Subgroups — C₄₃×#25723 #24945740

Order 11008.

1624 conjugacy classes of subgroups.

The subgroup lattice has 552 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×#495	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#452	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₃×#449	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1958	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₄₃	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	8	no	—
18	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#121×C₄₃	—	2	2	no	—
24	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₃	—	2	2	no	—
26	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#495	—	2	8	no	—
28	C₄₃×#452	—	2	8	no	—
29	C₄₃×#449	—	2	8	no	—
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×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
36	C₄₃×#391	C₂²	1	1	yes	characteristic
37	C₄₃×#390	C₂²	1	1	yes	characteristic
38	C₄₃×#388	—	2	2	no	—
39	C₄₃×#386	—	2	2	no	—
40	C₄₃×#382	C₂²	1	1	yes	characteristic
41	C₄₃×#336	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₂×#41×C₄₃	—	2	4	no	—
44	C₂×#41×C₄₃	—	2	4	no	—
45	C₂×#41×C₄₃	—	2	4	no	—
46	C₂×#41×C₄₃	—	2	4	no	—
47	C₂×#41×C₄₃	—	4	2	no	—
48	C₂×#41×C₄₃	—	4	2	no	—
49	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
51	C₂²×D₄×C₄₃	—	2	2	no	—
52	C₂²×D₄×C₄₃	—	2	1	no	—
53	C₂²×D₄×C₄₃	—	2	2	no	—
54	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₃	—	2	2	no	—
57	C₂³×C₄×C₄₃	D₄	1	2	yes	—
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂×Q₁₆×C₄₃	—	2	4	no	—
60	C₂×Q₁₆×C₄₃	—	2	4	no	—
61	C₂×Q₁₆×C₄₃	—	4	2	no	—
62	C₂×SD₁₆×C₄₃	—	2	4	no	—
63	C₂×SD₁₆×C₄₃	—	2	4	no	—
64	C₂×SD₁₆×C₄₃	—	2	4	no	—
65	C₂×SD₁₆×C₄₃	—	2	4	no	—
66	C₂×SD₁₆×C₄₃	—	4	2	no	—
67	C₂×SD₁₆×C₄₃	—	4	2	no	—
68	C₂×D₈×C₄₃	—	2	4	no	—
69	C₂×D₈×C₄₃	—	2	4	no	—
70	C₂×D₈×C₄₃	—	4	2	no	—
71	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
73	C₄⋊Q₈×C₄₃	—	2	4	no	—
74	#127×C₄₃	—	2	4	no	—
75	#124×C₄₃	—	2	4	no	—
76	#124×C₄₃	—	2	4	no	—
77	#124×C₄₃	D₄	1	8	yes	complemented
78	C₂²⋊Q₈×C₄₃	—	2	4	no	—
79	#121×C₄₃	—	2	16	no	—
80	#121×C₄₃	—	2	4	no	—
81	C₄×D₄×C₄₃	—	2	16	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
91	C₂×C₄²×C₄₃	—	2	4	no	—
92	C₂×C₄²×C₄₃	D₄	1	2	yes	—
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	#103×C₄₃	—	2	4	no	—
96	#103×C₄₃	—	2	4	no	—
97	#102×C₄₃	—	2	4	no	—
98	#102×C₄₃	—	2	4	no	—
99	C₂²⋊C₈×C₄₃	D₄	1	8	yes	complemented
100	C₄×C₈×C₄₃	—	2	4	no	—
101	#95×C₄₃	—	2	2	no	—
102	#95×C₄₃	—	2	2	no	—
103	C₂⁴×C₄₃	—	2	2	no	—
104	C₂⁴×C₄₃	—	2	1	no	—
105	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
106	#41×C₄₃	—	4	8	no	—
107	#41×C₄₃	—	4	8	no	—
108	#41×C₄₃	—	4	8	no	—
109	#41×C₄₃	—	4	8	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	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	—	2	1	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
120	C₂×D₄×C₄₃	—	2	8	no	—
121	C₂×D₄×C₄₃	—	2	8	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	2	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	2	2	no	—
129	C₂×D₄×C₄₃	—	2	1	no	—
130	C₂×D₄×C₄₃	—	2	1	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂×D₄×C₄₃	—	4	4	no	—
133	C₂×D₄×C₄₃	—	4	4	no	—
134	C₂×D₄×C₄₃	—	4	4	no	—
135	C₂×D₄×C₄₃	—	4	4	no	—
136	C₂×D₄×C₄₃	—	4	2	no	—
