Subgroups — C₄₃×#34614 #24954631

Order 11008.

2474 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2637	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2636	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2630	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2629	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2625	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2624	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2620	C₂	1	2	yes	maximal, complemented
10	C₄₃×#2616	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2615	C₂	1	1	yes	maximal, characteristic
12	C₄₃×#2396	C₂	1	2	yes	maximal, complemented
13	C₄₃×#2392	C₂	1	2	yes	maximal, complemented
14	C₄₃×#2392	C₂	1	4	yes	maximal, complemented
15	C₄×C₂²⋊Q₈×C₄₃	C₂	1	2	yes	maximal, complemented
16	C₄×#121×C₄₃	C₂	1	2	yes	maximal, complemented
17	C₄₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#529	—	2	8	no	—
20	C₂×#126×C₄₃	C₂²	1	2	yes	—
21	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#123×C₄₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#121×C₄₃	C₂²	1	2	yes	—
27	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
28	C₄×#41×C₄₃	—	2	8	no	—
29	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
39	C₂×#117×C₄₃	C₂²	1	2	yes	—
40	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#117×C₄₃	C₂²	1	2	yes	—
42	C₂×#117×C₄₃	C₂²	1	2	yes	—
43	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
44	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#400	C₂²	1	2	yes	—
46	C₄₃×#399	C₂²	1	2	yes	—
47	C₄₃×#398	C₂²	1	2	yes	—
48	C₄₃×#398	C₂²	1	4	yes	—
49	C₄₃×#398	C₂²	1	4	yes	—
50	C₄₃×#397	C₂²	1	2	yes	—
51	C₄₃×#397	C₂²	1	4	yes	—
52	C₄₃×#396	C₂²	1	4	yes	—
53	C₄₃×#396	C₂²	1	4	yes	—
54	C₄₃×#396	C₂²	1	4	yes	—
55	C₄₃×#396	C₂²	1	4	yes	—
56	C₄₃×#395	C₂²	1	2	yes	—
57	C₄₃×#394	C₂²	1	4	yes	—
58	C₄₃×#394	C₂²	1	2	yes	—
59	C₄₃×#394	C₂²	1	4	yes	—
60	C₄₃×#394	C₂²	1	4	yes	—
61	C₄₃×#394	C₂²	1	4	yes	—
62	C₄₃×#393	C₂²	1	2	yes	—
63	C₄₃×#392	C₂²	1	4	yes	—
64	C₄₃×#392	C₂²	1	2	yes	—
65	C₄₃×#391	C₂²	1	2	yes	—
66	C₄₃×#390	C₂²	1	2	yes	—
67	C₄₃×#389	C₂²	1	2	yes	—
68	C₄₃×#389	C₂²	1	2	yes	—
69	C₄₃×#388	C₂²	1	4	yes	—
70	C₄₃×#387	C₂²	1	4	yes	—
71	C₄₃×#386	C₂²	1	4	yes	—
72	C₄₃×#385	C₂²	1	4	yes	—
73	C₄₃×#384	C₂²	1	2	yes	—
74	C₄₃×#382	C₂²	1	2	yes	—
75	C₄₃×#380	C₂²	1	1	yes	characteristic
76	C₄₃×#380	C₂²	1	2	yes	—
77	C₄₃×#380	C₂²	1	1	yes	characteristic
78	C₄₃×#380	C₂²	1	2	yes	—
79	C₄₃×#380	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
82	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
84	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
85	C₂×#41×C₄₃	—	2	4	no	—
