Subgroups — C₄₃×#24415 #24944432

Order 11008.

1402 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3485	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3056	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#455	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#413	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2038	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2005	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1885	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1871	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1792	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#137×C₄₃	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	complemented
16	C₄₃×#547	—	2	2	no	—
17	C₄₃×#547	—	2	2	no	—
18	C₄₃×#546	—	2	2	no	—
19	C₄₃×#546	—	2	2	no	—
20	C₄₃×#536	C₂²	1	2	yes	—
21	C₄₃×#534	—	2	2	no	—
22	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#525	C₂²	1	2	yes	—
25	C₂×#123×C₄₃	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
27	C₄₃×#518	C₂²	1	1	yes	characteristic
28	C₄₃×#470	—	2	2	no	—
29	C₄₃×#468	—	2	2	no	—
30	C₄₃×#467	—	2	2	no	—
31	C₄₃×#465	—	2	2	no	—
32	C₄₃×#455	—	2	4	no	—
33	C₄₃×#428	C₂²	1	2	yes	complemented
34	C₂×#104×C₄₃	C₂²	1	2	yes	—
35	C₂×#104×C₄₃	C₂²	1	2	yes	—
36	C₄₃×#419	C₂²	1	2	yes	complemented
37	C₄₃×#417	C₂²	1	2	yes	—
38	C₄₃×#413	—	2	4	no	—
39	C₂×#101×C₄₃	C₂²	1	2	yes	complemented
40	C₂×#100×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#100×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#394	—	2	2	no	—
43	C₄₃×#391	C₂²	1	1	yes	characteristic, complemented
44	C₄₃×#390	C₂²	1	1	yes	characteristic
45	C₄₃×#385	—	2	2	no	—
46	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
47	C₄₃×#339	C₂²	1	2	yes	complemented
48	C₄₃×#339	C₂²	1	2	yes	complemented
49	H(5,𝔽₂)×C₄₃	—	2	2	no	—
50	H(5,𝔽₂)×C₄₃	—	2	2	no	—
51	H(5,𝔽₂)×C₄₃	—	4	2	no	—
52	C₂×#41×C₄₃	—	2	2	no	—
53	C₂×#41×C₄₃	—	2	2	no	—
54	C₂×#41×C₄₃	—	2	2	no	—
55	C₂×#41×C₄₃	—	2	2	no	—
56	C₂×#41×C₄₃	—	2	2	no	—
57	C₂×#41×C₄₃	—	4	2	no	—
58	C₂×#41×C₄₃	C₂³	1	2	yes	—
59	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₄₃	—	2	2	no	—
62	C₂²×D₄×C₄₃	—	2	2	no	—
63	C₂²×D₄×C₄₃	D₄	1	2	yes	—
64	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	D₄	1	2	yes	—
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	#137×C₄₃	—	2	4	no	—
68	#137×C₄₃	—	4	2	no	—
69	C₂×Q₁₆×C₄₃	—	2	2	no	—
70	C₂×SD₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	—	2	4	no	—
73	C₂×M₁₆×C₄₃	—	4	2	no	—
74	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
