Subgroups — C₂×C₄₃×#1906 #24941016

Order 11008.

1798 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#410	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1906	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#575	—	2	2	no	—
12	C₄₃×#575	—	2	2	no	—
13	C₄₃×#575	C₄	1	4	yes	complemented
14	C₄₃×#575	C₂²	1	4	yes	—
15	C₂×#137×C₄₃	—	2	1	no	—
16	C₂×#137×C₄₃	C₄	1	2	yes	complemented
17	C₂×AGL(1,ℤ/8)×C₄₃	—	2	1	no	—
18	C₂×AGL(1,ℤ/8)×C₄₃	C₄	1	2	yes	complemented
19	C₂×#135×C₄₃	—	2	2	no	—
20	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×#41×C₄₃	—	2	2	no	—
23	C₄×#41×C₄₃	—	2	2	no	—
24	C₄×#41×C₄₃	—	2	2	no	—
25	C₄×#41×C₄₃	C₂²	1	4	yes	complemented
26	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
27	C₂×C₄×D₄×C₄₃	—	2	1	no	—
28	C₂×C₄×D₄×C₄₃	—	2	2	no	—
29	C₂×#117×C₄₃	—	2	1	no	—
30	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₃	—	2	1	no	—
33	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#421	—	2	2	no	—
35	C₄₃×#421	C₂²	1	4	yes	complemented
36	C₂×#104×C₄₃	—	2	2	no	—
37	C₂×#104×C₄₃	—	2	1	no	—
38	C₂×#104×C₄₃	—	2	1	no	—
39	C₂×#104×C₄₃	—	2	2	no	—
40	C₂×#104×C₄₃	C₂²	1	4	yes	complemented
41	C₄₃×#410	—	2	2	no	—
42	C₄₃×#410	C₂²	1	4	yes	complemented
43	C₂×#99×C₄₃	—	2	2	no	—
44	C₄₃×#344	C₂²	1	4	yes	complemented
45	C₄₃×#339	C₂²	1	4	yes	complemented
46	C₂×#41×C₄₃	—	2	1	no	—
47	C₂×#41×C₄₃	—	2	1	no	—
48	C₂×#41×C₄₃	—	2	1	no	—
49	C₂×#41×C₄₃	—	2	1	no	—
50	C₂×#41×C₄₃	—	2	1	no	—
51	C₂×#41×C₄₃	—	2	1	no	—
52	C₂×#41×C₄₃	—	2	1	no	—
53	C₂×#41×C₄₃	—	2	1	no	—
54	C₂×#41×C₄₃	—	2	1	no	—
55	C₂×#41×C₄₃	—	2	1	no	—
56	C₂×#41×C₄₃	—	2	1	no	—
57	C₂×#41×C₄₃	—	2	1	no	—
58	C₂×#41×C₄₃	—	2	1	no	—
59	C₂×#41×C₄₃	—	2	1	no	—
60	C₂×#41×C₄₃	—	2	1	no	—
61	C₂×#41×C₄₃	—	2	1	no	—
62	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
63	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
64	C₂×#41×C₄₃	C₂×C₄	1	2	yes	complemented
65	C₂×#41×C₄₃	D₄	1	2	yes	—
66	C₂×#41×C₄₃	D₄	1	2	yes	—
67	C₂×#41×C₄₃	D₄	1	2	yes	—
68	C₂×#41×C₄₃	C₂³	1	2	yes	—
69	C₂×#41×C₄₃	C₂³	1	2	yes	—
70	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₄₃	—	2	1	no	—
73	C₂²×D₄×C₄₃	—	2	1	no	—
74	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic, complemented
75	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
76	C₂³×C₄×C₄₃	—	2	1	no	—
77	C₂³×C₄×C₄₃	—	2	2	no	—
78	C₂³×C₄×C₄₃	—	2	1	no	—
79	C₂³×C₄×C₄₃	—	2	1	no	—
80	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
81	#137×C₄₃	—	2	4	no	—
82	#137×C₄₃	—	2	4	no	—
83	#137×C₄₃	—	2	4	no	—
84	#137×C₄₃	C₂×C₄	1	8	yes	complemented
85	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
86	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
87	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
88	AGL(1,ℤ/8)×C₄₃	C₂×C₄	1	8	yes	complemented
89	#135×C₄₃	—	2	8	no	—
90	#135×C₄₃	—	2	8	no	—
91	C₂×Q₁₆×C₄₃	—	2	2	no	—
92	C₂×SD₁₆×C₄₃	—	2	2	no	—
93	C₂×SD₁₆×C₄₃	—	2	2	no	—
94	C₂×D₈×C₄₃	—	2	2	no	—
95	C₂×M₁₆×C₄₃	—	2	1	no	—
96	C₂×M₁₆×C₄₃	—	2	1	no	—
97	C₂×M₁₆×C₄₃	—	2	1	no	—
98	C₂×M₁₆×C₄₃	—	2	1	no	—
99	C₂×M₁₆×C₄₃	—	2	1	no	—
100	C₂×M₁₆×C₄₃	—	2	1	no	—
101	C₂×M₁₆×C₄₃	—	2	1	no	—
102	C₂×M₁₆×C₄₃	—	2	1	no	—
103	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	complemented
104	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	complemented
105	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₄₃	—	2	1	no	—