86	C₂×#41×C₄₃	—	2	8	no	—
87	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
96	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
101	#126×C₄₃	—	2	8	no	—
102	#125×C₄₃	—	2	4	no	—
103	#124×C₄₃	—	2	4	no	—
104	#123×C₄₃	—	2	8	no	—
105	C₂²⋊Q₈×C₄₃	—	2	4	no	—
106	C₂²⋊Q₈×C₄₃	—	2	8	no	—
107	#121×C₄₃	—	2	4	no	—
108	#121×C₄₃	—	2	8	no	—
109	C₄×Q₈×C₄₃	—	2	4	no	—
110	C₄×Q₈×C₄₃	—	2	4	no	—
111	C₄×Q₈×C₄₃	—	2	4	no	—
112	C₄×D₄×C₄₃	—	2	8	no	—
113	C₄×D₄×C₄₃	—	2	8	no	—
114	C₄×D₄×C₄₃	—	2	8	no	—
115	C₄×D₄×C₄₃	—	2	4	no	—
116	C₄×D₄×C₄₃	—	2	4	no	—
117	C₄×D₄×C₄₃	—	2	4	no	—
118	C₄×D₄×C₄₃	—	4	8	no	—
119	#117×C₄₃	—	2	4	no	—
120	#117×C₄₃	—	2	8	no	—
121	#117×C₄₃	—	2	8	no	—
122	#117×C₄₃	—	4	4	no	—
123	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
154	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
155	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
156	C₂×C₄²×C₄₃	—	2	8	no	—
157	C₂×C₄²×C₄₃	D₄	1	8	yes	complemented
158	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
159	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
163	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
167	#95×C₄₃	C₂³	1	4	yes	—
168	#95×C₄₃	C₂³	1	4	yes	—
169	#95×C₄₃	C₂³	1	4	yes	—
170	#95×C₄₃	C₂³	1	4	yes	—
171	#95×C₄₃	C₂³	1	4	yes	—
172	#95×C₄₃	C₂³	1	2	yes	—
173	#95×C₄₃	C₂³	1	2	yes	—
174	#95×C₄₃	C₂³	1	4	yes	—
175	#95×C₄₃	C₂³	1	4	yes	—
176	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
177	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
178	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
179	#41×C₄₃	—	2	32	no	—
180	C₂×Q₈×C₄₃	—	2	2	no	—
181	C₂×Q₈×C₄₃	—	2	2	no	—
182	C₂×Q₈×C₄₃	—	2	4	no	—
183	C₂×Q₈×C₄₃	—	2	4	no	—
184	C₂×D₄×C₄₃	—	2	2	no	—
185	C₂×D₄×C₄₃	—	2	2	no	—
186	C₂×D₄×C₄₃	—	2	4	no	—
187	C₂×D₄×C₄₃	—	2	4	no	—
188	C₂×D₄×C₄₃	—	2	4	no	—
189	C₂×D₄×C₄₃	—	2	4	no	—
190	C₂×D₄×C₄₃	—	2	4	no	—
191	C₂×D₄×C₄₃	—	2	4	no	—
192	C₂×D₄×C₄₃	—	2	8	no	—
193	C₂×D₄×C₄₃	—	4	4	no	—
194	C₂×D₄×C₄₃	—	4	4	no	—
195	C₂×D₄×C₄₃	—	4	4	no	—
196	C₂²×C₄×C₄₃	—	2	4	no	—
197	C₂²×C₄×C₄₃	—	2	4	no	—
198	C₂²×C₄×C₄₃	—	2	4	no	—
199	C₂²×C₄×C₄₃	—	2	2	no	—
200	C₂²×C₄×C₄₃	—	2	2	no	—
201	C₂²×C₄×C₄₃	—	2	4	no	—
202	C₂²×C₄×C₄₃	—	2	4	no	—
203	C₂²×C₄×C₄₃	—	2	4	no	—
204	C₂²×C₄×C₄₃	—	2	4	no	—
205	C₂²×C₄×C₄₃	—	2	4	no	—
206	C₂²×C₄×C₄₃	—	2	4	no	—
207	C₂²×C₄×C₄₃	—	2	4	no	—
208	C₂²×C₄×C₄₃	—	4	2	no	—
209	C₂²×C₄×C₄₃	—	4	2	no	—
210	C₂²×C₄×C₄₃	—	4	2	no	—
211	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₄₃	#41	1	8	yes	—
215	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
229	C₄⋊C₄×C₄₃	—	2	4	no	—
230	C₄⋊C₄×C₄₃	—	2	4	no	—
231	C₄⋊C₄×C₄₃	—	2	2	no	—
232	C₄⋊C₄×C₄₃	—	2	2	no	—
233	C₄⋊C₄×C₄₃	—	2	4	no	—
