Subgroups — #25961450

Order 11008.

2212 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#532×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#19143672	C₂	1	2	yes	maximal, complemented
3	#19143669	C₂	1	2	yes	maximal, complemented
4	#19143660	C₂	1	2	yes	maximal, complemented
5	#19143658	C₂	1	2	yes	maximal, complemented
6	#19143633	C₂	1	2	yes	maximal, complemented
7	#19143628	C₂	1	2	yes	maximal, complemented
8	#19143627	C₂	1	2	yes	maximal, complemented
9	#19143616	C₂	1	2	yes	maximal, complemented
10	#19143337	C₂	1	2	yes	maximal, complemented
11	#19143335	C₂	1	2	yes	maximal, complemented
12	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143307	C₂	1	1	yes	maximal, characteristic, complemented
14	#19143306	C₂	1	1	yes	maximal, characteristic, complemented
15	#19143227	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14582950	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143043	C₂	1	2	yes	maximal, complemented
18	#19143042	C₂	1	2	yes	maximal, complemented
19	C₄₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×D₄₃	C₂²	1	2	yes	—
21	C₂×#13063333	C₂²	1	2	yes	complemented
22	C₂×#13063332	C₂²	1	2	yes	complemented
23	C₂×#13063331	C₂²	1	2	yes	complemented
24	#14583450	C₄	1	1	yes	characteristic
25	#14583449	C₂²	1	1	yes	characteristic
26	#14583448	C₄	1	2	yes	—
27	#14583447	C₄	1	1	yes	characteristic
28	#14583446	C₂²	1	2	yes	—
29	#14583446	C₂²	1	2	yes	—
30	#14583445	C₂²	1	2	yes	—
31	#14583444	C₄	1	2	yes	—
32	#14583444	C₄	1	2	yes	—
33	C₄⋊Q₈×D₄₃	C₄	1	1	yes	characteristic
34	#127×D₄₃	C₄	1	1	yes	characteristic
35	#124×D₄₃	C₄	1	2	yes	—
36	#121×D₄₃	C₄	1	2	yes	—
37	#121×D₄₃	C₄	1	2	yes	—
38	C₄×D₄×D₄₃	C₂²	1	2	yes	—
39	C₄×D₄×D₄₃	C₂²	1	2	yes	—
40	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
41	#14582978	C₂²	1	2	yes	complemented
42	#14582978	C₂²	1	2	yes	complemented
43	#14582977	C₂²	1	2	yes	complemented
44	#14582977	C₂²	1	2	yes	complemented
45	#14582976	C₂²	1	2	yes	complemented
46	#14582976	C₂²	1	2	yes	complemented
47	#14582975	C₂²	1	4	yes	complemented
48	#14582974	C₂²	1	4	yes	complemented
49	#14582973	C₂²	1	4	yes	complemented
50	#14582970	C₂²	1	4	yes	complemented
51	#14582968	C₂²	1	4	yes	complemented
52	#14582967	C₂²	1	4	yes	complemented
53	C₈×D₁₇₂	C₂²	1	2	yes	complemented
54	C₈×D₁₇₂	C₂²	1	2	yes	complemented
55	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
56	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
57	#14582964	C₂²	1	2	yes	complemented
58	#14582964	C₂²	1	2	yes	complemented
59	C₈×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
60	(C₂²⋊D₄₃)⋊C₈	C₂²	1	4	yes	complemented
61	#14582955	C₂²	1	2	yes	—
62	#14582955	C₂²	1	2	yes	complemented
63	#14582951	C₂²	1	2	yes	—
64	#14582951	C₂²	1	2	yes	complemented
65	#14582950	C₂²	1	1	yes	characteristic
66	#14582950	C₂²	1	1	yes	characteristic
67	#14582950	C₂²	1	1	yes	characteristic
68	#14582950	C₂²	1	1	yes	characteristic
69	#14582950	C₂²	1	1	yes	characteristic, complemented
70	#14582950	C₂²	1	1	yes	characteristic, complemented
71	#14582950	C₂²	1	1	yes	characteristic, complemented
72	#14582950	C₂²	1	1	yes	characteristic, complemented
73	#14582923	C₂²	1	1	yes	characteristic, complemented
74	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
75	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
76	#14582867	C₂²	1	2	yes	complemented
77	#14582867	C₂²	1	4	yes	complemented
78	#14582866	C₂²	1	2	yes	complemented
79	#14582865	C₂²	1	2	yes	complemented
80	#14582865	C₂²	1	4	yes	complemented
81	#14582864	C₂²	1	4	yes	complemented
82	#14582864	C₂²	1	4	yes	complemented
83	#14582862	C₂²	1	2	yes	—
84	#14582862	C₂²	1	4	yes	—
85	#14582861	C₂²	1	4	yes	—
86	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
87	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
88	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	4	yes	—
89	C₂²⋊C₈×D₄₃	C₂²	1	4	yes	—
90	M₁₆×Dic₄₃	C₂²	1	2	yes	complemented
91	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
92	C₂×#131×C₄₃	C₂²	1	2	yes	complemented
93	C₄₃×#532	C₂²	1	1	yes	characteristic
94	C₄₃×#436	C₂²	1	2	yes	complemented
95	C₄₃×#436	C₂²	1	2	yes	complemented
96	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
