Subgroups — C₄₃×#29816 #24949833

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2619	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2055	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2054	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2000	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1999	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#496	—	2	4	no	—
21	C₄₃×#433	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#102×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#396	—	2	2	no	—
31	C₄₃×#394	—	2	2	no	—
32	C₄₃×#394	—	2	2	no	—
33	C₄₃×#392	—	2	2	no	—
34	C₄₃×#391	C₂²	1	1	yes	characteristic
35	C₄₃×#390	C₂²	1	2	yes	—
36	C₄₃×#390	C₂²	1	1	yes	characteristic
37	C₄₃×#384	C₂²	1	1	yes	characteristic
38	C₄₃×#382	C₂²	1	1	yes	characteristic
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₄₃	—	2	2	no	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	—	2	2	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×SD₁₆×C₄₃	—	2	4	no	—
49	C₂×SD₁₆×C₄₃	—	4	2	no	—
50	C₂×SD₁₆×C₄₃	—	4	2	no	—
51	C₂×D₈×C₄₃	—	2	4	no	—
52	C₂×D₈×C₄₃	—	4	2	no	—
53	C₂×D₈×C₄₃	—	4	2	no	—
54	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	#127×C₄₃	—	2	2	no	—
57	#127×C₄₃	—	2	2	no	—
58	#124×C₄₃	—	2	2	no	—
59	#124×C₄₃	—	2	2	no	—
60	C₂²⋊Q₈×C₄₃	—	4	2	no	—
61	#121×C₄₃	—	4	2	no	—
62	#121×C₄₃	—	4	2	no	—
63	#121×C₄₃	—	4	2	no	—
64	#117×C₄₃	—	2	2	no	—
65	#117×C₄₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₄₃	—	2	4	no	—
83	#103×C₄₃	—	4	2	no	—
84	#102×C₄₃	—	4	2	no	—
85	#102×C₄₃	—	4	2	no	—
86	#102×C₄₃	—	4	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	4	no	—
88	#97×C₄₃	D₄	1	4	yes	complemented
89	C₄×C₈×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	2	no	—
91	#95×C₄₃	—	2	2	no	—
92	C₂⁴×C₄₃	—	2	1	no	—
93	C₂⁴×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	1	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	4	2	no	—
110	C₂×D₄×C₄₃	—	4	4	no	—
111	C₂×D₄×C₄₃	—	4	4	no	—
112	C₂×D₄×C₄₃	—	8	2	no	—
113	C₂×D₄×C₄₃	—	8	2	no	—
114	C₂×D₄×C₄₃	—	8	2	no	—
115	C₂×D₄×C₄₃	—	8	2	no	—
116	C₂×D₄×C₄₃	—	8	2	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	SD₁₆×C₄₃	—	4	8	no	—
130	D₈×C₄₃	—	4	8	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₄₃	—	2	4	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	4	2	no	—
143	C₄⋊C₄×C₄₃	—	8	2	no	—
144	C₂²⋊C₄×C₄₃	—	2	4	no	—
145	C₂²⋊C₄×C₄₃	—	4	2	no	—
146	C₂²⋊C₄×C₄₃	—	4	4	no	—
147	C₂²⋊C₄×C₄₃	—	4	2	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₂²⋊C₄×C₄₃	—	8	2	no	—
150	C₂²⋊C₄×C₄₃	—	8	2	no	—
151	C₂²⋊C₄×C₄₃	—	8	2	no	—
152	C₄²×C₄₃	—	2	1	no	—
153	C₄²×C₄₃	—	2	1	no	—
154	C₄²×C₄₃	C₂×D₄	1	2	yes	—
155	C₄²×C₄₃	#41	1	2	yes	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	2	no	—
166	C₂³×C₄₃	—	4	1	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	—	4	2	no	—
172	C₂³×C₄₃	—	4	2	no	—
173	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₄₃	—	4	2	no	—
175	Q₈×C₄₃	—	4	2	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	4	2	no	—
178	D₄×C₄₃	—	4	2	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	4	2	no	—
181	D₄×C₄₃	—	4	2	no	—
182	D₄×C₄₃	—	8	8	no	—
183	D₄×C₄₃	—	8	4	no	—
184	D₄×C₄₃	—	8	8	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	1	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	1	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	#121	1	4	yes	—