234	C₄⋊C₄×C₄₃	—	2	4	no	—
235	C₄⋊C₄×C₄₃	—	2	2	no	—
236	C₄⋊C₄×C₄₃	—	2	4	no	—
237	C₄⋊C₄×C₄₃	—	2	2	no	—
238	C₄⋊C₄×C₄₃	—	2	4	no	—
239	C₄⋊C₄×C₄₃	—	2	4	no	—
240	C₄⋊C₄×C₄₃	—	2	4	no	—
241	C₄⋊C₄×C₄₃	—	2	8	no	—
242	C₄⋊C₄×C₄₃	—	4	4	no	—
243	C₄⋊C₄×C₄₃	—	4	4	no	—
244	C₄⋊C₄×C₄₃	—	4	4	no	—
245	C₄⋊C₄×C₄₃	—	4	4	no	—
246	C₂²⋊C₄×C₄₃	—	2	4	no	—
247	C₂²⋊C₄×C₄₃	—	2	4	no	—
248	C₂²⋊C₄×C₄₃	—	2	4	no	—
249	C₂²⋊C₄×C₄₃	—	2	4	no	—
250	C₂²⋊C₄×C₄₃	—	2	4	no	—
251	C₂²⋊C₄×C₄₃	—	2	4	no	—
252	C₂²⋊C₄×C₄₃	—	2	8	no	—
253	C₂²⋊C₄×C₄₃	—	2	4	no	—
254	C₂²⋊C₄×C₄₃	—	2	4	no	—
255	C₂²⋊C₄×C₄₃	—	2	8	no	—
256	C₂²⋊C₄×C₄₃	—	4	4	no	—
257	C₂²⋊C₄×C₄₃	—	4	4	no	—
258	C₂²⋊C₄×C₄₃	—	4	2	no	—
259	C₂²⋊C₄×C₄₃	—	4	2	no	—
260	C₂²⋊C₄×C₄₃	—	4	4	no	—
261	C₂²⋊C₄×C₄₃	—	4	4	no	—
262	C₄²×C₄₃	—	2	4	no	—
263	C₄²×C₄₃	—	2	4	no	—
264	C₄²×C₄₃	—	2	4	no	—
265	C₄²×C₄₃	—	2	4	no	—
266	C₄²×C₄₃	—	2	8	no	—
267	C₄²×C₄₃	C₂×D₄	1	4	yes	—
268	C₄²×C₄₃	C₂×D₄	1	4	yes	—
269	C₄²×C₄₃	C₂×D₄	1	4	yes	—
270	C₄²×C₄₃	C₂×D₄	1	4	yes	—
271	C₂³×C₄₃	—	2	2	no	—
272	C₂³×C₄₃	—	2	2	no	—
273	C₂³×C₄₃	—	2	2	no	—
274	C₂³×C₄₃	—	2	1	no	—
275	C₂³×C₄₃	—	2	2	no	—
276	C₂³×C₄₃	—	2	1	no	—
277	C₂³×C₄₃	—	2	2	no	—
278	C₂³×C₄₃	—	2	2	no	—
279	C₂³×C₄₃	—	2	2	no	—
280	C₂³×C₄₃	—	2	2	no	—
281	C₂³×C₄₃	—	2	2	no	—
282	C₂³×C₄₃	—	2	4	no	—
283	C₂³×C₄₃	—	2	2	no	—
284	C₂³×C₄₃	—	2	2	no	—
285	C₂³×C₄₃	—	2	4	no	—
286	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₄₃	C₂×#41	1	4	yes	—
288	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
289	Q₈×C₄₃	—	2	8	no	—
290	Q₈×C₄₃	—	4	4	no	—
291	D₄×C₄₃	—	2	8	no	—
292	D₄×C₄₃	—	2	16	no	—
293	D₄×C₄₃	—	4	8	no	—
294	D₄×C₄₃	—	4	16	no	—
295	D₄×C₄₃	—	4	4	no	—
296	C₂×C₄×C₄₃	—	2	2	no	—
297	C₂×C₄×C₄₃	—	2	2	no	—
298	C₂×C₄×C₄₃	—	2	2	no	—
299	C₂×C₄×C₄₃	—	2	1	no	—
300	C₂×C₄×C₄₃	—	2	1	no	—
301	C₂×C₄×C₄₃	—	2	2	no	—
302	C₂×C₄×C₄₃	—	2	2	no	—
303	C₂×C₄×C₄₃	—	2	8	no	—
304	C₂×C₄×C₄₃	—	2	16	no	—
305	C₂×C₄×C₄₃	—	2	8	no	—
306	C₂×C₄×C₄₃	—	2	2	no	—
307	C₂×C₄×C₄₃	—	2	2	no	—
308	C₂×C₄×C₄₃	—	2	2	no	—
309	C₂×C₄×C₄₃	—	2	2	no	—
310	C₂×C₄×C₄₃	—	2	2	no	—
311	C₂×C₄×C₄₃	—	2	4	no	—
312	C₂×C₄×C₄₃	—	2	4	no	—
313	C₂×C₄×C₄₃	—	2	4	no	—
314	C₂×C₄×C₄₃	—	2	4	no	—
315	C₂×C₄×C₄₃	—	2	4	no	—
316	C₂×C₄×C₄₃	—	2	2	no	—
317	C₂×C₄×C₄₃	—	2	2	no	—
318	C₂×C₄×C₄₃	—	2	2	no	—
319	C₂×C₄×C₄₃	—	2	2	no	—
320	C₂×C₄×C₄₃	—	2	2	no	—
321	C₂×C₄×C₄₃	—	2	4	no	—
322	C₂×C₄×C₄₃	—	2	4	no	—
323	C₂×C₄×C₄₃	—	2	4	no	—
324	C₂×C₄×C₄₃	—	2	2	no	—
325	C₂×C₄×C₄₃	—	4	4	no	—
326	C₂×C₄×C₄₃	—	4	8	no	—
327	C₂×C₄×C₄₃	—	4	8	no	—
328	C₂×C₄×C₄₃	—	4	8	no	—
329	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
332	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
336	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
