Subgroups — C₄₃×#18568 #24938585

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1631	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1630	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1621	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1620	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₃	—	2	2	no	—
13	C₄₃×#559	—	2	1	no	—
14	C₄₃×#559	C₂²	1	2	yes	—
15	C₄₃×#550	—	2	1	no	—
16	C₄₃×#550	C₂²	1	2	yes	—
17	C₄₃×#546	—	2	2	no	—
18	C₄₃×#546	—	2	2	no	—
19	C₄₃×#540	—	2	2	no	—
20	C₄₃×#535	—	2	1	no	—
21	C₄₃×#533	C₂²	1	1	yes	characteristic
22	C₄₃×#532	—	2	1	no	—
23	C₄₃×#532	—	2	1	no	—
24	C₄₃×#532	C₂²	1	1	yes	characteristic
25	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#518	—	2	1	no	—
27	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#496	—	2	2	no	—
29	C₄₃×#493	C₂²	1	2	yes	—
30	C₄₃×#492	C₂²	1	2	yes	—
31	C₄₃×#482	—	2	1	no	—
32	C₄₃×#477	C₂²	1	1	yes	characteristic, complemented
33	C₄₃×#477	C₂²	1	2	yes	complemented
34	C₄₃×#476	C₂²	1	1	yes	characteristic, complemented
35	C₄₃×#474	—	2	1	no	—
36	C₄₃×#468	—	2	2	no	—
37	C₄₃×#461	—	2	1	no	—
38	C₄₃×#460	C₂²	1	1	yes	characteristic, complemented
39	C₄₃×#460	C₂²	1	2	yes	complemented
40	C₄₃×#459	C₂²	1	1	yes	characteristic, complemented
41	C₄₃×#449	—	2	1	no	—
42	C₄×SD₁₆×C₄₃	—	2	1	no	—
43	C₄×D₈×C₄₃	—	2	1	no	—
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#331	C₂²	1	2	yes	—
48	C₄₃×#331	C₂²	1	2	yes	—
49	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
50	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
51	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₄₃×D₄⋊C₈	C₂²	1	2	yes	complemented
53	C₂×#41×C₄₃	—	2	2	no	—
54	C₂×#41×C₄₃	—	2	2	no	—
55	C₂×#41×C₄₃	—	2	1	no	—
56	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₄₃	—	2	1	no	—
58	C₂²×D₄×C₄₃	—	2	1	no	—
59	C₂²×D₄×C₄₃	D₄	1	2	yes	—
60	AGL(1,ℤ/8)×C₄₃	—	4	8	no	—
61	C₂×SD₁₆×C₄₃	—	2	1	no	—
62	C₂×SD₁₆×C₄₃	—	2	4	no	—
63	C₂×SD₁₆×C₄₃	—	2	2	no	—
64	C₂×D₈×C₄₃	—	2	4	no	—
65	C₂×D₈×C₄₃	—	2	1	no	—
66	C₂×M₁₆×C₄₃	—	2	1	no	—
67	C₂×M₁₆×C₄₃	—	2	1	no	—
68	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
71	#127×C₄₃	—	2	2	no	—
72	#127×C₄₃	—	2	1	no	—
73	#127×C₄₃	—	2	1	no	—
74	#127×C₄₃	D₄	1	2	yes	—
75	#127×C₄₃	C₂³	1	1	yes	characteristic
76	#127×C₄₃	C₂³	1	2	yes	—
77	#125×C₄₃	—	2	1	no	—
78	#124×C₄₃	—	2	2	no	—
79	#124×C₄₃	—	2	2	no	—
80	#124×C₄₃	—	2	2	no	—
81	#124×C₄₃	—	2	1	no	—
82	#123×C₄₃	—	2	4	no	—
83	#123×C₄₃	—	2	4	no	—
84	C₂²⋊Q₈×C₄₃	—	2	1	no	—
85	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
86	#121×C₄₃	—	2	2	no	—
87	#121×C₄₃	—	2	2	no	—
88	#121×C₄₃	—	2	2	no	—
89	#121×C₄₃	—	2	4	no	—
90	#121×C₄₃	—	2	4	no	—
91	#121×C₄₃	—	2	2	no	—
92	#121×C₄₃	—	2	1	no	—
93	#121×C₄₃	—	2	1	no	—
