Subgroups — C₄₃×#20927 #24940944

Order 11008.

1830 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1878	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1877	C₂	1	4	yes	maximal, complemented
8	C₄₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×#137×C₄₃	—	2	4	no	—
13	C₂×#137×C₄₃	—	2	4	no	—
14	C₂×#137×C₄₃	C₄	1	8	yes	complemented
15	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₄×#41×C₄₃	—	2	4	no	—
20	C₄×#41×C₄₃	—	2	4	no	—
21	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₄₃	—	2	2	no	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
24	C₂×#117×C₄₃	—	2	1	no	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₃	—	2	1	no	—
28	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#419	—	2	4	no	—
30	C₄₃×#417	—	2	4	no	—
31	C₂×#103×C₄₃	C₂²	1	4	yes	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	2	yes	—
34	C₄₃×#391	—	2	1	no	—
35	C₄₃×#391	—	2	1	no	—
36	C₄₃×#391	C₂²	1	4	yes	—
37	C₂×#95×C₄₃	—	2	2	no	—
38	C₄₃×#340	C₂²	1	4	yes	—
39	C₄₃×#336	C₂²	1	4	yes	—
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	—	2	2	no	—
42	C₂×#41×C₄₃	—	2	2	no	—
43	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
44	C₂×#41×C₄₃	D₄	1	4	yes	—
45	C₂×#41×C₄₃	D₄	1	4	yes	—
46	C₂²×Q₈×C₄₃	—	2	1	no	—
47	C₂²×Q₈×C₄₃	—	2	2	no	—
48	C₂²×Q₈×C₄₃	—	2	2	no	—
49	C₂²×Q₈×C₄₃	—	2	2	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	2	2	no	—
52	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
53	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
54	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	—	2	1	no	—
58	C₂³×C₄×C₄₃	—	2	1	no	—
59	C₂³×C₄×C₄₃	—	2	2	no	—
60	C₂³×C₄×C₄₃	—	2	1	no	—
61	C₂³×C₄×C₄₃	D₄	1	2	yes	—
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	#137×C₄₃	—	2	32	no	—
64	C₂×Q₁₆×C₄₃	—	2	4	no	—
65	C₂×Q₁₆×C₄₃	—	2	4	no	—
66	C₂×Q₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
67	C₂×SD₁₆×C₄₃	—	2	4	no	—
68	C₂×SD₁₆×C₄₃	—	2	4	no	—
69	C₂×SD₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
70	C₂×M₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	—	2	2	no	—
73	C₂×M₁₆×C₄₃	—	2	2	no	—
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
76	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	C₄×Q₈×C₄₃	—	2	4	no	—
79	C₄×Q₈×C₄₃	—	2	4	no	—
80	C₄×D₄×C₄₃	—	2	16	no	—
81	C₄×D₄×C₄₃	—	2	4	no	—
82	C₄×D₄×C₄₃	—	2	4	no	—
83	#117×C₄₃	—	2	8	no	—
84	#117×C₄₃	—	2	2	no	—
85	#117×C₄₃	D₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₄²×C₄₃	—	2	8	no	—
95	C₂×C₄²×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	—	2	2	no	—
97	C₂×C₄²×C₄₃	—	2	2	no	—
98	C₂×C₄²×C₄₃	—	2	2	no	—
99	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
102	#103×C₄₃	—	2	4	no	—
103	#103×C₄₃	—	2	8	no	—
104	#102×C₄₃	—	2	4	no	—
105	#95×C₄₃	—	2	4	no	—
106	#95×C₄₃	—	2	4	no	—
107	C₂⁴×C₄₃	—	2	1	no	—
108	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
109	#41×C₄₃	—	2	8	no	—
110	#41×C₄₃	—	2	8	no	—
111	#41×C₄₃	—	2	8	no	—
112	#41×C₄₃	C₂²⋊C₄	1	16	yes	—
113	C₂×Q₈×C₄₃	—	2	4	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×Q₈×C₄₃	—	2	1	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	8	no	—
119	C₂×Q₈×C₄₃	—	2	8	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	4	2	no	—
125	C₂×Q₈×C₄₃	—	4	2	no	—
126	C₂×Q₈×C₄₃	—	4	4	no	—
127	C₂×Q₈×C₄₃	—	4	4	no	—
128	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
129	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
130	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₄₃	—	2	1	no	—
133	C₂×D₄×C₄₃	—	2	1	no	—
134	C₂×D₄×C₄₃	—	2	1	no	—
135	C₂×D₄×C₄₃	—	2	4	no	—
136	C₂×D₄×C₄₃	—	2	4	no	—
137	C₂×D₄×C₄₃	—	2	4	no	—
138	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₃	—	2	4	no	—
142	C₂²×C₄×C₄₃	—	2	4	no	—
143	C₂²×C₄×C₄₃	—	2	4	no	—
144	C₂²×C₄×C₄₃	—	2	8	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	4	no	—
