Subgroups — C₂×C₄₃×#1876 #24940933

Order 11008.

1754 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1876	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄₃×#341	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#336	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	C₂×#135×C₄₃	—	2	4	no	—
12	C₂×#135×C₄₃	—	2	4	no	—
13	C₂×#135×C₄₃	C₄	1	4	yes	complemented
14	C₂×#135×C₄₃	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₄₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×SD₁₆×C₄₃	C₄	1	1	yes	characteristic, complemented
17	C₂²×SD₁₆×C₄₃	C₄	1	1	yes	characteristic, complemented
18	C₂²×D₈×C₄₃	C₄	1	1	yes	characteristic, complemented
19	C₂×#131×C₄₃	—	2	4	no	—
20	C₂×#131×C₄₃	—	2	4	no	—
21	C₂×#131×C₄₃	—	2	2	no	—
22	C₂×#131×C₄₃	C₂²	1	4	yes	complemented
23	C₂²×M₁₆×C₄₃	—	2	1	no	—
24	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
25	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₄₃	—	2	1	no	—
27	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×#104×C₄₃	—	2	4	no	—
31	C₂×#104×C₄₃	—	2	4	no	—
32	C₂×#104×C₄₃	C₂²	1	4	yes	complemented
33	C₂×#104×C₄₃	C₂²	1	4	yes	complemented
34	C₄₃×#408	—	2	2	no	—
35	C₄₃×#408	C₂²	1	4	yes	complemented
36	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
37	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
38	C₄₃×#341	C₂²	1	4	yes	complemented
39	C₄₃×#336	C₂²	1	4	yes	complemented
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	—	2	1	no	—
42	C₂×#41×C₄₃	—	2	1	no	—
43	C₂×#41×C₄₃	—	2	1	no	—
44	C₂×#41×C₄₃	—	2	2	no	—
45	C₂×#41×C₄₃	—	2	1	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	2	2	no	—
48	C₂×#41×C₄₃	—	2	2	no	—
49	C₂×#41×C₄₃	—	2	2	no	—
50	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
51	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
52	C₂×#41×C₄₃	D₄	1	4	yes	—
53	C₂×#41×C₄₃	D₄	1	4	yes	—
54	C₂×#41×C₄₃	C₂³	1	2	yes	—
55	C₂×#41×C₄₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₄₃	—	2	1	no	—
59	C₂²×D₄×C₄₃	—	2	1	no	—
60	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂³×C₄×C₄₃	—	2	1	no	—
65	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	#135×C₄₃	—	2	16	no	—
67	#135×C₄₃	—	2	8	no	—
68	#135×C₄₃	—	2	8	no	—
69	C₂×Q₁₆×C₄₃	—	2	4	no	—
70	C₂×Q₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
71	C₂×SD₁₆×C₄₃	—	2	4	no	—
72	C₂×SD₁₆×C₄₃	—	2	4	no	—
73	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
74	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
75	C₂×D₈×C₄₃	—	2	4	no	—
76	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	complemented
77	#131×C₄₃	—	2	16	no	—
78	#131×C₄₃	—	2	8	no	—
79	#131×C₄₃	—	2	8	no	—
80	C₂×M₁₆×C₄₃	—	2	8	no	—
81	C₂×M₁₆×C₄₃	—	2	2	no	—
82	C₂×M₁₆×C₄₃	—	2	1	no	—
83	C₂×M₁₆×C₄₃	—	2	1	no	—
84	C₂×M₁₆×C₄₃	—	2	4	no	—
85	C₂×M₁₆×C₄₃	—	2	2	no	—
86	C₂×M₁₆×C₄₃	—	2	2	no	—
