Subgroups — C₄₃×#29714 #24949731

Order 11008.

1228 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#450	C₂	1	2	yes	maximal
2	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2071	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2055	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2013	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1872	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₄₃	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
15	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#450	—	2	8	no	—
18	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
19	C₂×#103×C₄₃	C₂²	1	4	yes	complemented
20	C₂×#102×C₄₃	C₂²	1	4	yes	—
21	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
22	C₄₃×#391	C₂²	1	2	yes	complemented
23	C₄₃×#390	—	2	1	no	—
24	C₄₃×#390	—	2	1	no	—
25	C₄₃×#390	C₂²	1	2	yes	—
26	C₄₃×#390	C₂²	1	2	yes	—
27	C₄₃×#389	—	2	1	no	—
28	C₄₃×#389	—	2	1	no	—
29	C₄₃×#384	C₂²	1	1	yes	characteristic, complemented
30	C₄₃×#380	—	2	1	no	—
31	C₄₃×#380	—	2	1	no	—
32	C₄₃×#340	C₂²	1	4	yes	complemented
33	C₄₃×#336	C₂²	1	2	yes	complemented
34	C₂⁵×C₄₃	—	2	1	no	—
35	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
36	C₂²×D₄×C₄₃	—	2	1	no	—
37	C₂²×D₄×C₄₃	—	2	2	no	—
38	C₂²×D₄×C₄₃	—	4	2	no	—
39	C₂²×D₄×C₄₃	—	4	2	no	—
40	C₂²×D₄×C₄₃	D₄	1	4	yes	—
41	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₃	—	2	1	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	C₂×SD₁₆×C₄₃	—	2	8	no	—
47	C₂×SD₁₆×C₄₃	—	4	4	no	—
48	C₂×SD₁₆×C₄₃	—	4	4	no	—
49	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
50	C₄⋊Q₈×C₄₃	—	4	2	no	—
51	C₂²⋊Q₈×C₄₃	—	2	4	no	—
52	C₂²⋊Q₈×C₄₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
69	C₂×C₄²×C₄₃	—	4	2	no	—
70	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₃	—	4	2	no	—
75	#103×C₄₃	—	4	4	no	—
76	#102×C₄₃	—	2	8	no	—
77	C₂²⋊C₈×C₄₃	—	2	4	no	—
78	#95×C₄₃	—	2	2	no	—
79	#95×C₄₃	—	2	2	no	—
80	C₂⁴×C₄₃	—	2	4	no	—
81	C₂⁴×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	—	4	2	no	—
83	C₂⁴×C₄₃	—	4	2	no	—
84	C₂⁴×C₄₃	—	4	2	no	—
85	C₂⁴×C₄₃	—	4	2	no	—
86	C₂⁴×C₄₃	—	4	2	no	—
87	C₂⁴×C₄₃	—	4	2	no	—
88	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	2	4	no	—
92	C₂×Q₈×C₄₃	—	2	4	no	—
93	C₂×D₄×C₄₃	—	2	4	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	2	4	no	—
97	C₂×D₄×C₄₃	—	4	8	no	—
98	C₂×D₄×C₄₃	—	4	8	no	—
99	C₂×D₄×C₄₃	—	4	2	no	—
100	C₂×D₄×C₄₃	—	4	2	no	—
101	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	4	1	no	—
110	C₂²×C₄×C₄₃	—	4	1	no	—
111	C₂²×C₄×C₄₃	—	4	1	no	—
112	C₂²×C₄×C₄₃	—	4	2	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	complemented
116	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	SD₁₆×C₄₃	—	4	16	no	—
125	C₂×C₈×C₄₃	—	2	4	no	—
126	C₂×C₈×C₄₃	—	2	4	no	—
127	C₂×C₈×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	4	no	—
131	C₄⋊C₄×C₄₃	—	4	2	no	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄⋊C₄×C₄₃	—	4	2	no	—
134	C₄⋊C₄×C₄₃	—	4	2	no	—
135	C₄⋊C₄×C₄₃	—	4	4	no	—
136	C₄⋊C₄×C₄₃	—	4	2	no	—
137	C₂²⋊C₄×C₄₃	—	4	4	no	—
138	C₂²⋊C₄×C₄₃	—	4	4	no	—
139	C₂²⋊C₄×C₄₃	—	4	4	no	—
140	C₂²⋊C₄×C₄₃	—	4	4	no	—
141	C₂²⋊C₄×C₄₃	—	4	4	no	—
142	C₄²×C₄₃	—	2	2	no	—
143	C₄²×C₄₃	—	2	2	no	—
144	C₄²×C₄₃	—	4	1	no	—
145	C₄²×C₄₃	—	4	1	no	—
146	C₂³×C₄₃	—	2	1	no	—
147	C₂³×C₄₃	—	2	1	no	—
148	C₂³×C₄₃	—	2	1	no	—
149	C₂³×C₄₃	—	2	1	no	—
150	C₂³×C₄₃	—	2	4	no	—
151	C₂³×C₄₃	—	4	8	no	—
152	C₂³×C₄₃	—	4	8	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	—	4	2	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	4	8	no	—
160	C₂³×C₄₃	—	8	4	no	—
161	C₂³×C₄₃	—	8	4	no	—
162	C₂³×C₄₃	—	8	4	no	—
163	C₂³×C₄₃	—	8	4	no	—
164	C₂³×C₄₃	#121	1	2	yes	—
165	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
166	C₂³×C₄₃	#137	1	2	yes	—
167	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₄₃	—	4	4	no	—
