Subgroups — C₄₃×#32917 #24952934

Order 11008.

1588 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#463	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#447	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1879	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1877	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1802	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#518	—	2	8	no	—
19	C₂×C₄×D₄×C₄₃	—	2	2	no	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
22	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₄₃	—	2	2	no	—
25	C₄₃×#463	—	2	8	no	—
26	C₄₃×#450	—	2	4	no	—
27	C₄₃×#447	—	2	4	no	—
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
29	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
33	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#396	—	2	2	no	—
36	C₄₃×#394	—	2	2	no	—
37	C₄₃×#391	C₂²	1	1	yes	characteristic, complemented
38	C₄₃×#390	C₂²	1	1	yes	characteristic, complemented
39	C₄₃×#384	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×#340	C₂²	1	2	yes	complemented
41	C₄₃×#340	C₂²	1	2	yes	complemented
42	C₄₃×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₄₃	—	2	1	no	—
44	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	—	2	4	no	—
46	C₂²×D₄×C₄₃	—	2	4	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	—	2	2	no	—
50	C₂²×D₄×C₄₃	D₄	1	4	yes	—
51	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₃	—	2	2	no	—
54	C₂³×C₄×C₄₃	—	2	2	no	—
55	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₄₃	—	2	4	no	—
57	C₂×SD₁₆×C₄₃	—	2	4	no	—
58	C₂×SD₁₆×C₄₃	—	2	4	no	—
59	C₂×D₈×C₄₃	—	2	4	no	—
60	C₂×D₈×C₄₃	—	2	4	no	—
61	C₂×D₈×C₄₃	—	2	4	no	—
62	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
64	#124×C₄₃	—	2	4	no	—
65	C₂²⋊Q₈×C₄₃	—	2	2	no	—
66	C₂²⋊Q₈×C₄₃	—	2	2	no	—
67	#121×C₄₃	—	2	2	no	—
68	#121×C₄₃	—	2	2	no	—
69	C₄×D₄×C₄₃	—	2	16	no	—
70	C₄×D₄×C₄₃	—	2	4	no	—
71	C₄×D₄×C₄₃	—	2	4	no	—
72	C₄×D₄×C₄₃	—	2	4	no	—
73	C₄×D₄×C₄₃	D₄	1	8	yes	complemented
74	#117×C₄₃	—	2	4	no	—
75	#117×C₄₃	—	2	4	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
83	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
91	C₂×C₄²×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₃	—	2	4	no	—
95	#103×C₄₃	—	2	4	no	—
96	#102×C₄₃	—	2	4	no	—
97	#102×C₄₃	—	2	4	no	—
98	#102×C₄₃	—	2	4	no	—
99	C₂²⋊C₈×C₄₃	—	2	2	no	—
100	C₂²⋊C₈×C₄₃	—	2	2	no	—
101	#95×C₄₃	—	2	2	no	—
102	C₂⁴×C₄₃	—	2	4	no	—
103	C₂⁴×C₄₃	—	2	4	no	—
104	C₂⁴×C₄₃	—	2	2	no	—
105	C₂⁴×C₄₃	—	2	4	no	—
106	C₂⁴×C₄₃	—	2	1	no	—
107	C₂⁴×C₄₃	—	8	2	no	—
108	C₂⁴×C₄₃	—	8	2	no	—
109	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	2	4	no	—
115	C₂×D₄×C₄₃	—	2	16	no	—
116	C₂×D₄×C₄₃	—	2	4	no	—
117	C₂×D₄×C₄₃	—	2	16	no	—
118	C₂×D₄×C₄₃	—	2	4	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	1	no	—
124	C₂×D₄×C₄₃	—	2	1	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	4	2	no	—
127	C₂×D₄×C₄₃	—	8	2	no	—
128	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₄₃	#41	1	4	yes	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	8	no	—
134	C₂²×C₄×C₄₃	—	2	8	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	—	2	1	no	—
139	C₂²×C₄×C₄₃	—	8	2	no	—
140	C₂²×C₄×C₄₃	—	8	2	no	—
141	C₂²×C₄×C₄₃	—	8	2	no	—
142	C₂²×C₄×C₄₃	—	8	2	no	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	#41	1	2	yes	—
148	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₄₃	—	4	8	no	—
