Subgroups — C₄₃×#60751 #24980768

Order 11008.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3196	C₂	1	4	yes	maximal, complemented
4	C₄₃×#3195	C₂	1	2	yes	maximal, complemented
5	C₄₃×#3193	C₂	1	2	yes	maximal, complemented
6	C₄₃×#3190	C₂	1	4	yes	maximal, complemented
7	C₄₃×#3189	C₂	1	2	yes	maximal, complemented
8	C₄₃×#3187	C₂	1	2	yes	maximal, complemented
9	C₄₃×#3095	C₂	1	2	yes	maximal, complemented
10	C₄₃×#3092	C₂	1	2	yes	maximal, complemented
11	C₄₃×#3056	C₂	1	4	yes	maximal, complemented
12	C₄₃×#3007	C₂	1	2	yes	maximal, complemented
13	C₄₃×#3004	C₂	1	2	yes	maximal, complemented
14	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
16	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#137×C₄₃	C₂²	1	4	yes	complemented
19	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	complemented
20	C₄₃×#525	—	2	1	no	—
21	C₄₃×#525	—	2	1	no	—
22	C₄₃×#525	—	2	1	no	—
23	C₄₃×#525	—	2	1	no	—
24	C₄₃×#525	C₂²	1	2	yes	—
25	C₄₃×#525	C₂²	1	2	yes	—
26	C₄₃×#525	C₂²	1	2	yes	—
27	C₄₃×#525	C₂²	1	2	yes	—
28	C₂×#123×C₄₃	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
30	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
31	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
32	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
35	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
43	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×#120×C₄₃	—	2	1	no	—
46	C₂×C₄×D₄×C₄₃	—	2	1	no	—
47	C₂×C₄×D₄×C₄₃	—	2	1	no	—
48	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
50	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
52	C₄₃×#485	C₂²	1	8	yes	complemented
53	C₄₃×#484	C₂²	1	4	yes	complemented
54	C₄₃×#484	C₂²	1	4	yes	complemented
55	C₄₃×#483	C₂²	1	4	yes	complemented
56	C₄₃×#483	C₂²	1	4	yes	complemented
57	C₄₃×#481	C₂²	1	4	yes	complemented
58	C₄₃×#480	C₂²	1	4	yes	complemented
59	C₄₃×#470	C₂²	1	8	yes	complemented
60	C₄₃×#468	C₂²	1	8	yes	complemented
61	C₄₃×#467	C₂²	1	8	yes	complemented
62	C₄₃×#465	C₂²	1	8	yes	complemented
63	C₄₃×#452	C₂²	1	8	yes	complemented
64	C₄₃×#451	C₂²	1	4	yes	complemented
65	C₄₃×#451	C₂²	1	4	yes	complemented
66	C₄₃×#451	C₂²	1	4	yes	complemented
67	C₄₃×#450	C₂²	1	4	yes	complemented
68	C₄₃×#448	C₂²	1	4	yes	complemented
69	C₄₃×#448	C₂²	1	4	yes	complemented
70	C₄₃×#428	C₂²	1	4	yes	complemented
71	C₄₃×#419	C₂²	1	4	yes	complemented
72	C₄₃×#417	C₂²	1	4	yes	complemented
73	C₄₃×#407	C₂²	1	2	yes	—
74	C₄₃×#407	C₂²	1	2	yes	—
75	C₄₃×#407	C₂²	1	2	yes	complemented
76	C₄₃×#407	C₂²	1	2	yes	complemented
77	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
78	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	complemented
79	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
80	C₂×#41×C₄₃	—	2	1	no	—
81	C₂×#41×C₄₃	—	2	1	no	—
82	C₂×#41×C₄₃	—	4	4	no	—
83	C₂×#41×C₄₃	C₂³	1	2	yes	—
84	C₂×#41×C₄₃	C₂³	1	2	yes	—
85	C₂²×Q₈×C₄₃	—	2	1	no	—
86	C₂²×Q₈×C₄₃	—	2	1	no	—
87	C₂²×Q₈×C₄₃	—	2	1	no	—
88	C₂²×Q₈×C₄₃	—	4	4	no	—
89	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
90	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
92	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₄₃	—	2	1	no	—
94	C₂²×D₄×C₄₃	—	2	1	no	—
95	C₂²×D₄×C₄₃	—	2	1	no	—
96	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₄₃	—	2	1	no	—
98	C₂³×C₄×C₄₃	—	2	1	no	—
99	C₂³×C₄×C₄₃	—	2	1	no	—
100	C₂³×C₄×C₄₃	—	4	4	no	—
101	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
102	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
103	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
104	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
105	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
106	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
