Subgroups — C₂×C₄₃×#3220 #24980808

Order 11008.

2342 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3220	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₃×#459	C₂	1	2	yes	maximal, complemented
10	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#447	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
16	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
17	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
18	C₂²×D₈×C₄₃	C₂²	1	2	yes	complemented
19	C₄₃×#540	—	2	4	no	—
20	C₄₃×#540	C₂²	1	8	yes	complemented
21	C₄₃×#535	—	2	4	no	—
22	C₄₃×#535	C₂²	1	8	yes	complemented
23	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#123×C₄₃	—	2	2	no	—
30	C₂×#121×C₄₃	—	2	2	no	—
31	C₂×#121×C₄₃	—	2	2	no	—
32	C₂×#121×C₄₃	C₂²	1	2	yes	—
33	C₂×#120×C₄₃	—	2	2	no	—
34	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
35	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#496	C₂²	1	8	yes	complemented
37	C₄₃×#493	C₂²	1	8	yes	complemented
38	C₄₃×#490	C₂²	1	8	yes	complemented
39	C₄₃×#488	C₂²	1	8	yes	complemented
40	C₄₃×#463	C₂²	1	16	yes	complemented
41	C₄₃×#459	C₂²	1	16	yes	complemented
42	C₄₃×#449	C₂²	1	16	yes	complemented
43	C₄₃×#447	C₂²	1	16	yes	complemented
44	C₄₃×#433	C₂²	1	8	yes	complemented
45	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
46	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
47	C₂×#102×C₄₃	C₂²	1	2	yes	—
48	C₂×#102×C₄₃	C₂²	1	2	yes	—
49	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
50	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
51	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
53	C₂⁵×C₄₃	—	2	1	no	—
54	C₂×#41×C₄₃	—	2	2	no	—
55	C₂×#41×C₄₃	—	4	4	no	—
56	C₂×#41×C₄₃	C₂³	1	4	yes	—
57	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₄₃	—	2	1	no	—
59	C₂²×D₄×C₄₃	—	2	2	no	—
60	C₂²×D₄×C₄₃	—	2	1	no	—
61	C₂²×D₄×C₄₃	—	2	2	no	—
62	C₂²×D₄×C₄₃	—	2	2	no	—
63	C₂²×D₄×C₄₃	—	2	2	no	—
64	C₂²×D₄×C₄₃	—	2	2	no	—
65	C₂²×D₄×C₄₃	—	4	4	no	—
66	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
71	C₂³×C₄×C₄₃	—	2	1	no	—
72	C₂³×C₄×C₄₃	—	2	2	no	—
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×SD₁₆×C₄₃	—	4	4	no	—
75	C₂×SD₁₆×C₄₃	C₂³	1	8	yes	complemented
76	C₂×D₈×C₄₃	—	4	4	no	—
77	C₂×D₈×C₄₃	—	4	4	no	—
78	C₂×D₈×C₄₃	—	4	4	no	—
79	C₂×D₈×C₄₃	C₂³	1	8	yes	—
80	C₂×D₈×C₄₃	C₂³	1	8	yes	—
81	C₂×D₈×C₄₃	C₂³	1	8	yes	complemented
82	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
84	#127×C₄₃	—	2	2	no	—
85	#127×C₄₃	—	2	2	no	—
86	#127×C₄₃	—	2	2	no	—
87	#127×C₄₃	C₂³	1	4	yes	—
88	#127×C₄₃	C₂³	1	4	yes	—
89	#127×C₄₃	C₂³	1	4	yes	complemented
90	#125×C₄₃	—	2	2	no	—
91	#125×C₄₃	C₂³	1	4	yes	complemented
92	#124×C₄₃	—	2	2	no	—
93	#124×C₄₃	—	2	2	no	—