108	C₂²×C₈×C₄₃	—	2	1	no	—
109	C₄×Q₈×C₄₃	—	2	4	no	—
110	C₄×Q₈×C₄₃	—	2	4	no	—
111	C₄×D₄×C₄₃	—	2	8	no	—
112	C₄×D₄×C₄₃	—	2	4	no	—
113	C₄×D₄×C₄₃	—	2	4	no	—
114	C₄×D₄×C₄₃	—	2	8	no	—
115	#117×C₄₃	—	2	4	no	—
116	#117×C₄₃	—	2	1	no	—
117	#117×C₄₃	—	2	1	no	—
118	#117×C₄₃	—	2	1	no	—
119	#117×C₄₃	—	2	4	no	—
120	#117×C₄₃	—	2	1	no	—
121	#117×C₄₃	—	2	1	no	—
122	#117×C₄₃	D₄	1	2	yes	—
123	#117×C₄₃	C₂³	1	2	yes	—
124	#117×C₄₃	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
131	C₂×C₄²×C₄₃	—	2	2	no	—
132	C₂×C₄²×C₄₃	—	2	4	no	—
133	C₂×C₄²×C₄₃	—	2	1	no	—
134	C₂×C₄²×C₄₃	—	2	1	no	—
135	C₂×C₄²×C₄₃	—	2	1	no	—
136	C₂×C₄²×C₄₃	—	2	1	no	—
137	C₂×C₄²×C₄₃	—	2	4	no	—
138	C₂×C₄²×C₄₃	—	2	1	no	—
139	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
140	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
141	C₂×C₄²×C₄₃	D₄	1	2	yes	—
142	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
143	#104×C₄₃	—	2	8	no	—
144	#104×C₄₃	—	2	4	no	—
145	#104×C₄₃	—	2	4	no	—
146	#99×C₄₃	—	2	8	no	—
147	C₂⁴×C₄₃	—	2	1	no	—
148	C₂⁴×C₄₃	—	2	1	no	—
149	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
150	#41×C₄₃	—	2	2	no	—
151	#41×C₄₃	—	2	2	no	—
152	#41×C₄₃	—	2	2	no	—
153	#41×C₄₃	—	2	2	no	—
154	#41×C₄₃	—	2	2	no	—
155	#41×C₄₃	—	2	2	no	—
156	#41×C₄₃	—	2	2	no	—
157	#41×C₄₃	—	2	2	no	—
158	#41×C₄₃	—	2	2	no	—
159	#41×C₄₃	—	2	2	no	—
160	#41×C₄₃	—	2	2	no	—
161	#41×C₄₃	—	2	2	no	—
162	#41×C₄₃	—	2	2	no	—
163	#41×C₄₃	—	2	2	no	—
164	#41×C₄₃	—	2	2	no	—
165	#41×C₄₃	—	2	2	no	—
166	#41×C₄₃	—	2	2	no	—
167	#41×C₄₃	—	2	2	no	—
168	#41×C₄₃	—	2	2	no	—
169	#41×C₄₃	—	2	2	no	—
170	#41×C₄₃	—	4	1	no	—
171	#41×C₄₃	—	4	1	no	—
172	#41×C₄₃	—	4	1	no	—
173	#41×C₄₃	—	4	1	no	—
174	#41×C₄₃	—	4	1	no	—
175	#41×C₄₃	—	4	1	no	—
176	#41×C₄₃	—	4	1	no	—
177	#41×C₄₃	—	4	1	no	—
178	#41×C₄₃	C₂²⋊C₄	1	4	yes	—
179	#41×C₄₃	C₂²⋊C₄	1	4	yes	—
180	#41×C₄₃	C₂²×C₄	1	4	yes	—
181	#41×C₄₃	C₂×D₄	1	4	yes	—
182	C₂×Q₈×C₄₃	—	2	1	no	—
183	C₂×Q₈×C₄₃	—	2	1	no	—
184	C₂×Q₈×C₄₃	—	2	1	no	—
185	C₂×Q₈×C₄₃	—	2	1	no	—
186	C₂×Q₈×C₄₃	—	2	1	no	—
187	C₂×Q₈×C₄₃	—	2	1	no	—
188	C₂×Q₈×C₄₃	—	2	1	no	—
189	C₂×Q₈×C₄₃	—	2	1	no	—
190	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
191	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
192	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	complemented
193	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
194	C₂×D₄×C₄₃	—	2	1	no	—
195	C₂×D₄×C₄₃	—	2	1	no	—
196	C₂×D₄×C₄₃	—	2	1	no	—
197	C₂×D₄×C₄₃	—	2	1	no	—
198	C₂×D₄×C₄₃	—	2	2	no	—
199	C₂×D₄×C₄₃	—	2	2	no	—
200	C₂×D₄×C₄₃	—	2	2	no	—
201	C₂×D₄×C₄₃	—	2	2	no	—
202	C₂×D₄×C₄₃	—	2	2	no	—
203	C₂×D₄×C₄₃	—	2	2	no	—
204	C₂×D₄×C₄₃	—	2	2	no	—
205	C₂×D₄×C₄₃	—	2	2	no	—
206	C₂×D₄×C₄₃	—	2	1	no	—
207	C₂×D₄×C₄₃	—	2	1	no	—
208	C₂×D₄×C₄₃	—	2	1	no	—
209	C₂×D₄×C₄₃	—	2	1	no	—
210	C₂×D₄×C₄₃	—	4	1	no	—
211	C₂×D₄×C₄₃	—	4	1	no	—
212	C₂×D₄×C₄₃	—	4	1	no	—
213	C₂×D₄×C₄₃	—	4	1	no	—
214	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
215	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
216	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	complemented
217	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₄₃	—	2	2	no	—
219	C₂²×C₄×C₄₃	—	2	2	no	—
220	C₂²×C₄×C₄₃	—	2	2	no	—
221	C₂²×C₄×C₄₃	—	2	2	no	—
222	C₂²×C₄×C₄₃	—	2	2	no	—
223	C₂²×C₄×C₄₃	—	2	2	no	—
224	C₂²×C₄×C₄₃	—	2	8	no	—
225	C₂²×C₄×C₄₃	—	2	2	no	—