150	D₈×C₄₃	—	4	8	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₂×C₈×C₄₃	—	2	2	no	—
154	C₂×C₈×C₄₃	—	2	2	no	—
155	C₂×C₈×C₄₃	—	2	2	no	—
156	C₂×C₈×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	—	2	4	no	—
158	C₄⋊C₄×C₄₃	—	2	2	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₄⋊C₄×C₄₃	—	2	1	no	—
163	C₄⋊C₄×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	—	8	2	no	—
165	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
166	C₂²⋊C₄×C₄₃	—	2	4	no	—
167	C₂²⋊C₄×C₄₃	—	2	8	no	—
168	C₂²⋊C₄×C₄₃	—	2	4	no	—
169	C₂²⋊C₄×C₄₃	—	2	8	no	—
170	C₂²⋊C₄×C₄₃	—	4	4	no	—
171	C₂²⋊C₄×C₄₃	—	4	2	no	—
172	C₂²⋊C₄×C₄₃	—	4	2	no	—
173	C₂²⋊C₄×C₄₃	—	8	2	no	—
174	C₄²×C₄₃	—	2	4	no	—
175	C₄²×C₄₃	—	2	2	no	—
176	C₄²×C₄₃	C₂×D₄	1	4	yes	—
177	C₂³×C₄₃	—	2	16	no	—
178	C₂³×C₄₃	—	2	1	no	—
179	C₂³×C₄₃	—	2	4	no	—
180	C₂³×C₄₃	—	2	4	no	—
181	C₂³×C₄₃	—	2	1	no	—
182	C₂³×C₄₃	—	2	4	no	—
183	C₂³×C₄₃	—	2	2	no	—
184	C₂³×C₄₃	—	2	2	no	—
185	C₂³×C₄₃	—	4	2	no	—
186	C₂³×C₄₃	—	4	2	no	—
187	C₂³×C₄₃	—	4	2	no	—
188	C₂³×C₄₃	—	4	2	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	—	4	1	no	—
191	C₂³×C₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	4	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	8	4	no	—
195	C₂³×C₄₃	—	8	4	no	—
196	C₂³×C₄₃	—	8	8	no	—
197	C₂³×C₄₃	—	8	8	no	—
198	C₂³×C₄₃	#121	1	2	yes	—
199	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₄₃	—	4	2	no	—
201	Q₈×C₄₃	—	4	2	no	—
202	D₄×C₄₃	—	2	16	no	—
203	D₄×C₄₃	—	2	4	no	—
204	D₄×C₄₃	—	2	4	no	—
205	D₄×C₄₃	—	2	4	no	—
206	D₄×C₄₃	—	4	2	no	—
207	D₄×C₄₃	—	4	2	no	—
208	D₄×C₄₃	—	8	4	no	—
209	D₄×C₄₃	#121	1	8	yes	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	4	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	—	4	1	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	8	8	no	—
230	C₂×C₄×C₄₃	—	8	8	no	—
231	C₂×C₄×C₄₃	#120	1	4	yes	—
232	C₂×C₄×C₄₃	#121	1	2	yes	—
233	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
237	C₈×C₄₃	—	4	2	no	—
238	C₈×C₄₃	—	4	2	no	—
239	#32917	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	—	2	8	no	—
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	2	2	no	—
244	C₂²×C₄₃	—	4	2	no	—
245	C₂²×C₄₃	—	4	4	no	—
246	C₂²×C₄₃	—	4	4	no	—
247	C₂²×C₄₃	—	4	2	no	—
248	C₂²×C₄₃	—	4	4	no	—
249	C₂²×C₄₃	—	4	4	no	—
250	C₂²×C₄₃	—	4	4	no	—
251	C₂²×C₄₃	—	4	4	no	—
252	C₂²×C₄₃	—	8	16	no	—
253	C₂²×C₄₃	—	8	1	no	—
254	C₂²×C₄₃	—	8	2	no	—
255	C₂²×C₄₃	—	8	2	no	—
256	C₂²×C₄₃	—	8	1	no	—
257	C₂²×C₄₃	—	8	1	no	—
258	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
259	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
260	C₂²×C₄₃	#525	1	1	yes	characteristic
261	C₂²×C₄₃	#576	1	2	yes	—
262	C₂²×C₄₃	#577	1	2	yes	—
263	C₄×C₄₃	—	2	2	no	—
264	C₄×C₄₃	—	2	4	no	—
265	C₄×C₄₃	—	4	2	no	—
266	C₄×C₄₃	—	4	4	no	—
267	C₄×C₄₃	—	8	1	no	—
268	C₄×C₄₃	—	8	1	no	—
269	C₄×C₄₃	—	8	1	no	—
270	C₄×C₄₃	C₂×#121	1	2	yes	—
271	C₄×C₄₃	#525	1	2	yes	—
272	C₂×#518	C₂×C₄₃	1	1	yes	characteristic, complemented
273	C₂×#463	C₂×C₄₃	1	2	yes	complemented
274	C₂×#450	C₂×C₄₃	1	1	yes	characteristic, complemented
275	C₂×#447	C₂×C₄₃	1	1	yes	characteristic
276	#2620	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#1879	C₂×C₄₃	1	2	yes	complemented
278	#1877	C₂×C₄₃	1	2	yes	complemented
279	#1875	C₂×C₄₃	1	1	yes	characteristic, complemented
280	#1873	C₂×C₄₃	1	1	yes	characteristic, complemented
281	#1802	C₂×C₄₃	1	2	yes	complemented
