Subgroups — C₄₃×#13906 #24933923

Order 11008.

2574 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#390	C₂	1	2	yes	maximal
3	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#380	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1439	C₂	1	4	yes	maximal, complemented
7	C₄₃×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₄₃	—	2	4	no	—
11	C₂×C₄×D₄×C₄₃	—	2	4	no	—
12	C₂×C₄×D₄×C₄₃	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	8	yes	—
19	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#390	—	2	8	no	—
23	C₄₃×#384	—	2	4	no	—
24	C₄₃×#380	—	2	16	no	—
25	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
26	C₂×#95×C₄₃	C₂²	1	8	yes	—
27	C₂×#95×C₄₃	C₂²	1	2	yes	—
28	C₂⁵×C₄₃	C₂³	1	2	yes	—
29	C₂²×D₄×C₄₃	—	2	2	no	—
30	C₂²×D₄×C₄₃	—	2	2	no	—
31	C₂²×D₄×C₄₃	—	2	2	no	—
32	C₂²×D₄×C₄₃	—	2	2	no	—
33	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
34	C₂²×D₄×C₄₃	D₄	1	4	yes	—
35	C₂²×D₄×C₄₃	Q₈	1	4	yes	—
36	C₂³×C₄×C₄₃	—	2	4	no	—
37	C₂³×C₄×C₄₃	—	2	4	no	—
38	C₂³×C₄×C₄₃	—	2	8	no	—
39	C₂³×C₄×C₄₃	—	2	8	no	—
40	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₄×D₄×C₄₃	—	2	32	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
58	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
59	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₃	D₄	1	8	yes	complemented
61	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	4	8	no	—
66	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
67	C₂×C₄²×C₄₃	—	2	4	no	—
68	C₂×C₄²×C₄₃	—	2	4	no	—
69	C₂×C₄²×C₄₃	—	2	4	no	—
70	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
71	C₂×C₄²×C₄₃	D₄	1	4	yes	—
72	C₂×C₄²×C₄₃	D₄	1	4	yes	—
73	#95×C₄₃	—	2	4	no	—
74	#95×C₄₃	—	2	16	no	—
75	C₂⁴×C₄₃	—	2	4	no	—
76	C₂⁴×C₄₃	—	2	2	no	—
77	C₂⁴×C₄₃	—	2	2	no	—
78	C₂⁴×C₄₃	—	2	4	no	—
79	C₂⁴×C₄₃	—	2	2	no	—
80	C₂⁴×C₄₃	—	2	2	no	—
81	C₂⁴×C₄₃	—	2	4	no	—
82	C₂⁴×C₄₃	—	2	4	no	—
83	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
84	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
85	C₂⁴×C₄₃	C₂×Q₈	1	4	yes	—
86	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
87	C₂×D₄×C₄₃	—	2	8	no	—
88	C₂×D₄×C₄₃	—	2	8	no	—
89	C₂×D₄×C₄₃	—	2	8	no	—
90	C₂×D₄×C₄₃	—	2	8	no	—
91	C₂×D₄×C₄₃	—	2	8	no	—
92	C₂×D₄×C₄₃	—	2	8	no	—
93	C₂×D₄×C₄₃	C₄⋊C₄	1	16	yes	complemented
94	C₂²×C₄×C₄₃	—	2	16	no	—
95	C₂²×C₄×C₄₃	—	2	32	no	—
96	C₂²×C₄×C₄₃	—	2	4	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	8	no	—
102	C₂²×C₄×C₄₃	—	2	4	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	4	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	8	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	4	16	no	—
114	C₂²×C₄×C₄₃	—	4	8	no	—
115	C₂²×C₄×C₄₃	—	4	8	no	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₄₃	#41	1	2	yes	—
131	C₂²×C₄×C₄₃	#41	1	2	yes	—
132	C₂²×C₄×C₄₃	#41	1	4	yes	—
133	C₄⋊C₄×C₄₃	—	2	8	no	—
134	C₄⋊C₄×C₄₃	—	2	16	no	—
135	C₄⋊C₄×C₄₃	—	4	8	no	—
136	C₄⋊C₄×C₄₃	—	4	8	no	—
137	C₄⋊C₄×C₄₃	—	4	8	no	—
138	C₂²⋊C₄×C₄₃	—	2	16	no	—
139	C₂²⋊C₄×C₄₃	—	4	32	no	—
140	C₄²×C₄₃	—	4	8	no	—
141	C₄²×C₄₃	C₂²⋊C₄	1	16	yes	complemented
142	C₂³×C₄₃	—	2	4	no	—
143	C₂³×C₄₃	—	2	4	no	—
144	C₂³×C₄₃	—	2	8	no	—
145	C₂³×C₄₃	—	2	8	no	—
146	C₂³×C₄₃	—	2	4	no	—
147	C₂³×C₄₃	—	2	4	no	—
148	C₂³×C₄₃	—	2	4	no	—
149	C₂³×C₄₃	—	2	4	no	—
150	C₂³×C₄₃	—	2	8	no	—
151	C₂³×C₄₃	—	2	8	no	—
152	C₂³×C₄₃	—	2	8	no	—
153	C₂³×C₄₃	—	2	8	no	—
154	C₂³×C₄₃	—	4	4	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	4	no	—
160	C₂³×C₄₃	—	4	4	no	—
161	C₂³×C₄₃	—	4	4	no	—
162	C₂³×C₄₃	—	4	4	no	—
163	C₂³×C₄₃	—	4	4	no	—
164	C₂³×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
165	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
166	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
