Subgroups — C₄₃×#34376 #24954393

Order 11008.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2376	C₂	1	4	yes	maximal, complemented
3	C₄₃×#2359	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2345	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2342	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2342	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₄₃	C₂	1	2	yes	maximal
8	C₄₃×#2335	C₂	1	4	yes	maximal, complemented
9	C₄₃×#2322	C₂	1	4	yes	maximal, complemented
10	C₄₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#123×C₄₃	C₄	1	16	yes	complemented
19	C₂×#123×C₄₃	C₂²	1	2	yes	—
20	C₂×#123×C₄₃	C₂²	1	2	yes	—
21	C₂×#123×C₄₃	C₂²	1	2	yes	—
22	C₂×#123×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
24	C₂×#117×C₄₃	C₂²	1	2	yes	—
25	C₂×#117×C₄₃	C₂²	1	2	yes	complemented
26	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#390	C₂²	1	4	yes	—
35	C₄₃×#389	C₂²	1	4	yes	complemented
36	C₄₃×#389	C₂²	1	4	yes	complemented
37	C₄₃×#389	C₂²	1	4	yes	complemented
38	C₄₃×#388	C₂²	1	4	yes	complemented
39	C₄₃×#388	C₂²	1	4	yes	complemented
40	C₄₃×#388	C₂²	1	4	yes	complemented
41	C₄₃×#388	C₂²	1	4	yes	complemented
42	C₄₃×#388	C₂²	1	4	yes	complemented
43	C₄₃×#388	C₂²	1	4	yes	complemented
44	C₄₃×#387	C₂²	1	4	yes	complemented
45	C₄₃×#387	C₂²	1	4	yes	complemented
46	C₄₃×#387	C₂²	1	4	yes	complemented
47	C₄₃×#387	C₂²	1	4	yes	complemented
48	C₄₃×#386	C₂²	1	4	yes	—
49	C₄₃×#386	C₂²	1	4	yes	—
50	C₄₃×#385	C₂²	1	4	yes	complemented
51	C₄₃×#385	C₂²	1	4	yes	complemented
52	C₄₃×#385	C₂²	1	4	yes	complemented
53	C₄₃×#385	C₂²	1	4	yes	complemented
54	C₄₃×#381	C₂²	1	2	yes	—
55	C₄₃×#381	C₂²	1	2	yes	complemented
56	C₄₃×#380	C₂²	1	2	yes	—
57	C₄₃×#380	C₂²	1	2	yes	—
58	C₄₃×#380	C₂²	1	2	yes	—
59	C₄₃×#380	C₂²	1	1	yes	characteristic
60	C₄₃×#380	C₂²	1	1	yes	characteristic
61	C₄₃×#380	C₂²	1	1	yes	characteristic
62	C₄₃×#380	C₂²	1	1	yes	characteristic
63	C₄₃×#380	C₂²	1	2	yes	complemented
64	C₄₃×#380	C₂²	1	2	yes	complemented
65	C₄₃×#380	C₂²	1	2	yes	complemented
66	C₄₃×#379	C₂²	1	2	yes	—
67	C₄₃×#379	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₄₃	C₂²	1	4	yes	complemented
69	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	complemented
75	C₂×#95×C₄₃	C₂²	1	2	yes	complemented
76	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
77	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₄₃	—	4	4	no	—
79	C₂²×D₄×C₄₃	C₂×C₄	1	8	yes	—
80	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₄₃	—	4	4	no	—
83	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	complemented
84	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
88	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
89	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
95	#123×C₄₃	C₂×C₄	1	16	yes	complemented
96	#123×C₄₃	C₂×C₄	1	16	yes	complemented
97	#123×C₄₃	C₂×C₄	1	16	yes	complemented
98	#123×C₄₃	C₂×C₄	1	16	yes	complemented
99	C₄×D₄×C₄₃	—	4	8	no	—
100	#117×C₄₃	—	4	4	no	—
101	#117×C₄₃	—	4	4	no	—
102	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
103	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
104	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
105	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
118	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
119	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