94	#124×C₄₃	C₂³	1	4	yes	—
95	#124×C₄₃	C₂³	1	4	yes	—
96	#123×C₄₃	—	2	16	no	—
97	#121×C₄₃	—	2	4	no	—
98	#121×C₄₃	—	2	16	no	—
99	#121×C₄₃	—	2	16	no	—
100	#121×C₄₃	C₂³	1	8	yes	—
101	#120×C₄₃	—	2	16	no	—
102	C₄×D₄×C₄₃	—	2	4	no	—
103	C₄×D₄×C₄₃	C₂³	1	8	yes	complemented
104	#117×C₄₃	D₄	1	4	yes	—
105	#117×C₄₃	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
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	2	no	—
113	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
114	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₄₃	C₂³	1	8	yes	complemented
117	#103×C₄₃	C₂³	1	8	yes	complemented
118	#102×C₄₃	C₂³	1	8	yes	—
119	#102×C₄₃	C₂³	1	8	yes	—
120	#102×C₄₃	C₂³	1	8	yes	complemented
121	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	—
122	#97×C₄₃	C₂³	1	4	yes	complemented
123	C₄×C₈×C₄₃	C₂³	1	4	yes	complemented
124	C₂⁴×C₄₃	—	2	2	no	—
125	C₂⁴×C₄₃	—	2	1	no	—
126	C₂⁴×C₄₃	—	2	1	no	—
127	C₂⁴×C₄₃	—	2	1	no	—
128	C₂⁴×C₄₃	—	2	4	no	—
129	C₂⁴×C₄₃	—	4	4	no	—
130	C₂⁴×C₄₃	—	8	4	no	—
131	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
132	#41×C₄₃	—	4	8	no	—
133	#41×C₄₃	—	4	8	no	—
134	C₂×Q₈×C₄₃	—	2	1	no	—
135	C₂×Q₈×C₄₃	—	2	4	no	—
136	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	4	no	—
139	C₂×D₄×C₄₃	—	2	1	no	—
140	C₂×D₄×C₄₃	—	2	1	no	—
141	C₂×D₄×C₄₃	—	2	1	no	—
142	C₂×D₄×C₄₃	—	2	8	no	—
143	C₂×D₄×C₄₃	—	2	8	no	—
144	C₂×D₄×C₄₃	—	2	8	no	—
145	C₂×D₄×C₄₃	—	2	4	no	—
146	C₂×D₄×C₄₃	—	2	8	no	—
147	C₂×D₄×C₄₃	—	2	4	no	—
148	C₂×D₄×C₄₃	—	2	4	no	—
149	C₂×D₄×C₄₃	—	2	4	no	—
150	C₂×D₄×C₄₃	—	2	4	no	—
151	C₂×D₄×C₄₃	—	2	4	no	—
152	C₂×D₄×C₄₃	—	4	4	no	—
153	C₂×D₄×C₄₃	—	4	8	no	—
154	C₂×D₄×C₄₃	—	4	8	no	—
155	C₂×D₄×C₄₃	—	4	4	no	—
156	C₂×D₄×C₄₃	—	8	4	no	—
157	C₂×D₄×C₄₃	—	8	4	no	—
158	C₂×D₄×C₄₃	—	8	4	no	—
159	C₂×D₄×C₄₃	—	8	4	no	—
160	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
161	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
162	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
163	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₄₃	—	2	4	no	—
165	C₂²×C₄×C₄₃	—	2	4	no	—
166	C₂²×C₄×C₄₃	—	2	8	no	—
167	C₂²×C₄×C₄₃	—	2	1	no	—
168	C₂²×C₄×C₄₃	—	2	2	no	—
169	C₂²×C₄×C₄₃	—	4	4	no	—
170	C₂²×C₄×C₄₃	—	8	4	no	—
171	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
177	SD₁₆×C₄₃	—	4	8	no	—
178	D₈×C₄₃	—	4	8	no	—
179	D₈×C₄₃	—	4	8	no	—
180	D₈×C₄₃	—	4	8	no	—
181	C₂×C₈×C₄₃	—	2	4	no	—
182	C₂×C₈×C₄₃	—	2	4	no	—
183	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
184	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₄₃	—	2	8	no	—
186	C₄⋊C₄×C₄₃	—	2	2	no	—
187	C₄⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
188	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
189	C₂²⋊C₄×C₄₃	—	2	8	no	—
