Subgroups — C₄₃×#29593 #24949610

Order 11008.

1520 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2847	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2035	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2000	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1779	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
13	C₂×C₂²⋊Q₈×C₄₃	—	2	4	no	—
14	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
15	C₂×C₂²⋊Q₈×C₄₃	—	2	4	no	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
17	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₃	C₂²	1	2	yes	—
19	C₂×#120×C₄₃	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
23	C₄₃×#481	—	2	4	no	—
24	C₄₃×#448	—	2	4	no	—
25	C₂×#106×C₄₃	C₂²	1	2	yes	complemented
26	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
27	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
28	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
32	C₄₃×#386	—	2	1	no	—
33	C₄₃×#386	—	2	2	no	—
34	C₄₃×#380	C₂²	1	1	yes	characteristic
35	C₄₃×#380	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	4	yes	complemented
37	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₄₃	—	2	2	no	—
39	C₂²×Q₈×C₄₃	—	2	1	no	—
40	C₂²×Q₈×C₄₃	—	4	4	no	—
41	C₂²×Q₈×C₄₃	D₄	1	4	yes	complemented
42	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₃	—	2	2	no	—
44	C₂²×D₄×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	—	2	2	no	—
49	C₂³×C₄×C₄₃	—	2	2	no	—
50	C₂³×C₄×C₄₃	—	4	4	no	—
51	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	D₄	1	2	yes	—
53	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₄₃	—	2	4	no	—
56	C₂×SD₁₆×C₄₃	—	4	4	no	—
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	C₂²⋊Q₈×C₄₃	—	2	16	no	—
60	C₂²⋊Q₈×C₄₃	—	2	8	no	—
61	C₂²⋊Q₈×C₄₃	—	2	8	no	—
62	#121×C₄₃	—	2	2	no	—
63	#121×C₄₃	—	2	2	no	—
64	#121×C₄₃	—	4	4	no	—
65	#120×C₄₃	—	4	4	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	complemented
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	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	#106×C₄₃	—	2	4	no	—
81	#103×C₄₃	—	2	4	no	—
82	#103×C₄₃	—	4	4	no	—
83	#102×C₄₃	—	2	4	no	—
84	C₂²⋊C₈×C₄₃	—	2	2	no	—
85	C₂²⋊C₈×C₄₃	—	2	2	no	—
86	C₂²⋊C₈×C₄₃	—	4	4	no	—
87	#95×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	1	no	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	—	2	1	no	—
92	C₂⁴×C₄₃	—	4	2	no	—
93	C₂⁴×C₄₃	—	4	2	no	—
94	C₂⁴×C₄₃	SD₁₆	1	4	yes	complemented
95	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
96	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₄₃	—	2	4	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	4	no	—
100	C₂×Q₈×C₄₃	—	2	4	no	—
101	C₂×Q₈×C₄₃	—	4	8	no	—
102	C₂×Q₈×C₄₃	—	4	4	no	—
103	C₂×Q₈×C₄₃	—	4	8	no	—
104	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	4	no	—
108	C₂×D₄×C₄₃	—	4	4	no	—
109	C₂×D₄×C₄₃	—	4	4	no	—
110	C₂×D₄×C₄₃	—	4	2	no	—
111	C₂×D₄×C₄₃	—	4	4	no	—
112	C₂×D₄×C₄₃	—	4	2	no	—
113	C₂×D₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	4	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	4	no	—
120	C₂²×C₄×C₄₃	—	2	4	no	—
121	C₂²×C₄×C₄₃	—	2	4	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	4	2	no	—
