Subgroups — C₄₃×#29599 #24949616

Order 11008.

1442 conjugacy classes of subgroups.

The subgroup lattice has 482 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
2	C₂×C₄₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2848	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2035	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2001	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1823	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
10	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×Q₁₆×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	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
22	C₄₃×#483	—	2	4	no	—
23	C₄₃×#451	—	2	4	no	—
24	C₂×#106×C₄₃	C₂²	1	2	yes	complemented
25	C₂×#103×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×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
31	C₄₃×#385	—	2	1	no	—
32	C₄₃×#385	—	2	2	no	—
33	C₄₃×#380	C₂²	1	1	yes	characteristic
34	C₄₃×#380	C₂²	1	2	yes	—
35	C₄₃×#379	—	2	1	no	—
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	—
42	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₃	—	2	1	no	—
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	—	2	2	no	—
47	C₂³×C₄×C₄₃	—	2	2	no	—
48	C₂³×C₄×C₄₃	—	4	4	no	—
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	D₄	1	2	yes	—
51	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
53	C₂×Q₁₆×C₄₃	—	2	4	no	—
54	C₂×Q₁₆×C₄₃	—	4	4	no	—
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₂²⋊Q₈×C₄₃	—	2	16	no	—
58	C₂²⋊Q₈×C₄₃	—	2	8	no	—
59	C₂²⋊Q₈×C₄₃	—	2	8	no	—
60	C₂²⋊Q₈×C₄₃	—	2	2	no	—
61	C₂²⋊Q₈×C₄₃	—	2	2	no	—
62	C₂²⋊Q₈×C₄₃	—	4	4	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	#106×C₄₃	—	2	4	no	—
80	#103×C₄₃	—	2	4	no	—
81	#103×C₄₃	—	2	4	no	—
82	#103×C₄₃	—	4	4	no	—
83	C₂²⋊C₈×C₄₃	—	2	2	no	—
84	C₂²⋊C₈×C₄₃	—	2	2	no	—
85	C₂²⋊C₈×C₄₃	—	4	4	no	—
86	#95×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	1	no	—
88	C₂⁴×C₄₃	—	2	2	no	—
89	C₂⁴×C₄₃	—	2	4	no	—
90	C₂⁴×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	—	2	2	no	—
92	C₂⁴×C₄₃	—	4	2	no	—
93	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	2	4	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	2	4	no	—
100	C₂×Q₈×C₄₃	—	2	4	no	—
101	C₂×Q₈×C₄₃	—	2	4	no	—
102	C₂×Q₈×C₄₃	—	4	8	no	—
103	C₂×Q₈×C₄₃	—	4	4	no	—
104	C₂×Q₈×C₄₃	—	4	8	no	—
105	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₃	—	2	4	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	—	4	2	no	—
123	C₂²×C₄×C₄₃	—	4	4	no	—
124	C₂²×C₄×C₄₃	—	4	8	no	—
125	C₂²×C₄×C₄₃	—	4	8	no	—
126	C₂²×C₄×C₄₃	—	4	2	no	—
127	C₂²×C₄×C₄₃	—	4	2	no	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
133	Q₁₆×C₄₃	—	4	8	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	4	no	—
137	C₂×C₈×C₄₃	—	2	4	no	—
138	C₄⋊C₄×C₄₃	—	2	16	no	—
139	C₄⋊C₄×C₄₃	—	2	4	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	4	no	—
144	C₄⋊C₄×C₄₃	—	4	4	no	—
145	C₄⋊C₄×C₄₃	—	4	2	no	—
146	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
147	C₂²⋊C₄×C₄₃	—	2	16	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	4	2	no	—
150	C₂²⋊C₄×C₄₃	—	4	2	no	—
151	C₂²⋊C₄×C₄₃	—	4	4	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	8	no	—
155	C₂³×C₄₃	—	2	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	—	4	8	no	—
162	C₂³×C₄₃	—	4	8	no	—
163	C₂³×C₄₃	—	4	4	no	—
164	C₂³×C₄₃	—	4	4	no	—
165	C₂³×C₄₃	#120	1	2	yes	—
166	C₂³×C₄₃	#135	1	2	yes	—
167	C₂³×C₄₃	#137	1	4	yes	—
168	C₂³×C₄₃	#137	1	2	yes	—
169	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₄₃	—	2	4	no	—
171	Q₈×C₄₃	—	2	4	no	—
172	Q₈×C₄₃	—	4	8	no	—
173	Q₈×C₄₃	—	4	4	no	—
