Subgroups — C₄₃×#25727 #24945744

Order 11008.

1612 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#452	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#532	—	2	4	no	—
18	C₄₃×#532	—	2	4	no	—
19	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#124×C₄₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₄₃	—	2	2	no	—
25	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₃	—	2	2	no	—
27	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#497	—	2	4	no	—
29	C₄₃×#496	—	2	4	no	—
30	C₄₃×#452	—	2	8	no	—
31	C₄₃×#449	—	2	8	no	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#103×C₄₃	C₂²	1	2	yes	—
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₂×#102×C₄₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
37	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#391	C₂²	1	1	yes	characteristic
40	C₄₃×#390	C₂²	1	1	yes	characteristic
41	C₄₃×#388	—	2	2	no	—
42	C₄₃×#386	—	2	2	no	—
43	C₄₃×#382	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₃	—	2	4	no	—
46	C₂×#41×C₄₃	—	2	4	no	—
47	C₂×#41×C₄₃	—	2	4	no	—
48	C₂×#41×C₄₃	—	2	4	no	—
49	C₂×#41×C₄₃	—	4	2	no	—
50	C₂×#41×C₄₃	—	4	2	no	—
51	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₄₃	—	2	2	no	—
54	C₂²×D₄×C₄₃	—	2	1	no	—
55	C₂²×D₄×C₄₃	—	2	2	no	—
56	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₄₃	—	2	2	no	—
59	C₂³×C₄×C₄₃	D₄	1	2	yes	—
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂×Q₁₆×C₄₃	—	2	4	no	—
62	C₂×Q₁₆×C₄₃	—	2	4	no	—
63	C₂×Q₁₆×C₄₃	—	4	2	no	—
64	C₂×SD₁₆×C₄₃	—	2	4	no	—
65	C₂×SD₁₆×C₄₃	—	2	4	no	—
66	C₂×SD₁₆×C₄₃	—	2	4	no	—
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×SD₁₆×C₄₃	—	4	2	no	—
69	C₂×SD₁₆×C₄₃	—	4	2	no	—
70	C₂×D₈×C₄₃	—	2	4	no	—
71	C₂×D₈×C₄₃	—	2	4	no	—
72	C₂×D₈×C₄₃	—	4	2	no	—
73	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
74	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
75	C₄⋊Q₈×C₄₃	—	2	2	no	—
76	C₄⋊Q₈×C₄₃	D₄	1	4	yes	complemented
77	#127×C₄₃	—	2	2	no	—
78	#127×C₄₃	D₄	1	4	yes	complemented
79	#124×C₄₃	—	2	4	no	—
80	#124×C₄₃	—	2	4	no	—
81	#124×C₄₃	—	2	2	no	—
82	#124×C₄₃	—	2	2	no	—
83	C₂²⋊Q₈×C₄₃	—	2	4	no	—
84	#121×C₄₃	—	2	16	no	—
85	#121×C₄₃	—	2	4	no	—
86	C₄×D₄×C₄₃	—	2	16	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
96	C₂×C₄²×C₄₃	—	2	2	no	—
97	C₂×C₄²×C₄₃	—	2	2	no	—
98	C₂×C₄²×C₄₃	D₄	1	2	yes	—
99	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	#103×C₄₃	—	2	4	no	—
102	#103×C₄₃	—	2	4	no	—
103	#102×C₄₃	—	2	4	no	—
104	#102×C₄₃	—	2	4	no	—
105	C₂²⋊C₈×C₄₃	D₄	1	8	yes	complemented
106	#97×C₄₃	—	2	2	no	—
107	#97×C₄₃	—	2	2	no	—
108	#95×C₄₃	—	2	2	no	—
109	#95×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
113	#41×C₄₃	—	4	8	no	—
114	#41×C₄₃	—	4	8	no	—
115	#41×C₄₃	—	4	8	no	—
116	#41×C₄₃	—	4	8	no	—
117	C₂×Q₈×C₄₃	—	2	2	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	1	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₄₃	—	2	8	no	—
128	C₂×D₄×C₄₃	—	2	8	no	—
129	C₂×D₄×C₄₃	—	2	2	no	—
130	C₂×D₄×C₄₃	—	2	2	no	—
131	C₂×D₄×C₄₃	—	2	2	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	1	no	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	4	4	no	—
139	C₂×D₄×C₄₃	—	4	4	no	—
140	C₂×D₄×C₄₃	—	4	4	no	—
141	C₂×D₄×C₄₃	—	4	4	no	—
142	C₂×D₄×C₄₃	—	4	4	no	—
143	C₂×D₄×C₄₃	—	4	2	no	—
144	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₄₃	—	2	1	no	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	8	no	—
