Subgroups — C₄₃×#29964 #24949981

Order 11008.

838 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#2311	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2068	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1852	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1788	C₂	1	2	yes	maximal
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#107×C₄₃	C₂²	1	2	yes	—
17	C₂×#107×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
19	C₂×#103×C₄₃	C₂²	1	2	yes	—
20	C₂×#103×C₄₃	C₂²	1	2	yes	—
21	C₂×#102×C₄₃	C₂²	1	2	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₄₃×#398	—	2	2	no	—
25	C₄₃×#396	—	2	2	no	—
26	C₄₃×#391	C₂²	1	1	yes	characteristic
27	C₄₃×#391	C₂²	1	1	yes	characteristic
28	C₄₃×#390	C₂²	1	1	yes	characteristic
29	C₄₃×#390	C₂²	1	1	yes	characteristic
30	C₄₃×#389	C₂²	1	2	yes	—
31	C₄₃×#386	—	2	2	no	—
32	C₄₃×#384	C₂²	1	1	yes	characteristic
33	C₄₃×#380	—	2	2	no	—
34	C₄₃×#380	C₂²	1	2	yes	—
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#336	C₂²	1	1	yes	characteristic
38	C₄₃×#336	C₂²	1	1	yes	characteristic
39	C₂×#41×C₄₃	—	2	2	no	—
40	C₂×#41×C₄₃	—	4	2	no	—
41	C₂×#41×C₄₃	—	4	2	no	—
42	C₂×#41×C₄₃	Q₈	1	4	yes	—
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
51	#125×C₄₃	—	4	2	no	—
52	#117×C₄₃	—	4	2	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
58	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	#107×C₄₃	—	4	2	no	—
70	#107×C₄₃	—	4	2	no	—
71	C₄⋊C₈×C₄₃	—	4	2	no	—
72	#103×C₄₃	—	4	2	no	—
73	#103×C₄₃	—	4	2	no	—
74	#102×C₄₃	—	4	2	no	—
75	#102×C₄₃	—	4	2	no	—
76	C₂²⋊C₈×C₄₃	—	2	4	no	—
77	#95×C₄₃	—	2	2	no	—
78	#95×C₄₃	—	2	2	no	—
79	#95×C₄₃	—	2	2	no	—
80	#95×C₄₃	—	2	2	no	—
81	C₂⁴×C₄₃	—	2	1	no	—
82	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
83	#41×C₄₃	—	4	8	no	—
84	#41×C₄₃	—	4	8	no	—
85	C₂×Q₈×C₄₃	—	2	1	no	—
86	C₂×Q₈×C₄₃	—	2	2	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
89	C₂×D₄×C₄₃	—	2	1	no	—
90	C₂×D₄×C₄₃	—	2	4	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	2	2	no	—
93	C₂×D₄×C₄₃	—	4	2	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	—	4	2	no	—
106	C₂²×C₄×C₄₃	—	4	2	no	—
107	C₂²×C₄×C₄₃	—	8	2	no	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₄₃	#41	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	4	2	no	—
127	C₄⋊C₄×C₄₃	—	4	2	no	—
128	C₄⋊C₄×C₄₃	—	4	4	no	—
129	C₄⋊C₄×C₄₃	—	8	2	no	—
130	C₄⋊C₄×C₄₃	—	8	2	no	—
131	C₂²⋊C₄×C₄₃	—	4	2	no	—
132	C₂²⋊C₄×C₄₃	—	8	2	no	—
133	C₂²⋊C₄×C₄₃	—	8	2	no	—
134	C₂²⋊C₄×C₄₃	—	8	2	no	—
135	C₄²×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	1	no	—
138	C₂³×C₄₃	—	2	1	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	2	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	2	no	—
145	C₂³×C₄₃	—	4	2	no	—
146	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
147	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₄₃	—	2	4	no	—
149	Q₈×C₄₃	—	4	2	no	—
150	D₄×C₄₃	—	2	4	no	—
151	D₄×C₄₃	—	4	8	no	—
152	D₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	4	8	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	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	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	8	4	no	—
178	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
182	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
183	C₈×C₄₃	—	4	2	no	—
184	C₈×C₄₃	—	4	2	no	—
185	#29964	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₃	—	2	4	no	—
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	4	2	no	—
189	C₂²×C₄₃	—	4	1	no	—
190	C₂²×C₄₃	—	4	1	no	—
191	C₂²×C₄₃	—	4	4	no	—
192	C₂²×C₄₃	—	4	2	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	1	no	—
195	C₂²×C₄₃	—	8	1	no	—
196	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
197	C₂²×C₄₃	#534	1	1	yes	characteristic
198	C₂²×C₄₃	#535	1	1	yes	characteristic
199	C₂²×C₄₃	#576	1	2	yes	—
200	C₂²×C₄₃	#578	1	2	yes	—
201	C₄×C₄₃	—	2	2	no	—
202	C₄×C₄₃	—	4	2	no	—
203	C₄×C₄₃	—	4	2	no	—
204	C₄×C₄₃	—	4	2	no	—
205	C₄×C₄₃	—	8	2	no	—
206	C₄×C₄₃	—	8	2	no	—
207	C₄×C₄₃	—	8	1	no	—
208	C₄×C₄₃	—	8	1	no	—
209	C₄×C₄₃	#538	1	2	yes	—
210	C₄×C₄₃	#543	1	2	yes	—
211	#2629	C₂×C₄₃	1	1	yes	characteristic, complemented
212	#2311	C₂×C₄₃	1	1	yes	characteristic
213	#2095	C₂×C₄₃	1	1	yes	characteristic, complemented
214	#2093	C₂×C₄₃	1	1	yes	characteristic, complemented
215	#2068	C₂×C₄₃	1	2	yes	complemented
216	#2067	C₂×C₄₃	1	2	yes	complemented