174	Q₈×C₄₃	—	4	2	no	—
175	Q₈×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	4	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	4	8	no	—
185	C₂×C₄×C₄₃	—	4	4	no	—
186	C₂×C₄×C₄₃	—	4	8	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	8	no	—
191	C₂×C₄×C₄₃	—	4	4	no	—
192	C₂×C₄×C₄₃	—	4	4	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	1	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	#120	1	2	yes	—
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
204	C₈×C₄₃	—	4	2	no	—
205	C₈×C₄₃	—	4	2	no	—
206	#29599	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	4	no	—
209	C₂²×C₄₃	—	2	4	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	2	4	no	—
212	C₂²×C₄₃	—	2	4	no	—
213	C₂²×C₄₃	—	2	4	no	—
214	C₂²×C₄₃	—	4	16	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	4	2	no	—
219	C₂²×C₄₃	#452	1	4	yes	—
220	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
221	C₂²×C₄₃	#534	1	2	yes	—
222	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
223	C₂²×C₄₃	C₂×#137	1	2	yes	—
224	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	—	4	4	no	—
228	C₄×C₄₃	—	4	4	no	—
229	C₄×C₄₃	—	8	1	no	—
230	C₄×C₄₃	—	8	2	no	—
231	C₄×C₄₃	—	8	1	no	—
232	C₄×C₄₃	#534	1	2	yes	—
233	C₄×C₄₃	#535	1	2	yes	—
234	C₂²×C₂²⋊Q₈	C₂×C₄₃	1	1	yes	characteristic
235	C₂×#483	C₂×C₄₃	1	1	yes	characteristic, complemented
236	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
237	#2848	C₂×C₄₃	1	1	yes	characteristic
238	#2035	C₂×C₄₃	1	4	yes	complemented
239	#2001	C₂×C₄₃	1	4	yes	complemented
240	#1823	C₂×C₄₃	1	1	yes	characteristic, complemented
241	#1787	C₂×C₄₃	1	1	yes	characteristic, complemented
242	#1779	C₂×C₄₃	1	1	yes	characteristic
243	C₂×C₄₃	—	2	4	no	—
244	C₂×C₄₃	—	4	4	no	—
245	C₂×C₄₃	#2613	1	1	yes	characteristic
246	C₂×C₄₃	C₂×#452	1	1	yes	characteristic
247	C₂×C₄₃	#3004	1	1	yes	characteristic
248	C₂×C₄₃	#3190	1	2	yes	—
249	C₂×C₄₃	#3195	1	2	yes	—
250	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
251	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
252	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	complemented
253	C₂×C₂²⋊Q₈	—	2	4	no	—
254	C₂×C₂²⋊Q₈	—	2	2	no	—
255	C₂×C₂²⋊Q₈	—	2	4	no	—
256	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	—
258	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
259	C₂²×C₄⋊C₄	—	2	1	no	—
260	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	—	2	1	no	—
262	#483	—	2	4	no	—
263	#451	—	2	4	no	—
264	C₂×#106	C₂²×C₄₃	1	2	yes	complemented
265	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
266	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
267	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
268	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
271	#385	—	2	1	no	—
272	#385	—	2	2	no	—
273	#380	C₂²×C₄₃	1	1	yes	characteristic
274	#380	C₂²×C₄₃	1	2	yes	—
275	#379	—	2	1	no	—
276	#340	C₂²×C₄₃	1	4	yes	complemented
277	C₄₃	#29599	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	—	4	4	no	—
282	C₂²×Q₈	D₄×C₄₃	1	4	yes	—
283	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
284	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	—	2	2	no	—
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	—	4	4	no	—
290	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₄₃	1	2	yes	—
292	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
293	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×Q₁₆	—	4	4	no	—
296	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
297	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
298	C₂²⋊Q₈	—	2	16	no	—
299	C₂²⋊Q₈	—	2	8	no	—
