Subgroups — C₄₃×#24659 #24944676

Order 11008.

960 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2036	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2000	C₂	1	2	yes	maximal
7	C₄₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1973	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1935	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₃	—	2	1	no	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#461	—	2	4	no	—
20	C₄₃×#432	—	2	4	no	—
21	C₂×#107×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#103×C₄₃	C₂²	1	2	yes	—
26	C₂×#103×C₄₃	C₂²	1	2	yes	—
27	C₂×#102×C₄₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₂×#97×C₄₃	C₂²	1	2	yes	—
30	C₄₃×#391	C₂²	1	2	yes	—
31	C₄₃×#390	C₂²	1	1	yes	characteristic
32	C₄₃×#389	—	2	1	no	—
33	C₄₃×#389	—	2	1	no	—
34	C₄₃×#389	C₂²	1	1	yes	characteristic
35	C₄₃×#388	—	2	1	no	—
36	C₄₃×#386	—	2	1	no	—
37	C₄₃×#384	C₂²	1	1	yes	characteristic
38	C₄₃×#380	—	2	1	no	—
39	C₄₃×#380	—	2	1	no	—
40	C₄₃×#380	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	—	2	1	no	—
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₄₃	—	2	4	no	—
53	C₂×SD₁₆×C₄₃	—	2	4	no	—
54	C₂×SD₁₆×C₄₃	—	4	2	no	—
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₂²⋊Q₈×C₄₃	—	4	2	no	—
60	C₂²⋊Q₈×C₄₃	—	4	2	no	—
61	#121×C₄₃	—	2	2	no	—
62	#121×C₄₃	—	2	2	no	—
63	C₄×D₄×C₄₃	—	2	2	no	—
64	C₄×D₄×C₄₃	—	2	2	no	—
65	C₄×D₄×C₄₃	—	4	4	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄²×C₄₃	—	2	2	no	—
83	C₂×C₄²×C₄₃	—	2	2	no	—
84	C₂×C₄²×C₄₃	—	2	1	no	—
85	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	#107×C₄₃	—	4	2	no	—
90	C₄⋊C₈×C₄₃	—	2	2	no	—
91	C₄⋊C₈×C₄₃	D₄	1	4	yes	complemented
92	#103×C₄₃	—	2	4	no	—
93	#103×C₄₃	—	2	4	no	—
94	#103×C₄₃	—	4	2	no	—
95	#102×C₄₃	—	4	2	no	—
96	C₂²⋊C₈×C₄₃	—	2	4	no	—
97	#97×C₄₃	—	2	4	no	—
98	#95×C₄₃	—	2	1	no	—
99	#95×C₄₃	—	2	1	no	—
100	#95×C₄₃	—	2	1	no	—
101	#95×C₄₃	—	2	2	no	—
102	#95×C₄₃	—	2	2	no	—
103	C₂⁴×C₄₃	—	2	1	no	—
104	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	4	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	4	2	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	#41	1	2	yes	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	1	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	4	1	no	—
137	C₂²×C₄×C₄₃	—	4	2	no	—
138	C₂²×C₄×C₄₃	—	4	2	no	—
139	C₂²×C₄×C₄₃	—	4	2	no	—
140	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
146	SD₁₆×C₄₃	—	4	8	no	—
147	C₂×C₈×C₄₃	—	2	2	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
153	C₄⋊C₄×C₄₃	—	2	1	no	—
154	C₄⋊C₄×C₄₃	—	2	1	no	—
155	C₄⋊C₄×C₄₃	—	2	1	no	—
156	C₄⋊C₄×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₄⋊C₄×C₄₃	—	4	2	no	—
161	C₄⋊C₄×C₄₃	—	4	2	no	—
162	C₄⋊C₄×C₄₃	—	4	4	no	—
163	C₄⋊C₄×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	—	4	2	no	—
165	C₄⋊C₄×C₄₃	—	4	2	no	—
166	C₄⋊C₄×C₄₃	#41	1	2	yes	—
167	C₂²⋊C₄×C₄₃	—	2	4	no	—
168	C₂²⋊C₄×C₄₃	—	4	2	no	—
169	C₂²⋊C₄×C₄₃	—	4	4	no	—
170	C₂²⋊C₄×C₄₃	—	4	2	no	—
171	C₂²⋊C₄×C₄₃	—	4	2	no	—
172	C₂²⋊C₄×C₄₃	—	4	2	no	—