75	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₃	—	2	2	no	—
77	C₄⋊Q₈×C₄₃	—	2	2	no	—
78	C₄⋊Q₈×C₄₃	—	4	2	no	—
79	#124×C₄₃	—	2	2	no	—
80	#124×C₄₃	—	2	2	no	—
81	#124×C₄₃	—	2	2	no	—
82	#123×C₄₃	—	2	4	no	—
83	#123×C₄₃	—	2	4	no	—
84	#123×C₄₃	—	2	4	no	—
85	#123×C₄₃	—	2	2	no	—
86	#123×C₄₃	—	2	4	no	—
87	C₂²⋊Q₈×C₄₃	—	2	2	no	—
88	C₂²⋊Q₈×C₄₃	—	2	2	no	—
89	C₂²⋊Q₈×C₄₃	—	2	2	no	—
90	C₂²⋊Q₈×C₄₃	—	2	2	no	—
91	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
92	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
93	#121×C₄₃	—	2	4	no	—
94	#121×C₄₃	—	2	4	no	—
95	#121×C₄₃	D₄	1	2	yes	—
96	#121×C₄₃	D₄	1	2	yes	—
97	#120×C₄₃	—	2	4	no	—
98	#120×C₄₃	—	2	2	no	—
99	C₄×D₄×C₄₃	—	2	2	no	—
100	C₄×D₄×C₄₃	—	2	2	no	—
101	C₄×D₄×C₄₃	—	2	2	no	—
102	C₄×D₄×C₄₃	—	2	2	no	—
103	#117×C₄₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
106	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
118	#107×C₄₃	—	2	2	no	—
119	#106×C₄₃	—	2	2	no	—
120	#104×C₄₃	—	2	4	no	—
121	#104×C₄₃	—	4	2	no	—
122	#103×C₄₃	—	2	2	no	—
123	#103×C₄₃	—	2	2	no	—
124	#103×C₄₃	—	2	2	no	—
125	#102×C₄₃	—	2	2	no	—
126	#101×C₄₃	—	2	4	no	—
127	#100×C₄₃	—	2	2	no	—
128	#100×C₄₃	D₄	1	4	yes	complemented
129	#95×C₄₃	—	2	1	no	—
130	#95×C₄₃	—	2	2	no	—
131	C₂⁴×C₄₃	—	2	2	no	—
132	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
134	#41×C₄₃	—	2	2	no	—
135	#41×C₄₃	—	2	2	no	—
136	#41×C₄₃	—	2	2	no	—
137	#41×C₄₃	—	2	2	no	—
138	#41×C₄₃	—	4	4	no	—
139	#41×C₄₃	—	4	4	no	—
140	#41×C₄₃	—	4	4	no	—
141	#41×C₄₃	—	4	4	no	—
142	#41×C₄₃	—	4	4	no	—
143	#41×C₄₃	—	4	4	no	—
144	C₂×Q₈×C₄₃	—	2	1	no	—
145	C₂×Q₈×C₄₃	—	2	2	no	—
146	C₂×Q₈×C₄₃	—	2	1	no	—
147	C₂×Q₈×C₄₃	—	2	2	no	—
148	C₂×Q₈×C₄₃	—	2	2	no	—
149	C₂×Q₈×C₄₃	—	2	1	no	—
150	C₂×Q₈×C₄₃	—	2	1	no	—
151	C₂×Q₈×C₄₃	—	2	2	no	—
152	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₄₃	—	2	4	no	—
154	C₂×D₄×C₄₃	—	2	2	no	—
155	C₂×D₄×C₄₃	—	2	2	no	—
156	C₂×D₄×C₄₃	—	2	4	no	—
157	C₂×D₄×C₄₃	—	2	2	no	—
158	C₂×D₄×C₄₃	—	2	2	no	—
159	C₂×D₄×C₄₃	—	2	4	no	—
160	C₂×D₄×C₄₃	—	2	2	no	—
161	C₂×D₄×C₄₃	—	4	2	no	—
162	C₂×D₄×C₄₃	—	4	4	no	—
163	C₂×D₄×C₄₃	—	4	4	no	—
164	C₂×D₄×C₄₃	—	4	4	no	—
165	C₂×D₄×C₄₃	—	4	4	no	—
166	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
167	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
168	C₂×D₄×C₄₃	#41	1	2	yes	—
169	C₂²×C₄×C₄₃	—	2	1	no	—
170	C₂²×C₄×C₄₃	—	2	1	no	—
171	C₂²×C₄×C₄₃	—	2	2	no	—
172	C₂²×C₄×C₄₃	—	2	2	no	—
173	C₂²×C₄×C₄₃	—	2	2	no	—
174	C₂²×C₄×C₄₃	—	2	2	no	—
175	C₂²×C₄×C₄₃	—	2	2	no	—
176	C₂²×C₄×C₄₃	—	2	2	no	—
177	C₂²×C₄×C₄₃	—	2	2	no	—
178	C₂²×C₄×C₄₃	—	2	4	no	—
179	C₂²×C₄×C₄₃	—	2	1	no	—
180	C₂²×C₄×C₄₃	—	2	1	no	—
