Subgroups — C₄₃×#29748 #24949765

Order 11008.

956 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3006	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2078	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2051	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2018	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1900	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	4	yes	—
11	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₃	C₂²	1	2	yes	—
15	C₄₃×#466	—	2	2	no	—
16	C₄₃×#466	—	2	2	no	—
17	C₄₃×#449	—	2	4	no	—
18	C₄₃×#448	—	2	2	no	—
19	C₄₃×#447	—	2	2	no	—
20	C₂×#108×C₄₃	C₂²	1	2	yes	complemented
21	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
22	C₄₃×#417	C₂²	1	4	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
24	C₂×#100×C₄₃	C₂²	1	4	yes	complemented
25	C₄₃×#408	—	2	2	no	—
26	C₄₃×#408	C₂²	1	2	yes	—
27	C₄₃×#408	C₂²	1	2	yes	—
28	C₄₃×#407	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₃	—	2	2	no	—
30	C₄₃×#343	C₂²	1	4	yes	complemented
31	C₄₃×#341	C₂²	1	2	yes	complemented
32	C₂×#41×C₄₃	—	2	1	no	—
33	C₂×#41×C₄₃	—	2	1	no	—
34	C₂×#41×C₄₃	—	4	2	no	—
35	C₂×#41×C₄₃	—	4	2	no	—
36	C₂×#41×C₄₃	D₄	1	2	yes	—
37	C₂×#41×C₄₃	C₂³	1	2	yes	—
38	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	—	2	2	no	—
41	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₃	—	2	1	no	—
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	AGL(1,ℤ/8)×C₄₃	—	4	4	no	—
46	AGL(1,ℤ/8)×C₄₃	—	4	4	no	—
47	C₂×SD₁₆×C₄₃	—	2	4	no	—
48	C₂×D₈×C₄₃	—	2	4	no	—
49	C₂×D₈×C₄₃	—	2	2	no	—
50	C₂×D₈×C₄₃	—	4	2	no	—
51	C₂×M₁₆×C₄₃	—	2	1	no	—
52	C₂×M₁₆×C₄₃	—	4	2	no	—
53	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
54	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
55	C₂²×C₈×C₄₃	—	2	1	no	—
56	C₂²×C₈×C₄₃	—	4	2	no	—
57	C₂²×C₈×C₄₃	D₄	1	2	yes	—
58	C₂²×C₈×C₄₃	D₄	1	2	yes	—
59	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
61	#121×C₄₃	—	2	2	no	—
62	#121×C₄₃	—	2	2	no	—
63	#121×C₄₃	—	2	2	no	—
64	#121×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
67	#108×C₄₃	—	4	2	no	—
68	#107×C₄₃	—	2	2	no	—
69	#103×C₄₃	—	2	4	no	—
70	#102×C₄₃	—	2	4	no	—
71	#102×C₄₃	—	2	4	no	—
72	#100×C₄₃	—	4	4	no	—
73	C₂²⋊C₈×C₄₃	—	2	2	no	—
74	C₂²⋊C₈×C₄₃	—	2	2	no	—
75	C₂²⋊C₈×C₄₃	—	2	4	no	—
76	C₂²⋊C₈×C₄₃	—	2	4	no	—
77	C₂⁴×C₄₃	—	2	1	no	—
78	C₂⁴×C₄₃	—	2	2	no	—
79	C₂⁴×C₄₃	#41	1	1	yes	characteristic
80	#41×C₄₃	—	2	4	no	—
81	#41×C₄₃	—	2	4	no	—
82	#41×C₄₃	—	4	4	no	—
83	#41×C₄₃	—	4	4	no	—
84	#41×C₄₃	—	4	2	no	—
85	#41×C₄₃	—	4	2	no	—
86	C₂×Q₈×C₄₃	—	2	1	no	—
87	C₂×Q₈×C₄₃	—	4	2	no	—
88	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
89	C₂×D₄×C₄₃	—	2	1	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	2	2	no	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	4	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	4	4	no	—
97	C₂×D₄×C₄₃	—	4	2	no	—
98	C₂×D₄×C₄₃	—	4	2	no	—
99	C₂×D₄×C₄₃	—	4	2	no	—
100	C₂×D₄×C₄₃	—	8	4	no	—
101	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	4	2	no	—
109	C₂²×C₄×C₄₃	—	4	2	no	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₄₃	—	4	8	no	—
117	D₈×C₄₃	—	4	4	no	—
118	D₈×C₄₃	—	4	8	no	—
119	M₁₆×C₄₃	—	2	4	no	—
120	M₁₆×C₄₃	—	2	4	no	—
121	M₁₆×C₄₃	—	2	4	no	—
122	M₁₆×C₄₃	—	4	2	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	4	no	—
127	C₂×C₈×C₄₃	—	4	2	no	—
128	C₂×C₈×C₄₃	—	4	2	no	—
129	C₂×C₈×C₄₃	—	4	2	no	—
130	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₂²⋊C₄×C₄₃	—	4	2	no	—
135	C₂²⋊C₄×C₄₃	—	4	2	no	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	2	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	—	4	2	no	—
