Subgroups — C₄₃×#34218 #24954235

Order 11008.

3014 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2368	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2364	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2359	C₂	1	4	yes	maximal, complemented
5	C₄₃×#2353	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2349	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2329	C₂	1	2	yes	maximal, complemented
10	C₄₃×#2325	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2318	C₂	1	2	yes	maximal, complemented
12	C₄×#120×C₄₃	C₂	1	4	yes	maximal, complemented
13	C₄₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#2275	C₂	1	2	yes	maximal, complemented
15	C₂²×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#525	C₄	1	16	yes	complemented
20	C₂×#123×C₄₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#120×C₄₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
31	C₂×#117×C₄₃	C₂²	1	2	yes	—
32	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#391	C₂²	1	4	yes	complemented
34	C₄₃×#389	C₂²	1	4	yes	complemented
35	C₄₃×#388	C₂²	1	4	yes	complemented
36	C₄₃×#388	C₂²	1	4	yes	complemented
37	C₄₃×#387	C₂²	1	4	yes	complemented
38	C₄₃×#387	C₂²	1	4	yes	complemented
39	C₄₃×#387	C₂²	1	4	yes	complemented
40	C₄₃×#387	C₂²	1	4	yes	complemented
41	C₄₃×#386	C₂²	1	4	yes	—
42	C₄₃×#386	C₂²	1	4	yes	—
43	C₄₃×#386	C₂²	1	4	yes	—
44	C₄₃×#386	C₂²	1	4	yes	complemented
45	C₄₃×#385	C₂²	1	4	yes	—
46	C₄₃×#385	C₂²	1	4	yes	—
47	C₄₃×#385	C₂²	1	4	yes	—
48	C₄₃×#385	C₂²	1	4	yes	complemented
49	C₄₃×#383	C₂²	1	2	yes	complemented
50	C₄₃×#382	C₂²	1	2	yes	complemented
51	C₄₃×#381	C₂²	1	2	yes	—
52	C₄₃×#381	C₂²	1	2	yes	complemented
53	C₄₃×#380	C₂²	1	2	yes	—
54	C₄₃×#380	C₂²	1	1	yes	characteristic
55	C₄₃×#380	C₂²	1	1	yes	characteristic
56	C₄₃×#380	C₂²	1	2	yes	complemented
57	C₄₃×#379	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
59	C₄×C₄⋊C₄×C₄₃	C₂²	1	4	yes	complemented
60	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
61	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	complemented
67	C₄₃×#376	C₂²	1	2	yes	complemented
68	C₂×#95×C₄₃	C₂²	1	2	yes	—
69	C₂×#95×C₄₃	C₂²	1	2	yes	—
70	C₂×#95×C₄₃	C₂²	1	2	yes	—
71	C₂×#95×C₄₃	C₂²	1	2	yes	—
72	C₂×#95×C₄₃	C₂²	1	2	yes	—
73	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
74	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
75	C₂×#95×C₄₃	C₂²	1	2	yes	complemented
76	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×#41×C₄₃	—	4	4	no	—
78	C₂×#41×C₄₃	C₂×C₄	1	8	yes	complemented
79	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₃	—	2	8	no	—
85	C₂³×C₄×C₄₃	—	4	4	no	—
86	C₂³×C₄×C₄₃	—	4	4	no	—
87	C₂³×C₄×C₄₃	—	4	4	no	—
88	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	complemented
89	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
91	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
100	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
101	#123×C₄₃	C₂×C₄	1	16	yes	complemented
102	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