120	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
121	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
122	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
138	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
140	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
141	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
142	#95×C₄₃	C₂³	1	4	yes	—
143	#95×C₄₃	C₂³	1	2	yes	—
144	#95×C₄₃	C₂³	1	2	yes	—
145	#95×C₄₃	C₂³	1	4	yes	—
146	#95×C₄₃	C₂³	1	4	yes	—
147	#95×C₄₃	C₂³	1	4	yes	—
148	#95×C₄₃	C₂³	1	2	yes	—
149	#95×C₄₃	C₂³	1	2	yes	—
150	#95×C₄₃	C₂³	1	4	yes	—
151	#95×C₄₃	C₂³	1	4	yes	—
152	#95×C₄₃	C₂³	1	4	yes	—
153	#95×C₄₃	C₂³	1	4	yes	—
154	C₂⁴×C₄₃	—	2	2	no	—
155	C₂⁴×C₄₃	—	2	4	no	—
156	C₂⁴×C₄₃	—	2	2	no	—
157	C₂⁴×C₄₃	—	2	2	no	—
158	C₂⁴×C₄₃	—	2	2	no	—
159	C₂⁴×C₄₃	—	4	2	no	—
160	C₂⁴×C₄₃	—	4	2	no	—
161	C₂⁴×C₄₃	—	4	2	no	—
162	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
163	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
164	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
166	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₂×D₄×C₄₃	—	2	8	no	—
169	C₂×D₄×C₄₃	—	4	4	no	—
170	C₂×D₄×C₄₃	—	4	16	no	—
171	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
173	C₂²×C₄×C₄₃	—	2	4	no	—
174	C₂²×C₄×C₄₃	—	2	2	no	—
175	C₂²×C₄×C₄₃	—	2	4	no	—
176	C₂²×C₄×C₄₃	—	2	8	no	—
177	C₂²×C₄×C₄₃	—	2	2	no	—
178	C₂²×C₄×C₄₃	—	4	16	no	—
179	C₂²×C₄×C₄₃	—	4	2	no	—
180	C₂²×C₄×C₄₃	—	4	2	no	—
181	C₂²×C₄×C₄₃	—	4	2	no	—
182	C₂²×C₄×C₄₃	—	4	2	no	—
183	C₂²×C₄×C₄₃	—	4	2	no	—
184	C₂²×C₄×C₄₃	—	4	2	no	—
185	C₂²×C₄×C₄₃	—	4	4	no	—
186	C₂²×C₄×C₄₃	—	4	4	no	—
187	C₂²×C₄×C₄₃	—	4	4	no	—
188	C₂²×C₄×C₄₃	—	4	4	no	—
189	C₂²×C₄×C₄₃	—	4	4	no	—
190	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
191	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
195	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
196	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
197	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
199	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
210	C₄⋊C₄×C₄₃	—	4	2	no	—
211	C₄⋊C₄×C₄₃	—	4	4	no	—
212	C₄⋊C₄×C₄₃	—	4	2	no	—
213	C₄⋊C₄×C₄₃	—	4	4	no	—
214	C₄⋊C₄×C₄₃	—	4	4	no	—
215	C₄⋊C₄×C₄₃	—	4	2	no	—
216	C₄⋊C₄×C₄₃	—	4	2	no	—
217	C₄⋊C₄×C₄₃	—	4	4	no	—
218	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
219	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
220	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
221	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₄₃	—	2	4	no	—
223	C₂²⋊C₄×C₄₃	—	2	4	no	—
224	C₂²⋊C₄×C₄₃	—	2	4	no	—
225	C₂²⋊C₄×C₄₃	—	2	8	no	—
226	C₂²⋊C₄×C₄₃	—	2	4	no	—
227	C₂²⋊C₄×C₄₃	—	4	4	no	—
228	C₂²⋊C₄×C₄₃	—	4	4	no	—
229	C₂²⋊C₄×C₄₃	—	4	4	no	—
230	C₂²⋊C₄×C₄₃	—	4	4	no	—
231	C₂²⋊C₄×C₄₃	—	4	4	no	—
232	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
233	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
234	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
236	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
237	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
238	C₄²×C₄₃	—	4	4	no	—
239	C₄²×C₄₃	—	4	4	no	—
240	C₄²×C₄₃	—	4	4	no	—
241	C₄²×C₄₃	—	4	4	no	—
242	C₂³×C₄₃	—	2	1	no	—
243	C₂³×C₄₃	—	2	2	no	—
244	C₂³×C₄₃	—	2	1	no	—
245	C₂³×C₄₃	—	2	2	no	—
246	C₂³×C₄₃	—	2	2	no	—
247	C₂³×C₄₃	—	2	8	no	—
