Subgroups — C₄₃×#20924 #24940941

Order 11008.

1858 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1880	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1879	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1878	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1877	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#336	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#135×C₄₃	—	2	4	no	—
15	C₂×#135×C₄₃	—	2	4	no	—
16	C₂×#135×C₄₃	C₄	1	8	yes	complemented
17	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₄×#41×C₄₃	—	2	4	no	—
24	C₄×#41×C₄₃	—	2	4	no	—
25	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₄₃	—	2	2	no	—
27	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
28	C₂×#117×C₄₃	—	2	1	no	—
29	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₃	—	2	1	no	—
32	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#416	—	2	4	no	—
34	C₄₃×#416	—	2	4	no	—
35	C₂×#103×C₄₃	C₂²	1	2	yes	—
36	C₂×#103×C₄₃	C₂²	1	2	yes	—
37	C₂×#102×C₄₃	C₂²	1	2	yes	—
38	C₂×#102×C₄₃	C₂²	1	2	yes	—
39	C₄₃×#391	C₂²	1	2	yes	—
40	C₄₃×#390	C₂²	1	2	yes	—
41	C₄₃×#386	—	2	2	no	—
42	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
43	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#340	C₂²	1	2	yes	—
46	C₄₃×#336	C₂²	1	2	yes	—
47	C₄₃×#336	C₂²	1	2	yes	—
48	C₂×#41×C₄₃	—	2	2	no	—
49	C₂×#41×C₄₃	—	2	2	no	—
50	C₂×#41×C₄₃	—	2	2	no	—
51	C₂×#41×C₄₃	—	2	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	C₂×C₄	1	4	yes	—
57	C₂×#41×C₄₃	C₂×C₄	1	4	yes	complemented
58	C₂×#41×C₄₃	D₄	1	4	yes	—
59	C₂×#41×C₄₃	D₄	1	4	yes	—
60	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₄₃	—	2	1	no	—
63	C₂²×D₄×C₄₃	—	2	1	no	—
64	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	—	2	1	no	—
67	C₂³×C₄×C₄₃	—	2	2	no	—
68	C₂³×C₄×C₄₃	—	2	1	no	—
69	C₂³×C₄×C₄₃	D₄	1	2	yes	—
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	#135×C₄₃	—	2	32	no	—
72	C₂×Q₁₆×C₄₃	—	2	2	no	—
73	C₂×Q₁₆×C₄₃	—	2	2	no	—
74	C₂×Q₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
75	C₂×SD₁₆×C₄₃	—	2	2	no	—
76	C₂×SD₁₆×C₄₃	—	2	2	no	—
77	C₂×SD₁₆×C₄₃	—	2	2	no	—
78	C₂×SD₁₆×C₄₃	—	2	2	no	—
79	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
80	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
81	C₂×D₈×C₄₃	—	2	2	no	—
82	C₂×D₈×C₄₃	—	2	2	no	—
83	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	complemented
84	C₂²×C₈×C₄₃	—	2	2	no	—
85	C₂²×C₈×C₄₃	—	2	2	no	—
86	C₂²×C₈×C₄₃	—	2	2	no	—
87	C₂²×C₈×C₄₃	—	2	2	no	—
88	C₂²×C₈×C₄₃	—	2	2	no	—
89	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
90	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
91	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
93	C₄×Q₈×C₄₃	—	2	4	no	—
94	C₄×Q₈×C₄₃	—	2	4	no	—
95	C₄×D₄×C₄₃	—	2	16	no	—
96	C₄×D₄×C₄₃	—	2	4	no	—
97	C₄×D₄×C₄₃	—	2	4	no	—
98	#117×C₄₃	—	2	8	no	—
99	#117×C₄₃	—	2	2	no	—
100	#117×C₄₃	—	2	2	no	—
101	#117×C₄₃	—	2	2	no	—
102	#117×C₄₃	D₄	1	4	yes	—
103	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
111	C₂×C₄²×C₄₃	—	2	8	no	—
112	C₂×C₄²×C₄₃	—	2	2	no	—
113	C₂×C₄²×C₄₃	—	2	2	no	—
114	C₂×C₄²×C₄₃	—	2	2	no	—
115	C₂×C₄²×C₄₃	—	2	1	no	—
116	C₂×C₄²×C₄₃	—	2	1	no	—
117	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
