Subgroups — C₄₃×#21861 #24941878

Order 11008.

1166 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1991	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1958	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1874	C₂	1	2	yes	maximal
7	C₄₃×#1872	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1805	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1804	C₂	1	2	yes	maximal, complemented
10	C₄₃×#529	—	2	4	no	—
11	C₄₃×#529	C₄	1	8	yes	complemented
12	C₂×#126×C₄₃	—	2	1	no	—
13	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#123×C₄₃	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	—	2	1	no	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₃	—	2	1	no	—
22	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
23	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#431	—	2	4	no	—
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₂×#103×C₄₃	C₂²	1	4	yes	—
27	C₂×#102×C₄₃	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
30	C₄₃×#382	—	2	1	no	—
31	C₄₃×#382	—	2	1	no	—
32	C₄₃×#382	C₂²	1	2	yes	—
33	C₄₃×#382	C₂²	1	2	yes	—
34	C₂×#95×C₄₃	—	2	1	no	—
35	C₂×#95×C₄₃	—	2	1	no	—
36	C₄₃×#340	C₂²	1	4	yes	—
37	C₄₃×#340	C₂²	1	4	yes	—
38	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	—	2	1	no	—
42	C₂³×C₄×C₄₃	—	2	2	no	—
43	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
47	#126×C₄₃	—	2	8	no	—
48	#125×C₄₃	—	2	2	no	—
49	#125×C₄₃	C₂×C₄	1	4	yes	complemented
50	#124×C₄₃	—	2	2	no	—
51	#124×C₄₃	C₂×C₄	1	4	yes	complemented
52	#123×C₄₃	—	2	8	no	—
53	C₂²⋊Q₈×C₄₃	—	2	2	no	—
54	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
55	#121×C₄₃	—	2	2	no	—
56	#121×C₄₃	C₂×C₄	1	4	yes	—
57	C₄×Q₈×C₄₃	—	2	2	no	—
58	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
59	C₄×D₄×C₄₃	—	2	8	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	complemented
62	#117×C₄₃	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	—	2	1	no	—
78	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	D₄	1	4	yes	—
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₃	—	2	4	no	—
85	#103×C₄₃	—	4	4	no	—
86	#102×C₄₃	—	4	4	no	—
87	C₂²⋊C₈×C₄₃	—	2	4	no	—
88	C₄×C₈×C₄₃	—	2	4	no	—
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	2	no	—
91	#95×C₄₃	—	2	2	no	—
92	#95×C₄₃	—	2	2	no	—
93	C₂⁴×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₄₃	—	2	1	no	—
100	C₂×D₄×C₄₃	—	2	4	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	4	4	no	—
104	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	4	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	4	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	4	4	no	—
115	C₂²×C₄×C₄₃	—	4	4	no	—
116	C₂²×C₄×C₄₃	—	4	4	no	—
117	C₂²×C₄×C₄₃	—	4	4	no	—
118	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
119	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₄₃	—	2	4	no	—
129	C₂×C₈×C₄₃	—	2	4	no	—
130	C₂×C₈×C₄₃	—	2	4	no	—
131	C₄⋊C₄×C₄₃	—	2	4	no	—
132	C₄⋊C₄×C₄₃	—	2	4	no	—
133	C₄⋊C₄×C₄₃	—	2	4	no	—
134	C₄⋊C₄×C₄₃	—	2	4	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	4	no	—
138	C₄⋊C₄×C₄₃	—	2	4	no	—
139	C₄⋊C₄×C₄₃	—	4	4	no	—
140	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₄₃	—	2	4	no	—
143	C₂²⋊C₄×C₄₃	—	2	4	no	—
144	C₂²⋊C₄×C₄₃	—	2	4	no	—
145	C₂²⋊C₄×C₄₃	—	2	4	no	—
146	C₂²⋊C₄×C₄₃	—	2	4	no	—
147	C₄²×C₄₃	—	2	4	no	—
148	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
149	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
150	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
152	C₄²×C₄₃	C₂×D₄	1	2	yes	—
153	C₄²×C₄₃	C₂×D₄	1	2	yes	—