173	C₄²×C₄₃	—	2	2	no	—
174	C₄²×C₄₃	—	2	2	no	—
175	C₄²×C₄₃	—	2	1	no	—
176	C₄²×C₄₃	—	2	1	no	—
177	C₄²×C₄₃	—	4	2	no	—
178	C₄²×C₄₃	C₂×D₄	1	2	yes	—
179	C₄²×C₄₃	#41	1	2	yes	—
180	C₂³×C₄₃	—	2	1	no	—
181	C₂³×C₄₃	—	2	1	no	—
182	C₂³×C₄₃	—	2	1	no	—
183	C₂³×C₄₃	—	2	1	no	—
184	C₂³×C₄₃	—	2	1	no	—
185	C₂³×C₄₃	—	2	1	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	4	1	no	—
188	C₂³×C₄₃	—	4	1	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	—	4	1	no	—
191	C₂³×C₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	4	1	no	—
193	C₂³×C₄₃	#137	1	2	yes	—
194	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₄₃	—	4	2	no	—
196	Q₈×C₄₃	—	4	2	no	—
197	Q₈×C₄₃	—	4	2	no	—
198	Q₈×C₄₃	—	4	2	no	—
199	D₄×C₄₃	—	2	2	no	—
200	D₄×C₄₃	—	2	2	no	—
201	D₄×C₄₃	—	4	8	no	—
202	D₄×C₄₃	—	4	1	no	—
203	D₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	2	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	1	no	—
207	C₂×C₄×C₄₃	—	2	1	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	1	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	1	no	—
213	C₂×C₄×C₄₃	—	2	1	no	—
214	C₂×C₄×C₄₃	—	2	1	no	—
215	C₂×C₄×C₄₃	—	2	1	no	—
216	C₂×C₄×C₄₃	—	4	4	no	—
217	C₂×C₄×C₄₃	—	4	1	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	4	1	no	—
222	C₂×C₄×C₄₃	—	4	1	no	—
223	C₂×C₄×C₄₃	—	4	4	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	2	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	1	no	—
230	C₂×C₄×C₄₃	—	4	1	no	—
231	C₂×C₄×C₄₃	—	4	1	no	—
232	C₂×C₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	1	no	—
234	C₂×C₄×C₄₃	—	4	1	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	—	8	4	no	—
237	C₂×C₄×C₄₃	#121	1	2	yes	—
238	C₂×C₄×C₄₃	#121	1	2	yes	—
239	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
240	C₂×C₄×C₄₃	#137	1	2	yes	—
241	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
247	C₈×C₄₃	—	2	4	no	—
248	C₈×C₄₃	—	4	2	no	—
249	#24659	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂²×C₄₃	—	2	2	no	—
251	C₂²×C₄₃	—	2	2	no	—
252	C₂²×C₄₃	—	2	2	no	—
253	C₂²×C₄₃	—	4	1	no	—
254	C₂²×C₄₃	—	4	1	no	—
255	C₂²×C₄₃	—	4	1	no	—
256	C₂²×C₄₃	—	4	1	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	4	2	no	—
259	C₂²×C₄₃	—	4	2	no	—
260	C₂²×C₄₃	—	8	1	no	—
261	C₂²×C₄₃	—	8	1	no	—
262	C₂²×C₄₃	—	8	1	no	—
263	C₂²×C₄₃	—	8	1	no	—
264	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
265	C₂²×C₄₃	#525	1	1	yes	characteristic
266	C₂²×C₄₃	#535	1	1	yes	characteristic
267	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
268	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
269	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
270	C₂²×C₄₃	#575	1	1	yes	characteristic
271	C₄×C₄₃	—	2	2	no	—
272	C₄×C₄₃	—	4	2	no	—
273	C₄×C₄₃	—	4	1	no	—
274	C₄×C₄₃	—	4	1	no	—
275	C₄×C₄₃	—	4	1	no	—
276	C₄×C₄₃	—	8	2	no	—
277	C₄×C₄₃	—	8	2	no	—
278	C₄×C₄₃	—	8	1	no	—
279	C₄×C₄₃	—	8	1	no	—
280	C₄×C₄₃	#468	1	4	yes	—
281	C₄×C₄₃	#546	1	1	yes	characteristic
282	C₄×C₄₃	#550	1	1	yes	characteristic
283	C₄×C₄₃	#553	1	1	yes	characteristic
284	C₄×C₄₃	#555	1	1	yes	characteristic