103	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
104	#121×C₄₃	C₂×C₄	1	8	yes	complemented
105	#121×C₄₃	C₂×C₄	1	8	yes	complemented
106	#120×C₄₃	C₂×C₄	1	16	yes	complemented
107	C₄×D₄×C₄₃	—	2	16	no	—
108	C₄×D₄×C₄₃	—	4	8	no	—
109	C₄×D₄×C₄₃	—	4	8	no	—
110	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	complemented
111	C₄×D₄×C₄₃	C₂×C₄	1	16	yes	complemented
112	#117×C₄₃	—	4	4	no	—
113	#117×C₄₃	C₂×C₄	1	8	yes	complemented
114	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
137	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
138	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
140	#95×C₄₃	C₂³	1	2	yes	—
141	#95×C₄₃	C₂³	1	2	yes	—
142	#95×C₄₃	C₂³	1	2	yes	—
143	#95×C₄₃	C₂³	1	4	yes	—
144	#95×C₄₃	C₂³	1	4	yes	—
145	#95×C₄₃	C₂³	1	2	yes	—
146	#95×C₄₃	C₂³	1	2	yes	—
147	#95×C₄₃	C₂³	1	4	yes	—
148	#95×C₄₃	C₂³	1	2	yes	—
149	#95×C₄₃	C₂³	1	4	yes	—
150	#95×C₄₃	C₂³	1	4	yes	—
151	#95×C₄₃	C₂³	1	4	yes	—
152	#95×C₄₃	C₂³	1	4	yes	—
153	#95×C₄₃	C₂³	1	4	yes	—
154	#95×C₄₃	C₂³	1	4	yes	—
155	C₂⁴×C₄₃	—	2	4	no	—
156	C₂⁴×C₄₃	—	2	2	no	—
157	C₂⁴×C₄₃	—	2	4	no	—
158	C₂⁴×C₄₃	—	2	2	no	—
159	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
160	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
161	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
162	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
164	#41×C₄₃	—	4	16	no	—
165	C₂×Q₈×C₄₃	—	4	2	no	—
166	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	complemented
167	C₂×D₄×C₄₃	—	2	8	no	—
168	C₂×D₄×C₄₃	—	2	4	no	—
169	C₂×D₄×C₄₃	—	2	8	no	—
170	C₂×D₄×C₄₃	—	2	4	no	—
171	C₂×D₄×C₄₃	—	4	2	no	—
172	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
175	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	complemented
176	C₂²×C₄×C₄₃	—	2	8	no	—
177	C₂²×C₄×C₄₃	—	2	8	no	—
178	C₂²×C₄×C₄₃	—	2	8	no	—
179	C₂²×C₄×C₄₃	—	2	4	no	—
180	C₂²×C₄×C₄₃	—	2	4	no	—
181	C₂²×C₄×C₄₃	—	2	4	no	—
182	C₂²×C₄×C₄₃	—	2	8	no	—
183	C₂²×C₄×C₄₃	—	2	8	no	—
184	C₂²×C₄×C₄₃	—	4	16	no	—
185	C₂²×C₄×C₄₃	—	4	2	no	—
186	C₂²×C₄×C₄₃	—	4	2	no	—
187	C₂²×C₄×C₄₃	—	4	2	no	—
188	C₂²×C₄×C₄₃	—	4	2	no	—
189	C₂²×C₄×C₄₃	—	4	4	no	—
190	C₂²×C₄×C₄₃	—	4	4	no	—
191	C₂²×C₄×C₄₃	—	4	2	no	—
192	C₂²×C₄×C₄₃	—	4	2	no	—
193	C₂²×C₄×C₄₃	—	4	2	no	—
194	C₂²×C₄×C₄₃	—	4	2	no	—
195	C₂²×C₄×C₄₃	—	4	4	no	—
196	C₂²×C₄×C₄₃	—	4	4	no	—
197	C₂²×C₄×C₄₃	—	4	4	no	—
198	C₂²×C₄×C₄₃	—	4	32	no	—
199	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
200	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
203	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	complemented
206	C₂²×C₄×C₄₃	#41	1	8	yes	complemented
207	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
218	C₄⋊C₄×C₄₃	—	2	8	no	—
219	C₄⋊C₄×C₄₃	—	4	2	no	—
220	C₄⋊C₄×C₄₃	—	4	2	no	—
221	C₄⋊C₄×C₄₃	—	4	4	no	—
222	C₄⋊C₄×C₄₃	—	4	4	no	—
223	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	complemented
224	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	complemented
225	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	complemented