206	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
209	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
210	C₈×C₄₃	—	2	4	no	—
211	C₈×C₄₃	—	4	2	no	—
212	#29816	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₄₃	—	4	1	no	—
214	C₂²×C₄₃	—	4	1	no	—
215	C₂²×C₄₃	—	4	1	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	8	1	no	—
219	C₂²×C₄₃	—	8	2	no	—
220	C₂²×C₄₃	—	8	2	no	—
221	C₂²×C₄₃	—	8	1	no	—
222	C₂²×C₄₃	—	8	1	no	—
223	C₂²×C₄₃	—	8	2	no	—
224	C₂²×C₄₃	—	8	2	no	—
225	C₂²×C₄₃	—	8	2	no	—
226	C₂²×C₄₃	—	8	2	no	—
227	C₂²×C₄₃	—	8	2	no	—
228	C₂²×C₄₃	—	8	2	no	—
229	C₂²×C₄₃	—	8	2	no	—
230	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
231	C₂²×C₄₃	#535	1	1	yes	characteristic
232	C₂²×C₄₃	#535	1	1	yes	characteristic
233	C₂²×C₄₃	#576	1	2	yes	—
234	C₂²×C₄₃	#577	1	2	yes	—
235	C₄×C₄₃	—	2	4	no	—
236	C₄×C₄₃	—	4	1	no	—
237	C₄×C₄₃	—	4	2	no	—
238	C₄×C₄₃	—	8	1	no	—
239	C₄×C₄₃	—	8	1	no	—
240	C₄×C₄₃	—	8	1	no	—
241	C₄×C₄₃	—	8	2	no	—
242	C₄×C₄₃	#535	1	2	yes	—
243	C₄×C₄₃	#540	1	2	yes	—
244	C₂×#496	C₂×C₄₃	1	1	yes	characteristic, complemented
245	C₂×#433	C₂×C₄₃	1	1	yes	characteristic, complemented
246	#2620	C₂×C₄₃	1	1	yes	characteristic, complemented
247	#2619	C₂×C₄₃	1	1	yes	characteristic, complemented
248	#2055	C₂×C₄₃	1	2	yes	complemented
249	#2054	C₂×C₄₃	1	2	yes	complemented
250	#2000	C₂×C₄₃	1	2	yes	complemented
251	#1999	C₂×C₄₃	1	2	yes	complemented
252	#1958	C₂×C₄₃	1	1	yes	characteristic, complemented
253	#1957	C₂×C₄₃	1	1	yes	characteristic, complemented
254	#1836	C₂×C₄₃	1	1	yes	characteristic, complemented
255	C₂×C₄₃	—	8	1	no	—
256	C₂×C₄₃	—	16	2	no	—
257	C₂×C₄₃	—	16	1	no	—
258	C₂×C₄₃	#2619	1	1	yes	characteristic
259	C₂×C₄₃	#3062	1	2	yes	—
260	C₂×C₄₃	#3220	1	1	yes	characteristic
261	C₂×C₄₃	#3221	1	1	yes	characteristic
262	C₂×C₄₃	#3224	1	2	yes	—
263	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
264	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
265	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
268	C₂×#121	C₂²×C₄₃	1	2	yes	—
269	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
271	#496	—	2	4	no	—
272	#433	—	2	4	no	—
273	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
274	C₂×#103	C₂²×C₄₃	1	2	yes	—
275	C₂×#102	C₂²×C₄₃	1	2	yes	—
276	C₂×#102	C₂²×C₄₃	1	2	yes	—
277	C₂×#102	C₂²×C₄₃	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
279	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
280	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
281	#396	—	2	2	no	—
282	#394	—	2	2	no	—
283	#394	—	2	2	no	—
284	#392	—	2	2	no	—
285	#391	C₂²×C₄₃	1	1	yes	characteristic
286	#390	C₂²×C₄₃	1	1	yes	characteristic
287	#390	C₂²×C₄₃	1	2	yes	—
288	#384	C₂²×C₄₃	1	1	yes	characteristic
289	#382	C₂²×C₄₃	1	1	yes	characteristic
290	#340	C₂²×C₄₃	1	2	yes	—
291	#340	C₂²×C₄₃	1	2	yes	—
292	C₄₃	#29816	1	1	yes	characteristic, direct product factor, Sylow
293	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
298	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
299	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×SD₁₆	—	4	2	no	—
302	C₂×SD₁₆	—	4	2	no	—
303	C₂×D₈	—	2	4	no	—
304	C₂×D₈	—	4	2	no	—
305	C₂×D₈	—	4	2	no	—
306	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
307	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
308	#127	—	2	2	no	—
309	#127	—	2	2	no	—
310	#124	—	2	2	no	—
311	#124	—	2	2	no	—
