Subgroups — C₄₃×#29705 #24949722

Order 11008.

1018 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3460	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3079	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2061	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2040	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2037	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1806	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1800	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#544	C₂²	1	1	yes	characteristic
10	C₄₃×#542	—	2	2	no	—
11	C₄₃×#540	—	2	2	no	—
12	C₄₃×#538	—	2	2	no	—
13	C₄₃×#537	C₂²	1	1	yes	characteristic
14	C₄₃×#535	C₂²	1	2	yes	—
15	C₄₃×#532	—	2	2	no	—
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#529	—	2	2	no	—
18	C₄₃×#525	—	2	2	no	—
19	C₄×#41×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#477	—	2	2	no	—
22	C₄₃×#476	—	2	2	no	—
23	C₄₃×#475	—	2	2	no	—
24	C₄₃×#474	—	2	2	no	—
25	C₄₃×#428	C₂²	1	4	yes	—
26	C₄₃×#423	C₂²	1	2	yes	—
27	C₂×#104×C₄₃	C₂²	1	4	yes	—
28	C₄₃×#417	C₂²	1	4	yes	—
29	C₂×#100×C₄₃	C₂²	1	2	yes	—
30	C₄₃×#393	—	2	2	no	—
31	C₄₃×#390	C₂²	1	2	yes	—
32	C₄₃×#382	C₂²	1	2	yes	—
33	C₄₃×#380	—	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	—	2	2	no	—
38	C₂×#41×C₄₃	C₂³	1	2	yes	—
39	C₂²×Q₈×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	D₄	1	2	yes	—
42	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
43	C₄⋊Q₈×C₄₃	—	2	2	no	—
44	C₄⋊Q₈×C₄₃	—	2	2	no	—
45	C₄⋊Q₈×C₄₃	—	2	2	no	—
46	#127×C₄₃	—	2	2	no	—
47	#126×C₄₃	—	2	4	no	—
48	#125×C₄₃	—	2	2	no	—
49	#124×C₄₃	—	2	4	no	—
50	#124×C₄₃	—	2	2	no	—
51	#123×C₄₃	—	2	4	no	—
52	#123×C₄₃	—	2	4	no	—
53	C₂²⋊Q₈×C₄₃	—	2	2	no	—
54	C₂²⋊Q₈×C₄₃	—	2	2	no	—
55	C₂²⋊Q₈×C₄₃	—	2	2	no	—
56	#121×C₄₃	—	2	2	no	—
57	#121×C₄₃	—	2	4	no	—
58	#121×C₄₃	—	2	2	no	—
59	#121×C₄₃	—	2	2	no	—
60	#121×C₄₃	—	2	2	no	—
61	#121×C₄₃	—	2	2	no	—
62	#120×C₄₃	—	2	4	no	—
63	C₄×Q₈×C₄₃	D₄	1	2	yes	—
64	C₄×Q₈×C₄₃	D₄	1	2	yes	—
65	C₄×D₄×C₄₃	—	2	4	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	D₄	1	2	yes	—
71	C₄×D₄×C₄₃	D₄	1	2	yes	—
72	#117×C₄₃	—	2	2	no	—
73	#117×C₄₃	—	2	2	no	—
74	#117×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
81	C₂×C₄²×C₄₃	—	2	2	no	—
82	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	#107×C₄₃	—	2	4	no	—
85	#106×C₄₃	—	2	4	no	—
86	C₄⋊C₈×C₄₃	—	2	2	no	—
87	C₄⋊C₈×C₄₃	—	2	2	no	—
88	#104×C₄₃	—	4	4	no	—
89	#103×C₄₃	—	2	4	no	—
90	#102×C₄₃	—	2	4	no	—
91	#100×C₄₃	—	4	2	no	—
92	#95×C₄₃	—	2	1	no	—
93	#95×C₄₃	—	2	4	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
95	#41×C₄₃	—	2	2	no	—
96	#41×C₄₃	—	2	2	no	—
97	#41×C₄₃	—	2	2	no	—
98	#41×C₄₃	—	2	2	no	—
99	#41×C₄₃	—	8	4	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	—	4	2	no	—
102	C₂×Q₈×C₄₃	—	8	2	no	—
103	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₄₃	—	2	4	no	—
105	C₂×D₄×C₄₃	—	2	4	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	1	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	4	4	no	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	M₁₆×C₄₃	—	2	4	no	—
126	M₁₆×C₄₃	—	2	4	no	—
127	C₂×C₈×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	4	no	—
131	C₄⋊C₄×C₄₃	—	2	2	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	—	4	2	no	—
136	C₄⋊C₄×C₄₃	—	4	1	no	—
137	C₄⋊C₄×C₄₃	—	4	1	no	—
138	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₃	—	2	4	no	—
141	C₂²⋊C₄×C₄₃	—	2	4	no	—