128	C₂²×C₄×C₄₃	—	4	2	no	—
129	C₂²×C₄×C₄₃	—	4	2	no	—
130	C₂²×C₄×C₄₃	—	4	4	no	—
131	C₂²×C₄×C₄₃	—	4	4	no	—
132	C₂²×C₄×C₄₃	—	4	8	no	—
133	C₂²×C₄×C₄₃	—	4	8	no	—
134	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₄₃	—	4	8	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	4	no	—
143	C₂×C₈×C₄₃	—	2	4	no	—
144	C₄⋊C₄×C₄₃	—	2	16	no	—
145	C₄⋊C₄×C₄₃	—	2	4	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	1	no	—
148	C₄⋊C₄×C₄₃	—	2	1	no	—
149	C₄⋊C₄×C₄₃	—	2	4	no	—
150	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
151	C₂²⋊C₄×C₄₃	—	2	16	no	—
152	C₂²⋊C₄×C₄₃	—	4	4	no	—
153	C₂²⋊C₄×C₄₃	—	4	2	no	—
154	C₂²⋊C₄×C₄₃	—	4	4	no	—
155	C₂²⋊C₄×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	—	2	8	no	—
165	C₂³×C₄₃	—	4	8	no	—
166	C₂³×C₄₃	—	4	4	no	—
167	C₂³×C₄₃	—	4	8	no	—
168	C₂³×C₄₃	—	4	4	no	—
169	C₂³×C₄₃	—	4	1	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	—	4	1	no	—
172	C₂³×C₄₃	—	4	1	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	#120	1	2	yes	—
175	C₂³×C₄₃	C₂×SD₁₆	1	4	yes	—
176	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
177	C₂³×C₄₃	#137	1	2	yes	—
178	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₄₃	—	2	4	no	—
180	Q₈×C₄₃	—	2	4	no	—
181	Q₈×C₄₃	—	4	8	no	—
182	Q₈×C₄₃	—	4	4	no	—
183	D₄×C₄₃	—	4	2	no	—
184	D₄×C₄₃	—	4	2	no	—
185	D₄×C₄₃	—	8	8	no	—
186	D₄×C₄₃	—	8	4	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	4	no	—
189	C₂×C₄×C₄₃	—	2	4	no	—
190	C₂×C₄×C₄₃	—	2	4	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	4	8	no	—
196	C₂×C₄×C₄₃	—	4	8	no	—
197	C₂×C₄×C₄₃	—	4	4	no	—
198	C₂×C₄×C₄₃	—	4	8	no	—
199	C₂×C₄×C₄₃	—	4	4	no	—
200	C₂×C₄×C₄₃	—	4	4	no	—
201	C₂×C₄×C₄₃	—	4	4	no	—
202	C₂×C₄×C₄₃	—	4	4	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	#120	1	2	yes	—
210	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
213	C₈×C₄₃	—	4	2	no	—
214	C₈×C₄₃	—	4	2	no	—
215	#29593	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	2	4	no	—
218	C₂²×C₄₃	—	2	4	no	—
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	2	4	no	—
221	C₂²×C₄₃	—	2	4	no	—
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	4	16	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	4	2	no	—
226	C₂²×C₄₃	—	4	2	no	—
227	C₂²×C₄₃	—	4	2	no	—
228	C₂²×C₄₃	—	8	1	no	—
229	C₂²×C₄₃	—	8	2	no	—
230	C₂²×C₄₃	—	8	2	no	—
231	C₂²×C₄₃	—	8	1	no	—
232	C₂²×C₄₃	—	8	1	no	—
233	C₂²×C₄₃	#448	1	4	yes	—
234	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
235	C₂²×C₄₃	#534	1	2	yes	—
236	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
237	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
238	C₂²×C₄₃	#575	1	2	yes	—
239	C₄×C₄₃	—	2	2	no	—
240	C₄×C₄₃	—	4	2	no	—
241	C₄×C₄₃	—	4	4	no	—
242	C₄×C₄₃	—	4	4	no	—
243	C₄×C₄₃	—	8	2	no	—
244	C₄×C₄₃	—	8	1	no	—
245	C₄×C₄₃	#534	1	2	yes	—
246	C₄×C₄₃	#535	1	2	yes	—
247	C₂²×C₂²⋊Q₈	C₂×C₄₃	1	1	yes	characteristic, complemented
248	C₂×#481	C₂×C₄₃	1	1	yes	characteristic, complemented
249	C₂×#448	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#2847	C₂×C₄₃	1	1	yes	characteristic
251	#2035	C₂×C₄₃	1	4	yes	complemented
252	#2000	C₂×C₄₃	1	4	yes	complemented