226	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	complemented
227	C₂²⋊C₄×C₄₃	—	2	8	no	—
228	C₂²⋊C₄×C₄₃	—	2	8	no	—
229	C₂²⋊C₄×C₄₃	—	2	8	no	—
230	C₂²⋊C₄×C₄₃	—	2	4	no	—
231	C₂²⋊C₄×C₄₃	—	2	4	no	—
232	C₂²⋊C₄×C₄₃	—	4	4	no	—
233	C₂²⋊C₄×C₄₃	—	4	4	no	—
234	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
236	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
237	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	complemented
238	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	complemented
239	C₄²×C₄₃	—	2	8	no	—
240	C₄²×C₄₃	—	4	4	no	—
241	C₄²×C₄₃	—	4	4	no	—
242	C₄²×C₄₃	—	4	4	no	—
243	C₄²×C₄₃	C₂²×C₄	1	8	yes	complemented
244	C₂³×C₄₃	—	2	16	no	—
245	C₂³×C₄₃	—	2	16	no	—
246	C₂³×C₄₃	—	2	8	no	—
247	C₂³×C₄₃	—	2	8	no	—
248	C₂³×C₄₃	—	2	8	no	—
249	C₂³×C₄₃	—	2	2	no	—
250	C₂³×C₄₃	—	2	2	no	—
251	C₂³×C₄₃	—	2	2	no	—
252	C₂³×C₄₃	—	2	2	no	—
253	C₂³×C₄₃	—	2	1	no	—
254	C₂³×C₄₃	—	2	1	no	—
255	C₂³×C₄₃	—	2	1	no	—
256	C₂³×C₄₃	—	2	1	no	—
257	C₂³×C₄₃	—	2	4	no	—
258	C₂³×C₄₃	—	2	2	no	—
259	C₂³×C₄₃	—	2	4	no	—
260	C₂³×C₄₃	—	2	2	no	—
261	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
262	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
263	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
264	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
265	C₂³×C₄₃	C₂×#41	1	4	yes	—
266	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
267	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
268	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
269	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
270	Q₈×C₄₃	—	4	4	no	—
271	D₄×C₄₃	—	2	16	no	—
272	D₄×C₄₃	—	2	16	no	—
273	D₄×C₄₃	—	2	16	no	—
274	D₄×C₄₃	—	4	4	no	—
275	C₂×C₄×C₄₃	—	2	8	no	—
276	C₂×C₄×C₄₃	—	2	8	no	—
277	C₂×C₄×C₄₃	—	2	4	no	—
278	C₂×C₄×C₄₃	—	2	2	no	—
279	C₂×C₄×C₄₃	—	2	2	no	—
280	C₂×C₄×C₄₃	—	2	4	no	—
281	C₂×C₄×C₄₃	—	2	4	no	—
282	C₂×C₄×C₄₃	—	2	4	no	—
283	C₂×C₄×C₄₃	—	2	2	no	—
284	C₂×C₄×C₄₃	—	2	2	no	—
285	C₂×C₄×C₄₃	—	2	2	no	—
286	C₂×C₄×C₄₃	—	2	2	no	—
287	C₂×C₄×C₄₃	—	2	4	no	—
288	C₂×C₄×C₄₃	—	2	4	no	—
289	C₂×C₄×C₄₃	—	2	4	no	—
290	C₂×C₄×C₄₃	—	2	4	no	—
291	C₂×C₄×C₄₃	—	2	4	no	—
292	C₂×C₄×C₄₃	—	2	4	no	—
293	C₂×C₄×C₄₃	—	2	4	no	—
294	C₂×C₄×C₄₃	—	2	4	no	—
295	C₂×C₄×C₄₃	—	2	4	no	—
296	C₂×C₄×C₄₃	—	4	4	no	—
297	C₂×C₄×C₄₃	—	4	4	no	—
298	C₂×C₄×C₄₃	—	4	4	no	—
299	C₂×C₄×C₄₃	—	4	4	no	—
300	C₂×C₄×C₄₃	—	4	8	no	—
301	C₂×C₄×C₄₃	—	4	8	no	—
302	C₂×C₄×C₄₃	—	4	16	no	—
303	C₂×C₄×C₄₃	—	4	16	no	—
304	C₂×C₄×C₄₃	—	4	8	no	—
305	C₂×C₄×C₄₃	—	8	8	no	—
306	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
309	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
311	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₄₃	C₂×#41	1	8	yes	—
314	#34218	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂²×C₄₃	—	2	32	no	—
316	C₂²×C₄₃	—	2	2	no	—
317	C₂²×C₄₃	—	2	2	no	—
318	C₂²×C₄₃	—	2	2	no	—
319	C₂²×C₄₃	—	2	2	no	—
320	C₂²×C₄₃	—	2	2	no	—
321	C₂²×C₄₃	—	2	2	no	—
322	C₂²×C₄₃	—	2	4	no	—
323	C₂²×C₄₃	—	2	4	no	—
324	C₂²×C₄₃	—	2	4	no	—
325	C₂²×C₄₃	—	2	4	no	—
326	C₂²×C₄₃	—	2	4	no	—
327	C₂²×C₄₃	—	2	4	no	—