97	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
98	C₄₃×#423	C₂²	1	1	yes	characteristic, complemented
99	C₄₃×#408	C₂²	1	2	yes	complemented
100	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
101	C₂×#10621902	C₂×C₄	1	2	yes	—
102	C₂×#10621898	C₂³	1	2	yes	—
103	C₂×#10621898	C₂³	1	4	yes	—
104	C₂×#10621900	C₂×C₄	1	4	yes	—
105	C₂×#10621900	C₂×C₄	1	2	yes	—
106	#41×D₄₃	—	4	4	no	—
107	#41×D₄₃	—	4	4	no	—
108	C₂×Q₈×D₄₃	C₂×C₄	1	2	yes	—
109	C₂×D₄×D₄₃	C₂×C₄	1	2	yes	—
110	C₂×D₄×D₄₃	C₂×C₄	1	2	yes	—
111	C₂×D₄×D₄₃	C₂×C₄	1	4	yes	—
112	C₂×D₄×D₄₃	C₂×C₄	1	2	yes	—
113	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
114	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
115	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
117	#13063333	—	4	4	no	—
118	#13063332	—	4	4	no	—
119	#13063331	—	4	4	no	—
120	C₂×#10621877	C₂³	1	2	yes	—
121	C₂×#10621877	C₂³	1	4	yes	—
122	C₂×#10621872	C₂³	1	4	yes	—
123	C₂×#10621872	C₂³	1	4	yes	—
124	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
127	C₂×C₈×D₄₃	C₂³	1	4	yes	—
128	C₂×C₈×D₄₃	C₂³	1	4	yes	—
129	#13063325	C₂×C₄	1	1	yes	characteristic
130	#13063324	C₂×C₄	1	2	yes	—
131	#13063324	C₂×C₄	1	2	yes	—
132	#13063323	C₂×C₄	1	2	yes	—
133	#13063322	C₂×C₄	1	1	yes	characteristic
134	#13063321	C₂×C₄	1	2	yes	—
135	#13063321	C₂×C₄	1	2	yes	—
136	#13063321	C₂×C₄	1	2	yes	—
137	#13063314	C₂×C₄	1	2	yes	—
138	#13063313	C₂×C₄	1	2	yes	—
139	#13063312	C₂×C₄	1	2	yes	—
140	#13063311	C₂×C₄	1	4	yes	—
141	#13063311	C₂×C₄	1	4	yes	—
142	#13063300	C₂×C₄	1	2	yes	—
143	#13063300	C₂×C₄	1	2	yes	—
144	#13063299	C₂×C₄	1	2	yes	—
145	#13063299	C₂×C₄	1	2	yes	—
146	#13063298	C₂×C₄	1	4	yes	—
147	#13063298	C₂×C₄	1	4	yes	—
148	#13063297	C₂×C₄	1	4	yes	—
149	#13063297	C₂×C₄	1	4	yes	—
150	#13063296	C₂×C₄	1	2	yes	—
151	#13063296	C₂×C₄	1	2	yes	—
152	C₄×D₁₇₂	C₂³	1	2	yes	—
153	C₄×D₁₇₂	C₂³	1	2	yes	—
154	D₄×Dic₄₃	C₂×C₄	1	2	yes	—
155	D₄×Dic₄₃	C₂×C₄	1	2	yes	—
156	#13063287	C₂×C₄	1	2	yes	—
157	#13063287	C₂×C₄	1	2	yes	—
158	C₄×C₂²⋊D₄₃	C₂³	1	4	yes	—
159	C₄×C₂²⋊D₄₃	C₂³	1	4	yes	—
160	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	4	yes	—
161	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	4	yes	—
162	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
163	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
164	C₂²⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
165	C₂²⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
166	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
167	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
168	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
169	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
170	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
171	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
172	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
173	C₄²×D₄₃	C₂³	1	1	yes	characteristic
174	C₄²×D₄₃	C₂³	1	1	yes	characteristic
175	C₄²×D₄₃	C₂³	1	1	yes	characteristic
176	C₄²×D₄₃	C₂³	1	1	yes	characteristic
177	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
178	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
179	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
180	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
181	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
182	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
183	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
184	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
185	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
186	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
187	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
188	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
189	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
190	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
191	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
192	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
193	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
194	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
195	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
196	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
197	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
