Subgroups — C₄₃×#29631 #24949648

Order 11008.

1302 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#449	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2624	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2043	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2013	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#536	—	2	4	no	—
18	C₄₃×#536	—	2	4	no	—
19	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
20	C₂×#124×C₄₃	C₂²	1	2	yes	—
21	C₂×#123×C₄₃	—	2	2	no	—
22	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
24	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#449	—	2	4	no	—
27	C₄₃×#448	—	2	4	no	—
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₃	C₂²	1	2	yes	—
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#399	—	2	1	no	—
38	C₄₃×#397	—	2	1	no	—
39	C₄₃×#394	—	2	2	no	—
40	C₄₃×#390	C₂²	1	2	yes	—
41	C₄₃×#389	C₂²	1	2	yes	—
42	C₄₃×#380	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	4	2	no	—
47	C₂×#41×C₄₃	—	4	2	no	—
48	C₂×#41×C₄₃	D₄	1	4	yes	—
49	C₂²×Q₈×C₄₃	—	2	1	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	4	2	no	—
52	C₂²×Q₈×C₄₃	—	4	2	no	—
53	C₂²×Q₈×C₄₃	D₄	1	4	yes	—
54	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₄₃	—	2	1	no	—
57	C₂²×D₄×C₄₃	—	2	1	no	—
58	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	—	2	1	no	—
61	C₂³×C₄×C₄₃	—	2	1	no	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×SD₁₆×C₄₃	—	2	4	no	—
64	C₂×SD₁₆×C₄₃	—	2	2	no	—
65	C₂×SD₁₆×C₄₃	—	4	2	no	—
66	C₂×SD₁₆×C₄₃	—	4	2	no	—
67	C₂×SD₁₆×C₄₃	—	4	2	no	—
68	C₂×D₈×C₄₃	—	2	2	no	—
69	C₂×D₈×C₄₃	—	4	2	no	—
70	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
73	C₄⋊Q₈×C₄₃	—	2	4	no	—
74	C₄⋊Q₈×C₄₃	—	2	4	no	—
75	#124×C₄₃	—	2	4	no	—
76	#124×C₄₃	—	2	4	no	—
77	#123×C₄₃	—	2	16	no	—
78	C₂²⋊Q₈×C₄₃	—	2	8	no	—
79	C₂²⋊Q₈×C₄₃	—	2	8	no	—
80	#121×C₄₃	—	2	2	no	—
81	#121×C₄₃	—	2	2	no	—
82	#117×C₄₃	—	2	2	no	—
83	#117×C₄₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
98	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
99	#103×C₄₃	—	2	4	no	—
100	#103×C₄₃	—	2	2	no	—
101	#103×C₄₃	—	4	2	no	—
102	#103×C₄₃	—	4	2	no	—
103	#103×C₄₃	—	4	2	no	—
104	#102×C₄₃	—	2	2	no	—
105	#102×C₄₃	—	4	2	no	—
106	C₂²⋊C₈×C₄₃	—	2	2	no	—
107	C₂²⋊C₈×C₄₃	—	2	2	no	—
108	#95×C₄₃	—	2	1	no	—
109	#95×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	1	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₄₃	—	4	4	no	—
114	#41×C₄₃	—	4	4	no	—
115	#41×C₄₃	—	4	8	no	—
116	C₂×Q₈×C₄₃	—	2	4	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	4	8	no	—
126	C₂×Q₈×C₄₃	—	4	4	no	—
127	C₂×Q₈×C₄₃	—	4	4	no	—
128	C₂×Q₈×C₄₃	—	4	4	no	—
129	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₄₃	—	2	1	no	—
132	C₂×D₄×C₄₃	—	2	4	no	—
133	C₂×D₄×C₄₃	—	2	1	no	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	4	4	no	—
140	C₂×D₄×C₄₃	—	4	2	no	—
141	C₂×D₄×C₄₃	—	8	2	no	—
142	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	2	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	4	4	no	—
152	C₂²×C₄×C₄₃	—	4	4	no	—
153	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
