Subgroups — C₄₃×#24021 #24944038

Order 11008.

1314 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3485	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3093	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2038	C₂	1	4	yes	maximal, complemented
5	C₄₃×#1896	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1856	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1792	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1785	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×H(5,𝔽₂)×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#547	—	2	4	no	—
12	C₄₃×#546	—	2	4	no	—
13	C₄₃×#536	C₂²	1	2	yes	—
14	C₄₃×#534	—	2	2	no	—
15	C₄₃×#525	C₂²	1	2	yes	—
16	C₂×#123×C₄₃	—	2	2	no	—
17	C₄₃×#518	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic, complemented
20	C₄₃×#485	—	2	4	no	—
21	C₄₃×#482	—	2	4	no	—
22	C₄₃×#428	C₂²	1	4	yes	complemented
23	C₂×#104×C₄₃	C₂²	1	4	yes	—
24	C₄₃×#417	C₂²	1	4	yes	—
25	C₂×#101×C₄₃	C₂²	1	2	yes	complemented
26	C₂×#100×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#407	C₂²	1	2	yes	complemented
28	C₄₃×#391	C₂²	1	2	yes	complemented
29	C₄₃×#390	C₂²	1	2	yes	—
30	C₄₃×#386	—	2	2	no	—
31	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
32	C₄₃×#339	C₂²	1	4	yes	complemented
33	H(5,𝔽₂)×C₄₃	—	2	4	no	—
34	H(5,𝔽₂)×C₄₃	—	4	2	no	—
35	C₂×#41×C₄₃	—	2	2	no	—
36	C₂×#41×C₄₃	—	2	4	no	—
37	C₂×#41×C₄₃	—	2	4	no	—
38	C₂×#41×C₄₃	—	4	2	no	—
39	C₂×#41×C₄₃	C₂³	1	2	yes	—
40	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₄₃	—	2	2	no	—
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	D₄	1	2	yes	—
44	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	D₄	1	2	yes	—
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
49	C₄⋊Q₈×C₄₃	—	2	2	no	—
50	#124×C₄₃	—	2	2	no	—
51	#123×C₄₃	—	2	8	no	—
52	#123×C₄₃	—	2	4	no	—
53	#123×C₄₃	—	2	2	no	—
54	#123×C₄₃	—	2	4	no	—
55	C₂²⋊Q₈×C₄₃	—	2	4	no	—
56	C₂²⋊Q₈×C₄₃	D₄	1	4	yes	—
57	#121×C₄₃	—	2	8	no	—
58	#121×C₄₃	D₄	1	4	yes	—
59	#120×C₄₃	—	2	4	no	—
60	#120×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	—	2	4	no	—
62	C₄×D₄×C₄₃	—	2	4	no	—
63	#117×C₄₃	—	2	4	no	—
64	#117×C₄₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
71	C₂×C₄²×C₄₃	—	2	1	no	—
72	C₂×C₄²×C₄₃	—	2	1	no	—
73	C₂×C₄²×C₄₃	—	4	2	no	—
74	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
75	#107×C₄₃	—	2	4	no	—
76	#106×C₄₃	—	2	4	no	—
77	#104×C₄₃	—	4	4	no	—
78	#103×C₄₃	—	2	4	no	—
79	#102×C₄₃	—	2	4	no	—
80	#101×C₄₃	—	4	2	no	—
81	#100×C₄₃	—	2	4	no	—
82	C₂²⋊C₈×C₄₃	—	2	4	no	—
83	#95×C₄₃	—	2	4	no	—
84	C₂⁴×C₄₃	—	2	2	no	—
85	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
87	#41×C₄₃	—	2	4	no	—
88	#41×C₄₃	—	2	4	no	—
89	#41×C₄₃	—	4	16	no	—
90	#41×C₄₃	—	4	8	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	2	2	no	—
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	2	4	no	—
100	C₂×D₄×C₄₃	—	2	4	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	4	2	no	—
103	C₂×D₄×C₄₃	—	4	4	no	—
104	C₂×D₄×C₄₃	—	4	8	no	—
105	C₂×D₄×C₄₃	—	4	4	no	—
106	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₄₃	#41	1	4	yes	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	—	4	2	no	—
119	C₂²×C₄×C₄₃	—	4	4	no	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
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	M₁₆×C₄₃	—	2	4	no	—
125	M₁₆×C₄₃	—	2	4	no	—
126	C₂×C₈×C₄₃	—	2	4	no	—
127	C₄⋊C₄×C₄₃	—	2	8	no	—
128	C₄⋊C₄×C₄₃	—	2	4	no	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
131	C₂²⋊C₄×C₄₃	—	2	4	no	—
132	C₂²⋊C₄×C₄₃	—	2	8	no	—
133	C₂²⋊C₄×C₄₃	—	2	4	no	—
134	C₂²⋊C₄×C₄₃	—	2	4	no	—
135	C₂²⋊C₄×C₄₃	—	2	2	no	—
136	C₂²⋊C₄×C₄₃	—	4	8	no	—
