Subgroups — C₄₃×#13909 #24933926

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1441	C₂	1	4	yes	maximal
7	C₄₃×#1436	C₂	1	4	yes	maximal
8	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#384	—	2	4	no	—
21	C₄₃×#382	—	2	4	no	—
22	C₄₃×#382	—	2	4	no	—
23	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
24	C₄×C₄⋊C₄×C₄₃	C₄	1	8	yes	complemented
25	C₂×#95×C₄₃	C₂²	1	4	yes	—
26	C₂×#95×C₄₃	C₂²	1	2	yes	—
27	C₂×#95×C₄₃	C₂²	1	4	yes	—
28	C₂×#95×C₄₃	C₂²	1	2	yes	—
29	C₂×#95×C₄₃	C₂²	1	2	yes	—
30	C₂×#95×C₄₃	C₂²	1	4	yes	—
31	C₂×#95×C₄₃	C₂²	1	2	yes	—
32	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
56	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
57	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₃	Q₈	1	4	yes	—
59	C₂×C₄²×C₄₃	—	2	2	no	—
60	C₂×C₄²×C₄₃	—	2	2	no	—
61	C₂×C₄²×C₄₃	—	2	2	no	—
62	C₂×C₄²×C₄₃	—	2	2	no	—
63	C₂×C₄²×C₄₃	—	2	4	no	—
64	C₂×C₄²×C₄₃	—	4	4	no	—
65	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₃	D₄	1	4	yes	—
69	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
70	#95×C₄₃	—	2	4	no	—
71	#95×C₄₃	—	2	8	no	—
72	#95×C₄₃	—	2	4	no	—
73	#95×C₄₃	—	2	4	no	—
74	#95×C₄₃	—	2	8	no	—
75	#95×C₄₃	—	4	4	no	—
76	#95×C₄₃	C₂×C₄	1	8	yes	—
77	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	—	2	2	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	4	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	4	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	4	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	4	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
121	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₄₃	#41	1	4	yes	—
126	C₂²×C₄×C₄₃	#41	1	4	yes	—
127	C₂²×C₄×C₄₃	#41	1	2	yes	—
128	C₂²×C₄×C₄₃	#41	1	2	yes	—
129	C₄⋊C₄×C₄₃	—	2	16	no	—
130	C₄⋊C₄×C₄₃	—	2	8	no	—
131	C₄⋊C₄×C₄₃	—	2	8	no	—
132	C₄⋊C₄×C₄₃	—	4	16	no	—
133	C₄⋊C₄×C₄₃	—	4	4	no	—
134	C₄⋊C₄×C₄₃	—	4	4	no	—
135	C₄²×C₄₃	—	2	8	no	—
136	C₄²×C₄₃	—	2	8	no	—
137	C₄²×C₄₃	—	4	8	no	—
138	C₄²×C₄₃	C₄⋊C₄	1	16	yes	complemented
139	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
140	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
141	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
142	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
143	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
144	C₂³×C₄₃	C₂×#41	1	2	yes	—
145	C₂³×C₄₃	C₂×#41	1	2	yes	—
146	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
147	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
148	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
149	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
150	C₂×C₄×C₄₃	—	2	4	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	2	4	no	—
153	C₂×C₄×C₄₃	—	2	4	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	4	no	—
168	C₂×C₄×C₄₃	—	2	4	no	—
169	C₂×C₄×C₄₃	—	2	8	no	—
170	C₂×C₄×C₄₃	—	2	8	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	4	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	4	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	—	4	4	no	—
190	C₂×C₄×C₄₃	—	4	4	no	—
191	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
192	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
193	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
194	C₂×C₄×C₄₃	#117	1	8	yes	—
195	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
196	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
197	C₂×C₄×C₄₃	#121	1	4	yes	—
198	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
199	C₂×C₄×C₄₃	#125	1	4	yes	—
200	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
201	#13909	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×C₄₃	C₂×#117	1	2	yes	—
204	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
206	C₂²×C₄₃	#520	1	2	yes	—