248	C₂³×C₄₃	—	2	8	no	—
249	C₂³×C₄₃	—	2	1	no	—
250	C₂³×C₄₃	—	2	2	no	—
251	C₂³×C₄₃	—	2	4	no	—
252	C₂³×C₄₃	—	2	2	no	—
253	C₂³×C₄₃	—	2	1	no	—
254	C₂³×C₄₃	—	2	2	no	—
255	C₂³×C₄₃	—	2	2	no	—
256	C₂³×C₄₃	—	2	4	no	—
257	C₂³×C₄₃	—	2	8	no	—
258	C₂³×C₄₃	—	4	4	no	—
259	C₂³×C₄₃	—	4	4	no	—
260	C₂³×C₄₃	—	4	4	no	—
261	C₂³×C₄₃	—	4	8	no	—
262	C₂³×C₄₃	—	4	8	no	—
263	C₂³×C₄₃	—	8	4	no	—
264	C₂³×C₄₃	—	8	4	no	—
265	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
266	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
267	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
268	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
269	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
270	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
271	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
272	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
273	D₄×C₄₃	—	2	16	no	—
274	D₄×C₄₃	—	4	8	no	—
275	C₂×C₄×C₄₃	—	2	8	no	—
276	C₂×C₄×C₄₃	—	2	8	no	—
277	C₂×C₄×C₄₃	—	2	8	no	—
278	C₂×C₄×C₄₃	—	2	2	no	—
279	C₂×C₄×C₄₃	—	2	2	no	—
280	C₂×C₄×C₄₃	—	2	4	no	—
281	C₂×C₄×C₄₃	—	2	2	no	—
282	C₂×C₄×C₄₃	—	2	2	no	—
283	C₂×C₄×C₄₃	—	2	2	no	—
284	C₂×C₄×C₄₃	—	2	2	no	—
285	C₂×C₄×C₄₃	—	2	4	no	—
286	C₂×C₄×C₄₃	—	2	4	no	—
287	C₂×C₄×C₄₃	—	2	4	no	—
288	C₂×C₄×C₄₃	—	2	4	no	—
289	C₂×C₄×C₄₃	—	2	4	no	—
290	C₂×C₄×C₄₃	—	2	4	no	—
291	C₂×C₄×C₄₃	—	2	4	no	—
292	C₂×C₄×C₄₃	—	2	4	no	—
293	C₂×C₄×C₄₃	—	2	4	no	—
294	C₂×C₄×C₄₃	—	2	4	no	—
295	C₂×C₄×C₄₃	—	2	4	no	—
296	C₂×C₄×C₄₃	—	2	4	no	—
297	C₂×C₄×C₄₃	—	2	4	no	—
298	C₂×C₄×C₄₃	—	4	4	no	—
299	C₂×C₄×C₄₃	—	4	4	no	—
300	C₂×C₄×C₄₃	—	4	4	no	—
301	C₂×C₄×C₄₃	—	4	4	no	—
302	C₂×C₄×C₄₃	—	4	4	no	—
303	C₂×C₄×C₄₃	—	4	4	no	—
304	C₂×C₄×C₄₃	—	8	8	no	—
305	C₂×C₄×C₄₃	—	8	8	no	—
306	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
309	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
310	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
311	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
313	#34376	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂²×C₄₃	—	2	2	no	—
315	C₂²×C₄₃	—	2	2	no	—
316	C₂²×C₄₃	—	2	2	no	—
317	C₂²×C₄₃	—	2	2	no	—
318	C₂²×C₄₃	—	2	4	no	—
319	C₂²×C₄₃	—	2	4	no	—
320	C₂²×C₄₃	—	2	4	no	—
321	C₂²×C₄₃	—	2	4	no	—
322	C₂²×C₄₃	—	2	2	no	—
323	C₂²×C₄₃	—	2	4	no	—
324	C₂²×C₄₃	—	2	2	no	—
325	C₂²×C₄₃	—	2	4	no	—
326	C₂²×C₄₃	—	2	2	no	—
327	C₂²×C₄₃	—	2	4	no	—
328	C₂²×C₄₃	—	4	16	no	—
329	C₂²×C₄₃	—	4	2	no	—
330	C₂²×C₄₃	—	4	4	no	—
331	C₂²×C₄₃	—	4	2	no	—
332	C₂²×C₄₃	—	4	4	no	—
333	C₂²×C₄₃	—	8	8	no	—
334	C₂²×C₄₃	#518	1	4	yes	—
335	C₂²×C₄₃	#520	1	4	yes	—
336	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
337	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
338	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
340	C₂²×C₄₃	#585	1	2	yes	—
341	C₄×C₄₃	—	2	2	no	—
342	C₄×C₄₃	—	2	2	no	—
343	C₄×C₄₃	—	2	2	no	—
344	C₄×C₄₃	—	2	2	no	—
345	C₄×C₄₃	—	2	4	no	—
346	C₄×C₄₃	—	2	4	no	—
347	C₄×C₄₃	—	2	4	no	—
348	C₄×C₄₃	—	4	4	no	—
349	C₄×C₄₃	—	4	4	no	—
350	C₄×C₄₃	—	4	4	no	—
351	C₄×C₄₃	—	4	4	no	—
352	C₂²×#123	C₂×C₄₃	1	1	yes	characteristic
353	#2376	C₂×C₄₃	1	4	yes	complemented
354	#2359	C₂×C₄₃	1	4	yes	complemented
355	#2345	C₂×C₄₃	1	2	yes	complemented
356	#2342	C₂×C₄₃	1	2	yes	complemented
357	#2342	C₂×C₄₃	1	2	yes	complemented
358	D₄×C₂²⋊C₄	C₂×C₄₃	1	2	yes	—
359	#2335	C₂×C₄₃	1	4	yes	complemented