337	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
338	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
339	#34614	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂²×C₄₃	—	2	2	no	—
341	C₂²×C₄₃	—	2	4	no	—
342	C₂²×C₄₃	—	2	2	no	—
343	C₂²×C₄₃	—	2	2	no	—
344	C₂²×C₄₃	—	2	4	no	—
345	C₂²×C₄₃	—	2	4	no	—
346	C₂²×C₄₃	—	4	2	no	—
347	C₂²×C₄₃	—	4	2	no	—
348	C₂²×C₄₃	—	4	2	no	—
349	C₂²×C₄₃	—	4	2	no	—
350	C₂²×C₄₃	—	4	2	no	—
351	C₂²×C₄₃	—	4	2	no	—
352	C₂²×C₄₃	—	4	2	no	—
353	C₂²×C₄₃	—	4	2	no	—
354	C₂²×C₄₃	—	4	2	no	—
355	C₂²×C₄₃	—	4	4	no	—
356	C₂²×C₄₃	—	4	4	no	—
357	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
358	C₂²×C₄₃	C₂²×#41	1	2	yes	—
359	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
361	C₂²×C₄₃	#585	1	2	yes	—
362	C₄×C₄₃	—	2	2	no	—
363	C₄×C₄₃	—	2	4	no	—
364	C₄×C₄₃	—	2	2	no	—
365	C₄×C₄₃	—	2	2	no	—
366	C₄×C₄₃	—	2	2	no	—
367	C₄×C₄₃	—	4	2	no	—
368	C₄×C₄₃	—	4	2	no	—
369	C₄×C₄₃	—	4	2	no	—
370	C₄×C₄₃	—	4	2	no	—
371	C₄×C₄₃	—	4	2	no	—
372	C₄×C₄₃	—	4	4	no	—
373	C₄×C₄₃	—	4	4	no	—
374	C₄×C₄₃	#525	1	4	yes	—
375	C₄×C₄₃	#537	1	4	yes	—
376	C₂×#529	C₂×C₄₃	1	1	yes	characteristic, complemented
377	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic, complemented
378	#2637	C₂×C₄₃	1	2	yes	complemented
379	#2636	C₂×C₄₃	1	2	yes	complemented
380	#2630	C₂×C₄₃	1	4	yes	complemented
381	#2629	C₂×C₄₃	1	2	yes	complemented
382	#2625	C₂×C₄₃	1	1	yes	characteristic, complemented
383	#2624	C₂×C₄₃	1	1	yes	characteristic, complemented
384	#2620	C₂×C₄₃	1	2	yes	complemented
385	#2616	C₂×C₄₃	1	1	yes	characteristic, complemented
386	#2615	C₂×C₄₃	1	1	yes	characteristic
387	#2396	C₂×C₄₃	1	2	yes	complemented
388	#2392	C₂×C₄₃	1	2	yes	complemented
389	#2392	C₂×C₄₃	1	4	yes	complemented
390	C₄×C₂²⋊Q₈	C₂×C₄₃	1	2	yes	complemented
391	C₄×#121	C₂×C₄₃	1	2	yes	complemented
392	#2285	C₂×C₄₃	1	1	yes	characteristic, complemented
393	C₂×C₄₃	—	4	2	no	—
394	C₂×C₄₃	—	4	4	no	—
395	C₂×C₄₃	—	8	2	no	—
396	C₂×C₄₃	C₂×#525	1	1	yes	characteristic
397	C₂×C₄₃	C₂×#537	1	1	yes	characteristic
398	C₂×C₄₃	#3449	1	1	yes	characteristic
399	C₂×C₄₃	#3460	1	2	yes	—
400	C₂×C₄₃	#3461	1	2	yes	—
401	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
402	#529	—	2	8	no	—
403	C₂×#126	C₂²×C₄₃	1	2	yes	—
404	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
405	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
406	C₂×#123	C₂²×C₄₃	1	2	yes	—
407	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
408	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
409	C₂×#121	C₂²×C₄₃	1	2	yes	—
410	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
411	C₄×#41	—	2	8	no	—
