Subgroups — C₄₃×#60297 #24980314

Order 11008.

1684 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3455	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2995	C₂	1	2	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	2	yes	maximal, complemented
6	C₄₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2981	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#2977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2976	C₂	1	2	yes	maximal, complemented
12	C₄₃×#2969	C₂	1	2	yes	maximal, complemented
13	C₄₃×#2968	C₂	1	2	yes	maximal, complemented
14	C₄₃×#2967	C₂	1	2	yes	maximal, complemented
15	C₄₃×#2966	C₂	1	2	yes	maximal, complemented
16	C₄₃×#2925	C₂	1	2	yes	maximal, complemented
17	C₄₃×#2924	C₂	1	2	yes	maximal, complemented
18	C₄₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₃×#542	C₄	1	2	yes	—
21	C₄₃×#542	C₄	1	2	yes	—
22	C₄₃×#541	C₄	1	2	yes	—
23	C₄₃×#540	C₄	1	2	yes	—
24	C₄₃×#539	C₄	1	2	yes	—
25	C₄₃×#539	C₄	1	2	yes	—
26	C₄₃×#538	C₄	1	2	yes	—
27	C₄₃×#538	C₄	1	2	yes	—
28	C₄₃×#533	C₂²	1	1	yes	characteristic
29	C₄₃×#532	C₂²	1	1	yes	characteristic
30	C₄₃×#529	C₂²	1	2	yes	—
31	C₄₃×#529	C₂²	1	2	yes	—
32	C₄₃×#529	C₂²	1	2	yes	—
33	C₄₃×#529	C₂²	1	2	yes	—
34	C₄₃×#525	C₂²	1	1	yes	characteristic
35	C₄₃×#525	C₂²	1	1	yes	characteristic
36	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
37	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#446	C₂²	1	2	yes	complemented
40	C₄₃×#446	C₂²	1	2	yes	complemented
41	C₄₃×#446	C₂²	1	2	yes	complemented
42	C₄₃×#446	C₂²	1	2	yes	complemented
43	C₄₃×#446	C₂²	1	2	yes	complemented
44	C₄₃×#446	C₂²	1	2	yes	complemented
45	C₈×Q₈×C₄₃	C₂²	1	2	yes	complemented
46	C₈×Q₈×C₄₃	C₂²	1	2	yes	complemented
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	2	yes	—
51	C₄₃×#436	C₂²	1	2	yes	complemented
52	C₄₃×#436	C₂²	1	2	yes	complemented
53	C₄₃×#435	C₂²	1	2	yes	—
54	C₄₃×#435	C₂²	1	2	yes	—
55	C₄₃×#435	C₂²	1	2	yes	—
56	C₄₃×#435	C₂²	1	2	yes	—
57	C₄₃×#435	C₂²	1	2	yes	—
58	C₄₃×#435	C₂²	1	2	yes	—
59	C₄₃×#435	C₂²	1	2	yes	—
60	C₄₃×#435	C₂²	1	2	yes	—
61	C₄₃×#435	C₂²	1	2	yes	complemented
62	C₄₃×#435	C₂²	1	2	yes	complemented
63	C₄₃×#435	C₂²	1	2	yes	complemented
64	C₄₃×#435	C₂²	1	2	yes	complemented
65	C₈×D₄×C₄₃	C₂²	1	2	yes	—
66	C₈×D₄×C₄₃	C₂²	1	2	yes	—
67	C₈×D₄×C₄₃	C₂²	1	2	yes	—
68	C₈×D₄×C₄₃	C₂²	1	2	yes	—
69	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
70	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
71	C₄₃×#433	C₂²	1	1	yes	characteristic
72	C₄₃×#433	C₂²	1	1	yes	characteristic
73	C₄₃×#433	C₂²	1	1	yes	characteristic
74	C₄₃×#433	C₂²	1	1	yes	characteristic
75	C₄₃×#433	C₂²	1	2	yes	—
76	C₄₃×#433	C₂²	1	2	yes	—
77	C₄₃×#433	C₂²	1	2	yes	—
78	C₄₃×#433	C₂²	1	2	yes	—
79	C₄₃×#433	C₂²	1	2	yes	—
80	C₄₃×#433	C₂²	1	2	yes	—
81	C₄₃×#433	C₂²	1	1	yes	characteristic, complemented
82	C₄₃×#433	C₂²	1	1	yes	characteristic, complemented
83	C₄₃×#433	C₂²	1	1	yes	characteristic, complemented
84	C₄₃×#433	C₂²	1	1	yes	characteristic, complemented
85	C₄₃×#433	C₂²	1	2	yes	complemented
86	C₄₃×#433	C₂²	1	2	yes	complemented
87	C₄₃×#432	C₂²	1	2	yes	—
88	C₄₃×#432	C₂²	1	2	yes	—
89	C₄₃×#432	C₂²	1	2	yes	complemented
90	C₄₃×#432	C₂²	1	2	yes	complemented
91	C₄₃×#431	C₂²	1	2	yes	—
92	C₄₃×#431	C₂²	1	2	yes	—
93	C₄₃×#431	C₂²	1	2	yes	complemented
94	C₄₃×#431	C₂²	1	2	yes	complemented
95	C₄₃×#424	C₂²	1	2	yes	—
96	C₄₃×#424	C₂²	1	2	yes	—
97	C₄₃×#424	C₂²	1	2	yes	complemented
98	C₄₃×#424	C₂²	1	2	yes	complemented
99	C₄₃×#423	C₂²	1	2	yes	complemented
100	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
101	C₄₃×#408	C₂²	1	2	yes	—
102	C₄₃×#408	C₂²	1	2	yes	—
103	C₄₃×#408	C₂²	1	2	yes	—
104	C₄₃×#408	C₂²	1	2	yes	—
105	C₄₃×#407	C₂²	1	2	yes	—
106	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
107	C₄₃×#405	C₂²	1	2	yes	—
108	C₄₃×#405	C₂²	1	2	yes	—
109	C₄₃×#405	C₂²	1	2	yes	complemented
110	C₄₃×#405	C₂²	1	2	yes	complemented
111	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
116	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
119	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
120	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
121	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
122	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
123	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
124	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
125	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
126	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
127	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
128	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
129	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
131	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
132	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
133	#126×C₄₃	C₂×C₄	1	2	yes	—
134	#126×C₄₃	C₂×C₄	1	2	yes	—
135	#126×C₄₃	C₂×C₄	1	2	yes	—
136	#126×C₄₃	C₂×C₄	1	2	yes	—
137	#126×C₄₃	C₂×C₄	1	2	yes	—
138	#126×C₄₃	C₂×C₄	1	2	yes	—
139	#126×C₄₃	C₂×C₄	1	2	yes	—
140	#126×C₄₃	C₂×C₄	1	2	yes	—
