Subgroups — C₄₃×#29629 #24949646

Order 11008.

1378 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#452	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1788	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₄₃	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
15	C₄₃×#532	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#121×C₄₃	—	2	1	no	—
21	C₂×#121×C₄₃	—	2	1	no	—
22	C₂×C₄×D₄×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	—	2	1	no	—
24	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#452	—	2	8	no	—
26	C₂×#103×C₄₃	C₂²	1	2	yes	—
27	C₂×#103×C₄₃	C₂²	1	2	yes	—
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	2	yes	—
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
33	C₄₃×#391	C₂²	1	1	yes	characteristic
34	C₄₃×#391	C₂²	1	1	yes	characteristic
35	C₄₃×#389	C₂²	1	1	yes	characteristic
36	C₄₃×#389	C₂²	1	1	yes	characteristic
37	C₄₃×#387	—	2	1	no	—
38	C₄₃×#387	—	2	1	no	—
39	C₄₃×#385	—	2	1	no	—
40	C₄₃×#381	—	2	1	no	—
41	C₄₃×#380	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₄₃×#336	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₃	—	2	4	no	—
46	C₂×#41×C₄₃	—	4	2	no	—
47	C₂×#41×C₄₃	—	4	2	no	—
48	C₂×#41×C₄₃	—	4	2	no	—
49	C₂×#41×C₄₃	—	4	2	no	—
50	C₂×#41×C₄₃	D₄	1	8	yes	—
51	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₄₃	—	2	2	no	—
54	C₂²×D₄×C₄₃	—	2	1	no	—
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₃	—	2	2	no	—
58	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂×Q₁₆×C₄₃	—	2	4	no	—
62	C₂×Q₁₆×C₄₃	—	4	2	no	—
63	C₂×Q₁₆×C₄₃	—	4	2	no	—
64	C₂×SD₁₆×C₄₃	—	2	4	no	—
65	C₂×SD₁₆×C₄₃	—	4	2	no	—
66	C₂×SD₁₆×C₄₃	—	4	2	no	—
67	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
69	C₄⋊Q₈×C₄₃	—	2	4	no	—
70	#127×C₄₃	—	2	4	no	—
71	#124×C₄₃	—	2	4	no	—
72	#124×C₄₃	—	2	4	no	—
73	C₂²⋊Q₈×C₄₃	—	2	4	no	—
74	#121×C₄₃	—	2	8	no	—
75	#121×C₄₃	—	2	8	no	—
76	C₄×D₄×C₄₃	—	2	8	no	—
77	C₄×D₄×C₄₃	—	2	8	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	—	2	4	no	—
91	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	#103×C₄₃	—	2	4	no	—
96	#103×C₄₃	—	4	2	no	—
97	#103×C₄₃	—	4	2	no	—
98	#102×C₄₃	—	2	4	no	—
99	#102×C₄₃	—	4	2	no	—
100	#102×C₄₃	—	4	2	no	—
101	C₂²⋊C₈×C₄₃	—	2	4	no	—
102	#95×C₄₃	—	2	1	no	—
103	#95×C₄₃	—	2	1	no	—
104	#95×C₄₃	—	2	1	no	—
105	#95×C₄₃	—	2	1	no	—
106	#95×C₄₃	—	2	1	no	—
107	#95×C₄₃	—	2	1	no	—
108	#95×C₄₃	—	2	1	no	—
109	C₂⁴×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
111	#41×C₄₃	—	4	8	no	—
112	#41×C₄₃	—	4	8	no	—
113	#41×C₄₃	—	4	8	no	—
114	#41×C₄₃	—	4	8	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	2	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₄₃	—	2	4	no	—
126	C₂×D₄×C₄₃	—	2	4	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	8	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	4	4	no	—
134	C₂×D₄×C₄₃	—	4	4	no	—
135	C₂×D₄×C₄₃	—	4	2	no	—
136	C₂×D₄×C₄₃	—	4	2	no	—
137	C₂×D₄×C₄₃	—	4	2	no	—
138	C₂×D₄×C₄₃	—	4	2	no	—
139	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₄₃	—	2	2	no	—
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	2	1	no	—
143	C₂²×C₄×C₄₃	—	2	8	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	4	1	no	—
154	C₂²×C₄×C₄₃	—	4	1	no	—