87	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
88	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
89	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₄₃	—	2	8	no	—
91	C₂²×C₈×C₄₃	—	2	2	no	—
92	C₂²×C₈×C₄₃	—	2	2	no	—
93	C₂²×C₈×C₄₃	—	2	2	no	—
94	C₂²×C₈×C₄₃	—	2	2	no	—
95	C₂²×C₈×C₄₃	—	2	1	no	—
96	C₂²×C₈×C₄₃	—	2	4	no	—
97	C₂²×C₈×C₄₃	—	2	1	no	—
98	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
101	C₂²×C₈×C₄₃	D₄	1	2	yes	—
102	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
103	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
104	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
106	C₂×C₄²×C₄₃	—	2	2	no	—
107	C₂×C₄²×C₄₃	—	2	2	no	—
108	C₂×C₄²×C₄₃	—	2	1	no	—
109	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
110	#104×C₄₃	—	2	8	no	—
111	#104×C₄₃	—	2	8	no	—
112	C₂²⋊C₈×C₄₃	—	2	4	no	—
113	C₂²⋊C₈×C₄₃	—	2	4	no	—
114	C₂⁴×C₄₃	—	2	1	no	—
115	C₂⁴×C₄₃	—	2	1	no	—
116	C₂⁴×C₄₃	#41	1	1	yes	characteristic
117	#41×C₄₃	—	2	4	no	—
118	#41×C₄₃	—	2	4	no	—
119	#41×C₄₃	—	2	4	no	—
120	#41×C₄₃	—	2	4	no	—
121	#41×C₄₃	—	2	4	no	—
122	#41×C₄₃	—	2	2	no	—
123	#41×C₄₃	—	2	2	no	—
124	#41×C₄₃	—	2	4	no	—
125	#41×C₄₃	—	2	4	no	—
126	#41×C₄₃	—	2	2	no	—
127	#41×C₄₃	—	2	2	no	—
128	#41×C₄₃	—	2	2	no	—
129	#41×C₄₃	—	2	2	no	—
130	#41×C₄₃	—	4	2	no	—
131	#41×C₄₃	—	4	2	no	—
132	#41×C₄₃	—	4	2	no	—
133	#41×C₄₃	—	4	2	no	—
134	#41×C₄₃	C₂²⋊C₄	1	8	yes	—
135	#41×C₄₃	C₂×D₄	1	4	yes	—
136	#41×C₄₃	C₂×D₄	1	4	yes	—
137	C₂×Q₈×C₄₃	—	2	1	no	—
138	C₂×Q₈×C₄₃	—	2	2	no	—
139	C₂×Q₈×C₄₃	—	2	1	no	—
140	C₂×Q₈×C₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	2	2	no	—
142	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
143	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
144	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₄₃	—	2	1	no	—
146	C₂×D₄×C₄₃	—	2	2	no	—
147	C₂×D₄×C₄₃	—	2	1	no	—
148	C₂×D₄×C₄₃	—	2	2	no	—
149	C₂×D₄×C₄₃	—	2	2	no	—
150	C₂×D₄×C₄₃	—	2	4	no	—
151	C₂×D₄×C₄₃	—	2	4	no	—
152	C₂×D₄×C₄₃	—	2	2	no	—
153	C₂×D₄×C₄₃	—	2	2	no	—
154	C₂×D₄×C₄₃	—	2	2	no	—
155	C₂×D₄×C₄₃	—	2	2	no	—
156	C₂×D₄×C₄₃	—	4	2	no	—
157	C₂×D₄×C₄₃	—	4	2	no	—
158	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
159	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₄₃	—	2	2	no	—
162	C₂²×C₄×C₄₃	—	2	4	no	—
163	C₂²×C₄×C₄₃	—	2	4	no	—
164	C₂²×C₄×C₄₃	—	2	2	no	—
165	C₂²×C₄×C₄₃	—	2	4	no	—
166	C₂²×C₄×C₄₃	—	2	2	no	—
167	C₂²×C₄×C₄₃	—	2	2	no	—
168	C₂²×C₄×C₄₃	—	2	1	no	—
169	C₂²×C₄×C₄₃	—	2	1	no	—
170	C₂²×C₄×C₄₃	—	2	2	no	—
171	C₂²×C₄×C₄₃	—	4	2	no	—
172	C₂²×C₄×C₄₃	—	4	2	no	—
173	C₂²×C₄×C₄₃	—	4	2	no	—
174	C₂²×C₄×C₄₃	—	4	2	no	—
175	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₃	#41	1	2	yes	—
183	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
184	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
185	Q₁₆×C₄₃	—	2	8	no	—