328	C₂²×C₄₃	—	2	4	no	—
329	C₂²×C₄₃	—	2	4	no	—
330	C₂²×C₄₃	—	2	4	no	—
331	C₂²×C₄₃	—	4	4	no	—
332	C₂²×C₄₃	—	4	4	no	—
333	C₂²×C₄₃	C₄×#41	1	4	yes	—
334	C₂²×C₄₃	#518	1	4	yes	—
335	C₂²×C₄₃	#520	1	4	yes	—
336	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
337	C₂²×C₄₃	C₂²×#41	1	2	yes	—
338	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
339	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
341	C₄×C₄₃	—	2	4	no	—
342	C₄×C₄₃	—	2	2	no	—
343	C₄×C₄₃	—	2	2	no	—
344	C₄×C₄₃	—	2	2	no	—
345	C₄×C₄₃	—	2	2	no	—
346	C₄×C₄₃	—	2	4	no	—
347	C₄×C₄₃	—	2	4	no	—
348	C₄×C₄₃	—	2	8	no	—
349	C₄×C₄₃	—	4	4	no	—
350	C₄×C₄₃	—	4	4	no	—
351	C₄×C₄₃	—	4	4	no	—
352	C₂×#525	C₂×C₄₃	1	1	yes	characteristic
353	#2368	C₂×C₄₃	1	2	yes	complemented
354	#2364	C₂×C₄₃	1	2	yes	complemented
355	#2359	C₂×C₄₃	1	4	yes	complemented
356	#2353	C₂×C₄₃	1	2	yes	complemented
357	#2349	C₂×C₄₃	1	2	yes	complemented
358	#2343	C₂×C₄₃	1	2	yes	complemented
359	#2339	C₂×C₄₃	1	2	yes	complemented
360	#2329	C₂×C₄₃	1	2	yes	complemented
361	#2325	C₂×C₄₃	1	2	yes	complemented
362	#2318	C₂×C₄₃	1	2	yes	complemented
363	C₄×#120	C₂×C₄₃	1	4	yes	complemented
364	#2280	C₂×C₄₃	1	1	yes	characteristic, complemented
365	#2275	C₂×C₄₃	1	2	yes	complemented
366	C₂²×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
367	C₂×C₄₃	—	2	4	no	—
368	C₂×C₄₃	—	2	4	no	—
369	C₂×C₄₃	—	2	4	no	—
370	C₂×C₄₃	—	4	4	no	—
371	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
372	C₂×C₄₃	C₂×#518	1	1	yes	characteristic
373	C₂×C₄₃	C₂×#520	1	1	yes	characteristic
374	C₂×C₄₃	#3490	1	2	yes	—
375	C₂×C₄₃	#3492	1	2	yes	—
376	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
377	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
378	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
379	#525	C₄×C₄₃	1	16	yes	complemented
380	C₂×#123	C₂²×C₄₃	1	2	yes	—
381	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
382	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
383	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
384	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
385	C₂×#120	C₂²×C₄₃	1	2	yes	—
386	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
387	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
388	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
389	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
390	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
391	C₂×#117	C₂²×C₄₃	1	2	yes	—
392	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
393	#391	C₂²×C₄₃	1	4	yes	complemented
394	#389	C₂²×C₄₃	1	4	yes	complemented
395	#388	C₂²×C₄₃	1	4	yes	complemented
396	#388	C₂²×C₄₃	1	4	yes	complemented
397	#387	C₂²×C₄₃	1	4	yes	complemented
398	#387	C₂²×C₄₃	1	4	yes	complemented
399	#387	C₂²×C₄₃	1	4	yes	complemented
400	#387	C₂²×C₄₃	1	4	yes	complemented
401	#386	C₂²×C₄₃	1	4	yes	—
402	#386	C₂²×C₄₃	1	4	yes	—
403	#386	C₂²×C₄₃	1	4	yes	—
404	#386	C₂²×C₄₃	1	4	yes	complemented
405	#385	C₂²×C₄₃	1	4	yes	—
406	#385	C₂²×C₄₃	1	4	yes	—
407	#385	C₂²×C₄₃	1	4	yes	—