170	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
171	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
172	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₂³×C₄₃	C₂×#41	1	2	yes	—
174	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
175	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
176	D₄×C₄₃	—	2	32	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	4	no	—
182	C₂×C₄×C₄₃	—	2	8	no	—
183	C₂×C₄×C₄₃	—	2	8	no	—
184	C₂×C₄×C₄₃	—	2	8	no	—
185	C₂×C₄×C₄₃	—	2	8	no	—
186	C₂×C₄×C₄₃	—	4	4	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	4	no	—
191	C₂×C₄×C₄₃	—	4	4	no	—
192	C₂×C₄×C₄₃	—	4	4	no	—
193	C₂×C₄×C₄₃	—	4	32	no	—
194	C₂×C₄×C₄₃	—	4	4	no	—
195	C₂×C₄×C₄₃	—	4	4	no	—
196	C₂×C₄×C₄₃	—	4	4	no	—
197	C₂×C₄×C₄₃	—	4	8	no	—
198	C₂×C₄×C₄₃	—	4	8	no	—
199	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
200	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
201	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
202	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
203	C₂×C₄×C₄₃	#117	1	4	yes	—
204	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
205	C₂×C₄×C₄₃	#121	1	4	yes	—
206	C₂×C₄×C₄₃	#121	1	4	yes	—
207	C₂×C₄×C₄₃	#121	1	8	yes	—
208	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
209	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
210	C₂×C₄×C₄₃	#124	1	4	yes	—
211	C₂×C₄×C₄₃	#127	1	4	yes	—
212	#13906	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₄₃	—	2	16	no	—
214	C₂²×C₄₃	—	2	8	no	—
215	C₂²×C₄₃	—	4	4	no	—
216	C₂²×C₄₃	—	4	4	no	—
217	C₂²×C₄₃	—	4	8	no	—
218	C₂²×C₄₃	—	4	8	no	—
219	C₂²×C₄₃	—	4	8	no	—
220	C₂²×C₄₃	—	4	4	no	—
221	C₂²×C₄₃	—	4	4	no	—
222	C₂²×C₄₃	—	4	4	no	—
223	C₂²×C₄₃	—	4	4	no	—
224	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
225	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
226	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
227	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
228	C₂²×C₄₃	#520	1	2	yes	—
229	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
230	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
231	C₂²×C₄₃	C₂×#121	1	2	yes	—
232	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
233	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
234	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
235	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
236	C₂²×C₄₃	#535	1	1	yes	characteristic
237	C₂²×C₄₃	#536	1	1	yes	characteristic
238	C₂²×C₄₃	#537	1	2	yes	—
239	C₂²×C₄₃	D₄²	1	2	yes	—
240	C₂²×C₄₃	#547	1	2	yes	—
241	C₂²×C₄₃	#547	1	2	yes	—
242	C₂²×C₄₃	D₄×Q₈	1	2	yes	—
243	C₂²×C₄₃	#550	1	2	yes	—
244	C₂²×C₄₃	#554	1	2	yes	—
245	C₂²×C₄₃	#555	1	2	yes	—
246	C₂²×C₄₃	#556	1	2	yes	—
247	C₄×C₄₃	—	2	4	no	—
248	C₄×C₄₃	—	4	8	no	—
249	C₄×C₄₃	—	4	4	no	—
250	C₄×C₄₃	—	8	4	no	—
251	C₄×C₄₃	#380	1	8	yes	complemented
252	C₄×C₄₃	#390	1	8	yes	complemented
253	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
254	C₂×#390	C₂×C₄₃	1	2	yes	—
255	C₂×#384	C₂×C₄₃	1	1	yes	characteristic, complemented
256	C₂×#380	C₂×C₄₃	1	4	yes	complemented
257	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
258	#1439	C₂×C₄₃	1	4	yes	complemented
259	C₄⋊#95	C₂×C₄₃	1	2	yes	complemented
260	C₂×C₄₃	—	4	8	no	—
261	C₂×C₄₃	C₂×#380	1	1	yes	characteristic
262	C₂×C₄₃	C₂×#390	1	1	yes	characteristic
263	C₂×C₄₃	#2311	1	1	yes	characteristic
264	C₂×C₄₃	D₄×C₄⋊C₄	1	2	yes	—
265	C₂×C₄₃	#2354	1	2	yes	—
266	C₂×C₄₃	#2537	1	2	yes	—
267	C₂×C₄₃	#2538	1	2	yes	—
268	C₂×C₄₃	#2541	1	1	yes	characteristic
269	C₂×C₄₃	#2542	1	1	yes	characteristic
270	C₂×C₄₃	#2547	1	1	yes	characteristic
271	C₂×C₄₃	#2563	1	1	yes	characteristic
272	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
274	C₂×C₄×D₄	—	2	4	no	—
275	C₂×C₄×D₄	—	2	4	no	—