186	SD₁₆×C₄₃	—	2	8	no	—
187	SD₁₆×C₄₃	—	2	8	no	—
188	D₈×C₄₃	—	2	8	no	—
189	M₁₆×C₄₃	—	2	16	no	—
190	M₁₆×C₄₃	—	2	4	no	—
191	M₁₆×C₄₃	—	2	2	no	—
192	M₁₆×C₄₃	—	2	2	no	—
193	M₁₆×C₄₃	—	2	2	no	—
194	M₁₆×C₄₃	—	4	2	no	—
195	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
196	C₂×C₈×C₄₃	—	2	16	no	—
197	C₂×C₈×C₄₃	—	2	2	no	—
198	C₂×C₈×C₄₃	—	2	2	no	—
199	C₂×C₈×C₄₃	—	2	4	no	—
200	C₂×C₈×C₄₃	—	2	2	no	—
201	C₂×C₈×C₄₃	—	2	4	no	—
202	C₂×C₈×C₄₃	—	2	2	no	—
203	C₂×C₈×C₄₃	—	2	4	no	—
204	C₂×C₈×C₄₃	—	2	2	no	—
205	C₂×C₈×C₄₃	—	2	2	no	—
206	C₂×C₈×C₄₃	—	2	2	no	—
207	C₂×C₈×C₄₃	—	2	2	no	—
208	C₂×C₈×C₄₃	—	2	2	no	—
209	C₂×C₈×C₄₃	—	2	2	no	—
210	C₂×C₈×C₄₃	—	4	2	no	—
211	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
213	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
214	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
215	C₄²×C₄₃	—	2	2	no	—
216	C₄²×C₄₃	—	2	2	no	—
217	C₄²×C₄₃	—	4	2	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	2	2	no	—
220	C₂³×C₄₃	—	2	2	no	—
221	C₂³×C₄₃	—	2	4	no	—
222	C₂³×C₄₃	—	2	2	no	—
223	C₂³×C₄₃	—	4	2	no	—
224	C₂³×C₄₃	—	4	2	no	—
225	C₂³×C₄₃	—	4	2	no	—
226	C₂³×C₄₃	—	4	2	no	—
227	C₂³×C₄₃	—	4	2	no	—
228	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
229	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
230	C₂³×C₄₃	#121	1	2	yes	—
231	C₂³×C₄₃	#123	1	2	yes	—
232	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
233	Q₈×C₄₃	—	2	2	no	—
234	Q₈×C₄₃	—	2	4	no	—
235	Q₈×C₄₃	—	2	2	no	—
236	Q₈×C₄₃	—	2	2	no	—
237	Q₈×C₄₃	—	4	2	no	—
238	Q₈×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
239	D₄×C₄₃	—	2	4	no	—
240	D₄×C₄₃	—	2	4	no	—
241	D₄×C₄₃	—	2	8	no	—
242	D₄×C₄₃	—	2	2	no	—
243	D₄×C₄₃	—	2	2	no	—
244	D₄×C₄₃	—	2	2	no	—
245	D₄×C₄₃	—	2	4	no	—
246	D₄×C₄₃	—	4	2	no	—
247	D₄×C₄₃	—	4	2	no	—
248	D₄×C₄₃	—	4	4	no	—
249	D₄×C₄₃	—	4	2	no	—
250	D₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂×C₄×C₄₃	—	2	2	no	—
252	C₂×C₄×C₄₃	—	2	4	no	—
253	C₂×C₄×C₄₃	—	2	4	no	—
254	C₂×C₄×C₄₃	—	2	4	no	—
255	C₂×C₄×C₄₃	—	2	8	no	—
256	C₂×C₄×C₄₃	—	2	4	no	—
257	C₂×C₄×C₄₃	—	2	2	no	—
258	C₂×C₄×C₄₃	—	4	8	no	—
259	C₂×C₄×C₄₃	—	4	2	no	—
260	C₂×C₄×C₄₃	—	4	2	no	—
261	C₂×C₄×C₄₃	—	4	2	no	—
262	C₂×C₄×C₄₃	—	4	2	no	—
263	C₂×C₄×C₄₃	—	4	2	no	—
264	C₂×C₄×C₄₃	—	4	4	no	—
265	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
268	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
269	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₄₃	#120	1	2	yes	—
272	C₂×C₄×C₄₃	#120	1	2	yes	—
273	C₂×C₄×C₄₃	#121	1	2	yes	—
274	C₂×C₄×C₄₃	#121	1	2	yes	—
275	C₂×C₄×C₄₃	#121	1	2	yes	—
276	C₂×C₄×C₄₃	#123	1	2	yes	—
277	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
283	C₈×C₄₃	—	2	2	no	—
284	C₈×C₄₃	—	2	2	no	—
285	C₈×C₄₃	—	2	2	no	—
286	C₈×C₄₃	—	2	4	no	—
287	C₈×C₄₃	—	2	2	no	—
288	C₈×C₄₃	—	4	2	no	—
289	C₂×#1876	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂²×C₄₃	—	2	4	no	—
