Subgroups — C₄₃×#20913 #24940930

Order 11008.

1778 conjugacy classes of subgroups.

The subgroup lattice has 554 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
2	C₂×C₄₃×#520	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#103×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1873	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1872	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#536	—	2	4	no	—
15	C₄₃×#536	C₄	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
17	C₂×#124×C₄₃	—	2	1	no	—
18	C₂×#123×C₄₃	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
20	C₄₃×#520	—	2	4	no	—
21	C₄₃×#520	—	2	4	no	—
22	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
23	C₂×C₄×D₄×C₄₃	—	2	2	no	—
24	C₂×C₄×D₄×C₄₃	—	2	1	no	—
25	C₂×#117×C₄₃	C₂²	1	2	yes	—
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#419	—	2	4	no	—
31	C₂×#103×C₄₃	—	2	4	no	—
32	C₂×#103×C₄₃	C₂²	1	4	yes	—
33	C₂×#103×C₄₃	C₂²	1	2	yes	—
34	C₂×#103×C₄₃	C₂²	1	2	yes	—
35	C₄₃×#408	—	2	4	no	—
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
37	C₄₃×#340	C₂²	1	2	yes	—
38	C₄₃×#340	C₂²	1	4	yes	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	—	2	2	no	—
42	C₂×#41×C₄₃	—	2	2	no	—
43	C₂×#41×C₄₃	—	2	2	no	—
44	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
45	C₂×#41×C₄₃	D₄	1	4	yes	—
46	C₂²×Q₈×C₄₃	—	2	1	no	—
47	C₂²×Q₈×C₄₃	—	2	2	no	—
48	C₂²×Q₈×C₄₃	—	2	2	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	2	2	no	—
52	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
53	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₄₃	D₄	1	2	yes	—
56	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	—	2	1	no	—
58	C₂³×C₄×C₄₃	—	2	2	no	—
59	C₂³×C₄×C₄₃	—	2	1	no	—
60	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₄₃	—	2	2	no	—
63	C₂×M₁₆×C₄₃	—	2	2	no	—
64	C₂×M₁₆×C₄₃	—	2	2	no	—
65	C₂²×C₈×C₄₃	—	2	2	no	—
66	C₂²×C₈×C₄₃	—	2	2	no	—
67	C₂²×C₈×C₄₃	—	2	2	no	—
68	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₄₃	—	2	8	no	—
71	#124×C₄₃	—	2	8	no	—
72	#123×C₄₃	—	2	16	no	—
73	C₂²⋊Q₈×C₄₃	—	2	8	no	—
74	C₂²⋊Q₈×C₄₃	C₂×C₄	1	16	yes	complemented
75	C₄×Q₈×C₄₃	—	2	8	no	—
76	C₄×D₄×C₄₃	—	2	16	no	—
77	C₄×D₄×C₄₃	—	2	8	no	—
78	#117×C₄₃	—	2	2	no	—
79	#117×C₄₃	—	2	2	no	—
80	#117×C₄₃	—	2	4	no	—
81	#117×C₄₃	—	2	4	no	—
82	#117×C₄₃	C₂×C₄	1	4	yes	complemented
83	#117×C₄₃	D₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
90	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
99	C₂×C₄²×C₄₃	—	2	2	no	—
100	C₂×C₄²×C₄₃	—	2	1	no	—
101	C₂×C₄²×C₄₃	—	2	1	no	—
102	#103×C₄₃	—	2	8	no	—
103	#103×C₄₃	—	2	4	no	—
104	#103×C₄₃	—	2	4	no	—
105	C₂²⋊C₈×C₄₃	—	2	8	no	—
106	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
107	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
108	#41×C₄₃	—	2	8	no	—
109	#41×C₄₃	—	2	8	no	—
110	#41×C₄₃	—	2	8	no	—
111	#41×C₄₃	—	2	8	no	—
112	C₂×Q₈×C₄₃	—	2	4	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	8	no	—
117	C₂×Q₈×C₄₃	—	2	8	no	—
118	C₂×Q₈×C₄₃	—	2	2	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	—	4	2	no	—
123	C₂×Q₈×C₄₃	—	4	4	no	—
124	C₂×Q₈×C₄₃	—	4	4	no	—
125	C₂×Q₈×C₄₃	—	4	2	no	—
126	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
127	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	4	no	—
131	C₂×D₄×C₄₃	—	2	4	no	—
132	C₂×D₄×C₄₃	C₂²⋊C₄	1	8	yes	—
133	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	—	2	2	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	2	8	no	—
139	C₂²×C₄×C₄₃	—	2	4	no	—
140	C₂²×C₄×C₄₃	—	2	4	no	—
141	C₂²×C₄×C₄₃	—	2	1	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	1	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	4	2	no	—