142	C₂²⋊C₄×C₄₃	—	2	4	no	—
143	C₂²⋊C₄×C₄₃	—	2	4	no	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₂²⋊C₄×C₄₃	—	2	2	no	—
146	C₂²⋊C₄×C₄₃	—	2	2	no	—
147	C₂²⋊C₄×C₄₃	—	8	4	no	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₄²×C₄₃	—	2	2	no	—
151	C₄²×C₄₃	—	2	2	no	—
152	C₄²×C₄₃	—	2	2	no	—
153	C₄²×C₄₃	C₂×D₄	1	2	yes	—
154	C₄²×C₄₃	C₂×D₄	1	2	yes	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₄₃	—	2	2	no	—
163	Q₈×C₄₃	—	2	2	no	—
164	Q₈×C₄₃	—	8	4	no	—
165	Q₈×C₄₃	—	8	2	no	—
166	D₄×C₄₃	—	2	2	no	—
167	D₄×C₄₃	—	2	2	no	—
168	D₄×C₄₃	—	4	2	no	—
169	D₄×C₄₃	—	4	2	no	—
170	D₄×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	8	4	no	—
173	D₄×C₄₃	—	8	2	no	—
174	D₄×C₄₃	—	8	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	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	4	no	—
184	C₂×C₄×C₄₃	—	4	4	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	—	8	2	no	—
192	C₂×C₄×C₄₃	—	8	2	no	—
193	C₂×C₄×C₄₃	#120	1	2	yes	—
194	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
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	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
200	C₈×C₄₃	—	4	4	no	—
201	#29705	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	4	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	4	2	no	—
208	C₂²×C₄₃	—	4	2	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	—	4	2	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
213	C₂²×C₄₃	#536	1	1	yes	characteristic
214	C₂²×C₄₃	#537	1	1	yes	characteristic
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	—	2	2	no	—
217	C₄×C₄₃	—	4	2	no	—
218	C₄×C₄₃	—	4	2	no	—
219	C₄×C₄₃	—	4	2	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	—	8	2	no	—
222	C₄×C₄₃	—	8	2	no	—
223	C₄×C₄₃	#455	1	2	yes	—
224	C₄×C₄₃	#536	1	2	yes	—
225	C₄×C₄₃	#537	1	2	yes	—
226	#3460	C₂×C₄₃	1	1	yes	characteristic
227	#3079	C₂×C₄₃	1	2	yes	complemented
228	#2563	C₂×C₄₃	1	1	yes	characteristic, complemented
229	#2061	C₂×C₄₃	1	2	yes	complemented
230	#2040	C₂×C₄₃	1	2	yes	complemented
231	#2037	C₂×C₄₃	1	4	yes	complemented
232	#1806	C₂×C₄₃	1	2	yes	complemented
233	#1800	C₂×C₄₃	1	1	yes	characteristic, complemented
234	C₂×C₄₃	—	2	1	no	—
235	C₂×C₄₃	—	2	1	no	—
236	C₂×C₄₃	—	8	2	no	—
237	C₂×C₄₃	—	8	2	no	—
238	C₂×C₄₃	#2616	1	1	yes	characteristic
239	C₂×C₄₃	C₂×#455	1	1	yes	characteristic
240	C₂×C₄₃	#3021	1	1	yes	characteristic
241	#544	C₂²×C₄₃	1	1	yes	characteristic
242	#542	—	2	2	no	—
243	#540	—	2	2	no	—
244	#538	—	2	2	no	—
245	#537	C₂²×C₄₃	1	1	yes	characteristic
246	#535	C₂²×C₄₃	1	2	yes	—
247	#532	—	2	2	no	—
248	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
249	#529	—	2	2	no	—
250	#525	—	2	2	no	—
251	C₄×#41	C₂²×C₄₃	1	2	yes	—
252	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
253	#477	—	2	2	no	—
254	#476	—	2	2	no	—
255	#475	—	2	2	no	—
256	#474	—	2	2	no	—
257	#428	C₂²×C₄₃	1	4	yes	—
258	#423	C₂²×C₄₃	1	2	yes	—
259	C₂×#104	C₂²×C₄₃	1	4	yes	—
260	#417	C₂²×C₄₃	1	4	yes	—
261	C₂×#100	C₂²×C₄₃	1	2	yes	—
262	#393	—	2	2	no	—
263	#390	C₂²×C₄₃	1	2	yes	—
264	#382	C₂²×C₄₃	1	2	yes	—
265	#380	—	2	2	no	—
266	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
267	#343	C₂²×C₄₃	1	2	yes	—
268	#339	C₂²×C₄₃	1	4	yes	—
269	C₄₃	#29705	1	1	yes	characteristic, direct product factor, Sylow
270	C₂×#41	—	2	2	no	—
271	C₂×#41	C₂³×C₄₃	1	2	yes	—
272	C₂²×Q₈	—	2	1	no	—
273	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