94	#120×C₄₃	—	2	4	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
99	C₄×D₄×C₄₃	—	2	2	no	—
100	C₄×D₄×C₄₃	—	2	2	no	—
101	C₄×D₄×C₄₃	—	2	2	no	—
102	C₄×D₄×C₄₃	—	2	1	no	—
103	C₄×D₄×C₄₃	—	2	1	no	—
104	C₄×D₄×C₄₃	—	2	2	no	—
105	C₄×D₄×C₄₃	—	2	2	no	—
106	C₄×D₄×C₄₃	—	2	2	no	—
107	C₄×D₄×C₄₃	—	2	1	no	—
108	C₄×D₄×C₄₃	—	2	1	no	—
109	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
110	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
111	#117×C₄₃	—	2	1	no	—
112	#117×C₄₃	—	2	1	no	—
113	#117×C₄₃	D₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
115	C₂×C₄²×C₄₃	—	2	1	no	—
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	#107×C₄₃	—	2	1	no	—
118	#107×C₄₃	—	2	2	no	—
119	#106×C₄₃	—	2	1	no	—
120	C₄⋊C₈×C₄₃	—	2	1	no	—
121	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
122	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
124	#103×C₄₃	—	2	1	no	—
125	#103×C₄₃	—	2	2	no	—
126	#102×C₄₃	—	2	1	no	—
127	#102×C₄₃	—	2	1	no	—
128	#102×C₄₃	—	2	1	no	—
129	#102×C₄₃	—	2	2	no	—
130	C₂²⋊C₈×C₄₃	—	2	1	no	—
131	#97×C₄₃	—	2	1	no	—
132	C₄×C₈×C₄₃	—	2	1	no	—
133	C₄×C₈×C₄₃	C₂³	1	2	yes	—
134	C₂⁴×C₄₃	—	2	2	no	—
135	#41×C₄₃	—	4	1	no	—
136	#41×C₄₃	—	4	1	no	—
137	#41×C₄₃	—	4	4	no	—
138	#41×C₄₃	—	8	2	no	—
139	#41×C₄₃	—	8	2	no	—
140	#41×C₄₃	—	8	4	no	—
141	C₂×Q₈×C₄₃	—	2	1	no	—
142	C₂×Q₈×C₄₃	—	2	1	no	—
143	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₄₃	—	2	4	no	—
146	C₂×D₄×C₄₃	—	2	4	no	—
147	C₂×D₄×C₄₃	—	2	2	no	—
148	C₂×D₄×C₄₃	—	2	2	no	—
149	C₂×D₄×C₄₃	—	2	2	no	—
150	C₂×D₄×C₄₃	—	2	2	no	—
151	C₂×D₄×C₄₃	—	2	2	no	—
152	C₂×D₄×C₄₃	—	2	1	no	—
153	C₂×D₄×C₄₃	—	2	1	no	—
154	C₂×D₄×C₄₃	—	2	1	no	—
155	C₂×D₄×C₄₃	—	2	1	no	—
156	C₂×D₄×C₄₃	—	4	2	no	—
157	C₂×D₄×C₄₃	—	4	2	no	—
158	C₂×D₄×C₄₃	—	4	1	no	—
159	C₂×D₄×C₄₃	—	4	4	no	—
160	C₂×D₄×C₄₃	—	8	1	no	—
161	C₂×D₄×C₄₃	—	8	1	no	—
162	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₄₃	—	2	4	no	—
165	C₂²×C₄×C₄₃	—	2	4	no	—
166	C₂²×C₄×C₄₃	—	2	1	no	—
167	C₂²×C₄×C₄₃	—	2	1	no	—
168	C₂²×C₄×C₄₃	—	2	1	no	—
169	C₂²×C₄×C₄₃	—	4	1	no	—
170	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
173	SD₁₆×C₄₃	—	4	8	no	—
174	SD₁₆×C₄₃	—	4	2	no	—
175	SD₁₆×C₄₃	—	8	2	no	—
176	D₈×C₄₃	—	4	8	no	—
177	D₈×C₄₃	—	4	2	no	—
178	M₁₆×C₄₃	—	2	4	no	—
179	M₁₆×C₄₃	—	8	1	no	—
180	C₂×C₈×C₄₃	—	2	2	no	—
181	C₂×C₈×C₄₃	—	2	1	no	—
182	C₂×C₈×C₄₃	—	2	1	no	—
183	C₂×C₈×C₄₃	—	2	2	no	—
184	C₄⋊C₄×C₄₃	—	2	1	no	—
185	C₄⋊C₄×C₄₃	—	2	1	no	—
186	C₄⋊C₄×C₄₃	—	2	1	no	—
187	C₄⋊C₄×C₄₃	—	2	1	no	—
188	C₄⋊C₄×C₄₃	—	2	2	no	—
189	C₄⋊C₄×C₄₃	—	2	1	no	—
190	C₄⋊C₄×C₄₃	—	2	2	no	—
191	C₄⋊C₄×C₄₃	—	2	1	no	—
192	C₄⋊C₄×C₄₃	—	2	1	no	—
193	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
196	C₂²⋊C₄×C₄₃	—	2	4	no	—
197	C₂²⋊C₄×C₄₃	—	2	4	no	—
198	C₂²⋊C₄×C₄₃	—	2	4	no	—
199	C₂²⋊C₄×C₄₃	—	2	4	no	—