141	#125×C₄₃	C₂×C₄	1	2	yes	—
142	#125×C₄₃	C₂×C₄	1	2	yes	—
143	#125×C₄₃	C₂×C₄	1	2	yes	—
144	#125×C₄₃	C₂×C₄	1	2	yes	—
145	#125×C₄₃	C₂×C₄	1	2	yes	—
146	#124×C₄₃	C₂×C₄	1	2	yes	—
147	#124×C₄₃	C₂×C₄	1	2	yes	—
148	#124×C₄₃	C₂×C₄	1	2	yes	—
149	#124×C₄₃	C₂×C₄	1	2	yes	—
150	#124×C₄₃	C₂×C₄	1	1	yes	characteristic
151	#124×C₄₃	C₂×C₄	1	1	yes	characteristic
152	#123×C₄₃	C₂×C₄	1	1	yes	characteristic
153	#123×C₄₃	C₂×C₄	1	1	yes	characteristic
154	#123×C₄₃	C₂×C₄	1	2	yes	—
155	#123×C₄₃	C₂×C₄	1	2	yes	—
156	#123×C₄₃	C₂×C₄	1	2	yes	—
157	#123×C₄₃	C₂×C₄	1	2	yes	—
158	#123×C₄₃	C₂×C₄	1	2	yes	—
159	#123×C₄₃	C₂×C₄	1	2	yes	—
160	#123×C₄₃	C₂×C₄	1	2	yes	—
161	#123×C₄₃	C₂×C₄	1	2	yes	—
162	#123×C₄₃	C₂×C₄	1	2	yes	—
163	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
164	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
165	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
166	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
167	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
168	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
169	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
170	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
171	#121×C₄₃	C₂×C₄	1	2	yes	—
172	#121×C₄₃	C₂×C₄	1	2	yes	—
173	#121×C₄₃	C₂×C₄	1	2	yes	—
174	#121×C₄₃	C₂×C₄	1	2	yes	—
175	#121×C₄₃	C₂×C₄	1	2	yes	—
176	#121×C₄₃	C₂×C₄	1	2	yes	—
177	#121×C₄₃	C₂×C₄	1	2	yes	—
178	#121×C₄₃	C₂×C₄	1	2	yes	—
179	#120×C₄₃	C₂×C₄	1	1	yes	characteristic
180	#120×C₄₃	C₂×C₄	1	1	yes	characteristic
181	#120×C₄₃	C₂×C₄	1	2	yes	—
182	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
183	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
184	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
185	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
186	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
187	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
188	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
189	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
190	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
191	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
192	C₄×D₄×C₄₃	C₂³	1	2	yes	—
193	C₄×D₄×C₄₃	C₂³	1	2	yes	—
194	C₄×D₄×C₄₃	C₂³	1	2	yes	—
195	C₄×D₄×C₄₃	C₂³	1	2	yes	—
196	C₄×D₄×C₄₃	C₂³	1	2	yes	—
197	C₄×D₄×C₄₃	C₂³	1	2	yes	—
198	#117×C₄₃	C₂×C₄	1	2	yes	—
199	#117×C₄₃	C₂×C₄	1	2	yes	—
200	#117×C₄₃	C₂³	1	2	yes	—
201	#117×C₄₃	C₂³	1	2	yes	—
202	#117×C₄₃	C₂³	1	1	yes	characteristic
203	#117×C₄₃	C₂³	1	1	yes	characteristic
204	#117×C₄₃	C₂³	1	2	yes	—
205	#117×C₄₃	C₂³	1	1	yes	characteristic
206	#117×C₄₃	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
208	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
209	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
214	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
215	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
216	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
217	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
218	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
219	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
220	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
221	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
222	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
223	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
224	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
225	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
226	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
227	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
228	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
229	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
230	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
231	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
232	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
233	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
234	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
235	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
236	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
237	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
238	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
239	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
240	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
241	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
242	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
243	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
244	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
245	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
246	#97×C₄₃	C₂³	1	2	yes	—
247	#97×C₄₃	C₂³	1	1	yes	characteristic
248	#97×C₄₃	C₂³	1	1	yes	characteristic
249	#97×C₄₃	C₂³	1	2	yes	—
250	#97×C₄₃	C₂³	1	1	yes	characteristic
251	#97×C₄₃	C₂³	1	1	yes	characteristic
252	#97×C₄₃	C₂³	1	2	yes	—
253	#97×C₄₃	C₂³	1	2	yes	—
254	#97×C₄₃	C₂³	1	2	yes	—
255	#97×C₄₃	C₂³	1	2	yes	—
256	C₄×C₈×C₄₃	C₂³	1	2	yes	—
