Subgroups — C₄₃×#28439 #24948456

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#495	C₂	1	2	yes	maximal, complemented
2	C₂×C₄₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#124×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1958	C₂	1	2	yes	maximal, complemented
11	C₄×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	2	yes	—
19	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#124×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#495	—	2	8	no	—
24	C₄₃×#462	—	2	4	no	—
25	C₄₃×#461	—	2	4	no	—
26	C₄₃×#460	—	2	4	no	—
27	C₄₃×#459	—	2	4	no	—
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₃	C₂²	1	2	yes	—
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#102×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
35	C₄₃×#391	C₂²	1	1	yes	characteristic
36	C₄₃×#390	—	2	2	no	—
37	C₄₃×#390	—	2	2	no	—
38	C₄₃×#390	C₂²	1	1	yes	characteristic
39	C₄₃×#388	—	2	2	no	—
40	C₄₃×#382	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
42	C₄³×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	—	2	1	no	—
48	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	—	2	1	no	—
51	C₂×Q₁₆×C₄₃	—	2	4	no	—
52	C₂×Q₁₆×C₄₃	—	2	4	no	—
53	C₂×Q₁₆×C₄₃	—	4	2	no	—
54	C₂×SD₁₆×C₄₃	—	2	4	no	—
55	C₂×SD₁₆×C₄₃	—	2	4	no	—
56	C₂×SD₁₆×C₄₃	—	2	4	no	—
57	C₂×SD₁₆×C₄₃	—	2	4	no	—
58	C₂×SD₁₆×C₄₃	—	4	2	no	—
59	C₂×SD₁₆×C₄₃	—	4	2	no	—
60	C₂×D₈×C₄₃	—	2	4	no	—
61	C₂×D₈×C₄₃	—	2	4	no	—
62	C₂×D₈×C₄₃	—	4	2	no	—
63	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₄₃	—	2	2	no	—
66	C₄⋊Q₈×C₄₃	—	2	2	no	—
67	#127×C₄₃	—	2	2	no	—
68	#127×C₄₃	—	2	2	no	—
69	#124×C₄₃	—	2	4	no	—
70	#124×C₄₃	—	2	2	no	—
71	#124×C₄₃	—	2	4	no	—
72	#124×C₄₃	—	4	2	no	—
73	#124×C₄₃	—	4	2	no	—
74	#124×C₄₃	D₄	1	4	yes	complemented
75	C₄×Q₈×C₄₃	—	2	2	no	—
76	C₄×Q₈×C₄₃	—	2	2	no	—
77	C₄×D₄×C₄₃	—	2	2	no	—
78	C₄×D₄×C₄₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
89	C₂×C₄²×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	D₄	1	2	yes	—
91	C₂×C₄²×C₄₃	D₄	1	2	yes	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
96	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
97	#103×C₄₃	—	2	4	no	—
98	#103×C₄₃	—	2	4	no	—
99	#102×C₄₃	—	2	4	no	—
100	#102×C₄₃	—	2	4	no	—
101	C₄×C₈×C₄₃	—	2	4	no	—
102	#95×C₄₃	—	2	2	no	—
103	#95×C₄₃	—	2	2	no	—
104	C₂⁴×C₄₃	—	2	1	no	—
105	C₂⁴×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×Q₈×C₄₃	—	2	1	no	—
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	—	2	2	no	—
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	—	2	1	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₄₃	—	2	1	no	—
119	C₂×D₄×C₄₃	—	2	1	no	—
120	C₂×D₄×C₄₃	—	2	1	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	1	no	—
126	C₂×D₄×C₄₃	—	2	1	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	4	4	no	—
130	C₂×D₄×C₄₃	—	4	2	no	—
131	C₂×D₄×C₄₃	—	4	2	no	—
132	C₂×D₄×C₄₃	—	4	4	no	—
133	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	2	no	—
138	C₂²×C₄×C₄₃	—	4	2	no	—
139	C₂²×C₄×C₄₃	—	4	4	no	—
140	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₄₃	—	4	8	no	—