181	C₂²×C₄×C₄₃	—	2	1	no	—
182	C₂²×C₄×C₄₃	—	2	1	no	—
183	C₂²×C₄×C₄₃	—	4	2	no	—
184	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
189	Q₁₆×C₄₃	—	4	4	no	—
190	SD₁₆×C₄₃	—	4	4	no	—
191	M₁₆×C₄₃	—	2	2	no	—
192	M₁₆×C₄₃	—	2	2	no	—
193	M₁₆×C₄₃	—	2	2	no	—
194	M₁₆×C₄₃	—	4	4	no	—
195	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
196	C₂×C₈×C₄₃	—	2	2	no	—
197	C₂×C₈×C₄₃	—	2	2	no	—
198	C₂×C₈×C₄₃	—	4	4	no	—
199	C₄⋊C₄×C₄₃	—	2	4	no	—
200	C₄⋊C₄×C₄₃	—	2	4	no	—
201	C₄⋊C₄×C₄₃	—	2	2	no	—
202	C₄⋊C₄×C₄₃	—	2	2	no	—
203	C₄⋊C₄×C₄₃	—	2	2	no	—
204	C₄⋊C₄×C₄₃	—	4	4	no	—
205	C₄⋊C₄×C₄₃	—	4	1	no	—
206	C₄⋊C₄×C₄₃	—	4	1	no	—
207	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
209	C₂²⋊C₄×C₄₃	—	2	4	no	—
210	C₂²⋊C₄×C₄₃	—	2	4	no	—
211	C₂²⋊C₄×C₄₃	—	2	4	no	—
212	C₂²⋊C₄×C₄₃	—	2	2	no	—
213	C₂²⋊C₄×C₄₃	—	2	2	no	—
214	C₂²⋊C₄×C₄₃	—	2	2	no	—
215	C₂²⋊C₄×C₄₃	—	2	2	no	—
216	C₂²⋊C₄×C₄₃	—	2	2	no	—
217	C₂²⋊C₄×C₄₃	—	4	2	no	—
218	C₂²⋊C₄×C₄₃	—	4	4	no	—
219	C₂²⋊C₄×C₄₃	—	4	2	no	—
220	C₂²⋊C₄×C₄₃	—	4	4	no	—
221	C₄²×C₄₃	—	2	2	no	—
222	C₄²×C₄₃	—	2	1	no	—
223	C₄²×C₄₃	—	2	1	no	—
224	C₄²×C₄₃	—	2	2	no	—
225	C₂³×C₄₃	—	2	2	no	—
226	C₂³×C₄₃	—	2	1	no	—
227	C₂³×C₄₃	—	2	1	no	—
228	C₂³×C₄₃	—	2	2	no	—
229	C₂³×C₄₃	—	2	2	no	—
230	C₂³×C₄₃	—	4	1	no	—
231	C₂³×C₄₃	—	4	1	no	—
232	C₂³×C₄₃	—	4	2	no	—
233	C₂³×C₄₃	—	4	2	no	—
234	C₂³×C₄₃	—	4	4	no	—
235	C₂³×C₄₃	—	8	2	no	—
236	C₂³×C₄₃	—	8	2	no	—
237	C₂³×C₄₃	#120	1	2	yes	—
238	C₂³×C₄₃	#121	1	4	yes	—
239	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₄₃	—	2	2	no	—
241	Q₈×C₄₃	—	2	2	no	—
242	Q₈×C₄₃	—	4	2	no	—
243	Q₈×C₄₃	—	4	2	no	—
244	Q₈×C₄₃	—	4	2	no	—
245	Q₈×C₄₃	—	4	2	no	—
246	D₄×C₄₃	—	2	4	no	—
247	D₄×C₄₃	—	2	2	no	—
248	D₄×C₄₃	—	2	4	no	—
249	D₄×C₄₃	—	2	2	no	—
250	D₄×C₄₃	—	4	8	no	—
251	D₄×C₄₃	—	4	8	no	—
252	D₄×C₄₃	—	4	2	no	—
253	D₄×C₄₃	—	4	2	no	—
254	D₄×C₄₃	—	8	2	no	—
255	D₄×C₄₃	—	8	2	no	—
256	C₂×C₄×C₄₃	—	2	1	no	—
257	C₂×C₄×C₄₃	—	2	1	no	—
258	C₂×C₄×C₄₃	—	2	2	no	—
259	C₂×C₄×C₄₃	—	2	2	no	—
260	C₂×C₄×C₄₃	—	2	2	no	—
261	C₂×C₄×C₄₃	—	2	2	no	—
262	C₂×C₄×C₄₃	—	2	2	no	—
263	C₂×C₄×C₄₃	—	2	2	no	—
264	C₂×C₄×C₄₃	—	2	2	no	—
265	C₂×C₄×C₄₃	—	2	2	no	—
266	C₂×C₄×C₄₃	—	2	2	no	—
267	C₂×C₄×C₄₃	—	2	2	no	—
268	C₂×C₄×C₄₃	—	2	2	no	—
269	C₂×C₄×C₄₃	—	4	4	no	—
270	C₂×C₄×C₄₃	—	4	4	no	—
271	C₂×C₄×C₄₃	—	4	1	no	—
272	C₂×C₄×C₄₃	—	4	4	no	—
273	C₂×C₄×C₄₃	—	4	1	no	—
274	C₂×C₄×C₄₃	—	4	2	no	—
275	C₂×C₄×C₄₃	—	4	2	no	—
276	C₂×C₄×C₄₃	—	4	1	no	—
277	C₂×C₄×C₄₃	—	4	2	no	—
278	C₂×C₄×C₄₃	—	4	1	no	—
279	C₂×C₄×C₄₃	—	4	1	no	—
280	C₂×C₄×C₄₃	—	4	1	no	—
281	C₂×C₄×C₄₃	—	4	1	no	—
282	C₂×C₄×C₄₃	—	4	1	no	—
283	C₂×C₄×C₄₃	—	4	1	no	—