137	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₃	—	2	2	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	—	2	8	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	1	no	—
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	4	2	no	—
149	C₂²×C₄×C₄₃	—	4	4	no	—
150	C₂²×C₄×C₄₃	—	4	4	no	—
151	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
156	Q₁₆×C₄₃	—	4	8	no	—
157	SD₁₆×C₄₃	—	4	8	no	—
158	SD₁₆×C₄₃	—	4	8	no	—
159	D₈×C₄₃	—	4	8	no	—
160	C₂×C₈×C₄₃	—	2	2	no	—
161	C₂×C₈×C₄₃	—	2	2	no	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	2	no	—
164	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
165	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
166	C₄⋊C₄×C₄₃	—	2	8	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	—	2	2	no	—
169	C₄⋊C₄×C₄₃	—	4	2	no	—
170	C₂²⋊C₄×C₄₃	—	2	16	no	—
171	C₂²⋊C₄×C₄₃	—	4	4	no	—
172	C₂²⋊C₄×C₄₃	—	4	2	no	—
173	C₂²⋊C₄×C₄₃	—	4	4	no	—
174	C₂²⋊C₄×C₄₃	—	4	2	no	—
175	C₄²×C₄₃	—	2	4	no	—
176	C₄²×C₄₃	—	2	2	no	—
177	C₄²×C₄₃	C₂×D₄	1	4	yes	—
178	C₂³×C₄₃	—	2	1	no	—
179	C₂³×C₄₃	—	2	1	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	2	4	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	4	2	no	—
185	C₂³×C₄₃	—	4	4	no	—
186	C₂³×C₄₃	—	4	4	no	—
187	C₂³×C₄₃	—	4	1	no	—
188	C₂³×C₄₃	—	4	1	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	—	4	2	no	—
191	C₂³×C₄₃	—	4	2	no	—
192	C₂³×C₄₃	#127	1	2	yes	—
193	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₄₃	—	2	4	no	—
195	Q₈×C₄₃	—	2	4	no	—
196	Q₈×C₄₃	—	4	2	no	—
197	Q₈×C₄₃	—	4	2	no	—
198	Q₈×C₄₃	—	4	2	no	—
199	Q₈×C₄₃	—	4	2	no	—
200	D₄×C₄₃	—	2	4	no	—
201	D₄×C₄₃	—	2	4	no	—
202	D₄×C₄₃	—	4	16	no	—
203	D₄×C₄₃	—	4	16	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	4	2	no	—
206	D₄×C₄₃	—	4	2	no	—
207	D₄×C₄₃	—	4	2	no	—
208	D₄×C₄₃	—	8	4	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	4	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	4	8	no	—
219	C₂×C₄×C₄₃	—	4	16	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	—	4	1	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	#120	1	4	yes	—
230	C₂×C₄×C₄₃	#127	1	2	yes	—
231	C₂×C₄×C₄₃	#135	1	4	yes	—
232	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
236	C₈×C₄₃	—	2	4	no	—
237	C₈×C₄₃	—	2	4	no	—
238	#25723	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₄₃	—	2	2	no	—
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	—	2	2	no	—
242	C₂²×C₄₃	—	4	2	no	—
243	C₂²×C₄₃	—	4	2	no	—
244	C₂²×C₄₃	—	4	4	no	—
245	C₂²×C₄₃	—	4	8	no	—
246	C₂²×C₄₃	—	8	2	no	—
247	C₂²×C₄₃	—	8	2	no	—
248	C₂²×C₄₃	—	8	4	no	—
249	C₂²×C₄₃	—	8	1	no	—
250	C₂²×C₄₃	—	8	1	no	—
251	C₂²×C₄₃	—	8	1	no	—
252	C₂²×C₄₃	—	8	2	no	—
253	C₂²×C₄₃	—	8	2	no	—
254	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
255	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
256	C₂²×C₄₃	#535	1	1	yes	characteristic
257	C₂²×C₄₃	C₂×#135	1	2	yes	—
258	C₂²×C₄₃	#575	1	2	yes	—
259	C₄×C₄₃	—	2	2	no	—
260	C₄×C₄₃	—	2	4	no	—
261	C₄×C₄₃	—	2	4	no	—
262	C₄×C₄₃	—	4	4	no	—
263	C₄×C₄₃	—	8	1	no	—
264	C₄×C₄₃	—	8	1	no	—
265	C₄×C₄₃	—	8	1	no	—
266	C₄×C₄₃	D₄²	1	2	yes	—
267	C₄×C₄₃	D₄²	1	2	yes	—
268	C₂×#532	C₂×C₄₃	1	1	yes	characteristic, complemented
269	C₂×#495	C₂×C₄₃	1	2	yes	complemented
270	C₂×#452	C₂×C₄₃	1	2	yes	complemented
271	C₂×#449	C₂×C₄₃	1	2	yes	complemented