282	#1798	C₂×C₄₃	1	1	yes	characteristic, complemented
283	C₂×C₄₃	—	4	2	no	—
284	C₂×C₄₃	—	4	8	no	—
285	C₂×C₄₃	—	16	1	no	—
286	C₂×C₄₃	#2847	1	1	yes	characteristic
287	C₂×C₄₃	#3012	1	2	yes	—
288	C₂×C₄₃	#3041	1	1	yes	characteristic
289	C₂×C₄₃	#3042	1	1	yes	characteristic
290	C₂×C₄₃	#3118	1	2	yes	—
291	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
292	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
293	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
294	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic, complemented
295	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
297	#518	—	2	8	no	—
298	C₂×C₄×D₄	—	2	2	no	—
299	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
300	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
301	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
302	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
303	C₂²×C₂²⋊C₄	—	2	2	no	—
304	#463	—	2	8	no	—
305	#450	—	2	4	no	—
306	#447	—	2	4	no	—
307	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
308	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
309	C₂×#102	C₂²×C₄₃	1	2	yes	—
310	C₂×#102	C₂²×C₄₃	1	2	yes	—
311	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
312	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
313	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
314	#396	—	2	2	no	—
315	#394	—	2	2	no	—
316	#391	C₂²×C₄₃	1	1	yes	characteristic, complemented
317	#390	C₂²×C₄₃	1	1	yes	characteristic, complemented
318	#384	C₂²×C₄₃	1	1	yes	characteristic, complemented
319	#340	C₂²×C₄₃	1	2	yes	complemented
320	#340	C₂²×C₄₃	1	2	yes	complemented
321	#336	C₂²×C₄₃	1	2	yes	complemented
322	C₄₃	#32917	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁵	—	2	1	no	—
324	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
325	C₂²×D₄	—	2	4	no	—
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	D₄×C₄₃	1	4	yes	—
331	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
333	C₂³×C₄	—	2	2	no	—
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×D₈	—	2	4	no	—
340	C₂×D₈	—	2	4	no	—
341	C₂×D₈	—	2	4	no	—
342	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
343	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
344	#124	—	2	4	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	C₄×D₄	—	2	16	no	—
350	C₄×D₄	—	2	4	no	—
351	C₄×D₄	—	2	4	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	D₄×C₄₃	1	8	yes	complemented
354	#117	—	2	4	no	—
355	#117	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	16	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
374	C₄⋊C₈	—	2	4	no	—
375	#103	—	2	4	no	—
376	#102	—	2	4	no	—
377	#102	—	2	4	no	—
378	#102	—	2	4	no	—
379	C₂²⋊C₈	—	2	2	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	#95	—	2	2	no	—
382	C₂⁴	—	2	4	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	2	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	—	8	2	no	—
388	C₂⁴	—	8	2	no	—
389	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	16	no	—
397	C₂×D₄	—	2	16	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
409	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
410	C₂×D₄	#41×C₄₃	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	8	2	no	—
420	C₂²×C₄	—	8	2	no	—
421	C₂²×C₄	—	8	2	no	—
422	C₂²×C₄	—	8	2	no	—
423	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