285	C₂×#461	C₂×C₄₃	1	1	yes	characteristic, complemented
286	C₂×#432	C₂×C₄₃	1	1	yes	characteristic, complemented
287	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
288	C₄×#121	C₂×C₄₃	1	1	yes	characteristic
289	#2036	C₂×C₄₃	1	2	yes	complemented
290	#2000	C₂×C₄₃	1	2	yes	—
291	#1981	C₂×C₄₃	1	1	yes	characteristic, complemented
292	#1973	C₂×C₄₃	1	2	yes	complemented
293	#1947	C₂×C₄₃	1	1	yes	characteristic, complemented
294	#1935	C₂×C₄₃	1	2	yes	complemented
295	#1802	C₂×C₄₃	1	1	yes	characteristic, complemented
296	C₂×C₄₃	—	4	2	no	—
297	C₂×C₄₃	—	8	2	no	—
298	C₂×C₄₃	#2414	1	1	yes	characteristic
299	C₂×C₄₃	C₂×#468	1	1	yes	characteristic
300	C₂×C₄₃	#3056	1	1	yes	characteristic
301	C₂×C₄₃	#3110	1	1	yes	characteristic
302	C₂×C₄₃	#3116	1	1	yes	characteristic
303	C₂×C₄₃	#3214	1	1	yes	characteristic
304	C₂×C₄₃	#3218	1	1	yes	characteristic
305	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
306	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
307	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
308	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
309	C₂×C₄×D₄	—	2	1	no	—
310	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
311	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
312	#461	—	2	4	no	—
313	#432	—	2	4	no	—
314	C₂×#107	C₂²×C₄₃	1	2	yes	—
315	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
316	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
317	C₂×#103	C₂²×C₄₃	1	2	yes	—
318	C₂×#103	C₂²×C₄₃	1	2	yes	—
319	C₂×#103	C₂²×C₄₃	1	2	yes	—
320	C₂×#102	C₂²×C₄₃	1	2	yes	—
321	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
322	C₂×#97	C₂²×C₄₃	1	2	yes	—
323	#391	C₂²×C₄₃	1	2	yes	—
324	#390	C₂²×C₄₃	1	1	yes	characteristic
325	#389	—	2	1	no	—
326	#389	—	2	1	no	—
327	#389	C₂²×C₄₃	1	1	yes	characteristic
328	#388	—	2	1	no	—
329	#386	—	2	1	no	—
330	#384	C₂²×C₄₃	1	1	yes	characteristic
331	#380	—	2	1	no	—
332	#380	—	2	1	no	—
333	#380	C₂²×C₄₃	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
335	C₄×C₂²⋊C₄	—	2	1	no	—
336	#340	C₂²×C₄₃	1	2	yes	—
337	#340	C₂²×C₄₃	1	2	yes	—
338	C₄₃	#24659	1	1	yes	characteristic, direct product factor, Sylow
339	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
344	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
346	C₂×SD₁₆	—	2	4	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	4	2	no	—
349	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
350	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	4	2	no	—
354	C₂²⋊Q₈	—	4	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	4	4	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₄²	—	2	2	no	—
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
380	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
383	#107	—	4	2	no	—
384	C₄⋊C₈	—	2	2	no	—
385	C₄⋊C₈	D₄×C₄₃	1	4	yes	complemented
386	#103	—	2	4	no	—
387	#103	—	2	4	no	—
388	#103	—	4	2	no	—
389	#102	—	4	2	no	—
390	C₂²⋊C₈	—	2	4	no	—
391	#97	—	2	4	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	—	2	2	no	—