159	SD₁₆×C₄₃	—	4	8	no	—
160	SD₁₆×C₄₃	—	4	4	no	—
161	D₈×C₄₃	—	4	4	no	—
162	C₂×C₈×C₄₃	—	2	1	no	—
163	C₂×C₈×C₄₃	—	2	1	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₄⋊C₄×C₄₃	—	2	8	no	—
170	C₄⋊C₄×C₄₃	—	2	8	no	—
171	C₄⋊C₄×C₄₃	—	2	2	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₄⋊C₄×C₄₃	—	2	1	no	—
174	C₄⋊C₄×C₄₃	—	2	1	no	—
175	C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₄⋊C₄×C₄₃	—	2	2	no	—
177	C₄⋊C₄×C₄₃	—	8	2	no	—
178	C₂²⋊C₄×C₄₃	—	2	8	no	—
179	C₂²⋊C₄×C₄₃	—	2	8	no	—
180	C₂²⋊C₄×C₄₃	—	2	4	no	—
181	C₂²⋊C₄×C₄₃	—	4	2	no	—
182	C₂²⋊C₄×C₄₃	—	8	1	no	—
183	C₂²⋊C₄×C₄₃	—	8	2	no	—
184	C₂²⋊C₄×C₄₃	—	8	2	no	—
185	C₄²×C₄₃	—	2	2	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	2	2	no	—
188	C₂³×C₄₃	—	2	1	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	1	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	4	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	4	1	no	—
195	C₂³×C₄₃	—	4	1	no	—
196	C₂³×C₄₃	—	4	1	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	—	4	1	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	1	no	—
201	C₂³×C₄₃	#120	1	2	yes	—
202	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₄₃	—	2	4	no	—
204	Q₈×C₄₃	—	2	2	no	—
205	Q₈×C₄₃	—	2	4	no	—
206	Q₈×C₄₃	—	2	2	no	—
207	Q₈×C₄₃	—	4	8	no	—
208	Q₈×C₄₃	—	4	2	no	—
209	Q₈×C₄₃	—	4	2	no	—
210	Q₈×C₄₃	—	4	2	no	—
211	D₄×C₄₃	—	2	2	no	—
212	D₄×C₄₃	—	2	2	no	—
213	D₄×C₄₃	—	4	8	no	—
214	D₄×C₄₃	—	4	2	no	—
215	D₄×C₄₃	—	4	1	no	—
216	D₄×C₄₃	—	4	1	no	—
217	D₄×C₄₃	—	4	2	no	—
218	D₄×C₄₃	—	8	4	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	4	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	2	4	no	—
226	C₂×C₄×C₄₃	—	2	2	no	—
227	C₂×C₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	2	2	no	—
229	C₂×C₄×C₄₃	—	2	2	no	—
230	C₂×C₄×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	4	8	no	—
232	C₂×C₄×C₄₃	—	4	8	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	4	2	no	—
238	C₂×C₄×C₄₃	—	4	2	no	—
239	C₂×C₄×C₄₃	—	4	2	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	#120	1	2	yes	—
242	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
245	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
246	C₈×C₄₃	—	4	1	no	—
247	C₈×C₄₃	—	4	1	no	—
248	C₈×C₄₃	—	4	2	no	—
249	#29631	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	2	no	—
254	C₂²×C₄₃	—	4	2	no	—
255	C₂²×C₄₃	—	4	2	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	8	2	no	—
259	C₂²×C₄₃	—	8	2	no	—
260	C₂²×C₄₃	—	8	1	no	—
261	C₂²×C₄₃	—	8	2	no	—
262	C₂²×C₄₃	—	8	2	no	—
263	C₂²×C₄₃	—	8	1	no	—
264	C₂²×C₄₃	—	8	1	no	—
265	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
266	C₂²×C₄₃	#535	1	2	yes	—
267	C₂²×C₄₃	#577	1	1	yes	characteristic
268	C₂²×C₄₃	#577	1	2	yes	—
269	C₂²×C₄₃	#578	1	1	yes	characteristic
270	C₄×C₄₃	—	2	2	no	—
271	C₄×C₄₃	—	4	2	no	—
272	C₄×C₄₃	—	4	4	no	—
273	C₄×C₄₃	—	4	2	no	—
274	C₄×C₄₃	—	4	2	no	—
275	C₄×C₄₃	—	8	2	no	—
276	C₄×C₄₃	—	8	1	no	—
277	C₄×C₄₃	#534	1	1	yes	characteristic
278	C₄×C₄₃	#534	1	1	yes	characteristic
279	C₄×C₄₃	#534	1	2	yes	—