284	C₂×C₄×C₄₃	—	8	2	no	—
285	C₂×C₄×C₄₃	—	8	2	no	—
286	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
287	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
288	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
292	C₈×C₄₃	—	2	4	no	—
293	C₈×C₄₃	—	4	2	no	—
294	#24415	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂²×C₄₃	—	2	1	no	—
296	C₂²×C₄₃	—	2	1	no	—
297	C₂²×C₄₃	—	2	4	no	—
298	C₂²×C₄₃	—	2	2	no	—
299	C₂²×C₄₃	—	2	2	no	—
300	C₂²×C₄₃	—	2	2	no	—
301	C₂²×C₄₃	—	4	4	no	—
302	C₂²×C₄₃	—	4	2	no	—
303	C₂²×C₄₃	—	4	2	no	—
304	C₂²×C₄₃	—	4	2	no	—
305	C₂²×C₄₃	—	4	2	no	—
306	C₂²×C₄₃	—	4	2	no	—
307	C₂²×C₄₃	—	8	1	no	—
308	C₂²×C₄₃	—	8	2	no	—
309	C₂²×C₄₃	—	8	1	no	—
310	C₂²×C₄₃	—	16	4	no	—
311	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
312	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
313	C₂²×C₄₃	#534	1	1	yes	characteristic
314	C₄×C₄₃	—	2	1	no	—
315	C₄×C₄₃	—	2	1	no	—
316	C₄×C₄₃	—	4	2	no	—
317	C₄×C₄₃	—	4	2	no	—
318	C₄×C₄₃	—	4	2	no	—
319	C₄×C₄₃	—	4	2	no	—
320	C₄×C₄₃	—	4	2	no	—
321	C₄×C₄₃	—	8	1	no	—
322	C₄×C₄₃	—	8	1	no	—
323	C₄×C₄₃	—	8	1	no	—
324	C₄×C₄₃	D₄²	1	2	yes	—
325	C₄×C₄₃	#546	1	2	yes	—
326	#3485	C₂×C₄₃	1	1	yes	characteristic
327	#3056	C₂×C₄₃	1	2	yes	complemented
328	C₂×#455	C₂×C₄₃	1	1	yes	characteristic, complemented
329	C₂×#413	C₂×C₄₃	1	1	yes	characteristic, complemented
330	#2432	C₂×C₄₃	1	1	yes	characteristic, complemented
331	#2038	C₂×C₄₃	1	2	yes	complemented
332	#2005	C₂×C₄₃	1	2	yes	complemented
333	#1885	C₂×C₄₃	1	1	yes	characteristic, complemented
334	#1871	C₂×C₄₃	1	2	yes	complemented
335	#1856	C₂×C₄₃	1	1	yes	characteristic, complemented
336	#1792	C₂×C₄₃	1	1	yes	characteristic, complemented
337	C₂×C₄₃	—	2	1	no	—
338	C₂×C₄₃	—	2	1	no	—
339	C₂×C₄₃	—	4	2	no	—
340	C₂×C₄₃	—	4	4	no	—
341	C₂×C₄₃	—	8	2	no	—
342	C₂×C₄₃	#2410	1	1	yes	characteristic
343	C₂×C₄₃	#3018	1	1	yes	characteristic
344	C₂×C₄₃	#3022	1	1	yes	characteristic
345	C₂×H(5,𝔽₂)	C₂²×C₄₃	1	1	yes	characteristic
346	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
347	C₂×#137	C₂²×C₄₃	1	2	yes	—
348	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	complemented
349	#547	—	2	2	no	—
350	#547	—	2	2	no	—
351	#546	—	2	2	no	—
352	#546	—	2	2	no	—
353	#536	C₂²×C₄₃	1	2	yes	—
354	#534	—	2	2	no	—
355	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
356	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
357	#525	C₂²×C₄₃	1	2	yes	—
358	C₂×#123	—	2	2	no	—
359	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
360	#518	C₂²×C₄₃	1	1	yes	characteristic
361	#470	—	2	2	no	—
362	#468	—	2	2	no	—
