Subgroups — C₄₃×#23705 #24943722

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#433	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2323	C₂	1	2	yes	maximal
4	C₄₃×#2086	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2075	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2036	C₂	1	2	yes	maximal
9	C₄₃×#2001	C₂	1	1	yes	maximal, characteristic
10	C₄×#107×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₄₃	—	2	4	no	—
17	C₄₃×#433	—	2	4	no	—
18	C₂×#107×C₄₃	C₂²	1	2	yes	—
19	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#103×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#391	C₂²	1	2	yes	—
30	C₄₃×#389	—	2	2	no	—
31	C₄₃×#389	C₂²	1	2	yes	—
32	C₄₃×#388	—	2	2	no	—
33	C₄₃×#388	—	2	2	no	—
34	C₄₃×#387	—	2	2	no	—
35	C₄₃×#380	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	2	yes	—
38	C₄₃×#340	C₂²	1	1	yes	characteristic
39	C₄₃×#340	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂×Q₁₆×C₄₃	—	2	4	no	—
44	C₂×Q₁₆×C₄₃	—	2	2	no	—
45	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²⋊Q₈×C₄₃	—	2	4	no	—
50	C₂²⋊Q₈×C₄₃	—	2	4	no	—
51	C₄×Q₈×C₄₃	—	2	4	no	—
52	C₄×Q₈×C₄₃	—	2	4	no	—
53	#117×C₄₃	—	2	2	no	—
54	#117×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	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	—	2	2	no	—
68	C₂×C₄²×C₄₃	—	2	2	no	—
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
71	#107×C₄₃	—	2	2	no	—
72	#107×C₄₃	—	2	4	no	—
73	C₄⋊C₈×C₄₃	—	2	2	no	—
74	C₄⋊C₈×C₄₃	—	2	2	no	—
75	#103×C₄₃	—	2	4	no	—
76	#103×C₄₃	—	2	4	no	—
77	#103×C₄₃	—	2	4	no	—
78	C₂²⋊C₈×C₄₃	—	2	2	no	—
79	C₂²⋊C₈×C₄₃	—	2	2	no	—
80	#97×C₄₃	—	2	2	no	—
81	C₄×C₈×C₄₃	D₄	1	4	yes	—
82	#95×C₄₃	—	2	2	no	—
83	#95×C₄₃	—	2	2	no	—
84	#95×C₄₃	—	2	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	2	2	no	—
93	C₂×Q₈×C₄₃	#41	1	4	yes	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₄₃	—	2	8	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	1	no	—
112	C₂×C₈×C₄₃	—	2	1	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₄₃	—	2	8	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×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	—	4	4	no	—
126	C₄⋊C₄×C₄₃	—	8	2	no	—
127	C₄⋊C₄×C₄₃	#41	1	4	yes	—
128	C₂²⋊C₄×C₄₃	—	2	8	no	—
129	C₂²⋊C₄×C₄₃	—	2	2	no	—
130	C₂²⋊C₄×C₄₃	—	2	2	no	—
131	C₂²⋊C₄×C₄₃	—	8	2	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₄²×C₄₃	—	4	4	no	—
135	C₄²×C₄₃	—	8	2	no	—
136	C₄²×C₄₃	C₂×D₄	1	2	yes	—
137	C₄²×C₄₃	#41	1	2	yes	—
138	C₂³×C₄₃	—	2	1	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	1	no	—
143	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₃	—	2	4	no	—
145	Q₈×C₄₃	—	2	4	no	—
146	Q₈×C₄₃	—	4	2	no	—
147	Q₈×C₄₃	—	4	2	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	2	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	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	#121	1	2	yes	—
174	C₂×C₄×C₄₃	#121	1	2	yes	—
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
179	C₈×C₄₃	—	2	2	no	—
180	C₈×C₄₃	—	2	2	no	—
181	C₈×C₄₃	—	4	1	no	—
182	C₈×C₄₃	—	4	1	no	—
183	#23705	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₃	—	4	2	no	—
185	C₂²×C₄₃	—	4	2	no	—
186	C₂²×C₄₃	—	4	1	no	—
187	C₂²×C₄₃	—	4	1	no	—
188	C₂²×C₄₃	—	4	1	no	—
189	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
190	C₂²×C₄₃	#525	1	2	yes	—
191	C₂²×C₄₃	#576	1	1	yes	characteristic
192	C₂²×C₄₃	#578	1	2	yes	—
193	C₂²×C₄₃	#578	1	1	yes	characteristic
194	C₄×C₄₃	—	2	2	no	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	4	4	no	—
197	C₄×C₄₃	—	4	1	no	—
198	C₄×C₄₃	—	4	4	no	—
199	C₄×C₄₃	—	4	1	no	—
200	C₄×C₄₃	—	4	1	no	—
201	C₄×C₄₃	—	8	2	no	—
202	C₄×C₄₃	—	8	2	no	—
203	C₄×C₄₃	#525	1	1	yes	characteristic
204	C₄×C₄₃	#529	1	2	yes	—
205	C₄×C₄₃	#532	1	1	yes	characteristic
206	C₂×C₄×Q₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
207	C₂×#433	C₂×C₄₃	1	1	yes	characteristic
208	#2323	C₂×C₄₃	1	2	yes	—
209	#2086	C₂×C₄₃	1	1	yes	characteristic, complemented