198	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
199	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
200	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
201	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
202	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
203	#13063235	C₂³	1	4	yes	—
204	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
205	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
206	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
207	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
208	C₈×Dic₄₃	C₂³	1	4	yes	—
209	C₂×#41×C₄₃	C₂³	1	2	yes	—
210	#131×C₄₃	—	4	4	no	—
211	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
212	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
213	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
214	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
215	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
216	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
217	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
218	#124×C₄₃	C₂×C₄	1	2	yes	—
219	#121×C₄₃	C₂×C₄	1	2	yes	—
220	#121×C₄₃	C₂×C₄	1	2	yes	—
221	C₄×D₄×C₄₃	C₂³	1	2	yes	—
222	C₄×D₄×C₄₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
224	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
225	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
228	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
231	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
232	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
233	C₂³×D₄₃	C₂²×C₄	1	4	yes	—
234	#41×C₄₃	—	2	4	no	—
235	#41×C₄₃	—	2	4	no	—
236	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
237	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
238	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
239	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
240	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
241	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
244	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
246	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
247	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
248	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
249	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
250	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
251	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
252	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
253	C₂²×Dic₄₃	C₂²×C₄	1	4	yes	—
254	#10621902	—	4	4	no	—
255	Q₈×D₄₃	—	4	4	no	—
256	#10621900	—	4	4	no	—
257	#10621900	—	4	8	no	—
258	D₄×D₄₃	—	2	8	no	—
259	D₄×D₄₃	—	4	8	no	—
260	D₄×D₄₃	—	4	4	no	—
261	D₄×D₄₃	—	4	4	no	—
262	#10621898	—	2	4	no	—
263	#10621898	—	2	4	no	—
264	#10621898	—	4	4	no	—
265	#10621898	—	4	4	no	—
266	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
267	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
268	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
269	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
270	C₂×C₄×D₄₃	—	2	2	no	—
271	C₂×C₄×D₄₃	—	2	2	no	—
272	C₂×C₄×D₄₃	—	2	4	no	—
273	C₂×C₄×D₄₃	—	4	2	no	—
274	C₂×C₄×D₄₃	—	4	4	no	—
275	C₂×C₄×D₄₃	—	4	4	no	—
276	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
277	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
278	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
279	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
280	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
281	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
282	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
283	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
284	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
285	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
286	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
287	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
288	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
291	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
292	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
293	M₁₆×C₄₃	—	2	4	no	—
294	M₁₆×C₄₃	—	4	4	no	—
295	C₂×C₈×C₄₃	—	2	2	no	—
296	C₂×C₈×C₄₃	—	2	2	no	—
297	C₂×C₈×C₄₃	—	4	4	no	—