115	#137×C₄₃	—	4	8	no	—
116	C₂×Q₁₆×C₄₃	C₂³	1	8	yes	complemented
117	C₂×SD₁₆×C₄₃	C₂³	1	8	yes	complemented
118	C₂×M₁₆×C₄₃	—	4	4	no	—
119	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
120	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
121	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
122	#123×C₄₃	—	2	2	no	—
123	#123×C₄₃	—	2	2	no	—
124	#123×C₄₃	—	2	2	no	—
125	#123×C₄₃	—	2	2	no	—
126	C₂²⋊Q₈×C₄₃	—	2	2	no	—
127	C₂²⋊Q₈×C₄₃	—	2	2	no	—
128	C₂²⋊Q₈×C₄₃	—	2	2	no	—
129	C₂²⋊Q₈×C₄₃	—	2	2	no	—
130	C₂²⋊Q₈×C₄₃	—	2	2	no	—
131	C₂²⋊Q₈×C₄₃	—	2	2	no	—
132	C₂²⋊Q₈×C₄₃	—	2	2	no	—
133	C₂²⋊Q₈×C₄₃	—	2	2	no	—
134	C₂²⋊Q₈×C₄₃	—	2	2	no	—
135	C₂²⋊Q₈×C₄₃	—	2	2	no	—
136	C₂²⋊Q₈×C₄₃	—	2	2	no	—
137	C₂²⋊Q₈×C₄₃	—	2	2	no	—
138	C₂²⋊Q₈×C₄₃	—	2	1	no	—
139	C₂²⋊Q₈×C₄₃	—	2	1	no	—
140	C₂²⋊Q₈×C₄₃	—	2	1	no	—
141	C₂²⋊Q₈×C₄₃	—	2	1	no	—
142	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
143	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
144	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
145	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
146	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
149	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
150	#121×C₄₃	—	2	1	no	—
151	#121×C₄₃	—	2	1	no	—
152	#121×C₄₃	—	2	1	no	—
153	#121×C₄₃	—	2	1	no	—
154	#121×C₄₃	C₂³	1	2	yes	—
155	#121×C₄₃	C₂³	1	2	yes	—
156	#121×C₄₃	C₂³	1	2	yes	—
157	#121×C₄₃	C₂³	1	2	yes	—
158	#120×C₄₃	—	2	2	no	—
159	#120×C₄₃	—	2	2	no	—
160	#120×C₄₃	—	2	2	no	—
161	#120×C₄₃	—	2	2	no	—
162	C₄×D₄×C₄₃	—	2	2	no	—
163	C₄×D₄×C₄₃	—	2	2	no	—
164	C₄×D₄×C₄₃	—	2	2	no	—
165	C₄×D₄×C₄₃	—	2	2	no	—
166	C₄×D₄×C₄₃	—	2	2	no	—
167	C₄×D₄×C₄₃	—	2	2	no	—
168	C₄×D₄×C₄₃	—	2	2	no	—
169	C₄×D₄×C₄₃	—	2	2	no	—
170	#117×C₄₃	—	2	1	no	—
171	#117×C₄₃	—	2	1	no	—
172	#117×C₄₃	C₂³	1	2	yes	—
173	#117×C₄₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
177	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
178	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
179	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
180	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
181	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
182	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
183	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
184	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
185	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
191	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
192	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
193	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
194	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
195	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
199	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
201	C₂×C₄²×C₄₃	—	2	1	no	—
202	#107×C₄₃	C₂³	1	8	yes	complemented
203	#106×C₄₃	C₂³	1	8	yes	complemented
204	#103×C₄₃	C₂³	1	8	yes	complemented
205	#103×C₄₃	C₂³	1	8	yes	complemented
206	#103×C₄₃	C₂³	1	8	yes	complemented
207	#102×C₄₃	C₂³	1	8	yes	complemented
208	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
209	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
210	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
212	C₂⁴×C₄₃	—	2	4	no	—
213	C₂⁴×C₄₃	—	2	1	no	—
214	C₂⁴×C₄₃	—	4	2	no	—
215	C₂⁴×C₄₃	—	4	2	no	—
216	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
217	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
218	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
219	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
220	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
222	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
223	#41×C₄₃	—	2	8	no	—