207	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
208	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₂²×C₄₃	C₂×#125	1	1	yes	characteristic
210	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
211	C₂²×C₄₃	#532	1	1	yes	characteristic
212	C₂²×C₄₃	#532	1	1	yes	characteristic
213	C₂²×C₄₃	#533	1	2	yes	—
214	C₂²×C₄₃	#535	1	1	yes	characteristic
215	C₂²×C₄₃	#536	1	1	yes	characteristic
216	C₂²×C₄₃	#544	1	2	yes	—
217	C₂²×C₄₃	#546	1	2	yes	—
218	C₂²×C₄₃	#548	1	2	yes	—
219	C₂²×C₄₃	#552	1	2	yes	—
220	C₂²×C₄₃	#553	1	2	yes	—
221	C₂²×C₄₃	#554	1	2	yes	—
222	C₂²×C₄₃	#556	1	2	yes	—
223	C₂²×C₄₃	#557	1	2	yes	—
224	C₂²×C₄₃	#559	1	2	yes	—
225	C₄×C₄₃	—	2	4	no	—
226	C₄×C₄₃	—	2	8	no	—
227	C₄×C₄₃	—	2	4	no	—
228	C₄×C₄₃	—	4	4	no	—
229	C₄×C₄₃	—	4	4	no	—
230	C₄×C₄₃	—	4	4	no	—
231	C₄×C₄₃	—	8	2	no	—
232	C₄×C₄₃	—	8	2	no	—
233	C₄×C₄₃	#389	1	8	yes	—
234	C₂×#384	C₂×C₄₃	1	1	yes	characteristic
235	C₂×#382	C₂×C₄₃	1	1	yes	characteristic
236	C₂×#382	C₂×C₄₃	1	1	yes	characteristic
237	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
238	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
239	#1441	C₂×C₄₃	1	4	yes	—
240	#1436	C₂×C₄₃	1	4	yes	—
241	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
242	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
243	C₂×C₄₃	#2285	1	1	yes	characteristic
244	C₂×C₄₃	C₂×#389	1	1	yes	characteristic
245	C₂×C₄₃	#2317	1	1	yes	characteristic
246	C₂×C₄₃	#2352	1	2	yes	—
247	C₂×C₄₃	#2355	1	2	yes	—
248	C₂×C₄₃	#2544	1	1	yes	characteristic
249	C₂×C₄₃	#2545	1	1	yes	characteristic
250	C₂×C₄₃	#2550	1	2	yes	—
251	C₂×C₄₃	#2565	1	1	yes	characteristic
252	C₂×C₄₃	#2566	1	1	yes	characteristic
253	C₂×C₄₃	#2570	1	2	yes	—
254	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
257	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
258	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
260	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
261	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
262	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
263	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
264	#384	—	2	4	no	—
265	#382	—	2	4	no	—
266	#382	—	2	4	no	—
267	C₄×C₄⋊C₄	—	2	4	no	—
268	C₄×C₄⋊C₄	C₄×C₄₃	1	8	yes	complemented
269	C₂×#95	C₂²×C₄₃	1	4	yes	—
270	C₂×#95	C₂²×C₄₃	1	2	yes	—
271	C₂×#95	C₂²×C₄₃	1	4	yes	—
272	C₂×#95	C₂²×C₄₃	1	2	yes	—
273	C₂×#95	C₂²×C₄₃	1	2	yes	—
274	C₂×#95	C₂²×C₄₃	1	4	yes	—
275	C₂×#95	C₂²×C₄₃	1	2	yes	—
276	C₄₃	#13909	1	1	yes	characteristic, direct product factor, Sylow
277	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
278	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
280	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
281	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
282	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
285	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	2	4	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	8	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	8	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	4	4	no	—
301	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
302	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
303	C₂×C₄⋊C₄	Q₈×C₄₃	1	4	yes	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	—	4	4	no	—
310	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
311	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
312	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
313	C₂×C₄²	D₄×C₄₃	1	4	yes	—
314	C₂×C₄²	Q₈×C₄₃	1	4	yes	—
315	#95	—	2	4	no	—
316	#95	—	2	8	no	—
317	#95	—	2	4	no	—
318	#95	—	2	4	no	—
319	#95	—	2	8	no	—
320	#95	—	4	4	no	—
321	#95	C₂×C₄×C₄₃	1	8	yes	—
322	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
358	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
