Subgroups — C₄₃×#25451 #24945468

Order 11008.

834 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#476	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2542	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2084	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2065	C₂	1	2	yes	maximal
7	C₄₃×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1948	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1926	C₂	1	2	yes	maximal
11	C₄×#102×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
16	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#498	—	2	4	no	—
18	C₄₃×#476	—	2	4	no	—
19	C₂×#106×C₄₃	C₂²	1	2	yes	—
20	C₂×#106×C₄₃	C₂²	1	2	yes	—
21	C₂×#106×C₄₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#399	—	2	2	no	—
29	C₄₃×#391	—	2	2	no	—
30	C₄₃×#390	C₂²	1	2	yes	—
31	C₄₃×#389	—	2	1	no	—
32	C₄₃×#389	C₂²	1	2	yes	—
33	C₄₃×#384	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	—	2	1	no	—
44	C₂²×Q₈×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₄₃	—	2	2	no	—
51	C₄⋊Q₈×C₄₃	—	2	2	no	—
52	C₄⋊Q₈×C₄₃	—	2	2	no	—
53	C₄⋊Q₈×C₄₃	D₄	1	4	yes	—
54	C₂²⋊Q₈×C₄₃	—	4	4	no	—
55	C₂²⋊Q₈×C₄₃	—	4	4	no	—
56	C₄×D₄×C₄₃	—	2	2	no	—
57	C₄×D₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₄²×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	—	2	2	no	—
75	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#106×C₄₃	—	2	4	no	—
78	#106×C₄₃	—	2	4	no	—
79	#106×C₄₃	—	2	4	no	—
80	C₄⋊C₈×C₄₃	—	2	4	no	—
81	C₄⋊C₈×C₄₃	—	2	2	no	—
82	#102×C₄₃	—	2	2	no	—
83	#102×C₄₃	—	2	4	no	—
84	#102×C₄₃	Q₈	1	4	yes	complemented
85	C₄×C₈×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	2	no	—
87	#95×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	D₄	1	2	yes	—
90	C₂⁴×C₄₃	—	2	1	no	—
91	C₂×Q₈×C₄₃	—	2	4	no	—
92	C₂×Q₈×C₄₃	—	4	2	no	—
93	C₂×Q₈×C₄₃	—	4	2	no	—
94	C₂×Q₈×C₄₃	—	4	2	no	—
95	C₂×Q₈×C₄₃	—	8	1	no	—
96	C₂×Q₈×C₄₃	—	8	1	no	—
97	C₂×D₄×C₄₃	—	2	1	no	—
98	C₂×D₄×C₄₃	—	2	1	no	—
99	C₂×D₄×C₄₃	—	2	1	no	—
100	C₂×D₄×C₄₃	—	2	1	no	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	4	2	no	—
109	C₂²×C₄×C₄₃	—	4	2	no	—
110	C₂²×C₄×C₄₃	—	4	2	no	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	2	1	no	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
124	C₂×C₈×C₄₃	#41	1	2	yes	—
125	C₄⋊C₄×C₄₃	—	2	4	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	4	4	no	—
136	C₄⋊C₄×C₄₃	—	4	2	no	—
137	C₄⋊C₄×C₄₃	—	4	4	no	—
138	C₄⋊C₄×C₄₃	—	8	2	no	—
139	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
140	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
141	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
142	C₂²⋊C₄×C₄₃	—	4	4	no	—
143	C₂²⋊C₄×C₄₃	—	4	2	no	—
144	C₂²⋊C₄×C₄₃	—	4	4	no	—
145	C₄²×C₄₃	—	2	2	no	—
146	C₄²×C₄₃	—	2	2	no	—
147	C₄²×C₄₃	—	4	2	no	—
148	C₄²×C₄₃	—	8	2	no	—
149	C₄²×C₄₃	C₂×D₄	1	2	yes	—
150	C₄²×C₄₃	#41	1	2	yes	—
151	C₂³×C₄₃	—	2	2	no	—
152	C₂³×C₄₃	—	4	1	no	—
153	C₂³×C₄₃	—	4	1	no	—
154	C₂³×C₄₃	—	4	1	no	—
155	C₂³×C₄₃	—	4	1	no	—
156	C₂³×C₄₃	—	4	1	no	—
157	C₂³×C₄₃	—	4	1	no	—
158	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₃	—	8	4	no	—
160	Q₈×C₄₃	—	8	4	no	—
161	D₄×C₄₃	—	2	2	no	—
162	D₄×C₄₃	—	2	2	no	—
163	D₄×C₄₃	—	4	1	no	—
164	D₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	4	1	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	8	4	no	—
