Subgroups — C₄₃×#60275 #24980292

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3480	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2995	C₂	1	4	yes	maximal, complemented
3	C₄₃×#2994	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2993	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2992	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2990	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2989	C₂	1	2	yes	maximal, complemented
8	Q₈×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2935	C₂	1	2	yes	maximal, complemented
12	C₄₃×#2932	C₂	1	2	yes	maximal, complemented
13	C₄₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#2923	C₂	1	2	yes	maximal, complemented
15	C₄₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#2906	C₂	1	2	yes	maximal, complemented
18	C₂×#131×C₄₃	C₂²	1	2	yes	—
19	C₂×#131×C₄₃	C₂²	1	2	yes	—
20	C₂×#131×C₄₃	C₂²	1	2	yes	—
21	C₄₃×#559	C₄	1	1	yes	characteristic
22	C₄₃×#559	C₄	1	2	yes	—
23	C₄₃×#557	C₄	1	1	yes	characteristic
24	C₄₃×#556	C₄	1	1	yes	characteristic
25	C₄₃×#556	C₄	1	2	yes	—
26	C₄₃×#553	C₄	1	2	yes	—
27	C₄₃×#553	C₄	1	4	yes	—
28	C₄₃×#550	C₄	1	1	yes	characteristic
29	C₄₃×#548	C₄	1	2	yes	—
30	C₄₃×#532	C₂²	1	1	yes	characteristic
31	C₄₃×#532	C₂²	1	2	yes	—
32	C₄₃×#529	C₂²	1	4	yes	—
33	C₄₃×#529	C₂²	1	2	yes	—
34	C₄×#41×C₄₃	C₂²	1	2	yes	—
35	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
36	C₄×#41×C₄₃	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#446	C₂²	1	1	yes	characteristic
39	C₄₃×#446	C₂²	1	1	yes	characteristic
40	C₄₃×#446	C₂²	1	2	yes	—
41	C₄₃×#446	C₂²	1	1	yes	characteristic
42	C₄₃×#446	C₂²	1	1	yes	characteristic
43	C₄₃×#446	C₂²	1	2	yes	—
44	C₄₃×#446	C₂²	1	2	yes	—
45	C₄₃×#446	C₂²	1	4	yes	—
46	C₈×Q₈×C₄₃	C₂²	1	2	yes	—
47	C₄₃×#436	C₂²	1	2	yes	—
48	C₄₃×#436	C₂²	1	2	yes	—
49	C₄₃×#436	C₂²	1	2	yes	—
50	C₄₃×#436	C₂²	1	4	yes	—
51	C₄₃×#435	C₂²	1	4	yes	—
52	C₄₃×#435	C₂²	1	4	yes	—
53	C₄₃×#435	C₂²	1	4	yes	—
54	C₄₃×#435	C₂²	1	4	yes	—
55	C₄₃×#435	C₂²	1	4	yes	—
56	C₄₃×#435	C₂²	1	4	yes	—
57	C₄₃×#435	C₂²	1	4	yes	—
58	C₈×D₄×C₄₃	C₂²	1	2	yes	—
59	C₈×D₄×C₄₃	C₂²	1	2	yes	—
60	C₈×D₄×C₄₃	C₂²	1	2	yes	—
61	C₈×D₄×C₄₃	C₂²	1	4	yes	—
62	C₄₃×#433	C₂²	1	2	yes	—
63	C₄₃×#433	C₂²	1	2	yes	—
64	C₄₃×#433	C₂²	1	4	yes	—
65	C₄₃×#433	C₂²	1	4	yes	—
66	C₄₃×#432	C₂²	1	4	yes	—
67	C₄₃×#432	C₂²	1	4	yes	—
68	C₄₃×#431	C₂²	1	2	yes	—
69	C₄₃×#431	C₂²	1	2	yes	—
70	C₄₃×#424	C₂²	1	1	yes	characteristic
71	C₄₃×#424	C₂²	1	2	yes	—
72	C₄₃×#424	C₂²	1	4	yes	—
73	C₄₃×#424	C₂²	1	4	yes	—
74	C₄₃×#424	C₂²	1	4	yes	—
75	C₄₃×#424	C₂²	1	1	yes	characteristic
76	C₄₃×#423	C₂²	1	1	yes	characteristic
77	C₄₃×#423	C₂²	1	2	yes	—
78	C₄₃×#423	C₂²	1	4	yes	—
79	C₄₃×#423	C₂²	1	2	yes	—
80	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
81	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
83	C₂×C₄⋊C₈×C₄₃	C₂²	1	4	yes	—
84	C₄₃×#408	C₂²	1	1	yes	characteristic
85	C₄₃×#408	C₂²	1	1	yes	characteristic
86	C₄₃×#408	C₂²	1	2	yes	—
87	C₄₃×#408	C₂²	1	2	yes	—
88	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
89	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
90	C₂×#97×C₄₃	C₂²	1	2	yes	—
91	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
92	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
93	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×#41×C₄₃	C₂³	1	2	yes	—
95	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
96	#131×C₄₃	—	4	4	no	—
97	#131×C₄₃	—	4	4	no	—
98	#131×C₄₃	—	4	4	no	—
99	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
100	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
103	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
104	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
105	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
109	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
110	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
111	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
112	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
113	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
114	#127×C₄₃	C₂×C₄	1	2	yes	—
115	#126×C₄₃	C₂×C₄	1	4	yes	—
116	#126×C₄₃	C₂×C₄	1	4	yes	—
117	#126×C₄₃	C₂×C₄	1	4	yes	—
118	#125×C₄₃	C₂×C₄	1	4	yes	—
119	#125×C₄₃	C₂×C₄	1	2	yes	—
120	#124×C₄₃	C₂×C₄	1	2	yes	—
121	#124×C₄₃	C₂×C₄	1	4	yes	—
122	#124×C₄₃	C₂×C₄	1	2	yes	—
123	#124×C₄₃	C₂×C₄	1	2	yes	—
124	#124×C₄₃	C₂×C₄	1	2	yes	—
125	#123×C₄₃	C₂×C₄	1	4	yes	—