363	#467	—	2	2	no	—
364	#465	—	2	2	no	—
365	#455	—	2	4	no	—
366	#428	C₂²×C₄₃	1	2	yes	complemented
367	C₂×#104	C₂²×C₄₃	1	2	yes	—
368	C₂×#104	C₂²×C₄₃	1	2	yes	—
369	#419	C₂²×C₄₃	1	2	yes	complemented
370	#417	C₂²×C₄₃	1	2	yes	—
371	#413	—	2	4	no	—
372	C₂×#101	C₂²×C₄₃	1	2	yes	complemented
373	C₂×#100	C₂²×C₄₃	1	1	yes	characteristic
374	C₂×#100	C₂²×C₄₃	1	1	yes	characteristic
375	#394	—	2	2	no	—
376	#391	C₂²×C₄₃	1	1	yes	characteristic, complemented
377	#390	C₂²×C₄₃	1	1	yes	characteristic
378	#385	—	2	2	no	—
379	C₄×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic, complemented
380	#339	C₂²×C₄₃	1	2	yes	complemented
381	#339	C₂²×C₄₃	1	2	yes	complemented
382	C₄₃	#24415	1	1	yes	characteristic, direct product factor, Sylow
383	H(5,𝔽₂)	—	2	2	no	—
384	H(5,𝔽₂)	—	2	2	no	—
385	H(5,𝔽₂)	—	4	2	no	—
386	C₂×#41	—	2	2	no	—
387	C₂×#41	—	2	2	no	—
388	C₂×#41	—	2	2	no	—
389	C₂×#41	—	2	2	no	—
390	C₂×#41	—	2	2	no	—
391	C₂×#41	—	4	2	no	—
392	C₂×#41	C₂³×C₄₃	1	2	yes	—
393	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
395	C₂²×D₄	—	2	2	no	—
396	C₂²×D₄	—	2	2	no	—
397	C₂²×D₄	D₄×C₄₃	1	2	yes	—
398	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
399	C₂³×C₄	D₄×C₄₃	1	2	yes	—
400	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
401	#137	—	2	4	no	—
402	#137	—	4	2	no	—
403	C₂×Q₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	2	2	no	—
405	C₂×M₁₆	—	2	2	no	—
406	C₂×M₁₆	—	2	4	no	—
407	C₂×M₁₆	—	4	2	no	—
408	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
409	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
410	C₂²×C₈	—	2	2	no	—
411	C₄⋊Q₈	—	2	2	no	—
412	C₄⋊Q₈	—	4	2	no	—
413	#124	—	2	2	no	—
414	#124	—	2	2	no	—
415	#124	—	2	2	no	—
416	#123	—	2	4	no	—
417	#123	—	2	4	no	—
418	#123	—	2	4	no	—
419	#123	—	2	2	no	—
420	#123	—	2	4	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	D₄×C₄₃	1	2	yes	—
426	C₂²⋊Q₈	D₄×C₄₃	1	2	yes	—
427	#121	—	2	4	no	—
428	#121	—	2	4	no	—
429	#121	D₄×C₄₃	1	2	yes	—
430	#121	D₄×C₄₃	1	2	yes	—
431	#120	—	2	4	no	—
432	#120	—	2	2	no	—
433	C₄×D₄	—	2	2	no	—
434	C₄×D₄	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	#117	C₂³×C₄₃	1	2	yes	—
438	C₂×C₄⋊C₄	—	2	2	no	—
439	C₂×C₄⋊C₄	—	2	2	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	2	no	—
442	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	—	2	2	no	—
444	C₂×C₂²⋊C₄	—	2	2	no	—
445	C₂×C₂²⋊C₄	—	2	2	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	2	no	—
450	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
452	#107	—	2	2	no	—
453	#106	—	2	2	no	—
454	#104	—	2	4	no	—
455	#104	—	4	2	no	—