146	SD₁₆×C₄₃	—	4	8	no	—
147	SD₁₆×C₄₃	—	4	8	no	—
148	D₈×C₄₃	—	4	8	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
154	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
155	C₄⋊C₄×C₄₃	—	2	1	no	—
156	C₄⋊C₄×C₄₃	—	2	1	no	—
157	C₄⋊C₄×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	4	2	no	—
160	C₄⋊C₄×C₄₃	—	4	2	no	—
161	C₄⋊C₄×C₄₃	—	4	2	no	—
162	C₂²⋊C₄×C₄₃	—	2	8	no	—
163	C₂²⋊C₄×C₄₃	—	4	4	no	—
164	C₂²⋊C₄×C₄₃	—	4	8	no	—
165	C₂²⋊C₄×C₄₃	—	4	8	no	—
166	C₂²⋊C₄×C₄₃	—	4	2	no	—
167	C₄²×C₄₃	—	2	4	no	—
168	C₄²×C₄₃	—	2	1	no	—
169	C₄²×C₄₃	—	2	1	no	—
170	C₄²×C₄₃	—	4	2	no	—
171	C₄²×C₄₃	—	4	2	no	—
172	C₄²×C₄₃	C₂×D₄	1	2	yes	—
173	C₄²×C₄₃	C₂×D₄	1	2	yes	—
174	C₄²×C₄₃	C₂×D₄	1	2	yes	—
175	C₄²×C₄₃	#41	1	2	yes	—
176	C₂³×C₄₃	—	2	2	no	—
177	C₂³×C₄₃	—	4	1	no	—
178	C₂³×C₄₃	—	4	1	no	—
179	C₂³×C₄₃	—	4	2	no	—
180	C₂³×C₄₃	—	4	2	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	4	4	no	—
185	C₂³×C₄₃	—	4	4	no	—
186	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₄₃	—	2	2	no	—
188	Q₈×C₄₃	—	2	2	no	—
189	Q₈×C₄₃	—	4	1	no	—
190	Q₈×C₄₃	—	4	1	no	—
191	Q₈×C₄₃	—	4	2	no	—
192	Q₈×C₄₃	—	4	2	no	—
193	Q₈×C₄₃	—	4	2	no	—
194	Q₈×C₄₃	—	4	2	no	—
195	D₄×C₄₃	—	2	2	no	—
196	D₄×C₄₃	—	2	2	no	—
197	D₄×C₄₃	—	4	2	no	—
198	D₄×C₄₃	—	4	2	no	—
199	D₄×C₄₃	—	4	1	no	—
200	D₄×C₄₃	—	4	1	no	—
201	D₄×C₄₃	—	4	2	no	—
202	D₄×C₄₃	—	4	2	no	—
203	D₄×C₄₃	—	8	4	no	—
204	D₄×C₄₃	—	8	4	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	1	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	8	4	no	—
222	C₂×C₄×C₄₃	#121	1	4	yes	—
223	C₂×C₄×C₄₃	#127	1	2	yes	—
224	C₂×C₄×C₄₃	#127	1	2	yes	—
225	C₂×C₄×C₄₃	#135	1	4	yes	—
226	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
232	C₈×C₄₃	—	2	4	no	—
233	C₈×C₄₃	—	2	4	no	—
234	#28439	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₄₃	—	4	4	no	—
236	C₂²×C₄₃	—	4	2	no	—
237	C₂²×C₄₃	—	8	1	no	—
238	C₂²×C₄₃	—	8	1	no	—
239	C₂²×C₄₃	—	8	2	no	—
240	C₂²×C₄₃	—	8	2	no	—
241	C₂²×C₄₃	—	8	2	no	—
242	C₂²×C₄₃	—	8	4	no	—
243	C₂²×C₄₃	—	8	4	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
246	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
247	C₂²×C₄₃	#535	1	1	yes	characteristic
248	C₂²×C₄₃	C₂×#135	1	2	yes	—
249	C₂²×C₄₃	#575	1	2	yes	—
250	C₄×C₄₃	—	2	2	no	—
251	C₄×C₄₃	—	2	4	no	—
252	C₄×C₄₃	—	4	2	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	—	8	1	no	—
255	C₄×C₄₃	—	8	1	no	—
256	C₄×C₄₃	—	8	2	no	—
257	C₄×C₄₃	#495	1	4	yes	complemented
258	C₄×C₄₃	D₄²	1	1	yes	characteristic
259	C₄×C₄₃	D₄²	1	1	yes	characteristic
260	C₄×C₄₃	#550	1	1	yes	characteristic
261	C₄×C₄₃	#550	1	1	yes	characteristic
262	C₂×#495	C₂×C₄₃	1	2	yes	complemented
263	C₂×#462	C₂×C₄₃	1	1	yes	characteristic, complemented
264	C₂×#460	C₂×C₄₃	1	1	yes	characteristic, complemented
265	C₂×#461	C₂×C₄₃	1	1	yes	characteristic, complemented
266	C₂×#459	C₂×C₄₃	1	1	yes	characteristic
267	#2858	C₂×C₄₃	1	1	yes	characteristic, complemented
268	C₄×#124	C₂×C₄₃	1	1	yes	characteristic, complemented
269	#2015	C₂×C₄₃	1	2	yes	complemented
270	#2012	C₂×C₄₃	1	2	yes	complemented