253	#1824	C₂×C₄₃	1	1	yes	characteristic, complemented
254	#1787	C₂×C₄₃	1	1	yes	characteristic, complemented
255	#1779	C₂×C₄₃	1	1	yes	characteristic, complemented
256	C₂×C₄₃	—	2	4	no	—
257	C₂×C₄₃	—	4	4	no	—
258	C₂×C₄₃	—	16	1	no	—
259	C₂×C₄₃	#2613	1	1	yes	characteristic
260	C₂×C₄₃	C₂×#448	1	1	yes	characteristic
261	C₂×C₄₃	#3005	1	1	yes	characteristic
262	C₂×C₄₃	#3187	1	2	yes	—
263	C₂×C₄₃	#3196	1	2	yes	—
264	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
265	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
266	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
267	C₂×C₂²⋊Q₈	—	2	4	no	—
268	C₂×C₂²⋊Q₈	—	2	2	no	—
269	C₂×C₂²⋊Q₈	—	2	4	no	—
270	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	—
271	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
272	C₂×#121	C₂²×C₄₃	1	2	yes	—
273	C₂×#120	—	2	1	no	—
274	C₂²×C₄⋊C₄	—	2	1	no	—
275	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	—	2	1	no	—
277	#481	—	2	4	no	—
278	#448	—	2	4	no	—
279	C₂×#106	C₂²×C₄₃	1	2	yes	complemented
280	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
281	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
282	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
283	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
286	#386	—	2	1	no	—
287	#386	—	2	2	no	—
288	#380	C₂²×C₄₃	1	1	yes	characteristic
289	#380	C₂²×C₄₃	1	2	yes	—
290	#340	C₂²×C₄₃	1	4	yes	complemented
291	C₄₃	#29593	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
293	C₂²×Q₈	—	2	2	no	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	—	4	4	no	—
296	C₂²×Q₈	D₄×C₄₃	1	4	yes	complemented
297	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	—	4	4	no	—
306	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
307	C₂³×C₄	D₄×C₄₃	1	2	yes	—
308	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
309	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
310	C₂×SD₁₆	—	2	4	no	—
311	C₂×SD₁₆	—	4	4	no	—
312	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
313	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
314	C₂²⋊Q₈	—	2	16	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₂²⋊Q₈	—	2	8	no	—
317	#121	—	2	2	no	—
318	#121	—	2	2	no	—
319	#121	—	4	4	no	—
320	#120	—	4	4	no	—
321	C₂×C₄⋊C₄	—	2	8	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	complemented
326	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	8	no	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	#106	—	2	4	no	—
336	#103	—	2	4	no	—
337	#103	—	4	4	no	—
338	#102	—	2	4	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	—	4	4	no	—
342	#95	—	2	2	no	—
343	#95	—	2	1	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	1	no	—
347	C₂⁴	—	4	2	no	—
348	C₂⁴	—	4	2	no	—
349	C₂⁴	SD₁₆×C₄₃	1	4	yes	complemented
350	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
351	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	4	8	no	—
357	C₂×Q₈	—	4	4	no	—
358	C₂×Q₈	—	4	8	no	—
359	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	4	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	8	no	—
386	C₂²×C₄	—	4	8	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
