Subgroups — C₄₃×#17420 #24937437

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2924	C₂	1	2	yes	maximal, complemented
3	C₄₃×#1473	C₂	1	4	yes	maximal, complemented
4	C₄₃×#1472	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1467	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1465	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1461	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1459	C₂	1	1	yes	maximal, characteristic
9	C₄₃×#556	—	2	2	no	—
10	C₄₃×#556	—	2	2	no	—
11	C₄₃×#556	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
13	C₂×#126×C₄₃	C₄	1	2	yes	—
14	C₂×#126×C₄₃	C₂²	1	2	yes	—
15	C₂×#124×C₄₃	C₄	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₃	C₄	1	1	yes	characteristic
22	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#433	—	2	4	no	—
24	C₄₃×#432	C₂²	1	4	yes	—
25	C₄₃×#431	C₂²	1	4	yes	—
26	C₄₃×#424	—	2	2	no	—
27	C₄₃×#407	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#405	—	2	2	no	—
30	C₄₃×#324	C₂²	1	1	yes	characteristic
31	C₄₃×#324	C₂²	1	1	yes	characteristic
32	C₄₃×#324	C₂²	1	2	yes	—
33	C₄₃×#324	C₂²	1	4	yes	—
34	C₄₃×#324	C₂²	1	4	yes	—
35	C₄₃×#323	C₂²	1	2	yes	—
36	C₄₃×#323	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
38	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₄₃	—	2	2	no	—
43	C₂²×C₈×C₄₃	—	2	2	no	—
44	C₄⋊Q₈×C₄₃	—	2	2	no	—
45	C₄⋊Q₈×C₄₃	—	2	2	no	—
46	#126×C₄₃	—	2	4	no	—
47	#126×C₄₃	—	2	4	no	—
48	#126×C₄₃	—	2	4	no	—
49	#126×C₄₃	—	2	4	no	—
50	#124×C₄₃	—	2	4	no	—
51	#124×C₄₃	—	2	4	no	—
52	C₂²⋊Q₈×C₄₃	—	2	2	no	—
53	C₂²⋊Q₈×C₄₃	—	2	2	no	—
54	C₂²⋊Q₈×C₄₃	—	2	2	no	—
55	C₂²⋊Q₈×C₄₃	—	2	2	no	—
56	C₄×Q₈×C₄₃	—	2	2	no	—
57	C₄×Q₈×C₄₃	—	2	1	no	—
58	C₄×Q₈×C₄₃	—	2	1	no	—
59	C₄×Q₈×C₄₃	—	2	4	no	—
60	C₄×Q₈×C₄₃	—	2	4	no	—
61	C₄×D₄×C₄₃	—	2	2	no	—
62	C₄×D₄×C₄₃	—	2	2	no	—
63	#117×C₄₃	—	2	2	no	—
64	#117×C₄₃	—	2	1	no	—
65	#117×C₄₃	—	2	1	no	—
66	#117×C₄₃	D₄	1	2	yes	—
67	#117×C₄₃	D₄	1	2	yes	—
68	#117×C₄₃	D₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
87	C₄⋊C₈×C₄₃	—	2	4	no	—
88	C₄⋊C₈×C₄₃	—	2	4	no	—
89	C₂²⋊C₈×C₄₃	—	2	2	no	—
90	C₂²⋊C₈×C₄₃	—	2	2	no	—
91	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
92	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
93	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
94	#97×C₄₃	—	2	4	no	—
95	C₄×C₈×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	2	1	no	—
100	C₂×Q₈×C₄₃	—	2	4	no	—
101	C₂×Q₈×C₄₃	—	2	4	no	—
102	C₂×Q₈×C₄₃	—	4	2	no	—
103	C₂×Q₈×C₄₃	—	4	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	4	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	4	2	no	—
110	C₂²×C₄×C₄₃	—	4	2	no	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₄₃	—	4	4	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	4	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	4	4	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	4	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	4	no	—
135	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
138	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
139	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
140	C₂²⋊C₄×C₄₃	—	2	2	no	—
141	C₂²⋊C₄×C₄₃	—	2	2	no	—
142	C₂²⋊C₄×C₄₃	—	2	4	no	—
143	C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₂²⋊C₄×C₄₃	—	2	4	no	—
146	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
147	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₄²×C₄₃	—	2	1	no	—
151	C₄²×C₄₃	—	2	1	no	—
152	C₄²×C₄₃	—	2	2	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	C₂×D₄	1	4	yes	—
155	C₄²×C₄₃	C₂×D₄	1	4	yes	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	4	1	no	—
162	C₂³×C₄₃	—	4	1	no	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	—	4	1	no	—
165	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
167	Q₈×C₄₃	—	4	8	no	—
168	Q₈×C₄₃	—	4	2	no	—
169	Q₈×C₄₃	—	4	2	no	—
170	D₄×C₄₃	—	4	4	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	1	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
195	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#131	1	2	yes	—
197	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
198	C₈×C₄₃	—	4	2	no	—
199	C₈×C₄₃	—	4	2	no	—
200	C₈×C₄₃	—	4	4	no	—
201	#17420	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	4	1	no	—
208	C₂²×C₄₃	—	4	1	no	—
209	C₂²×C₄₃	—	4	1	no	—
210	C₂²×C₄₃	—	8	1	no	—
211	C₂²×C₄₃	—	8	1	no	—
212	C₂²×C₄₃	—	8	1	no	—
213	C₂²×C₄₃	—	8	1	no	—
214	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
215	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
216	C₂²×C₄₃	#568	1	1	yes	characteristic
217	C₄×C₄₃	—	2	4	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	4	2	no	—
224	C₄×C₄₃	—	4	1	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	4	1	no	—
227	C₄×C₄₃	#410	1	2	yes	—
228	C₂×#556	C₂×C₄₃	1	1	yes	characteristic
229	#2924	C₂×C₄₃	1	2	yes	complemented
230	#1473	C₂×C₄₃	1	4	yes	complemented
231	#1472	C₂×C₄₃	1	2	yes	complemented