226	C₂²×C₄×C₄₃	—	2	2	no	—
227	C₂²×C₄×C₄₃	—	2	1	no	—
228	C₂²×C₄×C₄₃	—	2	1	no	—
229	C₂²×C₄×C₄₃	—	2	1	no	—
230	C₂²×C₄×C₄₃	—	2	2	no	—
231	C₂²×C₄×C₄₃	—	2	1	no	—
232	C₂²×C₄×C₄₃	—	2	2	no	—
233	C₂²×C₄×C₄₃	—	2	2	no	—
234	C₂²×C₄×C₄₃	—	4	4	no	—
235	C₂²×C₄×C₄₃	—	4	8	no	—
236	C₂²×C₄×C₄₃	—	4	1	no	—
237	C₂²×C₄×C₄₃	—	4	1	no	—
238	C₂²×C₄×C₄₃	—	4	1	no	—
239	C₂²×C₄×C₄₃	—	4	1	no	—
240	C₂²×C₄×C₄₃	—	4	1	no	—
241	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
242	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
251	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
252	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
253	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
254	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
255	Q₁₆×C₄₃	—	2	8	no	—
256	SD₁₆×C₄₃	—	2	8	no	—
257	SD₁₆×C₄₃	—	2	8	no	—
258	D₈×C₄₃	—	2	8	no	—
259	M₁₆×C₄₃	—	2	2	no	—
260	M₁₆×C₄₃	—	2	2	no	—
261	M₁₆×C₄₃	—	2	2	no	—
262	M₁₆×C₄₃	—	2	2	no	—
263	M₁₆×C₄₃	—	2	2	no	—
264	M₁₆×C₄₃	—	4	1	no	—
265	M₁₆×C₄₃	—	4	1	no	—
266	M₁₆×C₄₃	C₂²×C₄	1	4	yes	complemented
267	C₂×C₈×C₄₃	—	2	2	no	—
268	C₂×C₈×C₄₃	—	2	2	no	—
269	C₂×C₈×C₄₃	—	2	2	no	—
270	C₂×C₈×C₄₃	—	2	2	no	—
271	C₂×C₈×C₄₃	—	4	1	no	—
272	C₂×C₈×C₄₃	—	4	1	no	—
273	C₄⋊C₄×C₄₃	—	2	8	no	—
274	C₄⋊C₄×C₄₃	—	2	2	no	—
275	C₄⋊C₄×C₄₃	—	2	2	no	—
276	C₄⋊C₄×C₄₃	—	2	2	no	—
277	C₄⋊C₄×C₄₃	—	4	1	no	—
278	C₂²⋊C₄×C₄₃	—	2	8	no	—
279	C₂²⋊C₄×C₄₃	—	2	2	no	—
280	C₂²⋊C₄×C₄₃	—	2	2	no	—
281	C₂²⋊C₄×C₄₃	—	4	1	no	—
282	C₂²⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
283	C₄²×C₄₃	—	2	8	no	—
284	C₄²×C₄₃	—	2	1	no	—
285	C₄²×C₄₃	—	2	2	no	—
286	C₄²×C₄₃	—	2	1	no	—
287	C₄²×C₄₃	—	2	2	no	—
288	C₄²×C₄₃	—	2	2	no	—
289	C₄²×C₄₃	—	2	2	no	—
290	C₄²×C₄₃	—	2	2	no	—
291	C₄²×C₄₃	—	4	1	no	—
292	C₄²×C₄₃	C₂×D₄	1	2	yes	—
293	C₄²×C₄₃	C₂×D₄	1	2	yes	—
294	C₂³×C₄₃	—	2	2	no	—
295	C₂³×C₄₃	—	2	2	no	—
296	C₂³×C₄₃	—	2	2	no	—
297	C₂³×C₄₃	—	2	2	no	—
298	C₂³×C₄₃	—	4	2	no	—
299	C₂³×C₄₃	—	4	4	no	—
300	C₂³×C₄₃	—	4	1	no	—
301	C₂³×C₄₃	—	4	1	no	—
302	C₂³×C₄₃	—	8	2	no	—
303	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
304	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
305	C₂³×C₄₃	#120	1	1	yes	characteristic
306	C₂³×C₄₃	#120	1	1	yes	characteristic
307	C₂³×C₄₃	#121	1	1	yes	characteristic
308	C₂³×C₄₃	#121	1	1	yes	characteristic
309	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₄₃	—	2	2	no	—
311	Q₈×C₄₃	—	2	2	no	—
312	Q₈×C₄₃	—	2	2	no	—
313	Q₈×C₄₃	—	2	2	no	—
314	Q₈×C₄₃	—	2	2	no	—
315	Q₈×C₄₃	—	4	1	no	—
316	Q₈×C₄₃	—	4	1	no	—
317	Q₈×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
318	D₄×C₄₃	—	2	4	no	—
319	D₄×C₄₃	—	2	4	no	—
320	D₄×C₄₃	—	2	4	no	—
321	D₄×C₄₃	—	2	4	no	—
322	D₄×C₄₃	—	2	2	no	—
323	D₄×C₄₃	—	2	2	no	—
324	D₄×C₄₃	—	2	2	no	—
325	D₄×C₄₃	—	2	2	no	—
326	D₄×C₄₃	—	2	2	no	—
327	D₄×C₄₃	—	4	2	no	—
328	D₄×C₄₃	—	4	2	no	—
329	D₄×C₄₃	—	4	2	no	—
330	D₄×C₄₃	—	4	2	no	—
331	D₄×C₄₃	—	4	1	no	—
332	D₄×C₄₃	—	4	1	no	—
333	D₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
334	C₂×C₄×C₄₃	—	2	4	no	—
335	C₂×C₄×C₄₃	—	2	2	no	—
336	C₂×C₄×C₄₃	—	2	2	no	—
337	C₂×C₄×C₄₃	—	2	2	no	—
338	C₂×C₄×C₄₃	—	2	2	no	—
339	C₂×C₄×C₄₃	—	2	4	no	—
340	C₂×C₄×C₄₃	—	2	4	no	—
341	C₂×C₄×C₄₃	—	2	4	no	—
342	C₂×C₄×C₄₃	—	2	4	no	—
343	C₂×C₄×C₄₃	—	2	2	no	—
344	C₂×C₄×C₄₃	—	2	4	no	—
345	C₂×C₄×C₄₃	—	2	2	no	—
346	C₂×C₄×C₄₃	—	4	4	no	—
347	C₂×C₄×C₄₃	—	4	4	no	—
348	C₂×C₄×C₄₃	—	4	16	no	—