190	C₂²⋊C₄×C₄₃	—	2	8	no	—
191	C₂²⋊C₄×C₄₃	—	2	8	no	—
192	C₂²⋊C₄×C₄₃	—	2	8	no	—
193	C₂²⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
194	C₄²×C₄₃	C₂×D₄	1	2	yes	—
195	C₄²×C₄₃	C₂×D₄	1	2	yes	—
196	C₄²×C₄₃	C₂⁴	1	2	yes	—
197	C₄²×C₄₃	C₂⁴	1	2	yes	—
198	C₂³×C₄₃	—	2	2	no	—
199	C₂³×C₄₃	—	2	4	no	—
200	C₂³×C₄₃	—	2	4	no	—
201	C₂³×C₄₃	—	2	2	no	—
202	C₂³×C₄₃	—	2	2	no	—
203	C₂³×C₄₃	—	2	2	no	—
204	C₂³×C₄₃	—	4	8	no	—
205	C₂³×C₄₃	—	4	2	no	—
206	C₂³×C₄₃	—	4	2	no	—
207	C₂³×C₄₃	—	4	2	no	—
208	C₂³×C₄₃	—	4	4	no	—
209	C₂³×C₄₃	—	4	4	no	—
210	C₂³×C₄₃	—	4	4	no	—
211	C₂³×C₄₃	—	4	4	no	—
212	C₂³×C₄₃	—	4	4	no	—
213	C₂³×C₄₃	—	4	4	no	—
214	C₂³×C₄₃	—	8	8	no	—
215	C₂³×C₄₃	—	8	16	no	—
216	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
217	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₄₃	—	2	4	no	—
219	Q₈×C₄₃	—	4	2	no	—
220	D₄×C₄₃	—	2	4	no	—
221	D₄×C₄₃	—	2	4	no	—
222	D₄×C₄₃	—	2	4	no	—
223	D₄×C₄₃	—	2	4	no	—
224	D₄×C₄₃	—	2	4	no	—
225	D₄×C₄₃	—	4	8	no	—
226	D₄×C₄₃	—	4	8	no	—
227	D₄×C₄₃	—	4	4	no	—
228	D₄×C₄₃	—	4	2	no	—
229	D₄×C₄₃	—	4	2	no	—
230	D₄×C₄₃	—	4	2	no	—
231	D₄×C₄₃	—	8	8	no	—
232	D₄×C₄₃	—	8	8	no	—
233	D₄×C₄₃	—	8	8	no	—
234	D₄×C₄₃	—	8	8	no	—
235	C₂×C₄×C₄₃	—	2	2	no	—
236	C₂×C₄×C₄₃	—	2	4	no	—
237	C₂×C₄×C₄₃	—	2	4	no	—
238	C₂×C₄×C₄₃	—	2	4	no	—
239	C₂×C₄×C₄₃	—	2	4	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	2	4	no	—
242	C₂×C₄×C₄₃	—	4	8	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	—	4	4	no	—
245	C₂×C₄×C₄₃	—	8	8	no	—
246	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
251	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
252	C₈×C₄₃	—	2	4	no	—
253	C₈×C₄₃	—	2	4	no	—
254	C₂×#3220	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₄₃	—	2	2	no	—
256	C₂²×C₄₃	—	2	4	no	—
257	C₂²×C₄₃	—	4	4	no	—
258	C₂²×C₄₃	—	4	2	no	—
259	C₂²×C₄₃	—	4	2	no	—
260	C₂²×C₄₃	—	4	2	no	—
261	C₂²×C₄₃	—	4	4	no	—
262	C₂²×C₄₃	—	4	4	no	—
263	C₂²×C₄₃	—	4	4	no	—
264	C₂²×C₄₃	—	4	4	no	—
265	C₂²×C₄₃	—	4	4	no	—
266	C₂²×C₄₃	—	4	4	no	—
267	C₂²×C₄₃	—	8	16	no	—
268	C₂²×C₄₃	—	8	4	no	—
269	C₂²×C₄₃	—	8	8	no	—
270	C₂²×C₄₃	—	8	4	no	—
271	C₂²×C₄₃	—	8	4	no	—
272	C₂²×C₄₃	#535	1	2	yes	—
273	C₂²×C₄₃	#576	1	4	yes	—
274	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
275	C₄×C₄₃	—	2	2	no	—
276	C₄×C₄₃	—	2	4	no	—
277	C₄×C₄₃	—	2	4	no	—
278	C₄×C₄₃	—	4	2	no	—
279	C₄×C₄₃	—	4	4	no	—
280	C₄×C₄₃	#535	1	2	yes	—
281	C₄×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
282	C₂×#540	C₂×C₄₃	1	1	yes	characteristic, complemented
283	C₂×#535	C₂×C₄₃	1	1	yes	characteristic, complemented
284	#3220	C₂×C₄₃	1	16	yes	direct product factor
285	C₂×#496	C₂×C₄₃	1	1	yes	characteristic, complemented
286	C₂×#493	C₂×C₄₃	1	1	yes	characteristic, complemented