298	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
299	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
300	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
301	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
302	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
304	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
305	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
306	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
307	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
308	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
309	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
311	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
312	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
313	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
314	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
315	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
316	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
317	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
318	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
319	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
320	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
321	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
322	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
323	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
324	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
325	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
326	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
327	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
328	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
329	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
330	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
331	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
332	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
333	#10621877	—	2	4	no	—
334	#10621877	—	4	4	no	—
335	C₂×C₄₃⋊C₈	—	2	2	no	—
336	C₂×C₄₃⋊C₈	—	2	2	no	—
337	C₂×C₄₃⋊C₈	—	4	4	no	—
338	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
339	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
340	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
341	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
342	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
343	#10621872	—	4	4	no	—
344	#10621872	—	4	4	no	—
345	C₈×D₄₃	—	4	4	no	—
346	C₈×D₄₃	—	4	4	no	—
347	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
348	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
349	C₂²×D₄₃	—	2	2	no	—
350	C₂²×D₄₃	—	2	2	no	—
351	C₂²×D₄₃	—	2	8	no	—
352	C₂²×D₄₃	—	4	1	no	—
353	C₂²×D₄₃	—	4	4	no	—
354	C₂²×D₄₃	—	4	4	no	—
355	C₂²×D₄₃	C₂³×C₄	1	4	yes	—
356	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
357	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
358	Q₈×C₄₃	—	2	4	no	—
359	D₄×C₄₃	—	2	8	no	—
360	D₄×C₄₃	—	2	4	no	—
361	D₄×C₄₃	—	2	4	no	—
362	D₄×C₄₃	—	2	4	no	—
363	C₂×C₄×C₄₃	—	2	2	no	—
364	C₂×C₄×C₄₃	—	2	2	no	—
365	C₂×C₄×C₄₃	—	2	4	no	—
366	C₂×C₄×C₄₃	—	2	4	no	—
367	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
369	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
370	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
372	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
373	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
374	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
376	C₂²⋊D₄₃	—	2	8	no	—
377	C₂²⋊D₄₃	—	2	8	no	—
378	C₂²⋊D₄₃	—	4	4	no	—
379	C₂²⋊D₄₃	—	4	4	no	—
380	C₂²⋊D₄₃	—	4	4	no	—
381	C₂×Dic₄₃	—	2	2	no	—
382	C₂×Dic₄₃	—	2	2	no	—
383	C₂×Dic₄₃	—	4	4	no	—
384	C₂×Dic₄₃	—	4	1	no	—
385	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
386	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
387	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
388	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
389	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
390	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
391	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
392	D₁₇₂	—	2	4	no	—
393	D₁₇₂	—	2	4	no	—
394	D₁₇₂	—	2	4	no	—
395	D₁₇₂	—	4	4	no	—