360	#2322	C₂×C₄₃	1	4	yes	complemented
361	#2316	C₂×C₄₃	1	1	yes	characteristic, complemented
362	#2315	C₂×C₄₃	1	1	yes	characteristic, complemented
363	#2313	C₂×C₄₃	1	1	yes	characteristic, complemented
364	#2312	C₂×C₄₃	1	1	yes	characteristic, complemented
365	#2280	C₂×C₄₃	1	1	yes	characteristic, complemented
366	C₂×#380	C₂×C₄₃	1	1	yes	characteristic, complemented
367	C₂×C₄₃	—	2	4	no	—
368	C₂×C₄₃	—	2	4	no	—
369	C₂×C₄₃	—	4	2	no	—
370	C₂×C₄₃	—	4	4	no	—
371	C₂×C₄₃	C₂×#518	1	1	yes	characteristic
372	C₂×C₄₃	C₂×#520	1	1	yes	characteristic
373	C₂×C₄₃	#3428	1	1	yes	characteristic
374	C₂×C₄₃	#3534	1	2	yes	—
375	C₂×C₄₃	#3535	1	2	yes	—
376	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
377	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
378	C₂×#123	C₄×C₄₃	1	16	yes	complemented
379	C₂×#123	C₂²×C₄₃	1	2	yes	—
380	C₂×#123	C₂²×C₄₃	1	2	yes	—
381	C₂×#123	C₂²×C₄₃	1	2	yes	—
382	C₂×#123	C₂²×C₄₃	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
384	C₂×#117	C₂²×C₄₃	1	2	yes	—
385	C₂×#117	C₂²×C₄₃	1	2	yes	complemented
386	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
389	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
390	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
391	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
394	#390	C₂²×C₄₃	1	4	yes	—
395	#389	C₂²×C₄₃	1	4	yes	complemented
396	#389	C₂²×C₄₃	1	4	yes	complemented
397	#389	C₂²×C₄₃	1	4	yes	complemented
398	#388	C₂²×C₄₃	1	4	yes	complemented
399	#388	C₂²×C₄₃	1	4	yes	complemented
400	#388	C₂²×C₄₃	1	4	yes	complemented
401	#388	C₂²×C₄₃	1	4	yes	complemented
402	#388	C₂²×C₄₃	1	4	yes	complemented
403	#388	C₂²×C₄₃	1	4	yes	complemented
404	#387	C₂²×C₄₃	1	4	yes	complemented
405	#387	C₂²×C₄₃	1	4	yes	complemented
406	#387	C₂²×C₄₃	1	4	yes	complemented
407	#387	C₂²×C₄₃	1	4	yes	complemented
408	#386	C₂²×C₄₃	1	4	yes	—
409	#386	C₂²×C₄₃	1	4	yes	—
410	#385	C₂²×C₄₃	1	4	yes	complemented
411	#385	C₂²×C₄₃	1	4	yes	complemented
412	#385	C₂²×C₄₃	1	4	yes	complemented
413	#385	C₂²×C₄₃	1	4	yes	complemented
414	#381	C₂²×C₄₃	1	2	yes	—
415	#381	C₂²×C₄₃	1	2	yes	complemented
416	#380	C₂²×C₄₃	1	1	yes	characteristic
417	#380	C₂²×C₄₃	1	1	yes	characteristic
418	#380	C₂²×C₄₃	1	1	yes	characteristic
419	#380	C₂²×C₄₃	1	1	yes	characteristic
420	#380	C₂²×C₄₃	1	2	yes	—
421	#380	C₂²×C₄₃	1	2	yes	—
422	#380	C₂²×C₄₃	1	2	yes	—
423	#380	C₂²×C₄₃	1	2	yes	complemented
424	#380	C₂²×C₄₃	1	2	yes	complemented
425	#380	C₂²×C₄₃	1	2	yes	complemented
426	#379	C₂²×C₄₃	1	2	yes	—
427	#379	C₂²×C₄₃	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₄₃	1	4	yes	complemented
429	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
430	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
431	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	complemented
433	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	complemented
434	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	complemented
435	C₂×#95	C₂²×C₄₃	1	2	yes	complemented
436	C₄₃	#34376	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
438	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
439	C₂²×D₄	—	4	4	no	—
440	C₂²×D₄	C₂×C₄×C₄₃	1	8	yes	—
441	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
442	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
443	C₂³×C₄	—	4	4	no	—