287	C₂×#490	C₂×C₄₃	1	1	yes	characteristic, complemented
288	C₂×#488	C₂×C₄₃	1	1	yes	characteristic, complemented
289	C₂×#463	C₂×C₄₃	1	2	yes	complemented
290	C₂×#459	C₂×C₄₃	1	2	yes	complemented
291	C₂×#449	C₂×C₄₃	1	2	yes	complemented
292	C₂×#447	C₂×C₄₃	1	2	yes	complemented
293	C₂×#433	C₂×C₄₃	1	1	yes	characteristic, complemented
294	C₂×C₄₃	—	4	2	no	—
295	C₂×C₄₃	—	8	2	no	—
296	C₂×C₄₃	—	8	4	no	—
297	C₂×C₄₃	—	8	2	no	—
298	C₂×C₄₃	—	8	2	no	—
299	C₂×C₄₃	#3220	1	4	yes	direct product factor
300	C₂×C₄₃	C₂×#535	1	1	yes	characteristic
301	C₂×C₄₃	C₂×#576	1	2	yes	—
302	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
303	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
304	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
305	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
306	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
307	C₂²×D₈	C₂²×C₄₃	1	2	yes	complemented
308	#540	—	2	4	no	—
309	#540	C₂²×C₄₃	1	8	yes	complemented
310	#535	—	2	4	no	—
311	#535	C₂²×C₄₃	1	8	yes	complemented
312	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
313	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
314	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic, complemented
315	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic, complemented
316	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
317	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
318	C₂×#123	—	2	2	no	—
319	C₂×#121	—	2	2	no	—
320	C₂×#121	—	2	2	no	—
321	C₂×#121	C₂²×C₄₃	1	2	yes	—
322	C₂×#120	—	2	2	no	—
323	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	complemented
324	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
325	#496	C₂²×C₄₃	1	8	yes	complemented
326	#493	C₂²×C₄₃	1	8	yes	complemented
327	#490	C₂²×C₄₃	1	8	yes	complemented
328	#488	C₂²×C₄₃	1	8	yes	complemented
329	#463	C₂²×C₄₃	1	16	yes	complemented
330	#459	C₂²×C₄₃	1	16	yes	complemented
331	#449	C₂²×C₄₃	1	16	yes	complemented
332	#447	C₂²×C₄₃	1	16	yes	complemented
333	#433	C₂²×C₄₃	1	8	yes	complemented
334	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
335	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
336	C₂×#102	C₂²×C₄₃	1	2	yes	—
337	C₂×#102	C₂²×C₄₃	1	2	yes	—
338	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
339	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
340	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic, complemented
341	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
342	C₄₃	C₂×#3220	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁵	—	2	1	no	—
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	4	4	no	—
346	C₂×#41	C₂³×C₄₃	1	4	yes	—