349	C₂×C₄×C₄₃	—	4	4	no	—
350	C₂×C₄×C₄₃	—	4	2	no	—
351	C₂×C₄×C₄₃	—	4	1	no	—
352	C₂×C₄×C₄₃	—	4	1	no	—
353	C₂×C₄×C₄₃	—	4	2	no	—
354	C₂×C₄×C₄₃	—	4	2	no	—
355	C₂×C₄×C₄₃	—	4	2	no	—
356	C₂×C₄×C₄₃	—	4	2	no	—
357	C₂×C₄×C₄₃	—	4	2	no	—
358	C₂×C₄×C₄₃	—	8	2	no	—
359	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
361	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
363	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
364	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
365	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
366	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
367	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
369	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
370	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
371	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
372	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
373	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
374	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
375	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
376	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
377	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
378	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
379	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
380	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
381	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
382	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
386	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
387	C₈×C₄₃	—	2	4	no	—
388	C₈×C₄₃	—	4	2	no	—
389	C₂×#1906	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂²×C₄₃	—	2	2	no	—
391	C₂²×C₄₃	—	2	2	no	—
392	C₂²×C₄₃	—	2	2	no	—
393	C₂²×C₄₃	—	2	4	no	—
394	C₂²×C₄₃	—	4	1	no	—
395	C₂²×C₄₃	—	4	1	no	—
396	C₂²×C₄₃	—	4	1	no	—
397	C₂²×C₄₃	—	4	1	no	—
398	C₂²×C₄₃	—	4	4	no	—
399	C₂²×C₄₃	—	4	4	no	—
400	C₂²×C₄₃	—	4	4	no	—
401	C₂²×C₄₃	—	4	2	no	—
402	C₂²×C₄₃	—	8	2	no	—
403	C₂²×C₄₃	—	8	2	no	—
404	C₂²×C₄₃	—	8	2	no	—
405	C₂²×C₄₃	#386	1	1	yes	characteristic
406	C₂²×C₄₃	#386	1	1	yes	characteristic
407	C₂²×C₄₃	#386	1	1	yes	characteristic
408	C₂²×C₄₃	#386	1	1	yes	characteristic
409	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
410	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
411	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
412	C₄×C₄₃	—	2	4	no	—
413	C₄×C₄₃	—	2	4	no	—
414	C₄×C₄₃	—	4	4	no	—
415	C₄×C₄₃	—	4	2	no	—
416	C₄×C₄₃	—	4	2	no	—
417	C₄×C₄₃	—	8	2	no	—
418	C₄×C₄₃	#386	1	1	yes	characteristic
419	C₄×C₄₃	#386	1	1	yes	characteristic
420	C₄×C₄₃	#386	1	1	yes	characteristic
421	C₄×C₄₃	#386	1	1	yes	characteristic
422	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
423	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
424	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
425	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
426	C₂×#575	C₂×C₄₃	1	1	yes	characteristic
427	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic, complemented
428	C₂×#421	C₂×C₄₃	1	1	yes	characteristic, complemented
429	C₂²×#104	C₂×C₄₃	1	1	yes	characteristic, complemented
430	C₂×#410	C₂×C₄₃	1	1	yes	characteristic, complemented
431	#1906	C₂×C₄₃	1	8	yes	direct product factor
432	C₂×#344	C₂×C₄₃	1	1	yes	characteristic, complemented
