Subgroups — C₂×C₄₃×#1861 #24940883

Order 11008.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#421	C₂	1	1	yes	maximal, characteristic
5	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1861	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	C₄₃×#568	—	2	2	no	—
11	C₄₃×#568	—	2	2	no	—
12	C₄₃×#568	—	2	2	no	—
13	C₄₃×#568	C₂²	1	4	yes	—
14	C₂×#131×C₄₃	—	2	2	no	—
15	C₂×#131×C₄₃	—	2	2	no	—
16	C₂²×M₁₆×C₄₃	—	2	2	no	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#430	—	2	2	no	—
24	C₄₃×#430	C₂²	1	4	yes	complemented
25	C₂×#108×C₄₃	—	2	2	no	—
26	C₄₃×#423	—	2	2	no	—
27	C₄₃×#423	C₂²	1	4	yes	complemented
28	C₂×C₄⋊C₈×C₄₃	—	2	2	no	—
29	C₄₃×#421	—	2	2	no	—
30	C₄₃×#421	C₂²	1	4	yes	—
31	C₂×#104×C₄₃	—	2	2	no	—
32	C₂×#104×C₄₃	C₄	1	2	yes	complemented
33	C₂×#104×C₄₃	C₄	1	4	yes	complemented
34	C₂×#104×C₄₃	C₄	1	2	yes	complemented
35	C₂×#104×C₄₃	C₂²	1	4	yes	—
36	C₄₃×#344	C₂²	1	4	yes	complemented
37	C₄₃×#339	C₂²	1	4	yes	complemented
38	C₂×#41×C₄₃	—	2	1	no	—
39	C₂×#41×C₄₃	—	2	1	no	—
40	C₂×#41×C₄₃	—	2	1	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	C₂×C₄	1	2	yes	—
45	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
46	C₂×#41×C₄₃	D₄	1	2	yes	—
47	C₂×#41×C₄₃	D₄	1	2	yes	—
48	C₂×#41×C₄₃	Q₈	1	2	yes	—
49	C₂×#41×C₄₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₄₃	Q₈	1	1	yes	characteristic
51	C₂²×D₄×C₄₃	—	2	1	no	—
52	C₂²×D₄×C₄₃	Q₈	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	—	2	1	no	—
54	C₂³×C₄×C₄₃	—	2	1	no	—
55	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
56	#131×C₄₃	—	2	8	no	—
57	#131×C₄₃	—	2	8	no	—
58	#131×C₄₃	—	2	8	no	—
59	#131×C₄₃	—	2	8	no	—
60	C₂×M₁₆×C₄₃	—	2	4	no	—
61	C₂×M₁₆×C₄₃	—	2	8	no	—
62	C₂×M₁₆×C₄₃	—	2	1	no	—
63	C₂×M₁₆×C₄₃	—	2	1	no	—
64	C₂×M₁₆×C₄₃	—	2	1	no	—
65	C₂×M₁₆×C₄₃	—	2	1	no	—
66	C₂×M₁₆×C₄₃	—	2	1	no	—
67	C₂×M₁₆×C₄₃	—	2	1	no	—
68	C₂×M₁₆×C₄₃	—	2	1	no	—
69	C₂×M₁₆×C₄₃	—	2	1	no	—
70	C₂×M₁₆×C₄₃	—	2	1	no	—
71	C₂×M₁₆×C₄₃	—	2	1	no	—
72	C₂×M₁₆×C₄₃	—	2	8	no	—
73	C₂×M₁₆×C₄₃	—	2	1	no	—
74	C₂×M₁₆×C₄₃	—	2	1	no	—
75	C₂×M₁₆×C₄₃	—	2	1	no	—
76	C₂×M₁₆×C₄₃	—	2	1	no	—
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
79	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
81	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
82	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
83	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
84	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
85	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
86	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₃	—	2	4	no	—
88	C₂²×C₈×C₄₃	—	2	1	no	—
89	C₂²×C₈×C₄₃	—	2	1	no	—
90	C₂²×C₈×C₄₃	—	2	1	no	—
91	C₂²×C₈×C₄₃	D₄	1	2	yes	—
92	#117×C₄₃	—	2	1	no	—
93	#117×C₄₃	—	2	1	no	—
94	#117×C₄₃	—	2	1	no	—
95	#117×C₄₃	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₄²×C₄₃	—	2	1	no	—
99	C₂×C₄²×C₄₃	—	2	1	no	—
100	C₂×C₄²×C₄₃	—	2	1	no	—
101	C₂×C₄²×C₄₃	—	2	1	no	—
102	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