444	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	complemented
445	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
449	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
450	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
455	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
456	#123	C₂×C₄×C₄₃	1	16	yes	complemented
457	#123	C₂×C₄×C₄₃	1	16	yes	complemented
458	#123	C₂×C₄×C₄₃	1	16	yes	complemented
459	#123	C₂×C₄×C₄₃	1	16	yes	complemented
460	C₄×D₄	—	4	8	no	—
461	#117	—	4	4	no	—
462	#117	—	4	4	no	—
463	C₂×C₄⋊C₄	—	4	4	no	—
464	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
465	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
466	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
473	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
474	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
478	C₂×C₂²⋊C₄	—	4	4	no	—
479	C₂×C₂²⋊C₄	—	4	4	no	—
480	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
481	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
482	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
483	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
499	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
500	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
501	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
502	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
503	#95	C₂³×C₄₃	1	4	yes	—
504	#95	C₂³×C₄₃	1	2	yes	—
505	#95	C₂³×C₄₃	1	2	yes	—
506	#95	C₂³×C₄₃	1	4	yes	—
507	#95	C₂³×C₄₃	1	4	yes	—
508	#95	C₂³×C₄₃	1	4	yes	—
509	#95	C₂³×C₄₃	1	2	yes	—
510	#95	C₂³×C₄₃	1	2	yes	—
511	#95	C₂³×C₄₃	1	4	yes	—
512	#95	C₂³×C₄₃	1	4	yes	—
513	#95	C₂³×C₄₃	1	4	yes	—
514	#95	C₂³×C₄₃	1	4	yes	—
515	C₂⁴	—	2	2	no	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	—	4	2	no	—
521	C₂⁴	—	4	2	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
524	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
525	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
526	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
527	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
528	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
529	C₂×D₄	—	2	8	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	—	4	16	no	—
532	C₂×D₄	C₂²×C₄×C₄₃	1	8	yes	—
533	C₂×D₄	C₂²×C₄×C₄₃	1	8	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	16	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	4	no	—
547	C₂²×C₄	—	4	4	no	—
548	C₂²×C₄	—	4	4	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
552	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
553	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
554	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
555	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
556	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
557	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
558	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
559	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
563	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
564	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	—	4	2	no	—
574	C₄⋊C₄	—	4	4	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	4	4	no	—
578	C₄⋊C₄	—	4	4	no	—
579	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