280	C₂×#536	C₂×C₄₃	1	1	yes	characteristic, complemented
281	C₂×#449	C₂×C₄₃	1	1	yes	characteristic
282	C₂×#448	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#2624	C₂×C₄₃	1	1	yes	characteristic, complemented
284	#2043	C₂×C₄₃	1	2	yes	complemented
285	#2042	C₂×C₄₃	1	2	yes	complemented
286	#2013	C₂×C₄₃	1	2	yes	complemented
287	#2012	C₂×C₄₃	1	2	yes	complemented
288	#1818	C₂×C₄₃	1	1	yes	characteristic, complemented
289	#1788	C₂×C₄₃	1	1	yes	characteristic, complemented
290	#1787	C₂×C₄₃	1	1	yes	characteristic, complemented
291	C₂×C₄₃	—	4	2	no	—
292	C₂×C₄₃	—	8	2	no	—
293	C₂×C₄₃	—	16	1	no	—
294	C₂×C₄₃	#2613	1	1	yes	characteristic
295	C₂×C₄₃	#3010	1	1	yes	characteristic
296	C₂×C₄₃	#3013	1	1	yes	characteristic
297	C₂×C₄₃	#3221	1	2	yes	—
298	C₂×C₄₃	#3225	1	2	yes	—
299	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
300	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
301	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
302	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
303	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
304	#536	—	2	4	no	—
305	#536	—	2	4	no	—
306	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
307	C₂×#124	C₂²×C₄₃	1	2	yes	—
308	C₂×#123	—	2	2	no	—
309	C₂×C₂²⋊Q₈	—	2	1	no	—
310	C₂×C₂²⋊Q₈	—	2	1	no	—
311	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
313	#449	—	2	4	no	—
314	#448	—	2	4	no	—
315	C₂×#103	C₂²×C₄₃	1	2	yes	—
316	C₂×#103	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	1	yes	characteristic
321	C₂×#102	C₂²×C₄₃	1	2	yes	—
322	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
324	#399	—	2	1	no	—
325	#397	—	2	1	no	—
326	#394	—	2	2	no	—
327	#390	C₂²×C₄₃	1	2	yes	—
328	#389	C₂²×C₄₃	1	2	yes	—
329	#380	C₂²×C₄₃	1	1	yes	characteristic
330	#336	C₂²×C₄₃	1	2	yes	—
331	#336	C₂²×C₄₃	1	2	yes	—
332	C₄₃	#29631	1	1	yes	characteristic, direct product factor, Sylow
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	4	2	no	—
335	C₂×#41	—	4	2	no	—
336	C₂×#41	D₄×C₄₃	1	4	yes	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	—	2	2	no	—
339	C₂²×Q₈	—	4	2	no	—
340	C₂²×Q₈	—	4	2	no	—
341	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
342	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
343	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
347	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	4	2	no	—
354	C₂×SD₁₆	—	4	2	no	—
355	C₂×SD₁₆	—	4	2	no	—
356	C₂×D₈	—	2	2	no	—
357	C₂×D₈	—	4	2	no	—
358	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
361	C₄⋊Q₈	—	2	4	no	—
362	C₄⋊Q₈	—	2	4	no	—
363	#124	—	2	4	no	—
364	#124	—	2	4	no	—
365	#123	—	2	16	no	—
366	C₂²⋊Q₈	—	2	8	no	—
367	C₂²⋊Q₈	—	2	8	no	—
368	#121	—	2	2	no	—
369	#121	—	2	2	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
386	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
387	#103	—	2	4	no	—
388	#103	—	2	2	no	—
389	#103	—	4	2	no	—
390	#103	—	4	2	no	—
391	#103	—	4	2	no	—
392	#102	—	2	2	no	—
393	#102	—	4	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	C₂²⋊C₈	—	2	2	no	—
396	#95	—	2	1	no	—
397	#95	—	2	2	no	—