104	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
106	#108×C₄₃	—	2	8	no	—
107	C₄⋊C₈×C₄₃	—	2	8	no	—
108	#104×C₄₃	—	2	8	no	—
109	#104×C₄₃	C₂×C₄	1	8	yes	complemented
110	#104×C₄₃	C₂×C₄	1	8	yes	complemented
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂⁴×C₄₃	#41	1	1	yes	characteristic
113	#41×C₄₃	—	2	2	no	—
114	#41×C₄₃	—	2	2	no	—
115	#41×C₄₃	—	2	2	no	—
116	#41×C₄₃	—	2	2	no	—
117	#41×C₄₃	—	2	2	no	—
118	#41×C₄₃	—	2	2	no	—
119	#41×C₄₃	—	2	2	no	—
120	#41×C₄₃	—	2	2	no	—
121	#41×C₄₃	—	2	2	no	—
122	#41×C₄₃	—	2	2	no	—
123	#41×C₄₃	—	2	2	no	—
124	#41×C₄₃	—	2	2	no	—
125	#41×C₄₃	C₄⋊C₄	1	4	yes	—
126	#41×C₄₃	C₄⋊C₄	1	4	yes	—
127	#41×C₄₃	C₂²×C₄	1	4	yes	—
128	#41×C₄₃	C₂×D₄	1	4	yes	—
129	C₂×Q₈×C₄₃	—	2	1	no	—
130	C₂×Q₈×C₄₃	—	2	1	no	—
131	C₂×Q₈×C₄₃	—	2	1	no	—
132	C₂×Q₈×C₄₃	C₄⋊C₄	1	2	yes	—
133	C₂×Q₈×C₄₃	C₄⋊C₄	1	2	yes	—
134	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
135	C₂×D₄×C₄₃	—	2	1	no	—
136	C₂×D₄×C₄₃	—	2	1	no	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	2	2	no	—
143	C₂×D₄×C₄₃	—	2	2	no	—
144	C₂×D₄×C₄₃	C₄⋊C₄	1	2	yes	—
145	C₂×D₄×C₄₃	C₄⋊C₄	1	2	yes	—
146	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	2	2	no	—
149	C₂²×C₄×C₄₃	—	2	2	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	2	2	no	—
152	C₂²×C₄×C₄₃	—	2	2	no	—
153	C₂²×C₄×C₄₃	—	2	1	no	—
154	C₂²×C₄×C₄₃	—	2	1	no	—
155	C₂²×C₄×C₄₃	—	2	2	no	—
156	C₂²×C₄×C₄₃	—	2	1	no	—
157	C₂²×C₄×C₄₃	—	2	2	no	—
158	C₂²×C₄×C₄₃	—	4	4	no	—
159	C₂²×C₄×C₄₃	—	4	1	no	—
160	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
169	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
170	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
171	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
172	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
173	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₄₃	—	2	16	no	—
175	M₁₆×C₄₃	—	2	2	no	—
176	M₁₆×C₄₃	—	2	2	no	—
177	M₁₆×C₄₃	—	2	2	no	—
178	M₁₆×C₄₃	—	2	2	no	—
179	M₁₆×C₄₃	—	2	2	no	—
180	M₁₆×C₄₃	—	2	2	no	—
181	M₁₆×C₄₃	—	2	2	no	—
182	M₁₆×C₄₃	—	2	2	no	—
183	M₁₆×C₄₃	—	2	2	no	—
184	M₁₆×C₄₃	—	2	2	no	—
185	M₁₆×C₄₃	—	2	2	no	—
186	M₁₆×C₄₃	—	2	2	no	—
187	M₁₆×C₄₃	—	4	1	no	—
188	M₁₆×C₄₃	—	4	1	no	—
189	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
190	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
191	C₂×C₈×C₄₃	—	2	16	no	—
192	C₂×C₈×C₄₃	—	2	2	no	—
193	C₂×C₈×C₄₃	—	2	2	no	—
194	C₂×C₈×C₄₃	—	2	2	no	—
195	C₂×C₈×C₄₃	—	2	2	no	—
196	C₂×C₈×C₄₃	—	2	2	no	—
197	C₂×C₈×C₄₃	—	2	2	no	—
198	C₂×C₈×C₄₃	—	2	2	no	—
199	C₂×C₈×C₄₃	—	2	2	no	—
200	C₂×C₈×C₄₃	—	2	2	no	—
201	C₂×C₈×C₄₃	—	4	1	no	—
202	C₂×C₈×C₄₃	—	4	1	no	—
203	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
204	C₄⋊C₄×C₄₃	—	2	2	no	—
205	C₄⋊C₄×C₄₃	—	4	1	no	—
206	C₂²⋊C₄×C₄₃	—	2	2	no	—
207	C₂²⋊C₄×C₄₃	—	4	1	no	—
208	C₄²×C₄₃	—	2	1	no	—
209	C₄²×C₄₃	—	2	2	no	—
210	C₄²×C₄₃	—	2	1	no	—
211	C₄²×C₄₃	—	2	2	no	—
212	C₄²×C₄₃	—	2	2	no	—
213	C₄²×C₄₃	—	4	1	no	—