155	C₂²×C₄×C₄₃	—	4	4	no	—
156	C₂²×C₄×C₄₃	—	4	4	no	—
157	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
164	Q₁₆×C₄₃	—	4	8	no	—
165	SD₁₆×C₄₃	—	4	8	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	2	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₄⋊C₄×C₄₃	—	2	4	no	—
173	C₄⋊C₄×C₄₃	—	2	4	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	1	no	—
176	C₄⋊C₄×C₄₃	—	2	2	no	—
177	C₄⋊C₄×C₄₃	—	2	1	no	—
178	C₄⋊C₄×C₄₃	—	4	2	no	—
179	C₄⋊C₄×C₄₃	—	4	2	no	—
180	C₄⋊C₄×C₄₃	—	4	2	no	—
181	C₂²⋊C₄×C₄₃	—	2	8	no	—
182	C₂²⋊C₄×C₄₃	—	2	8	no	—
183	C₂²⋊C₄×C₄₃	—	4	2	no	—
184	C₂²⋊C₄×C₄₃	—	4	2	no	—
185	C₄²×C₄₃	—	2	2	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₄²×C₄₃	—	2	2	no	—
188	C₄²×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	1	no	—
190	C₂³×C₄₃	—	2	1	no	—
191	C₂³×C₄₃	—	2	1	no	—
192	C₂³×C₄₃	—	2	1	no	—
193	C₂³×C₄₃	—	2	1	no	—
194	C₂³×C₄₃	—	2	1	no	—
195	C₂³×C₄₃	—	2	4	no	—
196	C₂³×C₄₃	—	4	2	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	—	4	2	no	—
202	C₂³×C₄₃	#120	1	2	yes	—
203	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₄₃	—	2	4	no	—
205	Q₈×C₄₃	—	2	4	no	—
206	Q₈×C₄₃	—	4	2	no	—
207	Q₈×C₄₃	—	4	2	no	—
208	Q₈×C₄₃	—	4	2	no	—
209	Q₈×C₄₃	—	4	2	no	—
210	D₄×C₄₃	—	2	4	no	—
211	D₄×C₄₃	—	2	4	no	—
212	D₄×C₄₃	—	4	8	no	—
213	D₄×C₄₃	—	4	8	no	—
214	D₄×C₄₃	—	4	16	no	—
215	D₄×C₄₃	—	4	2	no	—
216	D₄×C₄₃	—	4	2	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	1	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	2	4	no	—
225	C₂×C₄×C₄₃	—	2	1	no	—
226	C₂×C₄×C₄₃	—	2	1	no	—
227	C₂×C₄×C₄₃	—	2	4	no	—
228	C₂×C₄×C₄₃	—	2	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	1	no	—
231	C₂×C₄×C₄₃	—	2	1	no	—
232	C₂×C₄×C₄₃	—	4	4	no	—
233	C₂×C₄×C₄₃	—	4	4	no	—
234	C₂×C₄×C₄₃	—	4	16	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	4	1	no	—
238	C₂×C₄×C₄₃	—	4	1	no	—
239	C₂×C₄×C₄₃	—	4	1	no	—
240	C₂×C₄×C₄₃	—	4	1	no	—
241	C₂×C₄×C₄₃	—	4	1	no	—
242	C₂×C₄×C₄₃	—	4	1	no	—
243	C₂×C₄×C₄₃	—	4	1	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	#120	1	2	yes	—
250	C₂×C₄×C₄₃	#135	1	2	yes	—
251	C₂×C₄×C₄₃	#137	1	2	yes	—
252	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
254	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
256	C₈×C₄₃	—	4	2	no	—
257	C₈×C₄₃	—	4	2	no	—
258	#29629	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₄₃	—	2	2	no	—
260	C₂²×C₄₃	—	2	2	no	—
261	C₂²×C₄₃	—	2	2	no	—
262	C₂²×C₄₃	—	4	1	no	—
263	C₂²×C₄₃	—	4	1	no	—
264	C₂²×C₄₃	—	4	1	no	—
265	C₂²×C₄₃	—	4	1	no	—
266	C₂²×C₄₃	—	4	4	no	—
267	C₂²×C₄₃	—	4	4	no	—
268	C₂²×C₄₃	—	4	4	no	—
269	C₂²×C₄₃	—	8	2	no	—
270	C₂²×C₄₃	—	8	2	no	—
271	C₂²×C₄₃	—	8	2	no	—
272	C₂²×C₄₃	—	8	2	no	—
273	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
274	C₂²×C₄₃	#535	1	1	yes	characteristic
275	C₂²×C₄₃	#535	1	1	yes	characteristic
276	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
277	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
278	C₂²×C₄₃	#575	1	1	yes	characteristic
279	C₂²×C₄₃	#575	1	1	yes	characteristic
280	C₄×C₄₃	—	2	2	no	—
281	C₄×C₄₃	—	2	2	no	—
282	C₄×C₄₃	—	2	2	no	—
283	C₄×C₄₃	—	4	4	no	—
284	C₄×C₄₃	—	4	1	no	—
285	C₄×C₄₃	—	4	1	no	—
286	C₄×C₄₃	—	8	1	no	—
287	C₄×C₄₃	—	8	1	no	—