224	#41×C₄₃	—	4	4	no	—
225	#41×C₄₃	—	4	4	no	—
226	#41×C₄₃	—	4	4	no	—
227	C₂×Q₈×C₄₃	—	2	2	no	—
228	C₂×Q₈×C₄₃	—	2	2	no	—
229	C₂×Q₈×C₄₃	—	2	2	no	—
230	C₂×Q₈×C₄₃	—	2	1	no	—
231	C₂×Q₈×C₄₃	—	2	8	no	—
232	C₂×Q₈×C₄₃	—	4	4	no	—
233	C₂×Q₈×C₄₃	—	4	4	no	—
234	C₂×Q₈×C₄₃	—	4	2	no	—
235	C₂×Q₈×C₄₃	—	4	4	no	—
236	C₂×Q₈×C₄₃	—	4	4	no	—
237	C₂×Q₈×C₄₃	—	4	4	no	—
238	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₄₃	—	2	1	no	—
241	C₂×D₄×C₄₃	—	2	2	no	—
242	C₂×D₄×C₄₃	—	2	2	no	—
243	C₂×D₄×C₄₃	—	2	2	no	—
244	C₂×D₄×C₄₃	—	2	2	no	—
245	C₂×D₄×C₄₃	—	2	2	no	—
246	C₂×D₄×C₄₃	—	2	2	no	—
247	C₂×D₄×C₄₃	—	4	4	no	—
248	C₂×D₄×C₄₃	—	4	4	no	—
249	C₂×D₄×C₄₃	—	4	2	no	—
250	C₂×D₄×C₄₃	—	4	4	no	—
251	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₄₃	—	2	4	no	—
253	C₂²×C₄×C₄₃	—	2	4	no	—
254	C₂²×C₄×C₄₃	—	2	4	no	—
255	C₂²×C₄×C₄₃	—	2	2	no	—
256	C₂²×C₄×C₄₃	—	2	2	no	—
257	C₂²×C₄×C₄₃	—	2	1	no	—
258	C₂²×C₄×C₄₃	—	2	1	no	—
259	C₂²×C₄×C₄₃	—	2	2	no	—
260	C₂²×C₄×C₄₃	—	2	2	no	—
261	C₂²×C₄×C₄₃	—	2	2	no	—
262	C₂²×C₄×C₄₃	—	2	1	no	—
263	C₂²×C₄×C₄₃	—	2	2	no	—
264	C₂²×C₄×C₄₃	—	2	2	no	—
265	C₂²×C₄×C₄₃	—	2	2	no	—
266	C₂²×C₄×C₄₃	—	4	2	no	—
267	C₂²×C₄×C₄₃	—	4	2	no	—
268	C₂²×C₄×C₄₃	—	4	2	no	—
269	C₂²×C₄×C₄₃	—	4	4	no	—
270	C₂²×C₄×C₄₃	—	4	4	no	—
271	C₂²×C₄×C₄₃	—	4	2	no	—
272	C₂²×C₄×C₄₃	—	4	2	no	—
273	C₂²×C₄×C₄₃	—	4	2	no	—
274	C₂²×C₄×C₄₃	—	4	2	no	—
275	C₂²×C₄×C₄₃	—	4	2	no	—
276	C₂²×C₄×C₄₃	—	4	2	no	—
277	C₂²×C₄×C₄₃	—	4	2	no	—
278	C₂²×C₄×C₄₃	—	4	2	no	—
279	C₂²×C₄×C₄₃	—	4	4	no	—
280	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
308	Q₁₆×C₄₃	—	4	8	no	—
309	SD₁₆×C₄₃	—	4	8	no	—
310	M₁₆×C₄₃	—	2	8	no	—
311	M₁₆×C₄₃	—	4	4	no	—
312	C₂×C₈×C₄₃	—	4	4	no	—
313	C₂×C₈×C₄₃	C₂⁴	1	8	yes	—
314	C₄⋊C₄×C₄₃	—	2	4	no	—
315	C₄⋊C₄×C₄₃	—	2	4	no	—
316	C₄⋊C₄×C₄₃	—	2	4	no	—
317	C₄⋊C₄×C₄₃	—	2	4	no	—
318	C₄⋊C₄×C₄₃	—	2	2	no	—
319	C₄⋊C₄×C₄₃	—	2	2	no	—
320	C₄⋊C₄×C₄₃	—	2	2	no	—
321	C₄⋊C₄×C₄₃	—	2	2	no	—
322	C₄⋊C₄×C₄₃	—	2	2	no	—
323	C₄⋊C₄×C₄₃	—	2	2	no	—
324	C₄⋊C₄×C₄₃	—	2	2	no	—
325	C₄⋊C₄×C₄₃	—	2	1	no	—
326	C₄⋊C₄×C₄₃	—	2	1	no	—
327	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
328	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
329	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
330	C₂²⋊C₄×C₄₃	—	2	2	no	—
331	C₂²⋊C₄×C₄₃	—	2	2	no	—
332	C₂²⋊C₄×C₄₃	—	2	2	no	—
333	C₂²⋊C₄×C₄₃	—	2	2	no	—
334	C₂²⋊C₄×C₄₃	—	2	4	no	—
335	C₂²⋊C₄×C₄₃	—	2	4	no	—
336	C₂²⋊C₄×C₄₃	—	2	4	no	—
337	C₂²⋊C₄×C₄₃	—	2	4	no	—
338	C₂²⋊C₄×C₄₃	—	2	2	no	—
339	C₂²⋊C₄×C₄₃	—	2	2	no	—
340	C₂²⋊C₄×C₄₃	—	2	2	no	—
341	C₂²⋊C₄×C₄₃	—	2	2	no	—
342	C₂²⋊C₄×C₄₃	—	2	2	no	—
343	C₂²⋊C₄×C₄₃	—	2	2	no	—
344	C₄²×C₄₃	—	2	2	no	—
345	C₄²×C₄₃	—	2	2	no	—
346	C₂³×C₄₃	—	2	2	no	—
347	C₂³×C₄₃	—	2	2	no	—
348	C₂³×C₄₃	—	2	2	no	—
349	C₂³×C₄₃	—	2	2	no	—
350	C₂³×C₄₃	—	2	2	no	—
351	C₂³×C₄₃	—	2	2	no	—
352	C₂³×C₄₃	—	2	2	no	—
353	C₂³×C₄₃	—	2	2	no	—
354	C₂³×C₄₃	—	2	2	no	—
355	C₂³×C₄₃	—	2	2	no	—
356	C₂³×C₄₃	—	2	2	no	—
357	C₂³×C₄₃	—	2	2	no	—
358	C₂³×C₄₃	—	2	2	no	—
359	C₂³×C₄₃	—	4	1	no	—
360	C₂³×C₄₃	—	4	1	no	—
361	C₂³×C₄₃	—	4	1	no	—
362	C₂³×C₄₃	—	4	1	no	—
363	C₂³×C₄₃	—	4	1	no	—
364	C₂³×C₄₃	—	4	1	no	—
365	C₂³×C₄₃	—	4	1	no	—
366	C₂³×C₄₃	—	4	1	no	—
367	C₂³×C₄₃	—	4	16	no	—
368	C₂³×C₄₃	—	4	2	no	—
369	C₂³×C₄₃	—	4	2	no	—
370	C₂³×C₄₃	—	4	2	no	—
371	C₂³×C₄₃	#137	1	4	yes	complemented
372	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
373	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
374	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
375	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
376	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
377	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
378	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