137	C₂²⋊C₄×C₄₃	—	4	2	no	—
138	C₄²×C₄₃	—	2	2	no	—
139	C₄²×C₄₃	—	2	4	no	—
140	C₄²×C₄₃	—	4	2	no	—
141	C₄²×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	1	no	—
144	C₂³×C₄₃	—	2	1	no	—
145	C₂³×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	—	2	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	—	4	4	no	—
149	C₂³×C₄₃	—	4	4	no	—
150	C₂³×C₄₃	—	8	4	no	—
151	C₂³×C₄₃	#120	1	2	yes	—
152	C₂³×C₄₃	#123	1	4	yes	—
153	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₄₃	—	2	4	no	—
155	Q₈×C₄₃	—	4	4	no	—
156	D₄×C₄₃	—	2	8	no	—
157	D₄×C₄₃	—	2	4	no	—
158	D₄×C₄₃	—	4	8	no	—
159	D₄×C₄₃	—	4	8	no	—
160	D₄×C₄₃	—	4	2	no	—
161	D₄×C₄₃	—	4	2	no	—
162	D₄×C₄₃	—	8	4	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	8	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	4	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	4	8	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	4	no	—
175	C₂×C₄×C₄₃	—	4	8	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	4	no	—
178	C₂×C₄×C₄₃	—	4	4	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	8	4	no	—
181	C₂×C₄×C₄₃	#120	1	2	yes	—
182	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
184	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
185	C₈×C₄₃	—	4	4	no	—
186	#24021	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	4	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	2	4	no	—
191	C₂²×C₄₃	—	4	4	no	—
192	C₂²×C₄₃	—	4	2	no	—
193	C₂²×C₄₃	—	4	2	no	—
194	C₂²×C₄₃	—	4	4	no	—
195	C₂²×C₄₃	—	4	2	no	—
196	C₂²×C₄₃	—	4	4	no	—
197	C₂²×C₄₃	—	8	2	no	—
198	C₂²×C₄₃	—	16	4	no	—
199	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
201	C₂²×C₄₃	#534	1	1	yes	characteristic
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	—	4	4	no	—
204	C₄×C₄₃	—	4	2	no	—
205	C₄×C₄₃	—	4	2	no	—
206	C₄×C₄₃	—	4	4	no	—
207	C₄×C₄₃	—	8	2	no	—
208	C₄×C₄₃	#546	1	4	yes	—
209	#3485	C₂×C₄₃	1	1	yes	characteristic
210	#3093	C₂×C₄₃	1	2	yes	complemented
211	#2297	C₂×C₄₃	1	1	yes	characteristic, complemented
212	#2038	C₂×C₄₃	1	4	yes	complemented
213	#1896	C₂×C₄₃	1	2	yes	complemented
214	#1856	C₂×C₄₃	1	2	yes	complemented
215	#1792	C₂×C₄₃	1	2	yes	complemented
216	#1785	C₂×C₄₃	1	1	yes	characteristic, complemented
217	C₂×C₄₃	—	2	1	no	—
218	C₂×C₄₃	—	2	1	no	—
219	C₂×C₄₃	—	4	2	no	—
220	C₂×C₄₃	—	4	4	no	—
221	C₂×C₄₃	—	8	2	no	—
222	C₂×C₄₃	#2405	1	1	yes	characteristic
223	C₂×C₄₃	#3018	1	2	yes	—
224	C₂×H(5,𝔽₂)	C₂²×C₄₃	1	1	yes	characteristic
225	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
226	#547	—	2	4	no	—
227	#546	—	2	4	no	—
228	#536	C₂²×C₄₃	1	2	yes	—
229	#534	—	2	2	no	—
230	#525	C₂²×C₄₃	1	2	yes	—
231	C₂×#123	—	2	2	no	—
232	#518	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic, complemented
234	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic, complemented
235	#485	—	2	4	no	—
236	#482	—	2	4	no	—
237	#428	C₂²×C₄₃	1	4	yes	complemented
238	C₂×#104	C₂²×C₄₃	1	4	yes	—
239	#417	C₂²×C₄₃	1	4	yes	—
240	C₂×#101	C₂²×C₄₃	1	2	yes	complemented
241	C₂×#100	C₂²×C₄₃	1	2	yes	—
242	#407	C₂²×C₄₃	1	2	yes	complemented
243	#391	C₂²×C₄₃	1	2	yes	complemented
244	#390	C₂²×C₄₃	1	2	yes	—
245	#386	—	2	2	no	—
246	C₄×C₂²⋊C₄	—	2	2	no	—
247	#339	C₂²×C₄₃	1	4	yes	complemented
248	C₄₃	#24021	1	1	yes	characteristic, direct product factor, Sylow
249	H(5,𝔽₂)	—	2	4	no	—
250	H(5,𝔽₂)	—	4	2	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	4	2	no	—
255	C₂×#41	C₂³×C₄₃	1	2	yes	—
256	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	D₄×C₄₃	1	2	yes	—
260	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	D₄×C₄₃	1	2	yes	—
263	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