217	#2026	C₂×C₄₃	1	1	yes	characteristic, complemented
218	#2025	C₂×C₄₃	1	1	yes	characteristic, complemented
219	#1852	C₂×C₄₃	1	2	yes	complemented
220	#1798	C₂×C₄₃	1	1	yes	characteristic, complemented
221	#1788	C₂×C₄₃	1	2	yes	—
222	C₂×C₄₃	—	4	2	no	—
223	C₂×C₄₃	—	8	2	no	—
224	C₂×C₄₃	#2626	1	1	yes	characteristic
225	C₂×C₄₃	#3083	1	2	yes	—
226	C₂×C₄₃	#3203	1	2	yes	—
227	C₂×C₄₃	#3220	1	1	yes	characteristic
228	C₂×C₄₃	#3223	1	1	yes	characteristic
229	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
230	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
231	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#107	C₂²×C₄₃	1	2	yes	—
234	C₂×#107	C₂²×C₄₃	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
236	C₂×#103	C₂²×C₄₃	1	2	yes	—
237	C₂×#103	C₂²×C₄₃	1	2	yes	—
238	C₂×#102	C₂²×C₄₃	1	2	yes	—
239	C₂×#102	C₂²×C₄₃	1	2	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
241	#398	—	2	2	no	—
242	#396	—	2	2	no	—
243	#391	C₂²×C₄₃	1	1	yes	characteristic
244	#391	C₂²×C₄₃	1	1	yes	characteristic
245	#390	C₂²×C₄₃	1	1	yes	characteristic
246	#390	C₂²×C₄₃	1	1	yes	characteristic
247	#389	C₂²×C₄₃	1	2	yes	—
248	#386	—	2	2	no	—
249	#384	C₂²×C₄₃	1	1	yes	characteristic
250	#380	—	2	2	no	—
251	#380	C₂²×C₄₃	1	2	yes	—
252	#340	C₂²×C₄₃	1	2	yes	—
253	#340	C₂²×C₄₃	1	2	yes	—
254	#336	C₂²×C₄₃	1	1	yes	characteristic
255	#336	C₂²×C₄₃	1	1	yes	characteristic
256	C₄₃	#29964	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	4	2	no	—
259	C₂×#41	—	4	2	no	—
260	C₂×#41	Q₈×C₄₃	1	4	yes	—
261	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
268	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
269	#125	—	4	2	no	—
270	#117	—	4	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	4	2	no	—
276	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
287	#107	—	4	2	no	—
288	#107	—	4	2	no	—
289	C₄⋊C₈	—	4	2	no	—
290	#103	—	4	2	no	—
291	#103	—	4	2	no	—
292	#102	—	4	2	no	—
293	#102	—	4	2	no	—
294	C₂²⋊C₈	—	2	4	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	C₂⁴	—	2	1	no	—
300	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
301	#41	—	4	8	no	—
302	#41	—	4	8	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	8	2	no	—
326	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
330	C₂²×C₄	#41×C₄₃	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	8	2	no	—
348	C₄⋊C₄	—	8	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	8	2	no	—
351	C₂²⋊C₄	—	8	2	no	—
352	C₂²⋊C₄	—	8	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
365	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	4	2	no	—
368	D₄	—	2	4	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	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	—	4	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
397	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×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	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
414	C₂²	C₄₃×#534	1	1	yes	characteristic
415	C₂²	C₄₃×#535	1	1	yes	characteristic
416	C₂²	C₄₃×#576	1	2	yes	—
417	C₂²	C₄₃×#578	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	2	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	2	no	—
426	C₄	C₄₃×#538	1	2	yes	—
427	C₄	C₄₃×#543	1	2	yes	—
428	C₂	—	4	2	no	—
429	C₂	—	8	2	no	—
430	C₂	C₄₃×#2626	1	1	yes	characteristic
431	C₂	C₄₃×#3083	1	2	yes	—
432	C₂	C₄₃×#3203	1	2	yes	—
433	C₂	C₄₃×#3220	1	1	yes	characteristic
434	C₂	C₄₃×#3223	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#2629	C₂	semidirect
3. C₄₃×#2095	C₂	semidirect
4. C₄₃×#2093	C₂	semidirect
5. C₄₃×#2068	C₂	semidirect
6. C₄₃×#2067	C₂	semidirect
7. C₄₃×#2026	C₂	semidirect
8. C₄₃×#2025	C₂	semidirect
9. C₄₃×#1852	C₂	semidirect
10. C₄₃×#1798	C₂	semidirect
185. #29964	C₄₃	direct (N × H)
211. #2629	C₂×C₄₃	semidirect
213. #2095	C₂×C₄₃	semidirect
214. #2093	C₂×C₄₃	semidirect
215. #2068	C₂×C₄₃	semidirect
216. #2067	C₂×C₄₃	semidirect
217. #2026	C₂×C₄₃	semidirect
218. #2025	C₂×C₄₃	semidirect
219. #1852	C₂×C₄₃	semidirect
220. #1798	C₂×C₄₃	semidirect
256. C₄₃	#29964	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×#2629	2
C₄₃×#2311	2
C₄₃×#2095	2
C₄₃×#2093	2
C₄₃×#2068	2
C₄₃×#2067	2
C₄₃×#2026	2
C₄₃×#2025	2
C₄₃×#1852	2
C₄₃×#1798	2
C₄₃×#1788	2
#29964	43

Subgroups — C43×#29964 #24949981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29964 #24949981