄₃×#537	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	2	no	—
446	C₄	C₄₃×#456	1	2	yes	—
447	C₄	C₄₃×#535	1	2	yes	—
448	C₄	C₄₃×#537	1	2	yes	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	8	2	no	—
452	C₂	C₄₃×#2615	1	1	yes	characteristic
453	C₂	C₂×C₄₃×#456	1	1	yes	characteristic
454	C₂	C₄₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#537	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3039	C₂	semidirect
3. C₄₃×#2546	C₂	semidirect
4. C₄₃×#2028	C₂	semidirect
6. C₄₃×#2005	C₂	semidirect
7. C₄₃×#1806	C₂	semidirect
8. C₄₃×#1801	C₂	semidirect
201. #29681	C₄₃	direct (N × H)
223. #3039	C₂×C₄₃	semidirect
224. #2546	C₂×C₄₃	semidirect
225. #2028	C₂×C₄₃	semidirect
227. #2005	C₂×C₄₃	semidirect
228. #1806	C₂×C₄₃	semidirect
229. #1801	C₂×C₄₃	semidirect
264. C₄₃	#29681	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3461	2
C₄₃×#3039	2
C₄₃×#2546	2
C₄₃×#2028	2
C₄₃×#2007	2
C₄₃×#2005	2
C₄₃×#1806	2
C₄₃×#1801	2
#29681	43

Subgroups — C43×#29681 #24949698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29681 #24949698