347	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	2	no	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	4	4	no	—
356	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
357	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	—	2	2	no	—
363	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
364	C₂×SD₁₆	—	4	4	no	—
365	C₂×SD₁₆	C₂³×C₄₃	1	8	yes	complemented
366	C₂×D₈	—	4	4	no	—
367	C₂×D₈	—	4	4	no	—
368	C₂×D₈	—	4	4	no	—
369	C₂×D₈	C₂³×C₄₃	1	8	yes	—
370	C₂×D₈	C₂³×C₄₃	1	8	yes	—
371	C₂×D₈	C₂³×C₄₃	1	8	yes	complemented
372	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
373	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
374	#127	—	2	2	no	—
375	#127	—	2	2	no	—
376	#127	—	2	2	no	—
377	#127	C₂³×C₄₃	1	4	yes	—
378	#127	C₂³×C₄₃	1	4	yes	—
379	#127	C₂³×C₄₃	1	4	yes	complemented
380	#125	—	2	2	no	—
381	#125	C₂³×C₄₃	1	4	yes	complemented
382	#124	—	2	2	no	—
383	#124	—	2	2	no	—
384	#124	C₂³×C₄₃	1	4	yes	—
385	#124	C₂³×C₄₃	1	4	yes	—
386	#123	—	2	16	no	—
387	#121	—	2	4	no	—
388	#121	—	2	16	no	—
389	#121	—	2	16	no	—
390	#121	C₂³×C₄₃	1	8	yes	—
391	#120	—	2	16	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	C₂³×C₄₃	1	8	yes	complemented
394	#117	D₄×C₄₃	1	4	yes	—
395	#117	C₂³×C₄₃	1	4	yes	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
399	C₂×C₂²⋊C₄	—	2	2	no	—
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	2	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
404	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₄₃	1	8	yes	complemented
407	#103	C₂³×C₄₃	1	8	yes	complemented
408	#102	C₂³×C₄₃	1	8	yes	—
409	#102	C₂³×C₄₃	1	8	yes	—
410	#102	C₂³×C₄₃	1	8	yes	complemented
411	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	—
412	#97	C₂³×C₄₃	1	4	yes	complemented
413	C₄×C₈	C₂³×C₄₃	1	4	yes	complemented
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	1	no	—
416	C₂⁴	—	2	1	no	—
417	C₂⁴	—	2	1	no	—
418	C₂⁴	—	2	4	no	—
419	C₂⁴	—	4	4	no	—
420	C₂⁴	—	8	4	no	—
421	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
422	#41	—	4	8	no	—
423	#41	—	4	8	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	4	no	—
426	C₂×Q₈	C₂⁴×C₄₃	1	2	yes	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	8	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	—	4	4	no	—
444	C₂×D₄	—	4	8	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	—	8	4	no	—
447	C₂×D₄	—	8	4	no	—
448	C₂×D₄	—	8	4	no	—
449	C₂×D₄	—	8	4	no	—
450	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
451	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
452	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
453	C₂×D₄	C₂⁴×C₄₃	1	4	yes	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	4	4	no	—
460	C₂²×C₄	—	8	4	no	—