271	#1958	C₂×C₄₃	1	2	yes	complemented
272	C₄×C₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
273	C₂×C₄₃	—	8	2	no	—
274	C₂×C₄₃	—	16	2	no	—
275	C₂×C₄₃	#2541	1	1	yes	characteristic
276	C₂×C₄₃	#3035	1	2	yes	—
277	C₂×C₄₃	C₂×#495	1	1	yes	characteristic
278	C₂×C₄₃	#3153	1	1	yes	characteristic
279	C₂×C₄₃	#3212	1	2	yes	—
280	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
281	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
282	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
283	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
284	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
285	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
286	C₂×#124	C₂²×C₄₃	1	2	yes	—
287	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
288	C₂×#124	C₂²×C₄₃	1	2	yes	—
289	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
291	#495	—	2	8	no	—
292	#462	—	2	4	no	—
293	#461	—	2	4	no	—
294	#460	—	2	4	no	—
295	#459	—	2	4	no	—
296	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×#103	C₂²×C₄₃	1	2	yes	—
299	C₂×#103	C₂²×C₄₃	1	2	yes	—
300	C₂×#102	C₂²×C₄₃	1	2	yes	—
301	C₂×#102	C₂²×C₄₃	1	2	yes	—
302	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
303	#391	C₂²×C₄₃	1	1	yes	characteristic
304	#390	—	2	2	no	—
305	#390	—	2	2	no	—
306	#390	C₂²×C₄₃	1	1	yes	characteristic
307	#388	—	2	2	no	—
308	#382	C₂²×C₄₃	1	1	yes	characteristic
309	C₄×C₂²⋊C₄	—	2	2	no	—
310	C₄³	C₂²×C₄₃	1	1	yes	characteristic
311	#336	C₂²×C₄₃	1	2	yes	—
312	C₄₃	#28439	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
314	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
318	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
319	C₂³×C₄	—	2	1	no	—
320	C₂×Q₁₆	—	2	4	no	—
321	C₂×Q₁₆	—	2	4	no	—
322	C₂×Q₁₆	—	4	2	no	—
323	C₂×SD₁₆	—	2	4	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	4	no	—
327	C₂×SD₁₆	—	4	2	no	—
328	C₂×SD₁₆	—	4	2	no	—
329	C₂×D₈	—	2	4	no	—
330	C₂×D₈	—	2	4	no	—
331	C₂×D₈	—	4	2	no	—
332	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
333	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	2	no	—
336	#127	—	2	2	no	—
337	#127	—	2	2	no	—
338	#124	—	2	4	no	—
339	#124	—	2	2	no	—
340	#124	—	2	4	no	—
341	#124	—	4	2	no	—
342	#124	—	4	2	no	—
343	#124	D₄×C₄₃	1	4	yes	complemented
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	4	no	—
356	C₂×C₂²⋊C₄	—	2	4	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	D₄×C₄₃	1	2	yes	—
360	C₂×C₄²	D₄×C₄₃	1	2	yes	—
361	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
364	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
365	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
366	#103	—	2	4	no	—
367	#103	—	2	4	no	—
368	#102	—	2	4	no	—
369	#102	—	2	4	no	—
370	C₄×C₈	—	2	4	no	—
371	#95	—	2	2	no	—
372	#95	—	2	2	no	—
373	C₂⁴	—	2	1	no	—
374	C₂⁴	—	2	2	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	2	no	—
400	C₂×D₄	—	4	2	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
414	Q₁₆	—	4	8	no	—
415	SD₁₆	—	4	8	no	—
416	SD₁₆	—	4	8	no	—