188	C₂×C₄×C₄₃	#121	1	2	yes	—
189	C₂×C₄×C₄₃	#121	1	2	yes	—
190	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
191	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
193	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
199	C₈×C₄₃	—	2	2	no	—
200	C₈×C₄₃	—	2	2	no	—
201	C₈×C₄₃	—	4	2	no	—
202	#25451	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	8	1	no	—
207	C₂²×C₄₃	—	8	1	no	—
208	C₂²×C₄₃	—	8	1	no	—
209	C₂²×C₄₃	—	8	1	no	—
210	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
211	C₂²×C₄₃	#547	1	1	yes	characteristic
212	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
213	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
214	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂²×C₄₃	#577	1	1	yes	characteristic
216	C₂²×C₄₃	#577	1	1	yes	characteristic
217	C₄×C₄₃	—	2	4	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	4	2	no	—
220	C₄×C₄₃	—	4	2	no	—
221	C₄×C₄₃	—	4	4	no	—
222	C₄×C₄₃	—	8	1	no	—
223	C₄×C₄₃	—	8	1	no	—
224	C₄×C₄₃	—	8	2	no	—
225	C₄×C₄₃	#460	1	4	yes	—
226	C₄×C₄₃	#533	1	1	yes	characteristic
227	C₄×C₄₃	#541	1	1	yes	characteristic
228	C₄×C₄₃	#548	1	1	yes	characteristic
229	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
230	C₂×#498	C₂×C₄₃	1	1	yes	characteristic, complemented
231	C₂×#476	C₂×C₄₃	1	1	yes	characteristic
232	#2542	C₂×C₄₃	1	1	yes	characteristic
233	#2369	C₂×C₄₃	1	1	yes	characteristic, complemented
234	#2084	C₂×C₄₃	1	2	yes	complemented
235	#2065	C₂×C₄₃	1	2	yes	—
236	#1988	C₂×C₄₃	1	1	yes	characteristic, complemented
237	#1948	C₂×C₄₃	1	2	yes	complemented
238	#1939	C₂×C₄₃	1	1	yes	characteristic, complemented
239	#1926	C₂×C₄₃	1	2	yes	—
240	C₄×#102	C₂×C₄₃	1	1	yes	characteristic
241	C₂×C₄₃	—	8	2	no	—
242	C₂×C₄₃	#2429	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
244	C₂×C₄₃	#3042	1	1	yes	characteristic
245	C₂×C₄₃	#3335	1	1	yes	characteristic
246	C₂×C₄₃	#3354	1	1	yes	characteristic
247	C₂×C₄₃	Q₈×SD₁₆	1	1	yes	characteristic
248	C₂×C₄₃	#3384	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
251	C₂×C₂²⋊Q₈	—	2	1	no	—
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
254	#498	—	2	4	no	—
255	#476	—	2	4	no	—
256	C₂×#106	C₂²×C₄₃	1	2	yes	—
257	C₂×#106	C₂²×C₄₃	1	2	yes	—
258	C₂×#106	C₂²×C₄₃	1	2	yes	—
259	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
261	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
262	C₂×#102	C₂²×C₄₃	1	2	yes	—
263	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
265	#399	—	2	2	no	—
266	#391	—	2	2	no	—
267	#390	C₂²×C₄₃	1	2	yes	—
268	#389	—	2	1	no	—
269	#389	C₂²×C₄₃	1	2	yes	—
270	#384	C₂²×C₄₃	1	2	yes	—
271	C₄×C₄⋊C₄	—	2	1	no	—
272	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
273	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
275	#340	C₂²×C₄₃	1	2	yes	—
276	#340	C₂²×C₄₃	1	1	yes	characteristic
277	#340	C₂²×C₄₃	1	2	yes	—
278	#340	C₂²×C₄₃	1	1	yes	characteristic
279	#336	C₂²×C₄₃	1	2	yes	—
280	C₄₃	#25451	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
286	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	—	2	2	no	—
291	C₄⋊Q₈	D₄×C₄₃	1	4	yes	—
292	C₂²⋊Q₈	—	4	4	no	—
293	C₂²⋊Q₈	—	4	4	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