461	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
467	SD₁₆	—	4	8	no	—
468	D₈	—	4	8	no	—
469	D₈	—	4	8	no	—
470	D₈	—	4	8	no	—
471	C₂×C₈	—	2	4	no	—
472	C₂×C₈	—	2	4	no	—
473	C₂×C₈	C₂⁴×C₄₃	1	4	yes	—
474	C₂×C₈	C₂⁴×C₄₃	1	4	yes	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	C₂×D₄×C₄₃	1	8	yes	—
478	C₄⋊C₄	C₂⁴×C₄₃	1	4	yes	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	C₂×D₄×C₄₃	1	8	yes	—
484	C₄²	C₂×D₄×C₄₃	1	2	yes	—
485	C₄²	C₂×D₄×C₄₃	1	2	yes	—
486	C₄²	C₂⁴×C₄₃	1	2	yes	—
487	C₄²	C₂⁴×C₄₃	1	2	yes	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	4	8	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	4	no	—
503	C₂³	—	4	4	no	—
504	C₂³	—	8	8	no	—
505	C₂³	—	8	16	no	—
506	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
507	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
508	Q₈	—	2	4	no	—
509	Q₈	—	4	2	no	—
510	D₄	—	2	4	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	4	8	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	4	no	—
521	D₄	—	8	8	no	—
522	D₄	—	8	8	no	—
523	D₄	—	8	8	no	—
524	D₄	—	8	8	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	8	8	no	—
536	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
537	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
538	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
540	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
541	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
542	C₈	—	2	4	no	—
543	C₈	—	2	4	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	8	16	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	4	no	—
559	C₂²	—	8	4	no	—
560	C₂²	—	8	8	no	—
561	C₂²	C₄₃×#535	1	2	yes	—
562	C₂²	C₄₃×#576	1	4	yes	—
563	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	4	no	—
566	C₄	—	2	4	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	4	no	—
569	C₄	C₄₃×#535	1	2	yes	—
570	C₄	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
571	C₂	—	4	2	no	—
572	C₂	—	8	2	no	—
573	C₂	—	8	2	no	—
574	C₂	—	8	2	no	—
575	C₂	—	8	4	no	—
576	C₂	C₄₃×#3220	1	4	yes	direct product factor
577	C₂	C₂×C₄₃×#535	1	1	yes	characteristic
578	C₂	C₂×C₄₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
LCS	G ▷ C₂×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×#540	C₂	semidirect
2. C₂×C₄₃×#535	C₂	semidirect
3. C₄₃×#3220	C₂	direct (N × H)
4. C₂×C₄₃×#496	C₂	semidirect
5. C₂×C₄₃×#493	C₂	semidirect
6. C₂×C₄₃×#490	C₂	semidirect
7. C₂×C₄₃×#488	C₂	semidirect
8. C₂×C₄₃×#463	C₂	semidirect
9. C₂×C₄₃×#459	C₂	semidirect
10. C₂×C₄₃×#449	C₂	semidirect
11. C₂×C₄₃×#447	C₂	semidirect
12. C₂×C₄₃×#433	C₂	semidirect
15. C₂²×SD₁₆×C₄₃	C₂²	semidirect
18. C₂²×D₈×C₄₃	C₂²	semidirect
20. C₄₃×#540	C₂²	semidirect