169	Q₈×C₄₃	—	4	4	no	—
170	D₄×C₄₃	—	2	8	no	—
171	D₄×C₄₃	—	4	8	no	—
172	D₄×C₄₃	—	4	4	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	4	no	—
182	C₂×C₄×C₄₃	—	2	4	no	—
183	C₂×C₄×C₄₃	—	2	1	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	4	4	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	—	8	4	no	—
198	C₂×C₄×C₄₃	#121	1	2	yes	—
199	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
201	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
205	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₄₃	—	4	4	no	—
207	#29714	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	2	2	no	—
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	4	4	no	—
215	C₂²×C₄₃	—	4	4	no	—
216	C₂²×C₄₃	—	4	4	no	—
217	C₂²×C₄₃	—	8	16	no	—
218	C₂²×C₄₃	—	8	2	no	—
219	C₂²×C₄₃	—	8	2	no	—
220	C₂²×C₄₃	—	8	2	no	—
221	C₂²×C₄₃	—	8	2	no	—
222	C₂²×C₄₃	#461	1	4	yes	—
223	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
224	C₂²×C₄₃	#534	1	1	yes	characteristic
225	C₂²×C₄₃	#535	1	1	yes	characteristic
226	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
227	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
229	C₂²×C₄₃	#575	1	1	yes	characteristic
230	C₄×C₄₃	—	2	2	no	—
231	C₄×C₄₃	—	2	2	no	—
232	C₄×C₄₃	—	2	2	no	—
233	C₄×C₄₃	—	2	2	no	—
234	C₄×C₄₃	—	4	1	no	—
235	C₄×C₄₃	—	8	2	no	—
236	C₄×C₄₃	—	8	2	no	—
237	C₄×C₄₃	—	8	2	no	—
238	C₄×C₄₃	#534	1	2	yes	—
239	C₄×C₄₃	#538	1	2	yes	—
240	C₂×#450	C₂×C₄₃	1	2	yes	—
241	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
242	C₂×#390	C₂×C₄₃	1	1	yes	characteristic
243	#2071	C₂×C₄₃	1	2	yes	complemented
244	#2055	C₂×C₄₃	1	4	yes	complemented
245	#2013	C₂×C₄₃	1	2	yes	complemented
246	#1872	C₂×C₄₃	1	2	yes	complemented
247	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
248	C₂×C₄₃	—	2	4	no	—
249	C₂×C₄₃	—	8	4	no	—
250	C₂×C₄₃	#2617	1	1	yes	characteristic
251	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
252	C₂×C₄₃	#3036	1	1	yes	characteristic
253	C₂×C₄₃	#3187	1	1	yes	characteristic
254	C₂×C₄₃	#3193	1	1	yes	characteristic
255	C₂×C₄₃	#3208	1	1	yes	characteristic
256	C₂×C₄₃	#3215	1	1	yes	characteristic
257	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
258	C₂²×SD₁₆	C₂²×C₄₃	1	4	yes	—
259	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
260	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	—	2	1	no	—
263	C₂²×C₂²⋊C₄	—	2	1	no	—
264	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
265	#450	—	2	8	no	—
266	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
267	C₂×#103	C₂²×C₄₃	1	4	yes	complemented
268	C₂×#102	C₂²×C₄₃	1	4	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
270	#391	C₂²×C₄₃	1	2	yes	complemented
271	#390	—	2	1	no	—
272	#390	—	2	1	no	—
273	#390	C₂²×C₄₃	1	2	yes	—
274	#390	C₂²×C₄₃	1	2	yes	—
275	#389	—	2	1	no	—
276	#389	—	2	1	no	—
277	#384	C₂²×C₄₃	1	1	yes	characteristic, complemented
278	#380	—	2	1	no	—
279	#380	—	2	1	no	—
280	#340	C₂²×C₄₃	1	4	yes	complemented
281	#336	C₂²×C₄₃	1	2	yes	complemented
282	C₄₃	#29714	1	1	yes	characteristic, direct product factor, Sylow
283	C₂⁵	—	2	1	no	—
284	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	4	2	no	—
288	C₂²×D₄	—	4	2	no	—
289	C₂²×D₄	D₄×C₄₃	1	4	yes	—
290	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
293	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
295	C₂×SD₁₆	—	2	8	no	—
296	C₂×SD₁₆	—	4	4	no	—
297	C₂×SD₁₆	—	4	4	no	—
298	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
299	C₄⋊Q₈	—	4	2	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	4	2	no	—
309	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	4	4	no	—
317	C₂×C₂²⋊C₄	—	4	4	no	—
318	C₂×C₄²	—	4	2	no	—
319	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
323	C₄⋊C₈	—	4	2	no	—
324	#103	—	4	4	no	—
325	#102	—	2	8	no	—
