Subgroups — C₄₃×#20702 #24940719

Order 11008.

1542 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1825	C₂	1	4	yes	maximal, complemented
5	C₄₃×#1824	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1823	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1736	C₂	1	4	yes	maximal, complemented
8	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
10	C₂×#117×C₄₃	—	2	4	no	—
11	C₂×#117×C₄₃	—	2	1	no	—
12	C₂×#117×C₄₃	—	2	1	no	—
13	C₂×#117×C₄₃	C₄	1	8	yes	complemented
14	C₂×#117×C₄₃	C₂²	1	2	yes	—
15	C₂×#117×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
20	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
21	C₂²×C₄²×C₄₃	—	2	1	no	—
22	C₄₃×#407	—	2	4	no	—
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#380	—	2	1	no	—
26	C₄₃×#380	—	2	1	no	—
27	C₄₃×#380	C₂²	1	2	yes	—
28	C₄₃×#380	C₂²	1	2	yes	—
29	C₂×#95×C₄₃	—	2	1	no	—
30	C₄₃×#340	C₂²	1	8	yes	complemented
31	C₄₃×#340	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₃	—	2	8	no	—
34	C₂³×C₄×C₄₃	—	2	1	no	—
35	C₂³×C₄×C₄₃	—	2	1	no	—
36	C₂³×C₄×C₄₃	—	2	2	no	—
37	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
38	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	D₄	1	4	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₄₃	—	2	4	no	—
46	C₂×M₁₆×C₄₃	—	2	8	no	—
47	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
48	#117×C₄₃	—	2	8	no	—
49	#117×C₄₃	—	2	8	no	—
50	#117×C₄₃	—	2	4	no	—
51	#117×C₄₃	—	2	4	no	—
52	#117×C₄₃	C₂×C₄	1	8	yes	—
53	#117×C₄₃	C₂×C₄	1	8	yes	complemented
54	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	complemented
61	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	complemented
62	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
71	C₂×C₄²×C₄₃	—	2	8	no	—
72	C₂×C₄²×C₄₃	—	2	2	no	—
73	C₂×C₄²×C₄₃	—	2	2	no	—
74	C₂²⋊C₈×C₄₃	—	2	4	no	—
75	C₂²⋊C₈×C₄₃	—	2	4	no	—
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	2	no	—
78	C₂⁴×C₄₃	—	2	4	no	—
79	C₂⁴×C₄₃	—	2	2	no	—
80	C₂⁴×C₄₃	—	2	2	no	—
81	C₂⁴×C₄₃	—	4	2	no	—
82	C₂⁴×C₄₃	C₂²⋊C₄	1	4	yes	—
83	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	—	2	16	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	4	no	—
89	C₂²×C₄×C₄₃	—	2	16	no	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	4	no	—
93	C₂²×C₄×C₄₃	—	2	4	no	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	4	4	no	—
99	C₂²×C₄×C₄₃	—	4	4	no	—
100	C₂²×C₄×C₄₃	—	4	4	no	—
101	C₂²×C₄×C₄₃	—	4	4	no	—
102	C₂²×C₄×C₄₃	—	4	2	no	—
103	C₂²×C₄×C₄₃	—	4	2	no	—
104	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
106	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	8	yes	—
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	M₁₆×C₄₃	—	4	8	no	—
119	C₂×C₈×C₄₃	—	2	4	no	—
120	C₂×C₈×C₄₃	—	2	8	no	—
121	C₄⋊C₄×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	8	no	—
126	C₄⋊C₄×C₄₃	—	4	4	no	—
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
128	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₄₃	—	2	8	no	—
130	C₂²⋊C₄×C₄₃	—	2	8	no	—
131	C₂²⋊C₄×C₄₃	—	4	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	4	no	—
133	C₄²×C₄₃	—	2	8	no	—
134	C₄²×C₄₃	—	2	8	no	—
135	C₂³×C₄₃	—	2	2	no	—
136	C₂³×C₄₃	—	2	1	no	—
137	C₂³×C₄₃	—	2	1	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	2	no	—
141	C₂³×C₄₃	—	2	1	no	—
142	C₂³×C₄₃	—	2	1	no	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	8	no	—
145	C₂³×C₄₃	—	2	8	no	—
146	C₂³×C₄₃	—	4	4	no	—
147	C₂³×C₄₃	—	4	8	no	—
148	C₂³×C₄₃	—	4	8	no	—
149	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂³×C₄₃	#123	1	4	yes	—