456	#103	—	2	2	no	—
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#102	—	2	2	no	—
460	#101	—	2	4	no	—
461	#100	—	2	2	no	—
462	#100	D₄×C₄₃	1	4	yes	complemented
463	#95	—	2	1	no	—
464	#95	—	2	2	no	—
465	C₂⁴	—	2	2	no	—
466	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
467	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
468	#41	—	2	2	no	—
469	#41	—	2	2	no	—
470	#41	—	2	2	no	—
471	#41	—	2	2	no	—
472	#41	—	4	4	no	—
473	#41	—	4	4	no	—
474	#41	—	4	4	no	—
475	#41	—	4	4	no	—
476	#41	—	4	4	no	—
477	#41	—	4	4	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	2	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	2	no	—
482	C₂×Q₈	—	2	2	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	2	no	—
486	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	2	no	—
492	C₂×D₄	—	2	2	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	2	no	—
495	C₂×D₄	—	4	2	no	—
496	C₂×D₄	—	4	4	no	—
497	C₂×D₄	—	4	4	no	—
498	C₂×D₄	—	4	4	no	—
499	C₂×D₄	—	4	4	no	—
500	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
501	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
502	C₂×D₄	#41×C₄₃	1	2	yes	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
519	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
520	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
521	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
523	Q₁₆	—	4	4	no	—
524	SD₁₆	—	4	4	no	—
525	M₁₆	—	2	2	no	—
526	M₁₆	—	2	2	no	—
527	M₁₆	—	2	2	no	—
528	M₁₆	—	4	4	no	—
529	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
530	C₂×C₈	—	2	2	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	4	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	4	4	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
542	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₄²	—	2	2	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	2	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	8	2	no	—
570	C₂³	—	8	2	no	—
571	C₂³	#120×C₄₃	1	2	yes	—
572	C₂³	#121×C₄₃	1	4	yes	—
573	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	4	2	no	—
577	Q₈	—	4	2	no	—
578	Q₈	—	4	2	no	—
579	Q₈	—	4	2	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	8	no	—
585	D₄	—	4	8	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	8	2	no	—
589	D₄	—	8	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	4	no	—
604	C₂×C₄	—	4	4	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	8	2	no	—
619	C₂×C₄	—	8	2	no	—
620	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
621	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