214	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
215	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
216	C₂³×C₄₃	—	2	2	no	—
217	C₂³×C₄₃	—	2	2	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	4	2	no	—
220	C₂³×C₄₃	—	8	2	no	—
221	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
222	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
223	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₄₃	#123	1	1	yes	characteristic
226	C₂³×C₄₃	#123	1	1	yes	characteristic
227	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
228	Q₈×C₄₃	—	2	2	no	—
229	Q₈×C₄₃	—	2	2	no	—
230	Q₈×C₄₃	—	2	2	no	—
231	Q₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
232	D₄×C₄₃	—	2	4	no	—
233	D₄×C₄₃	—	2	4	no	—
234	D₄×C₄₃	—	2	4	no	—
235	D₄×C₄₃	—	2	4	no	—
236	D₄×C₄₃	—	2	2	no	—
237	D₄×C₄₃	—	2	2	no	—
238	D₄×C₄₃	—	2	2	no	—
239	D₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
240	C₂×C₄×C₄₃	—	2	4	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	2	2	no	—
243	C₂×C₄×C₄₃	—	2	2	no	—
244	C₂×C₄×C₄₃	—	2	2	no	—
245	C₂×C₄×C₄₃	—	2	4	no	—
246	C₂×C₄×C₄₃	—	2	4	no	—
247	C₂×C₄×C₄₃	—	2	4	no	—
248	C₂×C₄×C₄₃	—	2	4	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	4	4	no	—
251	C₂×C₄×C₄₃	—	4	4	no	—
252	C₂×C₄×C₄₃	—	4	2	no	—
253	C₂×C₄×C₄₃	—	4	2	no	—
254	C₂×C₄×C₄₃	—	8	2	no	—
255	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
264	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
266	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
267	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
268	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
276	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
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×Q₈	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
283	C₈×C₄₃	—	2	4	no	—
284	C₈×C₄₃	—	2	4	no	—
285	C₈×C₄₃	—	2	4	no	—
286	C₈×C₄₃	—	4	2	no	—
287	C₂×#1861	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂²×C₄₃	—	2	2	no	—
289	C₂²×C₄₃	—	2	2	no	—
290	C₂²×C₄₃	—	2	2	no	—
291	C₂²×C₄₃	—	2	4	no	—
292	C₂²×C₄₃	—	4	1	no	—
293	C₂²×C₄₃	—	4	1	no	—
294	C₂²×C₄₃	—	4	1	no	—
295	C₂²×C₄₃	—	4	1	no	—
296	C₂²×C₄₃	—	4	4	no	—
297	C₂²×C₄₃	—	8	2	no	—
298	C₂²×C₄₃	—	8	2	no	—
299	C₂²×C₄₃	#385	1	1	yes	characteristic
300	C₂²×C₄₃	#385	1	1	yes	characteristic
301	C₂²×C₄₃	#385	1	1	yes	characteristic
302	C₂²×C₄₃	#385	1	1	yes	characteristic
303	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
306	C₄×C₄₃	—	2	4	no	—
307	C₄×C₄₃	—	2	4	no	—
308	C₄×C₄₃	—	4	2	no	—
309	C₄×C₄₃	—	8	2	no	—
310	C₄×C₄₃	#385	1	1	yes	characteristic
311	C₄×C₄₃	#385	1	1	yes	characteristic
312	C₄×C₄₃	#385	1	1	yes	characteristic
313	C₄×C₄₃	#385	1	1	yes	characteristic
314	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
315	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
316	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
317	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
318	C₂×#568	C₂×C₄₃	1	1	yes	characteristic