120	#103×C₄₃	—	2	4	no	—
121	#103×C₄₃	—	2	4	no	—
122	#102×C₄₃	—	2	4	no	—
123	#102×C₄₃	—	2	4	no	—
124	#95×C₄₃	—	2	2	no	—
125	#95×C₄₃	—	2	2	no	—
126	C₂⁴×C₄₃	—	2	1	no	—
127	C₂⁴×C₄₃	—	2	1	no	—
128	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
129	#41×C₄₃	—	2	8	no	—
130	#41×C₄₃	—	2	8	no	—
131	#41×C₄₃	—	2	8	no	—
132	#41×C₄₃	—	2	8	no	—
133	#41×C₄₃	—	2	8	no	—
134	#41×C₄₃	—	4	4	no	—
135	#41×C₄₃	—	4	4	no	—
136	#41×C₄₃	C₂²⋊C₄	1	16	yes	complemented
137	C₂×Q₈×C₄₃	—	2	1	no	—
138	C₂×Q₈×C₄₃	—	2	1	no	—
139	C₂×Q₈×C₄₃	—	2	1	no	—
140	C₂×Q₈×C₄₃	—	2	1	no	—
141	C₂×Q₈×C₄₃	—	2	1	no	—
142	C₂×Q₈×C₄₃	—	2	1	no	—
143	C₂×Q₈×C₄₃	—	2	1	no	—
144	C₂×Q₈×C₄₃	—	2	1	no	—
145	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
146	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
147	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
148	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₄₃	—	2	1	no	—
150	C₂×D₄×C₄₃	—	2	1	no	—
151	C₂×D₄×C₄₃	—	2	1	no	—
152	C₂×D₄×C₄₃	—	2	1	no	—
153	C₂×D₄×C₄₃	—	2	4	no	—
154	C₂×D₄×C₄₃	—	2	4	no	—
155	C₂×D₄×C₄₃	—	2	4	no	—
156	C₂×D₄×C₄₃	—	2	4	no	—
157	C₂×D₄×C₄₃	—	2	1	no	—
158	C₂×D₄×C₄₃	—	2	1	no	—
159	C₂×D₄×C₄₃	—	2	1	no	—
160	C₂×D₄×C₄₃	—	2	1	no	—
161	C₂×D₄×C₄₃	—	4	2	no	—
162	C₂×D₄×C₄₃	—	4	2	no	—
163	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
165	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
166	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₄₃	—	2	4	no	—
168	C₂²×C₄×C₄₃	—	2	4	no	—
169	C₂²×C₄×C₄₃	—	2	4	no	—
170	C₂²×C₄×C₄₃	—	2	8	no	—
171	C₂²×C₄×C₄₃	—	2	4	no	—
172	C₂²×C₄×C₄₃	—	2	4	no	—
173	C₂²×C₄×C₄₃	—	2	4	no	—
174	C₂²×C₄×C₄₃	—	2	1	no	—
175	C₂²×C₄×C₄₃	—	2	1	no	—
176	C₂²×C₄×C₄₃	—	2	2	no	—
177	C₂²×C₄×C₄₃	—	2	2	no	—
178	C₂²×C₄×C₄₃	—	4	2	no	—
179	C₂²×C₄×C₄₃	—	4	4	no	—
180	C₂²×C₄×C₄₃	—	4	2	no	—
181	C₂²×C₄×C₄₃	—	4	2	no	—
182	C₂²×C₄×C₄₃	—	4	4	no	—
183	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
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	2	yes	—
188	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₃	#41	1	2	yes	—
191	C₂²×C₄×C₄₃	#41	1	2	yes	—
192	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
193	Q₁₆×C₄₃	—	2	8	no	—
194	SD₁₆×C₄₃	—	2	8	no	—
195	SD₁₆×C₄₃	—	2	8	no	—
196	D₈×C₄₃	—	2	8	no	—
197	C₂×C₈×C₄₃	—	2	8	no	—
198	C₂×C₈×C₄₃	—	2	1	no	—
199	C₂×C₈×C₄₃	—	2	1	no	—
200	C₂×C₈×C₄₃	—	2	1	no	—
201	C₂×C₈×C₄₃	—	2	1	no	—
202	C₂×C₈×C₄₃	—	2	2	no	—
203	C₂×C₈×C₄₃	—	2	2	no	—
204	C₂×C₈×C₄₃	—	2	2	no	—
205	C₂×C₈×C₄₃	—	4	4	no	—
206	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
207	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
208	C₄⋊C₄×C₄₃	—	2	8	no	—
209	C₄⋊C₄×C₄₃	—	2	2	no	—
210	C₄⋊C₄×C₄₃	—	2	2	no	—
211	C₄⋊C₄×C₄₃	—	2	2	no	—
212	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
213	C₂²⋊C₄×C₄₃	—	2	8	no	—
214	C₂²⋊C₄×C₄₃	—	2	4	no	—
215	C₂²⋊C₄×C₄₃	—	4	4	no	—
216	C₂²⋊C₄×C₄₃	—	4	4	no	—
217	C₂²⋊C₄×C₄₃	—	4	2	no	—
218	C₄²×C₄₃	—	2	8	no	—
219	C₄²×C₄₃	—	2	2	no	—
220	C₄²×C₄₃	—	2	4	no	—
221	C₄²×C₄₃	—	2	2	no	—
222	C₄²×C₄₃	—	2	2	no	—
223	C₄²×C₄₃	—	2	2	no	—
224	C₄²×C₄₃	—	4	2	no	—
225	C₂³×C₄₃	—	2	2	no	—
226	C₂³×C₄₃	—	2	2	no	—
227	C₂³×C₄₃	—	2	2	no	—
228	C₂³×C₄₃	—	2	2	no	—
229	C₂³×C₄₃	—	2	2	no	—
230	C₂³×C₄₃	—	2	2	no	—
231	C₂³×C₄₃	—	4	2	no	—