433	C₂×#339	C₂×C₄₃	1	1	yes	characteristic, complemented
434	C₂×C₄₃	—	2	1	no	—
435	C₂×C₄₃	—	2	1	no	—
436	C₂×C₄₃	—	2	1	no	—
437	C₂×C₄₃	—	2	1	no	—
438	C₂×C₄₃	—	2	1	no	—
439	C₂×C₄₃	—	2	1	no	—
440	C₂×C₄₃	—	4	4	no	—
441	C₂×C₄₃	—	8	2	no	—
442	C₂×C₄₃	#1906	1	2	yes	direct product factor
443	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
444	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
445	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
446	#575	—	2	2	no	—
447	#575	—	2	2	no	—
448	#575	C₄×C₄₃	1	4	yes	complemented
449	#575	C₂²×C₄₃	1	4	yes	—
450	C₂×#137	—	2	1	no	—
451	C₂×#137	C₄×C₄₃	1	2	yes	complemented
452	C₂×AGL(1,ℤ/8)	—	2	1	no	—
453	C₂×AGL(1,ℤ/8)	C₄×C₄₃	1	2	yes	complemented
454	C₂×#135	—	2	2	no	—
455	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
456	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
457	C₄×#41	—	2	2	no	—
458	C₄×#41	—	2	2	no	—
459	C₄×#41	—	2	2	no	—
460	C₄×#41	C₂²×C₄₃	1	4	yes	complemented
461	C₂×C₄×Q₈	—	2	1	no	—
462	C₂×C₄×D₄	—	2	1	no	—
463	C₂×C₄×D₄	—	2	2	no	—
464	C₂×#117	—	2	1	no	—
465	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
466	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
467	C₂²×C₄²	—	2	1	no	—
468	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
469	#421	—	2	2	no	—
470	#421	C₂²×C₄₃	1	4	yes	complemented
471	C₂×#104	—	2	2	no	—
472	C₂×#104	—	2	1	no	—
473	C₂×#104	—	2	2	no	—
474	C₂×#104	—	2	1	no	—
475	C₂×#104	C₂²×C₄₃	1	4	yes	complemented
476	#410	—	2	2	no	—
477	#410	C₂²×C₄₃	1	4	yes	complemented
478	C₂×#99	—	2	2	no	—
479	#344	C₂²×C₄₃	1	4	yes	complemented
480	#339	C₂²×C₄₃	1	4	yes	complemented
481	C₄₃	C₂×#1906	1	1	yes	characteristic, direct product factor, Sylow
482	C₂×#41	—	2	1	no	—
483	C₂×#41	—	2	1	no	—
484	C₂×#41	—	2	1	no	—
485	C₂×#41	—	2	1	no	—
486	C₂×#41	—	2	1	no	—
487	C₂×#41	—	2	1	no	—
488	C₂×#41	—	2	1	no	—
489	C₂×#41	—	2	1	no	—
490	C₂×#41	—	2	1	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	—	2	1	no	—
495	C₂×#41	—	2	1	no	—
496	C₂×#41	—	2	1	no	—
497	C₂×#41	—	2	1	no	—
498	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
499	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
500	C₂×#41	C₂×C₄×C₄₃	1	2	yes	complemented
501	C₂×#41	D₄×C₄₃	1	2	yes	—
502	C₂×#41	D₄×C₄₃	1	2	yes	—
503	C₂×#41	D₄×C₄₃	1	2	yes	—
504	C₂×#41	C₂³×C₄₃	1	2	yes	—
505	C₂×#41	C₂³×C₄₃	1	2	yes	—
506	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic, complemented
507	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	1	no	—
510	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic, complemented
511	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	2	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
517	#137	—	2	4	no	—
518	#137	—	2	4	no	—
519	#137	—	2	4	no	—
520	#137	C₂×C₄×C₄₃	1	8	yes	complemented
521	AGL(1,ℤ/8)	—	2	4	no	—
522	AGL(1,ℤ/8)	—	2	4	no	—
523	AGL(1,ℤ/8)	—	2	4	no	—
524	AGL(1,ℤ/8)	C₂×C₄×C₄₃	1	8	yes	complemented
525	#135	—	2	8	no	—
526	#135	—	2	8	no	—
527	C₂×Q₁₆	—	2	2	no	—
528	C₂×SD₁₆	—	2	2	no	—
529	C₂×SD₁₆	—	2	2	no	—
530	C₂×D₈	—	2	2	no	—
531	C₂×M₁₆	—	2	1	no	—
532	C₂×M₁₆	—	2	1	no	—
533	C₂×M₁₆	—	2	1	no	—
534	C₂×M₁₆	—	2	1	no	—
535	C₂×M₁₆	—	2	1	no	—
536	C₂×M₁₆	—	2	1	no	—
537	C₂×M₁₆	—	2	1	no	—
538	C₂×M₁₆	—	2	1	no	—
539	C₂×M₁₆	C₂×C₄×C₄₃	1	2	yes	complemented
540	C₂×M₁₆	C₂×C₄×C₄₃	1	2	yes	complemented