148	C₂²×C₄×C₄₃	—	2	1	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	—	4	2	no	—
153	C₂²×C₄×C₄₃	—	4	4	no	—
154	C₂²×C₄×C₄₃	—	4	4	no	—
155	C₂²×C₄×C₄₃	—	4	4	no	—
156	C₂²×C₄×C₄₃	—	4	2	no	—
157	C₂²×C₄×C₄₃	—	4	2	no	—
158	C₂²×C₄×C₄₃	—	4	2	no	—
159	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	#41	1	2	yes	—
167	C₂²×C₄×C₄₃	#41	1	2	yes	—
168	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₄₃	—	2	16	no	—
170	SD₁₆×C₄₃	—	2	16	no	—
171	M₁₆×C₄₃	—	2	8	no	—
172	M₁₆×C₄₃	—	4	4	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
179	C₄⋊C₄×C₄₃	—	2	8	no	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	2	2	no	—
183	C₄⋊C₄×C₄₃	—	4	2	no	—
184	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
185	C₂²⋊C₄×C₄₃	—	2	8	no	—
186	C₂²⋊C₄×C₄₃	—	2	4	no	—
187	C₄²×C₄₃	—	2	8	no	—
188	C₄²×C₄₃	—	2	2	no	—
189	C₄²×C₄₃	—	2	4	no	—
190	C₄²×C₄₃	—	2	2	no	—
191	C₄²×C₄₃	—	2	2	no	—
192	C₄²×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	2	no	—
195	C₂³×C₄₃	—	2	2	no	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	2	2	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	C₄×D₄	1	2	yes	—
201	C₂³×C₄₃	#120	1	2	yes	—
202	C₂³×C₄₃	#121	1	2	yes	—
203	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₄₃	—	2	2	no	—
205	Q₈×C₄₃	—	2	2	no	—
206	Q₈×C₄₃	—	2	2	no	—
207	Q₈×C₄₃	—	2	4	no	—
208	Q₈×C₄₃	—	2	4	no	—
209	Q₈×C₄₃	—	4	2	no	—
210	Q₈×C₄₃	—	4	2	no	—
211	Q₈×C₄₃	—	4	8	no	—
212	Q₈×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
213	D₄×C₄₃	—	2	16	no	—
214	D₄×C₄₃	—	2	2	no	—
215	D₄×C₄₃	—	2	2	no	—
216	D₄×C₄₃	—	2	2	no	—
217	D₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
218	C₂×C₄×C₄₃	—	2	2	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	2	no	—
223	C₂×C₄×C₄₃	—	2	16	no	—
224	C₂×C₄×C₄₃	—	2	4	no	—
225	C₂×C₄×C₄₃	—	2	2	no	—
226	C₂×C₄×C₄₃	—	2	4	no	—
227	C₂×C₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	2	2	no	—
229	C₂×C₄×C₄₃	—	4	8	no	—
230	C₂×C₄×C₄₃	—	4	16	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	8	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	4	4	no	—
238	C₂×C₄×C₄₃	—	8	4	no	—
239	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
240	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
241	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₄₃	#120	1	2	yes	—
243	C₂×C₄×C₄₃	#121	1	4	yes	—
244	C₂×C₄×C₄₃	#121	1	2	yes	—
245	C₂×C₄×C₄₃	#123	1	4	yes	—
246	C₂×C₄×C₄₃	#137	1	4	yes	complemented
247	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
253	C₈×C₄₃	—	2	4	no	—
254	C₈×C₄₃	—	4	2	no	—
255	#20927	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₃	—	2	4	no	—
257	C₂²×C₄₃	—	2	4	no	—
258	C₂²×C₄₃	—	2	2	no	—
259	C₂²×C₄₃	—	2	2	no	—
260	C₂²×C₄₃	—	2	4	no	—
261	C₂²×C₄₃	—	4	4	no	—
262	C₂²×C₄₃	—	4	4	no	—
263	C₂²×C₄₃	—	4	2	no	—
264	C₂²×C₄₃	—	4	2	no	—
265	C₂²×C₄₃	#386	1	4	yes	—
266	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
268	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
269	C₂²×C₄₃	C₂×#137	1	2	yes	—
270	C₂²×C₄₃	#575	1	2	yes	—
271	C₄×C₄₃	—	2	4	no	—
272	C₄×C₄₃	—	2	4	no	—
273	C₄×C₄₃	—	4	2	no	—
274	C₄×C₄₃	—	4	4	no	—
275	C₄×C₄₃	—	4	4	no	—
276	C₄×C₄₃	—	8	2	no	—
277	C₄×C₄₃	#386	1	4	yes	—
278	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
279	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
280	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
281	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
282	C₂²×#137	C₂×C₄₃	1	1	yes	characteristic
283	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic
284	C₂×#417	C₂×C₄₃	1	1	yes	characteristic
285	C₂×#419	C₂×C₄₃	1	1	yes	characteristic, complemented
286	C₂×#391	C₂×C₄₃	1	1	yes	characteristic, complemented
287	#1878	C₂×C₄₃	1	4	yes	complemented
288	#1877	C₂×C₄₃	1	4	yes	complemented
289	#1736	C₂×C₄₃	1	1	yes	characteristic, complemented