153	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
154	C₂³×C₄₃	#137	1	2	yes	—
155	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	8	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	8	no	—
164	C₂×C₄×C₄₃	—	2	8	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	4	8	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	4	no	—
171	C₂×C₄×C₄₃	—	4	8	no	—
172	C₂×C₄×C₄₃	—	4	4	no	—
173	C₂×C₄×C₄₃	—	4	4	no	—
174	C₂×C₄×C₄₃	—	4	4	no	—
175	C₂×C₄×C₄₃	—	8	8	no	—
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₃	#117	1	8	yes	—
180	C₂×C₄×C₄₃	#123	1	8	yes	—
181	C₂×C₄×C₄₃	#123	1	4	yes	—
182	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
185	C₈×C₄₃	—	4	4	no	—
186	#20702	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₃	—	2	4	no	—
188	C₂²×C₄₃	—	2	4	no	—
189	C₂²×C₄₃	—	2	4	no	—
190	C₂²×C₄₃	—	2	4	no	—
191	C₂²×C₄₃	—	2	2	no	—
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	—	2	2	no	—
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	—	4	16	no	—
199	C₂²×C₄₃	—	4	2	no	—
200	C₂²×C₄₃	—	4	2	no	—
201	C₂²×C₄₃	#381	1	4	yes	—
202	C₂²×C₄₃	#417	1	4	yes	—
203	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₄₃	C₂×#123	1	2	yes	—
205	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
207	C₂²×C₄₃	#575	1	2	yes	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	2	no	—
210	C₄×C₄₃	—	4	4	no	—
211	C₄×C₄₃	—	4	4	no	—
212	C₄×C₄₃	—	8	4	no	—
213	C₄×C₄₃	#381	1	4	yes	—
214	C₄×C₄₃	C₂×#117	1	2	yes	—
215	C₄×C₄₃	C₂×#123	1	2	yes	—
216	C₂²×#117	C₂×C₄₃	1	1	yes	characteristic
217	C₂×#407	C₂×C₄₃	1	1	yes	characteristic
218	C₂×#380	C₂×C₄₃	1	1	yes	characteristic
219	#1825	C₂×C₄₃	1	4	yes	complemented
220	#1824	C₂×C₄₃	1	2	yes	complemented
221	#1823	C₂×C₄₃	1	2	yes	complemented
222	#1736	C₂×C₄₃	1	4	yes	complemented
223	C₂×C₄₃	—	2	4	no	—
224	C₂×C₄₃	—	2	4	no	—
225	C₂×C₄₃	—	4	2	no	—
226	C₂×C₄₃	C₂×#381	1	1	yes	characteristic
227	C₂×C₄₃	C₂×#417	1	1	yes	characteristic
228	C₂×C₄₃	#2896	1	1	yes	characteristic
229	C₂×C₄₃	#3094	1	2	yes	—
230	C₂×C₄₃	#3095	1	2	yes	—
231	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
232	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
233	C₂×#117	—	2	4	no	—
234	C₂×#117	—	2	1	no	—
235	C₂×#117	—	2	1	no	—
236	C₂×#117	C₄×C₄₃	1	8	yes	complemented
237	C₂×#117	C₂²×C₄₃	1	2	yes	—
238	C₂×#117	C₂²×C₄₃	1	2	yes	—
239	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	—	2	1	no	—
243	C₂²×C₂²⋊C₄	—	2	1	no	—
244	C₂²×C₄²	—	2	1	no	—
245	#407	—	2	4	no	—
246	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
248	#380	—	2	1	no	—
249	#380	—	2	1	no	—
250	#380	C₂²×C₄₃	1	2	yes	—
251	#380	C₂²×C₄₃	1	2	yes	—
252	C₂×#95	—	2	1	no	—
253	#340	C₂²×C₄₃	1	8	yes	complemented
254	#340	C₂²×C₄₃	1	8	yes	complemented
255	C₄₃	#20702	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
257	C₂³×C₄	—	2	8	no	—
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
262	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
265	C₂³×C₄	D₄×C₄₃	1	4	yes	—
266	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
269	C₂×M₁₆	—	2	4	no	—
270	C₂×M₁₆	—	2	8	no	—
271	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
272	#117	—	2	8	no	—
273	#117	—	2	8	no	—
274	#117	—	2	4	no	—
275	#117	—	2	4	no	—
276	#117	C₂×C₄×C₄₃	1	8	yes	—
277	#117	C₂×C₄×C₄₃	1	8	yes	complemented
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	8	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	complemented
285	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	complemented
286	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