379	Q₈×C₄₃	—	2	8	no	—
380	Q₈×C₄₃	—	2	4	no	—
381	Q₈×C₄₃	—	4	4	no	—
382	Q₈×C₄₃	—	4	4	no	—
383	Q₈×C₄₃	—	4	2	no	—
384	Q₈×C₄₃	—	4	4	no	—
385	D₄×C₄₃	—	2	4	no	—
386	D₄×C₄₃	—	4	2	no	—
387	D₄×C₄₃	—	4	4	no	—
388	D₄×C₄₃	—	4	4	no	—
389	D₄×C₄₃	—	4	4	no	—
390	D₄×C₄₃	—	4	4	no	—
391	D₄×C₄₃	—	4	4	no	—
392	D₄×C₄₃	—	4	4	no	—
393	C₂×C₄×C₄₃	—	2	2	no	—
394	C₂×C₄×C₄₃	—	2	2	no	—
395	C₂×C₄×C₄₃	—	2	2	no	—
396	C₂×C₄×C₄₃	—	2	2	no	—
397	C₂×C₄×C₄₃	—	2	2	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	—	2	2	no	—
406	C₂×C₄×C₄₃	—	2	2	no	—
407	C₂×C₄×C₄₃	—	2	2	no	—
408	C₂×C₄×C₄₃	—	2	2	no	—
409	C₂×C₄×C₄₃	—	2	2	no	—
410	C₂×C₄×C₄₃	—	2	4	no	—
411	C₂×C₄×C₄₃	—	2	2	no	—
412	C₂×C₄×C₄₃	—	2	4	no	—
413	C₂×C₄×C₄₃	—	4	1	no	—
414	C₂×C₄×C₄₃	—	4	1	no	—
415	C₂×C₄×C₄₃	—	4	1	no	—
416	C₂×C₄×C₄₃	—	4	1	no	—
417	C₂×C₄×C₄₃	—	4	1	no	—
418	C₂×C₄×C₄₃	—	4	1	no	—
419	C₂×C₄×C₄₃	—	4	1	no	—
420	C₂×C₄×C₄₃	—	4	1	no	—
421	C₂×C₄×C₄₃	—	4	1	no	—
422	C₂×C₄×C₄₃	—	4	1	no	—
423	C₂×C₄×C₄₃	—	4	1	no	—
424	C₂×C₄×C₄₃	—	4	1	no	—
425	C₂×C₄×C₄₃	—	4	4	no	—
426	C₂×C₄×C₄₃	—	4	4	no	—
427	C₂×C₄×C₄₃	—	4	4	no	—
428	C₂×C₄×C₄₃	—	4	2	no	—
429	C₂×C₄×C₄₃	—	4	4	no	—
430	C₂×C₄×C₄₃	—	4	4	no	—
431	C₂×C₄×C₄₃	—	4	2	no	—
432	C₂×C₄×C₄₃	—	4	4	no	—
433	C₂×C₄×C₄₃	—	4	2	no	—
434	C₂×C₄×C₄₃	—	4	4	no	—
435	C₂×C₄×C₄₃	—	4	4	no	—
436	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
444	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
445	C₈×C₄₃	—	2	8	no	—
446	#60751	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂²×C₄₃	—	2	8	no	—
448	C₂²×C₄₃	—	2	1	no	—
449	C₂²×C₄₃	—	2	1	no	—
450	C₂²×C₄₃	—	2	1	no	—
451	C₂²×C₄₃	—	2	1	no	—
452	C₂²×C₄₃	—	2	1	no	—
453	C₂²×C₄₃	—	2	1	no	—
454	C₂²×C₄₃	—	2	1	no	—
455	C₂²×C₄₃	—	2	1	no	—
456	C₂²×C₄₃	—	2	1	no	—
457	C₂²×C₄₃	—	2	1	no	—
458	C₂²×C₄₃	—	2	1	no	—
459	C₂²×C₄₃	—	2	1	no	—
460	C₂²×C₄₃	—	2	1	no	—
461	C₂²×C₄₃	—	2	1	no	—
462	C₂²×C₄₃	—	2	1	no	—
463	C₂²×C₄₃	—	2	1	no	—
464	C₂²×C₄₃	—	4	4	no	—
465	C₂²×C₄₃	—	4	4	no	—
466	C₂²×C₄₃	—	4	4	no	—
467	C₂²×C₄₃	—	4	4	no	—
468	C₂²×C₄₃	—	4	4	no	—
469	C₂²×C₄₃	—	4	4	no	—
470	C₂²×C₄₃	—	4	2	no	—
471	C₂²×C₄₃	—	4	2	no	—
472	C₂²×C₄₃	—	4	2	no	—
473	C₂²×C₄₃	—	8	4	no	—
474	C₂²×C₄₃	#534	1	2	yes	—
475	C₂²×C₄₃	C₂×#137	1	2	yes	—
476	C₂²×C₄₃	C₂×#137	1	2	yes	—
477	C₂²×C₄₃	C₂×#137	1	2	yes	—
478	C₂²×C₄₃	#575	1	2	yes	—
479	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₄₃	—	2	1	no	—
481	C₄×C₄₃	—	2	1	no	—
482	C₄×C₄₃	—	2	1	no	—
483	C₄×C₄₃	—	2	1	no	—
484	C₄×C₄₃	—	2	1	no	—
485	C₄×C₄₃	—	2	1	no	—
486	C₄×C₄₃	—	4	2	no	—
487	C₄×C₄₃	—	4	4	no	—
488	C₄×C₄₃	—	4	2	no	—
489	C₄×C₄₃	—	4	4	no	—
490	C₄×C₄₃	—	4	2	no	—
491	C₄×C₄₃	#534	1	2	yes	—
492	C₄×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
493	C₂×#525	C₂×C₄₃	1	1	yes	characteristic
494	C₂²×C₂²⋊Q₈	C₂×C₄₃	1	1	yes	characteristic, complemented
495	#3196	C₂×C₄₃	1	4	yes	complemented
496	#3195	C₂×C₄₃	1	2	yes	complemented
497	#3193	C₂×C₄₃	1	2	yes	complemented
498	#3190	C₂×C₄₃	1	4	yes	complemented
499	#3189	C₂×C₄₃	1	2	yes	complemented
500	#3187	C₂×C₄₃	1	2	yes	complemented
501	#3095	C₂×C₄₃	1	2	yes	complemented
502	#3092	C₂×C₄₃	1	2	yes	complemented
503	#3056	C₂×C₄₃	1	4	yes	complemented
504	#3007	C₂×C₄₃	1	2	yes	complemented
505	#3004	C₂×C₄₃	1	2	yes	complemented
506	C₂×#407	C₂×C₄₃	1	1	yes	characteristic, complemented
507	C₂×C₄₃	—	2	2	no	—
508	C₂×C₄₃	—	2	2	no	—
509	C₂×C₄₃	—	2	2	no	—
510	C₂×C₄₃	—	2	2	no	—
511	C₂×C₄₃	—	2	2	no	—
512	C₂×C₄₃	—	4	1	no	—
513	C₂×C₄₃	—	4	1	no	—
514	C₂×C₄₃	—	8	2	no	—
515	C₂×C₄₃	C₂×#534	1	1	yes	characteristic
516	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
517	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
518	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
519	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