257	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
258	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
259	C₄×C₈×C₄₃	C₂³	1	2	yes	—
260	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₄₃	C₂³	1	2	yes	—
263	C₄×C₈×C₄₃	C₂³	1	2	yes	—
264	C₄×C₈×C₄₃	C₂³	1	2	yes	—
265	C₄×C₈×C₄₃	C₂³	1	2	yes	—
266	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
267	#41×C₄₃	—	4	2	no	—
268	#41×C₄₃	—	4	2	no	—
269	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
270	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
271	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
272	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
273	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
274	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
275	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
276	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
277	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
278	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
279	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
280	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
281	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
282	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
283	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
284	C₂²×C₄×C₄₃	—	4	2	no	—
285	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
286	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
287	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
288	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
289	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
290	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
291	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
292	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
293	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
298	M₁₆×C₄₃	—	4	2	no	—
299	M₁₆×C₄₃	—	4	2	no	—
300	M₁₆×C₄₃	—	4	2	no	—
301	M₁₆×C₄₃	—	4	2	no	—
302	M₁₆×C₄₃	—	4	2	no	—
303	M₁₆×C₄₃	—	4	2	no	—
304	C₂×C₈×C₄₃	—	4	2	no	—
305	C₂×C₈×C₄₃	—	4	2	no	—
306	C₂×C₈×C₄₃	—	4	2	no	—
307	C₂×C₈×C₄₃	—	4	2	no	—
308	C₂×C₈×C₄₃	—	4	2	no	—
309	C₂×C₈×C₄₃	—	4	2	no	—
310	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
311	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
312	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
313	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
318	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
319	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
320	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
321	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
322	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
323	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
324	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
325	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
326	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
327	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
328	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
329	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
330	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
331	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
332	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
333	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
334	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
335	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
336	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
337	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
338	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
339	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
340	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
341	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
342	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
343	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
344	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
345	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
346	C₂²⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
347	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
348	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
349	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
350	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
351	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
352	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
353	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
354	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
355	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
356	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
357	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
358	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
359	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
360	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
361	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