359	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
361	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
365	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
366	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
367	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
368	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
369	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
370	C₂²×C₄	#41×C₄₃	1	4	yes	—
371	C₂²×C₄	#41×C₄₃	1	4	yes	—
372	C₂²×C₄	#41×C₄₃	1	2	yes	—
373	C₂²×C₄	#41×C₄₃	1	2	yes	—
374	C₄⋊C₄	—	2	16	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	4	16	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄²	—	2	8	no	—
381	C₄²	—	2	8	no	—
382	C₄²	—	4	8	no	—
383	C₄²	C₄⋊C₄×C₄₃	1	16	yes	complemented
384	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
385	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
386	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
387	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
388	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
389	C₂³	C₂×#41×C₄₃	1	2	yes	—
390	C₂³	C₂×#41×C₄₃	1	2	yes	—
391	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
392	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
393	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
394	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
437	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
438	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
439	C₂×C₄	#117×C₄₃	1	8	yes	—
440	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
441	C₂×C₄	C₄×Q₈×C₄₃	1	4	yes	—
442	C₂×C₄	#121×C₄₃	1	4	yes	—
443	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
444	C₂×C₄	#125×C₄₃	1	4	yes	—
445	C₂×C₄	C₄⋊Q₈×C₄₃	1	4	yes	—
446	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
447	C₂²	C₂×#117×C₄₃	1	2	yes	—
448	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
449	C₂²	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
450	C₂²	C₄₃×#520	1	2	yes	—
451	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
452	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
453	C₂²	C₂×#125×C₄₃	1	1	yes	characteristic
454	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
455	C₂²	C₄₃×#532	1	1	yes	characteristic
456	C₂²	C₄₃×#532	1	1	yes	characteristic
457	C₂²	C₄₃×#533	1	2	yes	—
458	C₂²	C₄₃×#535	1	1	yes	characteristic
459	C₂²	C₄₃×#536	1	1	yes	characteristic
460	C₂²	C₄₃×#544	1	2	yes	—
461	C₂²	C₄₃×#546	1	2	yes	—
462	C₂²	C₄₃×#548	1	2	yes	—
463	C₂²	C₄₃×#552	1	2	yes	—
464	C₂²	C₄₃×#553	1	2	yes	—
465	C₂²	C₄₃×#554	1	2	yes	—
466	C₂²	C₄₃×#556	1	2	yes	—
467	C₂²	C₄₃×#557	1	2	yes	—
468	C₂²	C₄₃×#559	1	2	yes	—
469	C₄	—	2	8	no	—
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	4	no	—
475	C₄	—	8	2	no	—
476	C₄	—	8	2	no	—
477	C₄	C₄₃×#389	1	8	yes	—
478	C₂	C₄₃×#2285	1	1	yes	characteristic
479	C₂	C₂×C₄₃×#389	1	1	yes	characteristic
480	C₂	C₄₃×#2317	1	1	yes	characteristic
481	C₂	C₄₃×#2352	1	2	yes	—
482	C₂	C₄₃×#2355	1	2	yes	—
483	C₂	C₄₃×#2544	1	1	yes	characteristic
484	C₂	C₄₃×#2545	1	1	yes	characteristic
485	C₂	C₄₃×#2550	1	2	yes	—
486	C₂	C₄₃×#2565	1	1	yes	characteristic
487	C₂	C₄₃×#2566	1	1	yes	characteristic
488	C₂	C₄₃×#2570	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
24. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
138. C₄²×C₄₃	C₄⋊C₄	semidirect
201. #13909	C₄₃	direct (N × H)
268. C₄×C₄⋊C₄	C₄×C₄₃	semidirect
276. C₄₃	#13909	direct (N × H)
383. C₄²	C₄⋊C₄×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×#384	2
C₂×C₄₃×#382	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1441	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
#13909	43

Subgroups — C43×#13909 #24933926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13909 #24933926