520	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
521	C₂×#137	C₂²×C₄₃	1	4	yes	complemented
522	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	complemented
523	#525	—	2	1	no	—
524	#525	—	2	1	no	—
525	#525	—	2	1	no	—
526	#525	—	2	1	no	—
527	#525	C₂²×C₄₃	1	2	yes	—
528	#525	C₂²×C₄₃	1	2	yes	—
529	#525	C₂²×C₄₃	1	2	yes	—
530	#525	C₂²×C₄₃	1	2	yes	—
531	C₂×#123	—	2	1	no	—
532	C₂×C₂²⋊Q₈	—	2	1	no	—
533	C₂×C₂²⋊Q₈	—	2	1	no	—
534	C₂×C₂²⋊Q₈	—	2	1	no	—
535	C₂×C₂²⋊Q₈	—	2	1	no	—
536	C₂×C₂²⋊Q₈	—	2	1	no	—
537	C₂×C₂²⋊Q₈	—	2	1	no	—
538	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
539	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
540	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
541	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
542	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
543	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	complemented
544	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	complemented
545	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	complemented
546	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
547	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
548	C₂×#120	—	2	1	no	—
549	C₂×C₄×D₄	—	2	1	no	—
550	C₂×C₄×D₄	—	2	1	no	—
551	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
552	C₂²×C₄⋊C₄	—	2	1	no	—
553	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic, complemented
554	C₂²×C₂²⋊C₄	—	2	1	no	—
555	#485	C₂²×C₄₃	1	8	yes	complemented
556	#484	C₂²×C₄₃	1	4	yes	complemented
557	#484	C₂²×C₄₃	1	4	yes	complemented
558	#483	C₂²×C₄₃	1	4	yes	complemented
559	#483	C₂²×C₄₃	1	4	yes	complemented
560	#481	C₂²×C₄₃	1	4	yes	complemented
561	#480	C₂²×C₄₃	1	4	yes	complemented
562	#470	C₂²×C₄₃	1	8	yes	complemented
563	#468	C₂²×C₄₃	1	8	yes	complemented
564	#467	C₂²×C₄₃	1	8	yes	complemented
565	#465	C₂²×C₄₃	1	8	yes	complemented
566	#452	C₂²×C₄₃	1	8	yes	complemented
567	#451	C₂²×C₄₃	1	4	yes	complemented
568	#451	C₂²×C₄₃	1	4	yes	complemented
569	#451	C₂²×C₄₃	1	4	yes	complemented
570	#450	C₂²×C₄₃	1	4	yes	complemented
571	#448	C₂²×C₄₃	1	4	yes	complemented
572	#448	C₂²×C₄₃	1	4	yes	complemented
573	#428	C₂²×C₄₃	1	4	yes	complemented
574	#419	C₂²×C₄₃	1	4	yes	complemented
575	#417	C₂²×C₄₃	1	4	yes	complemented
576	#407	C₂²×C₄₃	1	2	yes	—
577	#407	C₂²×C₄₃	1	2	yes	—
578	#407	C₂²×C₄₃	1	2	yes	complemented
579	#407	C₂²×C₄₃	1	2	yes	complemented
580	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
581	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	complemented
582	C₄₃	#60751	1	1	yes	characteristic, direct product factor, Sylow
583	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
584	C₂×#41	—	2	1	no	—
585	C₂×#41	—	2	1	no	—
586	C₂×#41	—	4	4	no	—
587	C₂×#41	C₂³×C₄₃	1	2	yes	—
588	C₂×#41	C₂³×C₄₃	1	2	yes	—
589	C₂²×Q₈	—	2	1	no	—
590	C₂²×Q₈	—	2	1	no	—
591	C₂²×Q₈	—	2	1	no	—
592	C₂²×Q₈	—	4	4	no	—
593	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
594	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
595	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
596	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
601	C₂³×C₄	—	2	1	no	—
602	C₂³×C₄	—	2	1	no	—
603	C₂³×C₄	—	2	1	no	—
604	C₂³×C₄	—	4	4	no	—
605	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
606	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
607	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
608	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
609	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
610	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
611	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
619	#137	—	4	8	no	—