362	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
363	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
364	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
365	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
366	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
367	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
368	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
369	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
370	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
371	C₄²×C₄₃	C₂⁴	1	2	yes	—
372	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₄₃	C₂⁴	1	2	yes	—
375	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₂³×C₄₃	—	4	1	no	—
377	C₂³×C₄₃	—	4	2	no	—
378	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
379	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
380	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
381	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
382	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
383	Q₈×C₄₃	—	4	2	no	—
384	Q₈×C₄₃	—	4	2	no	—
385	Q₈×C₄₃	—	4	1	no	—
386	Q₈×C₄₃	—	4	1	no	—
387	D₄×C₄₃	—	4	2	no	—
388	D₄×C₄₃	—	4	2	no	—
389	D₄×C₄₃	—	4	2	no	—
390	D₄×C₄₃	—	4	2	no	—
391	D₄×C₄₃	—	4	2	no	—
392	D₄×C₄₃	—	4	2	no	—
393	D₄×C₄₃	—	4	1	no	—
394	D₄×C₄₃	—	4	1	no	—
395	D₄×C₄₃	—	4	2	no	—
396	D₄×C₄₃	—	4	1	no	—
397	D₄×C₄₃	—	4	1	no	—
398	C₂×C₄×C₄₃	—	2	2	no	—
399	C₂×C₄×C₄₃	—	2	2	no	—
400	C₂×C₄×C₄₃	—	2	2	no	—
401	C₂×C₄×C₄₃	—	2	2	no	—
402	C₂×C₄×C₄₃	—	2	2	no	—
403	C₂×C₄×C₄₃	—	2	2	no	—
404	C₂×C₄×C₄₃	—	2	2	no	—
405	C₂×C₄×C₄₃	—	4	1	no	—
406	C₂×C₄×C₄₃	—	4	2	no	—
407	C₂×C₄×C₄₃	—	4	2	no	—
408	C₂×C₄×C₄₃	—	4	2	no	—
409	C₂×C₄×C₄₃	—	4	2	no	—
410	C₂×C₄×C₄₃	—	4	2	no	—
411	C₂×C₄×C₄₃	—	4	2	no	—
412	C₂×C₄×C₄₃	—	4	2	no	—
413	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
414	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
415	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
417	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
418	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
419	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
420	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
424	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
425	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
426	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
427	C₈×C₄₃	—	2	2	no	—
428	C₈×C₄₃	—	2	2	no	—
429	C₈×C₄₃	—	2	2	no	—
430	C₈×C₄₃	—	2	2	no	—
431	C₈×C₄₃	—	2	2	no	—
432	C₈×C₄₃	—	2	2	no	—
433	C₈×C₄₃	—	2	2	no	—
434	C₈×C₄₃	—	2	2	no	—
435	#60297	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₂²×C₄₃	—	2	2	no	—
437	C₂²×C₄₃	—	2	1	no	—
438	C₂²×C₄₃	—	2	2	no	—
439	C₂²×C₄₃	—	2	1	no	—
440	C₂²×C₄₃	—	2	1	no	—
441	C₂²×C₄₃	—	2	2	no	—
442	C₂²×C₄₃	—	2	2	no	—
443	C₂²×C₄₃	—	2	2	no	—
444	C₂²×C₄₃	—	2	2	no	—
445	C₂²×C₄₃	—	2	2	no	—
446	C₂²×C₄₃	—	2	2	no	—
447	C₂²×C₄₃	—	2	2	no	—
448	C₂²×C₄₃	—	8	2	no	—
449	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
450	C₄×C₄₃	—	2	2	no	—
451	C₄×C₄₃	—	2	1	no	—
452	C₄×C₄₃	—	2	2	no	—
453	C₄×C₄₃	—	2	1	no	—
454	C₄×C₄₃	—	2	1	no	—
455	C₄×C₄₃	—	2	2	no	—
456	C₄×C₄₃	—	2	2	no	—
457	C₄×C₄₃	—	2	2	no	—
458	C₄×C₄₃	—	2	2	no	—
459	C₄×C₄₃	—	2	2	no	—
460	C₄×C₄₃	—	2	2	no	—
461	C₄×C₄₃	—	2	2	no	—
462	C₄×C₄₃	—	2	2	no	—
463	C₄×C₄₃	#585	1	2	yes	—
464	#3455	C₂×C₄₃	1	1	yes	characteristic
465	#2995	C₂×C₄₃	1	2	yes	complemented
466	#2994	C₂×C₄₃	1	2	yes	complemented
467	#2993	C₂×C₄₃	1	2	yes	complemented
468	#2992	C₂×C₄₃	1	2	yes	complemented
469	#2987	C₂×C₄₃	1	1	yes	characteristic, complemented
470	#2986	C₂×C₄₃	1	1	yes	characteristic, complemented
471	#2981	C₂×C₄₃	1	2	yes	complemented
472	#2978	C₂×C₄₃	1	1	yes	characteristic, complemented
473	#2977	C₂×C₄₃	1	1	yes	characteristic, complemented
474	#2976	C₂×C₄₃	1	2	yes	complemented
475	#2969	C₂×C₄₃	1	2	yes	complemented
476	#2968	C₂×C₄₃	1	2	yes	complemented
477	#2967	C₂×C₄₃	1	2	yes	complemented
478	#2966	C₂×C₄₃	1	2	yes	complemented
479	#2925	C₂×C₄₃	1	2	yes	complemented
480	#2924	C₂×C₄₃	1	2	yes	complemented
481	#2923	C₂×C₄₃	1	1	yes	characteristic, complemented
482	#2922	C₂×C₄₃	1	1	yes	characteristic, complemented
483	C₂×C₄₃	—	4	2	no	—
484	C₂×C₄₃	—	4	1	no	—
485	C₂×C₄₃	—	4	1	no	—
486	C₂×C₄₃	—	4	2	no	—
487	C₂×C₄₃	—	4	1	no	—
488	C₂×C₄₃	#3428	1	1	yes	characteristic
489	C₂×C₄₃	#3573	1	2	yes	—
490	#542	C₄×C₄₃	1	2	yes	—
491	#542	C₄×C₄₃	1	2	yes	—
492	#541	C₄×C₄₃	1	2	yes	—
493	#540	C₄×C₄₃	1	2	yes	—
494	#539	C₄×C₄₃	1	2	yes	—
495	#539	C₄×C₄₃	1	2	yes	—
496	#538	C₄×C₄₃	1	2	yes	—
497	#538	C₄×C₄₃	1	2	yes	—
498	#533	C₂²×C₄₃	1	1	yes	characteristic
499	#532	C₂²×C₄₃	1	1	yes	characteristic
500	#529	C₂²×C₄₃	1	2	yes	—
501	#529	C₂²×C₄₃	1	2	yes	—
502	#529	C₂²×C₄₃	1	2	yes	—
503	#529	C₂²×C₄₃	1	2	yes	—
504	#525	C₂²×C₄₃	1	1	yes	characteristic
505	#525	C₂²×C₄₃	1	1	yes	characteristic
506	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
507	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
508	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