276	C₂×C₄×D₄	C₄×C₄₃	1	8	yes	complemented
277	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
278	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
282	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	8	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
284	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
285	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
286	#390	—	2	8	no	—
287	#384	—	2	4	no	—
288	#380	—	2	16	no	—
289	C₄×C₄⋊C₄	—	2	4	no	—
290	C₂×#95	C₂²×C₄₃	1	8	yes	—
291	C₂×#95	C₂²×C₄₃	1	2	yes	—
292	C₄₃	#13906	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁵	C₂³×C₄₃	1	2	yes	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	2	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
299	C₂²×D₄	D₄×C₄₃	1	4	yes	—
300	C₂²×D₄	Q₈×C₄₃	1	4	yes	—
301	C₂³×C₄	—	2	4	no	—
302	C₂³×C₄	—	2	4	no	—
303	C₂³×C₄	—	2	8	no	—
304	C₂³×C₄	—	2	8	no	—
305	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	—
306	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
307	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
308	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
309	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
312	C₄×D₄	—	2	32	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	8	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	4	4	no	—
324	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
325	C₂×C₄⋊C₄	D₄×C₄₃	1	8	yes	complemented
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	—	2	4	no	—
328	C₂×C₂²⋊C₄	—	2	16	no	—
329	C₂×C₂²⋊C₄	—	2	16	no	—
330	C₂×C₂²⋊C₄	—	4	8	no	—
331	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
332	C₂×C₄²	—	2	4	no	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
336	C₂×C₄²	D₄×C₄₃	1	4	yes	—
337	C₂×C₄²	D₄×C₄₃	1	4	yes	—
338	#95	—	2	4	no	—
339	#95	—	2	16	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	—	2	2	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	4	no	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
349	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
350	C₂⁴	C₂×Q₈×C₄₃	1	4	yes	—
351	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	C₄⋊C₄×C₄₃	1	16	yes	complemented
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	16	no	—
372	C₂²×C₄	—	2	32	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	4	16	no	—
379	C₂²×C₄	—	4	8	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
382	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
383	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
384	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
386	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
391	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
393	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
394	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
395	C₂²×C₄	#41×C₄₃	1	2	yes	—
396	C₂²×C₄	#41×C₄₃	1	2	yes	—
397	C₂²×C₄	#41×C₄₃	1	4	yes	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	16	no	—
400	C₄⋊C₄	—	4	8	no	—
401	C₄⋊C₄	—	4	8	no	—
402	C₄⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	2	16	no	—
404	C₂²⋊C₄	—	4	32	no	—
405	C₄²	—	4	8	no	—
406	C₄²	C₂²⋊C₄×C₄₃	1	16	yes	complemented
407	C₂³	—	2	4	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	8	no	—
410	C₂³	—	2	8	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	8	no	—
418	C₂³	—	2	8	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	C₂×C₄⋊C₄×C₄₃	1	8	yes	—
430	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
431	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
432	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
433	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
434	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