396	C₄×D₄₃	—	2	2	no	—
397	C₄×D₄₃	—	2	2	no	—
398	C₄×D₄₃	—	2	2	no	—
399	C₄×D₄₃	—	2	2	no	—
400	C₄×D₄₃	—	2	2	no	—
401	C₄×D₄₃	—	2	2	no	—
402	C₄×D₄₃	—	2	4	no	—
403	C₄×D₄₃	—	2	4	no	—
404	C₄×D₄₃	—	2	1	no	—
405	C₄×D₄₃	—	2	1	no	—
406	C₄×D₄₃	—	2	1	no	—
407	C₄×D₄₃	—	2	1	no	—
408	C₄×D₄₃	—	2	2	no	—
409	C₄×D₄₃	—	4	1	no	—
410	C₄×D₄₃	—	4	1	no	—
411	C₄×D₄₃	—	4	4	no	—
412	C₄×D₄₃	—	4	4	no	—
413	C₄×D₄₃	#131	1	4	yes	complemented
414	Dic₈₆	—	2	4	no	—
415	Dic₈₆	—	4	4	no	—
416	C₈×C₄₃	—	2	1	no	—
417	C₈×C₄₃	—	2	4	no	—
418	C₈×C₄₃	—	2	1	no	—
419	C₈×C₄₃	—	2	1	no	—
420	C₈×C₄₃	—	2	1	no	—
421	C₄₃⋊C₈	—	2	1	no	—
422	C₄₃⋊C₈	—	2	4	no	—
423	C₄₃⋊C₈	—	2	1	no	—
424	C₄₃⋊C₈	—	2	1	no	—
425	C₄₃⋊C₈	—	2	1	no	—
426	#60236	—	43	1	no	maximal, Sylow
427	C₂²×C₄₃	—	2	1	no	—
428	C₂²×C₄₃	—	2	1	no	—
429	C₂²×C₄₃	—	2	4	no	—
430	C₂²×C₄₃	—	2	4	no	—
431	C₂²×C₄₃	—	2	4	no	—
432	C₂²×C₄₃	#518	1	2	yes	—
433	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
434	C₂×D₄₃	—	2	1	no	—
435	C₂×D₄₃	—	2	1	no	—
436	C₂×D₄₃	—	2	1	no	—
437	C₂×D₄₃	—	2	4	no	—
438	C₂×D₄₃	—	2	1	no	—
439	C₂×D₄₃	—	2	4	no	—
440	C₂×D₄₃	—	2	1	no	—
441	C₂×D₄₃	—	2	4	no	—
442	C₂×D₄₃	—	4	4	no	—
443	C₂×D₄₃	—	8	8	no	—
444	C₂×D₄₃	C₂×#131	1	2	yes	—
445	C₄×C₄₃	—	2	4	no	—
446	C₄×C₄₃	—	2	1	no	—
447	C₄×C₄₃	—	2	1	no	—
448	C₄×C₄₃	#518	1	2	yes	—
449	C₄×C₄₃	C₂×#131	1	2	yes	—
450	C₄×C₄₃	#568	1	2	yes	—
451	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	Dic₄₃	—	2	4	no	—
454	Dic₄₃	—	2	1	no	—
455	Dic₄₃	—	2	1	no	—
456	Dic₄₃	—	2	1	no	—
457	Dic₄₃	—	2	1	no	—
458	Dic₄₃	—	2	1	no	—
459	Dic₄₃	C₂×#131	1	2	yes	—
460	C₂×#532	—	43	1	no	—
461	#2981	—	43	2	no	—
462	#2981	—	43	2	no	—
463	#2979	—	43	2	no	—
464	#2979	—	43	2	no	—
465	#2975	—	43	2	no	—
466	#2974	—	43	2	no	—
467	#2974	—	43	2	no	—
468	#2972	—	43	2	no	—
469	#2935	—	43	2	no	—
470	#2935	—	43	2	no	—
471	#2931	—	43	1	no	—
472	#2931	—	43	1	no	—
473	#2931	—	43	1	no	—
474	#2931	D₄₃	1	1	yes	characteristic, complemented
475	#2920	—	43	1	no	—
476	C₂×#431	—	43	1	no	—
477	#2880	—	43	2	no	—
478	#2880	—	43	2	no	—
479	C₂×C₄₃	—	2	2	no	—
480	C₂×C₄₃	—	4	4	no	—
481	C₂×C₄₃	C₂×#518	1	1	yes	characteristic
482	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
483	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
484	D₄₃	—	2	2	no	—
485	D₄₃	—	4	1	no	—
486	D₄₃	—	4	4	no	—
487	C₂²×#41	—	43	2	no	—
488	C₂×#131	—	43	2	no	—
489	C₂×#131	—	43	2	no	—
490	C₂×#131	—	43	2	no	—
491	C₂×#131	C₂×D₄₃	1	2	yes	complemented
492	#532	—	43	2	no	—
493	#532	—	43	1	no	—
494	#532	—	43	1	no	—
495	#532	—	43	2	no	—
496	#532	—	43	2	no	—
497	#532	—	43	2	no	—
498	#532	—	43	2	no	—
499	#532	—	43	2	no	—
500	#532	—	43	1	no	—
501	#532	C₂×D₄₃	1	1	yes	characteristic
502	C₂×C₄⋊Q₈	—	43	1	no	—
503	C₂×#127	—	43	1	no	—
504	C₂×#124	—	43	2	no	—
505	C₂×#121	—	43	2	no	—
506	C₂×#121	—	43	2	no	—
507	C₂×C₄×D₄	—	43	2	no	—
508	C₂×C₄×D₄	—	43	2	no	—
509	C₂²×C₄²	—	43	1	no	—
510	#436	—	43	4	no	—
511	#436	—	43	2	no	—
512	#436	—	43	2	no	—
513	#436	—	43	2	no	—
514	#436	—	43	2	no	—
515	#436	—	43	4	no	—
516	#436	—	43	2	no	—
517	#436	—	43	2	no	—
518	#436	C₂×D₄₃	1	2	yes	complemented
519	#436	C₂×D₄₃	1	2	yes	complemented
520	#435	—	43	4	no	—
521	#435	—	43	4	no	—
522	#435	—	43	4	no	—
523	#435	—	43	4	no	—
524	C₈×D₄	—	43	4	no	—
525	C₈×D₄	—	43	2	no	—
526	C₈×D₄	—	43	2	no	—
527	C₈×D₄	—	43	2	no	—
528	C₈×D₄	—	43	2	no	—
529	C₈×D₄	—	43	4	no	—
530	C₈×D₄	—	43	2	no	—
531	C₈×D₄	—	43	2	no	—
532	C₈×D₄	C₂×D₄₃	1	2	yes	complemented
533	C₈×D₄	C₂×D₄₃	1	2	yes	complemented
534	#432	—	43	2	no	—
535	#432	—	43	2	no	—
536	#431	—	43	2	no	—
537	#431	—	43	2	no	—
538	#431	—	43	1	no	—
539	#431	—	43	1	no	—
540	#431	—	43	1	no	—
541	#431	—	43	1	no	—
542	#431	—	43	1	no	—
543	#431	—	43	1	no	—
544	#431	—	43	1	no	—
545	#431	—	43	1	no	—
546	#423	—	43	1	no	—
547	#423	C₂×D₄₃	1	1	yes	characteristic, complemented
548	C₂×C₄⋊C₈	—	43	1	no	—
549	C₂×C₄⋊C₈	—	43	1	no	—
550	#408	—	43	2	no	—
551	#408	—	43	2	no	—
552	#408	—	43	4	no	—
553	#408	—	43	2	no	—
554	#408	—	43	4	no	—
555	#408	—	43	4	no	—
556	#408	—	43	4	no	—
557	#408	C₂×D₄₃	1	2	yes	complemented
558	#407	—	43	2	no	—
559	#407	—	43	4	no	—
560	#407	—	43	4	no	—
561	C₂×C₂²⋊C₈	—	43	1	no	—
562	C₂×C₂²⋊C₈	—	43	1	no	—
563	C₂×C₂²⋊C₈	—	43	4	no	—
564	C₂×C₂²⋊C₈	—	43	4	no	—
565	C₄×M₁₆	—	43	2	no	—