126	#123×C₄₃	C₂×C₄	1	4	yes	—
127	#123×C₄₃	C₂×C₄	1	4	yes	—
128	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
129	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
130	#121×C₄₃	C₂×C₄	1	2	yes	—
131	#121×C₄₃	C₂×C₄	1	4	yes	—
132	#121×C₄₃	C₂×C₄	1	2	yes	—
133	#121×C₄₃	C₂×C₄	1	4	yes	—
134	#121×C₄₃	C₂×C₄	1	2	yes	—
135	#121×C₄₃	C₂×C₄	1	4	yes	—
136	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
137	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
138	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
139	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
140	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
142	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
143	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
144	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
145	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
146	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
147	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
148	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
149	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
151	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
152	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
153	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
154	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
155	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
156	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
157	C₄×D₄×C₄₃	C₂³	1	2	yes	—
158	C₄×D₄×C₄₃	C₂³	1	4	yes	—
159	C₄×D₄×C₄₃	C₂³	1	2	yes	—
160	C₄×D₄×C₄₃	C₂³	1	4	yes	—
161	#117×C₄₃	C₂×C₄	1	2	yes	—
162	#117×C₄₃	C₂×C₄	1	4	yes	—
163	#117×C₄₃	C₂³	1	1	yes	characteristic
164	#117×C₄₃	C₂³	1	2	yes	—
165	#117×C₄₃	C₂³	1	4	yes	—
166	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
168	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
172	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
173	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
174	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
175	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
177	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
178	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
179	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
180	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
181	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
182	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
183	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
184	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
185	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
186	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
187	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
188	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
193	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
194	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
195	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
197	#97×C₄₃	C₂³	1	2	yes	—
198	#97×C₄₃	C₂³	1	2	yes	—
199	#97×C₄₃	C₂³	1	2	yes	—
200	#97×C₄₃	C₂³	1	2	yes	—
201	#97×C₄₃	C₂³	1	4	yes	—
202	#97×C₄₃	C₂³	1	2	yes	—
203	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
206	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
207	C₄×C₈×C₄₃	C₂³	1	2	yes	—
208	C₄×C₈×C₄₃	C₂³	1	4	yes	—
209	#41×C₄₃	—	2	4	no	—
210	#41×C₄₃	—	2	2	no	—
211	#41×C₄₃	—	2	2	no	—
212	#41×C₄₃	—	2	4	no	—
213	#41×C₄₃	—	4	4	no	—
214	C₂×Q₈×C₄₃	—	4	2	no	—
215	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
216	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
217	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
218	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
220	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
221	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
222	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
223	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
224	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
225	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
226	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
228	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
230	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
234	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
235	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