272	#2850	C₂×C₄₃	1	1	yes	characteristic, complemented
273	#2016	C₂×C₄₃	1	1	yes	characteristic, complemented
274	#2014	C₂×C₄₃	1	1	yes	characteristic, complemented
275	#2013	C₂×C₄₃	1	1	yes	characteristic, complemented
276	#2011	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#1958	C₂×C₄₃	1	2	yes	complemented
278	C₄×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
279	C₂×C₄₃	—	4	2	no	—
280	C₂×C₄₃	—	8	4	no	—
281	C₂×C₄₃	—	16	1	no	—
282	C₂×C₄₃	#2433	1	1	yes	characteristic
283	C₂×C₄₃	#3002	1	2	yes	—
284	C₂×C₄₃	#3147	1	1	yes	characteristic
285	C₂×C₄₃	#3153	1	1	yes	characteristic
286	C₂×C₄₃	#3212	1	2	yes	—
287	C₂²×#41	C₂²×C₄₃	1	2	yes	—
288	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
289	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
290	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
291	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
292	#532	—	2	8	no	—
293	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
295	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×#124	C₂²×C₄₃	1	2	yes	—
297	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×#121	—	2	2	no	—
299	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
300	C₂×C₄×D₄	—	2	2	no	—
301	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
302	#495	—	2	8	no	—
303	#452	—	2	8	no	—
304	#449	—	2	8	no	—
305	C₂×#103	C₂²×C₄₃	1	2	yes	—
306	C₂×#103	C₂²×C₄₃	1	2	yes	—
307	C₂×#102	C₂²×C₄₃	1	2	yes	—
308	C₂×#102	C₂²×C₄₃	1	2	yes	—
309	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
310	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
311	#391	C₂²×C₄₃	1	1	yes	characteristic
312	#390	C₂²×C₄₃	1	1	yes	characteristic
313	#388	—	2	2	no	—
314	#386	—	2	2	no	—
315	#382	C₂²×C₄₃	1	1	yes	characteristic
316	#336	C₂²×C₄₃	1	1	yes	characteristic
317	#336	C₂²×C₄₃	1	1	yes	characteristic
318	C₄₃	#25723	1	1	yes	characteristic, direct product factor, Sylow
319	C₂×#41	—	2	4	no	—
320	C₂×#41	—	2	4	no	—
321	C₂×#41	—	2	4	no	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	—	4	2	no	—
324	C₂×#41	—	4	2	no	—
325	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	D₄×C₄₃	1	2	yes	—
334	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
335	C₂×Q₁₆	—	2	4	no	—
336	C₂×Q₁₆	—	2	4	no	—
337	C₂×Q₁₆	—	4	2	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×SD₁₆	—	2	4	no	—
340	C₂×SD₁₆	—	2	4	no	—
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	4	2	no	—
343	C₂×SD₁₆	—	4	2	no	—
344	C₂×D₈	—	2	4	no	—
345	C₂×D₈	—	2	4	no	—
346	C₂×D₈	—	4	2	no	—
347	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
348	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
349	C₄⋊Q₈	—	2	4	no	—
350	#127	—	2	4	no	—
351	#124	—	2	4	no	—
352	#124	—	2	4	no	—
353	#124	D₄×C₄₃	1	8	yes	complemented
354	C₂²⋊Q₈	—	2	4	no	—
355	#121	—	2	16	no	—
356	#121	—	2	4	no	—
357	C₄×D₄	—	2	16	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₄²	—	2	4	no	—
368	C₂×C₄²	D₄×C₄₃	1	2	yes	—
369	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
371	#103	—	2	4	no	—
372	#103	—	2	4	no	—
373	#102	—	2	4	no	—
374	#102	—	2	4	no	—
375	C₂²⋊C₈	D₄×C₄₃	1	8	yes	complemented
376	C₄×C₈	—	2	4	no	—
377	#95	—	2	2	no	—
378	#95	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
382	#41	—	4	8	no	—
383	#41	—	4	8	no	—
384	#41	—	4	8	no	—