290	#1728	C₂×C₄₃	1	1	yes	characteristic, complemented
291	C₂×C₄₃	—	2	4	no	—
292	C₂×C₄₃	—	4	4	no	—
293	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
294	C₂×C₄₃	C₄×#137	1	2	yes	—
295	C₂×C₄₃	#3007	1	2	yes	—
296	C₂×C₄₃	#3039	1	1	yes	characteristic
297	C₂×C₄₃	#3040	1	1	yes	characteristic
298	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
299	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
300	C₂×#137	—	2	4	no	—
301	C₂×#137	—	2	4	no	—
302	C₂×#137	C₄×C₄₃	1	8	yes	complemented
303	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
304	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
305	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
306	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
307	C₄×#41	—	2	4	no	—
308	C₄×#41	—	2	4	no	—
309	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
310	C₂×C₄×D₄	—	2	2	no	—
311	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
312	C₂×#117	—	2	1	no	—
313	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
314	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
315	C₂²×C₄²	—	2	1	no	—
316	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
317	#419	—	2	4	no	—
318	#417	—	2	4	no	—
319	C₂×#103	C₂²×C₄₃	1	4	yes	—
320	C₂×#103	C₂²×C₄₃	1	2	yes	—
321	C₂×#102	C₂²×C₄₃	1	2	yes	—
322	#391	—	2	1	no	—
323	#391	—	2	1	no	—
324	#391	C₂²×C₄₃	1	4	yes	—
325	C₂×#95	—	2	2	no	—
326	#340	C₂²×C₄₃	1	4	yes	—
327	#336	C₂²×C₄₃	1	4	yes	—
328	C₄₃	#20927	1	1	yes	characteristic, direct product factor, Sylow
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
333	C₂×#41	D₄×C₄₃	1	4	yes	—
334	C₂×#41	D₄×C₄₃	1	4	yes	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	—	2	2	no	—
338	C₂²×Q₈	—	2	2	no	—
339	C₂²×Q₈	—	2	2	no	—
340	C₂²×Q₈	—	2	2	no	—
341	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
342	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
343	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	2	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	D₄×C₄₃	1	2	yes	—
351	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
352	#137	—	2	32	no	—
353	C₂×Q₁₆	—	2	4	no	—
354	C₂×Q₁₆	—	2	4	no	—
355	C₂×Q₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
356	C₂×SD₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	4	no	—
358	C₂×SD₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	2	no	—
361	C₂×M₁₆	—	2	2	no	—
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	C₂×C₄×C₄₃	1	4	yes	complemented
365	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
366	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
367	C₄×Q₈	—	2	4	no	—
368	C₄×Q₈	—	2	4	no	—
369	C₄×D₄	—	2	16	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	—	2	4	no	—
372	#117	—	2	8	no	—
373	#117	—	2	2	no	—
374	#117	D₄×C₄₃	1	4	yes	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₄²	—	2	8	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	—	2	2	no	—
387	C₂×C₄²	—	2	2	no	—
388	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
389	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
391	#103	—	2	4	no	—
392	#103	—	2	8	no	—
393	#102	—	2	4	no	—
394	#95	—	2	4	no	—
395	#95	—	2	4	no	—
396	C₂⁴	—	2	1	no	—
397	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
398	#41	—	2	8	no	—
399	#41	—	2	8	no	—
400	#41	—	2	8	no	—
401	#41	C₂²⋊C₄×C₄₃	1	16	yes	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	8	no	—
408	C₂×Q₈	—	2	8	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	4	2	no	—
414	C₂×Q₈	—	4	2	no	—
415	C₂×Q₈	—	4	4	no	—
416	C₂×Q₈	—	4	4	no	—
417	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
418	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
419	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
420	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
428	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
