Subgroups — C₄₃×#20732 #24940749

Order 11008.

1802 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1823	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1802	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1786	C₂	1	2	yes	maximal
7	C₄×#102×C₄₃	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	—	2	1	no	—
10	C₂×C₄×D₄×C₄₃	—	2	1	no	—
11	C₂×C₄×D₄×C₄₃	—	2	1	no	—
12	C₂×C₄×D₄×C₄₃	—	2	4	no	—
13	C₂×C₄×D₄×C₄₃	C₄	1	8	yes	complemented
14	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
16	C₂×#117×C₄₃	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#431	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
22	C₂×#102×C₄₃	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
25	C₄₃×#384	C₂²	1	2	yes	complemented
26	C₄₃×#382	—	2	1	no	—
27	C₄₃×#380	—	2	1	no	—
28	C₄₃×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
31	C₄₃×#340	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₃	—	2	1	no	—
33	C₂²×D₄×C₄₃	—	2	8	no	—
34	C₂²×D₄×C₄₃	—	2	2	no	—
35	C₂²×D₄×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₃	—	2	1	no	—
39	C₂³×C₄×C₄₃	—	2	8	no	—
40	C₂³×C₄×C₄₃	—	2	2	no	—
41	C₂³×C₄×C₄₃	—	2	2	no	—
42	C₂³×C₄×C₄₃	—	4	4	no	—
43	C₂³×C₄×C₄₃	—	4	4	no	—
44	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
48	C₄×D₄×C₄₃	—	2	8	no	—
49	C₄×D₄×C₄₃	—	2	8	no	—
50	C₄×D₄×C₄₃	—	2	4	no	—
51	C₄×D₄×C₄₃	—	2	4	no	—
52	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
53	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
54	#117×C₄₃	—	4	4	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	2	no	—
59	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	8	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×C₄²×C₄₃	—	2	2	no	—
67	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	D₄	1	4	yes	—
71	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₄₃	—	2	4	no	—
74	#102×C₄₃	—	2	16	no	—
75	C₂²⋊C₈×C₄₃	—	2	4	no	—
76	C₄×C₈×C₄₃	—	2	4	no	—
77	#95×C₄₃	—	2	2	no	—
78	#95×C₄₃	—	2	2	no	—
79	C₂⁴×C₄₃	—	2	8	no	—
80	C₂⁴×C₄₃	—	2	4	no	—
81	C₂⁴×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	—	4	4	no	—
83	C₂⁴×C₄₃	—	4	2	no	—
84	C₂⁴×C₄₃	—	4	2	no	—
85	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂×D₄×C₄₃	—	2	16	no	—
87	C₂×D₄×C₄₃	—	2	8	no	—
88	C₂×D₄×C₄₃	—	2	16	no	—
89	C₂×D₄×C₄₃	—	2	4	no	—
90	C₂×D₄×C₄₃	—	2	2	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
93	C₂×D₄×C₄₃	#41	1	8	yes	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	8	no	—
96	C₂²×C₄×C₄₃	—	2	8	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	4	2	no	—
101	C₂²×C₄×C₄₃	—	4	32	no	—
102	C₂²×C₄×C₄₃	—	4	4	no	—
103	C₂²×C₄×C₄₃	—	4	4	no	—
104	C₂²×C₄×C₄₃	—	4	4	no	—
105	C₂²×C₄×C₄₃	—	4	4	no	—
106	C₂²×C₄×C₄₃	—	4	2	no	—
107	C₂²×C₄×C₄₃	—	4	2	no	—
108	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
109	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
110	C₂²×C₄×C₄₃	D₈	1	4	yes	—
111	C₂²×C₄×C₄₃	SD₁₆	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₂×C₈×C₄₃	—	2	8	no	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	8	no	—
125	C₄⋊C₄×C₄₃	—	4	4	no	—
126	C₄⋊C₄×C₄₃	—	4	4	no	—
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
128	C₂²⋊C₄×C₄₃	—	2	8	no	—
129	C₂²⋊C₄×C₄₃	—	2	8	no	—
130	C₂²⋊C₄×C₄₃	—	4	4	no	—
131	C₄²×C₄₃	—	4	4	no	—
132	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
133	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
134	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
136	C₄²×C₄₃	C₂×D₄	1	2	yes	—
137	C₄²×C₄₃	C₂×D₄	1	2	yes	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	16	no	—
141	C₂³×C₄₃	—	2	4	no	—
142	C₂³×C₄₃	—	2	8	no	—
143	C₂³×C₄₃	—	4	16	no	—
144	C₂³×C₄₃	—	4	16	no	—
145	C₂³×C₄₃	—	4	8	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	—	4	4	no	—
149	C₂³×C₄₃	—	4	8	no	—
150	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂³×C₄₃	C₂×D₈	1	2	yes	—
152	C₂³×C₄₃	C₂×SD₁₆	1	2	yes	—
153	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
154	D₄×C₄₃	—	2	16	no	—
155	D₄×C₄₃	—	2	4	no	—
156	D₄×C₄₃	—	2	8	no	—
157	D₄×C₄₃	#117	1	8	yes	complemented