314	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
315	#106	—	2	4	no	—
316	#106	—	2	4	no	—
317	#106	—	2	4	no	—
318	C₄⋊C₈	—	2	4	no	—
319	C₄⋊C₈	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	4	no	—
322	#102	Q₈×C₄₃	1	4	yes	complemented
323	C₄×C₈	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	1	no	—
327	#95	D₄×C₄₃	1	2	yes	—
328	C₂⁴	—	2	1	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	8	1	no	—
334	C₂×Q₈	—	8	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
362	C₂×C₈	#41×C₄₃	1	2	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	8	2	no	—
377	C₄⋊C₄	SD₁₆×C₄₃	1	4	yes	—
378	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
379	C₄⋊C₄	C₂×Q₈×C₄₃	1	2	yes	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	2	no	—
386	C₄²	—	8	2	no	—
387	C₄²	C₂×D₄×C₄₃	1	2	yes	—
388	C₄²	#41×C₄₃	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
397	Q₈	—	8	4	no	—
398	Q₈	—	8	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	4	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	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	8	4	no	—
426	C₂×C₄	#121×C₄₃	1	2	yes	—
427	C₂×C₄	#121×C₄₃	1	2	yes	—
428	C₂×C₄	C₂×SD₁₆×C₄₃	1	4	yes	—
429	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
430	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
435	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
436	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	2	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	8	1	no	—
444	C₂²	—	8	1	no	—
445	C₂²	—	8	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
448	C₂²	C₄₃×#547	1	1	yes	characteristic
449	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
450	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
451	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
452	C₂²	C₄₃×#577	1	1	yes	characteristic
453	C₂²	C₄₃×#577	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	4	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	2	no	—
462	C₄	C₄₃×#460	1	4	yes	—
463	C₄	C₄₃×#533	1	1	yes	characteristic
464	C₄	C₄₃×#541	1	1	yes	characteristic
465	C₄	C₄₃×#548	1	1	yes	characteristic
466	C₄	D₄×Q₈×C₄₃	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	C₄₃×#2429	1	1	yes	characteristic
469	C₂	C₂×C₄₃×#460	1	1	yes	characteristic
470	C₂	C₄₃×#3042	1	1	yes	characteristic
471	C₂	C₄₃×#3335	1	1	yes	characteristic
472	C₂	C₄₃×#3354	1	1	yes	characteristic
473	C₂	Q₈×SD₁₆×C₄₃	1	1	yes	characteristic
474	C₂	C₄₃×#3384	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#498	C₂	semidirect
4. C₄₃×#2369	C₂	semidirect
5. C₄₃×#2084	C₂	semidirect
7. C₄₃×#1988	C₂	semidirect
8. C₄₃×#1948	C₂	semidirect
9. C₄₃×#1939	C₂	semidirect
84. #102×C₄₃	Q₈	semidirect
202. #25451	C₄₃	direct (N × H)
230. C₂×#498	C₂×C₄₃	semidirect
233. #2369	C₂×C₄₃	semidirect
234. #2084	C₂×C₄₃	semidirect
236. #1988	C₂×C₄₃	semidirect
237. #1948	C₂×C₄₃	semidirect
238. #1939	C₂×C₄₃	semidirect
280. C₄₃	#25451	direct (N × H)
322. #102	Q₈×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×#498	2
C₂×C₄₃×#476	2
C₄₃×#2542	2
C₄₃×#2369	2
C₄₃×#2084	2
C₄₃×#2065	2
C₄₃×#1988	2
C₄₃×#1948	2
C₄₃×#1939	2
C₄₃×#1926	2
C₄×#102×C₄₃	2
#25451	43

Subgroups — C43×#25451 #24945468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#25451 #24945468