288	C₄×C₄₃	—	8	1	no	—
289	C₄×C₄₃	—	8	1	no	—
290	C₄×C₄₃	#534	1	2	yes	—
291	C₄×C₄₃	#534	1	2	yes	—
292	C₂×#532	C₂×C₄₃	1	1	yes	characteristic
293	C₂×#452	C₂×C₄₃	1	2	yes	complemented
294	#2855	C₂×C₄₃	1	1	yes	characteristic, complemented
295	#2043	C₂×C₄₃	1	1	yes	characteristic, complemented
296	#2042	C₂×C₄₃	1	2	yes	complemented
297	#2041	C₂×C₄₃	1	1	yes	characteristic, complemented
298	#2016	C₂×C₄₃	1	1	yes	characteristic, complemented
299	#2015	C₂×C₄₃	1	2	yes	complemented
300	#2014	C₂×C₄₃	1	1	yes	characteristic, complemented
301	#1817	C₂×C₄₃	1	1	yes	characteristic, complemented
302	#1788	C₂×C₄₃	1	2	yes	complemented
303	C₂×C₄₃	—	4	2	no	—
304	C₂×C₄₃	—	8	4	no	—
305	C₂×C₄₃	#2613	1	1	yes	characteristic
306	C₂×C₄₃	#3002	1	1	yes	characteristic
307	C₂×C₄₃	#3007	1	1	yes	characteristic
308	C₂×C₄₃	#3210	1	1	yes	characteristic
309	C₂×C₄₃	#3212	1	1	yes	characteristic
310	C₂×C₄₃	#3216	1	1	yes	characteristic
311	C₂×C₄₃	#3219	1	1	yes	characteristic
312	C₂²×#41	C₂²×C₄₃	1	2	yes	—
313	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
314	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
315	#532	—	2	8	no	—
316	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
317	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
318	C₂×#124	C₂²×C₄₃	1	2	yes	—
319	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
320	C₂×#121	—	2	1	no	—
321	C₂×#121	—	2	1	no	—
322	C₂×C₄×D₄	—	2	1	no	—
323	C₂×C₄×D₄	—	2	1	no	—
324	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
325	#452	—	2	8	no	—
326	C₂×#103	C₂²×C₄₃	1	2	yes	—
327	C₂×#103	C₂²×C₄₃	1	2	yes	—
328	C₂×#103	C₂²×C₄₃	1	2	yes	—
329	C₂×#102	C₂²×C₄₃	1	2	yes	—
330	C₂×#102	C₂²×C₄₃	1	2	yes	—
331	C₂×#102	C₂²×C₄₃	1	2	yes	—
332	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
333	#391	C₂²×C₄₃	1	1	yes	characteristic
334	#391	C₂²×C₄₃	1	1	yes	characteristic
335	#389	C₂²×C₄₃	1	1	yes	characteristic
336	#389	C₂²×C₄₃	1	1	yes	characteristic
337	#387	—	2	1	no	—
338	#387	—	2	1	no	—
339	#385	—	2	1	no	—
340	#381	—	2	1	no	—
341	#380	C₂²×C₄₃	1	1	yes	characteristic
342	#336	C₂²×C₄₃	1	1	yes	characteristic
343	#336	C₂²×C₄₃	1	2	yes	—
344	#336	C₂²×C₄₃	1	1	yes	characteristic
345	C₄₃	#29629	1	1	yes	characteristic, direct product factor, Sylow
346	C₂×#41	—	2	4	no	—
347	C₂×#41	—	4	2	no	—
348	C₂×#41	—	4	2	no	—
349	C₂×#41	—	4	2	no	—
350	C₂×#41	—	4	2	no	—
351	C₂×#41	D₄×C₄₃	1	8	yes	—
352	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
353	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
358	C₂³×C₄	—	2	2	no	—
359	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
360	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
362	C₂×Q₁₆	—	2	4	no	—
363	C₂×Q₁₆	—	4	2	no	—
364	C₂×Q₁₆	—	4	2	no	—
365	C₂×SD₁₆	—	2	4	no	—
366	C₂×SD₁₆	—	4	2	no	—
367	C₂×SD₁₆	—	4	2	no	—
368	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
369	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
370	C₄⋊Q₈	—	2	4	no	—
371	#127	—	2	4	no	—
372	#124	—	2	4	no	—
373	#124	—	2	4	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	#121	—	2	8	no	—
376	#121	—	2	8	no	—
377	C₄×D₄	—	2	8	no	—
378	C₄×D₄	—	2	8	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₄²	—	2	4	no	—