274	C₂³×C₄	D₄×C₄₃	1	2	yes	—
275	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	#127	—	2	2	no	—
280	#126	—	2	4	no	—
281	#125	—	2	2	no	—
282	#124	—	2	4	no	—
283	#124	—	2	2	no	—
284	#123	—	2	4	no	—
285	#123	—	2	4	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	#121	—	2	2	no	—
290	#121	—	2	4	no	—
291	#121	—	2	2	no	—
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	#120	—	2	4	no	—
296	C₄×Q₈	D₄×C₄₃	1	2	yes	—
297	C₄×Q₈	D₄×C₄₃	1	2	yes	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	D₄×C₄₃	1	2	yes	—
304	C₄×D₄	D₄×C₄₃	1	2	yes	—
305	#117	—	2	2	no	—
306	#117	—	2	2	no	—
307	#117	C₂³×C₄₃	1	2	yes	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
316	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
317	#107	—	2	4	no	—
318	#106	—	2	4	no	—
319	C₄⋊C₈	—	2	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	#104	—	4	4	no	—
322	#103	—	2	4	no	—
323	#102	—	2	4	no	—
324	#100	—	4	2	no	—
325	#95	—	2	1	no	—
326	#95	—	2	4	no	—
327	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	8	4	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	8	2	no	—
336	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	C₂×C₈	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	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	—	2	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	1	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	4	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	8	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	C₂×D₄×C₄₃	1	2	yes	—
387	C₄²	C₂×D₄×C₄₃	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	4	no	—
398	Q₈	—	8	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	8	2	no	—
406	D₄	—	8	4	no	—
407	D₄	—	8	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	#120×C₄₃	1	2	yes	—
427	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
428	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
430	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
431	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
432	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
433	C₈	—	4	4	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
445	C₂²	C₄₃×#536	1	1	yes	characteristic
446	C₂²	C₄₃×#537	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	C₄₃×#455	1	2	yes	—
456	C₄	C₄₃×#536	1	2	yes	—
457	C₄	C₄₃×#537	1	2	yes	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	8	2	no	—
461	C₂	—	8	2	no	—
462	C₂	C₄₃×#2616	1	1	yes	characteristic
463	C₂	C₂×C₄₃×#455	1	1	yes	characteristic
464	C₂	C₄₃×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#3460	C₂
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×#3079	C₂	semidirect
3. C₄₃×#2563	C₂	semidirect
4. C₄₃×#2061	C₂	semidirect
5. C₄₃×#2040	C₂	semidirect
6. C₄₃×#2037	C₂	semidirect
7. C₄₃×#1806	C₂	semidirect
8. C₄₃×#1800	C₂	semidirect
201. #29705	C₄₃	direct (N × H)
227. #3079	C₂×C₄₃	semidirect
228. #2563	C₂×C₄₃	semidirect
229. #2061	C₂×C₄₃	semidirect
230. #2040	C₂×C₄₃	semidirect
231. #2037	C₂×C₄₃	semidirect
232. #1806	C₂×C₄₃	semidirect
233. #1800	C₂×C₄₃	semidirect
269. C₄₃	#29705	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×#3460	2
C₄₃×#3079	2
C₄₃×#2563	2
C₄₃×#2061	2
C₄₃×#2040	2
C₄₃×#2037	2
C₄₃×#1806	2
C₄₃×#1800	2
#29705	43

Subgroups — C43×#29705 #24949722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29705 #24949722