200	C₂²⋊C₄×C₄₃	—	2	1	no	—
201	C₂²⋊C₄×C₄₃	—	2	1	no	—
202	C₂²⋊C₄×C₄₃	—	2	1	no	—
203	C₂²⋊C₄×C₄₃	—	2	2	no	—
204	C₂²⋊C₄×C₄₃	—	4	1	no	—
205	C₂²⋊C₄×C₄₃	—	4	1	no	—
206	C₄²×C₄₃	—	2	1	no	—
207	C₄²×C₄₃	—	2	1	no	—
208	C₄²×C₄₃	—	2	1	no	—
209	C₄²×C₄₃	—	2	2	no	—
210	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
212	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
214	C₂³×C₄₃	—	2	4	no	—
215	C₂³×C₄₃	—	2	1	no	—
216	C₂³×C₄₃	—	4	4	no	—
217	C₂³×C₄₃	—	4	1	no	—
218	C₂³×C₄₃	—	8	2	no	—
219	C₂³×C₄₃	—	8	2	no	—
220	C₂³×C₄₃	#120	1	1	yes	characteristic
221	Q₈×C₄₃	—	2	1	no	—
222	Q₈×C₄₃	—	2	1	no	—
223	Q₈×C₄₃	—	2	2	no	—
224	Q₈×C₄₃	—	2	2	no	—
225	Q₈×C₄₃	—	4	2	no	—
226	Q₈×C₄₃	—	4	2	no	—
227	D₄×C₄₃	—	2	1	no	—
228	D₄×C₄₃	—	2	1	no	—
229	D₄×C₄₃	—	4	4	no	—
230	D₄×C₄₃	—	4	4	no	—
231	D₄×C₄₃	—	4	2	no	—
232	D₄×C₄₃	—	4	2	no	—
233	D₄×C₄₃	—	4	2	no	—
234	D₄×C₄₃	—	4	2	no	—
235	D₄×C₄₃	—	4	1	no	—
236	D₄×C₄₃	—	4	1	no	—
237	D₄×C₄₃	—	4	2	no	—
238	D₄×C₄₃	—	4	1	no	—
239	D₄×C₄₃	—	4	2	no	—
240	D₄×C₄₃	—	4	1	no	—
241	D₄×C₄₃	—	4	4	no	—
242	D₄×C₄₃	—	8	2	no	—
243	D₄×C₄₃	—	8	4	no	—
244	D₄×C₄₃	—	8	4	no	—
245	D₄×C₄₃	—	8	2	no	—
246	C₂×C₄×C₄₃	—	2	1	no	—
247	C₂×C₄×C₄₃	—	2	1	no	—
248	C₂×C₄×C₄₃	—	2	1	no	—
249	C₂×C₄×C₄₃	—	2	1	no	—
250	C₂×C₄×C₄₃	—	2	2	no	—
251	C₂×C₄×C₄₃	—	2	1	no	—
252	C₂×C₄×C₄₃	—	2	1	no	—
253	C₂×C₄×C₄₃	—	2	1	no	—
254	C₂×C₄×C₄₃	—	2	2	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	4	2	no	—
257	C₂×C₄×C₄₃	—	4	1	no	—
258	C₂×C₄×C₄₃	—	4	1	no	—
259	C₂×C₄×C₄₃	—	4	2	no	—
260	C₂×C₄×C₄₃	—	4	1	no	—
261	C₂×C₄×C₄₃	—	8	4	no	—
262	C₂×C₄×C₄₃	—	8	4	no	—
263	C₂×C₄×C₄₃	—	8	2	no	—
264	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
265	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
266	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
267	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
270	C₈×C₄₃	—	2	4	no	—
271	C₈×C₄₃	—	4	1	no	—
272	C₈×C₄₃	—	4	1	no	—
273	C₈×C₄₃	—	4	2	no	—
274	#18568	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂²×C₄₃	—	2	1	no	—
276	C₂²×C₄₃	—	2	1	no	—
277	C₂²×C₄₃	—	2	1	no	—
278	C₂²×C₄₃	—	4	4	no	—
279	C₂²×C₄₃	—	4	1	no	—
280	C₂²×C₄₃	—	4	4	no	—
281	C₂²×C₄₃	—	4	1	no	—
282	C₂²×C₄₃	—	4	4	no	—
283	C₂²×C₄₃	—	4	1	no	—
284	C₂²×C₄₃	—	8	1	no	—
285	C₂²×C₄₃	—	8	1	no	—
286	C₂²×C₄₃	—	8	1	no	—
287	C₂²×C₄₃	—	16	4	no	—
288	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
289	C₄×C₄₃	—	2	1	no	—
290	C₄×C₄₃	—	2	1	no	—
291	C₄×C₄₃	—	2	1	no	—
292	C₄×C₄₃	—	4	1	no	—
293	C₄×C₄₃	—	4	1	no	—
294	C₄×C₄₃	—	4	2	no	—
295	C₄×C₄₃	—	4	1	no	—
296	C₄×C₄₃	—	4	2	no	—
297	C₄×C₄₃	—	8	1	no	—
298	C₄×C₄₃	#453	1	2	yes	—
299	C₄×C₄₃	#575	1	1	yes	characteristic
300	C₄×C₄₃	#575	1	1	yes	characteristic
301	C₄×C₄₃	#576	1	1	yes	characteristic
302	C₄×C₄₃	#577	1	1	yes	characteristic