620	C₂×Q₁₆	C₂³×C₄₃	1	8	yes	complemented
621	C₂×SD₁₆	C₂³×C₄₃	1	8	yes	complemented
622	C₂×M₁₆	—	4	4	no	—
623	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
624	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
625	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	C₂²⋊Q₈	—	2	2	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
647	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
648	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
649	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
650	C₂²⋊Q₈	C₂³×C₄₃	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₄₃	1	2	yes	—
652	C₂²⋊Q₈	C₂³×C₄₃	1	2	yes	—
653	C₂²⋊Q₈	C₂³×C₄₃	1	2	yes	—
654	#121	—	2	1	no	—
655	#121	—	2	1	no	—
656	#121	—	2	1	no	—
657	#121	—	2	1	no	—
658	#121	C₂³×C₄₃	1	2	yes	—
659	#121	C₂³×C₄₃	1	2	yes	—
660	#121	C₂³×C₄₃	1	2	yes	—
661	#121	C₂³×C₄₃	1	2	yes	—
662	#120	—	2	2	no	—
663	#120	—	2	2	no	—
664	#120	—	2	2	no	—
665	#120	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	#117	—	2	1	no	—
675	#117	—	2	1	no	—
676	#117	C₂³×C₄₃	1	2	yes	—
677	#117	C₂³×C₄₃	1	2	yes	—
678	C₂×C₄⋊C₄	—	2	2	no	—
679	C₂×C₄⋊C₄	—	2	2	no	—
680	C₂×C₄⋊C₄	—	2	2	no	—
681	C₂×C₄⋊C₄	—	2	2	no	—
682	C₂×C₄⋊C₄	—	2	2	no	—
683	C₂×C₄⋊C₄	—	2	2	no	—
684	C₂×C₄⋊C₄	—	2	1	no	—
685	C₂×C₄⋊C₄	—	2	1	no	—
686	C₂×C₄⋊C₄	—	2	1	no	—
687	C₂×C₄⋊C₄	—	2	1	no	—
688	C₂×C₄⋊C₄	—	2	1	no	—
689	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	—	2	2	no	—
695	C₂×C₂²⋊C₄	—	2	2	no	—
696	C₂×C₂²⋊C₄	—	2	2	no	—
697	C₂×C₂²⋊C₄	—	2	2	no	—
698	C₂×C₂²⋊C₄	—	2	2	no	—
699	C₂×C₂²⋊C₄	—	2	2	no	—
700	C₂×C₂²⋊C₄	—	2	1	no	—
701	C₂×C₂²⋊C₄	—	2	1	no	—
702	C₂×C₂²⋊C₄	—	2	1	no	—
703	C₂×C₂²⋊C₄	—	2	1	no	—
704	C₂×C₂²⋊C₄	—	2	1	no	—
705	C₂×C₄²	—	2	1	no	—
706	#107	C₂³×C₄₃	1	8	yes	complemented
707	#106	C₂³×C₄₃	1	8	yes	complemented
708	#103	C₂³×C₄₃	1	8	yes	complemented
709	#103	C₂³×C₄₃	1	8	yes	complemented
710	#103	C₂³×C₄₃	1	8	yes	complemented
711	#102	C₂³×C₄₃	1	8	yes	complemented
712	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
713	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
714	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
715	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
716	C₂⁴	—	2	4	no	—
717	C₂⁴	—	2	1	no	—
718	C₂⁴	—	4	2	no	—
719	C₂⁴	—	4	2	no	—
720	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
721	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
722	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
723	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
724	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
725	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
726	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
727	#41	—	2	8	no	—
728	#41	—	4	4	no	—
729	#41	—	4	4	no	—
730	#41	—	4	4	no	—
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×Q₈	—	2	1	no	—
735	C₂×Q₈	—	2	8	no	—
736	C₂×Q₈	—	4	4	no	—
737	C₂×Q₈	—	4	4	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	—	4	4	no	—
740	C₂×Q₈	—	4	4	no	—
741	C₂×Q₈	—	4	4	no	—
742	C₂×Q₈	C₂⁴×C₄₃	1	4	yes	—
743	C₂×Q₈	C₂⁴×C₄₃	1	2	yes	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	4	2	no	—
752	C₂×D₄	—	4	4	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	4	no	—
755	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
756	C₂²×C₄	—	2	4	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	2	no	—
774	C₂²×C₄	—	4	2	no	—
775	C₂²×C₄	—	4	2	no	—
776	C₂²×C₄	—	4	2	no	—
777	C₂²×C₄	—	4	2	no	—
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	4	no	—
782	C₂²×C₄	—	4	4	no	—
783	C₂²×C₄	—	4	4	no	—
784	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
792	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
793	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
