Subgroups — C₄₃×#20858 #24940875

Order 11008.

1394 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#428	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#413	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2311	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1857	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1856	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1733	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
10	C₄₃×#520	—	2	2	no	—
11	C₄₃×#520	—	2	2	no	—
12	C₄₃×#519	C₂²	1	2	yes	—
13	C₄₃×#518	—	2	2	no	—
14	C₄₃×#518	C₂²	1	2	yes	—
15	C₄×#41×C₄₃	—	2	4	no	—
16	C₂×#117×C₄₃	—	2	2	no	—
17	C₂×#117×C₄₃	C₂²	1	2	yes	—
18	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#428	—	2	4	no	—
21	C₄₃×#428	C₂²	1	8	yes	—
22	C₂×#107×C₄₃	—	2	2	no	—
23	C₂×#106×C₄₃	—	2	2	no	—
24	C₄₃×#413	C₄	1	8	yes	complemented
25	C₂×#101×C₄₃	C₂²	1	2	yes	—
26	C₂×#100×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#391	C₂²	1	2	yes	—
28	C₄₃×#390	C₂²	1	2	yes	—
29	C₄₃×#386	—	2	2	no	—
30	C₄₃×#380	—	2	2	no	—
31	C₄₃×#339	C₂²	1	8	yes	—
32	C₂×#41×C₄₃	—	2	2	no	—
33	C₂×#41×C₄₃	—	2	2	no	—
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
36	C₂×#41×C₄₃	Q₈	1	4	yes	—
37	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₄₃	D₄	1	2	yes	—
39	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	—	2	1	no	—
41	C₂³×C₄×C₄₃	D₄	1	2	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₄₃	—	2	2	no	—
44	C₂×M₁₆×C₄₃	—	2	4	no	—
45	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
46	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
47	C₂²×C₈×C₄₃	—	2	2	no	—
48	C₄×Q₈×C₄₃	—	2	4	no	—
49	C₄×Q₈×C₄₃	—	2	4	no	—
50	C₄×D₄×C₄₃	—	2	8	no	—
51	C₄×D₄×C₄₃	—	2	8	no	—
52	C₄×D₄×C₄₃	—	2	4	no	—
53	C₄×D₄×C₄₃	—	2	4	no	—
54	#117×C₄₃	—	2	4	no	—
55	#117×C₄₃	—	2	4	no	—
56	#117×C₄₃	—	2	2	no	—
57	#117×C₄₃	—	2	4	no	—
58	#117×C₄₃	—	2	2	no	—
59	#117×C₄₃	—	2	4	no	—
60	#117×C₄₃	D₄	1	4	yes	—
61	#117×C₄₃	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₄²×C₄₃	—	2	4	no	—
76	C₂×C₄²×C₄₃	—	2	2	no	—
77	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
78	#107×C₄₃	—	2	8	no	—
79	#106×C₄₃	—	2	8	no	—
80	#101×C₄₃	C₂×C₄	1	8	yes	complemented
81	#100×C₄₃	C₂×C₄	1	8	yes	complemented
82	#95×C₄₃	—	2	4	no	—
83	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
84	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
85	#41×C₄₃	—	2	8	no	—
86	#41×C₄₃	—	2	8	no	—
87	#41×C₄₃	—	2	8	no	—
88	#41×C₄₃	—	2	8	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
92	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	2	4	no	—
97	C₂×D₄×C₄₃	C₄⋊C₄	1	8	yes	—
98	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	4	2	no	—
110	C₂²×C₄×C₄₃	—	8	2	no	—
111	C₂²×C₄×C₄₃	C₄⋊C₄	1	8	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₄₃	#41	1	4	yes	—
119	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₄₃	—	2	8	no	—
121	M₁₆×C₄₃	—	2	4	no	—
122	M₁₆×C₄₃	C₂²×C₄	1	8	yes	—
123	C₂×C₈×C₄₃	—	2	8	no	—
124	C₂×C₈×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	2	4	no	—
126	C₄⋊C₄×C₄₃	—	2	4	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	4	1	no	—
131	C₄⋊C₄×C₄₃	—	4	1	no	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
134	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
135	C₂²⋊C₄×C₄₃	—	2	8	no	—
136	C₂²⋊C₄×C₄₃	—	2	4	no	—
137	C₂²⋊C₄×C₄₃	—	2	4	no	—
138	C₂²⋊C₄×C₄₃	—	4	2	no	—
139	C₂²⋊C₄×C₄₃	—	8	4	no	—
140	C₄²×C₄₃	—	2	8	no	—
141	C₄²×C₄₃	—	2	4	no	—
142	C₄²×C₄₃	—	2	4	no	—
143	C₄²×C₄₃	—	2	4	no	—
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	—	4	1	no	—
147	C₂³×C₄₃	—	4	1	no	—
148	C₂³×C₄₃	—	4	2	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
151	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