303	#3508	C₂×C₄₃	1	1	yes	characteristic, complemented
304	#3254	C₂×C₄₃	1	1	yes	characteristic, complemented
305	#3151	C₂×C₄₃	1	1	yes	characteristic, complemented
306	#3106	C₂×C₄₃	1	1	yes	characteristic, complemented
307	#1631	C₂×C₄₃	1	2	yes	complemented
308	#1630	C₂×C₄₃	1	2	yes	complemented
309	#1621	C₂×C₄₃	1	2	yes	complemented
310	#1620	C₂×C₄₃	1	2	yes	complemented
311	#1545	C₂×C₄₃	1	1	yes	characteristic, complemented
312	#1489	C₂×C₄₃	1	1	yes	characteristic, complemented
313	#1485	C₂×C₄₃	1	1	yes	characteristic, complemented
314	C₂×C₄₃	—	4	1	no	—
315	C₂×C₄₃	—	8	1	no	—
316	C₂×C₄₃	—	8	4	no	—
317	C₂×C₄₃	—	16	1	no	—
318	C₂×C₄₃	#3005	1	1	yes	characteristic
319	C₂×C₄₃	#3012	1	1	yes	characteristic
320	C₂×C₄₃	C₂×#453	1	1	yes	characteristic
321	C₂×AGL(1,ℤ/8)	—	2	2	no	—
322	#559	—	2	1	no	—
323	#559	C₂²×C₄₃	1	2	yes	—
324	#550	—	2	1	no	—
325	#550	C₂²×C₄₃	1	2	yes	—
326	#546	—	2	2	no	—
327	#546	—	2	2	no	—
328	#540	—	2	2	no	—
329	#535	—	2	1	no	—
330	#533	C₂²×C₄₃	1	1	yes	characteristic
331	#532	—	2	1	no	—
332	#532	—	2	1	no	—
333	#532	C₂²×C₄₃	1	1	yes	characteristic
334	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
335	#518	—	2	1	no	—
336	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
337	#496	—	2	2	no	—
338	#493	C₂²×C₄₃	1	2	yes	—
339	#492	C₂²×C₄₃	1	2	yes	—
340	#482	—	2	1	no	—
341	#477	C₂²×C₄₃	1	1	yes	characteristic, complemented
342	#477	C₂²×C₄₃	1	2	yes	complemented
343	#476	C₂²×C₄₃	1	1	yes	characteristic, complemented
344	#474	—	2	1	no	—
345	#468	—	2	2	no	—
346	#461	—	2	1	no	—
347	#460	C₂²×C₄₃	1	1	yes	characteristic, complemented
348	#460	C₂²×C₄₃	1	2	yes	complemented
349	#459	C₂²×C₄₃	1	1	yes	characteristic, complemented
350	#449	—	2	1	no	—
351	C₄×SD₁₆	—	2	1	no	—
352	C₄×D₈	—	2	1	no	—
353	#431	C₂²×C₄₃	1	1	yes	characteristic
354	#423	C₂²×C₄₃	1	1	yes	characteristic
355	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
356	#331	C₂²×C₄₃	1	2	yes	—
357	#331	C₂²×C₄₃	1	2	yes	—
358	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	complemented
359	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	complemented
360	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	complemented
361	D₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
362	C₄₃	#18568	1	1	yes	characteristic, direct product factor, Sylow
363	C₂×#41	—	2	2	no	—
364	C₂×#41	—	2	2	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	D₄×C₄₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	D₄×C₄₃	1	2	yes	—
370	AGL(1,ℤ/8)	—	4	8	no	—
371	C₂×SD₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×D₈	—	2	4	no	—
375	C₂×D₈	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
379	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
380	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