622	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
623	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
624	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
625	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
626	C₈	—	2	4	no	—
627	C₈	—	4	2	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	2	no	—
642	C₂²	—	8	1	no	—
643	C₂²	—	16	4	no	—
644	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
645	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
646	C₂²	C₄₃×#534	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	D₄²×C₄₃	1	2	yes	—
658	C₄	C₄₃×#546	1	2	yes	—
659	C₂	—	2	1	no	—
660	C₂	—	2	1	no	—
661	C₂	—	4	2	no	—
662	C₂	—	4	4	no	—
663	C₂	—	8	2	no	—
664	C₂	C₄₃×#2410	1	1	yes	characteristic
665	C₂	C₄₃×#3018	1	1	yes	characteristic
666	C₂	C₄₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#3485	C₂
LCS	G ▷ C₂²×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. C₄₃×#3056	C₂	semidirect
3. C₂×C₄₃×#455	C₂	semidirect
4. C₂×C₄₃×#413	C₂	semidirect
5. C₄₃×#2432	C₂	semidirect
6. C₄₃×#2038	C₂	semidirect
7. C₄₃×#2005	C₂	semidirect
8. C₄₃×#1885	C₂	semidirect
9. C₄₃×#1871	C₂	semidirect
10. C₄₃×#1856	C₂	semidirect
11. C₄₃×#1792	C₂	semidirect
15. C₂²×M₁₆×C₄₃	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
33. C₄₃×#428	C₂²	semidirect
36. C₄₃×#419	C₂²	semidirect
39. C₂×#101×C₄₃	C₂²	semidirect
43. C₄₃×#391	C₂²	semidirect
46. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
47. C₄₃×#339	C₂²	semidirect
48. C₄₃×#339	C₂²	semidirect
128. #100×C₄₃	D₄	semidirect
294. #24415	C₄₃	direct (N × H)
327. #3056	C₂×C₄₃	semidirect
328. C₂×#455	C₂×C₄₃	semidirect
329. C₂×#413	C₂×C₄₃	semidirect
330. #2432	C₂×C₄₃	semidirect
331. #2038	C₂×C₄₃	semidirect
332. #2005	C₂×C₄₃	semidirect
333. #1885	C₂×C₄₃	semidirect
334. #1871	C₂×C₄₃	semidirect
335. #1856	C₂×C₄₃	semidirect
336. #1792	C₂×C₄₃	semidirect
348. C₂²×M₁₆	C₂²×C₄₃	semidirect
355. C₂×C₄⋊Q₈	C₂²×C₄₃	semidirect
359. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
366. #428	C₂²×C₄₃	semidirect
369. #419	C₂²×C₄₃	semidirect
372. C₂×#101	C₂²×C₄₃	semidirect
376. #391	C₂²×C₄₃	semidirect
379. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
380. #339	C₂²×C₄₃	semidirect
381. #339	C₂²×C₄₃	semidirect
382. C₄₃	#24415	direct (N × H)
462. #100	D₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3485	2
C₄₃×#3056	2
C₂×C₄₃×#455	2
C₂×C₄₃×#413	2
C₄₃×#2432	2
C₄₃×#2038	2
C₄₃×#2005	2
C₄₃×#1885	2
C₄₃×#1871	2
C₄₃×#1856	2
C₄₃×#1792	2
#24415	43

Subgroups — C43×#24415 #24944432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#24415 #24944432