232	C₂³×C₄₃	—	4	2	no	—
233	C₂³×C₄₃	—	4	1	no	—
234	C₂³×C₄₃	—	4	1	no	—
235	C₂³×C₄₃	—	4	2	no	—
236	C₂³×C₄₃	—	4	2	no	—
237	C₂³×C₄₃	C₄×D₄	1	2	yes	—
238	C₂³×C₄₃	#120	1	2	yes	—
239	C₂³×C₄₃	#121	1	2	yes	—
240	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₄₃	—	2	2	no	—
242	Q₈×C₄₃	—	2	2	no	—
243	Q₈×C₄₃	—	2	2	no	—
244	Q₈×C₄₃	—	2	2	no	—
245	Q₈×C₄₃	—	2	2	no	—
246	Q₈×C₄₃	—	4	1	no	—
247	Q₈×C₄₃	—	4	1	no	—
248	Q₈×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
249	D₄×C₄₃	—	2	16	no	—
250	D₄×C₄₃	—	2	2	no	—
251	D₄×C₄₃	—	2	2	no	—
252	D₄×C₄₃	—	2	2	no	—
253	D₄×C₄₃	—	2	2	no	—
254	D₄×C₄₃	—	2	2	no	—
255	D₄×C₄₃	—	4	8	no	—
256	D₄×C₄₃	—	4	1	no	—
257	D₄×C₄₃	—	4	1	no	—
258	D₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
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	16	no	—
265	C₂×C₄×C₄₃	—	2	2	no	—
266	C₂×C₄×C₄₃	—	2	2	no	—
267	C₂×C₄×C₄₃	—	2	4	no	—
268	C₂×C₄×C₄₃	—	2	2	no	—
269	C₂×C₄×C₄₃	—	2	2	no	—
270	C₂×C₄×C₄₃	—	4	8	no	—
271	C₂×C₄×C₄₃	—	4	16	no	—
272	C₂×C₄×C₄₃	—	4	1	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	8	no	—
277	C₂×C₄×C₄₃	—	4	2	no	—
278	C₂×C₄×C₄₃	—	4	2	no	—
279	C₂×C₄×C₄₃	—	4	2	no	—
280	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
281	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
282	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
283	C₂×C₄×C₄₃	#120	1	2	yes	—
284	C₂×C₄×C₄₃	#121	1	4	yes	—
285	C₂×C₄×C₄₃	#121	1	2	yes	—
286	C₂×C₄×C₄₃	#123	1	4	yes	—
287	C₂×C₄×C₄₃	#135	1	4	yes	complemented
288	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
289	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
294	C₈×C₄₃	—	2	2	no	—
295	C₈×C₄₃	—	2	2	no	—
296	C₈×C₄₃	—	4	2	no	—
297	#20924	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
298	C₂²×C₄₃	—	2	2	no	—
299	C₂²×C₄₃	—	2	2	no	—
300	C₂²×C₄₃	—	2	4	no	—
301	C₂²×C₄₃	—	2	4	no	—
302	C₂²×C₄₃	—	2	4	no	—
303	C₂²×C₄₃	—	4	2	no	—
304	C₂²×C₄₃	—	4	2	no	—
305	C₂²×C₄₃	—	4	4	no	—
306	C₂²×C₄₃	—	4	4	no	—
307	C₂²×C₄₃	—	4	2	no	—
308	C₂²×C₄₃	—	4	2	no	—
309	C₂²×C₄₃	—	4	2	no	—
310	C₂²×C₄₃	—	8	2	no	—
311	C₂²×C₄₃	—	8	2	no	—
312	C₂²×C₄₃	#386	1	4	yes	—
313	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
314	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
315	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
316	C₂²×C₄₃	C₂×#135	1	2	yes	—
317	C₂²×C₄₃	#575	1	2	yes	—
318	C₄×C₄₃	—	2	4	no	—
319	C₄×C₄₃	—	2	4	no	—
320	C₄×C₄₃	—	4	2	no	—
321	C₄×C₄₃	—	4	4	no	—
322	C₄×C₄₃	—	4	2	no	—
323	C₄×C₄₃	—	8	2	no	—
324	C₄×C₄₃	#386	1	4	yes	—
325	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
326	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
327	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
328	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
329	C₂²×#135	C₂×C₄₃	1	1	yes	characteristic
330	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic, complemented
331	C₂×#416	C₂×C₄₃	1	1	yes	characteristic, complemented
332	C₂×#416	C₂×C₄₃	1	1	yes	characteristic, complemented
333	#2297	C₂×C₄₃	1	1	yes	characteristic, complemented
334	#1880	C₂×C₄₃	1	2	yes	complemented
335	#1879	C₂×C₄₃	1	2	yes	complemented
336	#1878	C₂×C₄₃	1	2	yes	complemented
337	#1877	C₂×C₄₃	1	2	yes	complemented