147	C₂²×C₄×C₄₃	—	4	2	no	—
148	C₂²×C₄×C₄₃	—	8	2	no	—
149	C₂²×C₄×C₄₃	—	8	4	no	—
150	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
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	#41	1	2	yes	—
159	C₂²×C₄×C₄₃	#41	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
161	M₁₆×C₄₃	—	4	4	no	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	2	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	—	4	4	no	—
169	C₄⋊C₄×C₄₃	—	2	8	no	—
170	C₄⋊C₄×C₄₃	—	2	16	no	—
171	C₄⋊C₄×C₄₃	—	2	4	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	C₂²×C₄	1	4	yes	—
177	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
178	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
179	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
180	C₂²⋊C₄×C₄₃	—	2	8	no	—
181	C₂²⋊C₄×C₄₃	—	2	4	no	—
182	C₂²⋊C₄×C₄₃	—	2	16	no	—
183	C₂²⋊C₄×C₄₃	—	2	4	no	—
184	C₄²×C₄₃	—	2	8	no	—
185	C₄²×C₄₃	—	2	4	no	—
186	C₄²×C₄₃	—	2	4	no	—
187	C₂³×C₄₃	—	2	2	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	2	no	—
191	C₂³×C₄₃	—	2	4	no	—
192	C₂³×C₄₃	—	2	4	no	—
193	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
194	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂³×C₄₃	#120	1	2	yes	—
196	C₂³×C₄₃	#123	1	2	yes	—
197	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₄₃	—	2	8	no	—
199	Q₈×C₄₃	—	2	4	no	—
200	Q₈×C₄₃	—	2	4	no	—
201	Q₈×C₄₃	—	4	2	no	—
202	Q₈×C₄₃	—	4	2	no	—
203	Q₈×C₄₃	—	4	8	no	—
204	D₄×C₄₃	—	2	16	no	—
205	D₄×C₄₃	—	2	8	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	2	4	no	—
213	C₂×C₄×C₄₃	—	2	4	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	4	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	2	no	—
224	C₂×C₄×C₄₃	—	4	8	no	—
225	C₂×C₄×C₄₃	—	8	4	no	—
226	C₂×C₄×C₄₃	—	8	8	no	—
227	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
228	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
230	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
231	C₂×C₄×C₄₃	#120	1	2	yes	—
232	C₂×C₄×C₄₃	#121	1	4	yes	—
233	C₂×C₄×C₄₃	#121	1	4	yes	—
234	C₂×C₄×C₄₃	#123	1	2	yes	—
235	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
241	C₈×C₄₃	—	4	2	no	—
242	C₈×C₄₃	—	4	2	no	—
243	#20913	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂²×C₄₃	—	2	4	no	—
245	C₂²×C₄₃	—	2	4	no	—
246	C₂²×C₄₃	—	2	2	no	—
247	C₂²×C₄₃	—	2	2	no	—
248	C₂²×C₄₃	—	2	8	no	—
249	C₂²×C₄₃	—	2	4	no	—
250	C₂²×C₄₃	—	4	4	no	—
251	C₂²×C₄₃	—	4	2	no	—
252	C₂²×C₄₃	—	4	2	no	—
253	C₂²×C₄₃	#386	1	4	yes	—
254	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
256	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
257	C₂²×C₄₃	#577	1	2	yes	—
258	C₂²×C₄₃	#578	1	2	yes	—
259	C₄×C₄₃	—	2	4	no	—
260	C₄×C₄₃	—	4	4	no	—
261	C₄×C₄₃	—	4	4	no	—
262	C₄×C₄₃	—	4	2	no	—
263	C₄×C₄₃	—	4	2	no	—
264	C₄×C₄₃	—	4	4	no	—
265	C₄×C₄₃	#386	1	4	yes	—
266	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
268	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
269	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
270	C₂×#536	C₂×C₄₃	1	1	yes	characteristic
271	C₂×#520	C₂×C₄₃	1	1	yes	characteristic
272	C₂×#419	C₂×C₄₃	1	1	yes	characteristic, complemented
273	C₂²×#103	C₂×C₄₃	1	1	yes	characteristic, complemented
274	C₂×#408	C₂×C₄₃	1	1	yes	characteristic
275	#1873	C₂×C₄₃	1	4	yes	complemented
276	#1872	C₂×C₄₃	1	4	yes	complemented
277	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#1735	C₂×C₄₃	1	1	yes	characteristic, complemented
279	C₂×C₄₃	—	2	4	no	—
280	C₂×C₄₃	—	4	4	no	—
281	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
282	C₂×C₄₃	#2898	1	2	yes	—