566	C₂×C₄×C₈	—	43	1	no	—
567	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
568	C₄₃	#60236	1	1	yes	characteristic, complemented, Sylow
569	C₂×#41	—	43	2	no	—
570	C₂×#41	—	43	4	no	—
571	C₂×#41	—	43	2	no	—
572	C₂×#41	—	43	2	no	—
573	C₂×#41	—	43	4	no	—
574	C₂×#41	—	172	4	no	—
575	C₂×#41	—	172	4	no	—
576	C₂×#41	C₂²×D₄₃	1	2	yes	—
577	C₂²×Q₈	—	43	2	no	—
578	C₂²×D₄	—	43	2	no	—
579	C₂²×D₄	—	43	2	no	—
580	C₂²×D₄	—	43	4	no	—
581	C₂²×D₄	—	43	2	no	—
582	C₂³×C₄	—	43	1	no	—
583	C₂³×C₄	—	43	1	no	—
584	C₂³×C₄	—	43	1	no	—
585	C₂³×C₄	—	43	4	no	—
586	#131	—	4	4	no	—
587	#131	—	172	4	no	—
588	#131	—	172	4	no	—
589	#131	—	172	4	no	—
590	C₂×M₁₆	—	43	2	no	—
591	C₂×M₁₆	—	43	4	no	—
592	C₂×M₁₆	—	43	4	no	—
593	C₂×M₁₆	—	43	4	no	—
594	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
595	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
596	C₂²×C₈	—	43	1	no	—
597	C₂²×C₈	—	43	1	no	—
598	C₂²×C₈	—	43	4	no	—
599	C₂²×C₈	—	43	4	no	—
600	C₂²×C₈	—	43	4	no	—
601	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
602	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
603	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
604	C₄⋊Q₈	—	43	2	no	—
605	C₄⋊Q₈	—	43	2	no	—
606	C₄⋊Q₈	—	43	2	no	—
607	C₄⋊Q₈	—	43	1	no	—
608	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
609	#127	—	43	2	no	—
610	#127	—	43	2	no	—
611	#127	—	43	2	no	—
612	#127	—	43	1	no	—
613	#127	C₄×D₄₃	1	1	yes	characteristic
614	#124	—	43	2	no	—
615	#124	—	43	2	no	—
616	#124	—	43	4	no	—
617	#124	—	43	4	no	—
618	#124	—	43	2	no	—
619	#124	C₄×D₄₃	1	2	yes	—
620	#121	—	43	2	no	—
621	#121	—	43	2	no	—
622	#121	—	43	4	no	—
623	#121	—	43	4	no	—
624	#121	—	43	2	no	—
625	#121	—	43	2	no	—
626	#121	—	43	2	no	—
627	#121	—	43	2	no	—
628	#121	—	43	4	no	—
629	#121	—	43	4	no	—
630	#121	C₄×D₄₃	1	2	yes	—
631	#121	C₄×D₄₃	1	2	yes	—
632	C₄×D₄	—	43	2	no	—
633	C₄×D₄	—	43	2	no	—
634	C₄×D₄	—	43	4	no	—
635	C₄×D₄	—	43	4	no	—
636	C₄×D₄	—	43	2	no	—
637	C₄×D₄	—	43	2	no	—
638	C₄×D₄	—	43	4	no	—
639	C₄×D₄	—	43	4	no	—
640	C₄×D₄	—	43	2	no	—
641	C₄×D₄	—	43	2	no	—
642	C₄×D₄	C₂²×D₄₃	1	2	yes	—
643	C₄×D₄	C₂²×D₄₃	1	2	yes	—
644	C₂×C₄⋊C₄	—	43	2	no	—
645	C₂×C₄⋊C₄	—	43	2	no	—
646	C₂×C₂²⋊C₄	—	43	4	no	—
647	C₂×C₂²⋊C₄	—	43	4	no	—
648	C₂×C₄²	—	43	1	no	—
649	C₂×C₄²	—	43	1	no	—
650	C₂×C₄²	—	43	1	no	—
651	C₂×C₄²	—	43	1	no	—
652	C₂×C₄²	—	43	1	no	—
653	C₂×C₄²	—	43	1	no	—
654	C₂×C₄²	—	43	1	no	—
655	C₂×C₄²	—	43	1	no	—
656	C₂×C₄²	—	43	1	no	—
657	C₂×C₄²	—	43	1	no	—
658	C₂×C₄²	—	43	1	no	—
659	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
660	C₄⋊C₈	—	43	1	no	—
661	C₄⋊C₈	—	43	1	no	—
662	C₄⋊C₈	—	43	1	no	—
663	C₄⋊C₈	—	43	1	no	—
664	C₄⋊C₈	—	43	1	no	—
665	C₄⋊C₈	—	43	1	no	—
666	C₄⋊C₈	—	43	1	no	—
667	C₄⋊C₈	—	43	1	no	—
668	C₄⋊C₈	—	43	2	no	—
669	C₄⋊C₈	—	43	2	no	—
670	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
671	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
672	C₂²⋊C₈	—	43	4	no	—
673	C₂²⋊C₈	—	43	4	no	—
674	C₂²⋊C₈	—	43	1	no	—
675	C₂²⋊C₈	—	43	1	no	—
676	C₂²⋊C₈	—	43	4	no	—
677	C₂²⋊C₈	—	43	1	no	—
678	C₂²⋊C₈	—	43	1	no	—
679	C₂²⋊C₈	—	43	1	no	—
680	C₂²⋊C₈	—	43	1	no	—
681	C₂²⋊C₈	—	43	1	no	—
682	C₂²⋊C₈	—	43	1	no	—
683	C₂²⋊C₈	—	43	4	no	—
684	C₂²⋊C₈	—	43	4	no	—
685	C₂²⋊C₈	—	43	4	no	—
686	C₂²⋊C₈	—	43	4	no	—
687	C₂²⋊C₈	—	43	4	no	—
688	C₂²⋊C₈	C₂²×D₄₃	1	4	yes	—
689	C₂²⋊C₈	C₂²×D₄₃	1	4	yes	—
690	#97	—	43	4	no	—
691	C₄×C₈	—	43	4	no	—
692	C₄×C₈	—	43	1	no	—
693	C₄×C₈	—	43	1	no	—
694	C₄×C₈	—	43	1	no	—
695	C₄×C₈	—	43	1	no	—
696	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
697	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
698	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
699	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
700	C₂⁴	—	43	1	no	—
701	C₂⁴	—	43	4	no	—
702	#41	—	2	4	no	—
703	#41	—	2	4	no	—
704	#41	—	86	4	no	—
705	#41	—	86	4	no	—
706	#41	—	172	4	no	—
707	#41	—	172	4	no	—
708	#41	—	172	8	no	—
709	#41	—	172	4	no	—
710	#41	—	172	4	no	—
711	C₂×Q₈	—	43	2	no	—
712	C₂×Q₈	—	43	4	no	—
713	C₂×Q₈	—	172	4	no	—
714	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
715	C₂×D₄	—	43	4	no	—
716	C₂×D₄	—	43	4	no	—
717	C₂×D₄	—	43	4	no	—
718	C₂×D₄	—	43	4	no	—
719	C₂×D₄	—	43	4	no	—
720	C₂×D₄	—	43	2	no	—
721	C₂×D₄	—	43	2	no	—