319	C₂×#430	C₂×C₄₃	1	1	yes	characteristic, complemented
320	C₂×#423	C₂×C₄₃	1	1	yes	characteristic, complemented
321	C₂×#421	C₂×C₄₃	1	1	yes	characteristic
322	C₂²×#104	C₂×C₄₃	1	1	yes	characteristic
323	#1861	C₂×C₄₃	1	8	yes	direct product factor
324	C₂×#344	C₂×C₄₃	1	1	yes	characteristic, complemented
325	C₂×#339	C₂×C₄₃	1	1	yes	characteristic, complemented
326	C₂×C₄₃	—	2	1	no	—
327	C₂×C₄₃	—	2	1	no	—
328	C₂×C₄₃	—	2	1	no	—
329	C₂×C₄₃	—	2	1	no	—
330	C₂×C₄₃	—	2	1	no	—
331	C₂×C₄₃	—	2	1	no	—
332	C₂×C₄₃	—	4	4	no	—
333	C₂×C₄₃	#1861	1	2	yes	direct product factor
334	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
335	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
336	#568	—	2	2	no	—
337	#568	—	2	2	no	—
338	#568	—	2	2	no	—
339	#568	C₂²×C₄₃	1	4	yes	—
340	C₂×#131	—	2	2	no	—
341	C₂×#131	—	2	2	no	—
342	C₂²×M₁₆	—	2	2	no	—
343	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
344	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
346	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
347	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
349	#430	—	2	2	no	—
350	#430	C₂²×C₄₃	1	4	yes	complemented
351	C₂×#108	—	2	2	no	—
352	#423	—	2	2	no	—
353	#423	C₂²×C₄₃	1	4	yes	complemented
354	C₂×C₄⋊C₈	—	2	2	no	—
355	#421	—	2	2	no	—
356	#421	C₂²×C₄₃	1	4	yes	—
357	C₂×#104	—	2	2	no	—
358	C₂×#104	C₄×C₄₃	1	2	yes	complemented
359	C₂×#104	C₄×C₄₃	1	4	yes	complemented
360	C₂×#104	C₄×C₄₃	1	2	yes	complemented
361	C₂×#104	C₂²×C₄₃	1	4	yes	—
362	#344	C₂²×C₄₃	1	4	yes	complemented
363	#339	C₂²×C₄₃	1	4	yes	complemented
364	C₄₃	C₂×#1861	1	1	yes	characteristic, direct product factor, Sylow
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
372	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
373	C₂×#41	D₄×C₄₃	1	2	yes	—
374	C₂×#41	D₄×C₄₃	1	2	yes	—
375	C₂×#41	Q₈×C₄₃	1	2	yes	—
376	C₂×#41	C₂³×C₄₃	1	2	yes	—
377	C₂²×Q₈	Q₈×C₄₃	1	1	yes	characteristic
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	Q₈×C₄₃	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	2	1	no	—
382	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
383	#131	—	2	8	no	—
384	#131	—	2	8	no	—
385	#131	—	2	8	no	—
386	#131	—	2	8	no	—
387	C₂×M₁₆	—	2	4	no	—
388	C₂×M₁₆	—	2	8	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	1	no	—
399	C₂×M₁₆	—	2	8	no	—
400	C₂×M₁₆	—	2	1	no	—
401	C₂×M₁₆	—	2	1	no	—
402	C₂×M₁₆	—	2	1	no	—
403	C₂×M₁₆	—	2	1	no	—
404	C₂×M₁₆	—	2	1	no	—
405	C₂×M₁₆	C₂×C₄×C₄₃	1	2	yes	—
406	C₂×M₁₆	C₂×C₄×C₄₃	1	2	yes	—
407	C₂×M₁₆	D₄×C₄₃	1	2	yes	—
408	C₂×M₁₆	D₄×C₄₃	1	2	yes	—
409	C₂×M₁₆	D₄×C₄₃	1	2	yes	—
410	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
411	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
412	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
413	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
414	C₂²×C₈	—	2	4	no	—
415	C₂²×C₈	—	2	1	no	—
416	C₂²×C₈	—	2	1	no	—
417	C₂²×C₈	—	2	1	no	—