144	C₂³×C₄₃	—	4	4	no	—
145	C₂³×C₄₃	—	8	2	no	—
146	C₂³×C₄₃	—	8	2	no	—
147	C₂³×C₄₃	#121	1	1	yes	characteristic
148	C₂³×C₄₃	#121	1	1	yes	characteristic
149	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
150	Q₈×C₄₃	—	2	4	no	—
151	Q₈×C₄₃	—	4	2	no	—
152	D₄×C₄₃	—	2	4	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	4	4	no	—
155	D₄×C₄₃	—	4	4	no	—
156	D₄×C₄₃	—	4	2	no	—
157	D₄×C₄₃	—	4	4	no	—
158	D₄×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	8	4	no	—
160	D₄×C₄₃	—	8	4	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	4	4	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	8	2	no	—
175	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
180	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
181	C₈×C₄₃	—	2	2	no	—
182	C₈×C₄₃	—	2	2	no	—
183	C₈×C₄₃	—	4	4	no	—
184	C₈×C₄₃	—	4	2	no	—
185	#29748	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₃	—	2	1	no	—
187	C₂²×C₄₃	—	2	1	no	—
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	2	1	no	—
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	4	4	no	—
194	C₂²×C₄₃	—	4	2	no	—
195	C₂²×C₄₃	—	4	2	no	—
196	C₂²×C₄₃	—	4	2	no	—
197	C₂²×C₄₃	—	8	4	no	—
198	C₂²×C₄₃	—	8	2	no	—
199	C₂²×C₄₃	—	8	2	no	—
200	C₂²×C₄₃	—	8	2	no	—
201	C₂²×C₄₃	—	16	4	no	—
202	C₂²×C₄₃	#472	1	2	yes	—
203	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
204	C₂²×C₄₃	#538	1	2	yes	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	4	2	no	—
208	C₄×C₄₃	—	8	2	no	—
209	C₄×C₄₃	#534	1	1	yes	characteristic
210	C₄×C₄₃	#534	1	2	yes	—
211	C₄×C₄₃	#535	1	1	yes	characteristic
212	C₂×#466	C₂×C₄₃	1	1	yes	characteristic, complemented
213	#3006	C₂×C₄₃	1	2	yes	complemented
214	C₂×#408	C₂×C₄₃	1	1	yes	characteristic, complemented
215	#2078	C₂×C₄₃	1	2	yes	complemented
216	#2051	C₂×C₄₃	1	4	yes	complemented
217	#2018	C₂×C₄₃	1	2	yes	complemented
218	#1900	C₂×C₄₃	1	2	yes	complemented
219	#1810	C₂×C₄₃	1	1	yes	characteristic, complemented
220	C₂×C₄₃	—	2	2	no	—
221	C₂×C₄₃	—	2	2	no	—
222	C₂×C₄₃	—	4	1	no	—
223	C₂×C₄₃	—	8	2	no	—
224	C₂×C₄₃	—	16	2	no	—
225	C₂×C₄₃	#2617	1	1	yes	characteristic
226	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
227	C₂×C₄₃	#3067	1	1	yes	characteristic
228	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
229	C₂×AGL(1,ℤ/8)	C₂²×C₄₃	1	4	yes	—
230	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
231	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#121	C₂²×C₄₃	1	2	yes	—
234	#466	—	2	2	no	—
235	#466	—	2	2	no	—
236	#449	—	2	4	no	—
237	#448	—	2	2	no	—
238	#447	—	2	2	no	—
239	C₂×#108	C₂²×C₄₃	1	2	yes	complemented
240	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic, complemented
241	#417	C₂²×C₄₃	1	4	yes	—
242	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
243	C₂×#100	C₂²×C₄₃	1	4	yes	complemented
244	#408	—	2	2	no	—
245	#408	C₂²×C₄₃	1	2	yes	—
246	#408	C₂²×C₄₃	1	2	yes	—
247	#407	C₂²×C₄₃	1	2	yes	—
248	C₂×C₂²⋊C₈	—	2	2	no	—
249	#343	C₂²×C₄₃	1	4	yes	complemented
250	#341	C₂²×C₄₃	1	2	yes	complemented
251	C₄₃	#29748	1	1	yes	characteristic, direct product factor, Sylow
252	C₂×#41	—	2	1	no	—
253	C₂×#41	—	2	1	no	—
254	C₂×#41	—	4	2	no	—
255	C₂×#41	—	4	2	no	—
256	C₂×#41	D₄×C₄₃	1	2	yes	—
257	C₂×#41	C₂³×C₄₃	1	2	yes	—
258	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
262	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
265	AGL(1,ℤ/8)	—	4	4	no	—
266	AGL(1,ℤ/8)	—	4	4	no	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×D₈	—	2	4	no	—
269	C₂×D₈	—	2	2	no	—
270	C₂×D₈	—	4	2	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	4	2	no	—