435	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
436	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
437	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
438	C₂³	C₂×#41×C₄₃	1	2	yes	—
439	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
440	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
441	D₄	—	2	32	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	32	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
466	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
467	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
468	C₂×C₄	#117×C₄₃	1	4	yes	—
469	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
470	C₂×C₄	#121×C₄₃	1	4	yes	—
471	C₂×C₄	#121×C₄₃	1	4	yes	—
472	C₂×C₄	#121×C₄₃	1	8	yes	—
473	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
474	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
475	C₂×C₄	#124×C₄₃	1	4	yes	—
476	C₂×C₄	#127×C₄₃	1	4	yes	—
477	C₂²	—	2	16	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	4	8	no	—
480	C₂²	—	4	8	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
489	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
490	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
491	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
492	C₂²	C₄₃×#520	1	2	yes	—
493	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
494	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
495	C₂²	C₂×#121×C₄₃	1	2	yes	—
496	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
497	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
498	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
499	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
500	C₂²	C₄₃×#535	1	1	yes	characteristic
501	C₂²	C₄₃×#536	1	1	yes	characteristic
502	C₂²	C₄₃×#537	1	2	yes	—
503	C₂²	D₄²×C₄₃	1	2	yes	—
504	C₂²	C₄₃×#547	1	2	yes	—
505	C₂²	C₄₃×#547	1	2	yes	—
506	C₂²	D₄×Q₈×C₄₃	1	2	yes	—
507	C₂²	C₄₃×#550	1	2	yes	—
508	C₂²	C₄₃×#554	1	2	yes	—
509	C₂²	C₄₃×#555	1	2	yes	—
510	C₂²	C₄₃×#556	1	2	yes	—
511	C₄	—	2	4	no	—
512	C₄	—	4	8	no	—
513	C₄	—	4	4	no	—
514	C₄	—	8	4	no	—
515	C₄	C₄₃×#380	1	8	yes	complemented
516	C₄	C₄₃×#390	1	8	yes	complemented
517	C₂	—	4	8	no	—
518	C₂	C₂×C₄₃×#380	1	1	yes	characteristic
519	C₂	C₂×C₄₃×#390	1	1	yes	characteristic
520	C₂	C₄₃×#2311	1	1	yes	characteristic
521	C₂	D₄×C₄⋊C₄×C₄₃	1	2	yes	—
522	C₂	C₄₃×#2354	1	2	yes	—
523	C₂	C₄₃×#2537	1	2	yes	—
524	C₂	C₄₃×#2538	1	2	yes	—
525	C₂	C₄₃×#2541	1	1	yes	characteristic
526	C₂	C₄₃×#2542	1	1	yes	characteristic
527	C₂	C₄₃×#2547	1	1	yes	characteristic
528	C₂	C₄₃×#2563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
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
3. C₂×C₄₃×#384	C₂	semidirect
4. C₂×C₄₃×#380	C₂	semidirect
5. C₂×C₄×C₄⋊C₄×C₄₃	C₂	semidirect
6. C₄₃×#1439	C₂	semidirect
7. C₄₃×C₄⋊#95	C₂	semidirect
12. C₂×C₄×D₄×C₄₃	C₄	semidirect
60. C₂×C₄⋊C₄×C₄₃	D₄	semidirect
93. C₂×D₄×C₄₃	C₄⋊C₄	semidirect
141. C₄²×C₄₃	C₂²⋊C₄	semidirect
212. #13906	C₄₃	direct (N × H)
251. C₄×C₄₃	#380	semidirect
252. C₄×C₄₃	#390	semidirect
255. C₂×#384	C₂×C₄₃	semidirect
256. C₂×#380	C₂×C₄₃	semidirect
257. C₂×C₄×C₄⋊C₄	C₂×C₄₃	semidirect
258. #1439	C₂×C₄₃	semidirect
259. C₄⋊#95	C₂×C₄₃	semidirect
276. C₂×C₄×D₄	C₄×C₄₃	semidirect
292. C₄₃	#13906	direct (N × H)
325. C₂×C₄⋊C₄	D₄×C₄₃	semidirect
358. C₂×D₄	C₄⋊C₄×C₄₃	semidirect
406. C₄²	C₂²⋊C₄×C₄₃	semidirect
515. C₄	C₄₃×#380	semidirect
516. C₄	C₄₃×#390	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#390	2
C₂×C₄₃×#384	2
C₂×C₄₃×#380	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1439	2
C₄₃×C₄⋊#95	2
#13906	43

Subgroups — C43×#13906 #24933923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13906 #24933923