418	C₂²×C₈	D₄×C₄₃	1	2	yes	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	C₂³×C₄₃	1	2	yes	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
430	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
431	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
433	#108	—	2	8	no	—
434	C₄⋊C₈	—	2	8	no	—
435	#104	—	2	8	no	—
436	#104	C₂×C₄×C₄₃	1	8	yes	complemented
437	#104	C₂×C₄×C₄₃	1	8	yes	complemented
438	C₂⁴	—	2	1	no	—
439	C₂⁴	#41×C₄₃	1	1	yes	characteristic
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	C₄⋊C₄×C₄₃	1	4	yes	—
453	#41	C₄⋊C₄×C₄₃	1	4	yes	—
454	#41	C₂²×C₄×C₄₃	1	4	yes	—
455	#41	C₂×D₄×C₄₃	1	4	yes	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	C₄⋊C₄×C₄₃	1	2	yes	—
460	C₂×Q₈	C₄⋊C₄×C₄₃	1	2	yes	—
461	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₄⋊C₄×C₄₃	1	2	yes	—
472	C₂×D₄	C₄⋊C₄×C₄₃	1	2	yes	—
473	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×Q₈×C₄₃	1	1	yes	characteristic
496	C₂²×C₄	C₂×Q₈×C₄₃	1	1	yes	characteristic
497	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
498	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
499	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
501	M₁₆	—	2	16	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	2	2	no	—
505	M₁₆	—	2	2	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	2	2	no	—
508	M₁₆	—	2	2	no	—
509	M₁₆	—	2	2	no	—
510	M₁₆	—	2	2	no	—
511	M₁₆	—	2	2	no	—
512	M₁₆	—	2	2	no	—
513	M₁₆	—	2	2	no	—
514	M₁₆	—	4	1	no	—
515	M₁₆	—	4	1	no	—
516	M₁₆	C₂²×C₄×C₄₃	1	4	yes	—
517	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
518	C₂×C₈	—	2	16	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	2	2	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	4	1	no	—
529	C₂×C₈	—	4	1	no	—
530	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	2	no	—
540	C₄²	—	4	1	no	—
541	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
542	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
549	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
550	C₂³	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
551	C₂³	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
552	C₂³	#123×C₄₃	1	1	yes	characteristic
553	C₂³	#123×C₄₃	1	1	yes	characteristic
554	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	8	2	no	—
582	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
583	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
584	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
585	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
586	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
587	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
588	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
589	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
590	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
591	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
592	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
593	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