396	#95	—	2	2	no	—
397	C₂⁴	—	2	1	no	—
398	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	#41×C₄₃	1	2	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
440	SD₁₆	—	4	8	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	#41×C₄₃	1	2	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	4	2	no	—
472	C₄²	C₂×D₄×C₄₃	1	2	yes	—
473	C₄²	#41×C₄₃	1	2	yes	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	#137×C₄₃	1	2	yes	—
488	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	8	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	8	4	no	—
531	C₂×C₄	#121×C₄₃	1	2	yes	—
532	C₂×C₄	#121×C₄₃	1	2	yes	—
533	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
534	C₂×C₄	#137×C₄₃	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
536	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
537	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
539	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
540	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	4	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
558	C₂²	C₄₃×#525	1	1	yes	characteristic
559	C₂²	C₄₃×#535	1	1	yes	characteristic
560	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
561	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
562	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
563	C₂²	C₄₃×#575	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	8	2	no	—
570	C₄	—	8	2	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	C₄₃×#468	1	4	yes	—
574	C₄	C₄₃×#546	1	1	yes	characteristic
575	C₄	C₄₃×#550	1	1	yes	characteristic
576	C₄	C₄₃×#553	1	1	yes	characteristic
577	C₄	C₄₃×#555	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	8	2	no	—
580	C₂	C₄₃×#2414	1	1	yes	characteristic
581	C₂	C₂×C₄₃×#468	1	1	yes	characteristic
582	C₂	C₄₃×#3056	1	1	yes	characteristic
583	C₂	C₄₃×#3110	1	1	yes	characteristic
584	C₂	C₄₃×#3116	1	1	yes	characteristic
585	C₂	C₄₃×#3214	1	1	yes	characteristic
586	C₂	C₄₃×#3218	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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
1. C₂×C₄₃×#461	C₂	semidirect
2. C₂×C₄₃×#432	C₂	semidirect
3. C₄₃×#2857	C₂	semidirect
5. C₄₃×#2036	C₂	semidirect
7. C₄₃×#1981	C₂	semidirect
8. C₄₃×#1973	C₂	semidirect
9. C₄₃×#1947	C₂	semidirect
10. C₄₃×#1935	C₂	semidirect
11. C₄₃×#1802	C₂	semidirect
91. C₄⋊C₈×C₄₃	D₄	semidirect
249. #24659	C₄₃	direct (N × H)
285. C₂×#461	C₂×C₄₃	semidirect
286. C₂×#432	C₂×C₄₃	semidirect
287. #2857	C₂×C₄₃	semidirect
289. #2036	C₂×C₄₃	semidirect
291. #1981	C₂×C₄₃	semidirect
292. #1973	C₂×C₄₃	semidirect
293. #1947	C₂×C₄₃	semidirect
294. #1935	C₂×C₄₃	semidirect
295. #1802	C₂×C₄₃	semidirect
338. C₄₃	#24659	direct (N × H)
385. C₄⋊C₈	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×#461	2
C₂×C₄₃×#432	2
C₄₃×#2857	2
C₄×#121×C₄₃	2
C₄₃×#2036	2
C₄₃×#2000	2
C₄₃×#1981	2
C₄₃×#1973	2
C₄₃×#1947	2
C₄₃×#1935	2
C₄₃×#1802	2
#24659	43

Subgroups — C43×#24659 #24944676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#24659 #24944676