541	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
542	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
543	C₂²×C₈	—	2	1	no	—
544	C₂²×C₈	—	2	1	no	—
545	C₄×Q₈	—	2	4	no	—
546	C₄×Q₈	—	2	4	no	—
547	C₄×D₄	—	2	8	no	—
548	C₄×D₄	—	2	4	no	—
549	C₄×D₄	—	2	4	no	—
550	C₄×D₄	—	2	8	no	—
551	#117	—	2	4	no	—
552	#117	—	2	1	no	—
553	#117	—	2	1	no	—
554	#117	—	2	1	no	—
555	#117	—	2	4	no	—
556	#117	—	2	1	no	—
557	#117	—	2	1	no	—
558	#117	D₄×C₄₃	1	2	yes	—
559	#117	C₂³×C₄₃	1	2	yes	—
560	#117	C₂³×C₄₃	1	2	yes	—
561	C₂×C₄⋊C₄	—	2	2	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	2	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
567	C₂×C₄²	—	2	2	no	—
568	C₂×C₄²	—	2	4	no	—
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	—	2	1	no	—
573	C₂×C₄²	—	2	4	no	—
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
576	C₂×C₄²	D₄×C₄₃	1	2	yes	—
577	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
579	#104	—	2	8	no	—
580	#104	—	2	4	no	—
581	#104	—	2	4	no	—
582	#99	—	2	8	no	—
583	C₂⁴	—	2	1	no	—
584	C₂⁴	—	2	1	no	—
585	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
586	#41	—	2	2	no	—
587	#41	—	2	2	no	—
588	#41	—	2	2	no	—
589	#41	—	2	2	no	—
590	#41	—	2	2	no	—
591	#41	—	2	2	no	—
592	#41	—	2	2	no	—
593	#41	—	2	2	no	—
594	#41	—	2	2	no	—
595	#41	—	2	2	no	—
596	#41	—	2	2	no	—
597	#41	—	2	2	no	—
598	#41	—	2	2	no	—
599	#41	—	2	2	no	—
600	#41	—	2	2	no	—
601	#41	—	2	2	no	—
602	#41	—	2	2	no	—
603	#41	—	2	2	no	—
604	#41	—	2	2	no	—
605	#41	—	2	2	no	—
606	#41	—	4	1	no	—
607	#41	—	4	1	no	—
608	#41	—	4	1	no	—
609	#41	—	4	1	no	—
610	#41	—	4	1	no	—
611	#41	—	4	1	no	—
612	#41	—	4	1	no	—
613	#41	—	4	1	no	—
614	#41	C₂²⋊C₄×C₄₃	1	4	yes	—
615	#41	C₂²⋊C₄×C₄₃	1	4	yes	—
616	#41	C₂²×C₄×C₄₃	1	4	yes	—
617	#41	C₂×D₄×C₄₃	1	4	yes	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	C₂²⋊C₄×C₄₃	1	2	yes	—
627	C₂×Q₈	C₂²⋊C₄×C₄₃	1	2	yes	—
628	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	complemented
629	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	2	no	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂×D₄	—	4	1	no	—
650	C₂×D₄	C₂²⋊C₄×C₄₃	1	2	yes	—
651	C₂×D₄	C₂²⋊C₄×C₄₃	1	2	yes	—
652	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	complemented
653	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	8	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	4	4	no	—
671	C₂²×C₄	—	4	8	no	—
672	C₂²×C₄	—	4	1	no	—
673	C₂²×C₄	—	4	1	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
678	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
684	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
686	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
687	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
688	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
689	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
691	Q₁₆	—	2	8	no	—
692	SD₁₆	—	2	8	no	—
693	SD₁₆	—	2	8	no	—
694	D₈	—	2	8	no	—
695	M₁₆	—	2	2	no	—
696	M₁₆	—	2	2	no	—
697	M₁₆	—	2	2	no	—
698	M₁₆	—	2	2	no	—
699	M₁₆	—	2	2	no	—
700	M₁₆	—	4	1	no	—
701	M₁₆	—	4	1	no	—
702	M₁₆	C₂²×C₄×C₄₃	1	4	yes	complemented
703	C₂×C₈	—	2	2	no	—
704	C₂×C₈	—	2	2	no	—
705	C₂×C₈	—	2	2	no	—
706	C₂×C₈	—	2	2	no	—
707	C₂×C₈	—	4	1	no	—
708	C₂×C₈	—	4	1	no	—
709	C₄⋊C₄	—	2	8	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	4	1	no	—
714	C₂²⋊C₄	—	2	8	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