338	#1735	C₂×C₄₃	1	1	yes	characteristic, complemented
339	C₂×#336	C₂×C₄₃	1	1	yes	characteristic, complemented
340	C₂×C₄₃	—	2	4	no	—
341	C₂×C₄₃	—	4	4	no	—
342	C₂×C₄₃	—	8	2	no	—
343	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
344	C₂×C₄₃	C₄×#135	1	1	yes	characteristic
345	C₂×C₄₃	#2943	1	1	yes	characteristic
346	C₂×C₄₃	#3002	1	2	yes	—
347	C₂×C₄₃	#3035	1	2	yes	—
348	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
349	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
350	C₂×#135	—	2	4	no	—
351	C₂×#135	—	2	4	no	—
352	C₂×#135	C₄×C₄₃	1	8	yes	complemented
353	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
354	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
355	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic
356	C₂²×D₈	C₂²×C₄₃	1	1	yes	characteristic
357	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
358	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
359	C₄×#41	—	2	4	no	—
360	C₄×#41	—	2	4	no	—
361	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
362	C₂×C₄×D₄	—	2	2	no	—
363	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
364	C₂×#117	—	2	1	no	—
365	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
366	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
367	C₂²×C₄²	—	2	1	no	—
368	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
369	#416	—	2	4	no	—
370	#416	—	2	4	no	—
371	C₂×#103	C₂²×C₄₃	1	2	yes	—
372	C₂×#103	C₂²×C₄₃	1	2	yes	—
373	C₂×#102	C₂²×C₄₃	1	2	yes	—
374	C₂×#102	C₂²×C₄₃	1	2	yes	—
375	#391	C₂²×C₄₃	1	2	yes	—
376	#390	C₂²×C₄₃	1	2	yes	—
377	#386	—	2	2	no	—
378	C₄×C₂²⋊C₄	—	2	1	no	—
379	C₄×C₂²⋊C₄	—	2	1	no	—
380	#340	C₂²×C₄₃	1	2	yes	—
381	#340	C₂²×C₄₃	1	2	yes	—
382	#336	C₂²×C₄₃	1	2	yes	—
383	#336	C₂²×C₄₃	1	2	yes	—
384	C₄₃	#20924	1	1	yes	characteristic, direct product factor, Sylow
385	C₂×#41	—	2	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	—	2	2	no	—
392	C₂×#41	—	2	2	no	—
393	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
394	C₂×#41	C₂×C₄×C₄₃	1	4	yes	complemented
395	C₂×#41	D₄×C₄₃	1	4	yes	—
396	C₂×#41	D₄×C₄₃	1	4	yes	—
397	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
402	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	—	2	2	no	—
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	D₄×C₄₃	1	2	yes	—
407	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
408	#135	—	2	32	no	—
409	C₂×Q₁₆	—	2	2	no	—
410	C₂×Q₁₆	—	2	2	no	—
411	C₂×Q₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
412	C₂×SD₁₆	—	2	2	no	—
413	C₂×SD₁₆	—	2	2	no	—
414	C₂×SD₁₆	—	2	2	no	—
415	C₂×SD₁₆	—	2	2	no	—
416	C₂×SD₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
417	C₂×SD₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
418	C₂×D₈	—	2	2	no	—
419	C₂×D₈	—	2	2	no	—
420	C₂×D₈	C₂×C₄×C₄₃	1	4	yes	complemented
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	—	2	2	no	—
423	C₂²×C₈	—	2	2	no	—
424	C₂²×C₈	—	2	2	no	—
425	C₂²×C₈	—	2	2	no	—
426	C₂²×C₈	C₂×C₄×C₄₃	1	4	yes	complemented
427	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
428	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
430	C₄×Q₈	—	2	4	no	—
431	C₄×Q₈	—	2	4	no	—
432	C₄×D₄	—	2	16	no	—
433	C₄×D₄	—	2	4	no	—
434	C₄×D₄	—	2	4	no	—
435	#117	—	2	8	no	—