509	#446	C₂²×C₄₃	1	2	yes	complemented
510	#446	C₂²×C₄₃	1	2	yes	complemented
511	#446	C₂²×C₄₃	1	2	yes	complemented
512	#446	C₂²×C₄₃	1	2	yes	complemented
513	#446	C₂²×C₄₃	1	2	yes	complemented
514	#446	C₂²×C₄₃	1	2	yes	complemented
515	C₈×Q₈	C₂²×C₄₃	1	2	yes	complemented
516	C₈×Q₈	C₂²×C₄₃	1	2	yes	complemented
517	#436	C₂²×C₄₃	1	2	yes	—
518	#436	C₂²×C₄₃	1	2	yes	—
519	#436	C₂²×C₄₃	1	2	yes	—
520	#436	C₂²×C₄₃	1	2	yes	—
521	#436	C₂²×C₄₃	1	2	yes	complemented
522	#436	C₂²×C₄₃	1	2	yes	complemented
523	#435	C₂²×C₄₃	1	2	yes	—
524	#435	C₂²×C₄₃	1	2	yes	—
525	#435	C₂²×C₄₃	1	2	yes	—
526	#435	C₂²×C₄₃	1	2	yes	—
527	#435	C₂²×C₄₃	1	2	yes	—
528	#435	C₂²×C₄₃	1	2	yes	—
529	#435	C₂²×C₄₃	1	2	yes	—
530	#435	C₂²×C₄₃	1	2	yes	—
531	#435	C₂²×C₄₃	1	2	yes	complemented
532	#435	C₂²×C₄₃	1	2	yes	complemented
533	#435	C₂²×C₄₃	1	2	yes	complemented
534	#435	C₂²×C₄₃	1	2	yes	complemented
535	C₈×D₄	C₂²×C₄₃	1	2	yes	—
536	C₈×D₄	C₂²×C₄₃	1	2	yes	—
537	C₈×D₄	C₂²×C₄₃	1	2	yes	—
538	C₈×D₄	C₂²×C₄₃	1	2	yes	—
539	C₈×D₄	C₂²×C₄₃	1	2	yes	complemented
540	C₈×D₄	C₂²×C₄₃	1	2	yes	complemented
541	#433	C₂²×C₄₃	1	1	yes	characteristic
542	#433	C₂²×C₄₃	1	1	yes	characteristic
543	#433	C₂²×C₄₃	1	1	yes	characteristic
544	#433	C₂²×C₄₃	1	1	yes	characteristic
545	#433	C₂²×C₄₃	1	2	yes	—
546	#433	C₂²×C₄₃	1	2	yes	—
547	#433	C₂²×C₄₃	1	2	yes	—
548	#433	C₂²×C₄₃	1	2	yes	—
549	#433	C₂²×C₄₃	1	2	yes	—
550	#433	C₂²×C₄₃	1	2	yes	—
551	#433	C₂²×C₄₃	1	1	yes	characteristic, complemented
552	#433	C₂²×C₄₃	1	1	yes	characteristic, complemented
553	#433	C₂²×C₄₃	1	1	yes	characteristic, complemented
554	#433	C₂²×C₄₃	1	1	yes	characteristic, complemented
555	#433	C₂²×C₄₃	1	2	yes	complemented
556	#433	C₂²×C₄₃	1	2	yes	complemented
557	#432	C₂²×C₄₃	1	2	yes	—
558	#432	C₂²×C₄₃	1	2	yes	—
559	#432	C₂²×C₄₃	1	2	yes	complemented
560	#432	C₂²×C₄₃	1	2	yes	complemented
561	#431	C₂²×C₄₃	1	2	yes	—
562	#431	C₂²×C₄₃	1	2	yes	—
563	#431	C₂²×C₄₃	1	2	yes	complemented
564	#431	C₂²×C₄₃	1	2	yes	complemented
565	#424	C₂²×C₄₃	1	2	yes	—
566	#424	C₂²×C₄₃	1	2	yes	—
567	#424	C₂²×C₄₃	1	2	yes	complemented
568	#424	C₂²×C₄₃	1	2	yes	complemented
569	#423	C₂²×C₄₃	1	2	yes	complemented
570	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
571	#408	C₂²×C₄₃	1	2	yes	—
572	#408	C₂²×C₄₃	1	2	yes	—
573	#408	C₂²×C₄₃	1	2	yes	—
574	#408	C₂²×C₄₃	1	2	yes	—
575	#407	C₂²×C₄₃	1	2	yes	—
576	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
577	#405	C₂²×C₄₃	1	2	yes	—
578	#405	C₂²×C₄₃	1	2	yes	—
579	#405	C₂²×C₄₃	1	2	yes	complemented
580	#405	C₂²×C₄₃	1	2	yes	complemented
581	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
582	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
583	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic, complemented
584	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
585	C₄₃	#60297	1	1	yes	characteristic, direct product factor, Sylow
586	C₂×#41	C₂³×C₄₃	1	1	yes	characteristic
587	C₂×#41	C₂³×C₄₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
589	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
590	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
591	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
592	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
593	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
594	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
595	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
596	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
597	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
598	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
599	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
600	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
601	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
602	C₄⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
603	#127	C₂×C₄×C₄₃	1	1	yes	characteristic
604	#126	C₂×C₄×C₄₃	1	2	yes	—
605	#126	C₂×C₄×C₄₃	1	2	yes	—
606	#126	C₂×C₄×C₄₃	1	2	yes	—
607	#126	C₂×C₄×C₄₃	1	2	yes	—
608	#126	C₂×C₄×C₄₃	1	2	yes	—
609	#126	C₂×C₄×C₄₃	1	2	yes	—
610	#126	C₂×C₄×C₄₃	1	2	yes	—
611	#126	C₂×C₄×C₄₃	1	2	yes	—
612	#125	C₂×C₄×C₄₃	1	2	yes	—
613	#125	C₂×C₄×C₄₃	1	2	yes	—
614	#125	C₂×C₄×C₄₃	1	2	yes	—
615	#125	C₂×C₄×C₄₃	1	2	yes	—
616	#125	C₂×C₄×C₄₃	1	2	yes	—
617	#124	C₂×C₄×C₄₃	1	2	yes	—
618	#124	C₂×C₄×C₄₃	1	2	yes	—
619	#124	C₂×C₄×C₄₃	1	2	yes	—
620	#124	C₂×C₄×C₄₃	1	2	yes	—
621	#124	C₂×C₄×C₄₃	1	1	yes	characteristic
622	#124	C₂×C₄×C₄₃	1	1	yes	characteristic
623	#123	C₂×C₄×C₄₃	1	1	yes	characteristic
624	#123	C₂×C₄×C₄₃	1	1	yes	characteristic
625	#123	C₂×C₄×C₄₃	1	2	yes	—
626	#123	C₂×C₄×C₄₃	1	2	yes	—
627	#123	C₂×C₄×C₄₃	1	2	yes	—
628	#123	C₂×C₄×C₄₃	1	2	yes	—
629	#123	C₂×C₄×C₄₃	1	2	yes	—
630	#123	C₂×C₄×C₄₃	1	2	yes	—
631	#123	C₂×C₄×C₄₃	1	2	yes	—
632	#123	C₂×C₄×C₄₃	1	2	yes	—
633	#123	C₂×C₄×C₄₃	1	2	yes	—
634	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
635	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
636	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
637	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