273	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
274	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	—	4	2	no	—
277	C₂²×C₈	D₄×C₄₃	1	2	yes	—
278	C₂²×C₈	D₄×C₄₃	1	2	yes	—
279	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
281	#121	—	2	2	no	—
282	#121	—	2	2	no	—
283	#121	—	2	2	no	—
284	#121	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	#108	—	4	2	no	—
288	#107	—	2	2	no	—
289	#103	—	2	4	no	—
290	#102	—	2	4	no	—
291	#102	—	2	4	no	—
292	#100	—	4	4	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	4	no	—
296	C₂²⋊C₈	—	2	4	no	—
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	2	2	no	—
299	C₂⁴	#41×C₄₃	1	1	yes	characteristic
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	4	4	no	—
303	#41	—	4	4	no	—
304	#41	—	4	2	no	—
305	#41	—	4	2	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	8	4	no	—
321	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
334	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
336	SD₁₆	—	4	8	no	—
337	D₈	—	4	4	no	—
338	D₈	—	4	8	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	4	no	—
341	M₁₆	—	2	4	no	—
342	M₁₆	—	4	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	8	2	no	—
366	C₂³	—	8	2	no	—
367	C₂³	#121×C₄₃	1	1	yes	characteristic
368	C₂³	#121×C₄₃	1	1	yes	characteristic
369	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	2	no	—
379	D₄	—	8	4	no	—
380	D₄	—	8	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
396	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
399	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
400	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	4	4	no	—
404	C₈	—	4	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	8	4	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	16	4	no	—
421	C₂²	C₄₃×#472	1	2	yes	—
422	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
423	C₂²	C₄₃×#538	1	2	yes	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	2	no	—
428	C₄	C₄₃×#534	1	1	yes	characteristic
429	C₄	C₄₃×#534	1	2	yes	—
430	C₄	C₄₃×#535	1	1	yes	characteristic
431	C₂	—	2	2	no	—
432	C₂	—	2	2	no	—
433	C₂	—	4	1	no	—
434	C₂	—	8	2	no	—
435	C₂	—	16	2	no	—
436	C₂	C₄₃×#2617	1	1	yes	characteristic
437	C₂	C₂×C₄₃×#472	1	1	yes	characteristic
438	C₂	C₄₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
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
1. C₂×C₄₃×#466	C₂	semidirect
2. C₄₃×#3006	C₂	semidirect
3. C₂×C₄₃×#408	C₂	semidirect
4. C₄₃×#2078	C₂	semidirect
5. C₄₃×#2051	C₂	semidirect
6. C₄₃×#2018	C₂	semidirect
7. C₄₃×#1900	C₂	semidirect
8. C₄₃×#1810	C₂	semidirect
11. C₂²×D₈×C₄₃	C₂²	semidirect
20. C₂×#108×C₄₃	C₂²	semidirect
21. C₂×#107×C₄₃	C₂²	semidirect
23. C₂×#102×C₄₃	C₂²	semidirect
24. C₂×#100×C₄₃	C₂²	semidirect
30. C₄₃×#343	C₂²	semidirect
31. C₄₃×#341	C₂²	semidirect
185. #29748	C₄₃	direct (N × H)
212. C₂×#466	C₂×C₄₃	semidirect
213. #3006	C₂×C₄₃	semidirect
214. C₂×#408	C₂×C₄₃	semidirect
215. #2078	C₂×C₄₃	semidirect
216. #2051	C₂×C₄₃	semidirect
217. #2018	C₂×C₄₃	semidirect
218. #1900	C₂×C₄₃	semidirect
219. #1810	C₂×C₄₃	semidirect
230. C₂²×D₈	C₂²×C₄₃	semidirect
239. C₂×#108	C₂²×C₄₃	semidirect
240. C₂×#107	C₂²×C₄₃	semidirect
242. C₂×#102	C₂²×C₄₃	semidirect
243. C₂×#100	C₂²×C₄₃	semidirect
249. #343	C₂²×C₄₃	semidirect
250. #341	C₂²×C₄₃	semidirect
251. C₄₃	#29748	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×#466	2
C₄₃×#3006	2
C₂×C₄₃×#408	2
C₄₃×#2078	2
C₄₃×#2051	2
C₄₃×#2018	2
C₄₃×#1900	2
C₄₃×#1810	2
#29748	43

Subgroups — C43×#29748 #24949765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29748 #24949765