392	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
393	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
396	#103	—	2	4	no	—
397	#103	—	4	2	no	—
398	#103	—	4	2	no	—
399	#102	—	2	4	no	—
400	#102	—	4	2	no	—
401	#102	—	4	2	no	—
402	C₂²⋊C₈	—	2	4	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
412	#41	—	4	8	no	—
413	#41	—	4	8	no	—
414	#41	—	4	8	no	—
415	#41	—	4	8	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	4	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	8	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
462	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
465	Q₁₆	—	4	8	no	—
466	SD₁₆	—	4	8	no	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₄⋊C₄	—	2	4	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	#120×C₄₃	1	2	yes	—
504	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
505	Q₈	—	2	4	no	—
506	Q₈	—	2	4	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	8	no	—
515	D₄	—	4	16	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	16	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	#120×C₄₃	1	2	yes	—
551	C₂×C₄	#135×C₄₃	1	2	yes	—
552	C₂×C₄	#137×C₄₃	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
554	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
555	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
556	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
557	C₈	—	4	2	no	—
558	C₈	—	4	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
574	C₂²	C₄₃×#535	1	1	yes	characteristic
575	C₂²	C₄₃×#535	1	1	yes	characteristic
576	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
577	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
578	C₂²	C₄₃×#575	1	1	yes	characteristic
579	C₂²	C₄₃×#575	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	C₄₃×#534	1	2	yes	—
591	C₄	C₄₃×#534	1	2	yes	—
592	C₂	—	4	2	no	—
593	C₂	—	8	4	no	—
594	C₂	C₄₃×#2613	1	1	yes	characteristic
595	C₂	C₄₃×#3002	1	1	yes	characteristic
596	C₂	C₄₃×#3007	1	1	yes	characteristic
597	C₂	C₄₃×#3210	1	1	yes	characteristic
598	C₂	C₄₃×#3212	1	1	yes	characteristic
599	C₂	C₄₃×#3216	1	1	yes	characteristic
600	C₂	C₄₃×#3219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#532	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#452	C₂	semidirect
3. C₄₃×#2855	C₂	semidirect
4. C₄₃×#2043	C₂	semidirect
5. C₄₃×#2042	C₂	semidirect
6. C₄₃×#2041	C₂	semidirect
7. C₄₃×#2016	C₂	semidirect
8. C₄₃×#2015	C₂	semidirect
9. C₄₃×#2014	C₂	semidirect
10. C₄₃×#1817	C₂	semidirect
11. C₄₃×#1788	C₂	semidirect
258. #29629	C₄₃	direct (N × H)
293. C₂×#452	C₂×C₄₃	semidirect
294. #2855	C₂×C₄₃	semidirect
295. #2043	C₂×C₄₃	semidirect
296. #2042	C₂×C₄₃	semidirect
297. #2041	C₂×C₄₃	semidirect
298. #2016	C₂×C₄₃	semidirect
299. #2015	C₂×C₄₃	semidirect
300. #2014	C₂×C₄₃	semidirect
301. #1817	C₂×C₄₃	semidirect
302. #1788	C₂×C₄₃	semidirect
345. C₄₃	#29629	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×#532	2
C₂×C₄₃×#452	2
C₄₃×#2855	2
C₄₃×#2043	2
C₄₃×#2042	2
C₄₃×#2041	2
C₄₃×#2016	2
C₄₃×#2015	2
C₄₃×#2014	2
C₄₃×#1817	2
C₄₃×#1788	2
#29629	43

Subgroups — C43×#29629 #24949646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29629 #24949646