638	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
639	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
640	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
641	C₂²⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
642	#121	C₂×C₄×C₄₃	1	2	yes	—
643	#121	C₂×C₄×C₄₃	1	2	yes	—
644	#121	C₂×C₄×C₄₃	1	2	yes	—
645	#121	C₂×C₄×C₄₃	1	2	yes	—
646	#121	C₂×C₄×C₄₃	1	2	yes	—
647	#121	C₂×C₄×C₄₃	1	2	yes	—
648	#121	C₂×C₄×C₄₃	1	2	yes	—
649	#121	C₂×C₄×C₄₃	1	2	yes	—
650	#120	C₂×C₄×C₄₃	1	1	yes	characteristic
651	#120	C₂×C₄×C₄₃	1	1	yes	characteristic
652	#120	C₂×C₄×C₄₃	1	2	yes	—
653	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
654	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
655	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
656	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
657	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
658	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
659	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
660	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
661	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
662	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
663	C₄×D₄	C₂³×C₄₃	1	2	yes	—
664	C₄×D₄	C₂³×C₄₃	1	2	yes	—
665	C₄×D₄	C₂³×C₄₃	1	2	yes	—
666	C₄×D₄	C₂³×C₄₃	1	2	yes	—
667	C₄×D₄	C₂³×C₄₃	1	2	yes	—
668	C₄×D₄	C₂³×C₄₃	1	2	yes	—
669	#117	C₂×C₄×C₄₃	1	2	yes	—
670	#117	C₂×C₄×C₄₃	1	2	yes	—
671	#117	C₂³×C₄₃	1	2	yes	—
672	#117	C₂³×C₄₃	1	2	yes	—
673	#117	C₂³×C₄₃	1	1	yes	characteristic
674	#117	C₂³×C₄₃	1	1	yes	characteristic
675	#117	C₂³×C₄₃	1	2	yes	—
676	#117	C₂³×C₄₃	1	1	yes	characteristic
677	#117	C₂³×C₄₃	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
680	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
685	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
686	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
687	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
688	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
689	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
690	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
691	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
692	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
693	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
694	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
695	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
696	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
697	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
698	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
699	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
700	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
701	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
702	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
703	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
704	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
706	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
707	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
708	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
713	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
714	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
715	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
716	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
717	#97	C₂³×C₄₃	1	2	yes	—
718	#97	C₂³×C₄₃	1	1	yes	characteristic
719	#97	C₂³×C₄₃	1	1	yes	characteristic
720	#97	C₂³×C₄₃	1	2	yes	—
721	#97	C₂³×C₄₃	1	1	yes	characteristic
722	#97	C₂³×C₄₃	1	1	yes	characteristic
723	#97	C₂³×C₄₃	1	2	yes	—
724	#97	C₂³×C₄₃	1	2	yes	—
725	#97	C₂³×C₄₃	1	2	yes	—
726	#97	C₂³×C₄₃	1	2	yes	—
727	C₄×C₈	C₂³×C₄₃	1	2	yes	—
728	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
729	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
730	C₄×C₈	C₂³×C₄₃	1	2	yes	—
731	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
732	C₄×C₈	C₂³×C₄₃	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₄₃	1	2	yes	—
734	C₄×C₈	C₂³×C₄₃	1	2	yes	—
735	C₄×C₈	C₂³×C₄₃	1	2	yes	—
736	C₄×C₈	C₂³×C₄₃	1	2	yes	—
737	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
738	#41	—	4	2	no	—
739	#41	—	4	2	no	—
740	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
741	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
742	C₂×Q₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
743	C₂×Q₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
744	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
745	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
746	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
747	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
748	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
749	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
750	C₂×D₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
751	C₂×D₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
752	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