436	#117	—	2	2	no	—
437	#117	—	2	2	no	—
438	#117	—	2	2	no	—
439	#117	D₄×C₄₃	1	4	yes	—
440	C₂×C₄⋊C₄	—	2	2	no	—
441	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	2	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	2	no	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₄²	—	2	8	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	2	no	—
451	C₂×C₄²	—	2	2	no	—
452	C₂×C₄²	—	2	2	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
455	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
457	#103	—	2	4	no	—
458	#103	—	2	4	no	—
459	#102	—	2	4	no	—
460	#102	—	2	4	no	—
461	#95	—	2	2	no	—
462	#95	—	2	2	no	—
463	C₂⁴	—	2	1	no	—
464	C₂⁴	—	2	1	no	—
465	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
466	#41	—	2	8	no	—
467	#41	—	2	8	no	—
468	#41	—	2	8	no	—
469	#41	—	2	8	no	—
470	#41	—	2	8	no	—
471	#41	—	4	4	no	—
472	#41	—	4	4	no	—
473	#41	C₂²⋊C₄×C₄₃	1	16	yes	complemented
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
483	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
484	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
485	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	4	2	no	—
499	C₂×D₄	—	4	2	no	—
500	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
501	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
502	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
503	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	8	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
521	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
522	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
523	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
524	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
527	C₂²×C₄	#41×C₄₃	1	2	yes	—
528	C₂²×C₄	#41×C₄₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
530	Q₁₆	—	2	8	no	—
531	SD₁₆	—	2	8	no	—
532	SD₁₆	—	2	8	no	—
533	D₈	—	2	8	no	—
534	C₂×C₈	—	2	8	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	2	no	—
540	C₂×C₈	—	2	2	no	—
541	C₂×C₈	—	2	2	no	—
542	C₂×C₈	—	4	4	no	—
543	C₂×C₈	C₂²×C₄×C₄₃	1	2	yes	—
544	C₂×C₈	C₂²×C₄×C₄₃	1	2	yes	—
545	C₄⋊C₄	—	2	8	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
550	C₂²⋊C₄	—	2	8	no	—
551	C₂²⋊C₄	—	2	4	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₄²	—	2	8	no	—
556	C₄²	—	2	2	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	2	no	—
559	C₄²	—	2	2	no	—
560	C₄²	—	2	2	no	—
561	C₄²	—	4	2	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	4	2	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	4	2	no	—
574	C₂³	C₄×D₄×C₄₃	1	2	yes	—
575	C₂³	#120×C₄₃	1	2	yes	—
576	C₂³	#121×C₄₃	1	2	yes	—
577	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	2	2	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
586	D₄	—	2	16	no	—
587	D₄	—	2	2	no	—
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	4	8	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	1	no	—
595	D₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
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	16	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	8	no	—
608	C₂×C₄	—	4	16	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
618	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