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	8	no	—
168	C₂×C₄×C₄₃	—	4	16	no	—
169	C₂×C₄×C₄₃	—	4	16	no	—
170	C₂×C₄×C₄₃	—	4	4	no	—
171	C₂×C₄×C₄₃	—	4	4	no	—
172	C₂×C₄×C₄₃	—	4	4	no	—
173	C₂×C₄×C₄₃	#102	1	16	yes	complemented
174	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
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	C₂×D₈	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
181	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
182	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
183	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
186	C₈×C₄₃	—	4	4	no	—
187	#20732	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₄₃	—	2	4	no	—
189	C₂²×C₄₃	—	2	4	no	—
190	C₂²×C₄₃	—	2	2	no	—
191	C₂²×C₄₃	—	2	2	no	—
192	C₂²×C₄₃	—	2	8	no	—
193	C₂²×C₄₃	—	4	32	no	—
194	C₂²×C₄₃	—	4	8	no	—
195	C₂²×C₄₃	—	4	8	no	—
196	C₂²×C₄₃	—	4	4	no	—
197	C₂²×C₄₃	—	4	4	no	—
198	C₂²×C₄₃	C₂×#102	1	4	yes	—
199	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄₃	#525	1	2	yes	—
201	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
202	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
203	C₂²×C₄₃	#575	1	2	yes	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	4	4	no	—
208	C₄×C₄₃	—	8	4	no	—
209	C₄×C₄₃	C₂×#102	1	4	yes	—
210	C₄×C₄₃	C₂×#102	1	4	yes	—
211	C₄×C₄₃	C₂×#117	1	2	yes	—
212	C₄×C₄₃	#525	1	2	yes	—
213	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
214	C₂×#431	C₂×C₄₃	1	1	yes	characteristic, complemented
215	#2285	C₂×C₄₃	1	1	yes	characteristic, complemented
216	#1823	C₂×C₄₃	1	2	yes	complemented
217	#1802	C₂×C₄₃	1	4	yes	complemented
218	#1786	C₂×C₄₃	1	2	yes	—
219	C₄×#102	C₂×C₄₃	1	4	yes	complemented
220	C₂×C₄₃	—	2	4	no	—
221	C₂×C₄₃	—	4	8	no	—
222	C₂×C₄₃	#2280	1	1	yes	characteristic
223	C₂×C₄₃	C₂²×#102	1	1	yes	characteristic
224	C₂×C₄₃	#2896	1	1	yes	characteristic
225	C₂×C₄₃	#3100	1	2	yes	—
226	C₂×C₄₃	#3101	1	2	yes	—
227	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
228	C₂⁴×C₄	—	2	1	no	—
229	C₂×C₄×D₄	—	2	1	no	—
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	—	2	4	no	—
232	C₂×C₄×D₄	C₄×C₄₃	1	8	yes	complemented
233	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
235	C₂×#117	—	2	1	no	—
236	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	—	2	1	no	—
238	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
239	#431	—	2	4	no	—
240	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
241	C₂×#102	C₂²×C₄₃	1	8	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	complemented
244	#384	C₂²×C₄₃	1	2	yes	complemented
245	#382	—	2	1	no	—
246	#380	—	2	1	no	—
247	#380	C₂²×C₄₃	1	2	yes	—
248	C₄×C₄⋊C₄	—	2	1	no	—
249	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
250	#340	C₂²×C₄₃	1	8	yes	complemented
251	C₄₃	#20732	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁵	—	2	1	no	—
253	C₂²×D₄	—	2	8	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
257	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
258	C₂³×C₄	—	2	1	no	—
259	C₂³×C₄	—	2	8	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	—	4	4	no	—
263	C₂³×C₄	—	4	4	no	—
264	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
265	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
268	C₄×D₄	—	2	8	no	—
269	C₄×D₄	—	2	8	no	—
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	C₂×C₄×C₄₃	1	8	yes	—
273	C₄×D₄	C₂×C₄×C₄₃	1	8	yes	—
274	#117	—	4	4	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
288	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₄₃	1	4	yes	—
291	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
293	C₄⋊C₈	—	2	4	no	—
294	#102	—	2	16	no	—
295	C₂²⋊C₈	—	2	4	no	—
296	C₄×C₈	—	2	4	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	4	4	no	—
303	C₂⁴	—	4	2	no	—
304	C₂⁴	—	4	2	no	—
305	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
306	C₂×D₄	—	2	8	no	—
307	C₂×D₄	—	2	16	no	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
313	C₂×D₄	#41×C₄₃	1	8	yes	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	32	no	—