580	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
581	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
582	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	8	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	4	4	no	—
589	C₂²⋊C₄	—	4	4	no	—
590	C₂²⋊C₄	—	4	4	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	4	no	—
593	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
594	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
598	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
599	C₄²	—	4	4	no	—
600	C₄²	—	4	4	no	—
601	C₄²	—	4	4	no	—
602	C₄²	—	4	4	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	8	no	—
619	C₂³	—	4	4	no	—
620	C₂³	—	4	4	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	4	8	no	—
623	C₂³	—	4	8	no	—
624	C₂³	—	8	4	no	—
625	C₂³	—	8	4	no	—
626	C₂³	C₂³×C₄×C₄₃	1	4	yes	—
627	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
628	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
629	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
630	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
631	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
632	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
633	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
634	D₄	—	2	16	no	—
635	D₄	—	4	8	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	8	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	8	8	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₄×C₄₃	1	4	yes	—
668	C₂×C₄	C₂³×C₄×C₄₃	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
670	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
671	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
672	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₄₃	1	4	yes	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	4	16	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	4	no	—
693	C₂²	—	8	8	no	—
694	C₂²	C₄₃×#518	1	4	yes	—
695	C₂²	C₄₃×#520	1	4	yes	—
696	C₂²	C₂⁴×C₄×C₄₃	1	1	yes	characteristic
697	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
698	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
699	C₂²	C₂×2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
700	C₂²	C₄₃×#585	1	2	yes	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	4	4	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	4	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	4	2	no	—
715	C₂	—	4	4	no	—
716	C₂	C₂×C₄₃×#518	1	1	yes	characteristic
717	C₂	C₂×C₄₃×#520	1	1	yes	characteristic
718	C₂	C₄₃×#3428	1	1	yes	characteristic
719	C₂	C₄₃×#3534	1	2	yes	—
720	C₂	C₄₃×#3535	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₃
Frattini, cosocle	C₂³	C₂⁵×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2376	C₂	semidirect
3. C₄₃×#2359	C₂	semidirect
4. C₄₃×#2345	C₂	semidirect
5. C₄₃×#2342	C₂	semidirect
6. C₄₃×#2342	C₂	semidirect
8. C₄₃×#2335	C₂	semidirect
9. C₄₃×#2322	C₂	semidirect
10. C₄₃×#2316	C₂	semidirect
11. C₄₃×#2315	C₂	semidirect
12. C₄₃×#2313	C₂	semidirect
13. C₄₃×#2312	C₂	semidirect
14. C₄₃×#2280	C₂	semidirect
15. C₂×C₄₃×#380	C₂	semidirect
18. C₂×#123×C₄₃	C₄	semidirect
25. C₂×#117×C₄₃	C₂²	semidirect
28. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
35. C₄₃×#389	C₂²	semidirect
36. C₄₃×#389	C₂²	semidirect
37. C₄₃×#389	C₂²	semidirect
38. C₄₃×#388	C₂²	semidirect