719	C₄²	—	2	8	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	2	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	4	1	no	—
728	C₄²	C₂×D₄×C₄₃	1	2	yes	—
729	C₄²	C₂×D₄×C₄₃	1	2	yes	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	4	no	—
736	C₂³	—	4	1	no	—
737	C₂³	—	4	1	no	—
738	C₂³	—	8	2	no	—
739	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
740	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
741	C₂³	#120×C₄₃	1	1	yes	characteristic
742	C₂³	#120×C₄₃	1	1	yes	characteristic
743	C₂³	#121×C₄₃	1	1	yes	characteristic
744	C₂³	#121×C₄₃	1	1	yes	characteristic
745	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
746	Q₈	—	2	2	no	—
747	Q₈	—	2	2	no	—
748	Q₈	—	2	2	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	2	2	no	—
751	Q₈	—	4	1	no	—
752	Q₈	—	4	1	no	—
753	Q₈	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
754	D₄	—	2	4	no	—
755	D₄	—	2	4	no	—
756	D₄	—	2	4	no	—
757	D₄	—	2	4	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	4	2	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	2	no	—
766	D₄	—	4	2	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
770	C₂×C₄	—	2	4	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	4	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	4	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	—	4	16	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	8	2	no	—
795	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
796	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
797	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
798	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
799	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
800	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
801	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
802	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
803	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
804	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
805	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
806	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
807	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
808	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
809	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
810	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
811	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
812	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
813	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
814	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
815	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
816	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
817	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
820	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
821	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
822	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
823	C₈	—	2	4	no	—
824	C₈	—	4	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	4	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	8	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	—	8	2	no	—
840	C₂²	C₄₃×#386	1	1	yes	characteristic
841	C₂²	C₄₃×#386	1	1	yes	characteristic
842	C₂²	C₄₃×#386	1	1	yes	characteristic