753	C₂×D₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
754	C₂×D₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
757	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
758	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
759	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
760	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
761	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
762	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
763	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
769	M₁₆	—	4	2	no	—
770	M₁₆	—	4	2	no	—
771	M₁₆	—	4	2	no	—
772	M₁₆	—	4	2	no	—
773	M₁₆	—	4	2	no	—
774	M₁₆	—	4	2	no	—
775	C₂×C₈	—	4	2	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	—	4	2	no	—
778	C₂×C₈	—	4	2	no	—
779	C₂×C₈	—	4	2	no	—
780	C₂×C₈	—	4	2	no	—
781	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
782	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
783	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
784	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
785	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
786	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
787	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
788	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
789	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
790	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
791	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
792	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
793	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
794	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
795	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
796	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
797	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
798	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
799	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
800	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
801	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
802	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
803	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
804	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
805	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
806	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
807	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
808	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
809	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
810	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
811	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
819	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
820	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
821	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
822	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
823	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
824	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
825	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
826	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
827	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
828	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
829	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
830	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
831	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
832	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
833	C₂²⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
834	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
835	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
836	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
837	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
838	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
839	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
840	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
841	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
842	C₄²	C₂⁴×C₄₃	1	2	yes	—
843	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
844	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
845	C₄²	C₂⁴×C₄₃	1	2	yes	—
846	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
847	C₂³	—	4	1	no	—
848	C₂³	—	4	2	no	—
849	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
850	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
851	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
852	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
853	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
854	Q₈	—	4	1	no	—
855	Q₈	—	4	1	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	4	2	no	—
858	D₄	—	4	1	no	—
859	D₄	—	4	1	no	—
860	D₄	—	4	2	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	2	no	—
864	D₄	—	4	2	no	—
865	D₄	—	4	2	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	2	no	—
868	D₄	—	4	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	2	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	2	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	—	4	2	no	—