154	C₂³×C₄₃	—	2	1	no	—
155	C₂³×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	—	4	1	no	—
159	C₂³×C₄₃	—	4	1	no	—
160	C₂³×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂³×C₄₃	#135	1	4	yes	—
164	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₄₃	—	2	4	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	D₄×C₄₃	—	2	4	no	—
168	D₄×C₄₃	—	4	8	no	—
169	D₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	8	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	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	—	4	4	no	—
183	C₂×C₄×C₄₃	—	4	8	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	—	4	4	no	—
190	C₂×C₄×C₄₃	—	4	4	no	—
191	C₂×C₄×C₄₃	—	8	8	no	—
192	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
200	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
201	C₈×C₄₃	—	4	4	no	—
202	#21861	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	4	no	—
206	C₂²×C₄₃	—	2	4	no	—
207	C₂²×C₄₃	—	4	2	no	—
208	C₂²×C₄₃	—	4	2	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	—	8	2	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	#416	1	4	yes	—
213	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₄₃	#535	1	1	yes	characteristic
215	C₂²×C₄₃	#536	1	1	yes	characteristic
216	C₂²×C₄₃	C₂×#135	1	2	yes	—
217	C₂²×C₄₃	#575	1	2	yes	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	4	2	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	8	4	no	—
227	C₄×C₄₃	#520	1	2	yes	—
228	C₄×C₄₃	#537	1	2	yes	—
229	C₂×#529	C₂×C₄₃	1	1	yes	characteristic
230	C₂×#431	C₂×C₄₃	1	1	yes	characteristic, complemented
231	C₂×#382	C₂×C₄₃	1	1	yes	characteristic, complemented
232	#1991	C₂×C₄₃	1	2	yes	complemented
233	#1958	C₂×C₄₃	1	2	yes	complemented
234	#1874	C₂×C₄₃	1	2	yes	—
235	#1872	C₂×C₄₃	1	2	yes	complemented
236	#1805	C₂×C₄₃	1	2	yes	complemented
237	#1804	C₂×C₄₃	1	2	yes	complemented
238	C₂×C₄₃	—	2	4	no	—
239	C₂×C₄₃	—	8	2	no	—
240	C₂×C₄₃	#2311	1	1	yes	characteristic
241	C₂×C₄₃	C₂×#416	1	1	yes	characteristic
242	C₂×C₄₃	#2896	1	1	yes	characteristic
243	C₂×C₄₃	#3211	1	2	yes	—
244	C₂×C₄₃	#3232	1	2	yes	—
245	#529	—	2	4	no	—
246	#529	C₄×C₄₃	1	8	yes	complemented
247	C₂×#126	—	2	1	no	—
248	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
249	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×#123	—	2	1	no	—
251	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
252	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
254	C₂×C₄×D₄	—	2	1	no	—
255	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
256	C₂×#117	—	2	1	no	—
257	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
258	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
259	#431	—	2	4	no	—
260	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
261	C₂×#103	C₂²×C₄₃	1	4	yes	—
262	C₂×#102	C₂²×C₄₃	1	4	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
265	#382	—	2	1	no	—
266	#382	—	2	1	no	—
267	#382	C₂²×C₄₃	1	2	yes	—
268	#382	C₂²×C₄₃	1	2	yes	—
269	C₂×#95	—	2	1	no	—
270	C₂×#95	—	2	1	no	—
271	#340	C₂²×C₄₃	1	4	yes	—
272	#340	C₂²×C₄₃	1	4	yes	—
273	C₄₃	#21861	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
280	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
283	#126	—	2	8	no	—
284	#125	—	2	2	no	—
285	#125	C₂×C₄×C₄₃	1	4	yes	complemented
286	#124	—	2	2	no	—
287	#124	C₂×C₄×C₄₃	1	4	yes	complemented
288	#123	—	2	8	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	—
291	#121	—	2	2	no	—
292	#121	C₂×C₄×C₄₃	1	4	yes	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