300	C₂²⋊Q₈	—	2	8	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₂²⋊Q₈	—	4	4	no	—
304	C₂×C₄⋊C₄	—	2	8	no	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
311	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₂²⋊C₄	—	2	4	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	#106	—	2	4	no	—
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#103	—	4	4	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	4	4	no	—
327	#95	—	2	2	no	—
328	#95	—	2	1	no	—
329	C₂⁴	—	2	2	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	4	2	no	—
334	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
335	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	4	8	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	8	no	—
346	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	8	no	—
365	C₂²×C₄	—	4	8	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
374	Q₁₆	—	4	8	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	—	2	4	no	—
379	C₄⋊C₄	—	2	16	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
388	C₂²⋊C₄	—	2	16	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	8	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	4	8	no	—
403	C₂³	—	4	8	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	4	no	—
406	C₂³	#120×C₄₃	1	2	yes	—
407	C₂³	#135×C₄₃	1	2	yes	—
408	C₂³	#137×C₄₃	1	4	yes	—
409	C₂³	#137×C₄₃	1	2	yes	—
410	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	8	no	—
414	Q₈	—	4	4	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	#120×C₄₃	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
444	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
445	C₈	—	4	2	no	—
446	C₈	—	4	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	16	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₄₃×#452	1	4	yes	—
460	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
461	C₂²	C₄₃×#534	1	2	yes	—
462	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
463	C₂²	C₂×#137×C₄₃	1	2	yes	—
464	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	4	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	2	no	—
471	C₄	—	8	1	no	—
472	C₄	C₄₃×#534	1	2	yes	—
473	C₄	C₄₃×#535	1	2	yes	—
474	C₂	—	2	4	no	—
475	C₂	—	4	4	no	—
476	C₂	C₄₃×#2613	1	1	yes	characteristic
477	C₂	C₂×C₄₃×#452	1	1	yes	characteristic
478	C₂	C₄₃×#3004	1	1	yes	characteristic
479	C₂	C₄₃×#3190	1	2	yes	—
480	C₂	C₄₃×#3195	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁵×C₄₃	D₄
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
2. C₂×C₄₃×#483	C₂	semidirect
3. C₂×C₄₃×#451	C₂	semidirect
5. C₄₃×#2035	C₂	semidirect
6. C₄₃×#2001	C₂	semidirect
7. C₄₃×#1823	C₂	semidirect
8. C₄₃×#1787	C₂	semidirect
12. C₂²×Q₁₆×C₄₃	C₂²	semidirect
24. C₂×#106×C₄₃	C₂²	semidirect
25. C₂×#103×C₄₃	C₂²	semidirect
26. C₂×#103×C₄₃	C₂²	semidirect
27. C₂×#103×C₄₃	C₂²	semidirect
36. C₄₃×#340	C₂²	semidirect
206. #29599	C₄₃	direct (N × H)
235. C₂×#483	C₂×C₄₃	semidirect
236. C₂×#451	C₂×C₄₃	semidirect
238. #2035	C₂×C₄₃	semidirect
239. #2001	C₂×C₄₃	semidirect
240. #1823	C₂×C₄₃	semidirect
241. #1787	C₂×C₄₃	semidirect
252. C₂²×Q₁₆	C₂²×C₄₃	semidirect
264. C₂×#106	C₂²×C₄₃	semidirect
265. C₂×#103	C₂²×C₄₃	semidirect
266. C₂×#103	C₂²×C₄₃	semidirect
267. C₂×#103	C₂²×C₄₃	semidirect
276. #340	C₂²×C₄₃	semidirect
277. C₄₃	#29599	direct (N × H)

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×#483	2
C₂×C₄₃×#451	2
C₄₃×#2848	2
C₄₃×#2035	2
C₄₃×#2001	2
C₄₃×#1823	2
C₄₃×#1787	2
C₄₃×#1779	2
#29599	43

Subgroups — C43×#29599 #24949616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29599 #24949616