412	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
413	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
414	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
415	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
416	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
417	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
420	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
422	C₂×#117	C₂²×C₄₃	1	2	yes	—
423	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
424	C₂×#117	C₂²×C₄₃	1	2	yes	—
425	C₂×#117	C₂²×C₄₃	1	2	yes	—
426	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
427	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
428	#400	C₂²×C₄₃	1	2	yes	—
429	#399	C₂²×C₄₃	1	2	yes	—
430	#398	C₂²×C₄₃	1	2	yes	—
431	#398	C₂²×C₄₃	1	4	yes	—
432	#398	C₂²×C₄₃	1	4	yes	—
433	#397	C₂²×C₄₃	1	2	yes	—
434	#397	C₂²×C₄₃	1	4	yes	—
435	#396	C₂²×C₄₃	1	4	yes	—
436	#396	C₂²×C₄₃	1	4	yes	—
437	#396	C₂²×C₄₃	1	4	yes	—
438	#396	C₂²×C₄₃	1	4	yes	—
439	#395	C₂²×C₄₃	1	2	yes	—
440	#394	C₂²×C₄₃	1	4	yes	—
441	#394	C₂²×C₄₃	1	2	yes	—
442	#394	C₂²×C₄₃	1	4	yes	—
443	#394	C₂²×C₄₃	1	4	yes	—
444	#394	C₂²×C₄₃	1	4	yes	—
445	#393	C₂²×C₄₃	1	2	yes	—
446	#392	C₂²×C₄₃	1	4	yes	—
447	#392	C₂²×C₄₃	1	2	yes	—
448	#391	C₂²×C₄₃	1	2	yes	—
449	#390	C₂²×C₄₃	1	2	yes	—
450	#389	C₂²×C₄₃	1	2	yes	—
451	#389	C₂²×C₄₃	1	2	yes	—
452	#388	C₂²×C₄₃	1	4	yes	—
453	#387	C₂²×C₄₃	1	4	yes	—
454	#386	C₂²×C₄₃	1	4	yes	—
455	#385	C₂²×C₄₃	1	4	yes	—
456	#384	C₂²×C₄₃	1	2	yes	—
457	#382	C₂²×C₄₃	1	2	yes	—
458	#380	C₂²×C₄₃	1	1	yes	characteristic
459	#380	C₂²×C₄₃	1	2	yes	—
460	#380	C₂²×C₄₃	1	1	yes	characteristic
461	#380	C₂²×C₄₃	1	2	yes	—
462	#380	C₂²×C₄₃	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
465	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
467	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
468	C₄₃	#34614	1	1	yes	characteristic, direct product factor, Sylow
469	C₂×#41	—	2	4	no	—
470	C₂×#41	—	2	8	no	—
471	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
473	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
475	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
477	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
478	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
479	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
483	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
484	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
485	#126	—	2	8	no	—
486	#125	—	2	4	no	—
487	#124	—	2	4	no	—
488	#123	—	2	8	no	—
489	C₂²⋊Q₈	—	2	4	no	—
490	C₂²⋊Q₈	—	2	8	no	—
491	#121	—	2	4	no	—
492	#121	—	2	8	no	—
493	C₄×Q₈	—	2	4	no	—