283	C₂×C₄₃	#3009	1	1	yes	characteristic
284	C₂×C₄₃	#3011	1	1	yes	characteristic
285	C₂×C₄₃	#3097	1	2	yes	—
286	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
287	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
288	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
289	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
290	#536	—	2	4	no	—
291	#536	C₄×C₄₃	1	8	yes	complemented
292	C₂×C₄⋊Q₈	—	2	1	no	—
293	C₂×#124	—	2	1	no	—
294	C₂×#123	—	2	2	no	—
295	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	—
296	#520	—	2	4	no	—
297	#520	—	2	4	no	—
298	C₂×C₄×Q₈	—	2	1	no	—
299	C₂×C₄×D₄	—	2	2	no	—
300	C₂×C₄×D₄	—	2	1	no	—
301	C₂×#117	C₂²×C₄₃	1	2	yes	—
302	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
303	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
305	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
306	#419	—	2	4	no	—
307	C₂×#103	—	2	4	no	—
308	C₂×#103	C₂²×C₄₃	1	4	yes	—
309	C₂×#103	C₂²×C₄₃	1	2	yes	—
310	C₂×#103	C₂²×C₄₃	1	2	yes	—
311	#408	—	2	4	no	—
312	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
313	#340	C₂²×C₄₃	1	2	yes	—
314	#340	C₂²×C₄₃	1	4	yes	—
315	#340	C₂²×C₄₃	1	2	yes	—
316	C₄₃	#20913	1	1	yes	characteristic, direct product factor, Sylow
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
322	C₂×#41	D₄×C₄₃	1	4	yes	—
323	C₂²×Q₈	—	2	1	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	—	2	2	no	—
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	—	2	2	no	—
329	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
330	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
331	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
332	C₂²×D₄	D₄×C₄₃	1	2	yes	—
333	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	—	2	2	no	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	—	2	2	no	—
341	C₂×M₁₆	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
346	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
347	C₄⋊Q₈	—	2	8	no	—
348	#124	—	2	8	no	—
349	#123	—	2	16	no	—
350	C₂²⋊Q₈	—	2	8	no	—
351	C₂²⋊Q₈	C₂×C₄×C₄₃	1	16	yes	complemented
352	C₄×Q₈	—	2	8	no	—
353	C₄×D₄	—	2	16	no	—
354	C₄×D₄	—	2	8	no	—
355	#117	—	2	2	no	—
356	#117	—	2	2	no	—
357	#117	—	2	4	no	—
358	#117	—	2	4	no	—
359	#117	C₂×C₄×C₄₃	1	4	yes	complemented
360	#117	D₄×C₄₃	1	4	yes	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	4	no	—
365	C₂×C₄⋊C₄	—	2	4	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
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	4	no	—
376	C₂×C₄²	—	2	2	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	#103	—	2	8	no	—
380	#103	—	2	4	no	—
381	#103	—	2	4	no	—
382	C₂²⋊C₈	—	2	8	no	—
383	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
384	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
385	#41	—	2	8	no	—
386	#41	—	2	8	no	—
387	#41	—	2	8	no	—
388	#41	—	2	8	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	8	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	4	2	no	—
400	C₂×Q₈	—	4	4	no	—
401	C₂×Q₈	—	4	4	no	—
402	C₂×Q₈	—	4	2	no	—
403	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	—
404	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	C₂²⋊C₄×C₄₃	1	8	yes	—
410	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	8	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	8	2	no	—
426	C₂²×C₄	—	8	4	no	—
427	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
428	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
431	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
435	C₂²×C₄	#41×C₄₃	1	2	yes	—
436	C₂²×C₄	#41×C₄₃	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