594	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
595	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
596	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
597	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
598	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
599	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
600	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
601	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
602	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
603	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	2	4	no	—
612	C₈	—	2	4	no	—
613	C₈	—	4	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	C₄₃×#385	1	1	yes	characteristic
626	C₂²	C₄₃×#385	1	1	yes	characteristic
627	C₂²	C₄₃×#385	1	1	yes	characteristic
628	C₂²	C₄₃×#385	1	1	yes	characteristic
629	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
630	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
631	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	8	2	no	—
636	C₄	C₄₃×#385	1	1	yes	characteristic
637	C₄	C₄₃×#385	1	1	yes	characteristic
638	C₄	C₄₃×#385	1	1	yes	characteristic
639	C₄	C₄₃×#385	1	1	yes	characteristic
640	C₄	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
641	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
642	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
643	C₄	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	C₄₃×#1861	1	2	yes	direct product factor
652	C₂	C₂×C₄₃×#385	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	#120
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂²×C₄₃	#385
prime radical	C₂²×#41×C₄₃	C₂²
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×C₄₃×#430	C₂	semidirect
3. C₂×C₄₃×#423	C₂	semidirect
6. C₄₃×#1861	C₂	direct (N × H)
7. C₂×C₄₃×#344	C₂	semidirect
8. C₂×C₄₃×#339	C₂	semidirect
24. C₄₃×#430	C₂²	semidirect
27. C₄₃×#423	C₂²	semidirect
32. C₂×#104×C₄₃	C₄	semidirect
33. C₂×#104×C₄₃	C₄	semidirect
34. C₂×#104×C₄₃	C₄	semidirect
36. C₄₃×#344	C₂²	semidirect
37. C₄₃×#339	C₂²	semidirect
109. #104×C₄₃	C₂×C₄	semidirect
110. #104×C₄₃	C₂×C₄	semidirect
287. C₂×#1861	C₄₃	direct (N × H)
319. C₂×#430	C₂×C₄₃	semidirect
320. C₂×#423	C₂×C₄₃	semidirect
323. #1861	C₂×C₄₃	direct (N × H)
324. C₂×#344	C₂×C₄₃	semidirect
325. C₂×#339	C₂×C₄₃	semidirect
333. C₂×C₄₃	#1861	direct (N × H)
350. #430	C₂²×C₄₃	semidirect
353. #423	C₂²×C₄₃	semidirect
358. C₂×#104	C₄×C₄₃	semidirect
359. C₂×#104	C₄×C₄₃	semidirect
360. C₂×#104	C₄×C₄₃	semidirect
362. #344	C₂²×C₄₃	semidirect
363. #339	C₂²×C₄₃	semidirect
364. C₄₃	C₂×#1861	direct (N × H)
436. #104	C₂×C₄×C₄₃	semidirect
437. #104	C₂×C₄×C₄₃	semidirect
651. C₂	C₄₃×#1861	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×#568	2
C₂×C₄₃×#430	2
C₂×C₄₃×#423	2
C₂×C₄₃×#421	2
C₂²×#104×C₄₃	2
C₄₃×#1861	2
C₂×C₄₃×#344	2
C₂×C₄₃×#339	2
C₂×#1861	43

Subgroups — C2×C43×#1861 #24940883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1861 #24940883