722	C₂×D₄	—	43	2	no	—
723	C₂×D₄	—	43	4	no	—
724	C₂×D₄	—	86	8	no	—
725	C₂×D₄	—	172	4	no	—
726	C₂×D₄	—	172	4	no	—
727	C₂×D₄	—	172	8	no	—
728	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
729	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
730	C₂×D₄	C₂×C₄×D₄₃	1	4	yes	—
731	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
732	C₂²×C₄	—	43	1	no	—
733	C₂²×C₄	—	43	1	no	—
734	C₂²×C₄	—	43	1	no	—
735	C₂²×C₄	—	43	1	no	—
736	C₂²×C₄	—	43	4	no	—
737	C₂²×C₄	—	43	1	no	—
738	C₂²×C₄	—	43	1	no	—
739	C₂²×C₄	—	43	1	no	—
740	C₂²×C₄	—	43	1	no	—
741	C₂²×C₄	—	43	1	no	—
742	C₂²×C₄	—	43	1	no	—
743	C₂²×C₄	—	43	1	no	—
744	C₂²×C₄	—	43	1	no	—
745	C₂²×C₄	—	43	1	no	—
746	C₂²×C₄	—	43	4	no	—
747	C₂²×C₄	—	43	1	no	—
748	C₂²×C₄	—	43	1	no	—
749	C₂²×C₄	—	43	4	no	—
750	C₂²×C₄	—	43	4	no	—
751	C₂²×C₄	—	86	4	no	—
752	C₂²×C₄	—	86	2	no	—
753	C₂²×C₄	—	86	2	no	—
754	C₂²×C₄	—	172	4	no	—
755	C₂²×C₄	—	172	4	no	—
756	C₂²×C₄	—	172	2	no	—
757	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
758	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
759	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
760	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
761	M₁₆	—	2	4	no	—
762	M₁₆	—	4	4	no	—
763	M₁₆	—	86	4	no	—
764	M₁₆	—	172	4	no	—
765	M₁₆	—	172	4	no	—
766	M₁₆	—	172	4	no	—
767	C₂×C₈	—	2	2	no	—
768	C₂×C₈	—	2	2	no	—
769	C₂×C₈	—	4	4	no	—
770	C₂×C₈	—	43	1	no	—
771	C₂×C₈	—	43	1	no	—
772	C₂×C₈	—	43	1	no	—
773	C₂×C₈	—	43	1	no	—
774	C₂×C₈	—	43	4	no	—
775	C₂×C₈	—	86	2	no	—
776	C₂×C₈	—	86	2	no	—
777	C₂×C₈	—	172	4	no	—
778	C₂×C₈	—	172	4	no	—
779	C₂×C₈	—	172	4	no	—
780	C₂×C₈	C₂³×D₄₃	1	4	yes	—
781	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
782	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
783	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
784	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
785	C₄⋊C₄	—	43	4	no	—
786	C₄⋊C₄	—	43	4	no	—
787	C₄⋊C₄	—	43	2	no	—
788	C₄⋊C₄	—	43	2	no	—
789	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
790	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
791	C₂²⋊C₄	—	43	4	no	—
792	C₂²⋊C₄	—	43	4	no	—
793	C₂²⋊C₄	—	43	4	no	—
794	C₂²⋊C₄	—	43	4	no	—
795	C₂²⋊C₄	—	43	4	no	—
796	C₂²⋊C₄	—	43	4	no	—
797	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
798	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
799	C₄²	—	43	1	no	—
800	C₄²	—	43	1	no	—
801	C₄²	—	43	1	no	—
802	C₄²	—	43	1	no	—
803	C₄²	—	43	1	no	—
804	C₄²	—	43	1	no	—
805	C₄²	—	43	1	no	—
806	C₄²	—	43	1	no	—
807	C₄²	—	43	1	no	—
808	C₄²	—	43	1	no	—
809	C₄²	—	43	1	no	—
810	C₄²	—	43	1	no	—
811	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
812	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
813	C₄²	C₂³×D₄₃	1	1	yes	characteristic
814	C₄²	C₂³×D₄₃	1	1	yes	characteristic
815	C₂³	—	43	1	no	—
816	C₂³	—	43	4	no	—
817	C₂³	—	43	1	no	—
818	C₂³	—	86	8	no	—
819	C₂³	—	86	2	no	—
820	C₂³	—	86	2	no	—
821	C₂³	—	172	4	no	—
822	C₂³	—	172	4	no	—
823	C₂³	—	172	1	no	—
824	C₂³	C₂²×C₄×D₄₃	1	4	yes	—
825	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
826	Q₈	—	2	4	no	—
827	Q₈	—	86	4	no	—
828	Q₈	—	172	4	no	—
829	D₄	—	2	8	no	—
830	D₄	—	2	4	no	—
831	D₄	—	2	4	no	—
832	D₄	—	2	4	no	—
833	D₄	—	86	8	no	—
834	D₄	—	86	8	no	—
835	D₄	—	86	4	no	—
836	D₄	—	86	4	no	—
837	D₄	—	86	4	no	—
838	D₄	—	172	4	no	—
839	D₄	—	172	4	no	—
840	D₄	—	172	4	no	—
841	D₄	—	172	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	43	1	no	—
847	C₂×C₄	—	43	4	no	—
848	C₂×C₄	—	43	1	no	—
849	C₂×C₄	—	43	1	no	—
850	C₂×C₄	—	43	1	no	—
851	C₂×C₄	—	43	1	no	—
852	C₂×C₄	—	43	1	no	—
853	C₂×C₄	—	43	4	no	—
854	C₂×C₄	—	86	2	no	—
855	C₂×C₄	—	86	2	no	—
856	C₂×C₄	—	86	2	no	—
857	C₂×C₄	—	86	2	no	—
858	C₂×C₄	—	86	2	no	—
859	C₂×C₄	—	86	2	no	—
860	C₂×C₄	—	86	2	no	—
861	C₂×C₄	—	86	2	no	—
862	C₂×C₄	—	86	2	no	—
863	C₂×C₄	—	86	4	no	—
864	C₂×C₄	—	86	1	no	—
865	C₂×C₄	—	86	1	no	—
866	C₂×C₄	—	86	4	no	—
867	C₂×C₄	—	86	1	no	—
868	C₂×C₄	—	86	1	no	—
869	C₂×C₄	—	172	4	no	—
870	C₂×C₄	—	172	4	no	—
871	C₂×C₄	—	172	1	no	—
872	C₂×C₄	—	172	1	no	—
873	C₂×C₄	—	172	4	no	—
874	C₂×C₄	—	172	1	no	—
875	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
876	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