291	C₂²×C₄₃	—	2	4	no	—
292	C₂²×C₄₃	—	2	1	no	—
293	C₂²×C₄₃	—	2	1	no	—
294	C₂²×C₄₃	—	2	1	no	—
295	C₂²×C₄₃	—	2	1	no	—
296	C₂²×C₄₃	—	2	4	no	—
297	C₂²×C₄₃	—	4	8	no	—
298	C₂²×C₄₃	—	4	2	no	—
299	C₂²×C₄₃	—	4	2	no	—
300	C₂²×C₄₃	—	4	2	no	—
301	C₂²×C₄₃	—	4	2	no	—
302	C₂²×C₄₃	—	4	2	no	—
303	C₂²×C₄₃	—	8	4	no	—
304	C₂²×C₄₃	#386	1	2	yes	—
305	C₂²×C₄₃	#386	1	2	yes	—
306	C₂²×C₄₃	#443	1	2	yes	—
307	C₂²×C₄₃	#444	1	2	yes	—
308	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
310	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
311	C₄×C₄₃	—	2	4	no	—
312	C₄×C₄₃	—	4	4	no	—
313	C₄×C₄₃	—	4	2	no	—
314	C₄×C₄₃	#386	1	2	yes	—
315	C₄×C₄₃	#386	1	2	yes	—
316	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
317	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
319	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
320	C₂²×#135	C₂×C₄₃	1	1	yes	characteristic
321	C₂²×#131	C₂×C₄₃	1	1	yes	characteristic, complemented
322	C₂²×#104	C₂×C₄₃	1	1	yes	characteristic, complemented
323	C₂²×#104	C₂×C₄₃	1	1	yes	characteristic, complemented
324	C₂×#408	C₂×C₄₃	1	1	yes	characteristic, complemented
325	#1876	C₂×C₄₃	1	8	yes	direct product factor
326	C₂×#341	C₂×C₄₃	1	1	yes	characteristic, complemented
327	C₂×#336	C₂×C₄₃	1	1	yes	characteristic, complemented
328	C₂×C₄₃	—	2	1	no	—
329	C₂×C₄₃	—	2	1	no	—
330	C₂×C₄₃	—	2	2	no	—
331	C₂×C₄₃	—	4	4	no	—
332	C₂×C₄₃	—	8	2	no	—
333	C₂×C₄₃	#1876	1	4	yes	direct product factor
334	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
335	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
336	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
337	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
338	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
339	C₂×#135	—	2	4	no	—
340	C₂×#135	—	2	4	no	—
341	C₂×#135	C₄×C₄₃	1	4	yes	complemented
342	C₂×#135	C₂²×C₄₃	1	4	yes	—
343	C₂²×Q₁₆	C₄×C₄₃	1	1	yes	characteristic, complemented
344	C₂²×SD₁₆	C₄×C₄₃	1	1	yes	characteristic, complemented
345	C₂²×SD₁₆	C₄×C₄₃	1	1	yes	characteristic, complemented
346	C₂²×D₈	C₄×C₄₃	1	1	yes	characteristic, complemented
347	C₂×#131	—	2	4	no	—
348	C₂×#131	—	2	4	no	—
349	C₂×#131	—	2	2	no	—
350	C₂×#131	C₂²×C₄₃	1	4	yes	complemented
351	C₂²×M₁₆	—	2	1	no	—
352	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
353	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
354	C₂³×C₈	—	2	1	no	—
355	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
356	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
357	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
358	C₂×#104	—	2	4	no	—
359	C₂×#104	—	2	4	no	—
360	C₂×#104	C₂²×C₄₃	1	4	yes	complemented
361	C₂×#104	C₂²×C₄₃	1	4	yes	complemented
362	#408	—	2	2	no	—
363	#408	C₂²×C₄₃	1	4	yes	complemented
364	C₂×C₂²⋊C₈	—	2	1	no	—