884	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
885	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
886	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
887	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
888	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
889	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
891	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
892	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
893	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
894	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
895	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
896	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
897	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	2	no	—
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	2	no	—
904	C₈	—	2	2	no	—
905	C₈	—	2	2	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	8	2	no	—
919	C₂²	C₂⁴×C₄×C₄₃	1	1	yes	characteristic
920	C₄	—	2	1	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	C₄₃×#585	1	2	yes	—
934	C₂	—	4	1	no	—
935	C₂	—	4	2	no	—
936	C₂	—	4	2	no	—
937	C₂	—	4	1	no	—
938	C₂	—	4	1	no	—
939	C₂	C₄₃×#3428	1	1	yes	characteristic
940	C₂	C₄₃×#3573	1	2	yes	—

	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×#3455	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×#2987	C₂	semidirect
7. C₄₃×#2986	C₂	semidirect
8. C₄₃×#2981	C₂	semidirect
9. C₄₃×#2978	C₂	semidirect
10. C₄₃×#2977	C₂	semidirect
11. C₄₃×#2976	C₂	semidirect
12. C₄₃×#2969	C₂	semidirect
13. C₄₃×#2968	C₂	semidirect
14. C₄₃×#2967	C₂	semidirect
15. C₄₃×#2966	C₂	semidirect
16. C₄₃×#2925	C₂	semidirect
17. C₄₃×#2924	C₂	semidirect
18. C₄₃×#2923	C₂	semidirect
19. C₄₃×#2922	C₂	semidirect
39. C₄₃×#446	C₂²	semidirect
40. C₄₃×#446	C₂²	semidirect
41. C₄₃×#446	C₂²	semidirect
42. C₄₃×#446	C₂²	semidirect
43. C₄₃×#446	C₂²	semidirect
44. C₄₃×#446	C₂²	semidirect
45. C₈×Q₈×C₄₃	C₂²	semidirect
46. C₈×Q₈×C₄₃	C₂²	semidirect
51. C₄₃×#436	C₂²	semidirect
52. C₄₃×#436	C₂²	semidirect
61. C₄₃×#435	C₂²	semidirect
62. C₄₃×#435	C₂²	semidirect
63. C₄₃×#435	C₂²	semidirect
64. C₄₃×#435	C₂²	semidirect
69. C₈×D₄×C₄₃	C₂²	semidirect
70. C₈×D₄×C₄₃	C₂²	semidirect
81. C₄₃×#433	C₂²	semidirect
82. C₄₃×#433	C₂²	semidirect
83. C₄₃×#433	C₂²	semidirect
84. C₄₃×#433	C₂²	semidirect
85. C₄₃×#433	C₂²	semidirect
86. C₄₃×#433	C₂²	semidirect
89. C₄₃×#432	C₂²	semidirect
90. C₄₃×#432	C₂²	semidirect
93. C₄₃×#431	C₂²	semidirect
94. C₄₃×#431	C₂²	semidirect
97. C₄₃×#424	C₂²	semidirect
98. C₄₃×#424	C₂²	semidirect
99. C₄₃×#423	C₂²	semidirect
100. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
109. C₄₃×#405	C₂²	semidirect
110. C₄₃×#405	C₂²	semidirect
111. C₄×M₁₆×C₄₃	C₂²	semidirect
112. C₄×M₁₆×C₄₃	C₂²	semidirect
113. C₂×#97×C₄₃	C₂²	semidirect
114. C₂×C₄×C₈×C₄₃	C₂²	semidirect
435. #60297	C₄₃	direct (N × H)
465. #2995	C₂×C₄₃	semidirect
466. #2994	C₂×C₄₃	semidirect
467. #2993	C₂×C₄₃	semidirect
468. #2992	C₂×C₄₃	semidirect
469. #2987	C₂×C₄₃	semidirect
470. #2986	C₂×C₄₃	semidirect
471. #2981	C₂×C₄₃	semidirect
472. #2978	C₂×C₄₃	semidirect
473. #2977	C₂×C₄₃	semidirect
474. #2976	C₂×C₄₃	semidirect
475. #2969	C₂×C₄₃	semidirect
476. #2968	C₂×C₄₃	semidirect
477. #2967	C₂×C₄₃	semidirect
478. #2966	C₂×C₄₃	semidirect
479. #2925	C₂×C₄₃	semidirect
480. #2924	C₂×C₄₃	semidirect
481. #2923	C₂×C₄₃	semidirect
482. #2922	C₂×C₄₃	semidirect
509. #446	C₂²×C₄₃	semidirect
510. #446	C₂²×C₄₃	semidirect
511. #446	C₂²×C₄₃	semidirect
512. #446	C₂²×C₄₃	semidirect
513. #446	C₂²×C₄₃	semidirect
514. #446	C₂²×C₄₃	semidirect
515. C₈×Q₈	C₂²×C₄₃	semidirect
516. C₈×Q₈	C₂²×C₄₃	semidirect
521. #436	C₂²×C₄₃	semidirect
522. #436	C₂²×C₄₃	semidirect
531. #435	C₂²×C₄₃	semidirect
532. #435	C₂²×C₄₃	semidirect
533. #435	C₂²×C₄₃	semidirect
534. #435	C₂²×C₄₃	semidirect
539. C₈×D₄	C₂²×C₄₃	semidirect
540. C₈×D₄	C₂²×C₄₃	semidirect
551. #433	C₂²×C₄₃	semidirect
552. #433	C₂²×C₄₃	semidirect
553. #433	C₂²×C₄₃	semidirect
554. #433	C₂²×C₄₃	semidirect
555. #433	C₂²×C₄₃	semidirect
556. #433	C₂²×C₄₃	semidirect
559. #432	C₂²×C₄₃	semidirect
560. #432	C₂²×C₄₃	semidirect
563. #431	C₂²×C₄₃	semidirect
564. #431	C₂²×C₄₃	semidirect
567. #424	C₂²×C₄₃	semidirect
568. #424	C₂²×C₄₃	semidirect
569. #423	C₂²×C₄₃	semidirect
570. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
579. #405	C₂²×C₄₃	semidirect
580. #405	C₂²×C₄₃	semidirect
581. C₄×M₁₆	C₂²×C₄₃	semidirect
582. C₄×M₁₆	C₂²×C₄₃	semidirect
583. C₂×#97	C₂²×C₄₃	semidirect
584. C₂×C₄×C₈	C₂²×C₄₃	semidirect
585. C₄₃	#60297	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×#3455	2
C₄₃×#2995	2
C₄₃×#2994	2
C₄₃×#2993	2
C₄₃×#2992	2
C₄₃×#2987	2
C₄₃×#2986	2
C₄₃×#2981	2
C₄₃×#2978	2
C₄₃×#2977	2
C₄₃×#2976	2
C₄₃×#2969	2
C₄₃×#2968	2
C₄₃×#2967	2
C₄₃×#2966	2
C₄₃×#2925	2
C₄₃×#2924	2
C₄₃×#2923	2
C₄₃×#2922	2
#60297	43

Subgroups — C43×#60297 #24980314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#60297 #24980314