798	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
800	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
801	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
802	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
803	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
804	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
812	Q₁₆	—	4	8	no	—
813	SD₁₆	—	4	8	no	—
814	M₁₆	—	2	8	no	—
815	M₁₆	—	4	4	no	—
816	C₂×C₈	—	4	4	no	—
817	C₂×C₈	C₂⁴×C₄₃	1	8	yes	—
818	C₄⋊C₄	—	2	4	no	—
819	C₄⋊C₄	—	2	4	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	4	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	1	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	C₂⁴×C₄₃	1	4	yes	—
832	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
833	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	2	2	no	—
855	C₂³	—	2	2	no	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	4	1	no	—
864	C₂³	—	4	1	no	—
865	C₂³	—	4	1	no	—
866	C₂³	—	4	1	no	—
867	C₂³	—	4	1	no	—
868	C₂³	—	4	1	no	—
869	C₂³	—	4	1	no	—
870	C₂³	—	4	1	no	—
871	C₂³	—	4	16	no	—
872	C₂³	—	4	2	no	—
873	C₂³	—	4	2	no	—
874	C₂³	—	4	2	no	—
875	C₂³	#137×C₄₃	1	4	yes	complemented
876	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
877	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
878	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
879	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
881	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
882	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
883	Q₈	—	2	8	no	—
884	Q₈	—	2	4	no	—
885	Q₈	—	4	4	no	—
886	Q₈	—	4	4	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	4	no	—
889	D₄	—	2	4	no	—
890	D₄	—	4	2	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	4	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	4	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	4	1	no	—
925	C₂×C₄	—	4	1	no	—
926	C₂×C₄	—	4	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	4	no	—
933	C₂×C₄	—	4	4	no	—
934	C₂×C₄	—	4	4	no	—
935	C₂×C₄	—	4	2	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
941	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
943	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
944	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
945	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
947	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
948	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
949	C₈	—	2	8	no	—
950	C₂²	—	2	8	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	4	4	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	4	no	—
970	C₂²	—	4	4	no	—
971	C₂²	—	4	4	no	—
972	C₂²	—	4	4	no	—
973	C₂²	—	4	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	8	4	no	—
977	C₂²	C₄₃×#534	1	2	yes	—
978	C₂²	C₂×#137×C₄₃	1	2	yes	—
979	C₂²	C₂×#137×C₄₃	1	2	yes	—
980	C₂²	C₂×#137×C₄₃	1	2	yes	—
981	C₂²	C₄₃×#575	1	2	yes	—
982	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	4	2	no	—
990	C₄	—	4	4	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	4	no	—
993	C₄	—	4	2	no	—
994	C₄	C₄₃×#534	1	2	yes	—
995	C₄	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
996	C₂	—	2	2	no	—
997	C₂	—	2	2	no	—
998	C₂	—	2	2	no	—
999	C₂	—	2	2	no	—
1000	C₂	—	2	2	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	4	1	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₂×C₄₃×#534	1	1	yes	characteristic
1005	C₂	C₂²×#137×C₄₃	1	1	yes	characteristic
1006	C₂	C₂×C₄₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
prime radical	C₂×C₄₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂²⋊Q₈×C₄₃	C₂	semidirect
3. C₄₃×#3196	C₂	semidirect
4. C₄₃×#3195	C₂	semidirect