398	C₂⁴	—	2	1	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
401	#41	—	4	4	no	—
402	#41	—	4	4	no	—
403	#41	—	4	8	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	4	8	no	—
414	C₂×Q₈	—	4	4	no	—
415	C₂×Q₈	—	4	4	no	—
416	C₂×Q₈	—	4	4	no	—
417	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
418	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	8	2	no	—
430	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
442	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
443	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
447	SD₁₆	—	4	8	no	—
448	SD₁₆	—	4	4	no	—
449	D₈	—	4	4	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	8	2	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	4	2	no	—
470	C₂²⋊C₄	—	8	2	no	—
471	C₂²⋊C₄	—	8	2	no	—
472	C₂²⋊C₄	—	8	1	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	1	no	—
489	C₂³	#120×C₄₃	1	2	yes	—
490	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
491	Q₈	—	2	4	no	—
492	Q₈	—	2	2	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	4	8	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	Q₈	—	4	2	no	—
499	D₄	—	2	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	4	8	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	#120×C₄₃	1	2	yes	—
530	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
531	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
532	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
533	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
553	C₂²	C₄₃×#535	1	2	yes	—
554	C₂²	C₄₃×#577	1	1	yes	characteristic
555	C₂²	C₄₃×#577	1	2	yes	—
556	C₂²	C₄₃×#578	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	8	2	no	—
563	C₄	—	8	1	no	—
564	C₄	C₄₃×#534	1	1	yes	characteristic
565	C₄	C₄₃×#534	1	1	yes	characteristic
566	C₄	C₄₃×#534	1	2	yes	—
567	C₂	—	4	2	no	—
568	C₂	—	8	2	no	—
569	C₂	—	16	1	no	—
570	C₂	C₄₃×#2613	1	1	yes	characteristic
571	C₂	C₄₃×#3010	1	1	yes	characteristic
572	C₂	C₄₃×#3013	1	1	yes	characteristic
573	C₂	C₄₃×#3221	1	2	yes	—
574	C₂	C₄₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#449	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×#536	C₂	semidirect
3. C₂×C₄₃×#448	C₂	semidirect
4. C₄₃×#2624	C₂	semidirect
5. C₄₃×#2043	C₂	semidirect
6. C₄₃×#2042	C₂	semidirect
7. C₄₃×#2013	C₂	semidirect
8. C₄₃×#2012	C₂	semidirect
9. C₄₃×#1818	C₂	semidirect
10. C₄₃×#1788	C₂	semidirect
11. C₄₃×#1787	C₂	semidirect
249. #29631	C₄₃	direct (N × H)
280. C₂×#536	C₂×C₄₃	semidirect
282. C₂×#448	C₂×C₄₃	semidirect
283. #2624	C₂×C₄₃	semidirect
284. #2043	C₂×C₄₃	semidirect
285. #2042	C₂×C₄₃	semidirect
286. #2013	C₂×C₄₃	semidirect
287. #2012	C₂×C₄₃	semidirect
288. #1818	C₂×C₄₃	semidirect
289. #1788	C₂×C₄₃	semidirect
290. #1787	C₂×C₄₃	semidirect
332. C₄₃	#29631	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×#536	2
C₂×C₄₃×#449	2
C₂×C₄₃×#448	2
C₄₃×#2624	2
C₄₃×#2043	2
C₄₃×#2042	2
C₄₃×#2013	2
C₄₃×#2012	2
C₄₃×#1818	2
C₄₃×#1788	2
C₄₃×#1787	2
#29631	43

Subgroups — C43×#29631 #24949648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29631 #24949648