236	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
239	M₁₆×C₄₃	—	2	4	no	—
240	M₁₆×C₄₃	—	2	2	no	—
241	M₁₆×C₄₃	—	2	2	no	—
242	M₁₆×C₄₃	—	4	4	no	—
243	M₁₆×C₄₃	—	4	4	no	—
244	M₁₆×C₄₃	—	4	4	no	—
245	C₂×C₈×C₄₃	—	2	2	no	—
246	C₂×C₈×C₄₃	—	2	4	no	—
247	C₂×C₈×C₄₃	—	2	2	no	—
248	C₂×C₈×C₄₃	—	4	4	no	—
249	C₂×C₈×C₄₃	—	4	4	no	—
250	C₂×C₈×C₄₃	—	4	4	no	—
251	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
257	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
258	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
259	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
261	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
262	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
263	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
264	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
265	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
266	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
267	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
268	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
270	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
271	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
272	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
273	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
274	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
275	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
276	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
277	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
278	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
279	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
280	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
281	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
282	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
283	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
284	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
285	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
287	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
288	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
289	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
290	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
291	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
292	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
293	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
294	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
295	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
296	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
297	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
298	C₄²×C₄₃	C₂⁴	1	2	yes	—
299	C₄²×C₄₃	C₂⁴	1	2	yes	—
300	C₄²×C₄₃	C₂⁴	1	2	yes	—
301	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
302	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
303	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
304	Q₈×C₄₃	—	2	2	no	—
305	Q₈×C₄₃	—	2	4	no	—
306	Q₈×C₄₃	—	2	2	no	—
307	Q₈×C₄₃	—	2	2	no	—
308	Q₈×C₄₃	—	4	2	no	—
309	D₄×C₄₃	—	2	4	no	—
310	D₄×C₄₃	—	2	8	no	—
311	D₄×C₄₃	—	2	2	no	—
312	D₄×C₄₃	—	2	4	no	—
313	D₄×C₄₃	—	2	4	no	—
314	D₄×C₄₃	—	4	4	no	—
315	D₄×C₄₃	—	4	2	no	—
316	D₄×C₄₃	—	4	4	no	—
317	C₂×C₄×C₄₃	—	2	2	no	—
318	C₂×C₄×C₄₃	—	2	4	no	—
319	C₂×C₄×C₄₃	—	2	4	no	—
320	C₂×C₄×C₄₃	—	2	2	no	—
321	C₂×C₄×C₄₃	—	2	2	no	—
322	C₂×C₄×C₄₃	—	2	4	no	—
323	C₂×C₄×C₄₃	—	4	2	no	—
324	C₂×C₄×C₄₃	—	4	4	no	—
325	C₂×C₄×C₄₃	—	4	1	no	—
326	C₂×C₄×C₄₃	—	4	2	no	—
327	C₂×C₄×C₄₃	—	4	2	no	—
328	C₂×C₄×C₄₃	—	4	4	no	—
329	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
331	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
332	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
333	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
334	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
335	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
336	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
337	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
338	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
339	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
340	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
343	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
344	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
345	C₈×C₄₃	—	2	1	no	—
346	C₈×C₄₃	—	2	2	no	—
347	C₈×C₄₃	—	2	2	no	—
348	C₈×C₄₃	—	2	1	no	—