5. C₄₃×#3193	C₂	semidirect
6. C₄₃×#3190	C₂	semidirect
7. C₄₃×#3189	C₂	semidirect
8. C₄₃×#3187	C₂	semidirect
9. C₄₃×#3095	C₂	semidirect
10. C₄₃×#3092	C₂	semidirect
11. C₄₃×#3056	C₂	semidirect
12. C₄₃×#3007	C₂	semidirect
13. C₄₃×#3004	C₂	semidirect
14. C₂×C₄₃×#407	C₂	semidirect
16. C₂³×Q₈×C₄₃	C₂²	semidirect
18. C₂×#137×C₄₃	C₂²	semidirect
19. C₂²×M₁₆×C₄₃	C₂²	semidirect
40. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
41. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
42. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
50. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
52. C₄₃×#485	C₂²	semidirect
53. C₄₃×#484	C₂²	semidirect
54. C₄₃×#484	C₂²	semidirect
55. C₄₃×#483	C₂²	semidirect
56. C₄₃×#483	C₂²	semidirect
57. C₄₃×#481	C₂²	semidirect
58. C₄₃×#480	C₂²	semidirect
59. C₄₃×#470	C₂²	semidirect
60. C₄₃×#468	C₂²	semidirect
61. C₄₃×#467	C₂²	semidirect
62. C₄₃×#465	C₂²	semidirect
63. C₄₃×#452	C₂²	semidirect
64. C₄₃×#451	C₂²	semidirect
65. C₄₃×#451	C₂²	semidirect
66. C₄₃×#451	C₂²	semidirect
67. C₄₃×#450	C₂²	semidirect
68. C₄₃×#448	C₂²	semidirect
69. C₄₃×#448	C₂²	semidirect
70. C₄₃×#428	C₂²	semidirect
71. C₄₃×#419	C₂²	semidirect
72. C₄₃×#417	C₂²	semidirect
75. C₄₃×#407	C₂²	semidirect
76. C₄₃×#407	C₂²	semidirect
78. C₂×C₂²⋊C₈×C₄₃	C₂²	semidirect
116. C₂×Q₁₆×C₄₃	C₂³	semidirect
117. C₂×SD₁₆×C₄₃	C₂³	semidirect
202. #107×C₄₃	C₂³	semidirect
203. #106×C₄₃	C₂³	semidirect
204. #103×C₄₃	C₂³	semidirect
205. #103×C₄₃	C₂³	semidirect
206. #103×C₄₃	C₂³	semidirect
207. #102×C₄₃	C₂³	semidirect
371. C₂³×C₄₃	#137	semidirect
446. #60751	C₄₃	direct (N × H)
494. C₂²×C₂²⋊Q₈	C₂×C₄₃	semidirect
495. #3196	C₂×C₄₃	semidirect
496. #3195	C₂×C₄₃	semidirect
497. #3193	C₂×C₄₃	semidirect
498. #3190	C₂×C₄₃	semidirect
499. #3189	C₂×C₄₃	semidirect
500. #3187	C₂×C₄₃	semidirect
501. #3095	C₂×C₄₃	semidirect
502. #3092	C₂×C₄₃	semidirect
503. #3056	C₂×C₄₃	semidirect
504. #3007	C₂×C₄₃	semidirect
505. #3004	C₂×C₄₃	semidirect
506. C₂×#407	C₂×C₄₃	semidirect
519. C₂³×Q₈	C₂²×C₄₃	semidirect
521. C₂×#137	C₂²×C₄₃	semidirect
522. C₂²×M₁₆	C₂²×C₄₃	semidirect
543. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
544. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
545. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
553. C₂²×C₄⋊C₄	C₂²×C₄₃	semidirect
555. #485	C₂²×C₄₃	semidirect
556. #484	C₂²×C₄₃	semidirect
557. #484	C₂²×C₄₃	semidirect
558. #483	C₂²×C₄₃	semidirect
559. #483	C₂²×C₄₃	semidirect
560. #481	C₂²×C₄₃	semidirect
561. #480	C₂²×C₄₃	semidirect
562. #470	C₂²×C₄₃	semidirect
563. #468	C₂²×C₄₃	semidirect
564. #467	C₂²×C₄₃	semidirect
565. #465	C₂²×C₄₃	semidirect
566. #452	C₂²×C₄₃	semidirect
567. #451	C₂²×C₄₃	semidirect
568. #451	C₂²×C₄₃	semidirect
569. #451	C₂²×C₄₃	semidirect
570. #450	C₂²×C₄₃	semidirect
571. #448	C₂²×C₄₃	semidirect
572. #448	C₂²×C₄₃	semidirect
573. #428	C₂²×C₄₃	semidirect
574. #419	C₂²×C₄₃	semidirect
575. #417	C₂²×C₄₃	semidirect
578. #407	C₂²×C₄₃	semidirect
579. #407	C₂²×C₄₃	semidirect
581. C₂×C₂²⋊C₈	C₂²×C₄₃	semidirect
582. C₄₃	#60751	direct (N × H)
620. C₂×Q₁₆	C₂³×C₄₃	semidirect
621. C₂×SD₁₆	C₂³×C₄₃	semidirect
706. #107	C₂³×C₄₃	semidirect
707. #106	C₂³×C₄₃	semidirect
708. #103	C₂³×C₄₃	semidirect
709. #103	C₂³×C₄₃	semidirect
710. #103	C₂³×C₄₃	semidirect
711. #102	C₂³×C₄₃	semidirect
875. C₂³	#137×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×#525	2
C₂²×C₂²⋊Q₈×C₄₃	2
C₄₃×#3196	2
C₄₃×#3195	2
C₄₃×#3193	2
C₄₃×#3190	2
C₄₃×#3189	2
C₄₃×#3187	2
C₄₃×#3095	2
C₄₃×#3092	2
C₄₃×#3056	2
C₄₃×#3007	2
C₄₃×#3004	2
C₂×C₄₃×#407	2
#60751	43

Subgroups — C43×#60751 #24980768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#60751 #24980768