494	C₄×Q₈	—	2	4	no	—
495	C₄×Q₈	—	2	4	no	—
496	C₄×D₄	—	2	8	no	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	8	no	—
499	C₄×D₄	—	2	4	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	—	4	8	no	—
503	#117	—	2	4	no	—
504	#117	—	2	8	no	—
505	#117	—	2	8	no	—
506	#117	—	4	4	no	—
507	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
520	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
521	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
522	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
523	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
540	C₂×C₄²	—	2	8	no	—
541	C₂×C₄²	D₄×C₄₃	1	8	yes	complemented
542	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
543	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
544	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
545	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
546	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
547	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
551	#95	C₂³×C₄₃	1	4	yes	—
552	#95	C₂³×C₄₃	1	4	yes	—
553	#95	C₂³×C₄₃	1	4	yes	—
554	#95	C₂³×C₄₃	1	4	yes	—
555	#95	C₂³×C₄₃	1	4	yes	—
556	#95	C₂³×C₄₃	1	2	yes	—
557	#95	C₂³×C₄₃	1	2	yes	—
558	#95	C₂³×C₄₃	1	4	yes	—
559	#95	C₂³×C₄₃	1	4	yes	—
560	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
561	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
562	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
563	#41	—	2	32	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	8	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	4	no	—
576	C₂×D₄	—	2	4	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	—	4	4	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
596	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
597	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
598	C₂²×C₄	#41×C₄₃	1	8	yes	—
599	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
603	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	8	no	—
626	C₄⋊C₄	—	4	4	no	—
627	C₄⋊C₄	—	4	4	no	—
628	C₄⋊C₄	—	4	4	no	—
629	C₄⋊C₄	—	4	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	—	2	8	no	—
651	C₄²	C₂×D₄×C₄₃	1	4	yes	—
652	C₄²	C₂×D₄×C₄₃	1	4	yes	—
653	C₄²	C₂×D₄×C₄₃	1	4	yes	—
654	C₄²	C₂×D₄×C₄₃	1	4	yes	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
671	C₂³	C₂×#41×C₄₃	1	4	yes	—
672	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
673	Q₈	—	2	8	no	—
674	Q₈	—	4	4	no	—
675	D₄	—	2	8	no	—
676	D₄	—	2	16	no	—
677	D₄	—	4	8	no	—
678	D₄	—	4	16	no	—
679	D₄	—	4	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	4	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	8	no	—
712	C₂×C₄	—	4	8	no	—