417	D₈	—	4	8	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
423	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	4	2	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	4	8	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	8	no	—
435	C₂²⋊C₄	—	4	2	no	—
436	C₄²	—	2	4	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	4	2	no	—
440	C₄²	—	4	2	no	—
441	C₄²	C₂×D₄×C₄₃	1	2	yes	—
442	C₄²	C₂×D₄×C₄₃	1	2	yes	—
443	C₄²	C₂×D₄×C₄₃	1	2	yes	—
444	C₄²	#41×C₄₃	1	2	yes	—
445	C₂³	—	2	2	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	4	1	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	8	4	no	—
473	D₄	—	8	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	8	4	no	—
491	C₂×C₄	#121×C₄₃	1	4	yes	—
492	C₂×C₄	#127×C₄₃	1	2	yes	—
493	C₂×C₄	#127×C₄₃	1	2	yes	—
494	C₂×C₄	#135×C₄₃	1	4	yes	—
495	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
498	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
499	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
500	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	2	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	4	no	—
511	C₂²	—	8	4	no	—
512	C₂²	—	8	2	no	—
513	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
514	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
515	C₂²	C₄₃×#535	1	1	yes	characteristic
516	C₂²	C₂×#135×C₄₃	1	2	yes	—
517	C₂²	C₄₃×#575	1	2	yes	—
518	C₄	—	2	2	no	—
519	C₄	—	2	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	1	no	—
524	C₄	—	8	2	no	—
525	C₄	C₄₃×#495	1	4	yes	complemented
526	C₄	D₄²×C₄₃	1	1	yes	characteristic
527	C₄	D₄²×C₄₃	1	1	yes	characteristic
528	C₄	C₄₃×#550	1	1	yes	characteristic
529	C₄	C₄₃×#550	1	1	yes	characteristic
530	C₂	—	8	2	no	—
531	C₂	—	16	2	no	—
532	C₂	C₄₃×#2541	1	1	yes	characteristic
533	C₂	C₄₃×#3035	1	2	yes	—
534	C₂	C₂×C₄₃×#495	1	1	yes	characteristic
535	C₂	C₄₃×#3153	1	1	yes	characteristic
536	C₂	C₄₃×#3212	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#495	C₂	semidirect
2. C₂×C₄₃×#462	C₂	semidirect
3. C₂×C₄₃×#460	C₂	semidirect
4. C₂×C₄₃×#461	C₂	semidirect
6. C₄₃×#2858	C₂	semidirect
7. C₄×#124×C₄₃	C₂	semidirect
8. C₄₃×#2015	C₂	semidirect
9. C₄₃×#2012	C₂	semidirect
10. C₄₃×#1958	C₂	semidirect
11. C₄×C₄⋊C₈×C₄₃	C₂	semidirect
74. #124×C₄₃	D₄	semidirect
234. #28439	C₄₃	direct (N × H)
257. C₄×C₄₃	#495	semidirect
262. C₂×#495	C₂×C₄₃	semidirect
263. C₂×#462	C₂×C₄₃	semidirect
264. C₂×#460	C₂×C₄₃	semidirect
265. C₂×#461	C₂×C₄₃	semidirect
267. #2858	C₂×C₄₃	semidirect
268. C₄×#124	C₂×C₄₃	semidirect
269. #2015	C₂×C₄₃	semidirect
270. #2012	C₂×C₄₃	semidirect
271. #1958	C₂×C₄₃	semidirect
272. C₄×C₄⋊C₈	C₂×C₄₃	semidirect
312. C₄₃	#28439	direct (N × H)
343. #124	D₄×C₄₃	semidirect
525. C₄	C₄₃×#495	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#495	2
C₂×C₄₃×#462	2
C₂×C₄₃×#460	2
C₂×C₄₃×#461	2
C₂×C₄₃×#459	2
C₄₃×#2858	2
C₄×#124×C₄₃	2
C₄₃×#2015	2
C₄₃×#2012	2
C₄₃×#1958	2
C₄×C₄⋊C₈×C₄₃	2
#28439	43

Subgroups — C43×#28439 #24948456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28439 #24948456