295	C₄×D₄	—	2	8	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	complemented
298	#117	—	2	8	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	4	4	no	—
305	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
315	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
316	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
317	C₂×C₄²	D₄×C₄₃	1	4	yes	—
318	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
320	C₄⋊C₈	—	2	4	no	—
321	#103	—	4	4	no	—
322	#102	—	4	4	no	—
323	C₂²⋊C₈	—	2	4	no	—
324	C₄×C₈	—	2	4	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	C₂⁴	—	2	1	no	—
330	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	4	no	—
351	C₂²×C₄	—	4	4	no	—
352	C₂²×C₄	—	4	4	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
355	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
377	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₄²	—	2	4	no	—
384	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
385	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
386	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
387	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
388	C₄²	C₂×D₄×C₄₃	1	2	yes	—
389	C₄²	C₂×D₄×C₄₃	1	2	yes	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
399	C₂³	#135×C₄₃	1	4	yes	—
400	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
401	Q₈	—	2	4	no	—
402	Q₈	—	4	2	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	8	no	—
405	D₄	—	4	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	8	8	no	—
428	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
433	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
435	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
436	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
437	C₈	—	4	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	C₄₃×#416	1	4	yes	—
448	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
449	C₂²	C₄₃×#535	1	1	yes	characteristic
450	C₂²	C₄₃×#536	1	1	yes	characteristic
451	C₂²	C₂×#135×C₄₃	1	2	yes	—
452	C₂²	C₄₃×#575	1	2	yes	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	8	4	no	—
462	C₄	C₄₃×#520	1	2	yes	—
463	C₄	C₄₃×#537	1	2	yes	—
464	C₂	—	2	4	no	—
465	C₂	—	8	2	no	—
466	C₂	C₄₃×#2311	1	1	yes	characteristic
467	C₂	C₂×C₄₃×#416	1	1	yes	characteristic
468	C₂	C₄₃×#2896	1	1	yes	characteristic
469	C₂	C₄₃×#3211	1	2	yes	—
470	C₂	C₄₃×#3232	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×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
2. C₂×C₄₃×#431	C₂	semidirect
3. C₂×C₄₃×#382	C₂	semidirect
4. C₄₃×#1991	C₂	semidirect
5. C₄₃×#1958	C₂	semidirect
7. C₄₃×#1872	C₂	semidirect
8. C₄₃×#1805	C₂	semidirect
9. C₄₃×#1804	C₂	semidirect
11. C₄₃×#529	C₄	semidirect
49. #125×C₄₃	C₂×C₄	semidirect
51. #124×C₄₃	C₂×C₄	semidirect
58. C₄×Q₈×C₄₃	C₂×C₄	semidirect
61. C₄×D₄×C₄₃	C₂×C₄	semidirect
202. #21861	C₄₃	direct (N × H)
230. C₂×#431	C₂×C₄₃	semidirect
231. C₂×#382	C₂×C₄₃	semidirect
232. #1991	C₂×C₄₃	semidirect
233. #1958	C₂×C₄₃	semidirect
235. #1872	C₂×C₄₃	semidirect
236. #1805	C₂×C₄₃	semidirect
237. #1804	C₂×C₄₃	semidirect
246. #529	C₄×C₄₃	semidirect
273. C₄₃	#21861	direct (N × H)
285. #125	C₂×C₄×C₄₃	semidirect
287. #124	C₂×C₄×C₄₃	semidirect
294. C₄×Q₈	C₂×C₄×C₄₃	semidirect
297. C₄×D₄	C₂×C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#529	2
C₂×C₄₃×#431	2
C₂×C₄₃×#382	2
C₄₃×#1991	2
C₄₃×#1958	2
C₄₃×#1874	2
C₄₃×#1872	2
C₄₃×#1805	2
C₄₃×#1804	2
#21861	43

Subgroups — C43×#21861 #24941878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#21861 #24941878