365	C₂×C₂²⋊C₈	—	2	1	no	—
366	#341	C₂²×C₄₃	1	4	yes	complemented
367	#336	C₂²×C₄₃	1	4	yes	complemented
368	C₄₃	C₂×#1876	1	1	yes	characteristic, direct product factor, Sylow
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	2	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	—	2	2	no	—
379	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
380	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
381	C₂×#41	D₄×C₄₃	1	4	yes	—
382	C₂×#41	D₄×C₄₃	1	4	yes	—
383	C₂×#41	C₂³×C₄₃	1	2	yes	—
384	C₂×#41	C₂³×C₄₃	1	2	yes	—
385	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
386	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
390	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
395	#135	—	2	16	no	—
396	#135	—	2	8	no	—
397	#135	—	2	8	no	—
398	C₂×Q₁₆	—	2	4	no	—
399	C₂×Q₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
400	C₂×SD₁₆	—	2	4	no	—
401	C₂×SD₁₆	—	2	4	no	—
402	C₂×SD₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
403	C₂×SD₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
404	C₂×D₈	—	2	4	no	—
405	C₂×D₈	C₂×C₄×C₄₃	1	4	yes	complemented
406	#131	—	2	16	no	—
407	#131	—	2	8	no	—
408	#131	—	2	8	no	—
409	C₂×M₁₆	—	2	8	no	—
410	C₂×M₁₆	—	2	2	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	4	no	—
414	C₂×M₁₆	—	2	2	no	—
415	C₂×M₁₆	—	2	2	no	—
416	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
417	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
418	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
419	C₂²×C₈	—	2	8	no	—
420	C₂²×C₈	—	2	1	no	—
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	—	2	2	no	—
423	C₂²×C₈	—	2	2	no	—
424	C₂²×C₈	—	2	2	no	—
425	C₂²×C₈	—	2	4	no	—
426	C₂²×C₈	—	2	1	no	—
427	C₂²×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
428	C₂²×C₈	C₂×C₄×C₄₃	1	1	yes	characteristic
429	C₂²×C₈	C₂×C₄×C₄₃	1	2	yes	—
430	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
431	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
432	C₂²×C₈	D₄×C₄₃	1	2	yes	—
433	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
434	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
435	C₂×C₄²	—	2	2	no	—
436	C₂×C₄²	—	2	2	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
439	#104	—	2	8	no	—
440	#104	—	2	8	no	—
441	C₂²⋊C₈	—	2	4	no	—
442	C₂²⋊C₈	—	2	4	no	—
443	C₂⁴	—	2	1	no	—
444	C₂⁴	—	2	1	no	—
445	C₂⁴	#41×C₄₃	1	1	yes	characteristic
446	#41	—	2	4	no	—
447	#41	—	2	4	no	—
448	#41	—	2	4	no	—
449	#41	—	2	4	no	—
450	#41	—	2	4	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	4	no	—
454	#41	—	2	4	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	4	2	no	—
460	#41	—	4	2	no	—
461	#41	—	4	2	no	—
462	#41	—	4	2	no	—
463	#41	C₂²⋊C₄×C₄₃	1	8	yes	—
464	#41	C₂×D₄×C₄₃	1	4	yes	—
465	#41	C₂×D₄×C₄₃	1	4	yes	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	C₂²⋊C₄×C₄₃	1	4	yes	—