326	C₂²⋊C₈	—	2	4	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	2	no	—
331	C₂⁴	—	4	2	no	—
332	C₂⁴	—	4	2	no	—
333	C₂⁴	—	4	2	no	—
334	C₂⁴	—	4	2	no	—
335	C₂⁴	—	4	2	no	—
336	C₂⁴	—	4	2	no	—
337	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	4	8	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	complemented
365	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
371	C₂²×C₄	#41×C₄₃	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
373	SD₁₆	—	4	16	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	4	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	4	1	no	—
394	C₄²	—	4	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	4	8	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	8	no	—
409	C₂³	—	8	4	no	—
410	C₂³	—	8	4	no	—
411	C₂³	—	8	4	no	—
412	C₂³	—	8	4	no	—
413	C₂³	#121×C₄₃	1	2	yes	—
414	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
415	C₂³	#137×C₄₃	1	2	yes	—
416	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
417	Q₈	—	4	4	no	—
418	Q₈	—	4	4	no	—
419	D₄	—	2	8	no	—
420	D₄	—	4	8	no	—
421	D₄	—	4	4	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	#121×C₄₃	1	2	yes	—
448	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
449	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
450	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
453	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
454	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
455	C₈	—	4	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	8	16	no	—
466	C₂²	—	8	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	8	2	no	—
470	C₂²	C₄₃×#461	1	4	yes	—
471	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
472	C₂²	C₄₃×#534	1	1	yes	characteristic
473	C₂²	C₄₃×#535	1	1	yes	characteristic
474	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
475	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
476	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
477	C₂²	C₄₃×#575	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	1	no	—
483	C₄	—	8	2	no	—
484	C₄	—	8	2	no	—
485	C₄	—	8	2	no	—
486	C₄	C₄₃×#534	1	2	yes	—
487	C₄	C₄₃×#538	1	2	yes	—
488	C₂	—	2	4	no	—
489	C₂	—	8	4	no	—
490	C₂	C₄₃×#2617	1	1	yes	characteristic
491	C₂	C₂×C₄₃×#461	1	1	yes	characteristic
492	C₂	C₄₃×#3036	1	1	yes	characteristic
493	C₂	C₄₃×#3187	1	1	yes	characteristic
494	C₂	C₄₃×#3193	1	1	yes	characteristic
495	C₂	C₄₃×#3208	1	1	yes	characteristic
496	C₂	C₄₃×#3215	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
LCS	G ▷ C₂²×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. C₄₃×#2857	C₂	semidirect
4. C₄₃×#2071	C₂	semidirect
5. C₄₃×#2055	C₂	semidirect
6. C₄₃×#2013	C₂	semidirect
7. C₄₃×#1872	C₂	semidirect
8. C₄₃×#1797	C₂	semidirect
11. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
18. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
19. C₂×#103×C₄₃	C₂²	semidirect
22. C₄₃×#391	C₂²	semidirect
29. C₄₃×#384	C₂²	semidirect
32. C₄₃×#340	C₂²	semidirect
33. C₄₃×#336	C₂²	semidirect
115. C₂²×C₄×C₄₃	SD₁₆	semidirect
207. #29714	C₄₃	direct (N × H)
241. #2857	C₂×C₄₃	semidirect
243. #2071	C₂×C₄₃	semidirect
244. #2055	C₂×C₄₃	semidirect
245. #2013	C₂×C₄₃	semidirect
246. #1872	C₂×C₄₃	semidirect
247. #1797	C₂×C₄₃	semidirect
259. C₂×C₄⋊Q₈	C₂²×C₄₃	semidirect
266. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
267. C₂×#103	C₂²×C₄₃	semidirect
270. #391	C₂²×C₄₃	semidirect
277. #384	C₂²×C₄₃	semidirect
280. #340	C₂²×C₄₃	semidirect
281. #336	C₂²×C₄₃	semidirect
282. C₄₃	#29714	direct (N × H)
364. C₂²×C₄	SD₁₆×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×#450	2
C₄₃×#2857	2
C₂×C₄₃×#390	2
C₄₃×#2071	2
C₄₃×#2055	2
C₄₃×#2013	2
C₄₃×#1872	2
C₄₃×#1797	2
#29714	43

Subgroups — C43×#29714 #24949731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29714 #24949731