429	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	8	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	4	4	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
452	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
455	C₂²×C₄	#41×C₄₃	1	2	yes	—
456	C₂²×C₄	#41×C₄₃	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
458	Q₁₆	—	2	16	no	—
459	SD₁₆	—	2	16	no	—
460	M₁₆	—	2	8	no	—
461	M₁₆	—	4	4	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₄²	—	2	8	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	C₄×D₄×C₄₃	1	2	yes	—
490	C₂³	#120×C₄₃	1	2	yes	—
491	C₂³	#121×C₄₃	1	2	yes	—
492	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
493	Q₈	—	2	2	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	2	2	no	—
496	Q₈	—	2	4	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	8	no	—
501	Q₈	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
502	D₄	—	2	16	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	16	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	—	4	16	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	8	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	8	4	no	—
528	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
529	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
530	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
531	C₂×C₄	#120×C₄₃	1	2	yes	—
532	C₂×C₄	#121×C₄₃	1	4	yes	—
533	C₂×C₄	#121×C₄₃	1	2	yes	—
534	C₂×C₄	#123×C₄₃	1	4	yes	—
535	C₂×C₄	#137×C₄₃	1	4	yes	complemented
536	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
538	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
540	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
542	C₈	—	2	4	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	C₄₃×#386	1	4	yes	—
554	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
555	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
556	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
557	C₂²	C₂×#137×C₄₃	1	2	yes	—
558	C₂²	C₄₃×#575	1	2	yes	—
559	C₄	—	2	4	no	—
560	C₄	—	2	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	4	no	—
564	C₄	—	8	2	no	—
565	C₄	C₄₃×#386	1	4	yes	—
566	C₄	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
567	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
568	C₄	C₂×#121×C₄₃	1	1	yes	characteristic
569	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
570	C₂	—	2	4	no	—
571	C₂	—	4	4	no	—
572	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
573	C₂	C₄×#137×C₄₃	1	2	yes	—
574	C₂	C₄₃×#3007	1	2	yes	—
575	C₂	C₄₃×#3039	1	1	yes	characteristic
576	C₂	C₄₃×#3040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₄₃×#419	C₂	semidirect
5. C₂×C₄₃×#391	C₂	semidirect
6. C₄₃×#1878	C₂	semidirect
7. C₄₃×#1877	C₂	semidirect
8. C₄₃×#1736	C₂	semidirect
9. C₄₃×#1728	C₂	semidirect
14. C₂×#137×C₄₃	C₄	semidirect
52. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
66. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
69. C₂×SD₁₆×C₄₃	C₂×C₄	semidirect
75. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
246. C₂×C₄×C₄₃	#137	semidirect
255. #20927	C₄₃	direct (N × H)
285. C₂×#419	C₂×C₄₃	semidirect
286. C₂×#391	C₂×C₄₃	semidirect
287. #1878	C₂×C₄₃	semidirect
288. #1877	C₂×C₄₃	semidirect
289. #1736	C₂×C₄₃	semidirect
290. #1728	C₂×C₄₃	semidirect
302. C₂×#137	C₄×C₄₃	semidirect
328. C₄₃	#20927	direct (N × H)
341. C₂²×Q₈	C₂×C₄×C₄₃	semidirect
355. C₂×Q₁₆	C₂×C₄×C₄₃	semidirect
358. C₂×SD₁₆	C₂×C₄×C₄₃	semidirect
364. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
535. C₂×C₄	#137×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₃	2
C₂×C₄×#41×C₄₃	2
C₂×C₄₃×#417	2
C₂×C₄₃×#419	2
C₂×C₄₃×#391	2
C₄₃×#1878	2
C₄₃×#1877	2
C₄₃×#1736	2
C₄₃×#1728	2
#20927	43

Subgroups — C43×#20927 #24940944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20927 #24940944