472	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
473	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
488	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
489	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
507	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
508	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
511	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
512	C₂²×C₄	#41×C₄₃	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
514	Q₁₆	—	2	8	no	—
515	SD₁₆	—	2	8	no	—
516	SD₁₆	—	2	8	no	—
517	D₈	—	2	8	no	—
518	M₁₆	—	2	16	no	—
519	M₁₆	—	2	4	no	—
520	M₁₆	—	2	2	no	—
521	M₁₆	—	2	2	no	—
522	M₁₆	—	2	2	no	—
523	M₁₆	—	4	2	no	—
524	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
525	C₂×C₈	—	2	16	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	2	4	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	—	2	4	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	2	4	no	—
533	C₂×C₈	—	2	2	no	—
534	C₂×C₈	—	2	2	no	—
535	C₂×C₈	—	2	2	no	—
536	C₂×C₈	—	2	2	no	—
537	C₂×C₈	—	2	2	no	—
538	C₂×C₈	—	2	2	no	—
539	C₂×C₈	—	4	2	no	—
540	C₂×C₈	C₂²×C₄×C₄₃	1	2	yes	—
541	C₂×C₈	C₂²×C₄×C₄₃	1	2	yes	—
542	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
543	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
544	C₄²	—	2	2	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	4	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
558	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
559	C₂³	#121×C₄₃	1	2	yes	—
560	C₂³	#123×C₄₃	1	2	yes	—
561	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
562	Q₈	—	2	2	no	—
563	Q₈	—	2	4	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	2	no	—
567	Q₈	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
568	D₄	—	2	4	no	—
569	D₄	—	2	4	no	—
570	D₄	—	2	8	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	4	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	4	no	—
578	D₄	—	4	2	no	—
579	D₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
595	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
596	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
597	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
598	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
599	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
600	C₂×C₄	#120×C₄₃	1	2	yes	—
601	C₂×C₄	#120×C₄₃	1	2	yes	—
602	C₂×C₄	#121×C₄₃	1	2	yes	—
603	C₂×C₄	#121×C₄₃	1	2	yes	—
604	C₂×C₄	#121×C₄₃	1	2	yes	—
605	C₂×C₄	#123×C₄₃	1	2	yes	—
606	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
610	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	—	2	4	no	—
616	C₈	—	2	2	no	—
617	C₈	—	4	2	no	—
618	C₂²	—	2	4	no	—
619	C₂²	—	2	4	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	8	4	no	—
632	C₂²	C₄₃×#386	1	2	yes	—
633	C₂²	C₄₃×#386	1	2	yes	—