408	#385	C₂²×C₄₃	1	4	yes	complemented
409	#383	C₂²×C₄₃	1	2	yes	complemented
410	#382	C₂²×C₄₃	1	2	yes	complemented
411	#381	C₂²×C₄₃	1	2	yes	—
412	#381	C₂²×C₄₃	1	2	yes	complemented
413	#380	C₂²×C₄₃	1	2	yes	—
414	#380	C₂²×C₄₃	1	1	yes	characteristic
415	#380	C₂²×C₄₃	1	1	yes	characteristic
416	#380	C₂²×C₄₃	1	2	yes	complemented
417	#379	C₂²×C₄₃	1	2	yes	—
418	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
419	C₄×C₄⋊C₄	C₂²×C₄₃	1	4	yes	complemented
420	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	complemented
426	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	complemented
427	#376	C₂²×C₄₃	1	2	yes	complemented
428	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
429	C₂×#95	C₂²×C₄₃	1	2	yes	—
430	C₂×#95	C₂²×C₄₃	1	2	yes	—
431	C₂×#95	C₂²×C₄₃	1	2	yes	—
432	C₂×#95	C₂²×C₄₃	1	2	yes	—
433	C₂×#95	C₂²×C₄₃	1	2	yes	—
434	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
435	C₂×#95	C₂²×C₄₃	1	2	yes	complemented
436	C₄₃	#34218	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
438	C₂×#41	—	4	4	no	—
439	C₂×#41	C₂×C₄×C₄₃	1	8	yes	complemented
440	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
442	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
443	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
444	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
445	C₂³×C₄	—	2	8	no	—
446	C₂³×C₄	—	4	4	no	—
447	C₂³×C₄	—	4	4	no	—
448	C₂³×C₄	—	4	4	no	—
449	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	complemented
450	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
451	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
452	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
455	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
458	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
461	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
462	#123	C₂×C₄×C₄₃	1	16	yes	complemented
463	C₂²⋊Q₈	C₂×C₄×C₄₃	1	8	yes	complemented
464	C₂²⋊Q₈	C₂×C₄×C₄₃	1	8	yes	complemented
465	#121	C₂×C₄×C₄₃	1	8	yes	complemented
466	#121	C₂×C₄×C₄₃	1	8	yes	complemented
467	#120	C₂×C₄×C₄₃	1	16	yes	complemented
468	C₄×D₄	—	2	16	no	—
469	C₄×D₄	—	4	8	no	—
470	C₄×D₄	—	4	8	no	—
471	C₄×D₄	C₂×C₄×C₄₃	1	16	yes	complemented
472	C₄×D₄	C₂×C₄×C₄₃	1	16	yes	complemented
473	#117	—	4	4	no	—
474	#117	C₂×C₄×C₄₃	1	8	yes	complemented
475	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
476	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
496	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
497	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
498	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
499	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
500	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
501	#95	C₂³×C₄₃	1	2	yes	—
502	#95	C₂³×C₄₃	1	2	yes	—
503	#95	C₂³×C₄₃	1	2	yes	—
504	#95	C₂³×C₄₃	1	4	yes	—
505	#95	C₂³×C₄₃	1	4	yes	—
506	#95	C₂³×C₄₃	1	2	yes	—
507	#95	C₂³×C₄₃	1	2	yes	—
508	#95	C₂³×C₄₃	1	4	yes	—
509	#95	C₂³×C₄₃	1	2	yes	—
510	#95	C₂³×C₄₃	1	4	yes	—
511	#95	C₂³×C₄₃	1	4	yes	—