349	C₈×C₄₃	—	2	4	no	—
350	C₈×C₄₃	—	2	2	no	—
351	C₈×C₄₃	—	2	1	no	—
352	C₈×C₄₃	—	2	1	no	—
353	C₈×C₄₃	—	2	2	no	—
354	#60275	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
355	C₂²×C₄₃	—	2	1	no	—
356	C₂²×C₄₃	—	2	1	no	—
357	C₂²×C₄₃	—	2	2	no	—
358	C₂²×C₄₃	—	2	4	no	—
359	C₂²×C₄₃	—	2	2	no	—
360	C₂²×C₄₃	—	2	4	no	—
361	C₂²×C₄₃	—	2	2	no	—
362	C₂²×C₄₃	—	2	4	no	—
363	C₂²×C₄₃	#520	1	2	yes	—
364	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
365	C₄×C₄₃	—	2	4	no	—
366	C₄×C₄₃	—	2	2	no	—
367	C₄×C₄₃	—	2	2	no	—
368	C₄×C₄₃	—	2	1	no	—
369	C₄×C₄₃	—	2	2	no	—
370	C₄×C₄₃	—	2	2	no	—
371	C₄×C₄₃	—	2	2	no	—
372	C₄×C₄₃	—	2	1	no	—
373	C₄×C₄₃	—	2	2	no	—
374	C₄×C₄₃	—	2	1	no	—
375	C₄×C₄₃	—	2	2	no	—
376	C₄×C₄₃	#520	1	2	yes	—
377	C₄×C₄₃	#568	1	2	yes	—
378	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
379	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
380	#3480	C₂×C₄₃	1	1	yes	characteristic
381	#2995	C₂×C₄₃	1	4	yes	complemented
382	#2994	C₂×C₄₃	1	2	yes	complemented
383	#2993	C₂×C₄₃	1	2	yes	complemented
384	#2992	C₂×C₄₃	1	4	yes	complemented
385	#2990	C₂×C₄₃	1	2	yes	complemented
386	#2989	C₂×C₄₃	1	2	yes	complemented
387	Q₈×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
388	C₂×#446	C₂×C₄₃	1	1	yes	characteristic, complemented
389	#2935	C₂×C₄₃	1	1	yes	characteristic, complemented
390	#2935	C₂×C₄₃	1	2	yes	complemented
391	#2932	C₂×C₄₃	1	2	yes	complemented
392	#2931	C₂×C₄₃	1	1	yes	characteristic, complemented
393	#2923	C₂×C₄₃	1	2	yes	complemented
394	#2922	C₂×C₄₃	1	1	yes	characteristic, complemented
395	#2906	C₂×C₄₃	1	1	yes	characteristic, complemented
396	#2906	C₂×C₄₃	1	2	yes	complemented
397	C₂×C₄₃	—	2	2	no	—
398	C₂×C₄₃	—	4	2	no	—
399	C₂×C₄₃	—	4	4	no	—
400	C₂×C₄₃	C₂×#520	1	1	yes	characteristic
401	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
402	C₂×C₄₃	#3573	1	1	yes	characteristic
403	C₂×#131	C₂²×C₄₃	1	2	yes	—
404	C₂×#131	C₂²×C₄₃	1	2	yes	—
405	C₂×#131	C₂²×C₄₃	1	2	yes	—
406	#559	C₄×C₄₃	1	1	yes	characteristic
407	#559	C₄×C₄₃	1	2	yes	—
408	#557	C₄×C₄₃	1	1	yes	characteristic
409	#556	C₄×C₄₃	1	1	yes	characteristic
410	#556	C₄×C₄₃	1	2	yes	—
411	#553	C₄×C₄₃	1	2	yes	—
412	#553	C₄×C₄₃	1	4	yes	—
413	#550	C₄×C₄₃	1	1	yes	characteristic
414	#548	C₄×C₄₃	1	2	yes	—
415	#532	C₂²×C₄₃	1	1	yes	characteristic
416	#532	C₂²×C₄₃	1	2	yes	—
417	#529	C₂²×C₄₃	1	4	yes	—
418	#529	C₂²×C₄₃	1	2	yes	—
419	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
420	C₄×#41	C₂²×C₄₃	1	2	yes	—
421	C₄×#41	C₂²×C₄₃	1	2	yes	—
422	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
423	#446	C₂²×C₄₃	1	1	yes	characteristic
424	#446	C₂²×C₄₃	1	1	yes	characteristic
425	#446	C₂²×C₄₃	1	2	yes	—
426	#446	C₂²×C₄₃	1	1	yes	characteristic
427	#446	C₂²×C₄₃	1	1	yes	characteristic
428	#446	C₂²×C₄₃	1	2	yes	—
429	#446	C₂²×C₄₃	1	2	yes	—
430	#446	C₂²×C₄₃	1	4	yes	—
431	C₈×Q₈	C₂²×C₄₃	1	2	yes	—
432	#436	C₂²×C₄₃	1	2	yes	—
433	#436	C₂²×C₄₃	1	2	yes	—
434	#436	C₂²×C₄₃	1	2	yes	—
435	#436	C₂²×C₄₃	1	4	yes	—
436	#435	C₂²×C₄₃	1	4	yes	—
437	#435	C₂²×C₄₃	1	4	yes	—
438	#435	C₂²×C₄₃	1	4	yes	—
439	#435	C₂²×C₄₃	1	4	yes	—
440	#435	C₂²×C₄₃	1	4	yes	—
441	#435	C₂²×C₄₃	1	4	yes	—
442	#435	C₂²×C₄₃	1	4	yes	—
443	C₈×D₄	C₂²×C₄₃	1	2	yes	—
444	C₈×D₄	C₂²×C₄₃	1	2	yes	—
445	C₈×D₄	C₂²×C₄₃	1	2	yes	—
446	C₈×D₄	C₂²×C₄₃	1	4	yes	—
447	#433	C₂²×C₄₃	1	2	yes	—
448	#433	C₂²×C₄₃	1	2	yes	—
449	#433	C₂²×C₄₃	1	4	yes	—
450	#433	C₂²×C₄₃	1	4	yes	—
451	#432	C₂²×C₄₃	1	4	yes	—
452	#432	C₂²×C₄₃	1	4	yes	—
453	#431	C₂²×C₄₃	1	2	yes	—
454	#431	C₂²×C₄₃	1	2	yes	—
455	#424	C₂²×C₄₃	1	1	yes	characteristic
456	#424	C₂²×C₄₃	1	2	yes	—
457	#424	C₂²×C₄₃	1	4	yes	—
458	#424	C₂²×C₄₃	1	4	yes	—
459	#424	C₂²×C₄₃	1	4	yes	—
460	#424	C₂²×C₄₃	1	1	yes	characteristic
461	#423	C₂²×C₄₃	1	1	yes	characteristic
462	#423	C₂²×C₄₃	1	2	yes	—
463	#423	C₂²×C₄₃	1	4	yes	—
464	#423	C₂²×C₄₃	1	2	yes	—
465	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
466	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
467	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
468	C₂×C₄⋊C₈	C₂²×C₄₃	1	4	yes	—
469	#408	C₂²×C₄₃	1	1	yes	characteristic
470	#408	C₂²×C₄₃	1	1	yes	characteristic
471	#408	C₂²×C₄₃	1	2	yes	—
472	#408	C₂²×C₄₃	1	2	yes	—
473	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
474	C₄×M₁₆	C₂²×C₄₃	1	2	yes	—
475	C₂×#97	C₂²×C₄₃	1	2	yes	—
476	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
477	C₄₃	#60275	1	1	yes	characteristic, direct product factor, Sylow