394	SD₁₆	—	4	8	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	4	no	—
399	C₄⋊C₄	—	2	16	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
406	C₂²⋊C₄	—	2	16	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	4	8	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	2	no	—
429	C₂³	#120×C₄₃	1	2	yes	—
430	C₂³	C₂×SD₁₆×C₄₃	1	4	yes	—
431	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
432	C₂³	#137×C₄₃	1	2	yes	—
433	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
434	Q₈	—	2	4	no	—
435	Q₈	—	2	4	no	—
436	Q₈	—	4	8	no	—
437	Q₈	—	4	4	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	2	no	—
440	D₄	—	8	8	no	—
441	D₄	—	8	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	8	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	8	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	#120×C₄₃	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
467	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	16	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	8	1	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	C₄₃×#448	1	4	yes	—
488	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
489	C₂²	C₄₃×#534	1	2	yes	—
490	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
491	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
492	C₂²	C₄₃×#575	1	2	yes	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	1	no	—
499	C₄	C₄₃×#534	1	2	yes	—
500	C₄	C₄₃×#535	1	2	yes	—
501	C₂	—	2	4	no	—
502	C₂	—	4	4	no	—
503	C₂	—	16	1	no	—
504	C₂	C₄₃×#2613	1	1	yes	characteristic
505	C₂	C₂×C₄₃×#448	1	1	yes	characteristic
506	C₂	C₄₃×#3005	1	1	yes	characteristic
507	C₂	C₄₃×#3187	1	2	yes	—
508	C₂	C₄₃×#3196	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊Q₈×C₄₃	C₂	semidirect
2. C₂×C₄₃×#481	C₂	semidirect
3. C₂×C₄₃×#448	C₂	semidirect
5. C₄₃×#2035	C₂	semidirect
6. C₄₃×#2000	C₂	semidirect
7. C₄₃×#1824	C₂	semidirect
8. C₄₃×#1787	C₂	semidirect
9. C₄₃×#1779	C₂	semidirect
12. C₂²×SD₁₆×C₄₃	C₂²	semidirect
25. C₂×#106×C₄₃	C₂²	semidirect
26. C₂×#103×C₄₃	C₂²	semidirect
27. C₂×#103×C₄₃	C₂²	semidirect
28. C₂×#102×C₄₃	C₂²	semidirect
36. C₄₃×#340	C₂²	semidirect
41. C₂²×Q₈×C₄₃	D₄	semidirect
70. C₂×C₄⋊C₄×C₄₃	D₄	semidirect
94. C₂⁴×C₄₃	SD₁₆	semidirect
215. #29593	C₄₃	direct (N × H)
247. C₂²×C₂²⋊Q₈	C₂×C₄₃	semidirect
248. C₂×#481	C₂×C₄₃	semidirect
249. C₂×#448	C₂×C₄₃	semidirect
251. #2035	C₂×C₄₃	semidirect
252. #2000	C₂×C₄₃	semidirect
253. #1824	C₂×C₄₃	semidirect
254. #1787	C₂×C₄₃	semidirect
255. #1779	C₂×C₄₃	semidirect
266. C₂²×SD₁₆	C₂²×C₄₃	semidirect
279. C₂×#106	C₂²×C₄₃	semidirect
280. C₂×#103	C₂²×C₄₃	semidirect
281. C₂×#103	C₂²×C₄₃	semidirect
282. C₂×#102	C₂²×C₄₃	semidirect
290. #340	C₂²×C₄₃	semidirect
291. C₄₃	#29593	direct (N × H)
296. C₂²×Q₈	D₄×C₄₃	semidirect
325. C₂×C₄⋊C₄	D₄×C₄₃	semidirect
349. C₂⁴	SD₁₆×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₄₃	2
C₂×C₄₃×#481	2
C₂×C₄₃×#448	2
C₄₃×#2847	2
C₄₃×#2035	2
C₄₃×#2000	2
C₄₃×#1824	2
C₄₃×#1787	2
C₄₃×#1779	2
#29593	43

Subgroups — C43×#29593 #24949610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29593 #24949610