385	#41	—	4	8	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
430	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
432	Q₁₆	—	4	8	no	—
433	SD₁₆	—	4	8	no	—
434	SD₁₆	—	4	8	no	—
435	D₈	—	4	8	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
441	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
442	C₄⋊C₄	—	2	8	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₂²⋊C₄	—	4	4	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	4	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	2	no	—
453	C₄²	C₂×D₄×C₄₃	1	4	yes	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	4	no	—
462	C₂³	—	4	4	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	#127×C₄₃	1	2	yes	—
469	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
470	Q₈	—	2	4	no	—
471	Q₈	—	2	4	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	2	no	—
475	Q₈	—	4	2	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	4	16	no	—
479	D₄	—	4	16	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	16	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	#120×C₄₃	1	4	yes	—
506	C₂×C₄	#127×C₄₃	1	2	yes	—
507	C₂×C₄	#135×C₄₃	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
509	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
510	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
511	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
512	C₈	—	2	4	no	—
513	C₈	—	2	4	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	8	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	4	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
530	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
531	C₂²	C₄₃×#535	1	1	yes	characteristic
532	C₂²	C₂×#135×C₄₃	1	2	yes	—
533	C₂²	C₄₃×#575	1	2	yes	—
534	C₄	—	2	2	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	4	no	—
537	C₄	—	4	4	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	1	no	—
540	C₄	—	8	1	no	—
541	C₄	D₄²×C₄₃	1	2	yes	—
542	C₄	D₄²×C₄₃	1	2	yes	—
543	C₂	—	4	2	no	—
544	C₂	—	8	4	no	—
545	C₂	—	16	1	no	—
546	C₂	C₄₃×#2433	1	1	yes	characteristic
547	C₂	C₄₃×#3002	1	2	yes	—
548	C₂	C₄₃×#3147	1	1	yes	characteristic
549	C₂	C₄₃×#3153	1	1	yes	characteristic
550	C₂	C₄₃×#3212	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×#495	C₂	semidirect
3. C₂×C₄₃×#452	C₂	semidirect
4. C₂×C₄₃×#449	C₂	semidirect
5. C₄₃×#2850	C₂	semidirect
6. C₄₃×#2016	C₂	semidirect
7. C₄₃×#2014	C₂	semidirect
8. C₄₃×#2013	C₂	semidirect
9. C₄₃×#2011	C₂	semidirect
10. C₄₃×#1958	C₂	semidirect
11. C₄×C₂²⋊C₈×C₄₃	C₂	semidirect
77. #124×C₄₃	D₄	semidirect
99. C₂²⋊C₈×C₄₃	D₄	semidirect
238. #25723	C₄₃	direct (N × H)
268. C₂×#532	C₂×C₄₃	semidirect
269. C₂×#495	C₂×C₄₃	semidirect
270. C₂×#452	C₂×C₄₃	semidirect
271. C₂×#449	C₂×C₄₃	semidirect
272. #2850	C₂×C₄₃	semidirect
273. #2016	C₂×C₄₃	semidirect
274. #2014	C₂×C₄₃	semidirect
275. #2013	C₂×C₄₃	semidirect
276. #2011	C₂×C₄₃	semidirect
277. #1958	C₂×C₄₃	semidirect
278. C₄×C₂²⋊C₈	C₂×C₄₃	semidirect
318. C₄₃	#25723	direct (N × H)
353. #124	D₄×C₄₃	semidirect
375. 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×#495	2
C₂×C₄₃×#452	2
C₂×C₄₃×#449	2
C₄₃×#2850	2
C₄₃×#2016	2
C₄₃×#2014	2
C₄₃×#2013	2
C₄₃×#2011	2
C₄₃×#1958	2
C₄×C₂²⋊C₈×C₄₃	2
#25723	43

Subgroups — C43×#25723 #24945740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25723 #24945740