478	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
479	C₂×#41	C₂³×C₄₃	1	1	yes	characteristic
480	C₂×#41	C₂³×C₄₃	1	2	yes	—
481	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
482	#131	—	4	4	no	—
483	#131	—	4	4	no	—
484	#131	—	4	4	no	—
485	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
486	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
487	C₂×M₁₆	C₂³×C₄₃	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
489	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
490	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
491	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
493	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
495	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
496	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
497	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
498	C₄⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
499	#127	C₂×C₄×C₄₃	1	1	yes	characteristic
500	#127	C₂×C₄×C₄₃	1	2	yes	—
501	#126	C₂×C₄×C₄₃	1	4	yes	—
502	#126	C₂×C₄×C₄₃	1	4	yes	—
503	#126	C₂×C₄×C₄₃	1	4	yes	—
504	#125	C₂×C₄×C₄₃	1	4	yes	—
505	#125	C₂×C₄×C₄₃	1	2	yes	—
506	#124	C₂×C₄×C₄₃	1	2	yes	—
507	#124	C₂×C₄×C₄₃	1	4	yes	—
508	#124	C₂×C₄×C₄₃	1	2	yes	—
509	#124	C₂×C₄×C₄₃	1	2	yes	—
510	#124	C₂×C₄×C₄₃	1	2	yes	—
511	#123	C₂×C₄×C₄₃	1	4	yes	—
512	#123	C₂×C₄×C₄₃	1	4	yes	—
513	#123	C₂×C₄×C₄₃	1	4	yes	—
514	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
515	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	—
516	#121	C₂×C₄×C₄₃	1	2	yes	—
517	#121	C₂×C₄×C₄₃	1	4	yes	—
518	#121	C₂×C₄×C₄₃	1	2	yes	—
519	#121	C₂×C₄×C₄₃	1	4	yes	—
520	#121	C₂×C₄×C₄₃	1	2	yes	—
521	#121	C₂×C₄×C₄₃	1	4	yes	—
522	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
523	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
524	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
525	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
526	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
527	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
528	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
529	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
530	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
531	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
532	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
533	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
534	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
535	C₄×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
536	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
537	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
538	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
539	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
540	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
541	C₄×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
542	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
543	C₄×D₄	C₂³×C₄₃	1	2	yes	—
544	C₄×D₄	C₂³×C₄₃	1	4	yes	—
545	C₄×D₄	C₂³×C₄₃	1	2	yes	—
546	C₄×D₄	C₂³×C₄₃	1	4	yes	—
547	#117	C₂×C₄×C₄₃	1	2	yes	—
548	#117	C₂×C₄×C₄₃	1	4	yes	—
549	#117	C₂³×C₄₃	1	1	yes	characteristic
550	#117	C₂³×C₄₃	1	2	yes	—
551	#117	C₂³×C₄₃	1	4	yes	—
552	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
554	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
556	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
558	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
559	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
560	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
561	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
562	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
563	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
564	C₄⋊C₈	C₂³×C₄₃	1	4	yes	—
565	C₄⋊C₈	C₂³×C₄₃	1	4	yes	—
566	C₄⋊C₈	C₂³×C₄₃	1	4	yes	—
567	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
568	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
569	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
570	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
571	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
572	C₄⋊C₈	C₂³×C₄₃	1	4	yes	—
573	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
574	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
575	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