713	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
717	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
719	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
720	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
721	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
722	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	4	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	4	no	—
740	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
741	C₂²	C₂²×#41×C₄₃	1	2	yes	—
742	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
743	C₂²	C₂×2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
744	C₂²	C₄₃×#585	1	2	yes	—
745	C₄	—	2	2	no	—
746	C₄	—	2	4	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	4	no	—
757	C₄	C₄₃×#525	1	4	yes	—
758	C₄	C₄₃×#537	1	4	yes	—
759	C₂	—	4	2	no	—
760	C₂	—	4	4	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₄₃×#525	1	1	yes	characteristic
763	C₂	C₂×C₄₃×#537	1	1	yes	characteristic
764	C₂	C₄₃×#3449	1	1	yes	characteristic
765	C₂	C₄₃×#3460	1	2	yes	—
766	C₂	C₄₃×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₃
socle	C₂³×C₄₃	C₂⁵
prime radical	C₄₃×#2615	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#529	C₂	semidirect
2. C₂×C₄×#41×C₄₃	C₂	semidirect
3. C₄₃×#2637	C₂	semidirect
4. C₄₃×#2636	C₂	semidirect
5. C₄₃×#2630	C₂	semidirect
6. C₄₃×#2629	C₂	semidirect
7. C₄₃×#2625	C₂	semidirect
8. C₄₃×#2624	C₂	semidirect
9. C₄₃×#2620	C₂	semidirect
10. C₄₃×#2616	C₂	semidirect
12. C₄₃×#2396	C₂	semidirect
13. C₄₃×#2392	C₂	semidirect
14. C₄₃×#2392	C₂	semidirect
15. C₄×C₂²⋊Q₈×C₄₃	C₂	semidirect
16. C₄×#121×C₄₃	C₂	semidirect
17. C₄₃×#2285	C₂	semidirect
157. C₂×C₄²×C₄₃	D₄	semidirect
339. #34614	C₄₃	direct (N × H)
376. C₂×#529	C₂×C₄₃	semidirect
377. C₂×C₄×#41	C₂×C₄₃	semidirect
378. #2637	C₂×C₄₃	semidirect
379. #2636	C₂×C₄₃	semidirect
380. #2630	C₂×C₄₃	semidirect
381. #2629	C₂×C₄₃	semidirect
382. #2625	C₂×C₄₃	semidirect
383. #2624	C₂×C₄₃	semidirect
384. #2620	C₂×C₄₃	semidirect
385. #2616	C₂×C₄₃	semidirect
387. #2396	C₂×C₄₃	semidirect
388. #2392	C₂×C₄₃	semidirect
389. #2392	C₂×C₄₃	semidirect
390. C₄×C₂²⋊Q₈	C₂×C₄₃	semidirect
391. C₄×#121	C₂×C₄₃	semidirect
392. #2285	C₂×C₄₃	semidirect
468. C₄₃	#34614	direct (N × H)
541. C₂×C₄²	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×#529	2
C₂×C₄×#41×C₄₃	2
C₄₃×#2637	2
C₄₃×#2636	2
C₄₃×#2630	2
C₄₃×#2629	2
C₄₃×#2625	2
C₄₃×#2624	2
C₄₃×#2620	2
C₄₃×#2616	2
C₄₃×#2615	2
C₄₃×#2396	2
C₄₃×#2392	2
C₄×C₂²⋊Q₈×C₄₃	2
C₄×#121×C₄₃	2
C₄₃×#2285	2
#34614	43

Subgroups — C43×#34614 #24954631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#34614 #24954631