512	#95	C₂³×C₄₃	1	4	yes	—
513	#95	C₂³×C₄₃	1	4	yes	—
514	#95	C₂³×C₄₃	1	4	yes	—
515	#95	C₂³×C₄₃	1	4	yes	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	2	no	—
518	C₂⁴	—	2	4	no	—
519	C₂⁴	—	2	2	no	—
520	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
521	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
522	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
523	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
524	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
525	#41	—	4	16	no	—
526	C₂×Q₈	—	4	2	no	—
527	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	complemented
528	C₂×D₄	—	2	8	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	4	2	no	—
533	C₂×D₄	C₂²×C₄×C₄₃	1	8	yes	—
534	C₂×D₄	C₂²×C₄×C₄₃	1	8	yes	—
535	C₂×D₄	C₂²×C₄×C₄₃	1	8	yes	—
536	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	complemented
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	8	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	2	8	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	—	2	8	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	4	4	no	—
550	C₂²×C₄	—	4	4	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	16	no	—
556	C₂²×C₄	—	4	4	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	32	no	—
560	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
561	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
562	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
563	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
564	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
565	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
566	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	complemented
567	C₂²×C₄	#41×C₄₃	1	8	yes	complemented
568	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
579	C₄⋊C₄	—	2	8	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	complemented
585	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	complemented
586	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	complemented
587	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	complemented
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
598	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	complemented
599	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	complemented
600	C₄²	—	2	8	no	—
601	C₄²	—	4	4	no	—
602	C₄²	—	4	4	no	—
603	C₄²	—	4	4	no	—
604	C₄²	C₂²×C₄×C₄₃	1	8	yes	complemented
605	C₂³	—	2	16	no	—
606	C₂³	—	2	16	no	—
607	C₂³	—	2	8	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	8	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	C₂³×C₄×C₄₃	1	4	yes	—
623	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
624	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
625	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
626	C₂³	C₂×#41×C₄₃	1	4	yes	—
627	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
628	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
629	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