576	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
577	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
578	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
579	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
580	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
581	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
583	#97	C₂³×C₄₃	1	2	yes	—
584	#97	C₂³×C₄₃	1	2	yes	—
585	#97	C₂³×C₄₃	1	2	yes	—
586	#97	C₂³×C₄₃	1	2	yes	—
587	#97	C₂³×C₄₃	1	4	yes	—
588	#97	C₂³×C₄₃	1	2	yes	—
589	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
590	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
591	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
592	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₄₃	1	2	yes	—
594	C₄×C₈	C₂³×C₄₃	1	4	yes	—
595	#41	—	2	4	no	—
596	#41	—	2	2	no	—
597	#41	—	2	2	no	—
598	#41	—	2	4	no	—
599	#41	—	4	4	no	—
600	C₂×Q₈	—	4	2	no	—
601	C₂×Q₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
602	C₂×Q₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
603	C₂×Q₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
604	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
605	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
606	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
607	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
608	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
609	C₂×D₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
610	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
611	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
612	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
613	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
614	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
615	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
616	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
618	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
619	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
620	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
621	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
622	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
624	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
625	M₁₆	—	2	4	no	—
626	M₁₆	—	2	2	no	—
627	M₁₆	—	2	2	no	—
628	M₁₆	—	4	4	no	—
629	M₁₆	—	4	4	no	—
630	M₁₆	—	4	4	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	4	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	4	4	no	—
635	C₂×C₈	—	4	4	no	—
636	C₂×C₈	—	4	4	no	—
637	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
638	C₂×C₈	C₂⁴×C₄₃	1	1	yes	characteristic
639	C₂×C₈	C₂⁴×C₄₃	1	1	yes	characteristic
640	C₂×C₈	C₂⁴×C₄₃	1	1	yes	characteristic
641	C₂×C₈	C₂⁴×C₄₃	1	1	yes	characteristic
642	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
643	C₂×C₈	C₂⁴×C₄₃	1	4	yes	—
644	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
645	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
646	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
647	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
648	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
649	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
650	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
651	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
652	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
653	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
654	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
655	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
656	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
657	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
658	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
659	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
660	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
661	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
662	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
663	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
664	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
665	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
666	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
667	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
668	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
669	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