149	C₂²×C₄×C₄₃	—	2	4	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	4	2	no	—
155	C₂²×C₄×C₄₃	—	4	2	no	—
156	C₂²×C₄×C₄₃	—	4	4	no	—
157	C₂²×C₄×C₄₃	—	4	4	no	—
158	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
163	Q₁₆×C₄₃	—	4	8	no	—
164	SD₁₆×C₄₃	—	4	8	no	—
165	SD₁₆×C₄₃	—	4	8	no	—
166	D₈×C₄₃	—	4	8	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	2	no	—
171	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
172	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
173	C₄⋊C₄×C₄₃	—	2	8	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₄⋊C₄×C₄₃	—	4	2	no	—
177	C₂²⋊C₄×C₄₃	—	2	16	no	—
178	C₂²⋊C₄×C₄₃	—	4	4	no	—
179	C₂²⋊C₄×C₄₃	—	4	4	no	—
180	C₂²⋊C₄×C₄₃	—	4	2	no	—
181	C₂²⋊C₄×C₄₃	—	4	2	no	—
182	C₄²×C₄₃	—	2	4	no	—
183	C₄²×C₄₃	—	2	1	no	—
184	C₄²×C₄₃	—	2	1	no	—
185	C₄²×C₄₃	C₂×D₄	1	2	yes	—
186	C₄²×C₄₃	C₂×D₄	1	2	yes	—
187	C₂³×C₄₃	—	2	1	no	—
188	C₂³×C₄₃	—	2	1	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	2	no	—
191	C₂³×C₄₃	—	2	4	no	—
192	C₂³×C₄₃	—	4	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	4	4	no	—
195	C₂³×C₄₃	—	4	4	no	—
196	C₂³×C₄₃	—	4	1	no	—
197	C₂³×C₄₃	—	4	1	no	—
198	C₂³×C₄₃	—	4	1	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	#127	1	2	yes	—
202	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₄₃	—	2	4	no	—
204	Q₈×C₄₃	—	2	4	no	—
205	Q₈×C₄₃	—	4	2	no	—
206	Q₈×C₄₃	—	4	2	no	—
207	Q₈×C₄₃	—	4	2	no	—
208	Q₈×C₄₃	—	4	2	no	—
209	D₄×C₄₃	—	2	4	no	—
210	D₄×C₄₃	—	2	4	no	—
211	D₄×C₄₃	—	4	16	no	—
212	D₄×C₄₃	—	4	16	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	4	2	no	—
215	D₄×C₄₃	—	4	2	no	—
216	D₄×C₄₃	—	4	2	no	—
217	D₄×C₄₃	—	8	4	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	4	no	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	2	2	no	—
225	C₂×C₄×C₄₃	—	2	4	no	—
226	C₂×C₄×C₄₃	—	2	2	no	—
227	C₂×C₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	4	8	no	—
229	C₂×C₄×C₄₃	—	4	16	no	—
230	C₂×C₄×C₄₃	—	4	2	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	—	4	1	no	—
233	C₂×C₄×C₄₃	—	4	1	no	—
234	C₂×C₄×C₄₃	—	4	1	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	4	2	no	—
238	C₂×C₄×C₄₃	—	4	2	no	—
239	C₂×C₄×C₄₃	#120	1	4	yes	—
240	C₂×C₄×C₄₃	#127	1	2	yes	—
241	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
245	C₈×C₄₃	—	2	4	no	—
246	C₈×C₄₃	—	2	4	no	—
247	#25727	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂²×C₄₃	—	2	2	no	—
249	C₂²×C₄₃	—	2	2	no	—
250	C₂²×C₄₃	—	2	2	no	—
251	C₂²×C₄₃	—	4	2	no	—
252	C₂²×C₄₃	—	4	2	no	—
253	C₂²×C₄₃	—	4	4	no	—
254	C₂²×C₄₃	—	4	8	no	—
255	C₂²×C₄₃	—	8	2	no	—
256	C₂²×C₄₃	—	8	2	no	—
257	C₂²×C₄₃	—	8	4	no	—
258	C₂²×C₄₃	—	8	1	no	—
259	C₂²×C₄₃	—	8	1	no	—
260	C₂²×C₄₃	—	8	1	no	—
261	C₂²×C₄₃	—	8	2	no	—
262	C₂²×C₄₃	—	8	2	no	—
263	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
264	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
265	C₂²×C₄₃	#535	1	1	yes	characteristic
266	C₂²×C₄₃	#575	1	2	yes	—
267	C₂²×C₄₃	#575	1	2	yes	—
268	C₄×C₄₃	—	2	2	no	—
269	C₄×C₄₃	—	2	4	no	—
270	C₄×C₄₃	—	4	4	no	—
271	C₄×C₄₃	—	4	2	no	—
272	C₄×C₄₃	—	8	1	no	—
273	C₄×C₄₃	—	8	1	no	—
274	C₄×C₄₃	—	8	1	no	—
275	C₄×C₄₃	D₄²	1	2	yes	—
276	C₄×C₄₃	D₄²	1	2	yes	—
277	C₂×#532	C₂×C₄₃	1	1	yes	characteristic, complemented
278	C₂×#497	C₂×C₄₃	1	1	yes	characteristic, complemented
279	C₂×#496	C₂×C₄₃	1	1	yes	characteristic, complemented
280	C₂×#452	C₂×C₄₃	1	2	yes	complemented
281	C₂×#449	C₂×C₄₃	1	2	yes	complemented