381	#127	—	2	2	no	—
382	#127	—	2	1	no	—
383	#127	—	2	1	no	—
384	#127	D₄×C₄₃	1	2	yes	—
385	#127	C₂³×C₄₃	1	1	yes	characteristic
386	#127	C₂³×C₄₃	1	2	yes	—
387	#125	—	2	1	no	—
388	#124	—	2	2	no	—
389	#124	—	2	2	no	—
390	#124	—	2	2	no	—
391	#124	—	2	1	no	—
392	#123	—	2	4	no	—
393	#123	—	2	4	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	C₂²⋊Q₈	D₄×C₄₃	1	2	yes	—
396	#121	—	2	2	no	—
397	#121	—	2	2	no	—
398	#121	—	2	2	no	—
399	#121	—	2	4	no	—
400	#121	—	2	4	no	—
401	#121	—	2	2	no	—
402	#121	—	2	1	no	—
403	#121	—	2	1	no	—
404	#120	—	2	4	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
407	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
408	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	D₄×C₄₃	1	1	yes	characteristic
420	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
421	#117	—	2	1	no	—
422	#117	—	2	1	no	—
423	#117	D₄×C₄₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	—	2	4	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
427	#107	—	2	1	no	—
428	#107	—	2	2	no	—
429	#106	—	2	1	no	—
430	C₄⋊C₈	—	2	1	no	—
431	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
432	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
433	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
434	#103	—	2	1	no	—
435	#103	—	2	2	no	—
436	#102	—	2	1	no	—
437	#102	—	2	1	no	—
438	#102	—	2	1	no	—
439	#102	—	2	2	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	#97	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	C₂³×C₄₃	1	2	yes	—
444	C₂⁴	—	2	2	no	—
445	#41	—	4	1	no	—
446	#41	—	4	1	no	—
447	#41	—	4	4	no	—
448	#41	—	8	2	no	—
449	#41	—	8	2	no	—
450	#41	—	8	4	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	C₂×D₄×C₄₃	1	1	yes	characteristic
454	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	—	4	1	no	—
470	C₂×D₄	—	8	1	no	—
471	C₂×D₄	—	8	1	no	—
472	C₂×D₄	C₂×D₄×C₄₃	1	1	yes	characteristic
473	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
483	SD₁₆	—	4	8	no	—
484	SD₁₆	—	4	2	no	—
485	SD₁₆	—	8	2	no	—
486	D₈	—	4	8	no	—
487	D₈	—	4	2	no	—
488	M₁₆	—	2	4	no	—
489	M₁₆	—	8	1	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
505	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	4	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	2	no	—
520	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
521	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
522	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
523	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
524	C₂³	—	2	4	no	—
525	C₂³	—	2	1	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	8	2	no	—
529	C₂³	—	8	2	no	—
530	C₂³	#120×C₄₃	1	1	yes	characteristic
531	Q₈	—	2	1	no	—
532	Q₈	—	2	1	no	—