634	C₂²	C₄₃×#443	1	2	yes	—
635	C₂²	C₄₃×#444	1	2	yes	—
636	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
637	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
638	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
639	C₄	—	2	4	no	—
640	C₄	—	4	4	no	—
641	C₄	—	4	2	no	—
642	C₄	C₄₃×#386	1	2	yes	—
643	C₄	C₄₃×#386	1	2	yes	—
644	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
645	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
646	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
647	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	2	2	no	—
651	C₂	—	4	4	no	—
652	C₂	—	8	2	no	—
653	C₂	C₄₃×#1876	1	4	yes	direct product factor
654	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
655	C₂	C₂×C₄₃×#443	1	1	yes	characteristic
656	C₂	C₂×C₄₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂²×#135×C₄₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂³×C₈×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#131×C₄₃	C₂	semidirect
3. C₂²×#104×C₄₃	C₂	semidirect
4. C₂²×#104×C₄₃	C₂	semidirect
5. C₂×C₄₃×#408	C₂	semidirect
6. C₄₃×#1876	C₂	direct (N × H)
7. C₂×C₄₃×#341	C₂	semidirect
8. C₂×C₄₃×#336	C₂	semidirect
13. C₂×#135×C₄₃	C₄	semidirect
15. C₂²×Q₁₆×C₄₃	C₄	semidirect
16. C₂²×SD₁₆×C₄₃	C₄	semidirect
17. C₂²×SD₁₆×C₄₃	C₄	semidirect
18. C₂²×D₈×C₄₃	C₄	semidirect
22. C₂×#131×C₄₃	C₂²	semidirect
32. C₂×#104×C₄₃	C₂²	semidirect
33. C₂×#104×C₄₃	C₂²	semidirect
35. C₄₃×#408	C₂²	semidirect
38. C₄₃×#341	C₂²	semidirect
39. C₄₃×#336	C₂²	semidirect
70. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
73. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
74. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
76. C₂×D₈×C₄₃	C₂×C₄	semidirect
289. C₂×#1876	C₄₃	direct (N × H)
321. C₂²×#131	C₂×C₄₃	semidirect
322. C₂²×#104	C₂×C₄₃	semidirect
323. C₂²×#104	C₂×C₄₃	semidirect
324. C₂×#408	C₂×C₄₃	semidirect
325. #1876	C₂×C₄₃	direct (N × H)
326. C₂×#341	C₂×C₄₃	semidirect
327. C₂×#336	C₂×C₄₃	semidirect
333. C₂×C₄₃	#1876	direct (N × H)
341. C₂×#135	C₄×C₄₃	semidirect
343. C₂²×Q₁₆	C₄×C₄₃	semidirect
344. C₂²×SD₁₆	C₄×C₄₃	semidirect
345. C₂²×SD₁₆	C₄×C₄₃	semidirect
346. C₂²×D₈	C₄×C₄₃	semidirect
350. C₂×#131	C₂²×C₄₃	semidirect
360. C₂×#104	C₂²×C₄₃	semidirect
361. C₂×#104	C₂²×C₄₃	semidirect
363. #408	C₂²×C₄₃	semidirect
366. #341	C₂²×C₄₃	semidirect
367. #336	C₂²×C₄₃	semidirect
368. C₄₃	C₂×#1876	direct (N × H)
399. C₂×Q₁₆	C₂×C₄×C₄₃	semidirect
402. C₂×SD₁₆	C₂×C₄×C₄₃	semidirect
403. C₂×SD₁₆	C₂×C₄×C₄₃	semidirect
405. C₂×D₈	C₂×C₄×C₄₃	semidirect
653. C₂	C₄₃×#1876	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₄₃	2
C₂²×#131×C₄₃	2
C₂²×#104×C₄₃	2
C₂×C₄₃×#408	2
C₄₃×#1876	2
C₂×C₄₃×#341	2
C₂×C₄₃×#336	2
C₂×#1876	43

Subgroups — C2×C43×#1876 #24940933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1876 #24940933