152	C₂³×C₄₃	#120	1	2	yes	—
153	C₂³×C₄₃	#123	1	2	yes	—
154	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₃	—	2	4	no	—
156	Q₈×C₄₃	—	2	4	no	—
157	D₄×C₄₃	—	2	16	no	—
158	D₄×C₄₃	—	2	4	no	—
159	D₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	8	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	4	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	8	2	no	—
172	C₂×C₄×C₄₃	—	8	2	no	—
173	C₂×C₄×C₄₃	—	8	4	no	—
174	C₂×C₄×C₄₃	—	8	4	no	—
175	C₂×C₄×C₄₃	—	8	4	no	—
176	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
177	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
179	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
183	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
184	C₂×C₄×C₄₃	#123	1	2	yes	—
185	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
189	C₈×C₄₃	—	2	8	no	—
190	#20858	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	4	no	—
196	C₂²×C₄₃	—	4	2	no	—
197	C₂²×C₄₃	—	4	2	no	—
198	C₂²×C₄₃	—	4	4	no	—
199	C₂²×C₄₃	—	4	2	no	—
200	C₂²×C₄₃	—	4	2	no	—
201	C₂²×C₄₃	—	8	2	no	—
202	C₂²×C₄₃	#385	1	4	yes	—
203	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
204	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
205	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
206	C₄×C₄₃	—	2	4	no	—
207	C₄×C₄₃	—	4	4	no	—
208	C₄×C₄₃	—	4	4	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	—	8	2	no	—
211	C₄×C₄₃	#385	1	2	yes	—
212	C₄×C₄₃	#385	1	2	yes	—
213	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
214	C₄×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
215	#3428	C₂×C₄₃	1	1	yes	characteristic
216	C₂×#428	C₂×C₄₃	1	2	yes	complemented
217	C₂×#413	C₂×C₄₃	1	1	yes	characteristic
218	#2311	C₂×C₄₃	1	1	yes	characteristic
219	#1857	C₂×C₄₃	1	4	yes	complemented
220	#1856	C₂×C₄₃	1	4	yes	complemented
221	#1733	C₂×C₄₃	1	2	yes	complemented
222	C₂×C₄₃	—	2	1	no	—
223	C₂×C₄₃	—	2	1	no	—
224	C₂×C₄₃	—	2	4	no	—
225	C₂×C₄₃	—	4	4	no	—
226	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
227	C₂×C₄₃	#3021	1	1	yes	characteristic
228	C₂×C₄₃	#3022	1	1	yes	characteristic
229	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
230	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
231	#520	—	2	2	no	—
232	#520	—	2	2	no	—
233	#519	C₂²×C₄₃	1	2	yes	—
234	#518	—	2	2	no	—
235	#518	C₂²×C₄₃	1	2	yes	—
236	C₄×#41	—	2	4	no	—
237	C₂×#117	—	2	2	no	—
238	C₂×#117	C₂²×C₄₃	1	2	yes	—
239	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
241	#428	—	2	4	no	—
242	#428	C₂²×C₄₃	1	8	yes	—
243	C₂×#107	—	2	2	no	—
244	C₂×#106	—	2	2	no	—
245	#413	C₄×C₄₃	1	8	yes	complemented
246	C₂×#101	C₂²×C₄₃	1	2	yes	—
247	C₂×#100	C₂²×C₄₃	1	2	yes	—
248	#391	C₂²×C₄₃	1	2	yes	—
249	#390	C₂²×C₄₃	1	2	yes	—
250	#386	—	2	2	no	—
251	#380	—	2	2	no	—
252	#339	C₂²×C₄₃	1	8	yes	—
253	C₄₃	#20858	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
258	C₂×#41	Q₈×C₄₃	1	4	yes	—
259	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
260	C₂²×D₄	D₄×C₄₃	1	2	yes	—
261	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	D₄×C₄₃	1	2	yes	—
264	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
268	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
269	C₂²×C₈	—	2	2	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	2	4	no	—
272	C₄×D₄	—	2	8	no	—
273	C₄×D₄	—	2	8	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	4	no	—
276	#117	—	2	4	no	—
277	#117	—	2	4	no	—
278	#117	—	2	2	no	—
279	#117	—	2	4	no	—
280	#117	—	2	2	no	—
281	#117	—	2	4	no	—
282	#117	D₄×C₄₃	1	4	yes	—
283	#117	C₂³×C₄₃	1	4	yes	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
291	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	4	no	—
297	C₂×C₄²	—	2	4	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
300	#107	—	2	8	no	—