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	2	no	—
536	Q₈	—	4	2	no	—
537	D₄	—	2	1	no	—
538	D₄	—	2	1	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	2	no	—
542	D₄	—	4	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	4	no	—
552	D₄	—	8	2	no	—
553	D₄	—	8	4	no	—
554	D₄	—	8	4	no	—
555	D₄	—	8	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	8	4	no	—
572	C₂×C₄	—	8	4	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
575	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
576	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
580	C₈	—	2	4	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	2	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	16	4	no	—
597	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	8	1	no	—
607	C₄	C₄₃×#453	1	2	yes	—
608	C₄	C₄₃×#575	1	1	yes	characteristic
609	C₄	C₄₃×#575	1	1	yes	characteristic
610	C₄	C₄₃×#576	1	1	yes	characteristic
611	C₄	C₄₃×#577	1	1	yes	characteristic
612	C₂	—	4	1	no	—
613	C₂	—	8	4	no	—
614	C₂	—	8	1	no	—
615	C₂	—	16	1	no	—
616	C₂	C₄₃×#3005	1	1	yes	characteristic
617	C₂	C₄₃×#3012	1	1	yes	characteristic
618	C₂	C₂×C₄₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3508	C₂	semidirect
2. C₄₃×#3254	C₂	semidirect
3. C₄₃×#3151	C₂	semidirect
4. C₄₃×#3106	C₂	semidirect
5. C₄₃×#1631	C₂	semidirect
6. C₄₃×#1630	C₂	semidirect
7. C₄₃×#1621	C₂	semidirect
8. C₄₃×#1620	C₂	semidirect
9. C₄₃×#1545	C₂	semidirect
10. C₄₃×#1489	C₂	semidirect
11. C₄₃×#1485	C₂	semidirect
32. C₄₃×#477	C₂²	semidirect
33. C₄₃×#477	C₂²	semidirect
34. C₄₃×#476	C₂²	semidirect
38. C₄₃×#460	C₂²	semidirect
39. C₄₃×#460	C₂²	semidirect
40. C₄₃×#459	C₂²	semidirect
49. C₄₃×Q₈⋊C₈	C₂²	semidirect
50. C₄₃×Q₈⋊C₈	C₂²	semidirect
51. C₄₃×Q₈⋊C₈	C₂²	semidirect
52. C₄₃×D₄⋊C₈	C₂²	semidirect
274. #18568	C₄₃	direct (N × H)
303. #3508	C₂×C₄₃	semidirect
304. #3254	C₂×C₄₃	semidirect
305. #3151	C₂×C₄₃	semidirect
306. #3106	C₂×C₄₃	semidirect
307. #1631	C₂×C₄₃	semidirect
308. #1630	C₂×C₄₃	semidirect
309. #1621	C₂×C₄₃	semidirect
310. #1620	C₂×C₄₃	semidirect
311. #1545	C₂×C₄₃	semidirect
312. #1489	C₂×C₄₃	semidirect
313. #1485	C₂×C₄₃	semidirect
341. #477	C₂²×C₄₃	semidirect
342. #477	C₂²×C₄₃	semidirect
343. #476	C₂²×C₄₃	semidirect
347. #460	C₂²×C₄₃	semidirect
348. #460	C₂²×C₄₃	semidirect
349. #459	C₂²×C₄₃	semidirect
358. Q₈⋊C₈	C₂²×C₄₃	semidirect
359. Q₈⋊C₈	C₂²×C₄₃	semidirect
360. Q₈⋊C₈	C₂²×C₄₃	semidirect
361. D₄⋊C₈	C₂²×C₄₃	semidirect
362. C₄₃	#18568	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3508	2
C₄₃×#3254	2
C₄₃×#3151	2
C₄₃×#3106	2
C₄₃×#1631	2
C₄₃×#1630	2
C₄₃×#1621	2
C₄₃×#1620	2
C₄₃×#1545	2
C₄₃×#1489	2
C₄₃×#1485	2
#18568	43

Subgroups — C43×#18568 #24938585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18568 #24938585