287	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	8	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	4	4	no	—
295	C₂×C₄²	—	2	8	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	C₂²⋊C₈	—	2	4	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	4	2	no	—
306	C₂⁴	C₂²⋊C₄×C₄₃	1	4	yes	—
307	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
308	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
309	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
329	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
330	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
331	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
340	C₂²×C₄	#41×C₄₃	1	8	yes	—
341	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
342	M₁₆	—	4	8	no	—
343	C₂×C₈	—	2	4	no	—
344	C₂×C₈	—	2	8	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
352	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₄²	—	2	8	no	—
358	C₄²	—	2	8	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	8	no	—
373	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
374	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
375	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
376	C₂³	#123×C₄₃	1	4	yes	—
377	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
378	C₂³	#137×C₄₃	1	2	yes	—
379	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	8	8	no	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
403	C₂×C₄	#117×C₄₃	1	8	yes	—
404	C₂×C₄	#123×C₄₃	1	8	yes	—
405	C₂×C₄	#123×C₄₃	1	4	yes	—
406	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
409	C₈	—	4	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	16	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	C₄₃×#381	1	4	yes	—
425	C₂²	C₄₃×#417	1	4	yes	—
426	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
427	C₂²	C₂×#123×C₄₃	1	2	yes	—
428	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
429	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
430	C₂²	C₄₃×#575	1	2	yes	—
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	4	no	—
435	C₄	—	8	4	no	—
436	C₄	C₄₃×#381	1	4	yes	—
437	C₄	C₂×#117×C₄₃	1	2	yes	—
438	C₄	C₂×#123×C₄₃	1	2	yes	—
439	C₂	—	2	4	no	—
440	C₂	—	2	4	no	—
441	C₂	—	4	2	no	—
442	C₂	C₂×C₄₃×#381	1	1	yes	characteristic
443	C₂	C₂×C₄₃×#417	1	1	yes	characteristic
444	C₂	C₄₃×#2896	1	1	yes	characteristic
445	C₂	C₄₃×#3094	1	2	yes	—
446	C₂	C₄₃×#3095	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	C₂⁵×C₄₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂⁴×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×#1825	C₂	semidirect
5. C₄₃×#1824	C₂	semidirect
6. C₄₃×#1823	C₂	semidirect
7. C₄₃×#1736	C₂	semidirect
13. C₂×#117×C₄₃	C₄	semidirect
30. C₄₃×#340	C₂²	semidirect
31. C₄₃×#340	C₂²	semidirect
53. #117×C₄₃	C₂×C₄	semidirect
60. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
61. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
186. #20702	C₄₃	direct (N × H)
219. #1825	C₂×C₄₃	semidirect
220. #1824	C₂×C₄₃	semidirect
221. #1823	C₂×C₄₃	semidirect
222. #1736	C₂×C₄₃	semidirect
236. C₂×#117	C₄×C₄₃	semidirect
253. #340	C₂²×C₄₃	semidirect
254. #340	C₂²×C₄₃	semidirect
255. C₄₃	#20702	direct (N × H)
277. #117	C₂×C₄×C₄₃	semidirect
284. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
285. C₂×C₄⋊C₄	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
C₂²×#117×C₄₃	2
C₂×C₄₃×#407	2
C₂×C₄₃×#380	2
C₄₃×#1825	2
C₄₃×#1824	2
C₄₃×#1823	2
C₄₃×#1736	2
#20702	43

Subgroups — C43×#20702 #24940719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20702 #24940719