301	#106	—	2	8	no	—
302	#101	C₂×C₄×C₄₃	1	8	yes	complemented
303	#100	C₂×C₄×C₄₃	1	8	yes	complemented
304	#95	—	2	4	no	—
305	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
306	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
307	#41	—	2	8	no	—
308	#41	—	2	8	no	—
309	#41	—	2	8	no	—
310	#41	—	2	8	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
314	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	C₄⋊C₄×C₄₃	1	8	yes	—
320	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
321	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	C₄⋊C₄×C₄₃	1	8	yes	—
334	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
339	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
340	C₂²×C₄	#41×C₄₃	1	4	yes	—
341	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
342	M₁₆	—	2	8	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	C₂²×C₄×C₄₃	1	8	yes	—
345	C₂×C₈	—	2	8	no	—
346	C₂×C₈	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
356	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
357	C₂²⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	8	4	no	—
362	C₄²	—	2	8	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
373	C₂³	C₂×C₄⋊C₄×C₄₃	1	2	yes	—
374	C₂³	#120×C₄₃	1	2	yes	—
375	C₂³	#123×C₄₃	1	2	yes	—
376	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	D₄	—	2	16	no	—
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	4	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	—	8	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	—	8	4	no	—
397	C₂×C₄	—	8	4	no	—
398	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
399	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	2	yes	—
400	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
401	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
402	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
403	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
405	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
406	C₂×C₄	#123×C₄₃	1	2	yes	—
407	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
409	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
411	C₈	—	2	8	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	C₄₃×#385	1	4	yes	—
424	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
425	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
426	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
427	C₄	—	2	4	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	4	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	C₄₃×#385	1	2	yes	—
433	C₄	C₄₃×#385	1	2	yes	—
434	C₄	C₂×C₄×D₄×C₄₃	1	2	yes	—
435	C₄	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	4	no	—
439	C₂	—	4	4	no	—
440	C₂	C₂×C₄₃×#385	1	1	yes	characteristic
441	C₂	C₄₃×#3021	1	1	yes	characteristic
442	C₂	C₄₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂×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. C₂×C₄₃×#428	C₂	semidirect
5. C₄₃×#1857	C₂	semidirect
6. C₄₃×#1856	C₂	semidirect
7. C₄₃×#1733	C₂	semidirect
24. C₄₃×#413	C₄	semidirect
45. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
80. #101×C₄₃	C₂×C₄	semidirect
81. #100×C₄₃	C₂×C₄	semidirect
190. #20858	C₄₃	direct (N × H)
216. C₂×#428	C₂×C₄₃	semidirect
219. #1857	C₂×C₄₃	semidirect
220. #1856	C₂×C₄₃	semidirect
221. #1733	C₂×C₄₃	semidirect
245. #413	C₄×C₄₃	semidirect
253. C₄₃	#20858	direct (N × H)
267. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
302. #101	C₂×C₄×C₄₃	semidirect
303. #100	C₂×C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3428	2
C₂×C₄₃×#428	2
C₂×C₄₃×#413	2
C₄₃×#2311	2
C₄₃×#1857	2
C₄₃×#1856	2
C₄₃×#1733	2
#20858	43

Subgroups — C43×#20858 #24940875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20858 #24940875