232	#1467	C₂×C₄₃	1	2	yes	complemented
233	#1465	C₂×C₄₃	1	1	yes	characteristic
234	#1461	C₂×C₄₃	1	2	yes	complemented
235	#1459	C₂×C₄₃	1	1	yes	characteristic
236	C₂×C₄₃	—	2	1	no	—
237	C₂×C₄₃	—	2	1	no	—
238	C₂×C₄₃	—	4	2	no	—
239	C₂×C₄₃	—	8	1	no	—
240	C₂×C₄₃	#2880	1	1	yes	characteristic
241	C₂×C₄₃	C₂×#410	1	1	yes	characteristic
242	C₂×C₄₃	#2889	1	1	yes	characteristic
243	#556	—	2	2	no	—
244	#556	—	2	2	no	—
245	#556	—	2	4	no	—
246	C₂×C₄⋊Q₈	C₄×C₄₃	1	1	yes	characteristic
247	C₂×#126	C₄×C₄₃	1	2	yes	—
248	C₂×#126	C₂²×C₄₃	1	2	yes	—
249	C₂×#124	C₄×C₄₃	1	2	yes	—
250	C₂×C₂²⋊Q₈	C₄×C₄₃	1	1	yes	characteristic
251	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₄×C₄₃	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
254	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
255	C₂×#117	C₄×C₄₃	1	1	yes	characteristic
256	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
257	#433	—	2	4	no	—
258	#432	C₂²×C₄₃	1	4	yes	—
259	#431	C₂²×C₄₃	1	4	yes	—
260	#424	—	2	2	no	—
261	#407	C₂²×C₄₃	1	2	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
263	#405	—	2	2	no	—
264	#324	C₂²×C₄₃	1	1	yes	characteristic
265	#324	C₂²×C₄₃	1	1	yes	characteristic
266	#324	C₂²×C₄₃	1	2	yes	—
267	#324	C₂²×C₄₃	1	4	yes	—
268	#324	C₂²×C₄₃	1	4	yes	—
269	#323	C₂²×C₄₃	1	2	yes	—
270	#323	C₂²×C₄₃	1	2	yes	—
271	C₄₃	#17420	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×Q₈	C₂×C₄×C₄₃	1	2	yes	—
273	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
274	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
275	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂×M₁₆	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	#126	—	2	4	no	—
282	#126	—	2	4	no	—
283	#126	—	2	4	no	—
284	#126	—	2	4	no	—
285	#124	—	2	4	no	—
286	#124	—	2	4	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	2	2	no	—
298	#117	—	2	2	no	—
299	#117	—	2	1	no	—
300	#117	—	2	1	no	—
301	#117	D₄×C₄₃	1	2	yes	—
302	#117	D₄×C₄₃	1	2	yes	—
303	#117	D₄×C₄₃	1	4	yes	—
304	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
312	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
313	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
314	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
318	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
319	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
320	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
321	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
322	C₄⋊C₈	—	2	4	no	—
323	C₄⋊C₈	—	2	4	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
327	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
328	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
329	#97	—	2	4	no	—
330	C₄×C₈	—	2	4	no	—
331	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
332	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
347	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
357	M₁₆	—	4	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	4	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
371	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
372	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
373	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
374	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
382	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	C₂×D₄×C₄₃	1	4	yes	—
390	C₄²	C₂×D₄×C₄₃	1	4	yes	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
401	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
402	Q₈	—	4	8	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	4	4	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
427	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
428	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
431	C₂×C₄	#131×C₄₃	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	4	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
449	C₂²	C₂×#131×C₄₃	1	1	yes	characteristic
450	C₂²	C₄₃×#568	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	1	no	—
461	C₄	C₄₃×#410	1	2	yes	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	4	2	no	—
465	C₂	—	8	1	no	—
466	C₂	C₄₃×#2880	1	1	yes	characteristic
467	C₂	C₂×C₄₃×#410	1	1	yes	characteristic
468	C₂	C₄₃×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₄×C₄₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2924	C₂	semidirect
3. C₄₃×#1473	C₂	semidirect
4. C₄₃×#1472	C₂	semidirect
5. C₄₃×#1467	C₂	semidirect
7. C₄₃×#1461	C₂	semidirect
201. #17420	C₄₃	direct (N × H)
229. #2924	C₂×C₄₃	semidirect
230. #1473	C₂×C₄₃	semidirect
231. #1472	C₂×C₄₃	semidirect
232. #1467	C₂×C₄₃	semidirect
234. #1461	C₂×C₄₃	semidirect
271. C₄₃	#17420	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×#556	2
C₄₃×#2924	2
C₄₃×#1473	2
C₄₃×#1472	2
C₄₃×#1467	2
C₄₃×#1465	2
C₄₃×#1461	2
C₄₃×#1459	2
#17420	43

Subgroups — C43×#17420 #24937437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17420 #24937437