324	C₂²×C₄	—	4	4	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	D₈×C₄₃	1	4	yes	—
331	C₂²×C₄	SD₁₆×C₄₃	1	4	yes	—
332	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
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	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	8	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₄²	—	4	4	no	—
352	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
353	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
354	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
355	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
356	C₄²	C₂×D₄×C₄₃	1	2	yes	—
357	C₄²	C₂×D₄×C₄₃	1	2	yes	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	16	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	4	16	no	—
364	C₂³	—	4	16	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	8	no	—
370	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
371	C₂³	C₂×D₈×C₄₃	1	2	yes	—
372	C₂³	C₂×SD₁₆×C₄₃	1	2	yes	—
373	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
374	D₄	—	2	16	no	—
375	D₄	—	2	4	no	—
376	D₄	—	2	8	no	—
377	D₄	#117×C₄₃	1	8	yes	complemented
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	—	4	16	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	#102×C₄₃	1	16	yes	complemented
394	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
395	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
396	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
398	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
399	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
400	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
401	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
402	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
403	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
406	C₈	—	4	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	4	32	no	—
413	C₂²	—	4	8	no	—
414	C₂²	—	4	8	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	C₂×#102×C₄₃	1	4	yes	—
418	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
419	C₂²	C₄₃×#525	1	2	yes	—
420	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
421	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
422	C₂²	C₄₃×#575	1	2	yes	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	4	no	—
427	C₄	—	8	4	no	—
428	C₄	C₂×#102×C₄₃	1	4	yes	—
429	C₄	C₂×#102×C₄₃	1	4	yes	—
430	C₄	C₂×#117×C₄₃	1	2	yes	—
431	C₄	C₄₃×#525	1	2	yes	—
432	C₂	—	2	4	no	—
433	C₂	—	4	8	no	—
434	C₂	C₄₃×#2280	1	1	yes	characteristic
435	C₂	C₂²×#102×C₄₃	1	1	yes	characteristic
436	C₂	C₄₃×#2896	1	1	yes	characteristic
437	C₂	C₄₃×#3100	1	2	yes	—
438	C₂	C₄₃×#3101	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂³×D₄×C₄₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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. C₄₃×#2285	C₂	semidirect
4. C₄₃×#1823	C₂	semidirect
5. C₄₃×#1802	C₂	semidirect
7. C₄×#102×C₄₃	C₂	semidirect
13. C₂×C₄×D₄×C₄₃	C₄	semidirect
21. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
24. C₂×C₄×C₈×C₄₃	C₂²	semidirect
25. C₄₃×#384	C₂²	semidirect
30. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
31. C₄₃×#340	C₂²	semidirect
157. D₄×C₄₃	#117	semidirect
173. C₂×C₄×C₄₃	#102	semidirect
187. #20732	C₄₃	direct (N × H)
214. C₂×#431	C₂×C₄₃	semidirect
215. #2285	C₂×C₄₃	semidirect
216. #1823	C₂×C₄₃	semidirect
217. #1802	C₂×C₄₃	semidirect
219. C₄×#102	C₂×C₄₃	semidirect
232. C₂×C₄×D₄	C₄×C₄₃	semidirect
240. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
243. C₂×C₄×C₈	C₂²×C₄₃	semidirect
244. #384	C₂²×C₄₃	semidirect
249. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
250. #340	C₂²×C₄₃	semidirect
251. C₄₃	#20732	direct (N × H)
377. D₄	#117×C₄₃	semidirect
393. C₂×C₄	#102×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#431	2
C₄₃×#2285	2
C₄₃×#1823	2
C₄₃×#1802	2
C₄₃×#1786	2
C₄×#102×C₄₃	2
#20732	43

Subgroups — C43×#20732 #24940749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20732 #24940749