877	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
878	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
881	C₂×C₄	#13063370	1	2	yes	—
882	C₂×C₄	#13063371	1	2	yes	—
883	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	2	4	no	—
887	C₈	—	2	1	no	—
888	C₈	—	2	1	no	—
889	C₈	—	86	1	no	—
890	C₈	—	86	1	no	—
891	C₈	—	86	1	no	—
892	C₈	—	86	1	no	—
893	C₈	—	86	4	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	43	2	no	—
900	C₂²	—	86	1	no	—
901	C₂²	—	86	1	no	—
902	C₂²	—	86	1	no	—
903	C₂²	—	86	4	no	—
904	C₂²	—	86	1	no	—
905	C₂²	—	86	4	no	—
906	C₂²	—	86	1	no	—
907	C₂²	—	86	4	no	—
908	C₂²	—	344	8	no	—
909	C₂²	—	172	4	no	—
910	C₂²	#14583371	1	2	yes	—
911	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
912	C₄	—	2	4	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	1	no	—
915	C₄	—	43	2	no	—
916	C₄	—	86	1	no	—
917	C₄	—	86	1	no	—
918	C₄	—	86	4	no	—
919	C₄	—	86	1	no	—
920	C₄	—	86	1	no	—
921	C₄	—	86	1	no	—
922	C₄	#14583371	1	2	yes	—
923	C₄	#131×D₄₃	1	2	yes	—
924	C₄	#14583664	1	2	yes	—
925	C₄	C₂×#13063370	1	1	yes	characteristic
926	C₄	C₂×#13063371	1	1	yes	characteristic
927	C₂	—	2	2	no	—
928	C₂	—	4	4	no	—
929	C₂	—	86	2	no	—
930	C₂	—	172	4	no	—
931	C₂	—	172	1	no	—
932	C₂	C₂×#14583371	1	1	yes	characteristic
933	C₂	C₂×#131×D₄₃	1	1	yes	characteristic
934	C₂	C₂×#14583664	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₄₃×#2931	C₂
prime radical	#532×D₄₃	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2931	D₄₃
hypocenter	C₄₃	#60236
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. #19143672	C₂	semidirect
3. #19143669	C₂	semidirect
4. #19143660	C₂	semidirect
5. #19143658	C₂	semidirect
6. #19143633	C₂	semidirect
7. #19143628	C₂	semidirect
8. #19143627	C₂	semidirect
9. #19143616	C₂	semidirect
10. #19143337	C₂	semidirect
11. #19143335	C₂	semidirect
12. #19143308	C₂	semidirect
13. #19143307	C₂	semidirect
14. #19143306	C₂	semidirect
15. #19143227	C₂	semidirect
16. C₂×#14582950	C₂	semidirect
17. #19143043	C₂	semidirect
18. #19143042	C₂	semidirect
19. C₄₃×#2931	C₂	semidirect
21. C₂×#13063333	C₂²	semidirect
22. C₂×#13063332	C₂²	semidirect
23. C₂×#13063331	C₂²	semidirect
41. #14582978	C₂²	semidirect
42. #14582978	C₂²	semidirect
43. #14582977	C₂²	semidirect
44. #14582977	C₂²	semidirect
45. #14582976	C₂²	semidirect
46. #14582976	C₂²	semidirect
47. #14582975	C₂²	semidirect
48. #14582974	C₂²	semidirect
49. #14582973	C₂²	semidirect
50. #14582970	C₂²	semidirect
51. #14582968	C₂²	semidirect
52. #14582967	C₂²	semidirect
53. C₈×D₁₇₂	C₂²	semidirect
54. C₈×D₁₇₂	C₂²	semidirect
55. D₄×C₄₃⋊C₈	C₂²	semidirect
56. D₄×C₄₃⋊C₈	C₂²	semidirect
57. #14582964	C₂²	semidirect
58. #14582964	C₂²	semidirect
59. C₈×C₂²⋊D₄₃	C₂²	semidirect
60. (C₂²⋊D₄₃)⋊C₈	C₂²	semidirect
62. #14582955	C₂²	semidirect
64. #14582951	C₂²	semidirect
69. #14582950	C₂²	semidirect
70. #14582950	C₂²	semidirect
71. #14582950	C₂²	semidirect
72. #14582950	C₂²	semidirect
73. #14582923	C₂²	semidirect
74. C₂×Dic₄₃⋊C₈	C₂²	semidirect
75. C₂×Dic₄₃⋊C₈	C₂²	semidirect
76. #14582867	C₂²	semidirect
77. #14582867	C₂²	semidirect
78. #14582866	C₂²	semidirect
79. #14582865	C₂²	semidirect
80. #14582865	C₂²	semidirect
81. #14582864	C₂²	semidirect
82. #14582864	C₂²	semidirect
90. M₁₆×Dic₄₃	C₂²	semidirect
91. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
92. C₂×#131×C₄₃	C₂²	semidirect
94. C₄₃×#436	C₂²	semidirect
95. C₄₃×#436	C₂²	semidirect
96. C₈×D₄×C₄₃	C₂²	semidirect
97. C₈×D₄×C₄₃	C₂²	semidirect
98. C₄₃×#423	C₂²	semidirect
99. C₄₃×#408	C₂²	semidirect
100. C₂×C₄×C₈×C₄₃	C₂²	semidirect
413. C₄×D₄₃	#131	semidirect
474. #2931	D₄₃	semidirect
491. C₂×#131	C₂×D₄₃	semidirect
518. #436	C₂×D₄₃	semidirect
519. #436	C₂×D₄₃	semidirect
532. C₈×D₄	C₂×D₄₃	semidirect
533. C₈×D₄	C₂×D₄₃	semidirect
547. #423	C₂×D₄₃	semidirect
557. #408	C₂×D₄₃	semidirect
567. C₂×C₄×C₈	C₂×D₄₃	semidirect
568. C₄₃	#60236	semidirect

Maximal subgroups

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

subgroup	index
#532×D₄₃	2
#19143672	2
#19143669	2
#19143660	2
#19143658	2
#19143633	2
#19143628	2
#19143627	2
#19143616	2
#19143337	2
#19143335	2
#19143308	2
#19143307	2
#19143306	2
#19143227	2
C₂×#14582950	2
#19143043	2
#19143042	2
C₄₃×#2931	2
#60236	43