39. C₄₃×#388	C₂²	semidirect
40. C₄₃×#388	C₂²	semidirect
41. C₄₃×#388	C₂²	semidirect
42. C₄₃×#388	C₂²	semidirect
43. C₄₃×#388	C₂²	semidirect
44. C₄₃×#387	C₂²	semidirect
45. C₄₃×#387	C₂²	semidirect
46. C₄₃×#387	C₂²	semidirect
47. C₄₃×#387	C₂²	semidirect
50. C₄₃×#385	C₂²	semidirect
51. C₄₃×#385	C₂²	semidirect
52. C₄₃×#385	C₂²	semidirect
53. C₄₃×#385	C₂²	semidirect
55. C₄₃×#381	C₂²	semidirect
63. C₄₃×#380	C₂²	semidirect
64. C₄₃×#380	C₂²	semidirect
65. C₄₃×#380	C₂²	semidirect
68. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
74. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
75. C₂×#95×C₄₃	C₂²	semidirect
83. C₂³×C₄×C₄₃	C₂×C₄	semidirect
95. #123×C₄₃	C₂×C₄	semidirect
96. #123×C₄₃	C₂×C₄	semidirect
97. #123×C₄₃	C₂×C₄	semidirect
98. #123×C₄₃	C₂×C₄	semidirect
103. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
104. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
119. C₂×C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
120. C₂×C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
121. C₂×C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
313. #34376	C₄₃	direct (N × H)
353. #2376	C₂×C₄₃	semidirect
354. #2359	C₂×C₄₃	semidirect
355. #2345	C₂×C₄₃	semidirect
356. #2342	C₂×C₄₃	semidirect
357. #2342	C₂×C₄₃	semidirect
359. #2335	C₂×C₄₃	semidirect
360. #2322	C₂×C₄₃	semidirect
361. #2316	C₂×C₄₃	semidirect
362. #2315	C₂×C₄₃	semidirect
363. #2313	C₂×C₄₃	semidirect
364. #2312	C₂×C₄₃	semidirect
365. #2280	C₂×C₄₃	semidirect
366. C₂×#380	C₂×C₄₃	semidirect
378. C₂×#123	C₄×C₄₃	semidirect
385. C₂×#117	C₂²×C₄₃	semidirect
388. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
395. #389	C₂²×C₄₃	semidirect
396. #389	C₂²×C₄₃	semidirect
397. #389	C₂²×C₄₃	semidirect
398. #388	C₂²×C₄₃	semidirect
399. #388	C₂²×C₄₃	semidirect
400. #388	C₂²×C₄₃	semidirect
401. #388	C₂²×C₄₃	semidirect
402. #388	C₂²×C₄₃	semidirect
403. #388	C₂²×C₄₃	semidirect
404. #387	C₂²×C₄₃	semidirect
405. #387	C₂²×C₄₃	semidirect
406. #387	C₂²×C₄₃	semidirect
407. #387	C₂²×C₄₃	semidirect
410. #385	C₂²×C₄₃	semidirect
411. #385	C₂²×C₄₃	semidirect
412. #385	C₂²×C₄₃	semidirect
413. #385	C₂²×C₄₃	semidirect
415. #381	C₂²×C₄₃	semidirect
423. #380	C₂²×C₄₃	semidirect
424. #380	C₂²×C₄₃	semidirect
425. #380	C₂²×C₄₃	semidirect
428. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
432. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
433. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
434. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
435. C₂×#95	C₂²×C₄₃	semidirect
436. C₄₃	#34376	direct (N × H)
444. C₂³×C₄	C₂×C₄×C₄₃	semidirect
456. #123	C₂×C₄×C₄₃	semidirect
457. #123	C₂×C₄×C₄₃	semidirect
458. #123	C₂×C₄×C₄₃	semidirect
459. #123	C₂×C₄×C₄₃	semidirect
464. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
465. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
480. C₂×C₂²⋊C₄	C₂×C₄×C₄₃	semidirect
481. C₂×C₂²⋊C₄	C₂×C₄×C₄₃	semidirect
482. C₂×C₂²⋊C₄	C₂×C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#123×C₄₃	2
C₄₃×#2376	2
C₄₃×#2359	2
C₄₃×#2345	2
C₄₃×#2342	2
D₄×C₂²⋊C₄×C₄₃	2
C₄₃×#2335	2
C₄₃×#2322	2
C₄₃×#2316	2
C₄₃×#2315	2
C₄₃×#2313	2
C₄₃×#2312	2
C₄₃×#2280	2
C₂×C₄₃×#380	2
#34376	43

Subgroups — C43×#34376 #24954393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#34376 #24954393