312	C₂²⋊Q₈	—	4	2	no	—
313	#121	—	4	2	no	—
314	#121	—	4	2	no	—
315	#121	—	4	2	no	—
316	#117	—	2	2	no	—
317	#117	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
332	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
334	C₄⋊C₈	—	2	4	no	—
335	#103	—	4	2	no	—
336	#102	—	4	2	no	—
337	#102	—	4	2	no	—
338	#102	—	4	2	no	—
339	C₂²⋊C₈	—	2	4	no	—
340	#97	D₄×C₄₃	1	4	yes	complemented
341	C₄×C₈	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	C₂⁴	—	2	1	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	4	no	—
363	C₂×D₄	—	4	4	no	—
364	C₂×D₄	—	8	2	no	—
365	C₂×D₄	—	8	2	no	—
366	C₂×D₄	—	8	2	no	—
367	C₂×D₄	—	8	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
381	SD₁₆	—	4	8	no	—
382	D₈	—	4	8	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	8	2	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₂²⋊C₄	—	4	4	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₂²⋊C₄	—	4	2	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₂²⋊C₄	—	8	2	no	—
402	C₂²⋊C₄	—	8	2	no	—
403	C₂²⋊C₄	—	8	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	C₂×D₄×C₄₃	1	2	yes	—
407	C₄²	#41×C₄₃	1	2	yes	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	8	8	no	—
435	D₄	—	8	4	no	—
436	D₄	—	8	8	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	#121×C₄₃	1	4	yes	—
458	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
460	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
461	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
462	C₈	—	2	4	no	—
463	C₈	—	4	2	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	8	1	no	—
470	C₂²	—	8	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	—	8	2	no	—
481	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
482	C₂²	C₄₃×#535	1	1	yes	characteristic
483	C₂²	C₄₃×#535	1	1	yes	characteristic
484	C₂²	C₄₃×#576	1	2	yes	—
485	C₂²	C₄₃×#577	1	2	yes	—
486	C₄	—	2	4	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	—	8	2	no	—
493	C₄	C₄₃×#535	1	2	yes	—
494	C₄	C₄₃×#540	1	2	yes	—
495	C₂	—	8	1	no	—
496	C₂	—	16	1	no	—
497	C₂	—	16	2	no	—
498	C₂	C₄₃×#2619	1	1	yes	characteristic
499	C₂	C₄₃×#3062	1	2	yes	—
500	C₂	C₄₃×#3220	1	1	yes	characteristic
501	C₂	C₄₃×#3221	1	1	yes	characteristic
502	C₂	C₄₃×#3224	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
LCS	G ▷ C₂²×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×#496	C₂	semidirect
2. C₂×C₄₃×#433	C₂	semidirect
3. C₄₃×#2620	C₂	semidirect
4. C₄₃×#2619	C₂	semidirect
5. C₄₃×#2055	C₂	semidirect
6. C₄₃×#2054	C₂	semidirect
7. C₄₃×#2000	C₂	semidirect
8. C₄₃×#1999	C₂	semidirect
9. C₄₃×#1958	C₂	semidirect
10. C₄₃×#1957	C₂	semidirect
11. C₄₃×#1836	C₂	semidirect
88. #97×C₄₃	D₄	semidirect
212. #29816	C₄₃	direct (N × H)
244. C₂×#496	C₂×C₄₃	semidirect
245. C₂×#433	C₂×C₄₃	semidirect
246. #2620	C₂×C₄₃	semidirect
247. #2619	C₂×C₄₃	semidirect
248. #2055	C₂×C₄₃	semidirect
249. #2054	C₂×C₄₃	semidirect
250. #2000	C₂×C₄₃	semidirect
251. #1999	C₂×C₄₃	semidirect
252. #1958	C₂×C₄₃	semidirect
253. #1957	C₂×C₄₃	semidirect
254. #1836	C₂×C₄₃	semidirect
292. C₄₃	#29816	direct (N × H)
340. #97	D₄×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×#496	2
C₂×C₄₃×#433	2
C₄₃×#2620	2
C₄₃×#2619	2
C₄₃×#2055	2
C₄₃×#2054	2
C₄₃×#2000	2
C₄₃×#1999	2
C₄₃×#1958	2
C₄₃×#1957	2
C₄₃×#1836	2
#29816	43

Subgroups — C43×#29816 #24949833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29816 #24949833