438	M₁₆	—	4	4	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	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	—	4	4	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	16	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
454	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
455	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
456	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	16	no	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₄²	—	2	8	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	4	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	4	no	—
470	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
471	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
472	C₂³	#120×C₄₃	1	2	yes	—
473	C₂³	#123×C₄₃	1	2	yes	—
474	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
475	Q₈	—	2	8	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	2	4	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	8	no	—
481	D₄	—	2	16	no	—
482	D₄	—	2	8	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	8	4	no	—
503	C₂×C₄	—	8	8	no	—
504	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
505	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
506	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
507	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
508	C₂×C₄	#120×C₄₃	1	2	yes	—
509	C₂×C₄	#121×C₄₃	1	4	yes	—
510	C₂×C₄	#121×C₄₃	1	4	yes	—
511	C₂×C₄	#123×C₄₃	1	2	yes	—
512	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
517	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
518	C₈	—	4	2	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	8	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	C₄₃×#386	1	4	yes	—
530	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
531	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
532	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
533	C₂²	C₄₃×#577	1	2	yes	—
534	C₂²	C₄₃×#578	1	2	yes	—
535	C₄	—	2	4	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	4	no	—
541	C₄	C₄₃×#386	1	4	yes	—
542	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
543	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
544	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
545	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
546	C₂	—	2	4	no	—
547	C₂	—	4	4	no	—
548	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
549	C₂	C₄₃×#2898	1	2	yes	—
550	C₂	C₄₃×#3009	1	1	yes	characteristic
551	C₂	C₄₃×#3011	1	1	yes	characteristic
552	C₂	C₄₃×#3097	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₃×#419	C₂	semidirect
4. C₂²×#103×C₄₃	C₂	semidirect
6. C₄₃×#1873	C₂	semidirect
7. C₄₃×#1872	C₂	semidirect
8. C₄₃×#1736	C₂	semidirect
9. C₄₃×#1735	C₂	semidirect
15. C₄₃×#536	C₄	semidirect
52. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
74. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
82. #117×C₄₃	C₂×C₄	semidirect
243. #20913	C₄₃	direct (N × H)
272. C₂×#419	C₂×C₄₃	semidirect
273. C₂²×#103	C₂×C₄₃	semidirect
275. #1873	C₂×C₄₃	semidirect
276. #1872	C₂×C₄₃	semidirect
277. #1736	C₂×C₄₃	semidirect
278. #1735	C₂×C₄₃	semidirect
291. #536	C₄×C₄₃	semidirect
316. C₄₃	#20913	direct (N × H)
329. C₂²×Q₈	C₂×C₄×C₄₃	semidirect
351. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
359. #117	C₂×C₄×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×#536	2
C₂×C₄₃×#520	2
C₂×C₄₃×#419	2
C₂²×#103×C₄₃	2
C₂×C₄₃×#408	2
C₄₃×#1873	2
C₄₃×#1872	2
C₄₃×#1736	2
C₄₃×#1735	2
#20913	43

Subgroups — C43×#20913 #24940930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20913 #24940930