22. C₄₃×#535	C₂²	semidirect
25. C₂×#127×C₄₃	C₂²	semidirect
26. C₂×#125×C₄₃	C₂²	semidirect
34. C₂×C₄×D₄×C₄₃	C₂²	semidirect
36. C₄₃×#496	C₂²	semidirect
37. C₄₃×#493	C₂²	semidirect
38. C₄₃×#490	C₂²	semidirect
39. C₄₃×#488	C₂²	semidirect
40. C₄₃×#463	C₂²	semidirect
41. C₄₃×#459	C₂²	semidirect
42. C₄₃×#449	C₂²	semidirect
43. C₄₃×#447	C₂²	semidirect
44. C₄₃×#433	C₂²	semidirect
45. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
46. C₂×#103×C₄₃	C₂²	semidirect
49. C₂×#102×C₄₃	C₂²	semidirect
51. C₂×#97×C₄₃	C₂²	semidirect
52. C₂×C₄×C₈×C₄₃	C₂²	semidirect
75. C₂×SD₁₆×C₄₃	C₂³	semidirect
81. C₂×D₈×C₄₃	C₂³	semidirect
89. #127×C₄₃	C₂³	semidirect
91. #125×C₄₃	C₂³	semidirect
103. C₄×D₄×C₄₃	C₂³	semidirect
116. C₄⋊C₈×C₄₃	C₂³	semidirect
117. #103×C₄₃	C₂³	semidirect
120. #102×C₄₃	C₂³	semidirect
122. #97×C₄₃	C₂³	semidirect
123. C₄×C₈×C₄₃	C₂³	semidirect
254. C₂×#3220	C₄₃	direct (N × H)
282. C₂×#540	C₂×C₄₃	semidirect
283. C₂×#535	C₂×C₄₃	semidirect
284. #3220	C₂×C₄₃	direct (N × H)
285. C₂×#496	C₂×C₄₃	semidirect
286. C₂×#493	C₂×C₄₃	semidirect
287. C₂×#490	C₂×C₄₃	semidirect
288. C₂×#488	C₂×C₄₃	semidirect
289. C₂×#463	C₂×C₄₃	semidirect
290. C₂×#459	C₂×C₄₃	semidirect
291. C₂×#449	C₂×C₄₃	semidirect
292. C₂×#447	C₂×C₄₃	semidirect
293. C₂×#433	C₂×C₄₃	semidirect
299. C₂×C₄₃	#3220	direct (N × H)
304. C₂²×SD₁₆	C₂²×C₄₃	semidirect
307. C₂²×D₈	C₂²×C₄₃	semidirect
309. #540	C₂²×C₄₃	semidirect
311. #535	C₂²×C₄₃	semidirect
314. C₂×#127	C₂²×C₄₃	semidirect
315. C₂×#125	C₂²×C₄₃	semidirect
323. C₂×C₄×D₄	C₂²×C₄₃	semidirect
325. #496	C₂²×C₄₃	semidirect
326. #493	C₂²×C₄₃	semidirect
327. #490	C₂²×C₄₃	semidirect
328. #488	C₂²×C₄₃	semidirect
329. #463	C₂²×C₄₃	semidirect
330. #459	C₂²×C₄₃	semidirect
331. #449	C₂²×C₄₃	semidirect
332. #447	C₂²×C₄₃	semidirect
333. #433	C₂²×C₄₃	semidirect
334. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
335. C₂×#103	C₂²×C₄₃	semidirect
338. C₂×#102	C₂²×C₄₃	semidirect
340. C₂×#97	C₂²×C₄₃	semidirect
341. C₂×C₄×C₈	C₂²×C₄₃	semidirect
342. C₄₃	C₂×#3220	direct (N × H)
365. C₂×SD₁₆	C₂³×C₄₃	semidirect
371. C₂×D₈	C₂³×C₄₃	semidirect
379. #127	C₂³×C₄₃	semidirect
381. #125	C₂³×C₄₃	semidirect
393. C₄×D₄	C₂³×C₄₃	semidirect
406. C₄⋊C₈	C₂³×C₄₃	semidirect
407. #103	C₂³×C₄₃	semidirect
410. #102	C₂³×C₄₃	semidirect
412. #97	C₂³×C₄₃	semidirect
413. C₄×C₈	C₂³×C₄₃	semidirect
576. C₂	C₄₃×#3220	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×#540	2
C₂×C₄₃×#535	2
C₄₃×#3220	2
C₂×C₄₃×#496	2
C₂×C₄₃×#493	2
C₂×C₄₃×#490	2
C₂×C₄₃×#488	2
C₂×C₄₃×#463	2
C₂×C₄₃×#459	2
C₂×C₄₃×#449	2
C₂×C₄₃×#447	2
C₂×C₄₃×#433	2
C₂×#3220	43

Subgroups — C2×C43×#3220 #24980808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#3220 #24980808