427	C₂²×C₄	#41×C₄₃	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
429	SD₁₆	—	4	8	no	—
430	D₈	—	4	8	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	8	2	no	—
445	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	8	2	no	—
454	C₄²	—	2	4	no	—
455	C₄²	—	2	2	no	—
456	C₄²	C₂×D₄×C₄₃	1	4	yes	—
457	C₂³	—	2	16	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	8	4	no	—
475	C₂³	—	8	4	no	—
476	C₂³	—	8	8	no	—
477	C₂³	—	8	8	no	—
478	C₂³	#121×C₄₃	1	2	yes	—
479	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	2	16	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	4	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	8	4	no	—
489	D₄	#121×C₄₃	1	8	yes	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	8	8	no	—
510	C₂×C₄	—	8	8	no	—
511	C₂×C₄	#120×C₄₃	1	4	yes	—
512	C₂×C₄	#121×C₄₃	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
515	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
516	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
517	C₈	—	4	2	no	—
518	C₈	—	4	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	8	16	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
538	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
539	C₂²	C₄₃×#525	1	1	yes	characteristic
540	C₂²	C₄₃×#576	1	2	yes	—
541	C₂²	C₄₃×#577	1	2	yes	—
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	C₂×#121×C₄₃	1	2	yes	—
550	C₄	C₄₃×#525	1	2	yes	—
551	C₂	—	4	2	no	—
552	C₂	—	4	8	no	—
553	C₂	—	16	1	no	—
554	C₂	C₄₃×#2847	1	1	yes	characteristic
555	C₂	C₄₃×#3012	1	2	yes	—
556	C₂	C₄₃×#3041	1	1	yes	characteristic
557	C₂	C₄₃×#3042	1	1	yes	characteristic
558	C₂	C₄₃×#3118	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#447	C₂
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×C₄₃×#518	C₂	semidirect
2. C₂×C₄₃×#463	C₂	semidirect
3. C₂×C₄₃×#450	C₂	semidirect
5. C₄₃×#2620	C₂	semidirect
6. C₄₃×#1879	C₂	semidirect
7. C₄₃×#1877	C₂	semidirect
8. C₄₃×#1875	C₂	semidirect
9. C₄₃×#1873	C₂	semidirect
10. C₄₃×#1802	C₂	semidirect
11. C₄₃×#1798	C₂	semidirect
15. C₂×#124×C₄₃	C₂²	semidirect
28. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
29. C₂×#103×C₄₃	C₂²	semidirect
32. C₂×#102×C₄₃	C₂²	semidirect
37. C₄₃×#391	C₂²	semidirect
38. C₄₃×#390	C₂²	semidirect
39. C₄₃×#384	C₂²	semidirect
40. C₄₃×#340	C₂²	semidirect
41. C₄₃×#340	C₂²	semidirect
42. C₄₃×#336	C₂²	semidirect
73. C₄×D₄×C₄₃	D₄	semidirect
239. #32917	C₄₃	direct (N × H)
272. C₂×#518	C₂×C₄₃	semidirect
273. C₂×#463	C₂×C₄₃	semidirect
274. C₂×#450	C₂×C₄₃	semidirect
276. #2620	C₂×C₄₃	semidirect
277. #1879	C₂×C₄₃	semidirect
278. #1877	C₂×C₄₃	semidirect
279. #1875	C₂×C₄₃	semidirect
280. #1873	C₂×C₄₃	semidirect
281. #1802	C₂×C₄₃	semidirect
282. #1798	C₂×C₄₃	semidirect
294. C₂×#124	C₂²×C₄₃	semidirect
307. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
308. C₂×#103	C₂²×C₄₃	semidirect
311. C₂×#102	C₂²×C₄₃	semidirect
316. #391	C₂²×C₄₃	semidirect
317. #390	C₂²×C₄₃	semidirect
318. #384	C₂²×C₄₃	semidirect
319. #340	C₂²×C₄₃	semidirect
320. #340	C₂²×C₄₃	semidirect
321. #336	C₂²×C₄₃	semidirect
322. C₄₃	#32917	direct (N × H)
353. C₄×D₄	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#518	2
C₂×C₄₃×#463	2
C₂×C₄₃×#450	2
C₂×C₄₃×#447	2
C₄₃×#2620	2
C₄₃×#1879	2
C₄₃×#1877	2
C₄₃×#1875	2
C₄₃×#1873	2
C₄₃×#1802	2
C₄₃×#1798	2
#32917	43

Subgroups — C43×#32917 #24952934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#32917 #24952934