670	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
671	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
672	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
673	C₂²⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
674	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
675	C₄²	C₂²×C₄×C₄₃	1	4	yes	—
676	C₄²	C₂²×C₄×C₄₃	1	4	yes	—
677	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
678	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
679	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
680	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
681	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
682	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
683	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
684	C₄²	C₂⁴×C₄₃	1	2	yes	—
685	C₄²	C₂⁴×C₄₃	1	2	yes	—
686	C₄²	C₂⁴×C₄₃	1	2	yes	—
687	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
688	C₂³	C₂³×C₄×C₄₃	1	4	yes	—
689	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
690	Q₈	—	2	2	no	—
691	Q₈	—	2	4	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	4	2	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	8	no	—
697	D₄	—	2	2	no	—
698	D₄	—	2	4	no	—
699	D₄	—	2	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
716	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
717	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
718	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
719	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
720	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
721	C₂×C₄	C₂³×C₄×C₄₃	1	4	yes	—
722	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
723	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
724	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
725	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
726	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
727	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
728	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
729	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
730	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
731	C₈	—	2	1	no	—
732	C₈	—	2	2	no	—
733	C₈	—	2	2	no	—
734	C₈	—	2	1	no	—
735	C₈	—	2	4	no	—
736	C₈	—	2	2	no	—
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	2	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	4	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	4	no	—
748	C₂²	C₄₃×#520	1	2	yes	—
749	C₂²	C₂⁴×C₄×C₄₃	1	1	yes	characteristic
750	C₄	—	2	4	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	1	no	—
760	C₄	—	2	2	no	—
761	C₄	C₄₃×#520	1	2	yes	—
762	C₄	C₄₃×#568	1	2	yes	—
763	C₄	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
764	C₄	C₂×2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
765	C₂	—	2	2	no	—
766	C₂	—	4	2	no	—
767	C₂	—	4	4	no	—
768	C₂	C₂×C₄₃×#520	1	1	yes	characteristic
769	C₂	C₂×C₄₃×#568	1	1	yes	characteristic
770	C₂	C₄₃×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
socle	C₂²×C₄₃	C₂⁴×C₄
prime radical	C₄₃×#3480	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2995	C₂	semidirect
3. C₄₃×#2994	C₂	semidirect
4. C₄₃×#2993	C₂	semidirect
5. C₄₃×#2992	C₂	semidirect
6. C₄₃×#2990	C₂	semidirect
7. C₄₃×#2989	C₂	semidirect
8. Q₈×M₁₆×C₄₃	C₂	semidirect
9. C₂×C₄₃×#446	C₂	semidirect
10. C₄₃×#2935	C₂	semidirect
11. C₄₃×#2935	C₂	semidirect
12. C₄₃×#2932	C₂	semidirect
13. C₄₃×#2931	C₂	semidirect
14. C₄₃×#2923	C₂	semidirect
15. C₄₃×#2922	C₂	semidirect
16. C₄₃×#2906	C₂	semidirect
17. C₄₃×#2906	C₂	semidirect
354. #60275	C₄₃	direct (N × H)
381. #2995	C₂×C₄₃	semidirect
382. #2994	C₂×C₄₃	semidirect
383. #2993	C₂×C₄₃	semidirect
384. #2992	C₂×C₄₃	semidirect
385. #2990	C₂×C₄₃	semidirect
386. #2989	C₂×C₄₃	semidirect
387. Q₈×M₁₆	C₂×C₄₃	semidirect
388. C₂×#446	C₂×C₄₃	semidirect
389. #2935	C₂×C₄₃	semidirect
390. #2935	C₂×C₄₃	semidirect
391. #2932	C₂×C₄₃	semidirect
392. #2931	C₂×C₄₃	semidirect
393. #2923	C₂×C₄₃	semidirect
394. #2922	C₂×C₄₃	semidirect
395. #2906	C₂×C₄₃	semidirect
396. #2906	C₂×C₄₃	semidirect
477. C₄₃	#60275	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3480	2
C₄₃×#2995	2
C₄₃×#2994	2
C₄₃×#2993	2
C₄₃×#2992	2
C₄₃×#2990	2
C₄₃×#2989	2
Q₈×M₁₆×C₄₃	2
C₂×C₄₃×#446	2
C₄₃×#2935	2
C₄₃×#2932	2
C₄₃×#2931	2
C₄₃×#2923	2
C₄₃×#2922	2
C₄₃×#2906	2
#60275	43

Subgroups — C43×#60275 #24980292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#60275 #24980292