630	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
631	Q₈	—	4	4	no	—
632	D₄	—	2	16	no	—
633	D₄	—	2	16	no	—
634	D₄	—	2	16	no	—
635	D₄	—	4	4	no	—
636	C₂×C₄	—	2	8	no	—
637	C₂×C₄	—	2	8	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	—	4	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	8	no	—
662	C₂×C₄	—	4	8	no	—
663	C₂×C₄	—	4	16	no	—
664	C₂×C₄	—	4	16	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	8	8	no	—
667	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
668	C₂×C₄	C₂³×C₄×C₄₃	1	4	yes	—
669	C₂×C₄	C₂³×C₄×C₄₃	1	4	yes	—
670	C₂×C₄	C₂³×C₄×C₄₃	1	4	yes	—
671	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
672	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
673	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
674	C₂×C₄	C₂×#41×C₄₃	1	8	yes	—
675	C₂²	—	2	32	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	4	no	—
693	C₂²	C₄×#41×C₄₃	1	4	yes	—
694	C₂²	C₄₃×#518	1	4	yes	—
695	C₂²	C₄₃×#520	1	4	yes	—
696	C₂²	C₂⁴×C₄×C₄₃	1	1	yes	characteristic
697	C₂²	C₂²×#41×C₄₃	1	2	yes	—
698	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
699	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
700	C₂²	C₂×2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
701	C₄	—	2	4	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	4	no	—
708	C₄	—	2	8	no	—
709	C₄	—	4	4	no	—
710	C₄	—	4	4	no	—
711	C₄	—	4	4	no	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	2	4	no	—
715	C₂	—	4	4	no	—
716	C₂	C₂×C₄×#41×C₄₃	1	1	yes	characteristic
717	C₂	C₂×C₄₃×#518	1	1	yes	characteristic
718	C₂	C₂×C₄₃×#520	1	1	yes	characteristic
719	C₂	C₄₃×#3490	1	2	yes	—
720	C₂	C₄₃×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₃
Frattini, cosocle	C₂³	C₂⁵×C₄₃
prime radical	C₂×C₄₃×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2368	C₂	semidirect
3. C₄₃×#2364	C₂	semidirect
4. C₄₃×#2359	C₂	semidirect
5. C₄₃×#2353	C₂	semidirect
6. C₄₃×#2349	C₂	semidirect
7. C₄₃×#2343	C₂	semidirect
8. C₄₃×#2339	C₂	semidirect
9. C₄₃×#2329	C₂	semidirect
10. C₄₃×#2325	C₂	semidirect
11. C₄₃×#2318	C₂	semidirect
12. C₄×#120×C₄₃	C₂	semidirect
13. C₄₃×#2280	C₂	semidirect
14. C₄₃×#2275	C₂	semidirect
15. C₂²×#95×C₄₃	C₂	semidirect
19. C₄₃×#525	C₄	semidirect
33. C₄₃×#391	C₂²	semidirect
34. C₄₃×#389	C₂²	semidirect
35. C₄₃×#388	C₂²	semidirect
36. C₄₃×#388	C₂²	semidirect
37. C₄₃×#387	C₂²	semidirect
38. C₄₃×#387	C₂²	semidirect
39. C₄₃×#387	C₂²	semidirect
40. C₄₃×#387	C₂²	semidirect
44. C₄₃×#386	C₂²	semidirect
48. C₄₃×#385	C₂²	semidirect
49. C₄₃×#383	C₂²	semidirect
50. C₄₃×#382	C₂²	semidirect
52. C₄₃×#381	C₂²	semidirect
56. C₄₃×#380	C₂²	semidirect
58. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
59. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
65. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
66. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
67. C₄₃×#376	C₂²	semidirect
75. C₂×#95×C₄₃	C₂²	semidirect
78. C₂×#41×C₄₃	C₂×C₄	semidirect
88. C₂³×C₄×C₄₃	C₂×C₄	semidirect
101. #123×C₄₃	C₂×C₄	semidirect
102. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
103. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
104. #121×C₄₃	C₂×C₄	semidirect
105. #121×C₄₃	C₂×C₄	semidirect
106. #120×C₄₃	C₂×C₄	semidirect
110. C₄×D₄×C₄₃	C₂×C₄	semidirect
111. C₄×D₄×C₄₃	C₂×C₄	semidirect
113. #117×C₄₃	C₂×C₄	semidirect
166. C₂×Q₈×C₄₃	C₂²×C₄	semidirect
175. C₂×D₄×C₄₃	C₂²×C₄	semidirect
205. C₂²×C₄×C₄₃	C₂²×C₄	semidirect
206. C₂²×C₄×C₄₃	#41	semidirect
223. C₄⋊C₄×C₄₃	C₂²×C₄	semidirect
224. C₄⋊C₄×C₄₃	C₂²×C₄	semidirect
225. C₄⋊C₄×C₄₃	C₂²×C₄	semidirect
226. C₄⋊C₄×C₄₃	C₂²×C₄	semidirect
237. C₂²⋊C₄×C₄₃	C₂²×C₄	semidirect
238. C₂²⋊C₄×C₄₃	C₂²×C₄	semidirect
243. C₄²×C₄₃	C₂²×C₄	semidirect
314. #34218	C₄₃	direct (N × H)
353. #2368	C₂×C₄₃	semidirect
354. #2364	C₂×C₄₃	semidirect
355. #2359	C₂×C₄₃	semidirect
356. #2353	C₂×C₄₃	semidirect
357. #2349	C₂×C₄₃	semidirect
358. #2343	C₂×C₄₃	semidirect
359. #2339	C₂×C₄₃	semidirect
360. #2329	C₂×C₄₃	semidirect
361. #2325	C₂×C₄₃	semidirect
362. #2318	C₂×C₄₃	semidirect
363. C₄×#120	C₂×C₄₃	semidirect
364. #2280	C₂×C₄₃	semidirect
365. #2275	C₂×C₄₃	semidirect
366. C₂²×#95	C₂×C₄₃	semidirect
379. #525	C₄×C₄₃	semidirect
393. #391	C₂²×C₄₃	semidirect
394. #389	C₂²×C₄₃	semidirect
395. #388	C₂²×C₄₃	semidirect
396. #388	C₂²×C₄₃	semidirect
397. #387	C₂²×C₄₃	semidirect
398. #387	C₂²×C₄₃	semidirect
399. #387	C₂²×C₄₃	semidirect
400. #387	C₂²×C₄₃	semidirect
404. #386	C₂²×C₄₃	semidirect
408. #385	C₂²×C₄₃	semidirect
409. #383	C₂²×C₄₃	semidirect
410. #382	C₂²×C₄₃	semidirect
412. #381	C₂²×C₄₃	semidirect
416. #380	C₂²×C₄₃	semidirect
418. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
419. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
425. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
426. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
427. #376	C₂²×C₄₃	semidirect
435. C₂×#95	C₂²×C₄₃	semidirect
436. C₄₃	#34218	direct (N × H)
439. C₂×#41	C₂×C₄×C₄₃	semidirect
449. C₂³×C₄	C₂×C₄×C₄₃	semidirect
462. #123	C₂×C₄×C₄₃	semidirect
463. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
464. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
465. #121	C₂×C₄×C₄₃	semidirect
466. #121	C₂×C₄×C₄₃	semidirect
467. #120	C₂×C₄×C₄₃	semidirect
471. C₄×D₄	C₂×C₄×C₄₃	semidirect
472. C₄×D₄	C₂×C₄×C₄₃	semidirect
474. #117	C₂×C₄×C₄₃	semidirect
527. C₂×Q₈	C₂²×C₄×C₄₃	semidirect
536. C₂×D₄	C₂²×C₄×C₄₃	semidirect
566. C₂²×C₄	C₂²×C₄×C₄₃	semidirect
567. C₂²×C₄	#41×C₄₃	semidirect
584. C₄⋊C₄	C₂²×C₄×C₄₃	semidirect
585. C₄⋊C₄	C₂²×C₄×C₄₃	semidirect
586. C₄⋊C₄	C₂²×C₄×C₄₃	semidirect
587. C₄⋊C₄	C₂²×C₄×C₄₃	semidirect
598. C₂²⋊C₄	C₂²×C₄×C₄₃	semidirect
599. C₂²⋊C₄	C₂²×C₄×C₄₃	semidirect
604. C₄²	C₂²×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×#525	2
C₄₃×#2368	2
C₄₃×#2364	2
C₄₃×#2359	2
C₄₃×#2353	2
C₄₃×#2349	2
C₄₃×#2343	2
C₄₃×#2339	2
C₄₃×#2329	2
C₄₃×#2325	2
C₄₃×#2318	2
C₄×#120×C₄₃	2
C₄₃×#2280	2
C₄₃×#2275	2
C₂²×#95×C₄₃	2
#34218	43

Subgroups — C43×#34218 #24954235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#34218 #24954235