282	#2850	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#2015	C₂×C₄₃	1	2	yes	complemented
284	#2012	C₂×C₄₃	1	2	yes	complemented
285	#1961	C₂×C₄₃	1	1	yes	characteristic, complemented
286	#1960	C₂×C₄₃	1	1	yes	characteristic, complemented
287	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
288	C₂×C₄₃	—	4	2	no	—
289	C₂×C₄₃	—	8	4	no	—
290	C₂×C₄₃	—	16	1	no	—
291	C₂×C₄₃	#2433	1	1	yes	characteristic
292	C₂×C₄₃	#3005	1	2	yes	—
293	C₂×C₄₃	#3150	1	1	yes	characteristic
294	C₂×C₄₃	#3153	1	1	yes	characteristic
295	C₂×C₄₃	#3219	1	2	yes	—
296	C₂²×#41	C₂²×C₄₃	1	2	yes	—
297	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
298	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
299	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
300	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
301	#532	—	2	4	no	—
302	#532	—	2	4	no	—
303	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
304	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
305	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
306	C₂×#124	C₂²×C₄₃	1	2	yes	—
307	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
308	C₂×#121	—	2	2	no	—
309	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
310	C₂×C₄×D₄	—	2	2	no	—
311	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
312	#497	—	2	4	no	—
313	#496	—	2	4	no	—
314	#452	—	2	8	no	—
315	#449	—	2	8	no	—
316	C₂×#103	C₂²×C₄₃	1	2	yes	—
317	C₂×#103	C₂²×C₄₃	1	2	yes	—
318	C₂×#102	C₂²×C₄₃	1	2	yes	—
319	C₂×#102	C₂²×C₄₃	1	2	yes	—
320	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
321	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
322	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
323	#391	C₂²×C₄₃	1	1	yes	characteristic
324	#390	C₂²×C₄₃	1	1	yes	characteristic
325	#388	—	2	2	no	—
326	#386	—	2	2	no	—
327	#382	C₂²×C₄₃	1	1	yes	characteristic
328	#336	C₂²×C₄₃	1	2	yes	—
329	C₄₃	#25727	1	1	yes	characteristic, direct product factor, Sylow
330	C₂×#41	—	2	4	no	—
331	C₂×#41	—	2	4	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	—	2	4	no	—
334	C₂×#41	—	4	2	no	—
335	C₂×#41	—	4	2	no	—
336	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
338	C₂²×D₄	—	2	2	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
343	C₂³×C₄	—	2	2	no	—
344	C₂³×C₄	D₄×C₄₃	1	2	yes	—
345	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
346	C₂×Q₁₆	—	2	4	no	—
347	C₂×Q₁₆	—	2	4	no	—
348	C₂×Q₁₆	—	4	2	no	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	4	2	no	—
354	C₂×SD₁₆	—	4	2	no	—
355	C₂×D₈	—	2	4	no	—
356	C₂×D₈	—	2	4	no	—
357	C₂×D₈	—	4	2	no	—
358	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
359	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
360	C₄⋊Q₈	—	2	2	no	—
361	C₄⋊Q₈	D₄×C₄₃	1	4	yes	complemented
362	#127	—	2	2	no	—
363	#127	D₄×C₄₃	1	4	yes	complemented
364	#124	—	2	4	no	—
365	#124	—	2	4	no	—
366	#124	—	2	2	no	—
367	#124	—	2	2	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	#121	—	2	16	no	—
370	#121	—	2	4	no	—
371	C₄×D₄	—	2	16	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	—	2	2	no	—
383	C₂×C₄²	D₄×C₄₃	1	2	yes	—
384	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
386	#103	—	2	4	no	—
387	#103	—	2	4	no	—
388	#102	—	2	4	no	—
389	#102	—	2	4	no	—
390	C₂²⋊C₈	D₄×C₄₃	1	8	yes	complemented
391	#97	—	2	2	no	—
392	#97	—	2	2	no	—
393	#95	—	2	2	no	—
394	#95	—	2	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