843	C₂²	C₄₃×#386	1	1	yes	characteristic
844	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
845	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
846	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
847	C₄	—	2	4	no	—
848	C₄	—	2	4	no	—
849	C₄	—	4	4	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	8	2	no	—
853	C₄	C₄₃×#386	1	1	yes	characteristic
854	C₄	C₄₃×#386	1	1	yes	characteristic
855	C₄	C₄₃×#386	1	1	yes	characteristic
856	C₄	C₄₃×#386	1	1	yes	characteristic
857	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
858	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
859	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
860	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
861	C₂	—	2	1	no	—
862	C₂	—	2	1	no	—
863	C₂	—	2	1	no	—
864	C₂	—	2	1	no	—
865	C₂	—	2	1	no	—
866	C₂	—	2	1	no	—
867	C₂	—	4	4	no	—
868	C₂	—	8	2	no	—
869	C₂	C₄₃×#1906	1	2	yes	direct product factor
870	C₂	C₂×C₄₃×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	#121
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂²×C₄₃	#386
prime radical	C₂×C₄₃×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₄₃	C₂	semidirect
3. C₂×C₄₃×#421	C₂	semidirect
4. C₂²×#104×C₄₃	C₂	semidirect
5. C₂×C₄₃×#410	C₂	semidirect
6. C₄₃×#1906	C₂	direct (N × H)
7. C₂×C₄₃×#344	C₂	semidirect
8. C₂×C₄₃×#339	C₂	semidirect
13. C₄₃×#575	C₄	semidirect
16. C₂×#137×C₄₃	C₄	semidirect
18. C₂×AGL(1,ℤ/8)×C₄₃	C₄	semidirect
25. C₄×#41×C₄₃	C₂²	semidirect
35. C₄₃×#421	C₂²	semidirect
40. C₂×#104×C₄₃	C₂²	semidirect
42. C₄₃×#410	C₂²	semidirect
44. C₄₃×#344	C₂²	semidirect
45. C₄₃×#339	C₂²	semidirect
64. C₂×#41×C₄₃	C₂×C₄	semidirect
70. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
74. C₂²×D₄×C₄₃	C₂×C₄	semidirect
84. #137×C₄₃	C₂×C₄	semidirect
88. AGL(1,ℤ/8)×C₄₃	C₂×C₄	semidirect
103. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
104. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
192. C₂×Q₈×C₄₃	C₂²×C₄	semidirect
216. C₂×D₄×C₄₃	C₂²×C₄	semidirect
266. M₁₆×C₄₃	C₂²×C₄	semidirect
389. C₂×#1906	C₄₃	direct (N × H)
427. C₂×C₄×#41	C₂×C₄₃	semidirect
428. C₂×#421	C₂×C₄₃	semidirect
429. C₂²×#104	C₂×C₄₃	semidirect
430. C₂×#410	C₂×C₄₃	semidirect
431. #1906	C₂×C₄₃	direct (N × H)
432. C₂×#344	C₂×C₄₃	semidirect
433. C₂×#339	C₂×C₄₃	semidirect
442. C₂×C₄₃	#1906	direct (N × H)
448. #575	C₄×C₄₃	semidirect
451. C₂×#137	C₄×C₄₃	semidirect
453. C₂×AGL(1,ℤ/8)	C₄×C₄₃	semidirect
460. C₄×#41	C₂²×C₄₃	semidirect
470. #421	C₂²×C₄₃	semidirect
475. C₂×#104	C₂²×C₄₃	semidirect
477. #410	C₂²×C₄₃	semidirect
479. #344	C₂²×C₄₃	semidirect
480. #339	C₂²×C₄₃	semidirect
481. C₄₃	C₂×#1906	direct (N × H)
500. C₂×#41	C₂×C₄×C₄₃	semidirect
506. C₂²×Q₈	C₂×C₄×C₄₃	semidirect
510. C₂²×D₄	C₂×C₄×C₄₃	semidirect
520. #137	C₂×C₄×C₄₃	semidirect
524. AGL(1,ℤ/8)	C₂×C₄×C₄₃	semidirect
539. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
540. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
628. C₂×Q₈	C₂²×C₄×C₄₃	semidirect
652. C₂×D₄	C₂²×C₄×C₄₃	semidirect
702. M₁₆	C₂²×C₄×C₄₃	semidirect
869. C₂	C₄₃×#1906	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#575	2
C₂×C₄×#41×C₄₃	2
C₂×C₄₃×#421	2
C₂²×#104×C₄₃	2
C₂×C₄₃×#410	2
C₄₃×#1906	2
C₂×C₄₃×#344	2
C₂×C₄₃×#339	2
C₂×#1906	43

Subgroups — C2×C43×#1906 #24941016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1906 #24941016