619	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
620	C₂×C₄	#120×C₄₃	1	2	yes	—
621	C₂×C₄	#121×C₄₃	1	4	yes	—
622	C₂×C₄	#121×C₄₃	1	2	yes	—
623	C₂×C₄	#123×C₄₃	1	4	yes	—
624	C₂×C₄	#135×C₄₃	1	4	yes	complemented
625	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
626	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
627	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
629	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
631	C₈	—	2	2	no	—
632	C₈	—	2	2	no	—
633	C₈	—	4	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	8	2	no	—
647	C₂²	—	8	2	no	—
648	C₂²	C₄₃×#386	1	4	yes	—
649	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
650	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
651	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
652	C₂²	C₂×#135×C₄₃	1	2	yes	—
653	C₂²	C₄₃×#575	1	2	yes	—
654	C₄	—	2	4	no	—
655	C₄	—	2	4	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	2	no	—
659	C₄	—	8	2	no	—
660	C₄	C₄₃×#386	1	4	yes	—
661	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
662	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
663	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
664	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
665	C₂	—	2	4	no	—
666	C₂	—	4	4	no	—
667	C₂	—	8	2	no	—
668	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
669	C₂	C₄×#135×C₄₃	1	1	yes	characteristic
670	C₂	C₄₃×#2943	1	1	yes	characteristic
671	C₂	C₄₃×#3002	1	2	yes	—
672	C₂	C₄₃×#3035	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×#135×C₄₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₄₃	C₂	semidirect
3. C₂×C₄₃×#416	C₂	semidirect
4. C₂×C₄₃×#416	C₂	semidirect
5. C₄₃×#2297	C₂	semidirect
6. C₄₃×#1880	C₂	semidirect
7. C₄₃×#1879	C₂	semidirect
8. C₄₃×#1878	C₂	semidirect
9. C₄₃×#1877	C₂	semidirect
10. C₄₃×#1735	C₂	semidirect
11. C₂×C₄₃×#336	C₂	semidirect
16. C₂×#135×C₄₃	C₄	semidirect
57. C₂×#41×C₄₃	C₂×C₄	semidirect
74. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
79. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
80. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
83. C₂×D₈×C₄₃	C₂×C₄	semidirect
89. C₂²×C₈×C₄₃	C₂×C₄	semidirect
136. #41×C₄₃	C₂²⋊C₄	semidirect
287. C₂×C₄×C₄₃	#135	semidirect
297. #20924	C₄₃	direct (N × H)
330. C₂×C₄×#41	C₂×C₄₃	semidirect
331. C₂×#416	C₂×C₄₃	semidirect
332. C₂×#416	C₂×C₄₃	semidirect
333. #2297	C₂×C₄₃	semidirect
334. #1880	C₂×C₄₃	semidirect
335. #1879	C₂×C₄₃	semidirect
336. #1878	C₂×C₄₃	semidirect
337. #1877	C₂×C₄₃	semidirect
338. #1735	C₂×C₄₃	semidirect
339. C₂×#336	C₂×C₄₃	semidirect
352. C₂×#135	C₄×C₄₃	semidirect
384. C₄₃	#20924	direct (N × H)
394. C₂×#41	C₂×C₄×C₄₃	semidirect
411. C₂×Q₁₆	C₂×C₄×C₄₃	semidirect
416. C₂×SD₁₆	C₂×C₄×C₄₃	semidirect
417. C₂×SD₁₆	C₂×C₄×C₄₃	semidirect
420. C₂×D₈	C₂×C₄×C₄₃	semidirect
426. C₂²×C₈	C₂×C₄×C₄₃	semidirect
473. #41	C₂²⋊C₄×C₄₃	semidirect
624. C₂×C₄	#135×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₄₃	2
C₂×C₄×#41×C₄₃	2
C₂×C₄₃×#416	2
C₄₃×#2297	2
C₄₃×#1880	2
C₄₃×#1879	2
C₄₃×#1878	2
C₄₃×#1877	2
C₄₃×#1735	2
C₂×C₄₃×#336	2
#20924	43

Subgroups — C43×#20924 #24940941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20924 #24940941