398	#41	—	4	8	no	—
399	#41	—	4	8	no	—
400	#41	—	4	8	no	—
401	#41	—	4	8	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	—	4	4	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	8	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
444	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
448	Q₁₆	—	4	8	no	—
449	SD₁₆	—	4	8	no	—
450	SD₁₆	—	4	8	no	—
451	D₈	—	4	8	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
457	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	2	16	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₄²	—	2	4	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	C₂×D₄×C₄₃	1	2	yes	—
471	C₄²	C₂×D₄×C₄₃	1	2	yes	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	#127×C₄₃	1	2	yes	—
487	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
488	Q₈	—	2	4	no	—
489	Q₈	—	2	4	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	4	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	4	16	no	—
497	D₄	—	4	16	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	4	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	4	16	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	#120×C₄₃	1	4	yes	—
525	C₂×C₄	#127×C₄₃	1	2	yes	—
526	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
529	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
530	C₈	—	2	4	no	—
531	C₈	—	2	4	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	8	no	—
539	C₂²	—	8	2	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	4	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
548	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
549	C₂²	C₄₃×#535	1	1	yes	characteristic
550	C₂²	C₄₃×#575	1	2	yes	—
551	C₂²	C₄₃×#575	1	2	yes	—
552	C₄	—	2	2	no	—
553	C₄	—	2	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	2	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	D₄²×C₄₃	1	2	yes	—
560	C₄	D₄²×C₄₃	1	2	yes	—
561	C₂	—	4	2	no	—
562	C₂	—	8	4	no	—
563	C₂	—	16	1	no	—
564	C₂	C₄₃×#2433	1	1	yes	characteristic
565	C₂	C₄₃×#3005	1	2	yes	—
566	C₂	C₄₃×#3150	1	1	yes	characteristic
567	C₂	C₄₃×#3153	1	1	yes	characteristic
568	C₂	C₄₃×#3219	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 ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#532	C₂	semidirect
2. C₂×C₄₃×#497	C₂	semidirect
3. C₂×C₄₃×#496	C₂	semidirect
4. C₂×C₄₃×#452	C₂	semidirect
5. C₂×C₄₃×#449	C₂	semidirect
6. C₄₃×#2850	C₂	semidirect
7. C₄₃×#2015	C₂	semidirect
8. C₄₃×#2012	C₂	semidirect
9. C₄₃×#1961	C₂	semidirect
10. C₄₃×#1960	C₂	semidirect
11. C₄₃×#1749	C₂	semidirect
76. C₄⋊Q₈×C₄₃	D₄	semidirect
78. #127×C₄₃	D₄	semidirect
105. C₂²⋊C₈×C₄₃	D₄	semidirect
247. #25727	C₄₃	direct (N × H)
277. C₂×#532	C₂×C₄₃	semidirect
278. C₂×#497	C₂×C₄₃	semidirect
279. C₂×#496	C₂×C₄₃	semidirect
280. C₂×#452	C₂×C₄₃	semidirect
281. C₂×#449	C₂×C₄₃	semidirect
282. #2850	C₂×C₄₃	semidirect
283. #2015	C₂×C₄₃	semidirect
284. #2012	C₂×C₄₃	semidirect
285. #1961	C₂×C₄₃	semidirect
286. #1960	C₂×C₄₃	semidirect
287. #1749	C₂×C₄₃	semidirect
329. C₄₃	#25727	direct (N × H)
361. C₄⋊Q₈	D₄×C₄₃	semidirect
363. #127	D₄×C₄₃	semidirect
390. C₂²⋊C₈	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×#532	2
C₂×C₄₃×#497	2
C₂×C₄₃×#496	2
C₂×C₄₃×#452	2
C₂×C₄₃×#449	2
C₄₃×#2850	2
C₄₃×#2015	2
C₄₃×#2012	2
C₄₃×#1961	2
C₄₃×#1960	2
C₄₃×#1749	2
#25727	43

Subgroups — C43×#25727 #24945744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25727 #24945744