264	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
265	C₄⋊Q₈	—	2	2	no	—
266	#124	—	2	2	no	—
267	#123	—	2	8	no	—
268	#123	—	2	4	no	—
269	#123	—	2	2	no	—
270	#123	—	2	4	no	—
271	C₂²⋊Q₈	—	2	4	no	—
272	C₂²⋊Q₈	D₄×C₄₃	1	4	yes	—
273	#121	—	2	8	no	—
274	#121	D₄×C₄₃	1	4	yes	—
275	#120	—	2	4	no	—
276	#120	—	2	2	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	4	no	—
279	#117	—	2	4	no	—
280	#117	C₂³×C₄₃	1	2	yes	—
281	C₂×C₄⋊C₄	—	2	4	no	—
282	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	4	2	no	—
290	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
291	#107	—	2	4	no	—
292	#106	—	2	4	no	—
293	#104	—	4	4	no	—
294	#103	—	2	4	no	—
295	#102	—	2	4	no	—
296	#101	—	4	2	no	—
297	#100	—	2	4	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	#95	—	2	4	no	—
300	C₂⁴	—	2	2	no	—
301	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
302	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	4	16	no	—
306	#41	—	4	8	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
323	C₂×D₄	#41×C₄₃	1	4	yes	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
340	M₁₆	—	2	4	no	—
341	M₁₆	—	2	4	no	—
342	C₂×C₈	—	2	4	no	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	4	8	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	4	no	—
356	C₄²	—	4	2	no	—
357	C₄²	—	4	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	8	4	no	—
367	C₂³	#120×C₄₃	1	2	yes	—
368	C₂³	#123×C₄₃	1	4	yes	—
369	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	4	no	—
372	D₄	—	2	8	no	—
373	D₄	—	2	4	no	—
374	D₄	—	4	8	no	—
375	D₄	—	4	8	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	4	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	8	4	no	—
397	C₂×C₄	#120×C₄₃	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
399	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
400	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
401	C₈	—	4	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	4	no	—
414	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
415	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
416	C₂²	C₄₃×#534	1	1	yes	characteristic
417	C₄	—	2	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	8	2	no	—
423	C₄	C₄₃×#546	1	4	yes	—
424	C₂	—	2	1	no	—
425	C₂	—	2	1	no	—
426	C₂	—	4	2	no	—
427	C₂	—	4	4	no	—
428	C₂	—	8	2	no	—
429	C₂	C₄₃×#2405	1	1	yes	characteristic
430	C₂	C₄₃×#3018	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#3485	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3093	C₂	semidirect
3. C₄₃×#2297	C₂	semidirect
4. C₄₃×#2038	C₂	semidirect
5. C₄₃×#1896	C₂	semidirect
6. C₄₃×#1856	C₂	semidirect
7. C₄₃×#1792	C₂	semidirect
8. C₄₃×#1785	C₂	semidirect
18. C₂×#117×C₄₃	C₂²	semidirect
19. C₂²×C₄²×C₄₃	C₂²	semidirect
22. C₄₃×#428	C₂²	semidirect
25. C₂×#101×C₄₃	C₂²	semidirect
27. C₄₃×#407	C₂²	semidirect
28. C₄₃×#391	C₂²	semidirect
32. C₄₃×#339	C₂²	semidirect
186. #24021	C₄₃	direct (N × H)
210. #3093	C₂×C₄₃	semidirect
211. #2297	C₂×C₄₃	semidirect
212. #2038	C₂×C₄₃	semidirect
213. #1896	C₂×C₄₃	semidirect
214. #1856	C₂×C₄₃	semidirect
215. #1792	C₂×C₄₃	semidirect
216. #1785	C₂×C₄₃	semidirect
233. C₂×#117	C₂²×C₄₃	semidirect
234. C₂²×C₄²	C₂²×C₄₃	semidirect
237. #428	C₂²×C₄₃	semidirect
240. C₂×#101	C₂²×C₄₃	semidirect
242. #407	C₂²×C₄₃	semidirect
243. #391	C₂²×C₄₃	semidirect
247. #339	C₂²×C₄₃	semidirect
248. C₄₃	#24021	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×#3485	2
C₄₃×#3093	2
C₄₃×#2297	2
C₄₃×#2038	2
C₄₃×#1896	2
C₄₃×#1856	2
C₄₃×#1792	2
C₄₃×#1785	2
#24021	43

Subgroups — C43×#24021 #24944038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#24021 #24944038