210	#2075	C₂×C₄₃	1	1	yes	characteristic
211	#2068	C₂×C₄₃	1	2	yes	complemented
212	#2056	C₂×C₄₃	1	1	yes	characteristic, complemented
213	#2036	C₂×C₄₃	1	2	yes	—
214	#2001	C₂×C₄₃	1	1	yes	characteristic
215	C₄×#107	C₂×C₄₃	1	1	yes	characteristic, complemented
216	#1763	C₂×C₄₃	1	2	yes	complemented
217	C₂×C₄₃	—	8	1	no	—
218	C₂×C₄₃	#2392	1	1	yes	characteristic
219	C₂×C₄₃	#3059	1	1	yes	characteristic
220	C₂×C₄₃	#3061	1	1	yes	characteristic
221	C₂×C₄₃	#3124	1	2	yes	—
222	C₂×C₄₃	#3127	1	2	yes	—
223	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
226	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
227	C₄×Q₁₆	—	2	4	no	—
228	#433	—	2	4	no	—
229	C₂×#107	C₂²×C₄₃	1	2	yes	—
230	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#103	C₂²×C₄₃	1	2	yes	—
234	C₂×#103	C₂²×C₄₃	1	2	yes	—
235	C₂×#103	C₂²×C₄₃	1	2	yes	—
236	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
240	#391	C₂²×C₄₃	1	2	yes	—
241	#389	—	2	2	no	—
242	#389	C₂²×C₄₃	1	2	yes	—
243	#388	—	2	2	no	—
244	#388	—	2	2	no	—
245	#387	—	2	2	no	—
246	#380	C₂²×C₄₃	1	2	yes	—
247	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
248	#340	C₂²×C₄₃	1	1	yes	characteristic
249	#340	C₂²×C₄₃	1	2	yes	—
250	#340	C₂²×C₄₃	1	1	yes	characteristic
251	#340	C₂²×C₄₃	1	2	yes	—
252	C₄₃	#23705	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
254	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
255	C₂×Q₁₆	—	2	4	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	#117	—	2	2	no	—
266	#117	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
283	#107	—	2	2	no	—
284	#107	—	2	4	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	#103	—	2	4	no	—
288	#103	—	2	4	no	—
289	#103	—	2	4	no	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	D₄×C₄₃	1	4	yes	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	#41×C₄₃	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
320	Q₁₆	—	2	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
328	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	8	2	no	—
339	C₄⋊C₄	#41×C₄₃	1	4	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₂²⋊C₄	—	8	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	4	no	—
347	C₄²	—	8	2	no	—
348	C₄²	C₂×D₄×C₄₃	1	2	yes	—
349	C₄²	#41×C₄₃	1	2	yes	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	1	no	—
355	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	#121×C₄₃	1	2	yes	—
386	C₂×C₄	#121×C₄₃	1	2	yes	—
387	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
389	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	1	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
401	C₂²	C₄₃×#525	1	2	yes	—
402	C₂²	C₄₃×#576	1	1	yes	characteristic
403	C₂²	C₄₃×#578	1	2	yes	—
404	C₂²	C₄₃×#578	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₄₃×#525	1	1	yes	characteristic
415	C₄	C₄₃×#529	1	2	yes	—
416	C₄	C₄₃×#532	1	1	yes	characteristic
417	C₂	—	8	1	no	—
418	C₂	C₄₃×#2392	1	1	yes	characteristic
419	C₂	C₄₃×#3059	1	1	yes	characteristic
420	C₂	C₄₃×#3061	1	1	yes	characteristic
421	C₂	C₄₃×#3124	1	2	yes	—
422	C₂	C₄₃×#3127	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
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. C₂×C₄×Q₁₆×C₄₃	C₂	semidirect
4. C₄₃×#2086	C₂	semidirect
6. C₄₃×#2068	C₂	semidirect
7. C₄₃×#2056	C₂	semidirect
10. C₄×#107×C₄₃	C₂	semidirect
11. C₄₃×#1763	C₂	semidirect
183. #23705	C₄₃	direct (N × H)
206. C₂×C₄×Q₁₆	C₂×C₄₃	semidirect
209. #2086	C₂×C₄₃	semidirect
211. #2068	C₂×C₄₃	semidirect
212. #2056	C₂×C₄₃	semidirect
215. C₄×#107	C₂×C₄₃	semidirect
216. #1763	C₂×C₄₃	semidirect
252. C₄₃	#23705	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×C₄×Q₁₆×C₄₃	2
C₂×C₄₃×#433	2
C₄₃×#2323	2
C₄₃×#2086	2
C₄₃×#2075	2
C₄₃×#2068	2
C₄₃×#2056	2
C₄₃×#2036	2
C₄₃×#2001	2
C₄×#107×C₄₃	2
C₄₃×#1763	2
#23705	43

Subgroups — C43×#23705 #24943722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#23705 #24943722